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Essays on firm investment, innovation and productivity

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Essays on firm investment, innovation and productivity

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Content Essays on Firm Inv estment, Inno v ation and Productivity by Y u Cao A Dissertation Presented to the F ACUL TY OF THE GRADUA TE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial F ulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Economics) May 2020 Copyright 2020 Y u Cao Dedication This dissertation is dedicated . . . T o my p ar ents and family and to my feline friend: Penelop e ii Acknowledgements I w ould lik e to express m y sincere gratitude and pa y sp ecial appreciation to the follo wing p eople, who generously con tribute to the researc h presen ted in this dissertation and assisted me during m y do ctoral studies. First and foremost, I am incredibly grateful to m y advisor Caroline Betts for her in v aluable guidance, vital supp ort, immense kno wledge, and con tin uous encouragemen t during m y y ears at the Univ ersit y of Southern California. She has alw a ys b een an incredible teac her and advisor. I w an t to thank Jo el Da vid as w ell, for oering me the opp ortunit y to w ork with him in v arious researc h pro jects and for pro viding v aluable commen ts and advice on m y researc h. I am highly indebted to other mem b ers of m y committee Da vid Zek e and Vincenzo Quadrini, as w ell as Rob ert Dekle and Andrii P arkhomenk o, who serv ed in m y qualifying committee, for their insigh tful suggestions and advice. I w ould also lik e to express m y sincere gratitude to Romain Ranciere, Monica Morlacco, and P ablo Kurlat for their v aluable feedbac k and commen ts. This dissertation b enets greatly from discussion with colleagues and seminar participan ts at USC as w ell as conferences participan ts. I sincerely appreciate the supp ort from m y colleagues and friends Y uxin Su, Shic heng W ang, Kanik a Aggarw al, Jisu Cao, Brian Finley , Bada Han, W eining Xin, Yimeng Xie, Y an y an Y ang, and Jeongh w an Y un. Last but not least, I w ould lik e to thank the curren t and former administrativ e sta of the Eco- nomics Departmen t and INET. Alexander Karnazes, Y oung Miller, Morgan P onder, Anna Emerald, Irma Alfaro, and F atima P arez ha v e alw a ys b een patien t and pro vide v arious administrativ e supp ort iii throughout m y y ears at USC. I am also grateful to fello wships and gran ts from the Departmen t of Economics, the USC Graduate Sc ho ol and Dornsife College of Letters, Arts, and Science and INET at USC. iv T able of Contents Dedication ii A c kno wledgemen ts iii List Of T ables viii List Of Figures x Abstract xi Chapter 1: In tro duction 1 Chapter 2: Financial Constrain ts, Inno v ation Qualit y , and Gro wth 6 2.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Data and Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Data Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Measuring P aten t t yp e, qualit y and nancial constrain ts . . . . . . . . . . . . 13 2.2.3 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Theoretical Mo del . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 Preferences, T ec hnology and Mark et Structure . . . . . . . . . . . . . . . . . . 23 2.3.2 Inno v ation and Financial Constrain t . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.3 En try , Exit and Resource Constrain t . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.4 Equilibrium and Balanced Gro wth P ath . . . . . . . . . . . . . . . . . . . . . 30 2.3.5 Analytical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.4 Quan tativ e Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.4.1 Calibration Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4.1.1 Externally Calibrated P arameters . . . . . . . . . . . . . . . . . . . 44 2.4.1.2 Indirect Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.4.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.5 Coun terfactual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.5.1 The role of nancial constrain t . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.5.2 The role of industrial design paten ting . . . . . . . . . . . . . . . . . . . . . . 54 2.5.3 W elfare Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.5.4 P olicy Implication: T yp e-dep enden t tax Incen tiv e . . . . . . . . . . . . . . . . 58 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 v Chapter 3: Aggregate In v estmen t and Sto c k Mark et Information 64 3.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2 Benc hmark Mo del . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2.1 Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2.2 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2.3 Information Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.3 Equilibrium and Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4 The Sto c k Mark et and Public Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.5 Calibration and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.5.1 Data and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.5.2 Estimation and Iden tication . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.5.3 Estimation Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.6 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.6.1 Information Decomp osition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.6.2 Implied Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Chapter 4: Credit Reallo cation and Inno v ation Disparit y among POEs and SOEs in China 93 4.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2.1 Sample Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2.2 Main V ariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.2.3 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2.4 Inno v ation and Pro ductivit y Gap . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.3 Theoretical F ramew ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.1 Mo del en vironmen t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.2 Theoretical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.4 A dditional Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.4.1 Decomp osition of Con tributions to Inno v ation Gaps: Mediation Analysis . . . 120 4.4.2 Inno v ation and Pro ductivit y Gro wth . . . . . . . . . . . . . . . . . . . . . . . 125 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Chapter 5: Conclusion and P olicy Implication 130 Reference 134 App endix A Chapter 1 App endix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.1 Data Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.1.1 P aten t T yp es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.1.2 Measuring Financial Constrian t . . . . . . . . . . . . . . . . . . . . . . . . . . 143 A.2 Pro ofs and A dditional Theoretical Result . . . . . . . . . . . . . . . . . . . . . . . . 146 A.2.1 Firm Size Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 A.2.2 Financial Constrain ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 A.2.3 Pro of of Prop osition I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 A.2.4 Pro of of Prop osition I I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 A.2.5 Omitted Pro ofs of Prop osition IV . . . . . . . . . . . . . . . . . . . . . . . . . 152 vi A.2.6 Omitted pro of in section 5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 A.2.7 Pro of on Prop osition VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 A.2.8 Pro of on Prop osition VI I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 A.2.9 A dditional Theoretical Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 A.3 Computational Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 A.4 A dditional Empirical and Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 A.4.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 A.4.2 Financial constrain t and rm-size-inno v ation-in tensit y relationship . . . . . . 160 A.4.3 Calibration under tax deduction . . . . . . . . . . . . . . . . . . . . . . . . . 162 App endix B Chapter 2 App endix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 App endix C Chapter 3 App endix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 C.1 Pro ofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 C.1.1 Conditions for SOC<0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 C.1.2 The equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 C.1.3 Prop osition I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 C.1.4 Prop osition I I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 C.1.5 Prop osition I I I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 C.2 A dditional Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 C.2.1 Sample Construction Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 C.2.2 A dditional Mediation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 173 vii List Of T ables 2.1 Firm Size, Gro wth and Inno v ation In tensit y . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Firm size, Financial Constrain t and P aten t Qualit y Distribution . . . . . . . . . . . 20 2.3 Firm Gro wth and Inno v ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 P arameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.5 Momen ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.6 Gro wth and R&D Decomp osition (Changes in Financial Constrain ts) . . . . . . . . . 52 2.7 Gro wth and R&D Decomp osition (tax on industrial design) . . . . . . . . . . . . . . 56 2.8 W elfare Decomp osition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.9 Gro wth Decomp osition and W elfare Gain Under T w o P olicy Regimes . . . . . . . . . 61 3.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.2 Macro Momen ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.3 Implied Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.4 Impact from Mark et Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.1 Summary Statistics for Merged Sample . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.2 Inno v ation Gaps b et w een SOEs and POEs . . . . . . . . . . . . . . . . . . . . . . . . 107 4.3 Mediation Analysis - P aten t Application . . . . . . . . . . . . . . . . . . . . . . . . . 122 4.4 Mediation Analysis - P aten t Application to Capital Ratio . . . . . . . . . . . . . . . 124 4.5 Mediation Analysis - Pro ductivit y Gro wth . . . . . . . . . . . . . . . . . . . . . . . . 126 viii A.1 Summary Statistics of P aten t Category and A v erage Citation . . . . . . . . . . . . . 142 A.2 Endogenous Selection Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 A.3 Endogenous Switc hing Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 A.4 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 A.5 Firm Size, Gro wth and Inno v ation In tensit y (Prob of Constrained) . . . . . . . . . . 160 A.6 Firm Size, Gro wth and Inno v ation In tensit y . . . . . . . . . . . . . . . . . . . . . . . 160 A.7 Firm Size, Gro wth and Inno v ation In tensit y (Cash o w Sensitivit y) . . . . . . . . . . 161 A.8 Firm Size, Gro wth and Inno v ation In tensit y . . . . . . . . . . . . . . . . . . . . . . . 161 A.9 Firm Gro wth and Inno v ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 A.10 P arameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 A.11 Momen ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 C.1 Summary Statistics for Merged Sample . . . . . . . . . . . . . . . . . . . . . . . . . . 172 C.2 Economic and Inno v ation A ctivit y of Firms By Industries . . . . . . . . . . . . . . . 173 C.3 Mediation Analysis - All sample y ears . . . . . . . . . . . . . . . . . . . . . . . . . . 174 ix List Of Figures 2.1 Firm Size Distribution and Firm V alue . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.2 Firm Size Distribution and the V alue of ' n . . . . . . . . . . . . . . . . . . . . . . . 54 3.1 Impulse Resp onse F unction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.2 In v estmen t, Priv ate Signal and Pro ductivit y . . . . . . . . . . . . . . . . . . . . . . . 89 3.3 Estimated Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.1 The Dierence in Inno v ation A ctivities/Qualities b et w een State-Owned and Priv ate- Owned Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.2 The Dierence in Inno v ation A ctivities/Qualities b et w een State-Owned and Priv ate- Owned Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.3 Mediation Analysis: Inno v ation A ctivit y . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.4 Mediation Analysis: Pro ductivit y Gro wth . . . . . . . . . . . . . . . . . . . . . . . . 126 A.1 External Citation Distribution b y External and In ternal P aten t . . . . . . . . . . . . 143 x Abstract This dissertation studies rms’ inno v ation activities and their impact on aggregate outcomes suc h as aggregate gro wth, rm size distribution, rm en try and exit, and pro ductivit y disparities b et w een dieren t t yp es of rms. Chapter 2 in v estigates the role of nancial constrain ts in shaping inno v ation qualit y and rm- gro wth dynamics through heterogeneous inno v ation. I build a unique data-set com bining paten t activities with the op erating data of priv ate Chinese man ufacturing rms and sho w a strong negativ e relationship b et w een the sev erit y of nancial constrain ts and a) rm gro wth, b) inno v ation in tensit y , and c) inno v ation qualit y . Based on these empirical regularities, I build a tractable endogenous gro wth mo del in whic h a m ulti-pro duct rm in v ests in heterogeneous inno v ation in the face of imp erfect nancial mark ets. Tigh ter nancial constrain ts cause rms to undertak e more lo w-qualit y inno v ation, whic h yields temp orary pa y os but no longer-term pro ductivit y impro v emen ts. This lo w ers rm and aggregate gro wth rates. The quan titativ e mo del suggests nancial frictions reduce incum b en ts’ R&D in v estmen t b y 19.94% on a v erage and slo ws aggregate ann ual pro ductivit y gro wth b y 10.2 p ercen t (0.4 p ercen tage p oin t ann ually). Chapter 3, I use a rm’s and sto c k trader’s in v estmen t b eha vior to infer agen ts’ uncertain t y ab out the future. In particular, I dev elop a general equilibrium mo del with traders endo w ed with dieren tiated b eliefs on TFP sho c ks. W e study qualitativ ely ho w disp ersed b eliefs will b e gathered in the sto c k mark et and to what extend that aggregated information w ould inuence a rm’s in v estmen t b eha vior. Next, I use the observ ed relationship b et w een in v estmen t, sto c k prices and inno v ation in xi TFP to measure the information and its precision rm receiv ed. I nd a mo derate degree of learning from a rm’s o wn priv ate signal but no learning from the sto c k mark et. Our empirical w ork also sho ws that the existence of noise traders generate a h uge noise in the public signal rm receiv e. And suc h noise inhibits information transmission b et w een imp erfectly informed traders and rms. Chapter 4 empirically analyze the determinan ts of the observ ed inno v ation and pro ductivit y disparit y b et w een state-o wned rms (SOE) and priv ate-o wned rms (POE) b efore and after 2009- 2010 China’s scal stim ulus p olicy . It do cumen ts an enlarging disparit y in inno v ation activities b et w een SOEs and POEs after the nancial crisis. Empirically , the dierence in subsidies and skill lev els can explain as high as 90 p ercen t of the observ ed v ariation in paten t application b et w een SOEs and POEs. In the pre-2009 sample, subsidies can only explain 9.3 p ercen t of the observ ed dierence in paten t applications. Ho w ev er, it can tell 24 p ercen t of the observ ed dierence in paten t applications in the p ost-2009 sample. In addition, the observ ed dierence in pro ductivit y gro wth b et w een SOEs and POEs after the 2009-2010 scal stim ulus p olicy can b e attributed to an increase in subsidies SOEs receiv ed. Moreo v er, 31.4 p ercen t of subsidies’ impact on pro ductivit y gro wth can b e explained b y the rise in SOEs’ gran ted paten ts. xii Chapter 1 Introduction A gro wing b o dy of w ork originating in Sc h ump eter (1911) argues that nancial mark et dev elopmen t pla ys an imp ortan t role determining rms’ in v estmen t and driving economic gro wth (see Kerr and Nanda (2015) for a recen t review). This dissertation aims to understand ho w nancial factors w ould con tribute to rms’ ph ysical and in tangible in v estmen t. The three c hapters presen ted in this dissertation fo cus on t w o asp ects of the nancial mark et: 1) nancial friction caused b y information asymmetry b et w een lenders and b orro w ers, and 2) information friction caused b y noise traders. In eac h of the follo wing c hapter, I analyzed ho w those factors w ould impact on aggregate in v estmen t and pro ductivit y gro wth through rms’ c hoices o v er inno v ation t yp e, qualit y and in v estmen t. Previous studies sho w that nancial friction can lo w er the aggregate gro wth b y hindering rms’ R&D in v estmen t. But w e kno w that not all t yp es of inno v ation are equally pro ductiv e and few pap ers ha v e studied ho w nancial friction ma y aect the comp osition of R&D and inno v ation t yp es and so aggregate economic gro wth. In Chapter 2, I in v estigate the role of nancial friction in shaping inno v ation t yp es and its impact on aggregate gro wth. Wh y it is imp ortan t to study inno v ation heterogeneities? Eac h inno v ation’s con tribution to rms’ and aggregate pro ductivit y gro wth v aries with its t yp es. F or example, some ma jor inno v ations suc h as inno v ation in semi-conductors not only increase an individual rm’s long-run pro ductivit y but also ha v e a p ositiv e spillo v er that increases 1 the econom y’s future aggregate pro ductivit y . By con trast, some other inno v ations only increase a rm’s sales in the short-run, without fundamen tally c hanging its pro duction pro cess, pro duct, or future pro ductivit y . Industrial design paten ts, suc h as paten ting of pac k aging and con tainer design c hanges, are an example. An imp ortan t empirical observ ation motiv ating m y w ork is that more than 39 p ercen t of paten t applications among Chinese man ufacturing rms are lo w-qualit y industrial design paten ts, but in the United States only 6 p ercen t of all paten t applications are accoun ted for b y industrial design. Can the higher prop ortion of lo w-qualit y paten ts b e partially explained b y China’s less dev elop ed nancial mark ets? Will the o v er-in v estmen t in lo w-qualit y paten ts lo w ers China’s gro wth p oten tial? Chapter 2 answ ers these questions b oth theoretically and empirically . There are t w o main con tributions in c hapter 2. First, I em b edded c hoices o v er inno v ation t yp es and nancial constrain ts in an endogenous gro wth framew ork, whic h hasn’t b een explored m uc h in previous literature. In this mo del, a rm’s lo w-qualit y inno v ation can help it to generate immediate cash o w, but ha v e no impact on rm’s long-run pro ductivit y and sales gro wth. These k ey features link nancial constrain ts to aggregate gro wth through a rm;s c hoices o v er inno v ation t yp es. Second, m y empirical con tribution is to construct a no v el new dataset for priv ately-o wned Chinese man ufacturing rms. Previous studies in China only fo cus on inno v ation quan tities, due to the lac k of inno v ation qualit y data. I o v ercome this h urdle b y scraping and merging eac h Go ogle paten t citation data, with paten t activit y data from China’s State In tellectual Prop ert y Oce, and with rms’ op erating data from China’s Ann ual Surv ey of Man ufacturing. I use this new dataset to re-group and reclassify paten ts in to three dieren t t yp es, based on eac h paten t’s "qualit y", measured b y its citation and m y econometric estimates of its con tribution to a rm’s future pro ductivit y gro wth. T o m y kno wledge, this is the rst pap er to study inno v ation heterogeneit y and qualit y in China. 2 I then use this ric h and no v el dataset to empirically sho w that, among those priv ately-o wned Chinese man ufacturing rms, nancial frictions force rms to inno v ate relativ ely more on lo w-qualit y inno v ation and less on pro ductivit y-impro ving inno v ation. I then build an endogenous gro wth mo del featuring an inno v ation qualit y c hoice and rm-lev el nancial frictions to quan tify the impact of inno v ation shifting due to nancial frictions on macro economic gro wth. The calibrated mo del suggests that these c hanges in inno v ation quan tit y and comp osition can lo w er the aggregate gro wth rate as m uc h as 0.4 p ercen tage p oin t ann ually , relativ e to p erfect nancial mark et b enc hmark. I also use this framew ork to quan tify the impact of curren tly implemen ted R&D tax incen tiv e p olicy in China. The sim ulation result sho ws that suc h p olicy has increased Chin’a aggregate ann ual pro ductivit y gro wth rate b y 0.1 p ercen tage p oin ts. Impro v emen t on R&D tax p olicy whic h w ould result in higher pro ductivit y gro wth is then suggested b y this c hapter. Chapter 3 analyzes the impact of information friction on a rm’s in v estmen t and the aggregate in v estmen t uctuation. A recen t and gro wing literature has in v estigated the role of "news sho c ks", or c hanges in agen ts’ exp ectations, as p oten tially imp ortan t determinan ts of aggregate uctuations. In this c hapter, I use rms’ and sto c k traders’ in v estmen t b eha vior to infer agen ts’ uncertain t y ab out the future. In particular, I dev elop a general equilibrium mo del in whic h traders are endo w ed with dieren tiated b eliefs ab out TFP sho c ks. I study qualitativ ely ho w disp ersed b eliefs are aggregated in the sto c k mark et, and to what exten t aggregated information inuences rms’ in v estmen t b eha vior. Next, I use the observ ed relationship b et w een in v estmen t, sto c k prices, and inno v ations in TFP to measure the information and its precision that rms receiv e. I nd a mo derate degree of learning from rms’ o wn priv ate signal, but no rm learning from the sto c k mark et. My empirical w ork also sho ws that the existence of noise traders generates m uc h noise in the public signal rms receiv e. And suc h noise inhibits information transmission b et w een imp erfectly informed traders and rms. 3 Based on c hapter 2’s theoretical framew ork of ho w nancial constrain ts w ould alter a rm’s inno v ation strategy , c hapter 4 empirically study the impact of credit reallo cation on inno v ation qualit y and rm pro ductivit y disparit y b et w een state-o wned rms and priv ately-o wned rms in China. After the 2008-2009 global nancial crisis, the Chinese go v ernmen t announced an economic stim ulus plan to b o ost the econom y . Ho w ev er, this stim ulus plan disprop ortionately fa v ored state- o wned en terprises b y eectiv ely subsidizing them. I nd that, rst, the stim ulus plan relativ ely raising the nancing costs of priv ately-o wned rms. Second, priv ately-o wned rms started paten ting signican tly less high-qualit y pro ductivit y-impro ving inno v ations than state-o wned rms follo wing the p olicy c hange. Third, pro ductivit y grew faster in state-o wned rms than in priv ately-o wned rms follo wing the p olicy c hange. Based on those empirical evidence, I build a to y mo del to in v estigate the underlying mec hanisms. This to y mo del features t w o t yp es of rms state-o wned and priv ate-o wned that dier in go v ernmen t supp ort, nancing cost and inno v ation capacities. These three factors con tribute to the observ ed dierence in inno v ation in v estmen t and pro ductivit y gro wth b et w een state-o wned rms and priv ate-o wned rms. I then conduct t w o mediation analyses to do cumen t additional empirical evidence that can supp ort those theoretical mec hanisms discussed under m y theoretical framew ork. My empirical results suggest that dierence in subsidies and skill lev els can explain as high as 90% of the observ ed dierence in paten t application b et w een SOEs and POEs. Skill lev els con tributes the most to the dierence in paten t application throughout the sample y ear. Con tribution from subsidies increased after 2009 scal stim ulus p olicies. In pre-2009 sample, subsidies can only explain 9.3% of the observ ed dierence in paten t application. This n um b er increased to 24% in p ost-2009 sample. In the second mediation analysis, m y empirical ndings suggest that 31.4% of subsidies’ impact on pro ductivit y gro wth can b e explained b y an increase in rms’ gran ted paten ts. Th us, the observ ed increase in pro ductivit y gro wth among SOEs after scal stim ulus p olicy can b e attribute to an 4 increase in subsidies they receiv ed. These ndings can partially explain the shrinking pro ductivit y gap b et w een SOEs and POEs. The remainder of this dissertation is organized as follo ws: Chapter 2 examines the impact from nancial friction on inno v ation qualit y and aggregate gro wth; Chapter 3 ev aluates information friction in the sto c k mark et that migh t alter a rm’s in v estmen t. Chapter 4 explores the c hannel through whic h, nancial mark et w ould result in inno v ation and pro ductivit y dierence b et w een state-o wned rms and priv ate-o wned rms. Chapter 5 summarizes the ndings and discusses the future w orks. 5 Chapter 2 Financial Constraints, Innov ation Quality , and Growth This c hapter in v estigates the role of nancial constrain ts in shaping inno v ation qualit y and rm- gro wth dynamics through heterogeneous inno v ation. I build a unique data-set com bining paten t activities with the op erating data of priv ate Chinese man ufacturing rms and sho w a strong negativ e relationship b et w een the sev erit y of nancial constrain ts and a) rm gro wth, b) inno v ation in tensit y , and c) inno v ation qualit y . Based on these empirical regularities, I build a tractable endogenous gro wth mo del in whic h a m ulti-pro duct rm in v ests in heterogeneous inno v ation in the face of imp erfect nancial mark ets. Tigh ter nancial constrain ts cause rms to undertak e more lo w-qualit y inno v ation, whic h yields temp orary pa y os but no longer-term pro ductivit y impro v emen ts. This lo w ers rm and aggregate gro wth rates. The quan titativ e mo del suggests nancial frictions reduce incum b en ts’ R&D in v estmen t b y 19.94% on a v erage and slo ws aggregate ann ual pro ductivit y gro wth b y 10.2 p ercen t (0.4 p ercen tage p oin t ann ually). 2.1 Introduction A large b o dy of w ork argues that nancial mark et dev elopmen t pla ys an imp ortan t role in driving economic gro wth (see Kerr and Nanda (2015) for a recen t review). In this pap er, I explore empirically and theoretically one p oten tial imp ortan t source of this relationship: In v estmen t in R&D has limited 6 collateral v alue, in con trast to in v estmen t in ph ysical capital. Less dev elop ed nancial mark ets can therefore hinder a rm’s inno v ation activities, and p oten tially limit b oth rm and aggregate gro wth rats. In addition, not all t yp es of inno v ation are created equal. F or example, I nd that more than 40 p ercen t of paten t applications among Chinese man ufacturing rms are classied as industrial design paten ts, whic h are b eliev ed to b ear limited v alue. (I describ e in detail the in terpretation of paten t classications in section 2). In con trast, in the United States industrial designs accoun t for only 6 p ercen t of paten t applications. In addition, there is substan tial disparit y in rm-lev el inno v ation category and qualit y , y et little is kno wn ab out the relationship b et w een inno v ation comp osition and nancial mark et dev elopmen t. Do rms facing more sev ere nancial constrain ts that limit inno v ation activities conduct relativ ely more lo w-qualit y inno v ation, suc h as industrial design, reducing their gro wth p oten tial, and if so what is the mec hanism b y whic h this o ccurs? I build a unique dataset of inno v ation qualit y for a large sample of priv ately-o wned Chinese man ufacturing rms. I matc h eac h paten t application b y a rm in m y sample, recorded b y the State In tellectual Prop ert y Oce of China (SIPO), to paten t citation data in Go ogle P aten t. I exploit the forw ard citation data to construct a measuremen t of inno v ation qualit y . Utilizing information on a paten t’s bac kw ard citations and tec hnology eld, I classify a rm’s inno v ation in to three t yp es: industrial design, in ternal inno v ation, and external inno v ation. A rm conducts industrial design to b o ost its curren t prots temp orarily b y attracting more customers. A rm undertak es in ternal inno v ation to impro v e the pro ductivit y of its curren t pro duct lines p ermanen tly while it undertak es external inno v ation to impro v e the pro ductivit y of a second rm’s pro duct lines and capture mark ets from it. Both in ternal and external inno v ations are pro ductivit y-enhancing inno v ations and tak e time to complete. T o m y kno wledge, this is the rst pap er to construct suc h a qualit y and category index for Chinese paten ts. 7 I then link the paten t data to ann ual op erating data from the Chinese Ann ual Surv ey of Man- ufacturing (ASM). Using this merged dataset, I connect measures of rm-lev el paten t activit y to nancial conditions. I also compute a set of measuremen ts of a rm’s nancial constrain ts, as w ell as rm size and gro wth. I measure a rm’s nancial condition follo wing Ho v akimian and Titman (2006) and Almeida and Camp ello (2007), as the in v estmen t to cash o w sensitivit y . I measure a rm’s inno v ation in tensit y for eac h t yp e of inno v ation as the ratio of the n um b er of citation/qualit y- adjusted paten ts to deated rm sales rev en ue. These measuremen ts enable me to establish a set of new empirical facts for Chinese priv ate man ufacturing rms. My k ey empirical ndings are: 1) In ternal and external paten t in tensit y decreases with a rm’s nancial constrain t. On a v erage, industrial design in tensit y increases b y 1.53 p ercen t, in ternal inno v ation in tensit y decreases b y 7.37 p ercen t, and external inno v ation in tensit y decreases b y 6.19 p ercen t with a 1 p ercen t increase in a rm’s probabilit y of b eing nancially constrained. 2) The inno v ation comp osition of rms that are sub ject to tigh ter nancial constrain ts is more concen trated in industrial design and lo w er qualit y paten ts. 3) A rm’s one-y ear sales gro wth rate drops b y 0.70 p ercen tage p oin ts with a 1 p ercen t increase in a rm’s probabilit y of b eing nancially constrained, ev en after con trolling for rm size and rm age. Next, I build an endogenous gro wth mo del that incorp orates 1) dieren t forms of inno v ation, one of whic h industrial design has only immediate prot and cash o w b enets for a rm, and 2) nancial constrain ts in to a rm’s c hoices, whic h pro vides an imp ortan t c hannel linking nance and endogenous gro wth through inno v ation. The mo del is tractable and yields a clear prediction for inno v ation comp osition across nancially constrained rms. Once sub ject to nancial constrain ts, a rm’s a v ailable cash o w restricts its R&D in v estmen t exp enditure on inno v ation. As paten ting in industrial design immediately b o osts a rm’s curren t prot and cash o w, a nancially constrained rm undertak es more industrial design paten ting to relax its curren t nancial constrain t. Compared 8 with nancially unconstrained rms, nancially constrained rms then conduct less pro ductivit y- enhancing inno v ation, as their total in v estmen t exp enditure is restricted. A tigh ter nancial con- strain t forces a rm to substitute in to industrial design paten ting and out of pro ductivit y-enhancing inno v ation, whic h hinders its future gro wth. The existence of nancial constrain ts c hanges rms’ inno v ation comp osition as w ell as its p oten tial gro wth. Suc h c hanges v ary across rm size. In the mo del, a small rm’s R&D in v estmen t is nancially constrained. Th us, small rms undertak e more industrial design and less pro ductivit y-enhancing inno v ation than is optimal, and this results in a lo w er gro wth rate. Once a rm gro ws large enough, its R&D in v estmen t is no longer nancially constrained. Financial mark et frictions ha v e a smaller impact on a large rm’s inno v ation comp osition and gro wth. I then calibrate the mo del to matc h the empirical facts I ha v e iden tied for Chinese man ufactur- ing rms relating to rm dynamics, inno v ation in tensit y , and nancial conditions. The calibrated mo del can replicate the observ ed rm size distribution in the Chinese data, as w ell as the rela- tionships b et w een nancial constrain ts, inno v ation in tensit y , qualit y , and rm gro wth. The mo del implies that, ev en conditioning on rm size, on a v erage, nancial constrain ts pla y a quan titativ ely imp ortan t role in shaping a rm’s inno v ation in tensit y . A 10 p ercen t decrease in a rm’s nancial constrain t w ould, on a v erage, result in a 0.3 p ercen tage p oin ts increase in the share of external inno v ation and a 1.2 p ercen tage p oin t decrease in industrial design paten ting share. This shift from industrial design paten ting to external inno v ation raises a rm’s gro wth rate b y 4 p ercen t. In addition, while industrial design relaxes a rm’s nancial constrain t temp orarily , it reduces a small rm’s prot and sales through increased comp etition. Th us, sub-optimally high industrial design paten ting in the presence of nancial constrain ts could b e detrimen tal to aggregate gro wth. I nd that, rst, if all nancial constrain ts w ere remo v ed, the aggregate gro wth rate w ould rise b y 11.5 p ercen t, with m uc h of this increase b eing attributable to higher in ternal and external inno v ation 9 and lo w er industrial design. Second, sh utting do wn paten ting on industrial design w ould increase the aggregate gro wth rate b y 6.3 p ercen t, and encourage sligh tly higher en try rates b y new rms b y 0.01 p ercen t. Finally , I sho w that t yp e-dep enden t R&D tax incen tiv es, under whic h only R&D ex- p enses on in ternal and external inno v ation are en titled to a sup er deduction in computing corp orate income tax base, w ould generate higher aggregate gro wth and a larger w elfare gain than curren tly implemen ted uniform R&D tax incen tiv es. This pap er relates to sev eral branc hes of literature. First, I build closely on the seminal w ork of Klette and K ortum (2004), Len tz and Mortensen (2016), and Ak cigit and Kerr (2018). These framew orks allo w rms to o wn m ultiple pro duct lines through external inno v ation. Ak cigit and Kerr (2018) and Garcia-Macia, Hsieh, and Kleno w (2019) also in tro duce in ternal inno v ation and let rms inno v ate o v er their existing pro duct lines. In ternal inno v ation is found to b e a quan titativ ely imp ortan t c hannel in promoting aggregate pro ductivit y gro wth. I extend these framew orks in three main w a ys. First, I in tro duce paten ting in industrial design. Second, I in tro duce nancial constrain ts. I sho w the existence of nancial constrain ts can help explain the relativ ely lo w lev el of R&D in tensit y and a higher lev el of industrial design observ ed for Chinese man ufacturing rms. This pap er also relates to the literature on nance and R&D in v estmen t, nancial constrain ts and pro ductivit y gro wth. A w ell-functioning nancial mark et is b eliev ed to pla y an imp ortan t role in spurring economic gro wth. A large b o dy of w ork in v estigates ho w nancial dev elopmen t w ould p oten tially aect R&D nancing and inno v ation. Bro wn, F azzari, and P etersen (2009), Hall and Lerner (2010), Bro wn, Martinsson, and P etersen (2013), and Hsu, Tian, and Xu (2014) are examples. Their empirical studies sho w that small rms face a high cost of R&D capital, and their R&D in v estmen ts are more sensitiv e to cash o w than large rms. Th us, rms in coun tries with less dev elop ed nancial mark ets w ould b e more lik ely to underin v est in inno v ation. Aghion, Angeletos, Banerjee, and Mano v a (2010) build a mo del in whic h credit constrain ts c hange a rm’s in v estmen t 10 comp osition. In particular, with imp erfect nancial mark ets, in v estmen t shifts from long-run to short-run. I build on this literature b y dev eloping a mo del in whic h rms can use industrial design as a device to b o ost their curren t prots. Th us, nancial constrain ts not only aect the quan tit y of R&D in v estmen t, but also its comp osition. Once a rm’s R&D in v estmen t is restricted b y nancial constrain ts, it concen trates more on industrial design, whic h do es not con tribute to a rm’s future gro wth. The mo del then explores this new c hannel through whic h nancial constrain ts aect a rm’s gro wth. With this elemen t, the mo del can t the empirical regularities observ ed in the data. My results, b oth analytically and quan titativ ely , highligh t the imp ortance of nancial constrain ts in shaping the relationship b et w een inno v ation, rm size and gro wth. The rest of the pap er is organized as follo ws. Section 2 do cumen ts m y data set construction and empirical analysis for the priv ate, inno v ativ e rms in Chinese man ufacturing from 2003 to 2009. Section 3 la y out the theoretical mo del and its analytical implications. Section 4 and 5 conducts a quan titativ e analysis of the mo del and deriv es p olicy implications. Section 6 concludes. 2.2 Data and Empirical Analysis In this section, I do cumen t empirical relationships b et w een nancial constrain ts, inno v ation, and rm size and gro wth for a large sample of Chinese Man ufacturing rms. I rst do cumen t data sources and m y construction of the sample. I then describ e m y measuremen t of paten t t yp e, paten t qualit y , and nancial constrain ts. Finally , I examine econometrically ho w nancial constrain ts alter a rm’s inno v ation in tensit y and qualit y . These empirical regularities motiv ate the sp ecication of m y theoretical mo del, and I use them to discipline the quan titativ e analysis of the mo del. 11 2.2.1 Data Source T o assess the empirical relationship b et w een nancial constrain ts, inno v ation, and rm gro wth, I construct a panel data sample for Chinese priv ate man ufacturing rms from 2003 to 2009. I dra w the data from three large panel data sets. The rst is the paten t data from China’s State In tellectual Prop ert y Oce (SIPO). It con tains basic "fron t page" data for paten ts issued from 1985 to 2016. The v ariables I use are a paten t’s n um b er, application and gran ting dates, tec hnology domain, and description, and the assignee’s name and lo cation. The second is the relativ ely w ell-studied rm-lev el op eration data from the Chinese Ann ual Surv ey of Man ufacturing (ASM), whic h includes industrial rms with ann ual sales greater than 5 million RMB (appro ximately $800,000) from 1998 to 2013 1 . I clean the dataset and construct a panel follo wing the metho d outlined in Brandt, V an Biesebro ec k, and Zhang (2014). I use rms’ balance-sheet information from ASM to construct a set of measuremen ts on rms’ nancial constrain ts, rm size, and rm gro wth. These t w o data sources are collected b y dieren t agencies and do not share the same iden tication n um b er for eac h rm. They do, ho w ev er, pro vide rms’ names and lo cations. My linking of the t w o datasets follo ws the metho dology prop osed in He, T ong, Zhang and He (2016). I supplemen t the paten t data with information on paten t citations from Go ogle paten ts. Previous studies of inno v ation activities among Chinese rms fo cus only on inno v ation frequencies measured b y simple paten t coun ts, making it dicult to gauge paten t qualit y and v alue. P aten t v alue v aries across tec hnology elds, and dieren t paten ts ha v e div erse impacts on a rm’s size and pro ductivit y gro wth. One ma jor inno v ation could generate more future prot and pro ductivit y gro wth than sev eral minor inno v ations. I, therefore, construct a panel of paten t citations for eac h gran ted paten t in SIPO using Go ogle P aten t. Go ogle paten t do cumen ts the date and tec hnology domain of a paten t 1 After 2010, the ASM only con tains rms with ann ual sales greater than 20 million RMB (appro ximately $3,200,000) 12 when cited. This enables me to adjust eac h SIPO paten t’s citations based on the time windo w in whic h they o ccur, and the paten t’s tec hnology eld. After these adjustmen ts, I can compare paten ts o v er time and tec hnology domains. As state-o wned rms and foreign-o wned rms migh t ha v e dieren t paten ting incen tiv es than priv ately-o wned rms, I only use priv ate, non-foreign o wned, inno v ativ e rms in m y sample. I dene inno v ativ e rms as rms that paten t at least once in the p erio d 2003-2009. I dene priv ate, non- foreign o wned rms as rms that not registered as state-o wned or foreign-o wned, or ha v e con trolling shareholders that are non-state and non-foreign en tities. T o remo v e the impact of outliers, I trim the nal sample at the 1 p ercen t tails of rms’ sales rev en ue. The nal merged sample con tains 105,743 observ ations with 23,963 unique priv ate rms. Firms in m y sample applied for 276,015 paten ts b et w een y ear 2003 to y ear 2009, comprising 72,349 "in v en tion paten ts", 97,826 "utilit y mo del" paten ts and 105,840 "industrial design" paten ts. I describ e the prop erties of eac h t yp e of paten t in detail b elo w. App endix A.1 discusses in detail those datasets and the metho d I used to merge them. 2.2.2 Measuring P atent type, quality and nancial constraints Next, I briey in tro duce the main v ariables I use in m y empirical studies. App endix A.1 pro- vides detailed information on measuremen ts of eac h v ariable, and T able A.4 in app endix A.4.1 lists summary statistics for k ey v ariables. P aten t T yp e. Under SIPO classication of paten ts, 1) in v en tion paten ts are paten ts that mak e "signican t progress" relativ e to previous tec hnology , 2) utilit y mo dels are paten ts that represen t a minor impro v emen t of curren t pro ducts and are insucien t to b e gran ted as in v en tion paten ts, and 3) industrial design are paten ts of ornamen tal or aesthetic design of ph ysical or digital go o ds with a practical purp ose. In m y sample, around 70 p ercen t of industrial design paten ts are pac k aging, 13 or design of clothing, jew elry or furniture, whic h do not con tribute to the impro v emen t of a rm’s pro duction pro cess. In v en tion and utilit y mo dels, ho w ev er, con tribute to a rm’s pro duction pro cess and, th us its pro ductivit y . I regroup and reclassify in v en tion and utilit y mo dels in to t w o categories: 1) In ternal inno v ation, and 2) external inno v ation. In ternal inno v ation paten ts are "exploitation" inno v ations, whic h aim to impro v e a rm’s existing pro duction metho d or pro cess. One can view these inno v ations as renemen ts and extensions of curren t tec hnology . External inno v ation paten ts are "exploration" inno v ations, whic h aim to increase the n um b er of a rm’s pro duct lines b y in tro- ducing new pro ducts or an en tirely new pro duction tec hnology . As in ternal inno v ation relies more on the rm’s previous tec hnology , a rm’s external inno v ation paten t cites less its o wn, previous paten ts but cites more paten ts o wned b y other rms than do es an in ternal inno v ation paten t 2 . I classify in ternal inno v ation paten ts in t w o steps. First, for paten ts with bac kw ard citations, I classify a paten t as in ternal inno v ation if more than 50 p ercen t of bac kw ard citations are self- citations. Second, for paten ts without bac kw ard citations 3 , I classify a paten t as in ternal inno v ation if a) its tec hnology domains b elong to the rm’s previous paten t’s tec hnology domains, and b) there is a statemen t similar to "impro ving curren t pro duction pro cess" in the paten t description, or if the rm rep orts "no new pro duct is pro duced" in the y ear of the paten t’s application 4 . Using this metho d for distinguishing in ternal from external paten ts, there are 98,580 in ternal paten ts and 71,595 external paten ts in the sample p erio d. My metho d is sligh tly dieren t from the metho d prop osed b y Ak cigit and Kerr (2018). I compare these t w o metho ds in detail in App endix A.1. In general, m y metho d yields a more restrictiv e denition of external, exploratory inno v ation. 2 Galasso and Simco e (2011) and Ak cigit and Kerr (2018)). Levin thal and Marc h (1993) and Marc h (1991) pro vide detailed distinguish on exploration and exploitation inno v ations 3 In the merged sample, around 42 p ercen t of in v en tion paten ts lac k bac kw ard citation data and all utilit y paten ts do not ha v e bac kw ard citation. 4 In ASM, rms w ere ask ed to pro vide information on whether their curren t pro ducts are pro duced using new tec hnology or new pro duction pro cess. 14 P aten t Qualit y . F ollo ws the literature 5 , I measure paten t qualit y b y the n um b er of forw ard citations a giv en paten t receiv ed in a time windo w of v e y ears from its publication date 6 . I use a v e-y ear windo w to accoun t for truncation issues in the citation data; namely , more recen tly published paten ts ha v e less time to accum ulate citations. Next, I accoun t for the fact that paten t citations v ary a lot across tec hnology elds. T o mak e paten t qualit y comparable o v er dieren t tec hnology domains, I compute a paten t’s relativ e qualit y b y dividing its citation coun t b y the a v erage citation coun t for a paten t within a three-digit IPC eld. Then, I dene the relativ e qualit y of paten t j applied for b y rm f at time t, and rm f ’s total qualit y-adjusted paten t application at time t, as: q fjt = P ~ t+5 = ~ t citations fj 1 Nt P Nt f=1 P ~ t+5 = ~ t citations j ; Pat ft = Npt X j=1 q fjt Here, citation fj denotes the n um b er of citations of rm f ’s paten t j in y ear ~ t, ~ t t is the paten t’s publishing y ear recorded b y Go ogle paten ts, N t denotes the total n um b er of paten ts applied b y Chinese rms in the SIPO oce at time t whic h are gran ted or published later during sample p erio d, and N pt is the total n um b er of paten t applications led b y rm f in y ear t that are gran ted later during the sample p erio d. Patapp ft is m y measure of the inno v ation rate of rm f at datet. I can compute this only for in ternal and external inno v ation, as citation dates are only observ able for in ternal paten ts and external paten ts. Th us, I am forced to use simple paten t coun t data instead of citation/qualit y-adjusted paten t data to measure the rate of industrial design inno v ation for rm f at y ear t. 5 See Hall, Jae and T ra jten b erg (2001), Jae and T ra jten b erg (2001), Aghion (2017) 6 F or utilit y and industrial design paten ts, gran t date is publish date. F or in v en tion paten ts, publish date is earlier than gran t date. In China, in v en tion paten ts can b e a v ailable to the public (i.e. published) after preliminary examination b y paten t examiner. Then it should undergo "substan tiv e examination". A published paten t can b e rejected b y examiners if it is found to b e neither inno v ativ e enough nor conicts with paten t la w. As paten t b ecome a v ailable to the public after its publishing date, it starts accum ulating citations. I use a v e-y ear windo w for t w o reasons. First a v ailable data restrict the windo w; the merged rm sample ends in 2013, and the citation data ends in 2018, so paten t gran ted or published in the last y ear of m y merged rm sample p erio d ha v e only v e y ears to accum ulate citations. Second, it is the most relev an t, citation-activ e windo w; on a v erage, a paten t in SIPO receiv es more than 87 p ercen t of its ten-y ear-forw ard citations within v e y ears of its publication date. 15 Financial Constrain t. A rm b ecomes nancially constrained when external nancing through either debt or equit y is not a v ailable. R&D in v estmen t b y nancially constrained rms then hea vily dep ends on its in ternal cash o w. R&D in v estmen t cash-o w sensitivit y can then b e used to appro x- imate the degree of nancial constrain t faced b y a rm 7 . I measure in v estmen t cash-o w sensitivit y , follo wing Ho v akimian and Titman (2006) and Almeida and Camp ello (2007), b y using an endoge- nous switc hing regression. There are t w o adv an tages under their metho dology: 1) The estimation do es not rely on an a priori assignmen t of rms in to constrained and unconstrained categories; 2) in v estmen t-cash-o w sensitivit y , as w ell as the probabilit y of b eing nancially constrained, can b e join tly estimated through an in v estmen t equation and an endogenous selection equation. Th us, follo wing their framew ork, I appro ximate a rm’s nancial constrain t in t w o steps. First, I join tly estimate follo wing in v estmen t (equation 2.1) and selection (equation 2.2) equa- tions. Second, I compute the probabilit y of b eing nancially constrained using the estimated se- lection equation. I then use this probabilit y to appro ximate a rm’s nancial constrain ts. The regression equations are, RDInv j;iht = 1j RDInv j;iht1 + 2j GrowOpp j;iht1 + 3j Cash j;iht1 + ht +" j;iht ; j = 1; 2 (2.1) y it = 0 +Z 0 it1 +u it (2.2) In (1), rms are indexed b y i, h indexes a rm’s industry , t indexes time, ht measures industrial- y ear xed eects. j indicates regime 1 and regime 2. A rm mak es a constrained in v estmen t under regime 1, or an unconstrained in v estmen t under regime 2. In addition. GrowOpp it is an in v estmen t opp ortunit y for rm i, whic h is appro ximated b y the ratio of the rm’s c hange in turno v er to real 7 See Hall and Lerner (2010), Bro wn, F azzari and P etersen (2009) and Bro wn, Martinsson and P etersen (2013) on Compustat rms; P oncet, Steingress and V anden bussc he (2010), Guariglia, Liu and Song (2011) and Ho w ell (2016) for Chinese Man ufacturing rms. 16 capital. Cash j;iht1 is dened as real net income plus real curren t depreciation, divided b y the rm’s real capital sto c k at the b eginning of curren t p erio d. The dep enden t v ariable, RDInv j;iht is the real R&D in v estmen t of rm i normalized b y the rm’s real capital sto c k at the b eginning of p erio d t. A one y ear lagged v alue of the dep enden t v ariable is included to allo w for the correlation b et w een previous and curren t R&D in v estmen t decisions. In (2), y is a laten t v ariable that establishes a rm’s probabilit y of b eing in the constrained regime (regime 1) and unconstrained regime (regime 2). The v ector Z it1 is a set of selection v ariables that determine a rm’s prop ensit y of b eing in either regime. F ollo wing Almeida and Camp ello (2007) and Ho v akimian and Titman (2006), Z con tains 1) the log of total assets, 2) log age of rm, 3) the rm’s ratio of short-term debt to total assets, 4) the rm’s ratio of long-term debt to total asset, 5) nancial slac kness measured as a rm’s cash and mark etable securities to total assets, and 6) Tangibility , whic h is used to appro ximate the exp ected liquidation v alue of a rm’s op erating assets. F ollo wing Berger, Ofek, and Sw ary (1996) and Almeida and Camp ello (2007), I computeTangibilit asTangibility = 0:715Receivables it +0:547Inventory it +0:535 FixedAsset it +Cash+MarketableSecurities, scaled b y total assets, whereReceivables it are accoun t receiv ables. Cash and mark etable securities are computed as liquid assets min us accoun t receiv ables. These v ariables all en ter in lagged form in the selection equation. The parameters set in equation (2.1) and in equation (2.2), are then estimated join tly using the Exp ectation Maximization algorithm (see App endix A.1.2 for details). Ideally , for - nancially constrained rms, w e w ould exp ect 3 > 0, that is a rm’s R&D in v estmen t w ould increase with its cash o w. T able A.3 and A.2 sho w the estimation results. Cash o w sensitivit y is statistically signican t under the constrained regime, and larger than cash o w sensitivit y under the unconstrained regime. I then dene a rm’s nancial constrain t score, FC , as its probabilit y of b eing nancially constrained. The probabilit y can b e reco v ered through a Probit regression: 17 FC it d prob it = ( ^ 0 +Z 0 it1 ^ ) where is the cum ulativ e normal distribution. A rm with a higher lik eliho o d of b eing constrained has a higher nancial constrain t score FC . The a v erage probabilit y of b eing nancially constrained for rms in m y sample is 0.525. 2.2.3 Empirical Results I no w presen t the k ey empirical results on the link b et w een nancial constrain ts, inno v ation qualit y , and rm gro wth 8 . T o do so, I rst estimate a simple linear regressions of the follo wing form: y ijt = 0 + 1 log(Sales ijt ) + 2 Age ijt + 3 FC ijt + jt +" ijt where y ijt are rm i (in industry j ), y ear t dep enden t v ariables - suc h as: rm sales gro wth, industrial design in tensit y , in ternal inno v ation in tensit y , external inno v ation in tensit y , industrial design paten t share, and external and in ternal inno v ation share. A rm’s ann ual sales gro wth is dened as sale it+1 sale it . I set this gro wth rate to1 if a rm exits the mark et. Inno v ation in tensit y is dened as Pat it Sale it . Recall that paten t applications are all gran ted or published in the sample p erio d and citation adjusted for in ternal and external inno v ations. A rm’s paten t share in industrial design is the n um b er of industrial design paten ts applied at time t o v er all paten ts the rm applied for in the same p erio d. Firm size is measured b y the log of a rm’s real sales Sale ijt . FC ijt measures a rm’s nancial constrain t, measured in the previous section, as the lik eliho o d that a rm faces friction in the access to the credit mark et. jt con trols for industry-y ear xed eects, remo ving an y unobserv able y ear and industry-sp ecic demand shifters. The regression results are recorded in T able 2.1. 8 My empirical studies on inno v ativ e priv ate rms in Chinese man ufacturing also pro vide some other in teresting patterns on rm size and inno v ation, rm size and nancial constrain ts. App endix A.4 do cumen ts these additional empirical results. 18 F act 1. Financial c onstr aints incr e ase a rm’s investment in industrial design and lower a rm’s investment in internal and external innovation. T able 2.1: Firm Size, Gro wth and Inno v ation In tensit y Gro wth P aten t In tensit y P aten t Share (1) (2) (3) (4) (5) (6) (7) Sale it+1 Sale it Pat d it Sale it Pat I it Sale it Pat X it Sale it Pat d it Pat T it Pat I it Pat T it Pat X it Pat T it log(Sale) it 0:072 0:102 0:108 0:039 0:013 0:045 0:023 (0:008) (0:017) (0:007) (0:004) (0:003) (0:003) (0:002) age it 0:001 0:002 0:002 0:000 0:002 0:002 0:002 (0:001) (0:001) (0:000) (0:000) (0:000) (0:000) (0:000) FC it 0:702 0:072 0:266 0:275 0:191 0:184 0:270 (0:106) (0:188) (0:055) (0:044) (0:055) (0:030) (0:033) Industry Fix Y es Y es Y es Y es Y es Y es Y es Y ear Fix Y es Y es Y es Y es Y es Y es Y es N. Obs 106; 820 68; 566 72; 676 67; 317 23; 357 27; 467 22; 108 R-squared 0:038 0:014 0:029 0:013 0:171 0:076 0:064 Note: Firm size is measured b y real sales, log(sale). Pat it is (citation-w eigh ted) paten t applications for industrial design (denoted as d in the sup erscript), long-run in ternal (I ) and long-run external (x) inno v ation. Pat T it is a rm’s total paten t applications at time t. FC it measures a rm’s nancial condition dened as probabilit y of b eing constrained, whic h is calculated via endogenous switc hing regression in section 2.3. Industry-y ear xed eects and rm age are included as con trols, but I do not rep ort in regression. Robust standard errors clustered at rm lev el are in paren theses. , and indicate signican t at lev els 1%, 5% and 10%, resp ectiv ely . Columns (2) to (4) sho w that if a rm’s nancial constrain ts tigh ten, it reduces paten ting in in ternal and external inno v ation, and increases paten ting in industrial design, whic h is non- pro ductivit y enhancing. The co ecien t estimate ^ 3 indicates that with a 1 p ercen t increase in its probabilit y of b eing nancially constrained, a rm w ould increase its paten ting in industrial design b y 0.07 p er unit of real sales, whereas it w ould reduce its paten ting in in ternal and external inno v ation b y 0.27 and 0.28 p er real sales unit resp ectiv ely . The reduction in external inno v ation in tensit y is higher. This results in a drop in external inno v ation share, and an increase in b oth in ternal inno v ation and industrial design share. Columns (5) to (7) do cumen t that a one unit c hange in rm’s F C score is asso ciated with 19 p ercen t increase in industrial design share of inno v ation, an 18 p ercen t increase in its in ternal inno v ation share, and a 27 p ercen t reduction in its external inno v ation share. 19 Financial constrain ts not only aect a rm’s c hoice of inno v ation t yp e, but also its c hoice of inno v ation qualit y . T o estimate this, I rst construct a paten t qualit y distribution, based on eac h paten t’s external citations within 5 y ears of its publication date. F or eac h y ear, I calculate the p ercen tage of in ternal and external paten t applications in eac h qualit y quartile, to construct a v ariable named paten t share. Then, I estimate the regression of the form: PatQualShare q;ijt = 0 + 1 X ijt + jt +" ijt WherePatQualShare q;ijt is paten t share in eac h quartile q . with [0; 25) denoting the lo w est-qualit y quartile and [75; 100] denoting the highest-qualit y quartile. X ijt are indep enden t v ariables: A rm’s size and its nancial constrain ts measure. Again, industry and y ear xed eects are con trolled. T able 2.2 records the results. The co ecien ts in eac h ro w naturally sum to zero. T able 2.2: Firm size, Financial Constrain t and P aten t Qualit y Distribution P anel A: Share of Firm’s In ternal P aten ts in Qualit y Distribution [0; 25) [25; 50) [50; 75) [75; 100] [0; 25) [25; 50) [50; 75) [75; 100] log(Sale it ) 0:013 0:004 0:005 0:012 (0:002) (0:002) (0:002) (0:002) FC it 0:202 0:009 0:120 0:091 (0:033) (0:027) (0:026) (0:024) P anel B: Share of Firm’s External P aten ts in Qualit y Distribution [0; 25) [25; 50) [50; 75) [75; 100] [0; 25) [25; 50) [50; 75) [75; 100] log(Sale it ) 0:005 0:004 0:005 0:004 (0:003) (0:002) (0:002) (0:003) FC it 0:128 0:003 0:031 0:100 (0:039) (0:031) (0:032) (0:035) Note: The dep enden t v ariable is the share of a rm’s paten ts in eac h quartile of the paten t qualit y distribu- tion. The qualit y distribution is calculated using external citations. Eac h cell from column (1) to (4) rep orts the estimated OLS co ecien ts on rms size, measured as log of real sales rev en ue. Eac h cell from column (5) to (8) rep orts the estimated OLS co ecien ts on rms’s nancial constrain ts. Y ear and industry xed eects are included in the regression, but I do not rep ort the result. P anel A rep orts the regression co ecien ts for in ternal paten ts, and P anel B rep orts the co ecien ts for external paten ts. Robust standard errors clustered at rm lev el are in paren theses. , and indicate signican t at lev els 1%, 5% and 10%, resp ectiv ely . F act 2. Innovation quality incr e ases with rm size, and de cr e ases with nancial c onstr aints. 20 The tigh tening of nancial constrain ts is asso ciated with a shift in rms’ paten t applications from the top qualit y quartile in to the b ottom qualit y quartile for b oth in ternal and external paten ts. Co ecien ts on ro w FC it imply that a 10 p ercen t increase in a rm’s probabilit y of b eing nancially constrained is asso ciated with 2 p ercen t increase in the fraction of a rm’s in ternal paten ts in the b ottom quartile of the paten t qualit y distribution. A 10 p ercen t increase in FC is asso ciated with 0.9 p ercen t decrease in the fraction of a rm’s in ternal paten ts in the top quartile of the paten t qualit y distribution. As large rms are less lik ely to b e nancially constrained 9 , they ha v e a comparativ e adv an tage in ac hieving high-qualit y inno v ations. A 10 p ercen t increase in rm size is asso ciated with 0.13 p ercen t reduction in the fraction of rm’s in ternal paten t among the b ottom quartile of the paten t qualit y distribution, and a 0.12 p ercen t increase in the fraction of rm’s in ternal paten t among the top quartile of the paten t distribution. Similar patterns can b e found in a rm’s external inno v ation. Large and nancially unconstrained rms concen trate more on high-qualit y paten ts. F act 3. Tighter nancial c onstr aints ar e asso ciate d with a lower rm gr owth r ate. Column (1) in T able 2.1 do cumen ts a strong negativ e relationship b et w een nancial constrain ts and a rm’s size gro wth. A 10 p ercen t increase in a rm’s lik eliho o d of b eing nancially constrained is asso ciated with an 7.02 p ercen t decrease in a rm’s sales gro wth rate. F acts 1 and 2 sho w that tigh tened nancial constrain ts are asso ciated with lo w er quan tit y and qualit y of a rm’s in ternal and external inno v ation. T o further gauge p oten tial sources of the negativ e relationship b et w een nancial constrain ts and rm gro wth, I assess the relationship b et w een the inno v ation activit y of the rm and its future gro wth. I estimate the follo wing sp ecication: logSales ijt+k logSales ijt = 0 + 1 log(Patgrant h it + 1) + 2 X ijt + jt +" ijt 9 T able A.2 in App endix A.1.2 do cumen t the estimation result of selection equation 2.2. Firms with large size (measured with total assets) ha v e lo w er probabilit y switc hing in to constrained region. 21 Here, logSales ijt+k logSales ijt is a rm’s sales gro wth in k = 1; 2; 3 y ears’ ahead of time t. Patgrant h it is a rm’s time t gran ted paten ts in category h - industrial design, in ternal and external. X ijt are other rm-lev el con trols as rm size and age. The industry-y ear xed eect is included to accoun t for unobserv able factors at the industry and y ear lev el. T able 2.3 rep orts the results. T able 2.3: Firm Gro wth and Inno v ation One P erio d Ahead T w o P erio d Ahead Three P erio d Ahead (1) (2) (3) (4) (5) (6) (7) (8) (9) log(D + 1) 0:012 0:010 0:004 (0:007) (0:012) (0:017) log(LTE + 1) 0:072 0:104 0:118 (0:013) (0:019) (0:020) log(LTI + 1) 0:032 0:036 0:067 (0:008) (0:017) (0:019) FE Y es Y es Y es Y es Y es Y es Y es Y es Y es Con trols Y es Y es Y es Y es Y es Y es Y es Y es Y es N. Obs 57; 204 49; 511 45; 726 57; 204 49; 511 45; 726 57; 204 49; 511 45; 726 R-squared 0:016 0:048 0:070 0:016 0:048 0:070 0:016 0:048 0:070 Dep enden t v ariables are rm’s gro wth rate in real sales. D it is the log of n um b er of industrial design paten ting application at time t,LT it is the n um b er of pro ductivit y-enhancing paten ts: in v en tion and utilit y mo dels. Curren t, one p erio d and t w o p erio d are dep enden t v ariable measures rm’s real sales gro wth in one, t w o and three y ears, resp ectiv ely . P ast real sales, rm age and Industry-y ear xed eects are included as con trols, but I do not rep ort in regression. Robust standard errors clustered at rm lev el are in paren theses. , and indicate signican t at lev els 1%, 5% and 10%, resp ectiv ely . The rm’s curren t gro wth in one y ear is strongly p ositiv ely asso ciated with all three t yp es of inno v ation. Ho w ev er, the relationship b et w een future gro wth (i.e. sales gro wth in t w o and three y ears) and industrial design inno v ation activit y is statistically insignican t and economically small. Similar qualitativ e results can also b e found if the dep enden t v ariable is replaced with TFP gro wth. T able A.9 in App endix A.4 sho ws the result. Both in ternal and external inno v ation exert a strong p ositiv e impact on a rm’s future gro wth, and this impact increases with the time horizon. F or example, a 10 p ercen t increase in gran ted external inno v ation w ould raise a rm’s curren t sales gro wth b y 0.72 p ercen t and future gro wth b y 1.04 p ercen t in t w o y ears and 1.18 p ercen t in three y ears. In ternal inno v ation con tributes less to a rm’s future gro wth than external inno v ation at all horizons. It is also notable that the a v erage n um b er of external forw ard citations is 1.92 p er paten t 22 for in ternal inno v ation, and 1.51 for external inno v ation, suggesting that the so cial v alue of in ternal inno v ation is also smaller than that of external inno v ation. F acts 1 and 2 imply that tigh ter nancial constrain ts shift a rm’s inno v ation comp osition to- w ards industrial design and lo w-qualit y inno v ations. F act 3 suggests that suc h c hanges in inno v ation comp osition lo w er a rm’s gro wth rate. Th us, rm c hoices o v er inno v ation qualit y and t yp e pro vides a c hannel through whic h nancial constrain ts could lo w er rm and aggregate gro wth. 2.3 Theoretical Model I no w build an endogenous gro wth mo del to in v estigate a rm’s inno v ation c hoice, conditioning on the sev erit y of its nancial constrain t. The basic structure of the mo del is similar to that of Ak cigit and Kerr (2018), with three k ey dierences: 1) I in tro duce paten ting in industrial design as a demand shifter; 2) I include rm nancial constrain ts; and 3) I use a more general sp ecication of decreasing returns to scale in inno v ation tec hnologies. 2.3.1 Preferences, T echnology and Mark et Structure Household. I assume a represen tativ e household with family size L =L f + ~ L. ~ L is the n um b er of w ork ers emplo y ed in the in termediate go o ds sector and L f is the n um b er of w ork ers emplo y ed in the nal go o ds sector. Lab or is supplied in-elastically; hence, L equals aggregate emplo ymen t and the aggregate lab or endo wmen t. Let w b e the equilibrium w age at time t. The household maximize the lifetime utilit y function: U = Z 1 0 e t logC(t)dt 23 where C(t) is the instan taneous consumption rate of a single nal go o d with output Y (t), whic h is pro duced comp etitiv ely b y a represen tativ e nal go o ds pro ducer. This maximization is sub ject to the budget constrain t: _ S(t) +C(t)r(t)S(t) +w(t) L Here S(t) = R V k (t)dk is the total asset held b y the represen tativ e household. And V k (t) is rm v alue of eac h in termediate pro ducer k and nal go o ds pro ducer. r(t) is the equilibrium in terest rate on assets. Final Go o ds. Output of the nal go o d, Y (t), is pro duced using lab or input L f and a con tin uum of in termediate go o ds j2 [0; 1] on a unit circle. The pro duction tec hnology is: Y (t) = L f (t) 1 Z 1 0 A j (t)q 1 j (t)dj where q j (t) is the quan tit y of in termediate go o d j , A j (t) is the qualit y of in termediate go o ds j in nal go o ds pro duction, and 2 (0; 1) measures return to scale and is the in v erse of the substitution elasticit y b et w een in termediate go o ds. Industrial design paten ting - R&D activit y that aims to increase the qualit y of an in termediate go o d - A j (t) can b e expressed as A j (t) =A 0 (1 +(h dj (t))), where A 0 is a rm’s qualit y at instan t tex industrial design inno v ation, and (h dj (t)) is the return function of industrial design inno v ation h dj (t). Hence,(h dj (t)) is an instan taneous demand shifter, as seen in the adv ertising literature (for example, Ca v enaile and Roldan-Blanco (2019)). Based on the empirical results in T able 2:3, I assume that industrial design inno v ation h dj has only an instan taneous impact on the qualit y of go o d j A j (t). That is, go o d j ’s qualit y is reset to A 0 b efore an y industrial design paten ting tak es place in the instan t t + t. I normalize the price of the nal go o d Y to b e one in eac h p erio d. 24 In termediate Go o ds Pro ducer. There is a set of rms with measure M that pro duce in terme- diate go o ds under monop olistic comp etition. Eac h in termediate go o ds j is exclusiv ely o wned and pro duced b y rm f with tec hnology: q j (t) = Zz 1 j ~ l j where Z = R 1 0 z j dj is the a v erage pro ductivit y in t prior to an y inno v ation. The pro duction function is linear in aggregate pro ductivit y Z and lab or input ~ l; but exhibits curv ature o v er curren t o wn pro ductivit y z j . This pro duction function features a p ositiv e spillo v er eect from pro ductivit y- enhancing inno v ation; rm j ’s inno v ation in t can increase b oth future aggregate Z , and an y rm’s future total pro ductivit y Zz 1 j . I explain this in detail b elo w. Eac h rm f can pro duce sev eral dieren t in termediate go o ds, j . Let n f b e the total n um b er of pro duct lines o wned b y rm f at an y instan t t. Let z f =fz j :j2n f g b e the pro ductivit y p ortfolio in rm f . Eac h in termediate go o ds pro ducer can b e c haracterized b y the state v ector: (n f ;z f ). 2.3.2 Inno v ation and Financial Constraint As I sho w b elo w, the prot earned b y a monop oly pro ducer f of go o d j increases with curren t pro ductivit yfz j g j2n f as w ell as the n um b er of pro duct lines it o wns. F or eac h pro duct line rm f pro duces, it earns monop oly ren ts un til it is b eing replaced b y another incum b en t or new en tran t. Th us, b oth an incum b en t and new en tran ts ha v e incen tiv es to impro v e their curren t tec hnology and add new pro duct lines. Before an y pro duction tak es place, an in termediate go o ds pro ducer can conduct three t yp es of inno v ation. Industrial Design. Incum b en t rms can paten t in industrial design to temp orarily impro v e the qualit y instan taneously of an y of its existing pro duct lines. Sp ecically , the curren t qualit y will 25 instan taneously increase from A 0 toA 0 (1 +(h dj )) for sure with an exp enditure of R dj unit of nal go o ds. R dj is dened, for a rm with n um b er of pro duct lines n, R dj =x d h d dj n d Z where x d > 0 is a scalar to facilitate calibration, h dj is the n um b er of industrial design paten ts for eac h pro duct line j . d > 1 is the cost elasticit y of R&D input and the term n d with d > 0 go v erns decreasing return to scale in rm size. The cost of industrial design is also linear in aggregate pro ductivit y Z , implying that when aggregate pro ductivit y is high, paten ting in industrial design b ecomes harder. This reects the fact, that I record in T able 2.1, that industrial design paten ting in tensit y , h dj , decreases with rm size. As a rm gro ws larger, a qualit y impro v emen t of a curren t pro duct line is more costly , for example b ecause of higher managerial or co ordination costs. The return function for rm f ’s paten ting in industrial design, (h dj ), is giv en as: (h dj ) = h dj Z z j , whic h is linear in aggregate pro ductivit y Z and decrease in o wn pro ductivit y z j . The linear eects of aggregate pro ductivit y on the cost and on the return of industrial design R&D cancel, lea ving the qualit y impro v emen t h dj dep ending solely on the n um b er of a rm’s pro duct lines. The assumption that this impro v emen t is only instan taneous captures the empirical evidence I ha v e presen ted that curren t industrial design has no signican t p ositiv e impact on a rm’s future sales gro wth. In ternal Inno v ation An incum b en t undertak es in ternal inno v ation to impro v e the future pro- ductivit y of its curren t pro duct lines. An exp enditure R Ij unit of nal go o ds b y a rm with n pro duct lines generates h Ij units of in ternal paten ts in eac h pro duct line j . The return on in ternal inno v ation is realized with P oisson o w h Ij . The exp enditure R Ij is dened as R Ij =x I h I Ij n I Z 26 where x I > 0 is a scalar to facilitate calibration, I > 1 is the cost elasticit y of in ternal R&D input, and I measures the degree of decreasing return in rm size. This is used to capture the fact recorded in T able 2.1 that in ternal inno v ation in tensit y decreases with rm size, ev en con trolling for nancial constrain ts. Successful in ternal inno v ation increases the qualit y of pro duct line j toz j (t + t) =z j (t) + Z . In con trast to Aghion, Harris, Ho witt, and Vic k ers (2001) and Ak cigit and Kerr (2008), for example, the increase in future pro ductivit y accomplished through in ternal inno v ation is indep enden t of a rm’s o wn curren t pro ductivit y in the pro duct line, z j , rather than an increase that is prop ortional to that curren t pro ductivit y . A similar sp ecication is used b y Ak cigit (2009). This simplies the mo del, and yields a clear prediction on nancial constrain ts’ impact on optimal R&D in v estmen t. External Inno v ation External inno v ation is conducted b y b oth incum b en ts and p oten tial new en tran ts, to obtain pro duct lines they do not curren tly o wn. I discuss the case of new en tran ts b elo w. An incum b en t with n > 0 pro duct lines, pro duces nh x external paten ts b y sp ending nR x units of nal go o ds. It can then tak e o v er the previous pro ducer’s pro duct line with a P oisson o w rate of nh x . R x is dened as: R x =x x h x x n x Z where x x > 0 is a scalar to facilitate calibration, and x > 1 is the cost elasticit y of external R&D input. Lik e in ternal inno v ation, external inno v ation is linear in aggregate pro ductivit y , Z , indicating that when aggregate pro ductivit y is higher, replacing another rm’s pro duct line b ecomes harder. In addition, x go v erns the degree of return to scale. If x = 0, w e ha v e the Klette and K ortum (2004) mo del, where external inno v ation p erfectly scales up with rm size. x > 0 w e ha v e the case studied b y Ak cigit and Kerr (2018), where a rm’s external inno v ation in tensit y decreases sharply with its size. This latter case is consisten t with the empirical ndings in T able 2.1. 27 As external R&D eorts are undirected, inno v ation can b e realized for an y pro duct line j in rm s with equal probabilit y . Let pro duct line j ’s pro ductivit y b e z j when o wned b y rm s. Up on a successful external inno v ation and tak en o v er b y the rm ~ s, the line is tak en o v er b y rm ~ s, and the pro ductivit y of that line is increased to z j + Z . Successful external inno v ation extends a rm’s curren t pro duct lines in to n f (t + t) = n f (t) + 1 and the he pro ductivit y p ortfolio in to z f (t + t) = z f (t)[fz j + Zg. Financial Constrain t. T otal R&D exp enditure for an incum b en t in termediate go o ds pro ducer with pro duct line n f isR nf = P n f j=1 R dj + P n f j=1 R Ij +n f R x units of nal go o ds. I discuss the case of new en tran ts b elo w. As rms undertak e R&D b efore pro duction o ccurs, eac h monop oly pro ducer has to collateral its curren t pro duct lines to generate cash o w. I assume the collateral constrain t is static, and the v alue of rm’s collateral has t w o comp onen ts: 1) The v alue of rm’s one-p erio d cash o w without paten ting n Z 10 and 2) the v alue of industrial design paten ting P n f j=1 H(h dj ), where H(h dj ) increases withh dj and is determined in equilibrium. The collateral v alue of industrial design comes from the assumption that its outcome is certain. Through a limited enforcemen t argumen t 11 , a rm’s total R&D exp enditure R nf is limited b y a m ultiplier, , times its collateral v alue: R nf (t) 2 4 n f X j=1 H(h Ij ) +n Z 3 5 (2.3) In (2.3), measures the degree of credit mark et imp erfection: =1 implies a p erfect credit mark et and = 1 implies that all R&D exp enditure needs to b e self-nanced b y eac h in termediate 10 Assume there is an information asymmetry b et w een the monop oly pro ducer and the lender. The lender cannot v erify and observ e rm’s a v erage pro ductivit y , z f . Once a rm’s manager steal 1 p ortion of b orro w ed income, the lender can tak e all of the rm’s collateral. is the lender’s ev aluation of rm’s pro duct lines. The lender has to design a con tract so that the least pro ductiv e rms do not ha v e the incen tiv e to engage in tunneling. Hence, it ev aluate rm’s one-p erio d cash o w based on the least pro ductiv e rms. See App endix A.2.2 for details. 11 see Banerjee and Newman (2003), Buera and Shin (2009) and Moll (2014) for similar motiv ation 28 go o ds pro ducer. H(h dj ) increases withh dj . P aten ting in industrial design not only increases a rm’s instan taneous prot, but also relaxes its nancial constrain ts b y raising its collateral v alue. 2.3.3 En try , Exit and Resource Constraint New en tran ts can in v est in external R&D to b ecome monop oly in termediate pro ducers up on success- ful inno v ation. Let the P oisson arriv al rate of a successful inno v ation b e h e and the corresp onding R&D cost b e R e =x e h 2 e Z . x e measures the en try cost. A new en tran t’s optimization problem is: rV 0 _ V 0 =max he h e E j V (fz j + Zg)V 0 R e where V 0 is a new en tran t’s the exp ected v alue of successful inno v ation and V (fz j + Zg) is the v alue of a rm of one pro duct line with pro ductivit y of z j + Z . Notice that en tran ts do not face nancial constrain ts when en ter the mark et. As m y analysis only fo cuses on the relationship b et w een nancial constrain ts and inno v ation comp osition among incum b en ts. Analyzing nancial constrain ts’ impact on en try is not a ma jor fo cus of this pap er. Through external inno v ation, incum b en ts and p oten tial new en tran ts expand in to new pro duct lines, and some incum b en ts lose curren t pro duct lines. Let b e the aggregate creativ e destruction rate faced b y eac h pro duct line. It is endogenously determined through incum b en ts and new en- tran t’s R&D decision on external inno v ation. A rm is assumed to exit the mark et if it loses all of its pro duct lines. The econom y is closed b y assuming that lab or mark et clears and resource constrain t holds. Lab or mark et clearing implies: L =L f (t) + Z 1 0 ~ l j d j 29 where L f (t) is lab or emplo y ed in the nal go o ds sector and ~ l j is lab or demand b y the pro ducer of in termediate go o ds j . The resource constrain t at time t is Y (t) =C(t) + 1 X n=1 M n R nf (t) +R e (t) Here, M is the total measure of rms, and n is the prop ortion of rms with n pro duct lines. The rm size distribution parameter n and M are endogenously determined. R nf (t) is the total R&D exp enditure of an in termediate go o ds pro ducer f with n > 0 pro duct lines. R e is the total R&D exp enditure b y new en tran ts. 2.3.4 Equilibrium and Balanced Growth Path In this section, I c haracterize agen ts’ optimization problems and corresp onding p olicy functions. Then I solv e for the mo del’s balanced gro wth path, on whic h the aggregate v ariables Y , w , Z , C , R f and R e gro w at the constan t rate g . Household The optimization problem of a represen tativ e household yields the Euler Equation: _ C C =r. On a balanced gro wth path where consumption gro ws at a constan t rate g , asset returns are endogenously determined as g =r. Pro ducers The nal go o ds pro ducer’s optimization problem generates a demand function for lab or: w = 1 L f;1 R 1 0 A j q 1 j dj ; , and an in v erse demand function for eac h v ariet y j as: q d j = p 1 j L f A j . The marginal cost for eac h in termediate go o ds pro ducer j is w Zz 1 j . 30 In termediate go o ds pro ducers comp ete in a monop olistic mark et. Giv en the in v erse demand function for in termediate go o d j , the prot maximization problem of eac h monop olist giv es the optimal quan tit y and price for that in termediate go o d j : p j = w (1) Zz 1 j ; q j = 0 @ w (1) Zz 1 j 1 A 1 L f A j (2.4) Eac h in termediate go o ds pro ducer c harges the monop olistic price p j whic h is a constan t markup 1 1 o v er its marginal prot. In addition, note that q j is linear in the demand shifter parameter A j =A 0 (1+(h dj )), whilep j decreases in the rm’s pro ductivit y z j as w ell as aggregate pro ductivit y Z . In ternal and external inno v ation increase the optimal quan tit y pro duced of pro duct line j , q j b y decreasing its optimal price p j . Industrial design has a direct impact on the optimal quan tit y q j through the demand shifter A j . Equilibrium w ages and output Equation (2.4) together with the nal go o d pro ducer’s optimal lab or demand pin do wn the equilibrium w age rate in the econom y . w = (1) 12 A[1 + ] Z (2.5) where A =A 0 and = P 1 n=1 M n nh dn is aggregate paten ting in industrial design, and h dn is the total n um b er of industrial design paten ts in a rm with n> 0 pro duct lines. Notably , is constan t on a balanced gro wth path (I sho w this b elo w). Higher aggregate industrial design increases the equilibrium w age through an increase in the nal go o d pro ducer’s output and lab or demand. F rom equation (2.4), the increase in the equilibrium w age raises the price if eac h in termediate go o d and reduces the optimal quan tit y q j . 31 Imp osing the lab or mark et clearing condition, L(t) =L f (t) + R 1 0 ~ l j d j lab or demand and output for the nal go o ds are: Y = (1) 12 (1) 2 + A L Z [1 + ] ; L = (1) 2 + L (2.6) Pro ducer’s Prot Giv en equilibrium w ages and lab or demand, in termediate go o d pro ducer f ’s prot is f = n f X j=1 p j q j = ^ (1 + ) 1 n f X j=1 (z j +h dj Z) where ^ = +1 (1) 22 (1) 2 + A L is a scalar and indep enden t of state v ariables z ,n f and Z . Firmf sales are sale f = f . Both sales rev en ue and prot are decreasing in aggregate industrial design, , and increasing in rm f ’s o wn pro ductivit y and in its industrial design paten ting h dj . As < 1 the term (1 + ) 1 captures a negativ e spillo v er eect from other rms ’ industrial design paten ting activities. As a result, rms ha v e an incen tiv e to paten t in industrial design to a v oid losing mark et share. Prot, f , is linear in h dj . ^ (1 + ) 1 P n f j=1 Z can th us b e view ed as the marginal b enet of paten ting one additional unit of industrial design. The collateral v alue of industrial design for rm f in equation (2.3) is equal to H(h dj ) = ^ (1 + ) 1 P n f j=1 h dj Z . The v alue of the rm’s industrial design paten ting decreases with aggregate industrial design activit y , , as higher reduces rms’ prot b y raising equilibrium w ages, and lo w ering demand from the nal go o d pro ducer. Giv en the collateral v alue of industrial design, the App endix A.2.2 sho ws that the collateral v alue of a rm’s pro duct lines equals a m ultiplier times a rm’s p er-p erio d prots without inno v ation. That is: = z min Z ^ (1 + ) 1 . 32 V alue F unction and R&D c hoices Researc h input is determined b y an in termediate go o d pro ducers optimization of its discoun ted future v alue. Let V (z;n) b e rm’s v alue with n pro duct lines and pro ductivit y p ortfolio z. Giv en the equilibrium v alue of , r and g , a rm c ho oses optimal R&D eort fh dj ;h Ij g j2n f and h x to maximize the v alue, r V (z;n) _ V (z;n) = max fh dj ;h Ij g j2n f ;hx n X j=1 h ^ (1 + ) 1 (z j +h dj Z)x d h d dj n d Z i + n X j=1 h h Ij V (znfz j g[ (z j + Z);n)V (z;n) x I h I Ij n I Z i +nh x E i V (z[ (z i + Z);n + 1)V (z;n) x x h x x n x+1 Z + n X j=1 [V (znfz j g;n 1)V (z;n)] s:t: x x h x x n x+1 Z + n X j=1 h x d h d dj n d Z +x I h I Ij n I Z i 2 4 n X j=1 h dj ^ (1 + ) 1 Z +n Z 3 5 (2.7) Here,r is the equilibrium in terest rate. In termediate go o ds pro ducers use the same discoun t rate as the household. In addition, is the equilibrium creativ e destruction rate, with o w , the rm loses one of its pro duct lines. The second term on the LHS implies c hanges in a rm’s v alue due to c hanges in aggregate conditions. The rst line on the RHS is the instan taneous prot conditional on curren t paten ting in industrial design. The second line is the c hange in rm v alue after in ternal inno v ation, net of in ternal R&D cost. The third line is the c hange in the rm’s v alue after adding a new pro duct line through external inno v ation net of the corresp onding R&D cost. The last line sho ws the c hange in rm v alue after losing one of its pro duct lines. Let the p olicy function of eac h inno v ation b eh dj ,h Ij andh x . Belo w, I sho w that those p olicy - paten ting - functions are indep enden t of the rm’s curren t pro ductivit y p ortfolio z, but dep ends on the n um b er of rm’s pro duct lines n. By this construction, the equilibrium aggregate industrial design = P 1 n=1 M n nh dn is constan t on a balanced gro wth path. 33 The R&D c hoice from new en tran ts can b e determined through the free en try condition. Nor- malize the v alue of the outside option as V 0 = 0. Giv en p ositiv e en try , b oth the free en try and the optimization condition for a new en tran t imply: E j V (fz j +s Zg) =x e h e Z (2.8) Firm Size Distribution On a balanced gro wth path, the rm size distribution should b e sta- tionary . The equilibrium in v arian t distribution can b e written (see App endix A.2.1 for deriv ation): n = h e M n1 Y i=1 h x (i) 1 n (2.9) where n 2 [0; 1]. n denotes the p ercen tage of rms that o wn n > 0 pro duct lines. As h x (i) is indep enden t of the pro ductivit y p ortfolio z, the rm size distribution is indep enden t of the pro ductivit y distribution. M is the equilibrium mass of rms, it is solv ed through the equation: P 1 n=1 n = 1. , the equilibrium creativ e destruction rate, is the sum of optimal external inno v ation h x and the realized en try rate h e : = P 1 n=1 M n nh x (n) +h e The gro wth rate of aggregate pro ductivit y is determined b y in ternal inno v ation eort as w ell as the aggregate creativ e destruction rate . Prop osition I describ es it. Prop osition I: Aggregate Gro wth Rate Let the rm size distribution b e n and the equilib- rium measure of rms b e M . Then the balanced gro wth rate of aggregate pro ductivit y is g =h e + 1 X n=1 M n nh x (n) + 1 X n=1 M n nh I (n) (2.10) On a balanced gro wth path, the aggregate v ariable Y ,w ,C , and total R&D exp enditure R also gro w at the aggregate gro wth rate g . 34 Pr o of. See App endix A.2.3 In (2.10), h x (n) and h I (n) are the optimal c hoice of external and in ternal inno v ation for rms withn> 0 pro duct lines. is the step size, i.e. pro ductivit y impro v emen t p er unit of inno v ation for external inno v ation, and is the step size for in ternal inno v ation. The aggregate gro wth rate dep ends on rm size distributions, as b oth h x (n) andh I (n) dep end on rm size. The aggregate gro wth rate can b e decomp osed in to three parts: The con tribution from new en tran ts, the con tribution from incum b en ts’ in ternal inno v ation and the con tribution from incum b en ts’ external inno v ation. If total inno v ation eort - nh x and nh I - increases with rm size, large rms con tribute more to this aggregate gro wth rate. Giv en the aggregate gro wth rate g , I normalize (de-trend) a rm’s v alue V and pro ductivit y as ^ V = V Z and ^ z =f z j Z :j2ng. The v alue function in equation (2.7) can then b e rewritten in terms of the new state v ariable ^ z and _ V (z;n) =g ^ V (^ z;n) +g P n j=1 @ ^ V (^ z;n) @^ z ^ z j . The follo wing assumptions guaran tee the existence of the v alue function and the rm’s v alue satisfying the transv ersalit y condition: lim t!1 h e R t 0 rsds ^ V (z;n) i = 0 Assumption I P arameter v alues satisfy d 1 d 0, I 1 I 0 and x 1 x 0. Under assumption I, the follo wing prop osition holds; the v alue function can b e expressed in a tractable form, and is b ounded ab o v e, and w ell b eha v ed. Prop osition I I Let assumption 1 hold, and let the en try rate b e p ositiv e, h e > 0. Then i) an in termediate pro ducer’s v alue function can b e written as: ^ V (^ z;n) = B n X i=1 ^ z i +B n 35 where B = ^ ++g (1 + ) 1 and B n is a function of n, and the solution to the problem B n = max h d ;h I ;hx n^ (1 + ) 1 h d +nBh I +nh x [ B(1 +) +B n+1 B n ]x d h d d n d +1 x I h I I n I +1 x x h x x n x+1 +n(B n1 B n ) s:t: x d h d d n d +1 +x I h I I n I +1 +x x h x x n x+1 n^ (1 + ) 1 h d +n ii) B n is an increasing function of n and b ounded ab o v e. iii) B n+1 B n decreases in n. Pr o of. See App endix A.2.4 B is the a v erage de-trended v alue of pro duct line j . It is the discoun ted sum of future prots from the line, in the absence of inno v ation. B decreases with aggregate paten ting in industrial design (). The higher the elasticit y of substitution b et w een dieren tiated in termediate go o ds ( ), the more negativ e the impact from other rms’ industrial design paten ts on a rm’s curren t prot. Recall that a rm’s collateral v alue in equation (3) dep ends on the prot margin generated b y industrial design as w ell as p er-p erio d prot o w ^ (1+) 1 . Th us, a higher not only negativ ely aect a rm’s instan taneous prot f , but also tigh tens its nancial constrain ts b y lo w ering the collateral v alue of its pro duct lines. B n denotes a rm’s v alue in conducting inno v ation activities. The ab o v e prop osition states that there’s a decreasing returns to scale in a rm’s v alue function. The marginal b enet of expanding pro duct lines in large rms is smaller than that in small rms. 36 Let ' n 0 b e the Lagrange m ultiplier on nancial constrain t for a rm with n pro duct lines. The optimal R&D in tensit y for eac h pro duct line can b e expressed as h d = ^ (1 + ) 1 x d d 1 +' n 1 +' n 1 d 1 n ~ d h I = B x I I 1 1 +' n 1 I 1 n ~ I h x = B(1 +) +B n+1 B n x x x 1 1 +' n 1 x1 n ~ x (2.11) where ~ d = d d 1 < 0, ~ I = I I 1 < 0 and ~ x = x x1 < 0. The m ultiplier ' n is then dened through the nancial constrain t, +^ (1 + ) 1 h d =x d h d d n d +x I h I I n I +x x h x x n x (2.12) A rm that faces a more sev ere nancial constrain t has a higher v alue of ' n . I therefore use ' n to measure rm-sp ecic nancial friction. F or unconstrained rms, ' n = 0. The optimal R&D c hoices all decrease in n. The return to scale parameters d , I and x pla ys a crucial role at shaping the negativ e relationship b et w een rm size and R&D in tensities. No w consider the case where the s are all equal to zero. Then ' n is indep enden t of n. Giv en the v alue of , either all rms are nancially constrained or all rms are nancially unconstrained. The mo del is then equiv alen t to that studied b y Klette and K ortum (2004), where B n = ~ Bn for ~ B > 0. That is, the b enet of acquiring one additional pro duct line is constan t across rm size. Th us, h d ,h I andh n are constan t across rms. R&D exp enditure on all t yp es of inno v ation p erfectly scale with rm size. Giv en the optimal R&D c hoices, it is easy to v erify that the aggregate R&D exp enditure R P 1 n=1 M n R n +R e is linear in aggregate pro ductivit y , Z . Equations (2.5) and (2.6) sho w that the equilibrium w age and aggregate output are linear in Z . Th us, from the resource constrain t, consumption C is also linear in Z . The aggregate v ariables Y ,C ,w and R all therefore gro w at the 37 same rate as Z : g = _ C C = _ Y Y = _ R R = _ w w = _ Z Z , where, g is dened in prop osition I. Aggregate h d ,h I andh n , on the other hand, are constan t on a balanced gro wth path. Hence, = P 1 n=1 M n nh d (n) is also constan t on a balanced gro wth path. Another requiremen t for a balanced gro wth path equilibrium is p ositiv e en try . That is the en try cost x e < B +B 1 . This condition implies that the cost of en try should less than the gain from acquiring the rst pro duct line. As the mo del do es not ha v e an analytical solution for B 1 , I ex-p ost c hec k the condition x e < B +B 1 in m y computational analysis. I no w dene a balanced gro wth path equilibrium. Denition 1 (Balanced Gro wth P ath Equilibrium) A Balanced Gro wth Equilibrium P ath is fp j (t);q j (t);l j (t);h dj (t);h Ij (t);h x (t);h e (t);L f (t);Y (t);C (t);w (t); (t);r ;g ; n ;M g suc h that: 1) Giv en the w age,Y (t) andL (t) solv e the nal go o ds pro ducer’s problem and Y (t) and L (t) satisfy equation (2.6); 2)l j (t),q j (t) andp j (t) solv e the in termediate go o ds pro ducer’s problem and q j (t) and p j (t) satisfy equation (2.4); 3) optimal R&D in tensities h dj , h Ij and h x in equation (2.11) solv es the v alue function in equation (2.7); 4) h e satises the free en try condition of equation (2.8); 5) the in v arian t distribution of rm size and the equilibrium mass of rms satisfy equation (2.9); 6) the balanced gro wth rate satises (2.10); 7) the equilibrium in terest rate satises: g = r ; 8) the aggregate industrial design, , satises = P 1 n=1 M n nh d (n); 9) the equilibrium w age w in equation (2.5) clears the lab or mark et; and 10) resource constrain t holds. 38 2.3.5 Analytical Results The follo wing prop ositions la y out the main analytical results and sho w that the mo del is quali- tativ ely consisten t with the facts that I do cumen t in Section 2: 1) Firms shift from pro ductivit y- enhancing to industrial design when nancial constrain ts tigh ten; 2) small rms are more lik ely to b e nancially constrained, and 3) nancial constrain ts lo w ers a rm’s gro wth rate. Prop osition I I I (Firm Size and Financial F rictions) Large rms face a lo w er rm-sp ecic nancial friction ' n . That is, ' n decreases with rm size n. Pr o of. T ak e deriv ativ es with resp ect to n on eac h side of a rm’s nancial constrain t (2.12) and rearranging: d' n dn = 1 n ~ I R I (1 +' n ) + ~ x R x (1 +' n ) + ~ d d R d 1+'n 1+'n h ( 1 d ) +' n (1 1 d ) i R I I I 1 +R x x x1 + 1 (1+'n) 2 R d d d 1 < 0 The n umerator is negativ e as 1> 1 d and ~ d < 0, ~ I < 0 and ~ x < 0. As ' n decreases with n and is b ounded b elo w b y 0, large rms are more lik ely to b e nancially unconstrained. The decreasing return to scale parameters d , I and x are imp ortan t in shaping the relationship b et w een ' n and n. If R&D cost scales p erfectly with rm size (i.e. in the case of d = I = x = 0), ' n is indep enden t of n. If one of these s is greater than zero, total R&D in tensit y decreases with rm size. Th us, a rm with relativ ely larger size undertak es less in v estmen t p er pro duct line, relies less on external nance, and is less lik ely to b e nancially constrained. Prop osition IV (Financial constrain t and inno v ation in tensit y) Let h d , h I and h x b e a rm’s optimal inno v ation in tensities. F or nancially constrained rms: 1) An increase in credit 39 mark et imp erfectness, a reduction in , reduces pro ductivit y-enhancing inno v ation; 2) if the elas- ticit y of ' n satises d'n d 'n < 1 (1 +' n ), a reduction in increases industrial design paten ting. Otherwise, inno v ation in tensit y in all categories increases with . Pr o of. Once rm is nancially constrained ( ' n > 0), ' n is determined through a rm’s collateral constrain t. T ak e deriv ativ es with resp ect to on eac h side of the equation (2.12) and rearrange it: d' n d = (1 +' n ) d R d 1+'n 1+'n d d 1 R d 1 1+'n 1 1+'n R I I I 1 +R x x x1 + 1 (1+'n) 2 R d d d 1 < 0 The left hand side of this expression is negativ e if 1. A higher implies lo w er nancial constrain t. Hence, as ' n decreases with ,' n is p ositiv ely related to the degree of a rm’s nancial constrain t. Then, for eac h inno v ation in tensit y measure, dh x d =h x 1 1 +' n 1 1 x d' n d > 0 dh I d =h I 1 1 +' n 1 1 I d' n d > 0 dh d d =h d 1 1 +' n 1 d 1 1 1 +' n d' n d +' n < 0 if d' n d ' n < 1 (1 +' n ) This prop osition sho ws that pro ductivit y-enhancing inno v ation in tensit y is negativ ely related to the degree of a rm’s nancial constrain t. A higher credit mark et constrain t (a lo w er ) increases a rm’s marginal cost of inno v ating. Th us, it reduces rm’s incen tiv e to conduct b oth in ternal and external inno v ation. Ho w ev er, it is am biguous ho w aects a rm’s industrial design paten ting. First, for the self-nanced rm ( = 1), industrial design is indep enden t of credit mark et imp erfec- tion. When is close to 1, dh d d 'n 1+'n h d d 1 > 0. Th us, relaxing a nancial constrain t from = 1 w ould increase paten ting in industrial design. Second, in the case of > 1, whether h d increases 40 or decreases with dep ends on the elasticit y of ' n with resp ect to . A reduction in increases a rm’s marginal cost as w ell as the marginal b enet of paten ting industrial designs. When ' n is more elastic, a unit decrease in w ould cause more than a unit c hange in ' n . Th us, a rm has an incen tiv e to undertak e industrial design. In App endix A.2.5 I sho w that a sucien t condition for d'n d 'n < 1 (1+' n ) under a quadratic cost function (i.e. d = I = x = 2) is that' n 1 2 1 . As sho wn in prop osition I I I, ' n decreases with n. Th us, a relativ ely large constrained rm reduce paten ting in industrial design b y more when its nancial constrain t is relaxed. Ho w ev er, for small constrained rms with high v alue of ' n , industrial paten ting increase with . This result also implies that c hanges in shift a rm’s inno v ation comp osition. If the elasticit y of' n is large enough, a reduction in forces a rm to shift from pro ductivit y-enhancing inno v ation in to industrial design paten ting. T o see this, consider the case where all R&D cost functions are quadratic in inno v ation in tensit y (i.e. d = I = x = 2). Then the industrial-design/in ternal inno v ation ratio and industrial-design/external inno v ation ratio are: h d h I / 1+' n and h d h x / 1+' n . If d'n d 'n <1, b oth ratios decrease with . The follo wing corollary summarize this result. Corollary I (Financial constrain t and inno v ation comp osition) If d = I = x and if the elasticit y of ' n satises: d'n d 'n <1, a rm shift out of its pro ductivit y-enhancing inno v ation in to industrial design paten ting if its nancial constrain t tigh tens. Notice that as 1 (1 +' n ) > 1, once dh d d < 0 is satised, it m ust b e true that h d h I and h d h x decrease with . Under quadratic inno v ation costs, d'n d 'n < 1 (1 +' n ) is not necessary to guaran tee suc h shift in inno v ation comp osition. Ev en if all t yp es of inno v ation in tensit y decrease with a reduction in , inno v ation comp osition can shift in fa v or of industrial design as long as the decrease in industrial design is less than the decrease in in ternal and external inno v ation. In App endix A.2.5, I sho w that one sucien t condition for d'n d 'n <1 is ' n 1. As ' n decreases with n, constrained rms with relativ ely large size w ould b e most lik ely to meet this condition. 41 Th us, constrained large rms w ould shift their pro ductivit y-enhancing inno v ation in to industrial design if their nancial constrain ts tigh ten. The rm’s gro wth rate dep ends on its pro ductivit y-enhancing inno v ations. If a rm shifts its inno v ation comp osition in fa v or of industrial design when its nancial constrain t tigh tens, its gro wth rate will decline. Let z f = P n f j=1 z j b e the total pro ductivit y of a rm with n f pro duct lines, the follo wing prop osition states the relationship b et w een nancial constrain ts and the rm pro ductivit y gro wth rate, g f = _ z f z f . Prop osition V Financial constrain ts lo w ers rm’s pro ductivit y gro wth rate, g f , and mitigates the negativ e relationship b et w een rm size and rm gro wth. Pr o of. Giv en a rm’s optimal R&D decision, its pro ductivit y g rate can b e written as: g f = _ z f z f = lim !0 z f (t + t)z f z f = 1 z f [h I + (1 +)h x ] where z f = z f n f is the a v erage pro ductivit y of rm f . And w e ha v e: dg f d = 1 z f h x 1 1 x +h I 1 1 I 1 1 +' n d' n d > 0 dg f dn f = 1 z f h I ~ I n f + (1 +)h x ~ x n f 1 z f d' n dn f 1 1 +' n h I I 1 + (1 +)h x x 1 The rst term on the righ t hand side of dg f dn f is negativ e due to the decreasing returns to scale in in ternal and external inno v ation. It go v erns the relationship b et w een rm size and rm gro wth when a rm is nancially unconstrained. The last term on the righ t hand side of dg f dn f is p ositiv e, since d'n dn > 0. Th us, the existence of nancial constrain ts mitigates an otherwise negativ e relationship b et w een rm size and rm gro wth. 42 This prop osition implies that nancial constrain ts lo w er a rm’s gro wth rate through a reduction in in v estmen t in in ternal and external inno v ation. It also implies that when rms are all nancially constrained, a large rm migh t not necessarily ha v e lo w er gro wth rate ev en though pro ductivit y- enhancing inno v ation in tensit y decrease with rm size. If ' n is elastic enough, the cost of in ternal and external inno v ation w ould drop rapidly as rms gro ws larger. Th us, large rms in v est more in pro ductivit y-enhancing inno v ation to increase their gro wth rate. The term d'n dn f 1 1+'n captures the eect of cost reduction. If and is large enough, ev en though in ternal and external in tensit y decreases with rm size, a p ositiv e relationship b et w een rm size and rm gro wth can still hold. This is captured b y the term h I I 1 + (1+)h x x1 . As h I ~ I n f + (1 +)h x ~ x n f captures the eect from decreasing returns to scale, if it oset the eect of cost reduction, a rm’s gro wth rate is then indep enden t of rm size. This result is also found b y Klette and K ortum (2004) and consisten t with Gibrat’s la w. If the eect from decreasing returns to scale out w eighs the eect of cost reduction, a rm’s gro wth rate is negativ ely related to its rm size. Ho w ev er, if the eect from cost reduction out w eighs the eect from decreasing return to scale, large rms could gro w faster than small rms. 2.4 Quantative Analysis In this section, I calibrate the mo del using the data discussed in section 2. Sp ecically , I rst solv e the mo del on a balanced gro wth path using the uniformization metho d describ ed in A cemoglu and Ak cigit (2010) 12 . Then I matc h empirical momen ts and regression co ecien ts with mo del-implied momen ts and regression slop es from the sim ulating the solv ed mo del. 12 see App endix A.3 for detail 43 2.4.1 Calibration Strategy The mo del has 17 parameters to b e iden tied: f L;A;;; d ; I ; x ;;x d ;x I ;x x ;x e ; d ; I ; x ;;g. Some of them are calibrated externally to matc h aggregate momen ts in the data or from the extan t literature. The remaining are calibrated b y targeting relev an t momen ts for rms in the sample. 2.4.1.1 Externally Calibrated P arameters The parameter is the discoun t rate. I set equals 0:04 to matc h the ann ual discoun t factor of 0:96 in China. The parameter measures the qualit y share in nal go o ds pro duction. The theoretical mo del implies that can b e expressed as = f sale f . I set = 0:182 to matc h the a v erage prot to sales ratio in all priv ate rms in the sample of section 2. The parameters d , I and x measure the curv ature of industrial design, in ternal, external inno v ation resp ectiv ely . I tak e these v alues from Ak cigit and Kerr (2018), setting them equal to d = I = x = 2. This implies that the elasticit y of paten ting with resp ect to R&D exp enditure is around 0.5, whic h is supp orted b y man y empirical pap ers (Blundell, Grith, and Windmeijer (2002) and A cemoglu, Ak cigit, Alp, Blo om and Kerr (2019) for examples). L are normalized to 1. Using m y theoretical results, the meam sales for in termediate pro ducer without paten ting in industrial design is +1 (1) 22 (1) 2 + A L, , whic h is linear inA. Th us, I c ho ose the lev el A = 1 to roughly matc h with the mean of real sales for rms without industrial design paten ting the sample. 44 2.4.1.2 Indirect Inference The remaining 10 parameters =f;x d ;x I ;x x ;x e ; d ; I ; x ;;g are calibrated via indirect in- ference approac h. is estimated b y minimizing the follo wing v alue using sev eral mo del-implied momen ts from sim ulation, and data-generated momen ts: ^ =argmin 10 X k=1 kmodel() k data k k 1 2 kmodel() k k + 1 2 kdata k k With a guess of , the mo del is solv ed using uniformization metho d (see App endix A.3 for the solution algorithm). The v alue of momen t k2f1; ; 10g is computed b y sim ulating the mo del. data k is the corresp onding momen t k from data. ^ is estimated b y minimizing the ab o v e criteria. The mo del is sim ulated using 8; 192 rms and discretizes time to T = 150 p erio ds with time in terv al t = 0:02. Since the mo del do es not ha v e a closed-form solution, I cannot express mo del-sim ulated momen ts in analytical form. Belo w I pro vide some in tuition for m y c hoice of momen ts. En try cost Consider the case where inno v ation in tensit y is indep enden t of rm size. F rom equa- tion (2.9), it is easy to v erify that @hx @ < 0, and @he @ > 0. As the creativ e destruction rate decreases with en try cost x e , the en try rate h e also decreases with the en try cost. Higher en try rate implies a lo w er en try cost. The en try rate can then b e used to iden tify en try cost. En try rate h e = 0:113 is computed follo wing Song and Hsieh (2015), dened as "the n um b er of new priv ate rms created in a y ear relativ e to the n um b er of all priv ate rms in that y ear". The implied en try cost is then x e = 4:84 in the sample. Return to scale Consider the case without nancial constrain ts, where ' n = 0. F rom the rm’s optimal c hoice (2.11), the return to scale parameters d , I and x , go v ern the relationship b et w een optimal R&D in tensit y and rm size. A higher v alue of an generates a more negativ e relationship 45 T able 2.4: P arameters P arameter Description V alue Iden tication/Source P anel A: External Calibrated discoun t Rate 0.04 ann ual discoun t factor substitution elasticit y 0.182 prot to sales ratio A aggregate demand shifter 1 L total lab or supply 1 d curv ature of industrial design 2 quadratic cost function l curv ature of in ternal inno v ation 2 Ak cigit and Kerr (2018) x curv ature of external inno v ation 2 Ak cigit and Kerr (2018) P anel B: Indirect Inference x d scale of industrial design 0.276 9 = ; R&D In tensit y and P aten t Shares x I scale of in ternal inno v ation 0.107 x x scale of external inno v ation 4.971 x e en try cost 4.840 en try rate d return to scale in industrial design 0.200 9 = ; in tensit y-size regression co e. I return to scale in in ternal inno v ation 0.412 x return to scale in external inno v ation 0.537 pro ductivit y m ultiplier of in ternal inno v ation 0.105 citation ratio and gro wth rate pro ductivit y m ultiplier of external inno v ation 0.133 credit mark et imp erfectness 1.162 gro wth-size regression b et w een optimal R&D in tensit y and rm size. If d = I = x = 0, inno v ation in tensit y h d , h I and h x are indep enden t of rm size. Hence, the s can b e iden tied b y matc hing the in tensit y- size regression co ecien ts using date generated from the sim ulated mo del to the same in tensit y- regression co ecien t using empirical date in section 2. The v alue of the regression co ecien ts can b e found in T able A.6 in the App endix. My estimation on s nds decreasing returns to scale in all t yp es of inno v ations. Sp ecically , d = 0:200, I = 0:412 and x = 0:537. Firm size has the greatest negativ e impact on external inno v ation and the least negativ e impact on industrial design. External and in ternal inno v ation drops rapidly when a rm gro ws larger, making industrial design share increases. This is opp osite to the ndings of Ak cigit and Kerr (2018) and others; there, pro cess inno v ation is tigh tly link ed to rm size (Cohen and Klepp er (1996)). 46 Pro ductivit y m ultiplier Equation (2.10) sho ws that, giv en optimal R&D in v estmen t, the equi- librium gro wth rateg increases with the pro ductivit y m ultipliers, and . If higher citations imply a larger pro ductivit y impro v emen t, the citation ratio of in ternal v ersus external paten ts in the data can b e used to discipline the relationship b et w een the parameters and . Th us, I calibrate the relativ e v alue using the a v erage in ternal v ersus external citation ratio in m y data. During the sample p erio d, I nd = 0:789 for all priv ate rms. The theoretical result implies that g = +, where = P 1 n=1 M n nh I (n) is the aggregate in ternal inno v ation. Th us, giv en the citation ratio, = 0:789, the absolute v alue of and can iden tied b y matc hing the mo del implied aggregate gro wth rate g to the a v erage ann ual gro wth rate in the data sample. On a balanced gro wth path, the equilibrium gro wth rate g equals the gro wth rate of aggregate total factor pro ductivit y . T o measure this, I rst compute eac h rm’s total factor pro ductivit y , and follo wing Da vid and V enk atesw aran (2019) to remo v e the impact of lab or distorion issues in the Chinese man ufacturing data. I them compute ann ual aggregate TFP gro wth follo wing F oster, Haltiw anger, and Krizan (2001)’s aggregation metho d 13 . Lastly , I compute the equilibrium aggregate gro wth rate g as the geometric mean of ann ual aggregate TFP pro ductivit y gro wth during the sample y ears. The computed aggregate gro wth rate for all priv ate inno v ativ e rms is 3.48p ercen t. This is closer to Zh u (2012)’s computation of 3.7 p ercen t for non-state rms. Scale of inno v ation The scale parameters, x d , x I and x x go v ern the share of industrial design, in ternal and external inno v ation as w ell as R&D in tensit y . F rom a rm’s nancial constrain t (2.12) 13 As the mo del do es not ha v e capital accum ulation, in order to remo v e the eect from capital deep ening on the output gro wth rate (Chang, Chen, W aggoner and Zha (2016) nd that capital deep ening con tributes 73.9% gro wth in GDP p er capita in China from 1998 to 2011), I use TFP instead of lab or pro ductivit y to estimate pro ductivit y gro wth during the sample p erio d. Pro ductivit y is calculated as ln(zit) = vait kit with = 0:62. va is the log of real v alue added and k is the log of real capital sto c k after remo ving all y ear and industry xed eect. I The aggregate TFP ln( Z) is then computed as v alue-added w eigh ted sum of individual pro ductivities: ln( Zt) = P i Q it ln(zit). Then the gro wth rate of aggregate pro ductivit y is adjusted for rm’s en try and exit: ln( Zt) = P i2survivor h Q it ln(zit) Q it1 ln(zit1) i + P e2entrant Q et ln(zet) ln( Zt1) P e2exit Q xt1 ln(zet1) ln( Zt1) where Q it is the share of real v alue added in gross v alue added. 47 and optimal R&D c hoice (2.11), an increase in x d w ould lo w er a rm’s in v estmen t share in industrial design, regardless of whether a rm is constrained or not. Similarly , an increase in x I (orx x ) lo w ers the in ternal inno v ation share (or external share) in total inno v ation. Th us, I use industrial design and in ternal inno v ation shares, and measured R&D in tensities to x the scale of eac h t yp e of R&D exp enditure. The a v erage R&D in tensit y in m y sample is 2.9% for all inno v ativ e priv ate rms. The industrial design and in ternal inno v ation share are 38:3 p ercen t and 35:7 p ercen t for all inno v ativ e priv ate rms. The estimated scale parameters are then: x d = 0:276, x I = 0:107 and x x = 4:971. Financial constrain ts F or nancially constrained rms, aects the a v ailable cash o w for a rm to in v est. A higher indicates less nancial friction (lo w er ' n ) and encourages in v estmen t in in ternal and external inno v ation. Hence, alters the relationship b et w een rm gro wth and rm size as discussed in Prop osition V. A higher nancial friction mitigates the negativ e relationship b et w een rm gro wth and rm size. Th us the co ecien t on rm size from the gro wth-size regression is highly sensitiv e in . can hen b e iden tied b y matc hing the gro wth-size regression co ecien t using date generated from the sim ulated mo del to the same gro wth-size co ecien t using empirical date in section 2. The v alue of the empirical regression co ecien t can b e found in T able A.6 in the App endix A.4. The estimated is = 1:162. 2.4.2 Result T able 2.4 lists a full set of calibrated parameter v alues. T able 2.5 sho ws the v alue of sim ulated momen ts, compared to the v alues generated in the data. Ov erall, the mo del closely matc hes the targeted momen ts except for the R&D in tensit y and en try rates. The R&D to sales ratio is higher in the mo del than in the data. As R&D exp enditure is a v ailable only in the y ear 2005 to 2007 and the y ear 2010, the a v erage R&D to sales ratio in the sample migh t underestimate a rm’s true R&D in tensit y . The en try rate is also sligh tly lo w er in the mo del than in the data. The ASM data only 48 con tains medium to large scale rms. So the estimated en try rate are calculated based on medium to large scale rms, whic h mak es the denominator smaller and o v erestimate the en try rate. T able 2.5: Momen ts Momen ts Data Mo del R&D in tensit y 2.9% 4.2% Share of in ternal paten ts 0.357 0.359 Share of industrial design paten ts 0.383 0.369 A v erage gro wth rate 3.48% 3.48% En try rate 0.113 0.102 In ternal to external citation ratio 0.789 0.789 industrial design paten t in tensit y vs. size -0.109 -0.118 In ternal paten t in tensit y vs. size -0.111 -0.111 External paten t in tensit y vs. size -0.035 -0.035 Sales gro wth vs. size -0.077 -0.072 The mo del also pro duces a similar rm size distribution (measured using real sales) as the empirical one. Figure A.1 compares the t w o distributions. The left panel is the estimated rm size distribution sim ulated from mo del and the righ t panel is the actual rm’s size distribution measured in real sales (millions of RMB) in the sample (from 2003 to 2009). Firm size is hea vily righ t-sk ew ed. The sim ulated distribution is sligh tly more widely spread than the empirical distribution. The lo w er left panel of gure A.1 sho ws that rm v alue B n increases with the n um b er of pro duct lines a rm o wns, but at a decreasing rate. B n also reects a rm’s v alue in conducting inno v ation. This result therefore implies that the gain of inno v ation b ecomes smaller as a rm gro ws larger. ' n decreases with the n um b er of pro duct lines. Consisten t with prop osition I I I, small rms faces more sev ere nancial constrain ts. In more sim ulated mo del ' n b ecomes zero once a rm o wns more than 4 pro duct lines. This is the mo del-implied threshold for a rm b eing nancially unconstrained. Once a rm is nancially constrained, the share of paten ting in industrial design decreases with rm size. As stated in section 3, nancially constrained rms rely on paten ting in industrial design to generate instan taneous prot and relax their nancial constrain ts. Th us, the more sev ere nancial constrain t a rm faces, the more paten ting in industrial design it will conduct. As seen ab o v e, the return of 49 Figure 2.1: Firm Size Distribution and Firm V alue 0 .1 .2 .3 Fraction 0 2 4 6 8 10 Firm Size Distribution (in 10 Million real RMB) Note: Upp er left panel is the estimated rm size distribution from the mo del the upp er righ t panel is the actual rm size distribution in m y data. The lo w er left panel is the relationship b et w een rm size, rm v alue and rm-lev el nancial distortion 'n from sim ulated mo del and the lo w er righ t panel is the relationship b et w een rm size and paten t share in industrial design from sim ulated mo del in v estmen t in industrial design suers less from decreasing return to scale ( d is smaller than x and I ), so the share of paten ting in industrial design increases with rm size once rm b ecome nancially unconstrained. In m y sim ulation, only 0.5 p ercen t of rms o wn more than 4 pro duct lines. That is, most of the rms in the sim ulated sample are nancially constrained. Hence, the negativ e relationship b et w een rm size and the share of industrial design dominates. Gro wth Rate Decomp osition I use the estimated parameters to decomp ose the aggregate gro wth rate in to three parts: 1) gro wth from new en tran ts, 2) gro wth from incum b en ts’ in ternal 50 inno v ation and 3) gro wth from incum b en ts’ external inno v ation. Column (2) in T able 2.6 presen ts the result. In the calibrated mo del, the aggregate gro wth rate is 3.48 p ercen t ann ually . Of this, 18.4 p ercen t deriv es from external inno v ation conducted b y the incum b en ts, 51.9 p ercen t deriv es from in ternal inno v ation conducted b y the incum b en ts, and the remaining 30.7 p ercen t is con tributed b y new en tran ts. The pro ductivit y m ultiplier of in ternal inno v ation is smaller than external inno v ation. The estimated pro ductivit y m ultiplier for in ternal inno v ation is = 0:105; whereas estimated pro ductivit y m ultiplier for external inno v ation is = 0:133. Th us, on a v erage, external paten ts ha v e ab out 26.7 p ercen t higher impact for pro ductivit y than in ternal inno v ation. This is consisten t with the nding in T able 2.3 that in ternal inno v ation empirically con tributes less to rms’ gro wth than external inno v ation. Ho w ev er, the estimation of cost scalar parameters xs sho ws the R&D cost parameter for external inno v ation is ab out 46.5 times larger than for in ternal inno v ation. Conducting in ternal inno v ation costs m uc h less than external inno v ation. Th us, the con tribution to aggregate gro wth rate from in ternal inno v ation is mainly through the extensiv e margin. F urthermore, Column (2) of P anel C in T able 2.6 sho ws that among incum b en t rms, on a v er- age, share of in ternal paten t application is ab out 32 p ercen t higher than share of external paten t application. As the cost of external inno v ation is lo w er for new en tran t than for incum b en ts, the en try rate in the econom y is high. New en tran ts conduct more external inno v ations and con tribute more to the aggregate gro wth rate than incum b en ts’ external inno v ation. Column (2) of P anel C in T able 2.6 do cumen ts that most of the creativ e destruction rate comes from new en tran ts’ exter- nal inno v ation rather than incum b en ts’ external inno v ation. This is consisten t with the empirical ndings from Brandt, Biesebro ec k and Zhang (2012), where they nd that pro ductivit y gro wth is relativ ely higher among new en tran ts than incum b en ts. 51 T able 2.6: Gro wth and R&D Decomp osition (Changes in Financial Constrain ts) Self-Financed Baseline Increase 10% Increase 25% Unconstrained ( = 1) ( = 1:16) ( = 1:28) ( = 1:45) (!1) (1) (2) (3) (4) (5) P anel A: Gro wth Decomp osition Aggregate Gro wth Rate 0.0325 0.0348 0.0362 0.0377 0.0388 fr om incu. Ext. innov. 17.7% 18.4% 18.7% 19.1% 19.4% fr om incu. Int. innov. 48.7% 51.0% 52.2% 53.4% 54.3% fr om new entr ant 33.6% 30.7% 29.0% 27.5% 26.4% P anel B: Firm Distribution Decomp osition Threshold n 7 4 3 2 0 Creativ e destruction rate 0.126 0.129 0.130 0.132 0.134 fr om incumb ent 34.5% 37.5% 39.2% 41.0% 42.4% fr om new entr ant 65.5% 62.5% 60.8% 59.0% 57.6% Firm Measure M 0.809 0.791 0.780 0.770 0.763 En try Rate 0.102 0.102 0.102 0.101 0.101 P anel C: R&D in tensit y and Inno v ation Decomp osition R&D In tensit y (exclude design) 0.031 0.035 0.038 0.041 0.047 a v e. industrial design% 38.1% 36.9% 35.9% 34.7% 33.4% a v e. in ternal% 33.8% 35.9% 37.2% 38.7% 40.0% a v e. external% 28.1% 27.2% 26.9% 26.6% 26.6% 2.5 Counterfactual Analysis In this section, I rst quan tify the implications of nancial constrain ts and industrial design paten t on rm R&D c hoices and the aggregate gro wth rate. T o do so, I p erform t w o coun terfactual analyses: 1) I consider the impact of alternativ e v alues of credit mark et friction ; 2) I compute the eects of banning industrial design paten ting. T able 2.6 do cumen ts the results. Second, I ev aluate the R&D tax-incen tiv e p olicy curren tly implemen ted in China. 2.5.1 The role of nancial constraint An increase in the credit mark et friction tigh tens a rm’s nancial constrain t and it paten t more in industrial design. P anel C of T able 2.6 do cumen ts the quan titativ e c hanges. A 10 p ercen t increase in (decrease in credit mark et friction) results in a 1 p ercen t decrease in the share of paten t application in industrial design. If the nancial constrain t is remo v ed ( !1), on a v erage, a rm’s paten t applications in industrial design fall b y 9.49 p ercen t. A t the same time, paten t applications 52 in b oth in ternal and external inno v ation increase with . Column (3) in T able 2.6 sho ws that a 10 p ercen t increase in w ould result in a 4 p ercen t increase in the aggregate gro wth rate and most of this increase is con tributed b y incum b en ts’ in ternal inno v ation. Column (4) in T able 2.6 sho ws that the aggregate gro wth rate w ould increase b y 11.5 p ercen t if all rms w ere nancially unconstrained. Again, in ternal inno v ation con tributes most of the increase in aggregate gro wth rate, b ecause of the higher cost of external inno v ation. My empirical analysis in section 2 sho ws that in ternal paten ts ha v e less external citation than external paten ts; and eac h in ternal inno v ation con tribute less to rm’s gro wth rate than external inno v ation. Lik ewise, in the mo del, the con tribution to aggregate pro ductivit y gro wth from in ternal inno v ation is mostly at an extensiv e margin. Giv en the n um b er of pro duct lines, an increase in reduces a rm’s sp ecic nancial friction ' n (see Prop osition I I I and Figure 2.2 for illustration). The rst ro w of P anel B in T able 2.6 do cumen ts the threshold n um b er of pro duct lines, n, at whic h rms b ecome nancially unconstrained in the mo del. A 25 p ercen t increase in reduce this threshold from 4 in to 2, and 23.4 p ercen t of rms b ecome nancially unconstrained. In the case, when is set to b e 1, this threshold is n = 7. All rms in this econom y are nancially constrained. An increase in encourages a rm’s R&D in v estmen t in pro ductivit y-enhancing inno v ation and discourages its R&D in v estmen t in industrial design. As external inno v ation is more costly than in ternal inno v ation, once a rm’s nancial constrain t is relaxed, it w ould undertak e more in ternal inno v ations than external inno v ations. The last t w o ro ws of P anel C in T able 2.6 do cumen t these c hanges. Though a larger encourages more R&D in v estmen t among incum b en ts, it discourages inno- v ation and en try among new p oten tial en tran ts. With the decrease in credit mark et distortion, the en try rate drops and new en tran ts con tribute less to the aggregate gro wth rate. As a result, few er rms exist in the econom y and more of creativ e destruction rate comes from incum b en t rm’s external inno v ations. In the case in whic h ev en incum b en ts are not sub ject to nancial constrain ts, 53 Figure 2.2: Firm Size Distribution and the V alue of ' n Note: Left panel is estimated distribution of pro duct lines from mo del under dieren t . The righ t panel is estimated rm-lev el nancial distortion 'n under dieren t . the con tribution to gro wth from new en tran t drops from 30.7 p ercen t in the baseline case to 26.4 p ercen t. It is then the incum b en ts conduct the most creativ e destruction activities. Figure 2.2 also sho ws that the rm size distribution b ecomes less righ t-sk ew ed once nancial constrain t is relaxed. With nancial constrain ts, around 79.4 p ercen t of rms ha v e only one pro duct line. The n um b er drops to 75.4 p ercen t if the nancial constrain t is remo v ed. In the case without nancial constrain t, rm size distribution is more spread. T o sum up, an impro v emen t in credit mark et p erfection w ould encourage more pro ductivit y- enhancing R&D exp enditure among incum b en ts, reduce en try , and raise the a higher aggregate gro wth rate. 2.5.2 The role of industrial design patenting P aten ting in industrial design increases nal output and consumption through c hanges in pro ducts qualities. Ho w ev er it decreases prot and sales among in termediate go o ds pro ducers b y raising comp etition and the equilibrium w age (recall section 3.4 for this theoretical analysis). Higher aggregate paten ting in industrial design , results in a lo w er optimal quan tit y of in termediate 54 go o ds as w ell as lo w er in termediate pro ducers’ prot. This tigh tens a rm’s nancial constrain t b y reducing the collateral v alue of its pro duct lines. Though paten ting in industrial design increase an individual rm’s curren t prot instan taneously , this rm-lev el p ositiv e eect is less than the aggregate negativ e eect attributable to increasing comp etition and reducing prot. T o mitigate this negativ e aggregate eect of industrial design, I in tro duce an in v estmen t tax t d on industrial design paten ts. T able 2.7 records the n umerical results. A rm’s optimal industrial design in tensit y reects the tax, b ecoming: h d = ^ (1 + ) 1 x d d 1 +' n (1 +' n )(1 +t d ) 1 d 1 n ~ d In App endix A.2.6, I sho w that d'n dt d < 0 and dh d dt d < 0. That is, a higher in v estmen t tax t d lo w er a rms’s nancial constrain t, b y discouraging in v estmen t in industrial design. As the relativ e cost of in ternal and external inno v ation decreases, rms conduct more pro ductivit y-enhancing inno v ations (see App endix A.2.6 for the pro of of dh I dt d > 0 and dh x dt d > 0). The aggregate gro wth rate increases b y only 0.03 p ercen t-p oin t when the tax rate is 0.1 and it increases b y 0.06 p ercen t-p oin t when the tax rate is raised to 0.25. The small impro v emen t in aggregate gro wth rate implies that imp osing an in v estmen t tax on industrial design is quan titativ ely ineectiv e. Consider an extreme case, where paten ting in industrial design is not allo w ed. Column (5) in T able 2.7 do cumen ts these mo del-implied c hanges. Sh utting do wn paten ting in industrial design w ould increase eac h in termediate pro ducer’s prot, and relax its nancial constrain ts. The aggregate gro wth rate w ould increase b y 6.32 p ercen t, whic h is 0.22 p ercen tage-p oin ts higher than the baseline gro wth rate. Most of this increase comes from incum b en ts’ in ternal inno v ation. By con trast to remo ving nancial constrain ts, banning industrial design paten ting enc our ages R&D in v estmen t among p oten tial en tran ts. En try rate sligh tly increases, whereas the gro wth con tribution from 55 T able 2.7: Gro wth and R&D Decomp osition (tax on industrial design) cost-reduced Baseline tax rate 10% tax rate 25% remo v e design (t d =0:1) (t d = 0) (t d = 0:25) (t d = 0:5) (x d !1) (1) (2) (3) (4) (5) P anel A: Gro wth Decomp osition Aggregate Gro wth Rate 0.0345 0.0348 0.0351 0.0354 0.0370 fr om incu. Ext. innov. 18.4% 18.4% 18.4% 18.3% 19.1% fr om incu. Int. innov. 50.8% 51.0% 51.3% 51.5% 52.9% fr om new entr ant 30.9% 30.7% 30.4% 30.2% 28.0% P anel B: Firm Distribution Decomp osition Creativ e destruction rate 0.128 0.129 0.129 0.129 0.131 fr om incumb ent 37.4% 37.5% 37.7% 37.7% 40.5% fr om new entr ant 62.6% 62.5% 62.3% 62.3% 59.5% Firm Measure M 0.791 0.791 0.789 0.789 0.773 En try Rate 0.101 0.102 0.102 0.102 0.103 P anel C: R&D in tensit y and Inno v ation Decomp osition R&D In tensit y (exclude design) 0.035 0.035 0.036 0.036 0.040 a v e. industrial design% 39.3% 36.9% 34.7% 31.9% 0 a v e. in ternal% 34.4% 35.9% 37.3% 39.1% 61.4% a v e. external% 26.3% 27.2% 28.0% 29.0% 38.6% the new en tran ts decreases. Recall that rms’ prot o w decreases with aggregate paten ting in industrial design. Sh utting do wn industrial design w ould increase rm’s p er p erio d prot as w ell as relax its nancial constrain ts. Th us, in v estmen t in pro ductivit y-enhancing inno v ation increases. This push up the creativ e destruction rate and the aggregate gro wth rate. This is similar to ndings in the adv ertising and gro wth literature in whic h adv ertising is mo deled as demand shifter. F or instance, Ca v enaile and Roldan-Blancoz (2019) nd that sh utting do wn the adv ertising sector w ould increase a rm’s R&D exp enditure as w ell as the aggregate gro wth rate. Firms do not face nancial constrain ts in their pap er, th us, the estimated increase in aggregate gro wth rate is higher than the estimated v alue in this pap er. Sp ecically , in this pap er, paten ting in industrial design do es not only ha v e a negativ e aggregate spillo v er eect. It also has a p ositiv e eect as it can increase a rm’s liquidit y and relax its nancial constrain ts. Th us, remo ving industrial design paten ting migh t ha v e a negativ e eect that partially cancels the p ositiv e eect from increasing an in termediate go o d pro ducer’s prot and total R&D exp enditure. Th us, the increase in the gro wth rate after sh utting 56 do wn industrial design is lo w er in the case with nancial constrain ts, comparing to the case without nancial constrain ts. T o sum up, the aggregate gro wth rate increase due to more en tran ts, higher creativ e destruction conducted b y incum b en t, the impro v emen t o v er existing pro duct lines, and less industrial design paten ting, when industrial design is prohibited. 2.5.3 W elfare Analysis F ollo wing A cemoglu, Ak cigit, Alp, Blo om, and Kerr (2018), I conduct w elfare analysis b y comparing the consumption-equiv alen t c hanges, , along the balanced gro wth path for t w o economies: One with nancial constrain t, s 1 , and one without nancial constrain t s 2 . U(c 1 0 (s 1 );g 1 (s 1 )) =U(c 2 0 (s 2 );g 2 (s 2 )) Here,c 1 0 andg 1 are initial consumption and the aggregate gro wth rate of the econom y with nancial constrain ts and c 2 0 and g 2 are those for the econom y without nancial constrain ts. can then b e view ed as the fraction of initial consumption in econom y s 1 (with nancial constrain t) that will ensure the same discoun ted lifetime utilit y as s 2 (without nancial constrain t). The discoun ted utilit y under log preferences can b e written as: U 0 (c 0 ;g) = Z 1 0 exp(t) logC t d t = 1 logc 0 + g The required w elfare comp ensation 1 is 1 =exp 0 B B B @ logc 2 0 logc 1 0 | {z } c hanges in consumption + g 2 g 1 | {z } c hanges in gro wth 1 C C C A 1 57 The consumption-equiv alen t c hanges can b e decomp osed in to t w o parts: 1) Changes in the (initial) consumption lev el, and 2) c hanges in the aggregate gro wth rate. In addition to comparing economies with and without nancial constrain t, I also compare economies with and without industrial design, and the econom y , remo ving b oth nancial constrain ts and paten ting in industrial design. T able 2.8 lists the results. T able 2.8: W elfare Decomp osition w elfare gain c hanges in consumption c hanges in gro wth rate ( 1) ( logC ) ( g ) Remo v e Financial Constrain t 0.069 -0.034 0.237 Remo v e Industrial Design 0.036 -0.02 0.055 Remo v e Both 0.160 -0.018 0.166 The w elfare gain after remo ving nancial constrain ts is 0.069, with a small negativ e c hange in consumption and a higher, p ositiv e c hanges in the aggregate gro wth rate. Once rms are nancially unconstrained, rms ha v e less incen tiv e to paten t in industrial design. Th us, the aggregate demand shifter decreases, lo w ering the aggregate nal go o ds output as w ell as consumptions. As the decrease in consumption is lo w er than the gain in aggregate gro wth rate, the o v erall eect giv es rise to a w elfare gain after remo ving nancial constrain ts. Similarly , the increase in the gro wth rate is higher than the decrease in consumption lev el after remo ving industrial design. Sh utting do wn paten ting in industrial design then results in a w elfare gain. The w elfare gain is ev en higher if b oth nancial constrain ts and industrial design paten ting are remo v ed. 2.5.4 P olicy Implication: Type-dependent tax Incentive In this section, I ev aluate China’s curren t v olume-based R&D tax incen tiv e p olicy in the mo died mo del of this pap er 14 . Starting in 2003, eligible R&D exp enses can b e deducted at a 150 p ercen t 14 I re-sim ulate the mo del with corp orate tax and R&D deduction. The calibrated parameters are sligh tly dieren t from previous sections. See App endix A.4.3 for details 58 rate when calculating a rm’s corp orate income tax base. In 2018, this deduction rate w as increased to 175 p ercen t, and some qualied rms can receiv e a 200 p ercen t deduction rate 15 . The purp ose of this tax incen tiv e p olicy is to stim ulate more inno v ation and higher rm gro wth. Ho w ev er, it do es not distinguish R&D exp enditure b y paten t category . R&D exp enses for industrial design receiv e the same deduction as R&D exp enses for in ternal and external inno v ations. This tax incen tiv e p olicy encourages not only pro ductivit y-enhancing inno v ation, but also paten ting in industrial design. One p oten tial problem for this tax incen tiv e p olicy is that nancially constrained rm migh t conduct more industrial design paten ts, whic h can b e detrimen tal to rms and the aggregate gro wth rate. The follo wing prop osition explains the mec hanism. Let s b e the rate of sup er-deduction and tax b e the corp orate income tax rate, and the optimal R&D in v estmen t can b e written as: h d = ^ (1 + ) 1 x d d 1 +' n tax 1 +' n stax 1 d 1 n ~ d h I = B x I I 1 1 +' n stax 1 I 1 n ~ I h x = B(1 +) +B n+1 B n x x x 1 1 +' n stax 1 x1 n ~ x (2.13) Prop osition VI Under a uniform tax incen tiv e, 1) inno v ation in tensities h d , h I and h x increase with the deduction rate, s; 2) with a quadratic cost function, a higher deduction rate s encourages rms to concen trate inno v ation in industrial design: dh d ds > 0 dh I ds > 0 dh x ds > 0 d h d h I ds > 0 d h d h x ds > 0 Pr o of. see App endix A.2.7 15 Data is from State T axation A dministration 59 In the App endix A.2.7, I sho w that d'n ds > 0. A higher deduction decreases a rm’s marginal cost in conducting inno v ation and increase inno v ation in tensit y . Ho w ev er, it w on’t relax a rm’s nancial constrain t. Th us, the rm b ecomes more lik ely to b e nancially constrained with an incre- men t in the deduction rate s. This increases the marginal b enet of relaxing nancial constrain ts via paten ting more industrial design. Hence, a rm’s inno v ation c hoice shifts from pro ductivit y- enhancing inno v ation in to industrial design. Giv en calibrated parameters, d = I = x = 2, h d h I / 1 +' n and h d h x / 1 +' n , these t w o ratios increase with s as d'n ds > 0. The o v er-in v estmen t in industrial design is detrimen tal to a rm’s and aggregate gro wth rate. I prop ose a t yp e-dep enden t tax incen tiv e p olicies, suc h that only R&D exp enses on in ternal and external inno v ation are en titled to a sup er deduction. The follo wing prop osition sho ws that under a t yp e-dep enden t tax incen tiv e p olicy , R&D in v estmen t shifts to w ards pro ductivit y-enhancing inno v ation. Prop osition VI I Under a t yp e-dep enden t tax incen tiv e p olicy , suc h that only R&D exp enses on in ternal and external inno v ation are en titled to deduction rate s, a higher deduction rate s shifts R&D in v estmen t to w ards pro ductivit y-enhancing inno v ation. d h d h I ds < 0 d h d h x ds < 0 Pr o of. see App endix A.2.8 Similar to the uniform tax incen tiv e p olicy , ' n increases with the deduction rate s. An increase in s reduce the eectiv e marginal cost of in ternal and external inno v ation, and th us increases cor- resp onding inno v ation in tensities. P aten ting in industrial design also increases, as a larger s raises the marginal b enet of relaxing a rm’s nancial constrain ts b y increasing curren t prot. Ho w ev er, industrial design paten ting do es not receiv e the sup er deduction when computing the tax base. 60 The relativ e cost of conducting industrial design paten ts th us increases. An increase in s stim ulate in ternal and external inno v ation more than industrial design paten ts. Under this t yp e-dep enden t tax incen tiv e p olicy , the aggregate gro wth rate w ould b e higher than under a uniform tax incen tiv e p olicy . T o quan tify the impact of this tax incen tiv e p olicy on the aggregate gro wth rate, I use the calibrated parameters 16 in T able 2.4 to conduct three coun terfactuals: 1) No deduction, 2) higher deduction rate and 3) t yp e-dep enden t tax incen tiv e p olicy . T able 2.9 compares the aggregate gro wth rate and w elfare gain under those coun terfactuals. T able 2.9: Gro wth Decomp osition and W elfare Gain Under T w o P olicy Regimes No Incen tiv e Uniform T yp e-dep enden t tax = 0:25 s = 1 s = 1:5 s = 2 s = 1:5 s = 2 (1) (2) Baseline (3) (4) (5) Aggregate Gro wth Rate 0.0336 0.0346 0.0358 0.0350 0.0368 fr om incu. Ext. innov. 18.0% 17.6% 16.9% 17.5% 16.8% fr om incu. Int. innov. 52.8% 50.4% 47.1% 50.7% 48.3% fr om new entr ant 29.2% 32.1% 36.0% 31.8% 34.9% R&D In tensit y 0.043 0.047 0.051 0.044 0.044 Share of Industrial Design 35.4% 38.0% 40.5% 35.0% 34.3% W elfare gain 0.027 0.057 0.034 0.080 Column (2) in T able 2.9 is the baseline case, that is the curren tly implemen ted tax incen tiv e p olicy where all t yp es of R&D in v estmen t receiv e a sup er deductible rate of 1.5. Column (1) is the coun terfactual that no R&D in v estmen ts receiv e a sup er-deduction. The curren tly implemen ted tax incen tiv e p olicy increases the ann ual aggregate gro wth rate b y 3 p ercen t, whic h is 0.1 p ercen tage p oin ts. Most of this increase is con tributed b y new en tran ts. Columns (2) and (4) compare the result under uniform tax incen tiv es, and t yp e-dep enden t tax incen tiv es, when the deduction rate is 150 p ercen t, and Columns (3) and (5) compare these t w o p olicies when the deduction rate is raised to 200 p ercen t. Comparing to the case without sup er deductibles, The aggregate gro wth rate increase b y 3 p ercen t (6.6 p ercen t under 200 p ercen t deduction) under uniform tax incen tiv es 16 My baseline parameters in previous session is calibrated under a mo died mo del with a corp orate income tax rate equals to 0:25 and a deduction rate of 1:5. So the impact from tax rate and tax deductions are not reected in m y calibrated parameters. 61 and increase b y 4.2 p ercen t (9.5 p ercen t under 200 p ercen t deduction) under t yp e-dep enden t tax incen tiv es when the deduction rate is 150 p ercen t (or 200 p ercen t). The share of paten ting in industrial design drops under a t yp e-dep enden t tax incen tiv e p olicy due to a relativ e increase in its R&D cost. The reduction is larger with a higher deduction rate. Ho w ev er, under a uniform tax incen tiv e p olicy , the share of industrial design in total inno v ation rises. This increase is greater with higher deduction rate. Th us, t yp e-dep enden t tax incen tiv e generate more aggregate gro wth than uniform tax incen tiv e. The dierence b et w een these t w o p olicies is larger when the deduction rate is higher. The w elfare gain is also higher under a t yp e-dep enden t tax incen tiv e p olicy . T o sum up, a t yp e-dep enden t tax incen tiv e p olicy w ould generate a higher aggregate gro wth and w elfare b y shifting rms’ paten ting to w ards pro ductivit y-enhancing inno v ations. 2.6 Conclusion In this pap er, I build a mo del of endogenous gro wth through c hoices o v er inno v ation qualit y when rms confron t nancial constrain ts. I ha v e sho wn b oth theoretically and empirically that nancial constrain ts alter a rm’s R&D comp osition. When nancial constrain ts restrict a rm’s total R&D in v estmen t, the rm substitutes for pro ductivit y-enhancing inno v ation activit y with industrial de- sign. Suc h c hanges in inno v ation comp osition lo w er the aggregate gro wth rate. When I prohibit rms from paten ting in industrial design in the mo del, the aggregate gro wth rate increases b y 6.3 p ercen t. I nd that imp osing taxes on industrial design paten ting is ineectiv e, in that consequen t increases in the aggregate gro wth rate are negligible. Moreo v er, dev eloping nancial mark ets is more eectiv e for promoting gro wth and raising w elfare than imp osing taxes on, or prohibiting, industrial design. I also sho w that a t yp e-dep enden t R&D tax incen tiv e, under whic h only R&D exp enses on in ternal and external inno v ation are en titled to a sup er deduction when computing a corp oration’s income tax base, w ould generate higher aggregate gro wth and a larger w elfare gain than curren tly 62 implemen ted uniform R&D tax incen tiv es. A p oten tial extension is to consider size-dep enden t R&D tax incen tiv es, in whic h small rms receiv e a larger sup er deduction than large rms. This w ould relax small rms’ nancial constrain ts and generate a higher aggregate gro wth rate. In the mo del, I use reduced-form nancial constrain ts, deriv ed from a limited enforcemen t prob- lem, to study the impact of nancial constrain ts on rms’ inno v ation strategies. One natural extension is to in tro duce nance in termediaries, and deriv e an explicit microfoundation for a rm’s in termediated b orro wing problem. In addition, equit y nancing is not allo w ed in the mo del. An em- pirical study b y Bro wn, F azzari, and P eterson (2009) sho ws that b etter access to equit y nance can substan tially increase rms’ R&D in v estmen t. Th us, allo wing rms c ho osing from equit y and debt nancing for inno v ation activit y is p oten tially an imp ortan t extension of the mo del. F urthermore, new en tran ts in m y mo del do not face nancial constrain ts when en tering the mark et; m y analysis fo cuses on the relationship b et w een nancial constrain ts and inno v ation comp osition among incum- b en ts. Imp osing nancial constrain ts on en tran ts’ inno v ation c hoices is a third p oten tial extension. Finally , in the mo del, I assume the inno v ation decision on industrial design is static. Industrial design aects curren t demand, but has no long-run eects for consumer demand. I could allo w the impact of industrial design to accum ulate o v er time, con tributing to a rm’s brand equit y . In suc h a setting, in v esting in industrial design relaxes a rm’s curren t and future b orro wing constrain ts whic h migh t aect a rm’s curren t and future in v estmen t in pro ductivit y-enhancing inno v ations. Bey ond the scop e of the curren t pap er, I lea v e this a v en ues for future researc h. 63 Chapter 3 Aggregate Investment and Stock Market Information In this c hapter, I use a rm’s and sto c k trader’s in v estmen t b eha vior to infer agen ts’ uncertain t y ab out the future. In particular, I dev elop a general equilibrium mo del with traders endo w ed with dieren tiated b eliefs on TFP sho c ks. W e study qualitativ ely ho w disp ersed b eliefs will b e gathered in the sto c k mark et and to what extend that aggregated information w ould inuence a rm’s in v estmen t b eha vior. Next, I use the observ ed relationship b et w een in v estmen t, sto c k prices, and inno v ation in TFP to measure the information and its precision rm receiv ed. I nd a mo derate degree of learning from rms’ o wn priv ate signal but no learning from the sto c k mark et. Our empirical w ork also sho ws that the existence of noise traders generate a considerable noise in the public signal rm receiv e. And suc h noise inhibits information transmission b et w een imp erfectly informed traders and rms. 3.1 Introduction A recen t and gro wing literature has in v estigated the role of "news sho c ks", or c hanges in agen ts’ exp ectations as p oten tially imp ortan t determinan ts of aggregate uctuations. These ideas can date bac k to Pigou (1926), explaining business uctuation as consequence of exp ectation shifts. Most previous literature assumes that agen ts can fully an ticipate c hanges in pro ductivit y sev eral 64 p erio ds b efore sho c ks tak e place. Jaimo vic h and Reb elo (2009) sho w ed theoretically that p ositiv e news generates co-mo v emen t in capital and lab or and cause an economic b o om in the curren t p erio d, ho w ev er, o v ercondence cause rm o v erin v estmen t and result in a recession in the near future. Similarly , Sc hmitt-GrohØ and Urib e (2012) quan titativ ely sho w that half of the business cycle uctuation is attributed to an ticipated disturbance from the news. F ollo wing Beaudry and P ortier (2006)’s inno v ativ e w ork, most empirical news sho c k literature uses a V AR-based or other no v el econometric metho dologies to iden tify and extract news sho c ks from data. Barsky and Sims (2011) iden tify news sho c k as the sho c ks that orthogonal to TFP inno v ation that also b est explains future v ariation in measured TFP . Using a principal comp onen t strategy , they nd, at a medium frequency lev el, output uctuation is signican tly inuenced b y news sho c ks. They found that news sho c k to future fundamen tals w as an imp ortan t determinan t of aggregate uctuations and a driving force of the business cycle. Beaudry and P ortier (2006) uses a biv ariate V AR system to ev aluate the join t b eha vior of sto c k prices and measured TFP . They sho w ed that the sto c k price could immediately react to c hanges in information ab out TFP without an y lags. The iden tication problem is a large issue in those V AR-based estimations. If signals mix with noise and news sho c ks, then econometricians and agen ts w ould face the same information extraction problem. Hence structure estimation cannot reco v er the time series, ev en though the underlying parameters can b e estimated. Beaudry and P ortier (2006) put a long-run restriction on their V AR estimation. Ho w ev er, Kermann and Merten (2014) sho w ed that Beaudry and P ortier (2006)’s empirical mo del do es not ha v e a unique solution for the m ultiv ariate system. The restriction on the co-mo v emen t of output and consumption will lead to a large range of candidates that satisfy the solution to their empirical mo del. Among those, are sho c ks that con tain no information on future TFPs. Blanc hard et al. (2013) o v ercomes the iden tication issue b y incorp orating estimated 65 exp ectation (reco v ered b y Kalman lter) in to structural maxim um lik eliho o d estimation. They sho w ed that noise sho c ks pla y an imp ortan t role in short-run uctuation. Ho w ev er, those mo dels lac k structural explanations of ho w sho c ks or information w ould b e dis- p ersed in to the mark et as w ell as to what exten t rms and households w ould learn from suc h public signals. Quan tifying the inuence of these factors, i.e., measuring the qualit y of information re- garding aggregate fundamen tals, is imp ortan t, but also has b een c hallenging, as agen ts’ information sets are usually unobserv able. Sto c k returns are b eliev ed to b e one of those sources that con tain news ab out the future. F ama (1990) sho w ed a strong p ositiv e correlation b et w een sto c k returns and future pro ductivit y gro wth. In this pap er, w e study whether the co-mo v emen ts b et w een the sto c k price index and in v estmen t w ould pro vide an y information on information disp ersion and aggrega- tion. F ollo wing (Da vid and V enk atesw aran, 2016)’s empirical strategy , the amoun t of information on future pro ductivit y is measured b y using the observ ed relationship b et w een in v estmen t and inno- v ations in TFP . A standard mo del of aggregate in v estmen t is built to include noisy signals of future sho c ks to total factor pro ductivit y (TFP). These signals are essen tially news sho c ks as they are in- formativ e for predicting future TFP but do not aect - indeed are orthogonal - to its curren t lev el. In v estmen t dynamics are also driv en b y adjustmen t costs and c hanges in the sto c hastic discoun t factor. W e rst solv e the mo del using p erturbation metho ds, whic h yields analytic expressions for the k ey momen ts in aggregate in v estmen t and a theoretical impulse resp onse function of in v estmen t and sto c k price, from whic h w e can pin do wn k ey parameters and infer its impact on uncertain t y . The aggregate learning is found to b e 0:51 on hp-ltered data, similar to the estimation from Da vid and V enk atesw aran (2017). Giv en the estimation, w e bac k ed out a time series of noise in the priv ate signal that the rm observ ed in eac h p erio d as w ell as mark et noise. W e ha v e sho wn that the mag- nitude of mark et noise is w a y higher than priv ate signals receiv ed b y rms and traders. A Firm’s lo w learning on future pro ductivit y caused mainly b y the existence of noise traders. Those noise 66 traders prev en t imp erfectly informed traders to p erfectly transmit their kno wledge or exp ectation on future inno v ations in pro ductivit y , to the public. In addition, the v olatilit y in the sto c k price is mostly caused b y mark et noise, whic h mak es sto c k price as a p o or signal for pro ductivit y sho c ks. The pap er is organized as follo ws. Section I I giv es the b enc hmark mo del and in tro duces the information structure for all agen ts in the mo del. Section I I I discuss a mo died metho d w e use in solving the mo del. Section IV sho ws the role of heterogenous traders in aggregating disp ersed signals and ho w those signal w ould en ter rm’s information set. Section V calibrates the mo del b y matc hing the impulse resp onse function. Section VI discusses the estimation results, and Section VI I concludes. 3.2 Benchmark Model W e consider a discrete time, innite horizon en vironmen t with imp erfect comp etition and closed econom y . The econom y is p opulated b y a represen tativ e household, a represen tativ e nal go o ds pro ducer and sto c k mark et traders. 3.2.1 Firm W e ha v e con tin uous rms with output function as Y it = A t (U it K it ) (Z t N it ) 1 . A t is the lev el of TFP at time t and Z t is the deterministic lab or-augmen ting tec hnology , gro wing at a deterministic rate ofg . U t is capital utilization. A t the end of eac h p erio d, rms c ho ose in v estmen t in new capital, whic h b ecomes a v ailable for pro duction in the follo wing p erio d. In v estmen t is sub ject to con v ex adjustmen t costs function: I it K it = 1 I it K it 1 67 where 1 is the elasticit y of in v estmen t rate. F or the quadratic case, w e ha v e =1 1 . The total cost of new in v estmen t is giv en b y (K it+1 ;K it ) =gK it+1 (1(U it ))K it + 1 g K it+1 K it g 1 K it (3.1) where the term gK t+1 (1(U t ))K t =I t is net in v estmen t, (U t ) the rate of depreciation whic h is a function of capital utilization: (U t ) = 0 + 1 U 1+ t 1 1 + with (1) = 0 , 0 (1) = 1 u and 00 (u)u 0 (u) = . Depreciation is increasing in capital utilization, whereas the elasticit y of deprecation with resp ect to capital utilization is constan t. captures the sev erit y of the adjustmen t cost. Dieren t from setups in Jamo vic h and Reb elo (2009) or Blanc hard, et, al(2013), here w e assume rm w ould pa y for the adjustmen t cost b y part of his output. That is, there’s one to one con v erse b et w een output and capital go o ds. F or simplicit y , w e set =1 in estimation part. Firm c ho ose lab or, in v estmen t and capital utilization to maximize the presen ted discoun ted v alue to its shareholders. Eac h of them faces a demand function P it = Y it Yt 1 , where is the substitutabilit y among in termediate pro ducts. The rm’s problem (after detrending) can b e written in a recursiv e form as V it (K it ;I it ) = max N it ;K it+1 ;U it E t [P it Y it W t N it +M t+1 V it (K it+1 ;I it+1 )] s:t: Y op it =A t (U it K it ) (Z t N it ) 1 (K it+1 ;K it ) (3.2) 1 The cost for p er in v estmen t is then giv en b y C(It;Kt) = 1 I t K t . By the prop ert y for a con v ex cost function, w e need CII 0,CK < 0. It is easy to v erify that these t w o conditions are satised when 1. The function also satisfy the prop ert y that C(0;K) =C 0 (0;K) = 0. 68 where M t+1 is the sto c hastic discoun t factor of the household, whic h is the ultimate o wner of the rm, and E it [] denotes the rm’s exp ectations conditional on its time t information set, denoted I it . Lab or and capital utilization is c hosen to adjust capital c hoice, then the optimalit y condition giv es: N it =(1) 1 1 Y t Y op it 1 Y op it W t U it = 1 (1) 1 1 Y t Y op it Y op it K it 1 ! 1 1+ Firm’s in v estmen t is determined b y Euler Equation: E it [M t+1 R I it+1 jI t ] = 1 where R I it+1 is deter- mined b y R I it+1 = Y t+1 Y it+1 1 Y it+1 K it+1 + 1 0 1 U 1+ it+1 1 1+ + g 2 2 K it+2 K it+1 2 g 2 2 g +g 2 K it+1 K it 1 It equals the marginal b enets o v er the marginal cost of in v esting one unit of capital to da y . The n umerator indicates the marginal b enet. It equals the return on capital plus the sa ving on next p erio d adjustmen t cost. The denominator is the marginal cost. A t equilibrium, R I it =R t 8t. Firm will forecast the next p erio d return and pricing k ernel based on the information he has. Notice that in v estmen t return will b e dier among rms if they receiv e dieren t information regarding future pro ductivit y . Hence, ev en rm are iden tically ex an te, they will act dieren t ex p ost. 3.2.2 Household The represen tativ e household has a recursiv e preference with is non-separabilit y in time. The stationarized problem can b e written as V t = (1 ~ )U(C t ;N t ) 1 + ~ E t [V 1 t+1 ] 1 1 1 1 69 where ~ is the eectiv e discoun t factor, adjusted b y the deterministic gro wth rate g . W e need a utilit y function that is capable with balanced gro wth path and can generate emplo ymen t v olatilit y at the same time. go v erns the elasticit y of in tertemp oral substitution (EIS ) and is the risk a v ersion co ecien t. Then the eectiv e discoun t factor is p ositiv ely related to EIS . Higher EIS mak es household more easily to dela y consumption in to future. In eac h p erio d, household c ho ose a risk b ond B t+1 , consumption C t and lab or supply N t to maximize his lifetime utilit y . The the sto c hastic discoun t factor can b e written as: M t+1 = ~ g 1 U c (t + 1) U c (t) V t+1 E t [V 1 t+1 ] 1 1 ! Hence, if = ,M t+1 = ~ t+1 t the same as the CRRA utilit y function. W e consider three sp ecica- tion of the utilit y function: CRRA, KPR (U = [C (1N) 1 ] 1 ) and GHH ( CG N 1+ 1+ 1 ). The rst sp ecication is nested in KPR utilit y function when = 1 and in GHH utilit y function when!1. Hence, in KPR setup, b oth go v erns F risc h elasticit y of lab or supply and the steady state lab or supply . The F rsic h elasticit y of lab or supply is: 1N N 1(1) . Under GHH setup, the F risc h elasticit y of lab or supply equals 1 and con trols the lev el of steady state lab or supply . Later w e will sho w that under the KPR utilit y function, lab or and capital utilization will react to the news sho c ks due to the non-separabilit y in consumption and leisure. Ho w ev er, under GHH utilit y function, lab or and utilization w on’t react to news sho c ks. 3.2.3 Information Structure In previous section, w e kno w A t = (1 +g) t e at . Once w e stationarized the mo del, the aggregate pro ductivit y w ould b e e at . I assume a t con tains only transitory part and follo ws AR(1) pro cess: a t+1 = (1 a ) a + a a t + t+1 70 a is the mean of TFP and a 2 [0; 1] measures the p ersistence of tec hnology sho c k. The inno v ations to the transitory part follo ws Gaussian distribution t N(0; 2 u ) and it is indep enden t of an y other sho c ks, and i.i.d distributed o v er time. I it is the information set the household and rm ha v e when c ho osing next p erio d b ond holding and capital sto c k K it+1 . Supp ose at the b eginning of eac h p erio d t, the rm receiv e t w o noisy signals ab out the next p erio d’s inno v ations ( t+1 ). The true lev el of inno v ations w ould b e rev ealed at the end of p erio d t. No w dene: ^ s it+1 = t+1 + v z t+1 s it+1 = t+1 +e it+1 where ^ s t+1 is the public signal whic h is a v ailable for all agen ts (household, rm and traders). s it+1 is the priv ate signal whic h can only observ ed b y household and rm. v is a scalar (w e will discuss it later in section 4). e it+1 andz t+1 are the noise comp onen t in signals. F or simplicit y , let’s assume those signals are indep enden t of eac h other. These are similar to news sho c ks, whic h con tain the information o v er future pro ductivit y . Hence, the information set for household and rm at p erio d t is: I it =ffa ts g t s=0 ; ^ s t+1 ;s it+1 g In addition, let’s assume that z t+1 N(0; 2 z ) and e it+1 N(0; 2 e ) o v er time and e it+1 N(e t+1 ; 2 disp ) cross-sectionally . Applying the Ba y e’s rule, yield the conditional exp ectation of the next p erio d’s inno v ation to the pro ductivit y: t+1 jI it N(E t [ t+1 ];V); V = 1 2 u + 1 2 e + 1 2 z 2 v 1 71 where V is the p osterior v ariance after the realization of the signal. Applying the conditional exp ectation of normal distribution, w e ha v e: E it [ t+1 jI it ] = V 2 e s it+1 + V 2 v 2 z ^ s t+1 The co ecien t 1 = V 2 e and 2 = V 2 v 2 z measures the w eigh t that the rm puts on the realization of eac h observ ed signals. Firm w ould put more w eigh t on the signal with less noise. That is, rely more on public signal if 2 v 2 z 2 e and more on his o wn priv ate signal if 2 v 2 z 2 e . Giv en the p osterior v ariance, there is a one to one mapping b et w een these co ecien ts and the noisiness of corresp onding signals: 2 e and 2 v 2 z . In the absence of an y learning, 1 and 2 will b e 0. That is, all uncertain t y of future pro ductivit y mo v emen ts are remain unresolv ed. The mo del turns in to the neo classical mo del, whic h E t [a t+1 ] = (1 a ) a + a a t . On the other extreme case, when there’s a p erfect rev eal of future inno v ation ( 2 e and 2 z 2 v approac hes zeros, so that ^ s t+1 = s t+1 = u t+1 ), w e ha v e E t [a t+1 ] = a t+1 . 2 disp creates a distribution of output and in v estmen t among rms. If 2 disp = 0, w e returns to a represen tativ e econom y with all rms share the same information set. F or simplicit y , the follo wing studies assume 2 disp = 0. 3.3 Equilibrium and Solution A noisy r e cursive c omp etitive e quilibrium in this econom y is dened as (i) giv en the information set (including the distribution of the signals) and prices, a set of v alue function (V (K t ; t )) and asso- ciated p olicy functions solv es household optimization problem; ii) prices are comp etitiv ely dene; iii) all mark ets are clear 2 and iv) the join t distribution o v er noises and inno v ations are constan t through time. 2 the Bond mark et is so trivial that I neglect it from no w on. 72 Dene t U c (t) b e the marginal utilit y from consumption. Then the log-linearized SDF w ould b e: ^ m t+1 = ^ t+1 ^ t + ( )(^ v t+1 E t ^ v t+1 ) Notice that the exp ected pricing k ernel for household w ould not dep ends on the v alue function since E t [^ v t+1 E t [^ v t+1 ]] = 0. If household and rm share the same information set 3 , then rm’s Euler Equation for in v estmen t is indep enden t of the v alue function to o. This displa ys certain t y equiv alen t in Epstein-Zin preference. Dene ^ x t = [^ c t ; ^ y t ; ^ t ] 0 . Then w e can write the whole system in a compact form 4 : 0 =A ^ k t+1 +B ^ k t +C^ x t +D^ a t 0 =E t [G ^ k t+1 +H ^ k t +J ^ x t+1 +K^ x t +L^ a t+1 +M^ a t jI t ] 0 = ^ z t+1 N ^ z t q t+1 Then w e follo w a guess and v erify approac h (Uhlig, 1999) to solv e the whole system. Under this approac h, w e can easily compute the informativ eness of t w o signal. Guess: ^ k t+1 =P ^ k t +Q^ z t +O S t+1 ^ x t =R ^ k t +S^ z t +T S t+1 3 If household can observ e the aggregate in v estmen t of rm, and all rm’s in v estmen t follo ws same set of p olicy functions, household can bac k out the signals rm receiv ed. That is, they should share the same information set. Suc h assumption enable us to a v oid encoun tering the problem of higher order exp ectation. 4 This metho d pro vide the same estimation for the metho d used in Kalten brunner and Lo c hsto er (2010), i.e. guessing the p olicy function of w ealth to consumption ratio and then matc hing the momen ts. In the App endix, w e pro vide an estimation follo ws Kalten brunner and Lo c hsto er (2010) 73 where S t+1 = E[u t+1 j^ s t+1 ;s t+1 ] = f(^ s t+1 ;s t+1 ), is a function of signals rm and household face. F or a one sho c k mo del, is scalar. Plug these t w o guess in to the log-linearized system, w e can get: 0 =A(P ^ y t +Q^ a t +O S t+1 ) +B ^ k t +C(R ^ k t +S^ a t +T S t+1 ) +D^ a t 0 =E t [F (P (P ^ k t +Q^ a t +O S t+1 ) +Q(N^ a t + t+1 )) +G(P ^ k t +Q^ a t +O S t+1 ) +H ^ k t jI t ] +E t [J(R(P ^ k t +Q^ a t +O S t+1 ) +S(N^ a t + t+1 )) +K(R ^ k t +S^ a t +T S t+1 )jI t ] +E t [L(N^ a t + t+1 ) +M ^ z t jI t ] T o pro ceed, w e need to redene the signal the rm receiv es. Dene: ~ e t+1 = ~ V 2 e e t+1 + ~ V 2 z 2 v v z t+1 with: ~ V = 1 2 e + 1 2 v 2 z 1 Hence, ~ e t+1 is the aggregate noise con tained in the signals. ~ V 2 e and ~ V 2 z 2 v are the w eigh ts the rm put on eac h noise. Then the exp ectation can b e written as: E t [ t+1 j^ s t+1 ;s t+1 ] ='(u t+1 + ~ e t+1 ) ='S t+1 74 with S t+1 = u t+1 + ~ e t+1 . Hence, w e can simplify the ab o v e t w o equations. Suc h equation should hold for an y v alue of the state z t ,k t and signal S t . Hence, w e can solv e the six co ecien t P ,Q,O , R, S , T as 5 : 0 =AP +B +CR 0 =AQ +CS +D 0 =AO +CT ) 0 =AO +CT 0 =FPP +GP +H +JRP +KR 0 =FPQ +FQN +GQ +JRQ +JSN +KS +LN +M 0 = (FPO +Q +GO +JRO +JS +KT +L) ) 0 =FPO +Q +GO +JRO +JS +KT +L Notice that the solution of P , Q, R, S are indep enden t of O and T . Hence, w e can directly apply Uhlig’s tric k in solving these four co ecien ts. Then w e can get the solution for O and T as: O = [FP +G +JR +KC 1 A] 1 (Q +JS +L) T =C 1 AO Suc h mo died metho d can also b e used in estimating the mo del with more than one sho c k. 3.4 The Stock Market and Public Signals The structure on the sto c k mark et is hea vily follo ws Albagli et al. (2011) and Da vid et al. (2016). Firm issues a unit measure of sto c k, whic h is a claim to rm’s prot. Then eac h traders will pursue suc h claim the return the prot to the household at the end of the p erio d. These sto c ks are traded 5 this hold if is in v ertible. Hence, w e imp ose the assumption that all signals con tain at lease some part of the information. That is, w e rule out the case where ' = 0 75 b y t w o groups of traders: noise traders and traders who receiv e some information on rm’s future pro ductivit y . W e refer the later part as the imp erfectly informed traders. In eac h p erio d, the noise traders will en ter the sto c k mark et, randomly but the amoun t (z t )2 (0; 1), where z t follo ws Gaussian distribution with z t N(0; 2 z ) and indep enden tly distributed across p erio ds. () is the standard normal CDF. Here, w e assume no short sales can o ccur in the mark et. Hence, the existence of the noise trader w ould ensure the demand for the sto c k b e p ositiv e and less than one (the total supply). A t the b eginning of eac h p erio d, the imp erfectly informed traders observ e the curren t price lev el of the sto c k. Then they will decide the amoun t of sto c k he w ould buy from the rm, b y forecasting on the return on suc h claim. T raders discoun t future returns on household sto c hastic discoun t factor. Hence, dieren t from the set up in Da vid et al. (2016), in our mo del, traders are risk a v erse. W e will see in the later part, suc h risk a v ersion w ould not only aect the price lev el but also the p olicy function for the sto c k price. As the rm and household, eac h trader receiv e a noisy priv ate signal dened as: s i t+1 = t+1 +v i t+1 v i t+1 N(0; 2 v ) where v i t+1 are the noise con tained in the signal and w e assume it is i.i.d across time and traders. Hence, for eac h traders, w e dene his information set as: t =ffa ts g t s=0 ; ^ s t+1 ;s t+1 g A t eac h p erio d, w e can write their problem as: max B i t E i t [M t+1 i t+1 j t ] 76 where i t+1 =B i t1 (P t +D t )B i t P t whereD t is the dividend distributed b y the rm. The optimalit y condition: P t =E i t [M t+1 (P t+1 +D t+1 )] P t is monotone in s i t+1 , then w e m ust ha v e the cuto v alue ^ s t+1 suc h that trader will hold an y amoun t of sto c k up to one(no short selling), if his priv ate signal s j t+1 > ^ s t+1 (if P t is monotone increasing in s i t+1 ); or if his priv ate signal s j t+1 < ^ s t+1 (if P t is monotone decreasing in s i t+1 ). Let d i t b e the demand of sto c k for eac h trader. If P t is monotone increasing in s i t+1 , w e m ust ha v e: d i t = ( 1 P t <E i t [M t+1 (P t+1 +D t+1 )] 2 (0; 1) P t =E i t [M t+1 (P t+1 +D t+1 )] 0 P t >E i t [M t+1 (P t+1 +D t+1 )] If P t is monotone decreasing in s i t+1 , w e m ust ha v e: d i t = ( 1 P t >E i t [M t+1 (P t+1 +D t+1 )] 2 (0; 1) P t =E i t [M t+1 (P t+1 +D t+1 )] 0 P t <E i t [M t+1 (P t+1 +D t+1 )] This is the same as Albagli (2011), when the prot function is linear in in v estmen t returns, the price of a sto c k is determined b y the marginal traders: Pr(buy) =Pr(s i t+1 > ^ s t+1 ) = 1 ^ s t+1 t+1 v (Case I: income eect ) Pr(buy) =Pr(s i t+1 < ^ s t+1 ) = ^ s t+1 t+1 v (Case I I: w ealth eect ) The in tuition is simple. When income eect dominan t k 3 > 0 (lo w er , higher IES), p ositiv e future sho c k will mak e in v estmen t more protable, triggering rm in v est more in the curren t p erio d. Hence, 77 the output and dividend will increase in the next p erio d, whic h increase the sto c k price in curren t p erio d. On the other hand, if w ealth eect dominan t k 3 < 0 (higher , lo w er IES), p ositiv e future sho c k will increase the consumption in this p erio d, and at the same time decrease the in v estmen t. Then, output and dividend will decrease in the next p erio d, whic h decrease the sto c k price in the curren t p erio d. Let z t+1 N(0; 2 z ) as the noise trader. Imp osing the mark et clearing condition in the sto c k mark et: 1 = 1 ^ s t+1 t+1 v + (z t+1 ) (Case I: income eect ) 1 = ^ s t+1 t+1 v + (z t+1 ) (Case I I: w ealth eect ) By the prop ert y of normal distribution, w e can bac k out the signal receiv ed b y marginal traders: ^ s t+1 = t+1 + v z t+1 (Case I: income eect ) ^ s t+1 = t+1 v z t+1 (Case I I: w ealth eect ) This is the public signal that rm and household observ e at eac h p erio d. No w since there’s one to one mapping b et w een the price lev el and the signal, observing the price lev el P t is same as observing the public signal. Put it in another w a y , the public signal eac h agen t observ e at eac h p erio d, is con tained in the curren t price lev el of rm’s sto c k. Th us, it en ter eac h agen t’s information set. Suc h arrangemen t can also help us to distinguish the source of noise: whether the noise con tained in the public signal comes from the disp ersion of the b eliefs ( v ) or the trading leads b y noise traders ( z ). In later section, w e dev elop ed a metho dology whic h can help us to decomp ose the noise con tained in eac h signal. 78 In either cases, w e can write the exp ectation for rms, HH and traders as: E t [u t+1 js t+1 ; ^ s t+1 ] = V 2 e s t+1 + V 2 z 2 v ^ s t+1 E i t [u t+1 js t+1 ; ^ s t+1 ] = ^ V 2 v s i t+1 + ^ V 2 z 2 v ^ s t+1 E i t [E t [u t+1 js t+1 ; ^ s t+1 ]js t+1 ; ^ s t+1 ] = V 2 e ^ V 2 v ^ s i t+1 + V 2 e ^ V 2 v 2 z + V 2 v 2 z ! ^ s t+1 where V is the p osterior v ariance of rms and HHs exp ectations; ^ V is the p osterior v ariance of trader’s exp ectation: V = 1 2 u + 1 2 e + 1 2 z 2 v 1 and hatV = 1 2 u + 1 2 v + 1 2 z 2 v 1 . As rm’s exp ec- tation w ould alter the future dividend pro cess as w ell as the sto c hastic discoun t factor tak en b y traders, trader needs to mak e exp ectation o v er the signal rm receiv ed. Similar as the rm, eac h trader will conjecture the price lev el as a function of curren t state and a w eigh ted sum of signals he observ ed. T raders will put more w eigh t on the signal whic h has less v ariance. No w, imp osing the sto c k mark et clearing condition, whic h is, s i t+1 =s t+1 , the linearized sto c k price can b e written as: ^ p t = p 1 ^ k t + p 2 ^ a t +' p ^ s t+1 where ' p is dened as: ' p = h p 3 1 ^ V 2 u + p 4 V 2 e 1 ^ V 2 u + V 2 z 2 v i . p 3 measures the price resp onse to trader’s exp ectation o v er future pro ductivit y sho c ks and p 4 measures the price resp onse to trader’s exp ectation o v er rm’s exp ectation. Hence, ' p measures the total resp onse for the price lev el to public signal. Imp ortan tly , ' p dep ends on the risk a v ersion co ecien t , since all p 3 and p 4 are functions of . In previous literature, the risk a v ersion co ecien t w on’t aect the p olicy function of all con trol v ariables. The rst order appro ximation of Epstein Zin preference displa y certain t y equiv alence, whic h mak e this function no dieren t than other standard preference. The risk a v ersion co ecien t only aect the lev els, or aect eac h v ariable’s resp onse to unexp ected c hanges in v ariance of pro ductivit y inno v ations (V an Binsb ergen et al., 2012). Ho w ev er in this mo del w e will sho w 79 that ev en with rst order T a ylor expansion, the risk a v ersion co ecien t will aect b oth lev els and resp onse of the price with resp ect to sho c ks. The price lev el w ould b e largely inuenced b y risk a v ersion co ecien t through the exp ected sto c hastic discoun t factor tak en b y eac h trader: @E i t [^ p t ] @ = @E i t [ ^ m t+1 ] @ = v 3 " ^ V 2 u V 2 u V 2 e ^ V 2 u # ^ s t+1 inside the brac k et, w e ha v e: ^ V 2 u V 2 u V 2 e ^ V 2 u = V 2 u " ^ V V ^ V 2 e ! 1 # = V 2 u ^ V 1 V 1 2 e 1 = V 2 u ^ V 1 2 u + 1 2 v 2 z 1 = V 2 u " 1 2 u + 1 2 v 2 z 1 2 u + 1 2 v 2 z + 1 2 v 1 # < 0 The inuence from is through the dierence b et w een trader’s exp ectation of inno v ations and trader’s exp ectation of household’s exp ectation of inno v ations. Since @ p 4 @ = v 3 < 0 and @ 3 p @ = v 3 > 0, when traders are more risk a v erse, he w ould put less w eigh t in his exp ectation o v er the rm’s exp ectation of inno v ations. Th us, rely more on his o wn signal. Hence, when facing a p ositiv e signal ab out future inno v ation, the demand for sto c k w ould b e lo w er if traders are more risk a v erse, th us the increase in the price lev el w ould b e lo w er. Similarly , when traders are hit b y a negativ e signal, the demand for sto c k w ould also b e higher for traders with more risk a v erse, then the decrease in the price lev el w ould b e lo w er. No w, as p 1 to p 4 are kno wn and k t anda t are observ able for rm and household, then in v erting the price function, w e can appro ximate the public signal as: ^ s t+1 = 1 ' p [^ p t p 1 k t p 2 a t ] 80 Hence, if ' p > 0 (whic h is hold empirically), there’s one to one p ositiv e relationship b et w een ^ s t+1 and ^ p t . Th us, our assumption of the existence of suc h cuto v alue is v eried. And observing the price ^ p t is equiv alen t to observing the public signal. Put it in another w a y , the signal rm learned in the mark et are from the price lev el of his o wn sto c k. And the v ariance of suc h signal comes from t w o sources: the distribution of b eliev es among dieren t traders and the existence of noise traders. 3.5 Calibration and Estimation In this section w e p erform a quan titativ e analysis of the mo del, ev aluating the informativ eness of those signals. The mo del dep ends on 15 parameters. Hence, w e’ll rst in tro duce the data w e used and then our metho d in calibrating or estimating those parameters. 3.5.1 Data and Calibration a. Data Data on consumption C t , output Y t , in v estmen t I t and capital sto c k K t are ann ual data and adjusted b y p opulation (c hained dollars 2009, 1929:2016), tak en from BEA w ebsite. W e dene C t as the real p ersonal consumption exp enditure p er capita min us the real p ersonal consumption exp enditures p er capita in durable go o ds. In v estmen t I t is dened as real gross nonfarm busi- ness domestic in v estmen t p er capita plus the real p ersonal consumption exp enditure p er capita in durable go o ds. Y t is the real nonfarm output p er capita. The lab or input N t are nonfarm business emplo ymen t. Pro ductivit y A t are ann ual TFP data (adjusted b y utilization) calculated follo wing F ernald (2012). The capital sto c k K t is real xed asset in nonfarm priv ate sector. P t are S&P 500 lev el rep orted b y CRSP , deated b y GDP deator, whic h is a v ailable in BEA w ebsite. All data except the S&P 500 are hp-ltered. Since the hp-ltered data giv es high spurious dynamic relations (Hamilton, 2016), th us, the informativ eness of signals w e estimated under suc h metho d giv es an upp er b ound of its true lev el. 81 b. Calibration W e calibrate the mo del to an ann ual frequency . F ollo wing classic literature on real business cycles, w e set the discoun t factor equals 0:96 and capital depreciation rate = 0:1. The pro duction parameter is set to 0:34 as in most RBC literature. F or preference parameter and , w e adjusted it so that the steady state N is around 0:33. Hence, = 0:34 and = 1:15. 1 = 1:19 is the a v erage markup tak en from Basu and F ernald (1997). = 0:56 is elasticit y of utilization adjustmen t, tak en from Burnside and Eic hen baum (1993). (or 1.43 from Basu and Kim ball (1997)). The deterministic gro wth rate g is set to 2% p er y ear, follo wing Kalten brunner and Lo c hsto er (2010)’s calibration. The main sources of economic uctuation in this mo del are the aggregate pro ductivit y . a and 2 u is estimated b y regressing pro ductivit y gro wth on its lagged v alue and a time trend. 3.5.2 Estimation and Identication The rest parameters needs to b e determined are capital adjustmen t , in v erse of IES and in- formation parameters ', ~ ' and ^ ' (in the app endix, w e sho w there’s one-to-one mapping b et w een information parameters and the noise lev el 2 e , 2 v and 2 z ). Those parameters are estimated b y Structural V AR. Consider three time series (^ a t , ^ k t and ^ p t ). Our theoretical mo del implies: 0 B B B B B B @ ^ a t+1 ^ p t ^ k t+1 1 C C C C C C A = 0 B B B B B B @ a 0 0 p 2 0 p 1 k 2 0 k 1 1 C C C C C C A 0 B B B B B B @ ^ a t ^ p t1 ^ k t 1 C C C C C C A + 0 B B B B B B @ 1 0 0 ' p ' p v 0 k 3 ' k 3 ~ '' ^ ' 1 ^ ' v k 3 ' ~ ' 1 ^ ' 1 C C C C C C A 0 B B B B B B @ t+1 z t+1 e t+1 1 C C C C C C A where alls are functions of and only . As t+1 ,z t+1 ande t+1 are i.i.d distributed with v ariance ( 2 u , 2 z and 2 e only). Our ordering of data is equiv alen t to put short-run restrictions on V AR 82 estimation. Dene Y t+1 = [^ a t+1 ; ^ p t ; ^ k t+1 ] 0 and" t+1 = [u t+1 ;z t+1 ;e t+1 ] 0 , w e can then write the ab o v e equation compactly as: Y t+1 =AY t +B" t+1 =AY t +! t+1 where! t+1 =B" t+1 . Leta ij b e the elemen t in matrix A, w e put follo wing parameter restrictions in A witha 12 =a 13 =a 22 =a 32 = 0, and othera ij < 1. So that the matrix (IAL) is in v ertible. Let ! b e the v ariance-co v ariance matrix of the residue of Z t+1 ^ AZ t . By Cholesky decomp osition, w e can write ! as a pro ducts of t w o lo w er triangular matrix: ! = PP 0 . Then B can b e reco v ered (B = P ). Hence, the set of parameters ^ f;;'; ~ '; ^ 'g can b e estimated b y matc hing B with estimated ^ B =P : ^ =argmin 2 (B() ^ B) 0 W (B() ^ B) is the set of all p ossible v alues for ^ . W e put the follo wing restrictions on parameters (see App endix for detail): > 0, > 0, '2 (0; 1), ^ '2 (0; 1), ~ '2 (0; 1), ~ ' < min('; ^ ') and ~ ' > ' ^ '. W is the w eigh ting matrix whic h equals the in v erse of ! . T able 1 rep orts the calibration and estimation results. P anel A are xed parameter that w e set and calibrated outside the mo del. The fourth column giv es the source for the calibration. P anel B rep orts our estimation for targeted parameters. The third column giv es the estimated v alue. P anel C sho ws the v alue of implied k ey parameters. 3.5.3 Estimation Discussion Figure 1 sho ws the empirical and estimated impulse resp onse function. The blac k solid line is the IRF estimated using V AR equation with parameter restrictions describ ed ab o v e. The shaded area are one-standard error condence band for empirical IRF. The red dash line are the IRF computed under our theoretical mo del and estimated parameter ( ^ ). The upp er panel is the resp onse to future 83 T able 3.1: Calibration P arameter Description v alue P anel A: Fixed P arameters capital input elasticit y 0.34 discoun t factor 0.97 0 depreciation rate under full utilization 0.10 in v erse of lab or elasticit y 0.34 relativ e preference on leisure 1.15 capital adjustmen t con v exit y -1 elasticit y of capital utilization 0.56 g deterministic gro wth rate 2% a p ersistency of transitory sho c ks 0.9596 u s.t.d of transitory sho c k 0.0190 risk a v ersion 5 P anel B: P arameters Estimated using V AR EIS 0.0004 capital adjustmen t cost 0.2625 ' informativ eness of rm’s total signal 0.5017 ^ ' informativ eness of trader’s priv ate signal 0.9346 ~ ' informativ eness of public signal 0.4689 Figure 3.1: Impulse Resp onse F unction technology 0 5 10 Horizon 0 0.01 0.02 0.03 u t+1 stock price 0 5 10 Horizon -0.1 0 0.1 0.2 u t+1 capital 0 5 10 Horizon 0 0.01 0.02 0.03 u t+1 technology 0 5 10 Horizon -2 0 2 z t+1 10 -3 stock price 0 5 10 Horizon -0.2 0 0.2 0.4 z t+1 capital 0 5 10 Horizon -2 0 2 z t+1 10 -3 technology 0 5 10 Horizon -2 0 2 e t+1 10 -4 stock price 0 5 10 Horizon 0 5 10 e t+1 10 -3 capital 0 5 10 Horizon 0 10 20 e t+1 10 -3 84 pro ductivit y sho c ks (u t+1 ), the middle panel sho w the resp onse to mark et noise (z t+1 ) and the lo w er panel is the resp onse to the noise in rm’s priv ate signal ( e t+1 ). Our estimated IRF can closely matc hes empirical ones, except the magnitude of capital sto c k’s resp onse to future pro ductivit y sho c ks. The resp onse function for capital sto c k to u t+1 is h ump ed shap ed due to the income eects. 1% pro ductivit y sho c k in the near future will increase the rm’s curren t capital sto c k b y encouraging in v estmen t. As dividend in the next p erio d will b e increase, sto c k price also resp onde p ositiv ely to pro ductivit y sho c k. Suc h resp onse sho ws that income eect dominate the w ealth eect. This is consisten t with most news literature where they ha v e sho wn that in order to pro duce a p ositiv e co-mo v emen t among output, in v estmen t and consumption, w e need a relativ ely large income eect. Capital sto c k resp onse little to mark et noise z t+1 , indicating that rms w eigh t less on the public signal ^ s t+1 = t+1 + v z t+1 . Ho w ev er, the sto c k price ha v e a large resp onse to the mark et noise, sho wing the price lev el is dominated b y the noise traders. Th us, the sto c k price serv es as a bad signal for rm’s prediction o v er the future pro ductivit y sho c ks. This is dieren t from Beaudry and P ortier (2006)’s pioneer pap er, where they sho w ed that sto c k price resp onse immediately to future pro ductivit y sho c ks. This conclusion is c hallenged b y Kermann and Merten (2014). They ha v e sho wn that using a m ultiv ariate V AR with consumption, TFP and sto c k price, Beaudry and P ortier (2006)’s metho d cannot generate a signican t p ositiv e resp onse to news sho c ks. Base on our result, w e ha v e sho wn that the p ositiv e co-mo v emen t Beaudry and P ortier (2006) observ ed among sto c k price and TFP actually exhibit the p ositiv e correlation b et w een mark et noise the pro ductivit y sho c ks, whic h ha v e no prediction p o w er o v er the consumption or in v estmen t dynamics. T able 1 rep orts the estimation of ^ . The adjustmen t cost = 0:2625, whic h is lo w er than most studies. Based on Q theory , should lie in a range from 3 to 20 (Gilc hrist and Himmelb erg, 1995; Ha y ashi, 1982). Ho w ev er, Co op er and Haltiw anger (2006) sho w ed that in aggregate lev el, in order to matc h the high correlation b et w een in v estmen t and pro ductivit y sho c ks, w e need a lo w er v alue 85 of in a quadratic adjustmen t cost mo del. Their estimation of is = 0:195 whic h is closer to our estimates. The estimation of the in v erse of IES is = 0:0004, whic h is m uc h lo w er than the those used in most RBC literature ( = 2). Our estimation indicates that con temp orary utilit y is linear in consumption. Our lo w measure of migh t dep ends on the sto c k price data w e use. As measures the resp onse of consumption gro wth to risk free rate, it can also b e estimated b y regress c t on r f con trolling other instrumen ts. Hall (1988) giv e the estimate of = 0:066 when using c hanges in S&P 500 index as a measuremen t of return. All those indicating that consumption has little resp onse to sto c k returns. The lo w er lev el of implies a high v olatilit y in the consumption and lo w lev el in Equit y premium and Sharp e ratio. T able 2 sho ws the comparison of estimated momen ts and actual momen ts 6 : T able 3.2: Macro Momen ts Momen ts Data Estimated b y matc hing IRF Estimated b y SMM c y 0.7128 1.4903 0.7822 i y 3.3146 3.1569 3.4253 p 0.0878 0.2825 0.0901 E t [RR f ] 0.0460 0.0001 0.0290 Sharp e Ratio 0.2637 0.0003 0.2629 corr(p t ; t+1 ) 0.0123 0.0177 -0.2669 corr(i t ; t+1 ) 0.4725 0.4628 -0.2764 Our estimation can matc hes the relativ e v olatilit y of in v estmen t. Ho w ev er, it o v erestimate the v olatilit y of returns on sto c k price, and relativ e v olatilit y of consumption.The standard deviation of public noise can b e computed as ^ s = p u + v z = 0:6793. Hence, the v olatilit y of sto c k return is mostly driv en b y the v olatilit y in public noise. Relativ ely high v alue of consumption v olatilit y is driv en b y our estimates of lo w . As the estimated mo del displa y lo w lev el of consumption smo othing, the estimated equit y premium and Sharp e Ratio is so lo w. T able 2 also sho ws that b y matc hing the impulse resp onse function sp ecied ab o v e, our estimates can closely matc hes the 6 If unadjusted b y lev erage, p = 0:1702 86 dynamic of sto c k index returns and in v estmen t gro wth ( i y ,corr(p t ; t+1 ) and corr(i t ; t+1 ) ). Ho w ev er, our estimate p o orly matc hes other macro and sto c k mark et momen ts suc h as relativ e consumption v olatilit y , Sharp e Ratio and Equit y Premium. F ollo wing the results from section I I, p olicy functions can b e written as a function of curren t states: ^ a t , ^ k t and signals: ^ s t+1 ,s t+1 . Here w e consider estimating the set of parameters b y matc hing targeted momen ts: c y , i y , p ,E t [RR f ] and Sharp e Ratio. The results are sho wn in the last column of table 2. W e ha v e the estimates as: = 58:0550, = 23:9562, e = 0:0413, v = 361:0566 and z = 0:6465. This is quite dieren t from the estimation using structural V AR. The estimate of indicates an IES of 0:05, whic h is consisten t with Kalten brunner and Lo c hsto er (2010). The high Sharp e Ratio is caused b y the predictabilit y of p-d ratio b y consumption smo othing. Hence, in order to matc h the Sharp e Ratio, w e need p ersistence in consumption gro wth rate. Ho w ev er, lo w er lev el of IES mak es w ealth eect dominates the income eect, causing in v estmen t and sto c k price reacts negativ ely to future pro ductivit y sho c ks. The t w o estimation strategy giv es inconsisten t results. In order to study the impact from news sho c ks, w e will fo cus on the results giv en b y matc hing IRF. 3.6 Result 3.6.1 Information Decomposition F ollo wing the result from section I I, w e can dene eac h w eigh t rm and trader put on their observ ed signals: 1 V 2 e = ' ~ ' 1 ^ ' 2 V 2 z 2 v = ~ '' ^ ' 1 ^ ' m 1 ^ V 2 v 1 ^ V 2 e ! = ^ ' ~ ' 1' 1 ' ~ ' 1' m 2 ^ V 2 v 2 z 1 ^ V 2 e ! + V 2 v 2 z = ~ ' ^ '' 1' 1 ' ~ ' 1' + ~ '' ^ ' 1 ^ ' 87 The w eigh t on prior w ould b e 1 1 2 for rms and 1 m 1 m 2 for traders. T able 3 sho ws the results. The v ariance of noise trader’s trading amoun t is large, whic h dominan t the p osterior v ariances. The noise trading b eha vior prev en t the trader’s signal transmitted to rms through the mark et. Th us, the sto c k price do not con tain m uc h useful information rm can rely on. Hence, when rm ha v e his o wn priv ate signal, he w ould put m uc h w eigh t on the priv ate signal as its v ariance is m uc h smaller. So do es eac h traders. If in the absence of priv ate signal, rm w ould only dep ends on the public signal to mak e in v estmen t c hoice. T raders, on the other hand, still put more w eigh t on his priv ate signal, whic h has m uc h less v ariance. But the existence of the noise trader, prev en t rm receiv e an accurate signal as trader do es. Whic h mak e the p osterior v ariance of rm’s estimation m uc h higher than trader’s estimation. T able 3.3: Implied Noise P arameter Description Estimation e noise in rm’s priv ate signal 0.0189 v noise in trader’s priv ate signal 0.0050 z mark et noise 135.8127 0 rm’s w eigh t on prior 0.4983 1 rm’s w eigh t on priv ate signal 0.5013 2 rm’s w eigh t on public signal 0.0004 m 0 trader’s w eigh t on prior 0.2981 m 1 marginal trader’s w eigh t on priv ate signal 0.7016 m 2 marginal trader’s w eigh t on public signal 0.0003 s t+1 s.t.d of rm’s signal 0.0189 ^ s t+1 s.t.d of public signal 0.6793 3.6.2 Implied Noises By in v erting our V AR equation, w e can bac k out time series of pro ductivit y sho c ks, noise in rm’s priv ate signal and mark et noise. Hence, the public signal and rm’s priv ate signal can b e obtained. As rm and traders put almost zero w eigh t on the public signal, w e can simply ignore its impact. Figure 2 sho ws the relationship b et w een in v estmen t (solid blue line), rm’s priv ate signal (dashed 88 red line in left panel) and pro ductivit y c hanges (dashed red line in righ t panel). The shaded area are recession date dened b y NBER. Firm’s in v estmen t (hp-ltered) mo v es pro cylically and leads pro ductivit y c hanges. It closely mo v es with his priv ate signal. The correlation b et w een s t+1 and in v estmen t is around 0.79. Signal s t+1 is actually observ ed in time t, whic h induce in v estmen t at timet and increase timet+1’s capital sto c k. Th us, our assumption on time to build and the timing of information is supp orted empirically . Figure 3.2: In v estmen t, Priv ate Signal and Pro ductivit y 1940 1960 1980 2000 year -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 signal observed firm investment 1940 1960 1980 2000 year -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 recession productivity investment Figure 3 sho ws the estimated noise from V AR. The magnitude of mark et noise is m uc h higher than noises in rm’s priv ate signal. Firm’s information sho c ks mo v es pro cyclically with pro ductivit y sho c ks. The correlation b et w een these t w o are 0.64. Ho w ev er, the correlation b et w een mark et noises and pro ductivit y sho c ks are as lo w as 0.20. Comparing mark et noise with the recession date, it is easy to notice that the implied mark et noise is higher during eac h recession. Ho w ev er, as the v is lo w, the impact from mark et noise on in v estmen t is negligible. Ho w ev er, mark et noise has great impact on the mo v emen t of sto c k prices. The estimated correlation b et w een sto c k price and mark et noise is 0.96, whereas the estimated correlation b et w een sto c k price and pro ductivit y sho c k is only 0.21. The v olatilit y in the sto c k price is mostly driv en b y mark et noise. If w e reduce mark et noise in to one fth of the estimated v alue (i.e. z = 27), the v olatilit y of sto c k price is reduced to 0:056, 89 Figure 3.3: Estimated Noises firm info shock 1940 1960 1980 2000 year -0.06 -0.04 -0.02 0 0.02 0.04 market noise 1940 1960 1980 2000 year -1 -0.5 0 0.5 1 private signal of firm 1940 1960 1980 2000 year -0.1 -0.05 0 0.05 0.1 productivity shocks 1940 1960 1980 2000 year -0.1 -0.05 0 0.05 0.1 only one fth of our estimated v alue. In addition, the correlation b et w een sto c k price and mark et noise reduced to 0.6. Our results also sho w ed that the priv ate signal receiv ed b y traders are more informativ e than those receiv ed b y rms. Ho w ev er, the existence of the noise trader prohibit information transmis- sion b et w een traders and rms. Th us, sto c k price w ould serv e as a p o or signal indicating future pro ductivit y . T able 4 sho ws our coun terfactual analysis b y reducing mark et noise in to dieren t lev els while k eeping other parameters unc hanged. When mark et noise is reduced to z = 0:01, the mo del is close to full information situation where b oth rm and trader put almost all w eigh t on the public signals, whic h closely mo v es with pro ductivit y sho c ks. ' p and ' k measures the resp onse of sto c k price and in v estmen t to future pro ductivit y sho c ks. The last column of table 4 sho ws that: under full information case, 1% c hange in pro ductivit y sho c k u t+1 will increase p t b y 1.8% and i t b y 2.1%. Hence, unlik e classical RBC mo del, in v estmen t and sto c k price lead the business cycle as 90 c hanges in future pro ductivit y will b e released to the econom y one p erio d ahead. Hence, reducing noise trading b eha vior in the sto c k mark et w ould impro v e mark ets’ information aggregation. T able 3.4: Impact from Mark et Noise Mark et Noise Lev el 60 10 5 0.01 1 0.5018 0.4695 0.3937 0.0006 2 0.0017 0.0658 0.2167 0.9987 m 1 0.7021 0.6809 0.6291 0.0045 m 2 0.0010 0.0396 0.1326 0.9949 ' p 0.0060 0.0069 0.0088 0.0186 ' k 0.0108 0.0115 0.0131 0.0214 3.7 Conclusion In this pap er, w e use a rm’s and sto c k trader’s in v estmen t b eha vior to infer agen ts’ uncertain t y ab out the future. In particular, w e dev elop a general equilibrium mo del with traders endo w ed with dieren tiated b eliefs on TFP sho c ks. W e study qualitativ ely ho w disp ersed b eliefs will b e gathered in the sto c k mark et and to what extend that aggregated information w ould inuence a rm’s in v estmen t b eha vior. Next, w e use the observ ed relationship b et w een in v estmen t, sto c k prices, and inno v ation in TFP to measure the information and its precision rm receiv ed. W e nd a mo derate degree of learning from the agen t’s signals and almost no learning from the sto c k mark et. Our empirical w ork also sho ws that the existence of noise traders generate a considerable noise in the signal rm receiv e. And suc h noise inhibits information transmission b et w een traders and rms. This study also sho ws an inconsisten t measure of information and preference parameters when using a dieren t estimation strategy . The IRF matc hing strategy yields high relativ e v olatilit y in consumption and lo w lev el of Sharp e Ratio, whereas SMM strategy indicates no news in the business cycle. Hence, in future study , w e need to revise the mo del to matc hes b oth in v estmen t dynamics 91 and macro economic momen ts. Another direction is to incorp orate higher-order exp ectation to study ho w a rm’s disp ersed information w ould impact on in v estmen t disp ersions. 92 Chapter 4 Credit Reallocation and Innov ation Disparity among POEs and SOEs in China I empirically analyze the determinan ts of the observ ed inno v ation and pro ductivit y disparit y b et w een state-o wned rms (SOE) and priv ate-o wned rms (POE) b efore and after 2009-2010 China’s scal stim ulus p olicy . Suc h stim ulus p olicy disprop ortionately fa v ored SOEs. Empirically , the dierence in subsidies and skill lev els can explain as high as 90 p ercen t of the observ ed v ariation in paten t application b et w een SOEs and POEs. In the pre-2009 sample, subsidies can only explain 9.3 p ercen t of the observ ed dierence in paten t applications. Ho w ev er, it can tell 24 p ercen t of the observ ed dierence in paten t applications in the p ost-2009 sample. In addition, the observ ed dierence in pro ductivit y gro wth b et w een SOEs and POEs after the 2009-2010 scal stim ulus p olicy can b e attributed to an increase in subsidies SOEs receiv ed. Moreo v er, 31.4 p ercen t of subsidies’ impact on pro ductivit y gro wth can b e explained b y the rise in SOEs’ gran ted paten ts. 4.1 Introduction The last decade has witnessed astonishing gro wth in China’s inno v ation output and input. P aten t application explo ded around 2006, when China started to switc h its in v estmen t-led gro wth strategy 93 in to an inno v ation-led gro wth strategy . The go v ernmen t starts making additional subsidies and of- fering tax b enets for those rms that engaged in inno v ativ e activities. Ho w ev er, the R&D subsidies and China’s economic stim ulus plan after great recession disprop ortionately fa v ored state-o wned en- terprises (Cong, Gao, P on ticelli and Y ang (2019)). Th us, suc h p olicies not only increase the n um b er and qualit y of paten t applications (W ei, Xie and Zhang (2017)), but also increase the disparities in inno v ation activities b et w een state-o wned and priv ate-o wned rms. In this pap er, I empirically study the impact of China’s scal stim ulus p olicy on inno v ation qualit y and rm pro ductivit y disparit y b et w een state-o wned rms and priv ately-o wned rms in China. I construct a no v el new data-set for Chinese man ufacturing rms. Previous studies in China only fo cus on inno v ation quan tities, due to the lac k of inno v ation qualit y data. I o v ercome this h urdle b y scraping and merging eac h Go ogle paten t citation data, with paten t activit y data from China’s State In tellectual Oce (SIPO), and with rms’ op eration data from China’s Ann ual Surv ey of Man ufacturing (ASM). I utilize balance sheet information from ASM to measure a rm’s capital in v estmen t and in tangible go o ds in v estmen t. I use the link ed SIPO-Go ogle paten t data-set to measure the qualit y of eac h paten t a rm led in eac h y ear. Consisten t with ndings in previous literature (see P oncet, Steingress and Hylk e V anden bussc he (2010); Guariglia, Liu and Song (2011) and Ho w ell (2016)), I nd that, rst, priv ate rms are most lik ely to face higher b orro wing cost and receiv e less go v ernmen t subsidies than state-o wned rms. Suc h dierence b ecomes ev en larger after the 2009-2010 scal stim ulus p olicy . Second, priv ately-o wned rms started paten ting signican tly less high-qualit y inno v ations than state-o wned rms follo wing the p olicy c hange. Third, pro ductivit y grew faster in state-o wned rms than in priv ately-o wned rms follo wing the p olicy c hange. My empirical evidence suggests that China’s scal stim ulus p olicy in 2009 and 2010 ma y cause the inno v ation disparit y b et w een state-o wned and priv ately-o wned rms. And this can partially explain 94 the fact that priv ate-o wned rms ha v e lost some of their pro ductivit y adv an tage relativ e to state- o wned rms after 2009. Based on those empirical ndings, I build a st ylized theoretical mo del to explore the under- lying mec hanisms through whic h subsidizing state-o wned en terprises ma y increase nancing costs among priv ately-o wned en terprises. This can the trigger inno v ation gap b et w een state-o wned and priv ate-o wned en terprises. Under m y framew ork, monop olistic comp etitiv e rms mak e decisions on pro duction, in v estmen t in capital and in tangible go o ds. In tangible go o ds are pro ductivit y- enhancing. Hence, one can view the in v estmen t in in tangible go o ds as rms’ inno v ation activities. There are t w o t yp es of rms in m y mo del that dier in three dimensions: 1) inno v ation capacit y - the eciency of con v erting in tangible in v estmen t to pro ductivit y enhancemen t, 2) the amoun t of receiv ed go v ernmen t subsidies and 3) the in terest rate in their long-term loans. The rst t yp e is state-o wned en terprises (SOE). They receiv e go v ernmen t subsidies when making capital in v estmen ts and nance their in tangible in v estmen ts at a lo w er xed rate from lo cal banks. The second t yp e is priv ate-o wned rms (POE). They do not receiv e an y go v ernmen t subsidy and ha v e to nance their in tangible in v estmen ts at a mark et rate from lo cal banks. The mark et in terest rate is alw a ys higher than the xed rate. Those dierences in nancial cost and subsidies pro duce inno v ation disparities among SOEs and POEs. The mo del predicts that POEs mak e less capital and in tangible go o ds in v estmen t and ha v e lo w er in tangible-capital ratio than SOEs. An increase in go v ernmen t subsidies to w ards SOEs increase the total in v estmen ts and raise the mark et in terest rate. Suc h an increase in the mark et in terest rate lo w ers POEs’ in v estmen ts in b oth capital and in tangible go o ds. This also increases the disparit y in the in tangible-capital ratio b et w een SOEs and POEs. I then conduct t w o mediation analyses to do cumen t additional empirical evidence that can supp ort the theoretical mec hanisms whereb y state o wnership inuences rms’ inno v ation activities and pro ductivit y gro wth. Based on the theoretical mo del, I use subsidies and inno v ation capacities 95 (measured b y skill lev els) as mediators in m y rst mediation analysis. My results are consisten t with theoretical predictions. The dierence in subsidies and skill lev els can explain as high as 90% of the observ ed dierence in paten t application b et w een SOEs and POEs. Skill lev els con tribute the most to the dierence in paten t application throughout the sample y ear. Con tribution from subsidies increased after the 2009 scal stim ulus p olicies. In the pre-2009 sample, subsidies can only explain 9.28% of the observ ed dierence in paten t application. Ho w ev er, it can explain 23.98% of the observ ed dierence in paten t application in the p ost-2009 sample. In the second mediation analysis, I use gran ted paten ts as a mediator to analyze ho w subsidies/skill lev els can aect pro ductivit y gro wth. The empirical evidence suggests that 31.4% of subsidies’ impact on pro ductivit y gro wth can b e explained b y an increase in rms’ gran ted paten ts. Th us, the observ ed increase in pro ductivit y gro wth among SOEs after scal stim ulus p olicy can b e attributed to the rise in subsidies they receiv ed. These ndings can partially explain the shrinking pro ductivit y gap b et w een state-o wned and priv ate-o wned rms. Hsieh and Song (2015) found this "catc h up eect" is caused b y reform in state sectors. Findings in our empirical w ork pro vide another explanation. Suc h a "catc h up eect" in SOEs ma y also due to the slo w do wn in the gro wth rate of priv ate rms. The increased nancing cost faced b y priv ate rms forces them to lo w er in v estmen t on b oth capital and in tangible go o ds. The reduction in in tangible in v estmen t is ev en higher than the reduction in capital in v estmen t. Priv ate rms are b eliev ed to b e a driving force in China’s aggregate pro ductivit y gro wth. Song, Storesletten and Zilib otti (2011) nd that ab out 70% of TFP gro wth in the 1998-2005 p erio d is caused b y reallo cating resources from inecien t SOEs to more ecien t priv ate rms. Th us the rev erse of this reallo cation pro cess after 2008 migh t slo w do wn China’s gro wth rate b y hindering inno v ation and pro ductivit y gro wth in priv ate sectors. 96 This pap er is organized as follo ws. Section 2 presen ts data, measuremen t of k ey v ariables and preliminary empirical evidence. Section 3 la ys out a st ylized mo del to explain the empirical ndings and in v estigates the underlying mec hanisms that migh t explain empirical observ ations. Section 4 do cumen ts additional empirical evidence to supp ort the mo del’s predictions. Section 5 concludes. App endices con tain deriv ations and pro ofs in the mo del as w ell as additional empirical results. 4.2 Data 4.2.1 Sample Construction The empirical analysis is based on rm-lev el op eration and inno v ation activit y data from sev eral data source. The rst data source is China’s Ann ual Surv ey of Man ufacturing (ASM). ASM con tains balanced sheet information of all medium to large scale industrial rms with ann ual sales greater than 5 million RMB (appro ximately $800,000). The dataset is cleaned follo wing the metho d outlied in Brandt, V an Biesebro ec k, and Zhang (2014). I k eep rms that op erates at least three consecutiv e y ears and le paten t at least once during the sample p erio d. Firms in this sample are all domestic rms. That is, I remo v e all rms that is registered as foreign rms or its con trolling shareholders are foreign en tities. I obtain the information of paten ts that these rms applied from China’s State In tellectual Prop ert y Oce (SIPO) as w ell as Go ogle P aten ts. SIPO do cumen ts rm’s inno v ation activities from y ear 1985 to y ear 2016. It con tains information on paten t applican ts, application date, tec hnology domains and legal status. ASM and SIPO do not share the same iden tication n um b er for eac h rm. I link these t w o dataset b y using the information on rm names from ASM and the information on paten t applican ts from SIPO, follo wing the metho dology proprosed b y He, T ong, Zhang and He (2016). SIPO do es not con tains enough information on paten t citations, suc h as forw ard citation, 97 bac kw ard citation and self-citation. This mak es it dicult to measure paten t qualit y and v alue. P aten t v alue v aries a lot across tec hnology elds and dieren t paten ts ha v e div erse impacts on a rm’s rev en ue and pro ductivit y gro wth. I then supplemen t the paten t data with paten t citation data from Go ogle P aten ts. Go ogle P aten t do cumen ts detailed information ab out when the paten t is cited and who cites the paten t. This enables me to adjust eac h paten t’s citation based on its tec hnology eld and time windo w in whic h they o ccur. It also enables me to exclude those self-citations whic h migh t bias a paten t’s qualit y measure. After these adjustmen ts, I can compare paten t qualit y o v er time, tec hnology domains and rm size. The matc hed and cleaned ASM-SIPO sample con tains 21,280 medium to large-sized man ufac- turing rms that paten ted at least once during the sample p erio d from y ear 2003 to y ear 2011. Notice that ev en the sample do es not con tains all rms in China, but it is economically large. T otal output of the rms equals around 22% of GDP during the sample p erio d. Their R&D exp enditure equals around 32% of China’s industrial rm’s R&D exp enditure in y ear 2007. 4.2.2 Main V ariables The main v ariables of in terests are inno v ation activities and pro ductivit y gro wth b efore and after the scal stim ulus. Inno v ation activities are measured through R&D exp enditure and paten t appli- cations. ASM only rep orts rm’s R&D exp enditure on y ear 2010 and from y ear 2005 to y ear 2007. Inno v ation activities are mostly measured b y paten t applications and paten t qualities. P aten ts are classied in to three categories under SIPO: 1) in v en tion paten ts whic h ha v e "signi- can t progress" o v er previous tec hnology; 2) utilit y mo del whic h represen t minor impro v emen ts o v er curren t pro ducts and are insucien t to b e gran ted as in v en tion paten ts; and 3) industrial design whic h aim to create aesthetic feelings for consumers. The endogenous gro wth theory suggests that inno v ation are the main driv er for tec hnology and pro ductivit y gro wth. Ho w ev er, b y denition, 98 industrial design paten ts do not con tribute to rm’s tec hnology progress 1 . Th us, I do not include industrial design paten ts in to m y analysis. Due to the lac k of v alid citation data, previous literatures, whic h study inno v ation activities among Chinese rms, only fo cus on inno v ation frequencies (paten t coun ts) rather than paten t qual- ities. It is w ell kno wn that a paten t’s cost and v alue v ary in dieren t tec hnology elds. In addition, dieren t paten ts ha v e div erse impact on rms size and pro ductivit y gro wth. One ma jor inno v ation migh t cost more in v estmen t and could generate more future prots and pro ductivit y gro wth than sev eral minor inno v ations. T o o v ercome this, I construct a panel of paten t citations for eac h gran ted paten t using paten t forw ard citation data from Go ogle paten t. I rst measure a paten t’s qualit y b y the n um b er of forw ard citations it receiv ed in a time windo w of v e y ears from its publication date 2 Next, to mak e paten t qualit y comparable o v er dieren t tec hnology domains, I compute a paten t’s relativ e qualit y b y dividing its citation coun t b y the a v erage citation coun t for a paten t within a 3-digit IPC eld. The relativ e qualit y of paten t j led b y rm f at time t, is q fjt = P ~ t+5 = ~ t citations fj 1 Nt P Nt f=1 P ~ t+5 = ~ t citations j where N t stands for the n um b er of paten ts that led b y Chinese rms in the SIPO oce at time t and ha v e b een gran ted later during m y sample p erio d. As rm migh t not apply paten t eac h y ear, to smo oth its paten t application, I a v erage rm’s paten t application in a three-y ear rolling windo w: Patapp ft = 1 3 t+2 X =t Npt X j=1 q fj 1 In m y sample, more than 70% of industrial design paten ts are ab out c hanges in pac k aging, lab el, clothing/furniture designs, whic h do not impro v e a rm’s pro duction pro cess or pro ductivit y 2 On a v erage, paten ts in SIPO receiv es more than 87% of this ten-y ear-forw ard citations within v e y ear after its publication date. I use a v e-y ear time windo w to accoun t for the truncation issues in the citation data. That is, more recen tly published paten ts ha v e less time to accum ulate citations. 99 Figure 4.1: The Dierence in Inno v ation A ctivities/Qualities b et w een State-Owned and Priv ate- Owned Firms Note: Righ t panel sho ws the a v erage qualit y-adjusted paten t application p er rms in in v en tion category . Lo w er panel are the a v erage qualit y-adjusted utilit y mo dels that ha v e b een led b y eac h paten tees in a giv en y ear. The shaded areas (from y ear 2009 to y ear 2010) are p erio ds when Chinese go v ernmen t started scal stim ulus p olicy that fa v ors State-o wned en terprises. whereNp is the total n um b er paten t applican ts that rm i led in y ear t and are nally gran ted later. T able C.2 in the App endix C rep ort basic statistics on a rm’s inno v ation activities across 2-digit industries. Figure 1 sho ws the quan tit y and trend of qualit y-adjusted paten t application b et w een SOEs (blue solid line) and POEs (red dash line). The y-axis are the a v erage paten t application led b y eac h paten tees in a giv en y ear. Ov erall, paten t applications gro w steadily through y ear 2003 to 2011 in all paten t categories. In general, state-o wned en terprises (SOEs) le more in v en tion and utilit y paten ts than priv ately-o wned en terprises (POEs). The shaded areas are p erio ds when Chinese go v ernmen t started scal stim ulus p olicies that included credit expansion, extra subsidies and p olicy supp ort for rms in high tec hnology eld. Ho w ev er, those p olicies disprop ortionately fa v ors SOEs o v er POEs (Cong, Gao, P on ticelli and Y ang, 2019). It seems that the scal stim ulus p olices did trigger more rapid gro wth in paten t application for SOEs than for POEs. The endogenous gro wth h yp othesis suggests that an increase in inno v ation activit y faster the tec hnology progress. I use the rm-lev el ann ual gro wth rate in T otal F actor Pro ductivit y (TFP) to appro ximate the tec hnology progress. Pro ductivit y is estimated based on the metho d prop osed b y 100 A c k erb erg, Ca v es and F razer. (2015) with Cobb-Douglas pro duction function: ^ y ft = 0 + 1 k ft + 2 l ft +z ft +" ft . Where ^ y ft is the real v alue of v alue added, whic h calculated as real v alue of output min us real v alue of in termediate input plus the real v alue of v alue added tax. ^ k it is the real capital sto c k constructed follo wing Brand V an Biesebro ec k and Zhang (2012). l it is the emplo ymen t. z ft is the estimated pro ductivit y . T o further appro ximate rms’ heterogeneit y in input c hoice, I add additional con trols as rm’s o wnership t yp e, industry xed eect, lo cation and age in the estimation pro cess. Inno v ation activities dep ends on a rm’s nancial status as w ell as inno v ation capacit y . I use in terest rate on loans, subsidies to appro ximate a rm’s nancial status and use skill ratio and R&D eciency to appro ximate inno v ation capacit y . In terest rate on loans is dened as total in terest pa ymen t o v er total debt in a giv en y ear. Firms whic h face less nancial frictions tend to receiv e lo w er in terest rate on loans. In addition, rms with larger subsidies migh t b e less nancially constrained and ha v e more cash a v ailable for in v estmen t than those with less subsidies. Larger rms migh t receiv e more subsidies. In order to mak e subsidies comparable across rm size, I normalize eac h rm’s real v alue of subsidies b y dividing its capital sto c k. Skill ratio is dened as p ercen tage of emplo y ees with college degree and ab o v e. R&D eciency is calculated as Patapp ft RD ft +0:8RD ft1 +0:6RD ft1 . Firms with higher skill ratio or greater R&D eciency are b eliev ed to ha v e higher inno v ation capacit y . 4.2.3 Summary statistics T able 4.1 sho ws the descriptiv e statistics for b oth state-o wned and priv ately-o wned rm v ari- ables b efore and after 2009 scal stim ulus p olices. F ollo wing Song and Hsieh (2015), State-o wned rms (SOEs) are dened as rms either registered as SOEs, or its con trolling shareholders are state/go v ernmen t en tities. As data on skill lev els is only a v ailable in y ear 2004 and data on R&D 101 exp enditure is only a v ailable for three consecutiv e y ears from y ear 2005 to y ear 2007, I only ha v e the pre-2009 statistics on skill ratio and R&D eciency . Gro wth rate in TFP is calculated as c hanges in TFP lev els and then standardized eac h y ear to remo v e y ear eects. External citation p er paten t is the a v erage n um b er of external citation eac h paten t receiv ed within 5 y ears of paten t publication date. Column (1) and (4) list the mean of eac h v ariable among SOEs and column (2) and (5) are those among POEs. Column (3) and (6) lists the dierences in means b et w een SOEs and POEs. Comparing with POEs, SOEs mak e larger R&D exp enditure, receiv e more subsidies and face less external nancing costs. The dierences are ev en larger after 2009. The a v erage paten t qualit y (measured b y external citation p er paten t) is also higher in SOEs. The SOEs’ a v erage TFP lev el is lo w er than POEs’ b efore 2009 and higher after 2009. The a v erage pro ductivit y gro wth rate are alw a ys higher among SOEs. SOEs’ skill ratio and R&D eciency are all higher than POEs, reecting that, on a v erage, SOEs ma y ha v e b etter inno v ation capacit y . 4.2.4 Inno v ation and Productivity Gap T o estimate the lev el dierence in inno v ation activit y b et w een SOEs and POEs, I rst run a panel regression where R&D exp enditure or paten t application is regressed on a SOE dumm y . The estimated regression is: y fjt = 0p + jgt + 1p SOE fjt + 0 xp fjt +" fjt (4.1) wherey fjt denotes R&D exp enditure or paten t application of rm f in industryj at timet. SOE ft is a dumm y v ariable whic h equals 1 if a rm is classied as state-o wned en terprise at time t. jt are the y ear-industry-lo cation xed eect. I includes jt to remo v e an y unobserv able y ear, industry and lo cation-sp ecic demand shifter. ft are additional con trol v ariables includes capital in tensit y , rm 102 T able 4.1: Summary Statistics for Merged Sample Pre 2009 P ost 2009 (1) (2) (3) (4) (5) (6) SOE POE di in mean SOE POE di in mean R&D Capital Sto c k 0.0312 0.0134 0.0178 0.0330 0.0098 0.0232 (0.5209) (0.3179) (0.0050) (0.3210) (0.1596) (0.0071) in terest fee total debt 0.0186 0.0320 -0.0134 0.0179 0.0359 -0.0180 (0.0386) (0.0702) (0.0004) (0.0450) (0.0812) (0.0007) subsidies Capital Sto c k 0.0118 0.0115 0.0003 0.0123 0.0054 0.0069 (0.0557) (0.0612) (0.0004) (0.0527) (0.0345) (0.0007) Ex. citation p er paten t 1.2154 1.1758 0.0396 1.2686 1.1736 0.0950 (0.8446) (0.8962) (0.0124) (0.9459) (0.8196) (0.0190) log(TFP ) 0.6150 0.7443 -0.1293 0.9746 0.9274 0.0472 1.0905 0.9850 0.0084 1.1461 1.0621 0.0174 gro wth in TFP 0.0108 -0.0032 0.0140 0.0130 -0.0023 0.0152 (0.2230) (0.2157) (0.0017) (0.3201) (0.3065) (0.0049) skill ratio 0.2499 0.1689 0.0810 (0.1812) (0.1854) (0.0031) R&D eciency 0.4642 0.4471 0.0171 (1.9551) (1.9748) (0.0284) Note: Descriptiv e statistics for the merged AMS-P aten t sample from y ear 2003 to y ear 2011. Exclude all foreign o wned rms, rms that c hanged o wnership more than t wice and rms that op erates less than 3 consecutiv e y ears. Skill ratio data is only a v ailable in y ear 2004. R&D data is only a v ailable in y ear 2010 and from y ear 2005 to y ear 2007. See section 4.2.2 for the construction of eac h v ariable The brac k et under column (1), (2), (4) and (5) are standard deviation for eac h observ ations. The brac k et under column (3) and (6) are standard deviation for the t-test in mean b et w een SOEs and POEs. 103 size (measured b y log of emplo ymen t) and rm age. Standard errors are clustered at y ear-industry- lo cation lev el to absort an y unobserv ed driv ers that are common across rms within lo cations within sectors within a y ear. I run this panel regression in t w o p erio ds: b efore 2009 scal stim ulus p olicies (y ear 2003 to y ear 2008) and after 2009 scal stim ulus p olicies (y ear 2009 to y ear 2011). 1p reects the inno v ation premium in SOEs. Column (1) and (5) in table 4.2 do cumen ts the results. Before 2009, SOEs tend to inno v ate more and mak e more R&D in v estmen t than POEs. The dierence in paten t application is not signican t b efore 2009. Ho w ev er, after 2009, the dierence in R&D in v estmen t and paten t applications b ecome b oth signican t and larger. T o further assess these lev el dierences in inno v ation activit y and R&D in v estmen t, I then include extra con trol v ariables, whic h, b y theory can con tribute to a rm’s paten t application as w ell as R&D in v estmen ts. Based on previous literatures on inno v ation 3 , rms with higher inno v ation capacit y , face lo w er nancing cost or receiv e more go v ernmen t supp ort tend to mak e inno v ation in v estmen t than those with lo w er inno v ation capacit y , face higher nancing cost or receiv e less go v ernmen t supp ort. I use receiv ed subsidies to pro xy go v ernmen t supp ort. I then run a set of follo wing regressions: y fjt = 0p + jgt + ~ 1p SOE fjt + 2p sub fjt1 + 0 xp fjt +" fjt y fjt = 0p + jgt + ^ 1p SOE fjt + 2p sub fjt1 + 3p SR fj + 0 xp fjt +" fjt y fjt = 0p + jgt + 1p SOE fjt + 2p sub fjt1 + 3p SR fj + 4p Int fjt + 0 xp fjt +" fjt (4.2) where sub fjt1 is the amoun t of subsidies rm f receiv ed at time t-1. SR is the skill ratio. Since the data on skill ratio is only observ able in y ear 2004. SR can b e view ed as a rm xed eects. Int is the in terest pa ymen t to total debt ratio, whic h reecting the nancing cost of the rm. The co ecien t ~ 1p reects the dierence in y fjt after con trolling one-y ear lagged subsidies. And the 3 See A cemoglu, Ak cigit, Alp, Blo om, and Kerr (2019) and Hall and Lerner (2010) for inno v ation capacit y , Bro wn, F azzari and P eterson (2009) and Bro wn, Martinsson and P etersen (2013) for nancing cost 104 dierence b et w een ~ 1p and 1p do cumen ts the subsidy premium. That is, on a v erage, ho w m uc h dierence in y fjt b et w een SOEs and POEs can b e explained b y dieren t lev els of subsidies they receiv ed. Similarly , the dierence b et w een ^ 1p and ~ 1p do cumen ts the skill premium. Column (2) to column (4) and column (6) to column (8) presen t the regression results. Consisten t with our prediction that skill ratio and subsidies are p ositiv ely asso ciated with a rm’s R&D in v estmen t and paten t applications. Once adding additional con trols, the impact from state o wnership on b oth R&D in v estmen t and paten t applications are reduced. The co ecien ts 1p s in Column (3) and (4) sho w that b efore 2009, SOEs tends to inno v ate signican tly less than POEs after con trolling skill lev els. That is, the dierence in inno v ation activities I observ ed in gure 4.1 is mainly driv en b y the dieren t skill lev els. If priv ately-o wned rms could hire as man y highly- educated emplo y ees (emplo y ees with college degree and ab o v e) as state-o wned rms, they w ould mak e more R&D in v estmen t and pro duce more paten ts in eac h y ear. Comparing with skill lev el, subsidies and in terest rate do not ha v e suc h large impact on the lev el dierence. The dierences are small b et w een ~ 1p and and b et w een 1p and . One explanation is that rms migh t not con v ert all of its subsidies in to R&D in v estmen t and paten t applications. In fact, most of the subsidies are used to nance ph ysical in v estmen t (Cong, Gao, P on ticelli and Y ang (2019) and Chen, Gao, Higgins, W aggoner and Zha (2016)). Bai, Hsieh and Song (2016) sho w that the aggregate in v estmen t rate increased b y roughly 5% in 2009 and 2010, whic h is ab out 80% of China’s 4 trillion Y uan stim ulus pac k age. The impact from in terest rate is am biguous. In terest fee to total debt ratio is p ositiv ely asso ciated with paten t application b efore 2009 and R&D in v estmen t to capital ratio during the whole sample. It is only negativ ely asso ciated with paten t application after 2009. One p ossible explanations is that in terest fee to total debt ratio cannot reect a rm’s nancing cost. The total debt is y ear-end v alue, whereas in terest pa ymen t is the pa ymen t a rm made throughout the y ear. It is p ossible that nancially strong rms can repa y the debt b efore scal y ear end. Using y ear-end 105 v alue of total debt migh t underestimate the actual amoun t of debt a rm has during that y ear, and th us o v erestimate the nancing cost for nancially strong rms that ha v e suc h abilit y to repa y debt b efore the scal y ear ends. If those nancially strong rms mak e more R&D in v estmen t, w e migh t nd a p ositiv e asso ciation b et w een R&D in v estmen t and in terest rate to total debt ratio. 106 T able 4.2: Inno v ation Gaps b et w een SOEs and POEs pre 2009 p ost 2009 P anel A: dep enden t v ariable: Application in in v en tion an utilit y paten ts (1) (2) (3) (4) (5) (6) (7) (8) SOE 0:0278 0:0145 0:0467 0:0449 0:0830 0:0737 0:0102 0:0044 (0:0174) (0:0184) (0:0178) (0:0178) (0:0312) (0:0347) (0:0343) (0:0348) log(subsidies) 1 0:0679 0:0522 0:0523 0:1085 0:0925 0:0928 (0:0077) (0:0068) (0:0068) (0:0100) (0:0098) (0:0098) Skill Ratio 1:1037 1:1025 1:1891 1:1914 (0:0439) (0:0439) (0:0699) (0:0700) in terest fee total debt 0:0116 0:2139 (0:0039) (0:0917) Obs 106; 961 94; 800 94; 798 94; 356 39; 021 30; 727 30; 727 30; 335 R 2 0:2177 0:2242 0:2501 0:2507 0:1874 0:2026 0:2233 0:2239 P anel B: dep enden t v ariable: R&D in v estmen t to capital sto c k ratio (1) (2) (3) (4) (5) (6) (7) (8) SOE 0:0332 0:0300 0:0113 0:0117 0:0357 0:0202 0:0013 0:0023 (0:0106) (0:0102) (0:0107) (0:0107) (0:0106) (0:0088) (0:0111) (0:0109) log(subsidies) 1 0:0213 0:0159 0:0159 0:0143 0:0101 0:0103 (0:0034) (0:0027) (0:0027) (0:0038) (0:0030) (0:0031) Skill Ratio 0:3204 0:3215 0:2213 0:2229 (0:0457) (0:0457) (0:0589) (0:0591) in terest fee total debt 0:0792 0:0922 (0:0767) (0:0689) Obs 56; 541 53; 307 53; 307 53; 300 13; 172 10; 667 10; 667 10; 666 R 2 0:0600 0:0632 0:0807 0:0808 0:0469 0:0425 0:0595 0:0597 Dep enden t v ariable in the rst panel is R&D-capital sto c k ratio. R&D in v estmen t data only a v ailable in y ear 2010 and from y ear 2005 to y ear 2007. Dep enden t v ariable in the second panel is paten t application in in v en tion and utilit y . In eac h regression, capital in tensit y , rm age, size (measured as log of emplo ymen t) and xed eect of geographical lo cation, industry and y ear are included but not rep orted. In addition, pre-sample mean of paten t application is con trolled in regressions in the second panel. Robust standard errors clustered at y ear-lo cation-industry lev el are rep orted in paren these. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . 107 T o analyze the c hanges in lev el dierence eac h y ear, I estimate a set of equations similar to regression 4.1 and 4.2 y ear-b y-y ear. Figure 4.2 presen ts the results. The upp er left (righ t) panel sho ws the lev el dierence in applications of in v en tion (utilit y mo del) paten ts. The lo w er left panel sho ws the lev el dierence in paten t application to capital ratios. The lo w er righ t panel sho ws the lev el dierence in TFP . The solid blac k line is the estimated OLS co ecien ts 1t from regression 4.1. The dashed blue line is the estimated OLS co ecien ts 1t after con trolling skill ratio. The red dash-dot line is the estimated OLS co ecien t ^ 1t after con trolling b oth skill ratio and one-y ear lag of receiv ed subsidies. Eac h colored shaded area is eac h 1t ’s corresp onding condence in terv al (2 standard deviation). The upp er panel of gure 4.2 sho ws that the inno v ation gap b et w een SOEs and POEs ha v e enlarged since y ear 2007. Before 2009, most of these enlarged gap can b e explained b y the dierence in skill lev els. Ho w ev er, after 2009, subsidies start pla y an imp ortan t role in explain enlarged inno v ation gaps. The red dash-dot line lies w ell b elo w the blue dash line in upp er left panel in after y ear 2009. As do cumen ted in most literatures that state-o wned rms are less pro ductiv e than domestically priv ate-o wned rms (see Kleno w and Hsieh (2009), Brandt, Biesebro ec k and Zhang (2012), Hsieh and Song (2015)). Ho w ev er, this pro ductivit y gap has b een shrinking throughout y ears. As sho wn in the lo w er righ t panel, co ecien ts on SOE b ecame p ositiv e starting from y ear 2010. This "catc h up" eect in pro ductivit y is w ell do cumen ted in Hsieh and Song (2015). Some of these "catc h up" eect migh t result from China’s strategy on priv atization of SOEs. Less pro ductiv e rms has switc hed from b eing state o wned to priv ately o wned 4 . And more pro ductiv e priv ate rms migh t b e re-b ough t b y the go v ernmen t after its stim ulus pac k age in 2008. Those less pro ductiv e rms migh t reduce the a v erage pro ductivit y in the priv ate sectors in later p erio d (F ang, He and Li (2018)). T o address this selection bias problem, I only include rms with "constan t o wnership" in eac h of 4 In our sample, 20% of rms switc hed from SOE to POE and 9.5% of rms switc hed from POE to SOE. 108 Figure 4.2: The Dierence in Inno v ation A ctivities/Qualities b et w een State-Owned and Priv ate- Owned Firms Note: Eac h panel sho ws the estimated OLS co ecien t p1 s. The upp er left (righ t) panel sho ws the lev el dierence in applications of in v en tion (utilit y mo del) paten ts. The lo w er left panel sho ws the lev el dierence in paten t application to capital ratios. The lo w er righ t panel sho ws the lev el dierence in TFP . 109 regression. Th us gure 4.2 implies that the shrinking pro ductivit y gap migh t due to the fact that SOEs engage in more pro ductivit y enhancing inno v ation activities than POEs. Endogenous gro wth theory suggests that rms mak e more inno v ation in v estmen t enjo ys higher tec hnology progress, whic h is measured as pro ductivit y gro wth in this pap er. Hence, the dierence in pro ductivit y gap b ecome insignican t after skill lev el and subsidies are con trolled. 4.3 Theoretical F ramework In this section, I dev elop a st ylized mo del to discuss the in teraction b et w een credit reallo cation and rm’s c hoices among capital in v estmen t and in tangible in v estmen t. I use this mo del to explore un- derlying mec hanisms through whic h I can explain k ey empirical ndings that ha v e b een do cumen ted in previous section. 4.3.1 Model environmen t In this econom y , there is a single consumption go o ds that is pro duced b y a represen tativ e nal go o ds pro ducer with pro duction tec hnology Y t = R 1 0 y 1 1 it di 1 , where y it is the quan tit y of in termediate go o ds that is pro duced b y eac h in termediate go o ds pro ducer. > 1 go v erns the substitutabilit y b et w een dieren t in termediate go o ds. The standard optimization of nal go o ds pro ducer giv es a demand function of eac h in termediate go o ds as q it =p it . I assume, the econom y is p opulated b y t w o-p erio d-liv ed en trepreneurs, whic h are uniformly distributed in a unit circle [0,1]. The en trepreneur is b orn at time t. A t eac h p erio d, the en trepreneur pro duces in termediate go o ds and consumes nal go o ds. His preference is giv en b y: u it =c i;t +c i;t+1 110 There is also a represen tativ e t w o-p erio d-liv ed w ork er that b orn at time t with lab or endo wmen t L t . The w ork er only w orks in the rst p erio d and retires in the second p erio d. F ollo wing Song, Storesletten and Zilib otti (2011), I assume there are t w o t yp es of en trepreneurs that engage in in termediate go o ds pro duction. The k ey feature of the mo del is that those t w o t yp es of en trepreneurs dier in its access to the credit mark et. The rst half of the p opulation consists of rms that ha v e easy access to the bank loans and can receiv e subsidies from the go v ernmen t. I call these rms "S-rms", whic h is stands for State-o wned en terprise. The other half of the p opulation consists of rms that do not receiv e an y go v ernmen t subsidies and ha v e to b orro w at the mark et rate. I call these rms "P-rms", whic h is stands for Priv ate-o wned en terprise. Without loss of generalit y , I do not allo w switc hing b et w een these t w o t yp es of en trepreneurs. T ec hnology In the b eginning of rst p erio d, the en trepreneur has access to t w o tec hnologies that allo ws him to hire w ork ers to pro duce capital go o ds and in tangible go o ds. W ork ers are all hired at the mark et w age w t . The capital go o ds can b e pro duced immediately b y w ork ers and installed for pro duction in p erio d t andt + 1. Assume the capital go o ds w on’t depreciate b y the end of p erio d t, but b ecome fully depreciated at the end of p erio d t + 1. The in tangible go o ds tak es one p erio d to complete and is used to impro v e the rm’s pro ductivit y in the second p erio d. After the installmen t of capital, it cannot b e con v erted to in tangible go o ds during the en trepreneur’s life. Similar in the spirit to those in Aghion, Banerjee and Mano v a (2010), I assume the tec hnology of pro ducing capital go o ds b e k it = k;t l k;it . Here,l k;it is the amoun t of w ork er emplo y ed to pro duce capital go o ds k it and k;t is the corresp onding lab or pro ductivit y . k it is the amoun t of capital go o ds pro duced and installed in a rm. Similarly , the tec hnology of pro ducing in tangible go o ds is z it = z;t l z;it , with lab or input denoted as l z;it and corresp onding pro ductivit y z;t . Without loss an y generalit y , I assume the tec hnology k;t =z;t = > 0. So w ork ers are freely mo v able across these t w o pro duction sectors. 111 The tec hnology for pro ducing in termediate go o ds at eac h p erio d can b e written as: y it = it f(k it ). F rom the nal go o ds pro ducer’s optimization problem, the rev en ue pro duction function for eac h in termediate go o ds pro ducer can b e written as y it = it k ~ 1 =A it k it where it is an exogenous pro ductivit y . I dene A it = 1 it and = ~ (1) go v erns the curv ature of in termediate go o ds pro duction function. The in tangible go o ds aims to impro v e rm’s pro ductivit y in the second p erio d. Supp ose with the in v estmen t of z it , rm’s pro ductivit y in the second p erio d can b e impro v ed to: A it+1 =A it (1 +g(z it )) =A it +A it z it wherez it is the in tangible go o ds and < 1 2 go v erns the curv ature of the return function of in tangible go o ds. Assume < 1 2 and < 1 2 5 . The inno v ation step A it z it is mo deled prop ortional to curren t tec hnology . This sp ecication has b een used in Aghion, Harris, Ho witt and Vic k ers (2001) and A cemoglu and A c kigit (2012), to reect that higher pro ductiv e rms enjo ys higher return from the same unit of inno v ation input. < 1 is a scale parameter that captures the eectiv e of inno v ation in v estmen t. One can think of as the probabilit y that a rm’s in tangible input successfully impro v e its pro ductivit y lev el b y z it . 1 , hence, reect the probabilit y of failure in conducting inno v ation activit y . The parameter restriction < 1 ensures that the marginal return from inno v ation is decreasing with resp ect to in tangible go o ds input. F or simplicit y , I assume A it = A jt = A s;t for state-o wned rms and A it =A jt =A p;t for priv ate-o wned rms. That is, eac h rm with the same t yp e is b orn with the same pro ductivit y lev el. 5 See App endix for the deriv ation of parameter restrictions 112 State-o wned En terprise (SOE) Eac h SOE liv es for t w o p erio d. A t the b eginning of the rst p erio d, it emplo y ees l s;it w ork ers at the w age rate w t to pro duce capital go o ds k s;it and in tangible go o ds z s;it . The w age should b e paid b efore the pro duction tak e place at p erio d t. Eac h SOE can b orro w from the represen tativ e bank at a xed in terest rate 1 for short-term loans and R for long-term loans. The short-term loans are used to pa y w ork ers that are hired in pro ducing capital go o ds and the long-term loans are used to pa y w ork ers that are hired in pro ducing in tangible go o ds. The short-term loan m ust b e paid during p erio d t, so I normalized its in terest rate in to 1. The long-term loans can b e paid at the end of p erio d t + 1, with in terest rate R = 1 . That is, the in terest rate equals the discoun t rate. The problem of eac h SOE can b e the written as: max k s;it ;z s;it A s;t f(k s;it ) w t (k s;it s it ) +A s;t [1 +g(z s;it )]f(k s;it )R w t z s;it The rst term is the rev en ue collected at the end of p erio d t and the second term is the short-term loan paid bac k to the bank after pro duction tak es place. Supp ose SOEs can receiv e subsidies from lo cal go v ernmen ts it <k s;it . So it only b orro wsk it s it amoun t from the bank. Assume this subsidy is prop ortional to rm’s capital in v estmen t. That is s it = t k s;it with t 2 [0; ). Hence, the total short-term loan initiated b y eac h SOE is (1 t )k s;it . The third term is the rev en ue collected at the end of p erio d t + 1 and the last term is the long-term loan that paid bac k to the bank at the in terest rate of R. It is straigh t forw ard to sho w that giv en w t , the SOE’s optimal c hoices of capital go o ds and in tangible go o ds in v estmen t are pinned do wn b y the follo wing rst order conditions: A s;t f 0 (k s;it ) [1 + +g(z s;it )] =q t (1 t ) A s;t g 0 (z s;it )f(k s;it ) =Rq t 113 where q t wt can b e view ed as the price of capital go o ds and in tangible go o ds. Priv ate o wned Firms (POE) Similar to SOEs, eac h POE liv es for t w o p erio d. A t the b eginning of the rst p erio d, it emplo y ees l p;it w ork ers at the w age rate w t to pro duce capital go o ds k p;it and in tangible go o ds z s;it . The w age should b e paid b efore the pro duction tak e place at p erio d t. Eac h POE can b orro w from the represen tativ e bank at in terest rate 1 for short-term loans and a mark et- determined in terest rate R t for long-term loans. The long-term loans can b e paid at the end of p erio dt+1, with in terest rateR t that is determined b y the bank via its optimization problem. The problem of eac h POE can b e the written as: max k p;it ;z p;it A p;t f(k p;it ) w t k p;it +A p;t [1 +g(z p;it )]f(k p;it )R t w t z p;it The rst term is the rev en ue collected at the end of p erio d t and the second term is the short-term loan paid bac k to the bank after pro duction tak es place. The third term is the rev en ue collected at the end of p erio d t + 1 and the last term is the long-term loan that paid bac k to the bank at the in terest rate of R t . It is straigh t forw ard to sho w that giv en q t = wt and R t , the POE’s optimal c hoices of capital go o ds and in tangible go o ds in v estmen t are pinned do wn b y the follo wing rst order conditions: A p;t f 0 (k p;it ) [1 + +g(z p;it )] =q t A p;t g 0 (z p;it )f(k p;it ) =R t q t W ork er’s problem Similar to eac h en trepreneurs, w ork ers ha v e linear utilit y function and liv e only for t w o p erio d. Y oung w ork er w orks at p erio d t and dep osit their sa vings, denoted as s w;t , in to the represen tativ e bank at a xed in terest rate R. W ork ers cannot b orro w and they cannot lend to neither state-o wned en terprise nor priv ate-o wned en terprise. This assumption is consisten t 114 with Chang et al (2015) and the fact that the banking sector in China pla ys an imp ortan t role in business lending. W ork ers pro vide lab or to those t w o t yp es of rms and earn at w age rate w t during p erio d t. A t p erio dt + 1, old w ork ers are retired and consume their sa vings. Assume the total lab or endo wmen t is L t , then w ork ers’ budget constrain ts at p erio d t is: c w;t =w t L t s w;t . Their budget constrain ts at p erio d t + 1 is then: c w;t+1 = Rs w;t . With linear utilit y function and the in terest rate R = 1 , w ork ers’ life time utilit y can b e written as: c w;t +c w;t+1 =w t L t s w;t +Rs w;t =w t L t Bank’s problem The bank also liv es for t w o p erio ds with endo wmen t E at time t. It uses this endo wmen t to nance short-term and long-term debts for b oth state-o wned en terprise and priv ate- o wned en terprise. A t p erio d t it also receiv es dep osit from s w;t from w ork ers. The bank’s in terest rates on short-term debts for b oth t yp es for rms are xed at 1. The bank’s in terest rate on long- term debt for SOEs is xed at the discoun t rate R. Ho w ev er, the loan rate on long-term debt for POEs is R t . Similar to Chang, Chen, W aggoner and Zha (2015), I assume the bank is sub ject to a con v ex pro cessing cost function of long-term loans that lend to b oth POEs and SOEs. The bank’s ob jectiv e function is: max Bp;t;Bs;t =B p;t B s;t C( ~ B t ) +s w;t + [RB s;t +R t B p;t Rs w;t ] where B p;t =q t z p;t and B s;t =q t z s;t are long-term loans that lend out to POEs and SOEs resp ec- tiv ely . B t = B p;t +B s;t are total long-term loans that len t out. And ~ B t = Bt qt . Notice that since short-term loans are paid bac k during the same p erio d, they do not en ter bank’s ob jectiv e function. 115 C( ~ B t ) is the con v ex pro cessing cost function of long-term loans. I assume a quadratic cost function C( ~ B t ) = 2 ~ B 2 with 2 (0; 1). Since R = 1 , the bank’s ob jectiv e function can b e simplied as: max Bp;t =B p;t C( ~ B t )R t B p;t The mark et in terest rate R t is determined b y the bank’s rst-order condition: R t = 1 + 1 C 0 ( ~ B t ) As C 0 ()> 0 and C 00 ()> 0, this mark et in terest rate R t is higher than xed rate R and increases with the total amoun t of long-term debt. 4.3.2 Theoretical results In this section, I rst discuss the parameter and function assumption for eac h t yp e of rm’s opti- mization problem. I then discuss the mo del’s implication on in tangible go o ds’s in v estmen t across dieren t t yp es of rms. Assumption I 1 2 , 1 2 and s p Under assumption I, the second order conditions are satised for b oth SOE and POE’s opti- mization problem 6 . measures the capital share of income in eac h in termediate pro ducer. The estimated capital share of income among Chinese man ufacturing sectors uctuates b et w een 46% to 50% from 1978 to 2005 (Bai, Hsieh and Qian, 2010). This pro vides some empirical supp ort for the assumption I. s (or p ) is the probabilit y that an in tangible in v estmen t impro v es a SOE’s (or a POE’s) pro ductivit y in the second p erio d. It can also b e view ed as a scale parameter in exp ected 6 The assumption 1 2 and 1 2 is used to guaran tee that the determinan ts of Hessian Matrix in rm’s optimization problem is p ositiv e. See App endix C.1.1 for details 116 return for in tangible in v estmen t. The assumption s p indicates that for the same amoun t of in tangible in v estmen t, the return is higher in SOEs than those in POEs. If paten t application is used to appro ximate in tangible in v estmen t and if paten t citation is used to appro ximate paten t qualit y whic h measures the impro v emen t in a rm’s pro ductivit y , higher indicates higher qualit y for eac h paten t. The a v erage paten t citation 7 for eac h paten t led b y SOE is 1.225 from y ear 2003 to 2011, and the a v erage paten t citation led b y POE is 1.158 for the same sample p erio d. Hence, this empirical evidence pro vides some supp ort for assumption I. Assumption I I The go v ernmen t subsidies t lo cates in a region: t 2 [; ], where maxf0; 1 As Ap 1 g and 1+ Prop osition I Under assumption I I, SOEs mak e more capital in v estmen t and in tangible in v est- men t than POEs: z p;t <z s;t ;k p;t <k s;t Pr o of. This can b e easily seen through SOE and POEs’ rst order conditions A p g 0 (z p;t )f(k p;t ) = A s (1 +C 0 (B))g 0 (z s;t )f(k s;t ) and A s f 0 (k s;t )[1 + +g(z s;t )] = A p (1 t )f(k p;t )[1 + +g(z p;t )]. See App endix C.1.3 for details. In tuitiv ely , as R t = 1 + ~ B > 1 = R. The cost for in tangible in v estmen t is higher for POEs, this reduce its incen tiv e to in v estmen t in in tangible go o ds. As the return on capital in v estmen t con tains t w o part: the increase in curren t pro duction A t f 0 (k) and the increase in marginal return on in tangible go o ds A t f 0 (k)[1 +g(z s;t )]. The higher cost for long-term debt not only reduce the return on in tangible in v estmen t, but also reduce the return on capital in v estmen t (through the 7 P aten t citation is adjusted b y application y ear and tec hnology led. Suc h adjustmen t mak e paten t comparable across rms in dieren t sectors. See data section for details 117 second part) as w ell. Th us, POEs mak e less in v estmen t in b oth in tangible and capital go o ds than SOEs. Prop osition I I Under assumption I and I I, the in tangible-to-in v estmen t ratio is higher among SOEs and lo w er among POEs. z s;t k s;t > z p;t k p;t Pr o of. See App endix C.1.4 for detail. In the equilibrium, the in tangible-to-in v estmen t ratio can b e written as: z s;t k s;t =(1) s (1 +)z s;t + 1 z p;t k p;t = p 1 +(z s;t +z p;t ) (1 +)z s;t + 1 By prop osition I, z s;t >z p;t . Hence z s;t <z p;t . As s p , it m ust b e true that s p . Hence, one sucien t condition for z s;t k s;t > z p;t k p;t is that 1 1 < 1 +(z s;t +z p;t ). As b y lab or mark et clearing condition z s;t +z p;t < , 1 1 < 1 +(z p +z s ) implies: < 1+ . Th us if assumption I I holds, it m ust b e true that: z s;t k s;t > z p;t k p;t . Prop osition I I I Under assumption I and I I, in an equilibrium, an increase in go v ernmen t subsi- dies: 1. raise in v estmen t in capital and in tangible go o ds among state-o wned en terprise 2. reduce in v estmen t in capital and in tangible go o ds among priv ate-o wned en terprise 3. increase the in tangible-capital ratio for SOEs and reduce in tangible-capital ratio for POEs. Pr o of. See App endix C.1.5 for detail Prop osition I I I implies that a scal stim ulus plan, whic h disprop ortionately fa v ors SOEs, will in- crease the disparit y in inno v ation activities (measured as in tangible in v estmen t) b et w een SOEs and 118 POEs. In tuitiv ely , an increase in go v ernmen t subsidies lo w ers the eectiv e cost of capital in v estmen t for SOEs, increasing SOE’s capital in v estmen t. Suc h increase also raise the exp ected return on in- no v ation. Hence, the in tangible in v estmen t increases among SOEs. This raise the long-term loans in a lo cal bank. As the bank’s loan pro cessing cost increase with long-term loans, the mark et in terest rate,R t = 1 (1+(z s;t +z p;t ) raised, making POEs’s in tangible in v estmen t more costly . Hence, in an equilibrium, the in tangible in v estmen ts in POEs decrease, whic h also reduces the marginal return on POEs’ ph ysical capital in v estmen ts. Th us, with an increase in go v ernmen t subsidies to w ards SOEs, POEs in v estmen t in b oth capital and in tangible go o ds drop, whereas SOEs in v estmen t in b oth capital and in tangible increase. This prop osition also implies that 1) the increase in SOEs’ in tangible in v estmen t is higher than the increase in SOEs’ capital in v estmen t, and 2) the drop in POEs in tangible in v estmen t is larger than the drop in its capital in v estmen t. This means the capital in v estmen t is relativ ely less sensitiv e to subsidies than in tangible in v estmen t. The k ey comp onen t that generate this implication is that capital and in tangible go o ds are complemen tary input in the second p erio d and the curv ature in in tangible go o ds return function is steep. The credit reallo cation increases the in tangible-capital ratio among SOEs and at the same time reduce the in tangible-capital ratio among POEs. The pro ductivit y gro wth for eac h rm can b e written as: A i;t+1 A i;t = 1 + i z i ; i2fs;pg Prop osition I I I predicts an increase in SOEs pro ductivit y gro wth and a drop in POEs pro ductivit y gro wth after an increase in go v ernmen t subsidies to w ards SOEs. This is consisten t with the empirical evidence among Chinese rms that SOEs gro w relativ ely faster than POEs. And suc h dierence b ecome ev en higher after the nancial crisis and 4 trillion RMB scal stim ulus plan. 119 4.4 Additional Empirical Evidence Section 2 sho ws the lev el dierence in inno v ation and pro ductivit y b et w een SOEs and POEs b e- fore and after 2009 scal stim ulus p olicies. In this section, based on the theoretical prediction, I decomp ose those dierence in to sev eral factors suc h as inno v ation capacit y and nancial status. I then discuss eac h factor’s role in explain inno v ation and pro ductivit y disparit y b et w een SOEs and POEs. 4.4.1 Decomposition of Contributions to Innov ation Gaps: Mediation Analysis In this section, I conduct a mediation analysis to determine whether skill ratio, subsidies and nancing cost are eectiv e mec hanism through whic h state o wnership inuence inno v ation activities suc h as paten t applications and R&D in v estmen t. Figure 4.3 represen ts the framew ork for the mediation analysis. P ath c on the upp er panel of gure 4.3 represen t the total eect of state o wnership on the dep enden t v ariable Y inno v ation activities. P ath as (a 1 ,a 2 anda 3 ) on the lo w er panel of gure 4.3 represen ts the eect of state o wnership on eac h mediator M i . P ath bs (b 1 , b 2 and b 3 ) on the lo w er panel of gure 4.3 represen ts the eect of eac h mediator M i on the dep enden t v ariable Y inno v ation activities. P ath c 0 represen ts the direct eect of the indep enden t v ariables on Y after con trolling the eect from mediators. In the statistical mo dels, path as are deriv ed from regressing eac h mediator skill lev el, subsidies and in terest rate on the SOE dumm y . That is: M i ft = 0 +a i SOE ft +controls ft +" m ft . The eect of eac h M i on Y and the eect of SOE on Y are deriv ed from regressing the outcome v ariables on SOE dumm y and mediators. That is, Y ft = 1 +c 0 SOE ft + P 3 i=1 b i M i ft +controls ft +" Y ft . controls are additional con trol v ariables that migh t aect mediators and the outcome. I add capital in tensit y , log of emplo ymen t, rm age and industry-y ear-lo cation xed eect as con trols. The indirect eect ofX i onY through mediator M i isa i b i . The total indirect eect of X i onY is then P 3 i=1 a i b i . 120 Figure 4.3: Mediation Analysis: Inno v ation A ctivit y T able 4.3 and 4.4 presen ts the results of indirect eects and direct eects. The total eect of SOE on outcome Y can then b e computed as c =c 0 + P 3 i=1 a i b i . Column (1) in T able 4.3 sho ws the direct eects of SOE o wnership on a rm’s qualit y-adjusted paten t application. SOE has negativ e direct impact on paten t application b efore 2009 and p ositiv e direct impact on paten t application after 2009 8 . Column (2) sho ws an OLS regression of eac h mediator on a SOE dumm y . State o wnership has a p ositiv e eect on b oth skill ratio and subsidies, ev en after con trolling rms size, age, capital in tensit y and industry-y ear-lo cation eects. It has a negativ e eect on nancing cost (measured as in terest rate). Column (3) represen ts the results of paten t application on mediators (path b 1 , b 2 and b 3 ) and the SOE dumm y (path c 0 ), after con trol- ling rm size, age, capital in tensit y and industry-y ear-lo cation eects. Consisten t with theoretical prediction that subsidies and skill lev el are p ositiv ely asso ciated with a rm’s inno v ation output. In terest rate p ositiv ely asso ciated with a rm’s paten t application b efore 2009 and negativ ely asso- ciated a rm’s paten t application after 2009. I do not nd a statistically signican t indirect eect of SOE on paten t application via in terest rate. One explanation w ould b e the measuremen t issues in in terest rate whic h is discussed in section 4.1. That is, the nancing cost w ould b e o v erestimated 8 I only include rms with constan t o wnership in this regression. So rev erse causalit y i.e. paten t applica- tion/subsidies/skill ratio ha v e p ositiv e impact on o wnership do es not exist. 121 T able 4.3: Mediation Analysis - P aten t Application (1) (2) (3) (4) (5) (6) c 0 a b ab 95% CI on ab INE% P anel A: Pre 2009 Sample In terest Rate 0:0459 0:0108 0:0191 0:0002 [0:0018; 0:0014] 0:0028 (0:0092) (0:0036) (0:0158) (0:0078) Subsidies 0:0459 0:1274 0:0546 0:0070 [0:0058; 0:0081] 0:0928 (0:0092) (0:0097) (0:0031) (0:0006) Skill Lev el 0:0459 0:0619 1:1015 0:0682 [0:0631; 0:0733] 0:9099 (0:0092) (0:0016) (0:0190) (0:0026) P anel B: P ost 2009 Sample In terest Rate 0:0043 0:0134 0:2218 0:0030 [0:0006; 0:0053] 0:0289 (0:0218) (0:0012) (0:0959) (0:0012) Subsidies 0:0043 0:2637 0:0935 0:0247 [0:0196; 0:0298] 0:2398 (0:0218) (0:0181) (0:0069) (0:0026) Skill Lev el 0:0043 0:0619 1:2146 0:0752 [0:0644; 0:0860] 0:7313 (0:0218) (0:0030) (0:0415) (0:0055) Note: Mediation Analysis for the merged ASM-SIPO sample from y ear 2003 to y ear 2011. Exclude all foreign o wned rms, rms that c hanged o wnership during the sample p erio d and rms that op erates less than 3 consecutiv e y ears. Column (1) sho ws the direct eect of SOE on paten t application. Column (4) sho ws the indirect eect of SOE on paten t application through eac h mediator sp ecied in the v ariable column. Robust standard errors clustered at y ear-lo cation-industry lev el are rep orted in paren these. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . 122 in those nancially strong rms as they migh t repa y debt b efore the scal y ear ends. This migh t cause the p ositiv e asso ciation b et w een in terest rate and inno v ation activities giv en that nancially strong rms mak e larger inno v ation in v estmen t. Column (4) in table 4.3 computes the total indirect eect through whic h state o wnership aects a rm’s inno v ation output. Column (5) giv es the condence in terv al of suc h indirect eects and column (6) calculates the mediator i’s con tribution to the total indirect eects: a i b i P 3 i=1 a i b i . Skill Ratio con tributes the most to the indirect eects and nancing cost con tributes the least. Comparing the results from P anel B to P anel A, it is easy to notice that the con tribution from subsidies and nancing cost are increased after 2009. Subsidies con tributes 9.28% to indirect eects in pre-2009 sample, whereas it con tributes 23.98% to indirect eects in p ost-2009 sample. The total eect of SOE on paten t application can b e computed as c =c 0 + P 3 i=1 a i b i . Using gures from table 4.3, one can calculate that the total eect in pre-2009 sample is 0.029, whereas the total eect in p ost-2009 sample is 0.107. Notice that in the pre-2009 sample, the direct eect of SOE is negativ e, whic h sho ws the inconsisten t mediation problem. One explanation for the direct eect to b e negativ e is that SOEs’ pro ductivit y lev els are relativ ely small comparing to POEs b efore 2009. In the theoretical mo del, I ha v e sho w ed that paten t application is p ositiv ely asso ciated with the underlying pro ductivit y lev els. The summary statistics in table 4.1 ha v e sho wn that in the pre-2009 sample, on a v erage, SOEs’ pro ductivit y is only 87.8% of POEs’ pro ductivit y . Ho w ev er, as SOEs’ pro ductivit y b ecome larger than POEs’ pro ductivit y , the direct eect of SOE b ecomes p ositiv e in p ost-2009 sample. If c and c 0 ha v e the same sign, one can measure the mediation as the prop ortion of the eect that is mediated: P 3 i=1 a i b i c . Th us, in the p ost-2009 sample, 0:1028 0:107 = 96% of the total eect c can b e explained b y mediators. T able 4.4 rep eat the similar analysis as table 4.3. The dep enden t v ariable in this table is qualit y- adjusted paten t application to capital ratio (paten t-capital ratio). State o wnership also has p ositiv e 123 T able 4.4: Mediation Analysis - P aten t Application to Capital Ratio (1) (2) (3) (4) (5) (6) c 0 a b ab 95% CI on ab INE% P anel A: Pre 2009 Sample In terest Rate 0:0128 0:0108 0:0004 0:0000 [0:0000; 0:0000] 0:0004 (0:0022) (0:0036) (0:0019) (0:0000) Subsidies 0:0128 0:1274 0:0060 0:0008 [0:0006; 0:0010] 0:0673 (0:0022) (0:0097) (0:0007) (0:0001) Skill Lev el 0:0128 0:0619 0:1711 0:0106 [0:0096; 0:0116] 0:9330 (0:0022) (0:0016) (0:0045) (0:0005) P anel B: P ost 2009 Sample In terest Rate 0:0017 0:0134 0:0047 0:0001 [0:0001; 0:0003] 0:0107 (0:0022) (0:0012) (0:0097) (0:0001) Subsidies 0:0017 0:2637 0:0031 0:0008 [0:0004; 0:0012] 0:1388 (0:0022) (0:0181) (0:0007) (0:0002) Skill Lev el 0:0017 0:0619 0:0809 0:0050 [0:0040; 0:0060] 0:8505 (0:0022) (0:0030) (0:0042) (0:0005) Note: Mediation Analysis for the merged ASM-SIPO sample from y ear 2003 to y ear 2011. Exclude all foreign o wned rms, rms that c hanged o wnership during the sample p erio d and rms that op erates less than 3 consecutiv e y ears. Column (1) sho ws the direct eect of SOE on paten t application to capital ratio. Column (4) sho ws the indirect eect of SOE on paten t application to capital ratio through eac h mediator sp ecied in the v ariable column. Robust standard errors clustered at y ear-lo cation-industry lev el are rep orted in paren these. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . 124 direct impact on this ratio in b oth pre and p ost 2009 samples. The mediators, subsidies and skill lev els, are b oth p ositiv ely asso ciated with paten t-capital ratio. There exists a signican t indirect eect of SOE on paten t-capital ratio through b oth subsidies and skill lev els. Ho w ev er, similar to ndings in table 4.3, I do not nd a statistically signican t indirect eect of SOE on paten t-capital ratio via in terest rate. Skill lev el con tributes the most to the paten t-capital ratio. Comparing the results from P anel B to P anel A, it is easy to notice that the con tribution from subsidies and nancing cost is increased after 2009. Subsidies con tributes 6.73% to indirect eects in pre-2009 sample, whereas it con tributes 13.88% to indirect eects in p ost-2009 sample. The total eect c of SOE on paten t-capital ratio is 0:0241 in pre-2009 sample and 0:0076 in p ost-2009 sample. Using gures in table 4.4, one can calculate that 47% of those total eects in pre-2009 sample can b e explained b y mediators. In p ost-2009 sample, 77.6% of those total eects can b e explained b y mediators. Mediations pla y an imp ortan t role in explain the total eect of SOE on paten t-capital ratio. 4.4.2 Inno v ation and Productivity Gro wth Previous section sho ws that the inno v ation gap b et w een SOEs and POEs can b e largely explained b y their dierence in skill ratio and receiv ed subsidies. Endogenous gro wth theory suggests that inno v ation is the main driv er of pro ductivit y gro wth. Th us, the observ ed higher pro ductivit y gro wth in SOEs migh t b e explained b y their inno v ation activities. This section analyze whether suc h dierence in skill lev el and subsidies can con tribute to the dierence in pro ductivit y gro wth via inno v ation activities. And whether the dieren t gro wth in inno v ation activities can explain SOEs’ "catc h up" with POEs in terms of pro ductivit y lev els. I conduct a similar mediation analysis as section 4.4.1. Figure 4.4 represen ts the framew ork of the mediation analysis. The outcome v ariable Y under this framew ork is pro ductivit y gro wth whic h is measured as medium-term TFP gro wth. 125 Figure 4.4: Mediation Analysis: Pro ductivit y Gro wth T able 4.5: Mediation Analysis - Pro ductivit y Gro wth (1) (2) (3) (4) (5) (6) (7) c c 0 a b ab 95% CI on ab ab c Subsidies 0:0039 0:0032 0:0613 0:0200 0:0012 [0:0008; 0:0016] 0:3144 (0:0016) (0:0021) (0:0032) (0:0028) (0:0002) Skill Lev el 0:0236 0:0222 0:7184 0:0205 0:0147 [0:0106; 0:0188] 0:6240 (0:0093) (0:0137) (0:0206) (0:0028) (0:0021) Note: Mediation Analysis for the merged ASM-SIPO sample from y ear 2003 to y ear 2011. Exclude all foreign o wned rms, rms that c hanged o wnership during the sample p erio d and rms that op erates less than 3 consecutiv e y ears. Column (1) sho ws the total eect of skill lev el/subsidies on a rm’s pro ductivit y gro wth. Column (2) sho ws the direct eect of skill lev el/subsidies on a rm’s pro ductivit y gro wth. Column (5) sho ws the indirect eect of skill lev el/subsidies on a rm’s pro ductivit y gro wth through its inno v ation activities. Robust standard errors clustered at y ear-lo cation-industry lev el are rep orted in paren these. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . The mediator is inno v ation activit y , whic h is measured as the n um b er of gran ted in v en tion and utilit y mo del paten ts within a giv en y ear. The n um b er of gran ted paten ts is also qualit y-adjusted. In the statistical mo dels, path c is deriv ed from regression outcome v ariable Y on eac h causal v ariable X i . It measures the total eects of subsidies/skill lev els on the pro ductivit y gro wth. P ath a is deriv ed from regressing inno v ation activit y on eac h causal v ariable X i skill lev el and subsidies. That is: M ft = 0 +a i X i ft +controls ft +" m ft . The indirect eect of inno v ation on Y and the direct eect of eac h X i onY are deriv ed from follo wing regression: Y ft = 1 +c 0 X i ft +bM ft +controls ft +" Y ft . controls are additional con trol v ariables that migh t aect mediators and the outcome. I add capital in tensit y , log of emplo ymen t, TFP lev el, rm age and industry-y ear-lo cation xed eect as con trols. The indirect eect of X i on Y through mediator M is a i b. T able 4.5 presen ts the results. 126 Column (1) in table 4.5 sho ws subsidies and skill lev els are p ositiv ely asso ciated with pro- ductivit y gro wth and those correlation are statistically signican t. Once con trolling the media- tor, subsidies/skill lev els’s impact on pro ductivit y gro wth b ecome statistically insignican t and the magnitude is reduced (see path c 0 ). Column (3) do cumen ts a strong p ositiv e asso ciation b et w een inno v ation and pro ductivit y gro wth. One standard deviation increase in gran ted paten ts could result in 0.02 p ercen tage increase in the pro ductivit y gro wth. Column (5) implies the existence of a statistically signican t indirect eects of subsidies/skill lev els on pro ductivit y gro wth through inno v ation activities. One standard deviation increase in subsidies w ould result in a 0.3% direct increase in pro ductivit y and 0.1% p ercen tage indirect increase in pro ductivit y b y raising the n um b er of gran ted paten ts. Similarly , one standard deviation increase in skill lev els w ould result in a 2.2% direct increase in pro ductivit y and 1.5% indirect increase in pro ductivit y b y raising the n um b er of gran ted paten ts. Skill lev els con tributes more to a rm’s pro ductivit y gro wth and most of its con tribution can b e explained b y an increase in a rm’s gran ted paten ts. Column (7) sho ws that 31.4% of impact on pro ductivit y gro wth from subsidies can b e explained b y the p ositiv e asso ciation b et w een subsidies and the n um b er of gran ted paten ts. Similarly , 62.4% of impact on pro ductivit y gro wth from skill lev els can b e explained b y the p ositiv e asso ciation b et w een skill lev els and the n um b er of gran ted paten ts. Those empirical evidence from table 4.3 and table 4.5 ma y suggest that the observ ed increase in pro ductivit y gro wth among SOEs after scal stim ulus p olicy can b e attribute to an increase in subsidies they receiv ed. As skill ratio con tribute the most to a rm’s inno v ation activities, higher skill ratio in SOEs can explain the larger magnitude of paten t application and gran ted paten ts among SOEs, and m uc h faster pro ductivit y gro wth rate in SOEs. This indicates that the do cumen ted "shrinking gap" (or "catc h up" eect) in pro ductivit y b et w een SOEs and POEs, can b e partially explained b y their dierence in inno v ation activities, whic h results from their dieren t skill lev els 127 and receiv ed subsidies. If priv ate rms can hire the same n um b er of highly educated w ork ers (those with college degree and ab o v e), or if they can receiv e the same amoun t of subsidies as the SOEs do, they can enjo y m uc h higher pro ductivit y gro wth. 4.5 Conclusion In this pap er, I in v estigate the inno v ation b eha vior in state-o wned rms (SOEs) and priv ately- o wned rms (POEs). Using a merged ASM-SIPO-Go ogle P aten t data for Chinese man ufacturing rms from the y ear 2003 to the y ear 2011, I rst do cumen t inno v ation disparities b et w een state- o wned rms and priv ately-o wned rms. SOEs le more paten ts than POEs and suc h dierence ha v e b een enlarged since China’s 4 trillion RMB scal stim ulus p olicy in 2009 and 2010. I then build a theoretical mo del to explain the underlying mec hanism whereb y state-o wnership aects a rm’s inno v ation activities. Go v ernmen t subsidies and inno v ation capacities are the t w o main c hannels. SOEs usually receiv e more go v ernmen t subsidies (esp ecially after 2009-2010 scal stim ulus p olicy) and they ha v e higher inno v ation capacities. This encourages inno v ation in v estmen t among them. Theoretically , I also nd that an increase in go v ernmen t subsidies to w ards SOEs raise the nancing cost among POEs and discourage their inno v ation in v estmen t. I then conduct t w o mediation analyses to do cumen t additional empirical evidence that can supp ort those mec hanisms discussed under m y theoretical framew ork. My empirical results suggest that dierences in subsidies and skill lev els can explain as high as 90% of the observ ed dierence in paten t application b et w een SOEs and POEs. Skill lev els con tribute the most to the dierence in paten t application throughout the sample y ear. Con tribution from subsidies increased after the 2009 scal stim ulus p olicies. In the pre-2009 sample, subsidies can only explain 9.3% of the observ ed dierence in paten t application. This n um b er increased to 24% in the p ost-2009 sample. In the second mediation analysis, m y empirical ndings suggest that 31.4% of subsidies’ impact on 128 pro ductivit y gro wth can b e explained b y an increase in rms’ gran ted paten ts. Th us, the observ ed increase in pro ductivit y gro wth among SOEs after scal stim ulus p olicy can b e partially attributed to the rise in subsidies they receiv ed. These ndings can partly explain the shrinking pro ductivit y gap b et w een SOEs and POEs. This pap er examines the impact of scal stim ulus p olicy on inno v ation activit y and pro ductivit y gro wth at the rm lev el. One natural extension is to build a general equilibrium mo del to quan tify the stim ulus p olicy’s impact on aggregate gro wth. Previous literature suggests that more than 70% of aggregate pro ductivit y gro wth comes from resources reallo cation to priv ate-rms. Th us, it is p ossible that suc h rev erse reallo cation of credit resource ma y slo w the aggregate pro ductivit y gro wth b y dev astating priv ate rms’ gro wth p oten tial. 129 Chapter 5 Conclusion and Policy Implication This dissertation con tributes to the broad literature in the in teraction b et w een nancial mark et and rms’ v arious in v estmen ts. Although previous studies sho w that frictions in nancial mark et w ould lo w er the aggregate gro wth b y hindering rms’ in v estmen t, y et few studies fo cus on ho w those friction ma y c hange rms’ in v estmen t comp osition as w ell as inno v ation qualit y . This dissertation pro vides new evidence on the asso ciation b et w een nancial friction, inno v ation t yp es and qualit y , and the pro ductivit y gro wth. Empirical analyses in this dissertation utilize rms’ op eration data from China’s Ann ual Surv ey of Man ufacturing, rms’ inno v ation data from State In tellectual Prop ert y Oce, and inno v ation qualit y data from Go ogle P aten ts. One of the main empirical con tribution is to merge these three dieren t data sources. After merging these data-sets, I dev elop ed v arious measuremen t of a rm’s nancial constrain ts, inno v ation t yp es and inno v ation qualit y . Results in Chapter 2 suggests that when a rm’s nancial constrain ts tigh ten, the rm increases its application for lo w-qualit y paten ts, reduces its in ternal and external inno v ation. Second, there is a signican t negativ e relationship b et w een the sev erit y of a rm’s nancial constrain ts and its future sales and pro ductivit y gro wth. An endogenous gro wth mo del with nancial constrain ts and inno v ation t yp es is built to replicate and accoun t for these empirical facts. The mo del is 130 then calibrated carefully to matc h momen ts in m y data-set on Chinese rms and their inno v ation activities. I conduct sev eral coun terfactual exp erimen ts based on this calibrated v ersion of the mo del. In the rst exp erimen t, I remo v e the nancial constrain ts faced b y all rms. The p ercen tage application in lo w-qualit y inno v ation drops from 37% to 33%. The ann ual aggregate pro ductivit y gro wth rate increased from 3.5% to 3.9%. In the second exp erimen t, I ev aluate the impact of China’s curren t R&D tax incen tiv e p olicy , implemen ted since 2003. Under the curren t R&D tax incen tiv e p olicy , a rm’s R&D exp enditures are en titled to a "sup er-deduction". That is, eac h dollar sp en t on R&D coun ts as 1.5 dollars’ exp enditure when computing the corp orate income tax base. I sho w that this tax incen tiv e p olicy increases the aggregate gro wth rate 0.1 p ercen tage p oin ts ann ually . Ho w ev er, it also increases a rm’s paten ting in lo w-qualit y inno v ation b y 7.4% p ercen t, since the p olicy do es not distinguish b et w een dieren t t yp es of R&D exp enditure. T o reduce lo w-qualit y paten ting, a t yp e-dep enden t R&D tax incen tiv e p olicy is prop osed. In this prop osed tax p olicy , only R&D exp enses on in ternal and external inno v ation are en titled to a sup er deduction. This tax incen tiv e p olicy w ould generate higher aggregate gro wth and greater w elfare gain than the curren tly implemen ted uniform R&D tax incen tiv e. The gro wth rate w ould further increase b y 0.12 p ercen tage p oin ts under the t yp e-dep enden t R&D tax incen tiv e p olicy . Quan titativ e results in Chapter 3 suggests that the magnitude of mark et noise is w a y higher than priv ate signals receiv ed b y rms and traders. Firm’s slo w learning on future pro ductivit y largely caused b y the existence of noise traders. Those noise traders prev en t imp erfectly informed traders p erfectly transmit their kno wledge or exp ectation on future inno v ations in pro ductivit y , to the public. F uture w orks can fo cus on the relationship b et w een suc h information frictions and the rm’s R&D in v estmen t. A gro wing b o dy of w ork studies ho w "news sho c ks" or sen timen t can cause business cycle uctuations through their impact on ph ysical in v estmen t. If sen timen ts can also aect a rm’s R&D in v estmen t, this ma y pro duce uctuations around the econom y’s gro wth 131 path in an endogenous gro wth mo del. One can study ho w a rm’s b elief ab out future pro ductivit y sho c k w ould aect its ph ysical and R&D in v estmen t rates. Empirically , rms’ paten ting ma y aect their o wn and other relev an t rm’s sto c k prices and if so generate enough "news" for rms to infer c hanges in the future pro ductivit y . T w o mediation analyses in Chapter 4 suggest that dierence in subsidies and skill lev els can explain as high as 90% of the observ ed dierence in paten t application b et w een state-o wned rms and priv ate-o wned rms. Skill lev els con tributes the most to the dierence in paten t application throughout the sample y ear. Con tribution from subsidies increased after 2009 scal stim ulus p olicies. In pre-2009 sample, subsidies can only explain 9.3% of the observ ed dierence in paten t application. This n um b er increased to 24% in p ost-2009 sample. Chapter 4’s empirical ndings also suggest that 31.4% of subsidies’ impact on pro ductivit y gro wth can b e explained b y an increase in rms’ gran ted paten ts. Th us, the observ ed increase in pro ductivit y gro wth among state-o wned rms after scal stim ulus p olicy can b e attribute to an increase in subsidies they receiv ed. These ndings can partially explain the shrinking pro ductivit y gap b et w een state-o wned rms and priv ate-o wned rms. As priv ate-o wned rms con tributes more than 70% of aggregate pro ductivit y gro wth. The rev erse reallo cation of credit resource to w ards stat-o wned rms ma y slo w do wn China’s aggregate pro ductivit y gro wth. P olicies aim to stop suc h rev erse reallo cation should b e carried out. F uture studies can in v estigate the relationship b et w een a rm’s inno v ation comp osition and lab or unionization (or collectiv e bargaining). One migh t answ er the follo wing questions: Do es unionization alter a rm’s inno v ation comp osition? Do es the threat of unionization cause rms to shift their inno v ation to w ards dev eloping lab or-substituting tec hnology? Can unionization increase a coun try’s aggregate pro ductivit y? First, researc hes ha v e sho wn that lab or unions are asso ciated with higher w ages and w elfare in most dev eloping coun tries (see F reeman (2010) for a comprehensiv e summary). Suc h a w age push from union ma y tigh ten a rm’s nancial constrain ts and reduces 132 its inno v ation qualit y . In addition, it ma y lo w er a rm’s protabilit y and force it to adopt/create lab or-substituting tec hnology , suc h as automation. Automation w ould merely increase aggregate pro ductivit y if it w ere only used to displace lo w-skilled w ork ers (A cemoglu and Restrep o, 2018). 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Journal of Ec o- nomic Persp e ctives 26, no. 4 (2012): 103-24. 139 Appendix A Chapter 1 Appendix A.1 Data Construction A.1.1 P aten t Types P aten ts are classied in to three categories under SIPO: 1) in v en tion paten ts, those that mak e "sig- nican t progress" relativ e to previous tec hnology; 2) utilit y mo dels, those that represen t a minor impro v emen t of curren t pro ducts and are insucien t to b e gran ted as in v en tion paten ts; and 3) industrial design, those of ornamen tal or aesthetic design of ph ysical or digital go o ds with a prac- tical purp ose. In v en tion paten ts are in tensiv ely examined b y paten t ocers, and usually tak en t w o to v e y ears to b e gran ted. The protection p erio d for in v en tion paten ts is up to t w en t y y ears, or based on a rm’s o wn termination c hoice prior to the t w en t y y ear limit. The protection p erio d for utilit y mo dels and industrial designs are up to ten y ears, or based on a rm’s o wn termination c hoice within those ten y ears. Hence, in v en tion paten ts are usually harder to obtain. I reclassify paten ts in to three alternativ e categories: 1) industrial design paten ting; 2) long- run in ternal inno v ation, and 3) long-run external inno v ation. Industrial design paten ts are paten ts that do not con tribute to a rm’s long-run pro ductivit y gro wth, and ha v e short application and protection p erio ds. Firm engaged in industrial design paten ting to increase its instan taneous prot only . It do not con tain an y so cial v alues nor ha v e an y p ositiv e spillo v er eect o v er either rm’s or aggregate pro ductivit y gro wth 1 . Long-run in ternal inno v ation paten ts represen t inno v ations aiming to impro v e a rm’s existing pro duction metho d or pro cess, and th us its long-run pro ductivit y . Long-run external inno v ation paten ts represen t inno v ations aiming to increase the n um b er of rm’s pro duct lines b y in tro ducing new pro ducts or an en tirely new pro duction tec hnology . In ternal inno v ations are "exploitation" inno v ations and it can b e view ed as renemen ts and extension of curren t tec hnology (Marc h (1991), Gatignon, T ushman, Smith and Anderson (2002)). Th us, a rm’s in ternal paten t w ould cite its previous paten ts more than other rm’s paten ts. External inno v ation, on the other hand, are "exploration" inno v ations. A rm conduct external inno v ation to explore new tec hnology that it do es not curren tly o wned. Th us, a rm’s external inno v ation cite less its previous paten ts but more on paten ts o wned b y other rms. As rm migh t op en a new tec hnology eld through external inno v ation, external paten ts usually receiv es more citations from subsequen t paten ts applied b y other rms (Galasso and Simco e (2011) and Ak cigit and Kerr (2018)). Levin thal and Marc h (1993) and Marc h (1991) pro vide detailed distinguish on exploration and exploitation inno v ations. 1 In m y sample, around 70% of industrial designing are pac k aging, designing of clothing, jew elry and furniture, whic h do not con tribute to the impro v emen t of rm’s pro duction pro cess. But those paten ts ma y shift customers’ preference instan taneously . 140 T able A.1: Summary Statistics of P aten t Category and A v erage Citation Lo w-Qualit y In ternal Inno v ation External Inno v ation T otal T otal Mean T otal Mean P aten t Application 105,840 98,580 71,595 Bac kw ard Citation 1,537 0.016 36,016 0.503 self cite d 977 0.010 2,136 0.030 F orw ard Citation 163,136 1.655 150,228 2.098 external 149,136 1.513 137,233 1.917 P aten t v alue, b oth so cial and priv ate v alue, are p ositiv ely related to its forw ard citations, whic h is measured as the n um b er of subsequen t paten ts that cite the sp ecic paten t a rm les (T ra jten b erg (1990) and Hall, A dam and T ra jten b erg (2001)). P aten t without an y forw ard citations migh t b ear limited so cial v alues. Hence, as industrial design paten ts do es not ha v e an y forw ard citations, it do es not ha v e an y spillo v er eect on econom y’s aggregate pro ductivit y . The remaining paten ts, utilit y and in v en tion paten ts, classify as pro ductivit y-enhancing paten ts. In the nal paten t sample, there are 130,801 industrial design application during the sample p erio d (see T able A.1). Next, I classify pro ductivit y-enhancing paten ts in to in ternal and external inno v ation. My clas- sication of in ternal and external paten ts follo ws the metho d prop osed b y Ak cigit and Kerr (2018), with some mo dications. Based on USPTO paten ts applied b y US census rms, Ak cigit and Kerr classify paten ts as in ternal inno v ation if more than 50 p ercen t of bac kw ard citations, whic h is mea- sured as the n um b er of previous paten ts a paten t cite in its application do cumen t, are self-citations. Ho w ev er, in SIPO paten t data, around 30 p ercen t of paten ts do not ha v e an y bac kw ard citations, making it dicult to use their metho d to classify paten ts as in ternal inno v ation. T o o v ercome this, I utilize information on a rm’s paten t description, tec hnology domain and pro duct information 2 . I classify in ternal inno v ation in t w o steps. First, those paten ts with bac kw ard citations, I classify as in ternal inno v ation if more than 50 p ercen t of bac kw ard citations are self-citations. Second, for paten ts without bac kw ard citation, I classify a paten t as in ternal inno v ation if a) its tec hnology domains b elongs to the rm’s previous paten t’s tec hnology domains, and b) there is a statemen t similar to "impro ving curren t pro duction pro cess" in the paten t description, or if the rm rep orts "no new pro duct is pro duced" in the y ear of the paten t’s application. Using this mo died classi- cation metho d, I ha v e 98,580 in ternal paten ts and 71,595 external paten ts in the sample p erio d. Using Ak cigit and Kerr (2018)’s classication, there w ould b e 21,014 in ternal paten ts in 149,161 ex- ternal paten ts in m y data. My metho d yields a more restrictiv e denition for external, exploratory inno v ation. Figure A.1 sho ws the citation distribution of in ternal and external paten ts for m y sample of Chinese rms based on the paten t classications suggested b y Ak cigit and Kerr (2018) with the citation distribution based on m y mo died metho d. Ideally , in ternal paten ts are "exploitation" paten ts and external paten ts are "exploration" paten ts, and the latter ha v e a deep er inuence on tec hnology ev olution. Hence, in ternal paten ts should receiv e few er external (non-self ) citations than external paten ts. Applying Ak cigit and Kerr (2018)’s metho d to China’s paten t data, yields a v ery similar distribution for in ternal and external paten ts. The a v erage n um b er of external citations for eac h in ternal paten t is 1.89 and it is 1.91 for external paten ts. Ho w ev er, m y mo died metho d yields a somewhat larger distinction b et w een external citations for the t w o paten t t yp es; the a v erage 2 In ASM, rms are ask ed to pro vide information on whether their curren t pro ducts are pro duced using new tec hnology or new pro duction pro cess. 141 Figure A.1: External Citation Distribution b y External and In ternal P aten t 0 2 4 6 8 10 12 14 Number of External Citations Received 0.2 0.4 0.6 0.8 1 Cumulative Distribution of Patents Following Akcigit and Kerr (2018) Internal External 0 2 4 6 8 10 12 14 Number of External Citations Received 0.2 0.4 0.6 0.8 1 Cumulative Distribution of Patents Adjusted by Tech Field Internal External Note: Left panel is based on paten t classications suggested b y Ak cigit and Kerr (2018). P aten t dened as in ternal if more than 50% of bac kw ard citations are self-cited. Righ t panel is based on m y mo died metho d. external citation for eac h in ternal paten t is 1.51 and for external paten ts is 1.92. T able A.1 lists the summary statistics. In addition, external inno v ations, on a v erage, ha v e w a y less self citation than in ternal inno v ations. A.1.2 Measuring Financial Constriant F ollo wing Almeida and Camp ello (2007), the in v estmen t equation under constrained and uncon- strained regimes can b e written as I 1it =X it 1 +u 1it I 2it =X it 2 +u 2it y it = 0 +Z it +v it whereI 1it andI 2it are R&D in v estmen t under regime 1 and regime 2. X it are a v ector of exogenous v ariable that go v erns rm’s in v estmen t decision: 1) one p erio d lagged R&D in v estmen t, 2) gro wth opp ortunities, whic h is measured as turno v er o v er real capital; 3) real cash o w divided b y rm’s real capital sto c k at the b eginning of curren t p erio d. y it is unobserv ed determinan ts of rm’s nancial conditions. If y it < 0 rm is nancially constrained and I it = I 1it . If y it > 0, rm is nancially unconstrained and I it = I 2it . Th us Z it determine the probabilit y that whether rm w ould b e nancially constrained or not. F ollo wing Almeida and Camp ello (2007) and Ho v akimian and Titman (2006), Z it con tains 1) log of total asset, 2) log age, 3) the ratio of short term debt to total asset, 4) the ratio of long term debt to total asset, 5) nancial slac kness measured as cash and mark etable securities to total asset, and 6)Tangibility it , whic h is used to appro ximate the exp ected liquidation v alue of rm’s op erating assets. F ollo wing Berger, Ofek and Sw ary (1996) and Almeida and Camp ello (2007), I compute Tangibilit as Tangibility it = 0:715Receivables it + 0:547Inventory it + 0:535FixedAsset it +Cash +MarketableSecurities, scaled b y total asset. WhereReceviables are accoun t receiv ables. Cash and mark etable securities are computed as liquid asset min us accoun t receiv ables. This v ariables are all en tered in lagged form in the selection 142 equation. F ollo wing Ho v akimian and Titman (2006), the mo del can b e estimated using Exp ectation- Maximization Algorithm. lnL = n X i=1 ln 1 1 u 2i " 1 Z it 2 u 2i p 1 2 2 !# + 1 1 u 1i Z it 2 u 1i p 1 2 1 ! where j = jv j v . And the co v arian t matrix is dened as: = 2 4 11 12 1v 21 22 2v v1 v2 vv 3 5 with 1v 6= 0, 2v 6= 0 and normalize vv = 1. The parameter sets s and s are estimated in follo wing steps. 1) Guess an initial separation of the sample b et w een t w o regimes. I use tangibilit y to compute the initial guess. Firms with tan- gibilit y less than sample a v erage is classied as nancially constrained and Firms with tangibilit y more than sample a v erage is classied as nancially unconstrained. 2) Estimate the initial v alue of and after the initial guess, b y using the ab o v e lik eliho o d function. 3) Use the estimated and to calculate the probabilities that observ ation i b elongs to eac h group. 4) Plug these probabilities in to the ab o v e log lik eliho o d function, and then maximized again. The maximization of the ab o v e log lik eliho o d function will giv e new estimates of and . 5) Keep doing step 3) and 4) un til and con v erged. T able A.2 and Column (1) and (2) in T able A.3 lists the esti- mation results. As R&D in v estmen t relies hea vily on rm’s in ternal cash o w if it is nancially constrained, one should exp ect the co ecien t on CashFlow to b e statistically signican t p ositiv e under constrained regime (regime 1). F or a robust c hec k, I also run the regression suggested b y Almeida and Camp ello (2007) using ph ysical in v estmen t and include tangibilit y and its in teractiv e term with cash o w. The in teractiv e term of Cashflow and Tangibility captures the idea that tangibilit y increase the collateral v alue that can b e captured b y lenders if rm default. Higher tangibilit y mitigates the w edge b et w een in ternal and external nance and th us increase rm’s in- v estmen t cash o w sensitivit y . F or nancially constrained rms, one should exp ect the co ecien t b efore the in teractiv e term b ecomes p ositiv e. Column (3) and (4) in T able A.3 do cumen ts the result. 143 T able A.2: Endogenous Selection Regression Co ecien t Standard Deviation log(TotalAsset) it1 0:0684 (0:0014) log(Age) it1 0:1611 (0:0022) ShortTermDebt TotalAsset it1 0:4110 (0:0074) LongTermDebt TotalAsset it1 0:6708 (0:0156) FinancialSlack it1 0:5065 (0:0171) Tangibility it1 0:4046 (0:0261) Constant 0:4872 (0:0221) N. Obs 19,940 R-squared 0.6010 Note: log(TotalAsset) it1 is measured as log of total asset. ShortTermDebt TotalAsset it1 and LongTermDebt TotalAsset it1 is short term debt and long-term debt o v er total asset.FinancialSlack it1 is the ratio of cash and mark etable securities to total assets. Tangibility it1 is measured follo wing Almeida and Camp ello (2007) and Berger, Ofek and Sw ary (1996). Tangibility = 0:715Receivables + 0:547Inventory + 0:535FixedAsset + Cash +MarketableSecurities scaled b y total asset. Robust standard errors clustered at rm lev el are rep orted in paren theses. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . T able A.3: Endogenous Switc hing Regression R&D In v estmen t Regression Ph ysical In v estmen t Regression Constrained Unconstrained Constrained Unconstrained (1) (2) (3) (4) Investment it1 0:6999 0:0591 0:0007 0:0001 (0:1890) (0:0491) (0:0008) (0:0001) GrowthOpp it1 0:0046 0:0019 0:0063 0:0021 (0:0050) (0:0015) (0:0099) (0:0104) CashFlow it1 0:1146 0:0273 0:6610 0:9011 (0:0462) (0:0204) (0:1374) (1:2196) Tangibility it1 1:0102 1:8933 (0:6869) (2:0722) CashFlow it1 Tangibility it1 0:0460 0:9023 (0:3235) (1:7803) Industry Fix Y es Y es Y es Y es Y ear Fix Y es Y es Y es Y es N. Obs 18; 816 16; 474 64; 545 46; 474 R-Squared 0:2177 0:0769 0:0096 0:0185 Note: GrowthOpportunity is measured as total output gro wth at 3-digit industry lev el. Cash is measured as cash o w o v er total asset. Cash o w is dened as net income plus curren t depreciation. Tangibility is measured follo wing Almeida and Camp ello (2007) and Berger, Ofek and Sw ary (1996). Tangibility = 0:715Receivables + 0:547Inventory + 0:535FixedAsset +Cash +MarketableSecurities scaled b y total asset. Robust standard errors clustered at rm lev el are rep orted in paren theses. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . 144 A.2 Proofs and Additional Theoretical Result A.2.1 Firm Size Distribution F ollo wing Ak cigit and Kerr (2018), I write out follo wing o w equations for the fraction of rms with n pro duct lines. In a steady-state equilibrium, the inno v ation size distribution should b e stable. Th us, under eac h size lev el n, one should exp ect that the ino w of pro duct lines (second column) should equal outo w of the pro duct lines (third column): State Ino w Outo w n = 0 M 1 = h e n = 1 M 2 2 +h e = M 1 (h x (n) +) n 2 M n+1 (n + 1) +M n1 (n 1)h x (n) = M n (nh x (n) +n) where n is the fraction of rms with n pro duct lines. M is the total measure of rms. Com bining the ab o v e o w equations yield a relationship b et w een n and n1 : n = n1 n 1 n h x (n) Then n can b e written as: n = h e M n1 Y i=1 h x (i) 1 n A.2.2 Financial Constraints The total R&D exp enditure for an in termediate go o ds pro ducer with n f pro duct lines isR f units of nal go o ds. R&D is tak en b efore pro duction, eac h monop oly pro ducer has to collateral its ex p ost prot to generate cash to fund its R&D in v estmen t. A t equilibrium, for a rm with n f pro duct lines andh dj industrial design paten ts, its ex p ost prot is P n f j=1 ^ (1 + ) 1 z j + P n f j=1 ^ (1 + ) 1 h dj Z . The rst term is the prot o w without an y inno v ation and the second term is the additional prot margin generated b y paten ting in industrial design. No w, supp ose there are information asymmetries b et w een lenders and b orro w ers. That is lenders cannot observ e rms’ pro ductivit y lev el. F ollo wing a limited enforcemen t argumen t, supp ose a rm can steal 1 (with 1) amoun t of its b orro wing. As a punishmen t it w ould lose all of its collateral v alue. The lender needs to design a con tract so that the lease pro ductiv e rms w on’t steal b orro w ed money . Hence, it will ev aluate rm’s exp ected prot based on z min , whic h is the lo w est pro ductivit y in the econom y . Th us, rm’s nancial constrain t can b e written as: R nf (t) 2 4 n f X j=1 ^ (1 + ) 1 h dj Z +n f ^ (1 + ) 1 z min Z 3 5 A t the end of eac h p erio d, a rm’s manager pa y bac k all his b orro wing. Notice that since > 1, it is p ossible that the least pro ductiv e rm cannot pa ybac k all the b orro wing, then he giv es all one-p erio d income to the lender. I assume that the equit y holder of the compan y (household) will pa y the rest to the lender in the case the rm cannot pa y bac k b orro wing in full. That is, equit y holders ha v e to b ear a temp orary negativ e prot. Hence, the nancial constrain t is set to prev en t tunneling b eha vior of managers. 145 A.2.3 Proof of Proposition I By rm’s optimal R&D in v estmen t (2.11), long-run optimal inno v ation in tensit y h x and h I only dep ends on n um b er of pro duct line n only . Hence, the aggregate inno v ation only dep ends on the distribution of pro duct lines, indep enden t of an y qualit y distribution. The aggregate qualit y Z c hanges after an instan t t is: Z(t + t) Z = Z " t + t 1 X n=1 M n nh I (n) Z # where n is p ercen tage of rms with pro duct line n and M is the total measure of rms. The creativ e destruction rate is endogenously determined and equals total n um b er of pro duct lines that b e replaced: =h e + 1 X n=1 M n nh x (n) The aggregate gro wth rate then can b e written as: g = _ Z(t) Z(t) = lim t!0 Z(t + t) Z(t) Z(t)t =h e + 1 X n=1 M n nh x (n) + 1 X n=1 M n nh I (n) A.2.4 Proof of Proposition II Step I: Detrending Normalize rm’s v alue V and qualit y with ^ V = V Z and ^ z =f z j Z :j2ng, the v alue function can b e rewritten in new state v ariable ^ z and _ V (z;n) =g ^ V (^ z;n)+g P n j=1 @ ^ V (^ z;n) @^ z ^ z j . Rewrite the v alue function (2.7) as: (rg) ^ V (^ z;n) +g n X i=1 @ ^ V (^ z;n) @^ z j ^ z j = max fh dj ;h Ij g j2n f ;hx n X j=1 h ^ (1 + ) 1 (^ z j +h dj )x d h d dj n d i + n X j=1 h h Ij h ^ V (^ znf^ z j g[ (^ z j +);n) ^ V (^ z;n) i x I h I Ij n I i +nh x h E i ^ V (^ z[ (z i +);n + 1) ^ V (^ z;n) i x x h x x n x+1 + n X j=1 h ^ V (^ znf^ z j g;n 1) ^ V (^ z;n) i s:t: n X j=1 h x d h d dj n d +x I h I Ij n I i +x x h x x n x 2 4 n X j=1 h dj ^ (1 + ) 1 +n 3 5 Step I I: V alue F unction Guess the v alue function of the form ^ V (^ z;n) = B P n i=1 ^ z i + B n . Substitute the conjecture in to the ab o v e v alue function and equating the terms with ^ z i and constan t, one can get the follo wing: (rg +g +) B n X i=1 ^ z i = ^ (1 + ) 1 n X i=1 ^ z i 146 and (rg)B n = max fh dj ;h Ij g j2n f ;hx n X j=1 h ^ (1 + ) 1 h dj x d h d dj n d i + n X j=1 h h Ij Bx I h I Ij n I i +nh x E i ( B(1 +) +B n+1 B n ) x x h x x n x+1 + n X j=1 [B n1 B n ] Com bining the equilibrium condition that g =r, then B can b e solv ed as: B = ^ (1 + ) 1 +g + T ak e the rst order conditions,: h dj = ^ (1 + ) 1 x d d 1 +' n 1 +' n 1 d 1 n ~ d 8j h Ij = B x I I 1 1 +' n 1 I 1 n ~ I 8j h x = B(1 +) +B n+1 B n x x x 1 1 +' n 1 x1 n ~ x where ~ d = d d 1 < 0, ~ I = I I 1 < 0 and ~ x = x x1 < 0. As h dj are h Ij are indep enden t of individual relativ e qualit y ^ z j , it can b e written as: h dj = h d 8j and h Ij = h I 8j . The ' n then dened through the nancial constrain t: +^ (1 + ) 1 h d =x d h d d n d +x I h I I n I +x x h x x n x Plug in the optimal solution in to B n and the budget constrain ts, B n and ' n can b e solv ed as: = 1 +' n 1 +' n 1 d ^ (1 + ) 1 1 +' n 1 +' n ^ (1 + ) 1 x d d 1 d 1 n ~ d +x I 1 1 +' n B I x I I I 1 +x x 1 1 +' n B(1 +) +B n+1 B n x x x x x1 n ~ x B n =n 1 1 +' n 1 +' n 1 d ^ (1 + ) 1 1 +' n 1 +' n ^ x d d 1 d 1 n ~ d +n 1 1 1 +' n 1 I B 1 1 +' n B x I I 1 I 1 n ~ I +n 1 1 1 +' n 1 x B(1 +) +B n+1 B n 1 1 +' n B(1 +) +B n+1 B n x x x 1 x1 n ~ x +n(B n1 B n ) If the solution of ' n < 0, set ' n = 0 and rm is nancially unconstrained. Step I I I: Lemma I B n is b ounded ab o v e. 147 Pr o of. As B n j 'n>0 <B n j 'n=0 , Let’s consider the case where ' n = 0. Consider p er-p erio d return: (h d ;h I ;h x ;n) =n^ (1+) 1 h d +nh I B+nh x B(1+)x d h d d n d +1 x I h I I n I +1 x x h x x n x+1 Then, B(n) (h d ;h I ;hx;n) . Dene [ ~ h d ; ~ h I ; ~ h x ] argmax h d ;h I ;hx (h d ;h I ;h x ;n). They are de- termined through rst order condition: x d d h d 1 d n d = ^ (1 + ) 1 , x I I h I 1 I n I = B and x x x h x1 x = n B(1 +). The max exists as d > 1, I > 1 and x > 1. It m ust b e true that (h d ;h I ;h x ;n) ( ~ h d ; ~ h I ; ~ h x ;n). Dene ~ n argmax n (h d ;h I ;h x ;n). As minf d ; I ; x g > 0, the existence of ~ n is ensured b y the strict con v exit y . Then, it m ust b e true that: (h d ;h I ;h x ;n) ( ~ h d ; ~ h I ; ~ h x ; ~ n) Hence: B n j 'n>0 <B n j 'n=0 B max n ( ~ h d ; ~ h I ; ~ h x ; ~ n) Notice that: B n can also b e written as: B n = ~ B n n(B n B n1 ). Dene n+1 =B n+1 B n , then: ~ B n n = B n n + n where: ~ B n n = ^ (1 + ) 1 h dn +h I;n B(1 +) +h x;n B(1 +)x d h d dn n d x I h I I;n n I +h x;n n+1 is rm’s v alue without considering creativ e destruction. By the similar argumen t, w e m ust also ha v e: ~ B n j 'n>0 < ~ B n j 'n=0 B max n ( ~ h d ; ~ h I ; ~ h x ; ~ n) That is ~ B n is also b ounded ab o v e. Step IV: Lemma I I ~ Bn n 1 n=1 is a decreasing sequence. Pr o of. Let ~ B (n) b e the optimal v alue in whic h inno v ation in tensit y at its optimal v alue: h d =h d;n , h I =h I;n , h x =h x;n . Then: ~ B n n = ^ (1 + ) 1 h d;n +h I;n B +h x;n B(1 +)x d h d d;n n d x I h I I;n n I x x h x x;n n x +h x;n n+1 . Then it m ust b e true that (as h I;n+1 , h x;n+1 and h d;n+1 is not optimal p olicy under n): ~ B n n ^ (1+) 1 h d;n+1 +h I;n+1 B+h x;n+1 B(1+)x d h d d;n+1 n d x I h I I;n+1 n I x x h x x;n+1 n x +h x;n+1 n t+1 Then ~ B n+1 n + 1 ~ B n n g(n;n + 1) +h I;n+1 [ n+2 n+1 ] 148 where g(n;n+1) =x d h d d;n+1 [n d (n + 1) d ]+x I h I I;n+1 [n I (n + 1) I ]+x x h x x;n+1 [n x (n + 1) x ]< 0 Supp ose9N suc h that ~ B N N ~ B N+1 N+1 . As g(N;N + 1)< 0. It then m ust b e true that: h x;N+1 [ N+2 N+1 ] " ~ B N+1 N + 1 ~ B N N # g(N;N + 1)> 0 That is: N+2 > N+1 . T o sum up, giv en ~ B N N ~ B N+1 N+1 , it m ust b e true that N+2 > N+1 . That is if ~ Bn n 1 n=1 is nondecreasing sequence, w e can nd n > N suc h that n+1 > n alw a ys hold. This con tradict with Lemma I that ~ B n is b ounded from ab o v e. Hence, it m ust b e true that ~ Bn n 1 n=1 is an decreasing sequence. Step V: Lemma I I I If ~ Bn n 1 n=1 is a decreasing sequence, and if9N suc h that N+1 > N , then: 1) 2B N > N( N+1 + N ) and B N+1 N+1 2 B N N + B N1 N1 > 0; and 2) ~ N+1 > ~ N and 2 ~ B N > N( ~ N+1 + ~ N ), where ~ N = ~ B N ~ B N1 Pr o of. As ~ Bn n 1 n=1 is a decreasing sequence, and b y the denition of ~ B n , it m ust b e true that: B n n + n > B n+1 n + 1 + n+1 rearrange it: B n n B n+1 n + 1 > [ n+1 n ] If N+1 > N , b y the ab o v e inequalit y , B N N > B N+1 N+1 . Hence: B N N B N+1 N + 1 = B N (N + 1)B N+1 N N(N + 1) = B N N N+1 N(N + 1) > 0 Th us, B N >N N+1 >N N . That is: 2B N >N( N+1 + N ) B N+1 N + 1 2 B N N + B N1 N 1 = NB N+1 (N + 1)B N (N + 1)N + NB N1 (N 1)B N (N 1)N = N N+1 B N (N + 1)N N N B N (N 1)N = N 2 ( N+1 N ) + 2B N N( N+1 + N ) (N + 1)(N 1)N > 0 The last line hold as 2B N >N( N+1 + N ) 149 F or statemen t 2), in order to pro v e ~ N+1 > ~ N , it is equiv alen t to pro v e that B N+1 +(N + 1) N+1 B N N N > B N +N N B N1 (N 1) N1 . Rearrange it, w e need to pro v e: [ N+1 N ] +( N+1 N1 )N [ N+1 + N1 2 N ]> 0 Case 1): if N1 N , the ab o v e inequalit y hold for sure under N+1 > N . Case 2): if N1 < N , pro v e b y con tradiction. Supp ose ~ N+1 < ~ N , then b y the ab o v e inequalit y , w e m ust ha v e: N+1 + N1 2 N < 0. This implies: B N N B N1 N1 > B N N B N+1 N+1 . Rearrange it, w e ha v e: B N+1 N+1 2 B N N + B N1 N1 < 0. Con tradict with statemen t 1). Hence, w e m ust ha v e: ~ N+1 > ~ N if N+1 > N . With the same argumen t: ~ B N N ~ B N+1 N + 1 = ~ B N (N + 1) ~ B N+1 N N(N + 1) = ~ B N N ~ N+1 N(N + 1) > 0 Th us, ~ B N >N ~ N+1 >N ~ N and 2 ~ B N >N( ~ N + ~ N+1 ). Step VI: Lemma IV B n+1 B n decreases with n. Pr o of. Pro v e b y con tradiction. Assume9N suc h that N+1 > N , as: ~ B N+1 N + 1 ~ B N N g(N;N + 1) +h x;N+1 [ N+2 N+1 ] ~ B N N ~ B N1 N 1 g(N;N 1) +h x;N1 [ N+1 N ] Then: " ~ B N+1 N + 1 2 ~ B N N + ~ B N1 N 1 # g(N;N +1)+g(N;N1)+h x;N+1 [ N+2 N+1 ]h x;N [ N+1 N ] where g(N;N + 1) +g(N;N 1)< 0. As N+1 > N , then " ~ B N+1 N + 1 2 ~ B N N + ~ B N1 N 1 # <h x;N+1 [ N+2 N+1 ] Re-write the LHS: " ~ B N+1 N + 1 2 ~ B N N + ~ B N1 N 1 # = " N ~ B N+1 (N + 1) ~ B N (N + 1)N + N ~ B N1 (N 1) ~ B N (N 1)N # = " N ~ N+1 ~ B N (N + 1)N N ~ N ~ B N (N 1)N # = (N + 1)(N 1)N h N 2 ( ~ N+1 ~ N ) + 2B N N( ~ N+1 + ~ N ) i > 0 The last line hold under Lemma I I I statemen t 2). Th us, w e ha v e: " ~ B N+1 N + 1 2 ~ B N N + ~ B N1 N 1 # > 0 150 As the LHS>0, it m ust b e true that N+2 N+1 > 0. T o sum up, giv en N+1 > N and ~ Bn n 1 n=1 is a decreasing sequence, w e m ust ha v e N+2 > N+1 . Hence, w e can nd n>N suc h that n+1 > n alw a ys hold. This con tradict with Lemma I that B n is b ounded from ab o v e. Hence, w e cannot nd N with N > N1 . Th us, n decreases with n. That is B n B n1 decreases in n. A.2.5 Omitted Proofs of Proposition IV T aking deriv ativ es with resp ect to on rm’s nancial constrain t (2.12): dR d d + dR I d + dR x d + ^ (1 + ) 1 h d +^ (1 + ) 1 dh d d By equation (2.11): dh d d = h d d 1 1 1 +' n 1 1 +' n d' n d +' n dR d d = d x d h d 1 d n d dh d d = d d 1 R d 1 1 +' n 1 1 +' n d' n d +' n dh I d = h I 1 I 1 1 +' n d' n d ; dR I d = I 1 I R I 1 +' n d' n d dh x d = h x 1 x 1 1 +' n d' n d ; dR x d = x 1 x R x 1 +' n d' n d using the fact that: ^ (1 + ) 1 h d = d x d 1 +' n 1 +' n ^ (1 + ) 1 d x d 1 +' n 1 +' n d d 1 n ~ d = d R d 1 +' n 1 +' n Com bine the ab o v e deriv ativ es and rearrange it: d' n d = (1 +' n ) d R d 1+'n 1+'n d d 1 R d 1 1+'n 1 1+'n R I I I 1 +R x x x1 + 1 (1+'n) 2 R d d d 1 < 0 Consider the case where I = x = d = 2, the ab o v e deriv ativ es can b e simplied to: d' n d = (1 +' n ) 1 2 R d 1+'n 1+'n R d 1 1+'n 1 1+'n R I +R x + 1 (1+'n) 2 R d If constrained: R I +R x =^ (1 + ) 1 h d +R d = d 1 +' n 1 +' n 1 R d + =R d 2 1 +' n 1 +' n + (with d = 2) 151 Th us: d'n d 'n <1 implies 1' n 1 +' n (R I +R x ) + 2 ( 1) (1 +' n ) 2 + 1 R d > 0 The ab o v e equation is hold when ' n 1. Similarly , d'n d 1 1+'n <' n implies 1 2' n (R I +R x ) + 1 + 2 1 1 +' n 2 (1')n ! R d > 0 The ab o v e equation is hold when ' n 1 2 1 < 1 2 . A.2.6 Omitted proof in section 5.2 With in v estmen t tax t d on industrial design, the cost parameter x d c hanges to x d (1 +t d ) and the optimal quan tit y of h d b ecomes: h d = ^ (1 + ) 1 x d d 1 +' n 1 +' n 1 1 +t d 1 d 1 n ~ T aking deriv ativ es with resp ect to on rm’s nancial constrain t (2.12) and rearrange it: d' n dt d = (1 +' n )R d d d 1 1 1+'n R d d d 1 1 1+'n 2 (1 +t d ) +R I I I 1 +R x x x1 < 0 With > 1, d'n dt d < 0. Hence, if rm is not self-nanced (i.e. > 1), taxing on industrial design paten ts decrease rm-sp ecic nancial friction ' n . And: dh d dt d = h d d 1 1 1 +' n 1 1 +' n d n dt d 1 1 +t d < 0 dh I dt d = h I I 1 d' n dt d 1 1 +' n > 0 dh x dt d = h x x 1 d' n dt d 1 1 +' n > 0 Hence, b y taxing on industrial design paten ts, R&D in v estmen t is shifted to pro ductivit y-enhancing inno v ation. The higher the tax rate, the larger decrease in industrial design paten ting and more increase in in ternal and external inno v ation. A.2.7 Proof on Proposition VI Under uniform tax incen tiv e, where all t yp es of inno v ation receiv e sup er-deductable when calculating rms’ tax bases, the nancial constrain t b ecomes: (1stax)(R d +R I +R x ) (1tax)^ (1 + ) 1 h d + (1tax) 152 where s< 1 tax . T aking deriv ativ es w.r.p.t s on ab o v e nancial constrain t and rearrange it: d' n ds = R I I 1 + R x x1 + R d d 1 (1+'n) 1+'n R d R d d d 1 1 1+'n 2 +R I I I 1 +R x x x1 tax(1 +' n ) 1stax Under quadratic cost function d = I = x = 2, the nancial constrain ts implies: R I +R x +R d = 2 (1 +' n ) 1 +' n R d + (1tax) 1stax Hence, the n umerator of d'n ds b ecomes: R I +R x +R d (1+'n) 1+'n R d = (1+'n) 1+'n R d + (1tax) 1stax > 0. Th us, d'n ds > 0. An increase in deduction rate s tigh tens rm’s nancial constrain ts. And: dh d ds = h d d 1 1 1 +' n 1 1 +' n d' n ds + tax 1stax dh I ds = h I I 1 d' n ds 1 1 +' n + tax 1stax dh x ds = h x x 1 d' n ds 1 1 +' n + tax 1stax dh d ds > 0 as > 1 and d'n ds > 0. F or dh x ds > 0 and dh I ds > 0, need: d' n ds < tax 1stax (1 +' n ) Under quadratic cost functions, this requires: R I +R x +R d (1+'n) 1+'n R d 2R d 1 1+'n 2 + 2R I + 2R x < 1 ) R I +R x +R d (1 +' n ) 1 +' n R d < 2R d 1 1 +' n 2 + 2R I + 2R x ) " 1 (1 +' n ) 1 +' n 2 1 1 +' n 2 # R d <R I +R x ) " 1 1 +' n + 2 1 1 +' n 2 # R d <R I +R x With 1, the ab o v e inequalit y is hold for sure with p ositiv e R&D in v estmen t. Hence, dh x ds > 0 and dh I ds > 0. Under uniform tax incen tiv e, higher deduction rate s increases rm’s in v estmen t in 153 all t yp es of inno v ation. Ho w ev er, the increase in in ternal and external inno v ation is less than the increase in industrial design. This increases the share of industrial design. d h d h I ds / d1 +' n ds / d' n ds > 0 d h d h x ds / d1 +' n ds / d' n ds > 0 A.2.8 Proof on Proposition VII Under t yp e-dep enden t tax incen tiv e, where only in ternal and external inno v ation can receiv e sup er- deduction when calculating tax bases, the nancial constrain t b ecomes: (1tax)R d + (1stax)(R I +R x ) (1tax)^ (1 + ) 1 h d + (1tax) where s< 1 tax . T aking deriv ativ es w.r.p.t s on ab o v e nancial constrain t and rearrange it: d' n ds = R I I 1 + R x x1 1tax 1stax R d d d 1 1 1+'n 2 +R I I I 1 +R x x x1 tax(1 +' n ) 1stax > 0 Hence: dh d ds = h d d 1 1 1 +' n 1 1 +' n d' n ds > 0 dh I ds = h I I 1 d' n ds 1 1 +' n + tax 1stax > 0 dh x ds = h x x 1 d' n ds 1 1 +' n + tax 1stax > 0 The last t w o inequalit y hold under quadratic cost function. T o see this, for d'n ds < tax 1stax (1 +' n ) need: R I +R x 1tax 1stax 2R d 1 1+'n 2 + 2R I + 2R x < 1 ) 2 1tax 1stax R d 1 1 +' n 2 +R I +R x > 0 The last line holds for sure. The deriv ativ es of industrial-design-in ternal ratio w.r.p.t s is then: d h d h I ds / d(1 +' n ) 1stax 1tax ds / 1stax 1tax d n ds (1 +' n ) tax 1stax The ratio is less than 0 if d n ds < 1 +' n tax 1stax 154 Under quadratic cost function, this requires: R I +R x < 2 1tax 1stax R d ( 1) 2 (1 +' n )(1 +' n ) + (2R I + 2R x ) 1 +' n (1 +' n ) )2 1tax 1stax R d ( 1) 2 (1 +' n )(1 +' n ) + (R I +R x ) 2 +' n (1 +' n ) > 0 The last line holds under our calibration with < 2. Hence, d h d h I ds < 0 and with the similar steps, one can pro v e that d h d h x ds < 0. Hence, under t yp e-dep enden t tax incen tiv e, with an increase in deduction rate s, share of in ternal and external inno v ation increases. A.2.9 A dditional Theoretical Result My theoretical framew ork also generates a negativ e relationship b et w een inno v ation in tensit y and rm size. Suc h negativ e relationship stems from decreasing return to scale in external inno v ation. The follo wing prop osition sho ws that the existence of nancial constrain ts, mitigates the negativ e relationship b et w een in ternal and external inno v ation in tensit y , whereas it strengthen the negativ e relationship b et w een industrial design. Prop osition VI I I (Firm Size and R&D in tensit y) 1) Firm size is negativ ely related to R&D in tensit y . 2) As larger rms are less lik ely to b e constrained: i.e. d'n dn < 0, rm size migh t not ha v e a strong negativ e relationship with in ternal and external inno v ation in tensit y , but ha v e more stronger negativ e relationship with R&D in tensit y in industrial design. That is: dh d dn j 'n>0 < dh d dn j 'n=0 < 0; dh I dn j 'n>0 > dh I dn j 'n=0 ; dh x dn j 'n>0 > dh x dn j 'n=0 Pr o of. F rom rm’s optimal R&D decision (2.11): dh d dn j 'n>0 =h d 1 d 1 1 (1 +' n )(1 +' n ) d' n dn +h d ~ d n < ~ d n = dh d dn j 'n=0 dh I dn j 'n>0 =h I 1 I 1 1 1 +' n d' n dn +h I ~ I n >h I ~ I n = dh I dn j 'n=0 dh x dn j 'n>0 =h x 1 x 1 1 1 +' n d' n dn +h x ~ x n >h I ~ x n = dh x dn j 'n=0 F or nancially constrained rm, ' n decreases as rm gro ws larger. Th us, the marginal eectiv e cost of pro ductivit y-enhancing inno v ation drops. This increases rm’s incen tiv e to do b oth in ternal and external inno v ation. The termh I 1 I 1 1 1+'n d'n dn > 0 andh x 1 x1 1 1+'n d'n dn > 0 measure the decreases in a rm’s marginal cost due to reducing its nancial friction ' n when it gro ws larger. This reduction in marginal cost alleviate decreasing return to scale in in ternal and external in- no v ation. Hence, for nancially constrained rm, b oth in ternal and external inno v ation b ecome less sensitiv e to rm size, comparing with nancially unconstrained rm. If h I 1 I 1 1 1+'n d'n dn > 0 orh x 1 x1 1 1+'n d'n dn > 0 is large enough. It is p ossible that in ternal or external in tensit y in- creases with rm size under nancial constrain t. Similarly , the marginal b enet of paten ting in 155 industrial design decreases with rm size, as larger rm b enets less in relaxing its nancial con- strain ts. Large rms has less incen tiv e in paten ting industrial design. This is captured b y the term h d 1 d 1 1 (1+'n)(1+'n) d'n dn < 0. Hence, for nancially constrained rms, return on paten ting in indus- trial design exhibits more decreasing return to scale, comparing with nancially unconstrained rms. A.3 Computational Algorithm F ollo wing A cemoglu and Ak cigit (2010), the optimization problem can b e transferred in to a discrete time con trol problem through uniformization. Rewrite the optimization problem as: ( +n +nh x )B n = max h d ;h I ;hx n^ (1 + ) 1 h d +nh I B +nh x B(1 +)x d h d d n d +1 x I h I I n I +1 x x h x x n x+1 +nh x B n+1 +nB n1 s:t: x d h d d n d +x I h I I n I +x x h x x n x +^ (1 + ) 1 h d Redene (h d ;h I ;h x ;n) = n^ (1 + ) 1 h d +nh I B +nh x B(1 +)x d h d d n d +1 x I h I I n I +1 x x h x x n x+1 +n +nh x wheren is the state v ariable. Dene t w o transit probabilit y: p n;n+1 as transfer from state n to state n + 1 and p n;n1 as transfer from n to n 1: p n;n+1 = nh x n +nh x ; p n;n1 = n n +nh x dene a discoun t factor: = n +nh x +n +nh x The problem can b e re-written as: B n = max h d ;h I ;hx (h d ;h I ;h x ;n) +EB n 0 s:t: x d h d d n d +x I h I I n I +x x h x x n x +^ (1 + ) 1 h d B n is w ell dened and b ounded ab o v e (see the pro of of prop osition I I). Then B n can b e solv ed through v alue function iteration. The equilibrium is solv ed through follo wing steps: 1. Guess aggregate paten ting in industrial design . 2. Guess gro wth rate g and creativ e destruction rate . (a) solv e v alue function B n using uniformization metho d. (b) solv e the p olicy function h d , h I and h x for eac h pro duct lines in eac h rm as a function of (g;; ). 3. Solv e the equilibrium stationary distribution M , n and implied . V erify the free-en try condition (2.8). Lo op un til con v erged and free-en try condition (2.8) hold. 156 4. V erify the gro wth rate g in (2.10). Lo op un til g con v erged. 5. V erify the aggregate through = P 1 n=1 n Mnh d (n). Lo op un til g con v erged. 157 A.4 Additional Empirical and Result A.4.1 Summary Statistics T able A.4: Summary Statistics Domestic Priv ate Firms Unconstrained Firms Constrained Firms Mean St.Dev Mean St.Dev Mean St.Dev log(sale) 1.656 1.322 2.043 1.381 1.365 1.261 SaleGrowth 0.211 1.803 0.255 2.063 0.174 1.682 TFP 0.15 0.875 0.26 0.872 0.101 0.89 LP 0.071 0.844 0.271 0.845 -0.055 0.849 RDIntensity 0.009 0.038 0.012 0.043 0.007 0.031 Cash 0.113 0.176 0.124 0.174 0.103 0.186 Tangibility 0.567 0.22 0.595 0.228 0.552 0.217 FC 0.532 0.114 0.434 0.079 0.624 0.093 LongrunInnov 3.962 33.249 5.711 47.094 3.087 30.779 TotalPat 2.382 17.806 3.139 27.337 1.984 13.995 IndDesIntensity 0.213 3.047 0.16 2.78 0.268 3.801 InternalIntensity 0.277 1.682 0.284 1.778 0.273 1.709 ExternalIntensity 0.225 1.955 0.257 2.463 0.219 1.907 IndDesShare 0.229 0.38 0.204 0.36 0.252 0.396 ExternalShare 0.353 0.375 0.369 0.37 0.342 0.377 N.Obs 118,548 32,267 33,751 Note: log(sale) is measured as real total sale. SaleGrowth is ann ual gro wth rate in real total sales. TFP is total factor pro ductivit y , calculated follo wing Da vid and V enk atesw aran (2019). LP is lab or pro ductivit y , calculated as real v alue added o v er emplo ymen t after remo ving industrial and y ear eect. R&D in tensit y is dened as R&D o v er sales. Cash is measured as cash o w o v er total asset. Cash o w is dened as net income plus curren t depreciation. Tangibility it1 is measured follo wing Almeida and Camp ello (2007) and Berger, Ofek and Sw ary (1996). Tangibility = 0:715Receivables + 0:547Inventory + 0:535 FixedAsset +Cash +MarketableSecurities scaled b y total asset. FC it measure rm’s nancial condition dened as probabilit y of b eing constrained, whic h is calculated via endogenous switc hing regression in section 2.3. LongrunInnov is the citation-w eigh ted a v erage application in long-run inno v ation. TotalPat is total paten t application without citation adjustmen t. industrial design, In ternal and External in tensit y is dened as n um b er of paten t application in industrial design, in ternal and external o v er sales (p er ten million RMB). industrial design paten t share is the p ercen tage of industrial design paten ting in total paten t application. External inno v ation share is the p ercen tage of external paten ting in total paten t application. Firms with estimated lik eliho o d of b eing nancial constrained in the b ottom tertile is classied as unconstrained rms and in the upp er tertile is classied as constrained rms. 158 A.4.2 Financial constraint and rm-size-innov ation-intensity relationship T able A.5: Firm Size, Gro wth and Inno v ation In tensit y (Prob of Constrained) Gro wth P aten t In tensit y P aten t Share (1) (2) (3) (4) (5) (6) Sale it+1 Sale it Patapp d it Sale it Patapp I it Sale it Patapp X it Sale it Patapp d it Patapp T it Patapp X it Patapp T it log(Sale) it 0:108 0:105 0:110 0:073 0:005 0:011 (0:010) (0:027) (0:006) (0:008) (0:003) (0:003) Age it 0:001 0:003 0:002 0:001 0:002 0:001 (0:001) (0:001) (0:000) (0:000) (0:000) (0:000) FC it 1:186 0:431 0:294 0:464 0:213 0:274 (0:122) (0:357) (0:094) (0:116) (0:045) (0:039) log(Sale)ProbInd it 0:050 0:022 0:002 0:007 0:001 0:001 (0:009) (0:025) (0:007) (0:009) (0:004) (0:003) Industry Fix Y es Y es Y es Y es Y es Y es Y ear Fix Y es Y es Y es Y es Y es Y es N 61; 209 49; 144 50; 995 48; 584 17; 146 16; 586 R-squared 0:076 0:015 0:029 0:008 0:204 0:212 Note: log(sale) is measured in real total sales. Patapp it is the citation-w eigh ted paten t application in indus- trial design (denoted as d in sup erscript), long-run in ternal (I ), external (x). Patapp T it is rm’s total paten t application at time t. FC it measure rm’s nancial condition dened as probabilit y of b eing constrained, whic h is calculated via endogenous switc hing regression in section 2.3. ProbInd it is an index whic h equals 1 if rm is nancially constrained (i.e. probabilit y of b eing constrained greater than 0.5). Industry-y ear xed eect is con trolled but not rep orted. Robust standard errors clustered at rm lev el are rep orted in paren theses. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . T able A.6: Firm Size, Gro wth and Inno v ation In tensit y Gro wth P aten t In tensit y P aten t Share (1) (2) (3) (4) (5) (6) Sale it+1 Sale it Patapp d it Sale it Patapp I it Sale it Patapp X it Sale it Patapp d it Patapp T it Patapp X it Patapp T it log(Sale) it 0:077 0:109 0:111 0:035 0:020 0:031 (0:007) (0:018) (0:007) (0:004) (0:003) (0:002) Industry Fix Y es Y es Y es Y es Y es Y es Y ear Fix Y es Y es Y es Y es Y es Y es N. Obs 121; 091 74; 634 79; 635 73; 515 25; 505 24; 092 R-squared 0:035 0:014 0:028 0:011 0:171 0:061 Note: Industry-y ear xed eects are included as con trols, but I do not rep ort in regression. Robust standard errors clustered at rm lev el are in paren theses. , and indicate signican t at lev els 1%, 5% and 10%, resp ectiv ely . 159 T able A.7: Firm Size, Gro wth and Inno v ation In tensit y (Cash o w Sensitivit y) Gro wth P aten t In tensit y P aten t Share (1) (2) (3) (4) (5) (6) Sale it+1 Sale it Patapp d it Sale it Patapp I it Sale it Patapp X it Sale it Patapp d it Patapp T it Patapp X it Patapp T it log(Sale) it 0:091 0:113 0:111 0:063 0:006 0:014 (0:006) (0:019) (0:005) (0:004) (0:003) (0:002) Age it 0:002 0:002 0:004 0:002 0:001 0:000 (0:000) (0:001) (0:000) (0:000) (0:000) (0:000) Cash 0:083 0:004 0:016 0:015 0:010 0:004 (0:007) (0:008) (0:004) (0:005) (0:003) (0:002) Industry Fix Yes Yes Yes Yes Yes Yes Y ear Fix Yes Yes Yes Yes Yes Yes N 88; 843 70; 288 73; 026 69; 476 25; 297 24; 485 R-squared 0:098 0:014 0:031 0:009 0:194 0:206 Note: log(sale) is measured in real total sales. Patapp it is the citation-w eigh ted paten t application in industrial design (denoted as d in sup erscript), long-run in ternal (I ), external (x). Patapp T it is rm’s total paten t application at time t. Cash is measured as cash o w o v er total asset. Cash o w is dened as net income plus curren t depreciation. Tangibility it1 is measured follo wing Almeida and Camp ello (2007) and Berger, Ofek and Sw ary (1996). Industry-y ear xed eect is con trolled but not rep orted. Robust standard errors clustered at rm lev el are rep orted in paren theses. , and indicate signican t lev el at 1%, 5% and 10%, resp ectiv ely . T able A.8: Firm Size, Gro wth and Inno v ation In tensit y Gro wth P aten t In tensit y P aten t Share (1) (2) (3) (4) (5) (6) Sale it+1 Sale it Patapp d it Sale it Patapp I it Sale it Patapp X it Sale it Patapp d it Patapp T it Patapp X it Patapp L it unconstrained 0:057 0:115 0:111 0:031 0:018 0:027 (0:010) (0:031) (0:009) (0:004) (0:004) (0:003) constrained 0:071 0:095 0:099 0:044 0:010 0:025 (0:008) (0:020) (0:008) (0:006) (0:004) (0:003) Note: Eac h cell rep orts the estimated OLS co ecien ts on rms size, measured as log of real sales rev en ue. Firm age, FC score, and y ear and industry xed eects are included in the regression, but I do not rep ort the result. Ro w 1 rep orts the regression co ecien t on rm size for constrained rms, and ro w 2 rep orts the co ecien t for unconstrained rms. Robust standard errors clustered at rm lev el are in paren theses. , and indicate signican t at lev els 1%, 5% and 10%, resp ectiv ely . 160 T able A.9: Firm Gro wth and Inno v ation One P erio d Ahead T w o P erio d Ahead Three P erio d Ahead (1) (2) (3) (4) (5) (6) (7) (8) (9) log(D + 1) 0:013 0:004 0:002 (0:007) (0:012) (0:013) log(LTE + 1) 0:024 0:024 0:050 (0:006) (0:010) (0:018) log(LTI + 1) 0:012 0:019 0:027 (0:005) (0:008) (0:009) FE Y es Y es Y es Y es Y es Y es Y es Y es Y es Con trols Y es Y es Y es Y es Y es Y es Y es Y es Y es N. Obs 77; 564 66; 134 66; 134 41; 161 78; 353 51; 109 51; 109 41; 161 41; 161 R-squared 0:072 0:128 0:128 0:104 0:098 0:098 0:101 0:101 0:101 Dep enden t v ariables are rm’s gro wth rate in real sales. D it is the log of n um b er of industrial design paten ting application at time t,LT it is the n um b er of pro ductivit y-enhancing paten ts: in v en tion and utilit y mo dels. Curren t, one p erio d and t w o p erio d are dep enden t v ariable measures rm’s real sales gro wth in one, t w o and three y ears, resp ectiv ely . P ast real sales, rm age and Industry-y ear xed eects are included as con trols, but I do not rep ort in regression. Robust standard errors clustered at rm lev el are in paren theses. , and indicate signican t at lev els 1%, 5% and 10%, resp ectiv ely . A.4.3 Calibration under tax deduction T able A.10: P arameters P arameter Description V alue Iden tication/Source P anel A: External Calibrated discoun t Rate 0.04 ann ual discoun t factor substitution elasticit y 0.182 prot to sales ratio A aggregate demand shifter 1 L total lab or supply 1 d curv ature of industrial design 2 quadratic cost function l curv ature of in ternal inno v ation 2 Ak cigit and Kerr (2018) x curv ature of external inno v ation 2 Ak cigit and Kerr (2018) P anel B: Indirect Inference x d scale of industrial design 0.282 9 = ; R&D In tensit y and P aten t Shares x I scale of in ternal inno v ation 0.094 x x scale of external inno v ation 4.975 x e en try cost 4.819 en try rate d return to scale in industrial design 0.195 9 = ; in tensit y-size regression co e. I return to scale in in ternal inno v ation 0.436 x return to scale in external inno v ation 0.535 pro ductivit y m ultiplier of in ternal inno v ation 0.097 citation ratio and gro wth rate pro ductivit y m ultiplier of external inno v ation 0.123 credit mark et imp erfectness 1.212 gro wth-size regression 161 T able A.11: Momen ts Momen ts Data Mo del R&D in tensit y 2.9% 4.7% Share of in ternal paten ts 0.357 0.349 Share of industrial design paten ts 0.383 0.380 A v erage gro wth rate 3.48% 3.46% En try rate 0.113 0.113 In ternal to external citation ratio 0.789 0.789 industrial design paten t in tensit y vs. size -0.109 -0.124 In ternal paten t in tensit y vs. size -0.111 -0.113 External paten t in tensit y vs. size -0.035 -0.035 Sales gro wth vs. size -0.077 -0.078 162 Appendix B Chapter 2 Appendix Mapping b et w een 's and Noises The sto c k price can b e written as (m stands for marginal trader): ^ p t = p 1 ^ k t + p 2 ^ a t + p 3 E m t [ t+1 ] + p 4 E m t [E t [ t+1 ]] = p 1 ^ k t + p 2 ^ a t + " p 3 1 ^ V 2 u ! + p 4 V 2 e 1 ^ V 2 u ! + V 2 z 2 v !# ^ s t+1 = p 1 ^ k t + p 2 ^ a t +' p ^ s t+1 Observing the price ^ p t is the same as observing the signal ^ s t+1 . And w e ha v e ' p > 0 when income eect dominan t, ' p < 0 when w ealth eect dominan t. Dene: ^ ' = 1 ^ V 2 u , ~ ' = V 2 z 2 v + 1 ^ V 2 u V 2 e . Then: ' p = p 3 ^ ' + p 4 ~ ' T raders assign a w eigh t ' p on the signal he receiv ed, whic h is a com bination of his o wn estimation (public signal) o v er the future pro ductivit y sho c k and his estimation of rm’s signal (whic h w ould aect the future dividend). Then, instead of estimating 2 v , 2 e and 2 z , w e estimates ^ ', ~ ' and '. Using the cov(p t ;u t+1 ) and var(p t ), w e can get the estimation of ^ ' and ~ '. ' = 1 V 2 u )V = (1') 2 u ^ ' = 1 ^ V 2 u ) ^ V = (1 ^ ') 2 u ~ ' = V 2 z 2 v + V 2 e ^ ' Hence: V 2 e = 1 V 2 u ~ ' ^ V 2 u = ' ~ ' 1 ^ ' V 2 z 2 v =' V 2 e = ~ '' ^ ' 1 ^ ' ^ V 2 v = ^ ' ^ V 2 v 2 z = ^ ' ~ ' 1' 163 Some restriction on the parameters: 2 e , 2 v , 2 z should b e all greater than 0. ', ^ ' and ~ ' should b e all b ounded b et w een 0 and 1. W e need: '> ~ ' ^ '> ~ ' ~ '>' ^ ' Put follo wing restrictions on parameters; 0' 1 0 ^ ' 1 ^ '' ~ 'minf'; ^ 'g Three situations will b e nested: 2 e !1, 2 v !1 and 2 z !1: ~ ' =') 2 e !1 ~ ' = ^ ') 2 v !1 ~ ' =' ^ '<minf'; ^ 'g) 2 z !1 Later t w o cases b oth indicate there’s no information con tained in the sto c k price. 164 Appendix C Chapter 3 Appendix C.1 Proofs C.1.1 Conditions for SOC<0 Dene the ob jectiv e function as (k;z). The rst order condition in SOEs implies: k (k;z) =A s;t f 0 (k s;t ) [1 + +g(z s;t )]q t (1 t ) = 0 z (k;z) =A s;t g 0 (z s;t )f(k s;t )Rq t = 0 F or the solution to b e the lo cal maxim um of the ob jectiv e function, w e need: kk (k;z) zz (k;z) kz (k;z) zk (k;z)> 0 and kk (k;z) + zz (k;z)< 0. F rom F OC: kk (k;z) =A s;t [1 + +g(z s;t )]f 00 (k s;t ) zz (k;z) =A s;t g 00 (z s;t )f(k s;t ) zk (k;z) = kz (k;z) =A s;t f 0 (k s;t )g 0 (zs;t) By the curv ature of f() and g(), that is f 00 (k s;t ) < 0 and g 00 (z s;t ) < 0. It m ust b e true that kk (k;z) + zz (k;z)< 0. F or the determinan ts of Hessian Matrix to b e p ositiv e, w e need: kk (k;z) zz (k;z) ( zk (k;z)) 2 > 0 )f 00 (k s;t )g 00 (z s;t )f(k s;t )(1 +) +f 00 (k s;t )g 00 (z s;t )f(k s;t )g(z s;t ) g 0 (z s;t )f 0 (k s;t ) 2 > 0 )f 00 (k s;t )g 00 (z s;t )f(k s;t )(1 +) +(k s;t z s;t ) 2 2 (1) (1 ) 2 2 > 0 The ab o v e inequalit y m ust hold if 1 and 1 . That is, under the assumption 1 2 and 1 2 , the second order condition is satised. Using similar metho d, it is easy to sho w that under the assumption I, the Hessian Matrix for POE’s optimization problem is also negativ e dened. 165 C.1.2 The equilibrium conditions T o close the mo del, I imp ose a lab or mark et clearing condition: L t = P i=s;p (k i;t +z i;t ). Normalize L t = 1. The equilibrium conditions are listed as follo ws: q t (1 t ) =A s;t f 0 (k s;t ) [1 + +g(z s;t )] Rq t =A s;t g 0 (z s;t )f(k s;t ) q t =A p;t f 0 (k p;t ) [1 + +g(z p;t )] R t q t =A p;t g 0 (z p;t )f(k p;t ) R t = 1 + 1 C 0 ( ~ B t ) ~ B t =z s;t +z p;t =k s;t +k p;t +z s;t +z p;t w t =q t where t is the subsidy paid b y the go v ernmen t whic h is assumed to b e exogenous to the mo del. Hence, w e ha v e eigh t unk o wns: fk s;t ;z s;t ;k p;t ;z p;t ;q t ;R t ;w t ; ~ B t g and eigh t equations that listed ab o v e. C.1.3 Proposition I Prop osition I SOEs mak e more capital in v estmen t and in tangible in v estmen t than POEs: z p;t <z s;t ;k p;t <k s;t Pr o of. Giv en t 2 [0; ] and R t = 1 + ~ B >R, the F OCs imply: A p;t g 0 (z p;t )f(k p;t )>A s;t g 0 (z s;t )f(k s;t ) A s;t f 0 (k s;t )[1 + +g(z s;t )] =(1 t )A p;t f 0 (k p;t )[1 + +g(z p;t )] drop the subscript t, the second equation implies k s k p = A s A p 1 1 1 + + s z s 1 + + p z p 1 1 and the rst inequalit y can b e written as: p s > A s A p 1 1 1 1 1 1 + + s z s 1 + + p z p 1 z s z p 1 T o pro of z p <z s , I pro v e it b y con tradiction. First, assume z p z s and 1) case I: p z p > s z s and 2) case I I: p z p s z s . Under case I, w e ha v e: 1 + + s z s 1 + + p z p > s z s p z p 166 under assumption I I, w e ha v e: A s A p 1 1 1 1 1 > 1 Hence, the RHS of the ab o v e inequalit y implies: RHS > A s A p 1 1 1 1 1 s p 1 z s z p 2 1 > 1 as 1 1 1, s p and < 1 2 (b y assumption I). The RHS > 1. Hence: p s >RHS > 1 con tradict with our assumption that s p . Under case I I, p z p s z s and z p >z s , it m ust b e true that: A s A p 1 1 1 1 1 1 + + s z s 1 + + p z p 1 1 Hence, for the inequalit y implied b y F OC holds, w e need: zs zp 1 < 1. As < 1, this implies z s >z p , whic h con tradicts out assumption that z p >z s . T o sum up, it m ust b e true that z s >z p . Then, b y g 0 (z p;t )f(k p;t )>g 0 (z s;t )f(k s;t ),g 00 ()< 0 and f 0 ()> 0, it then m ust b e true that k s >k p . C.1.4 Proposition II F rom rms’ F OCs on z , w e can express k s and k p as functions of z and q k s = q A s s z 1 s 1 k p = (1 + ~ B)q A p p z 1 p ! 1 F rom rms’ F OCs on k : q A s 1 (1) =(1 +) 1 s 1 1 z (1)(1 ) s + s 1 s 1 1 z + 1 s q A p 1 (1 + ~ B) 1 =(1 +) 1 p 1 1 (1 + ~ B)z (1)(1 ) p + s 1 p 1 1 (1 + ~ B)z + 1 p 167 Substitute out q As 1 (1) and q Ap 1 (1 + ~ B) 1 in k s and k p , and rearrange them: k s z s = 1 1 1 s (1 +)z s + k p z p = 1 +B p (1 +)z p + By prop osition I, z s >z p . Hencez s <z p . As s p , it m ust b e true that 1 s 1 p . Hence, one sucien t condition for ks zs < kp zp is that 1 1 < 1 + ~ B . As B is the total long-term b orro wing andz p +z s < , 1 1 < 1+B implies: < 1+ . Th us if assumption I I holds, that is < = 1+ , it m ust b e true that: z s k s > z p p p That is, the in tangible-capital ratio is higher in SOEs than in POEs. C.1.5 Proposition III By SOE’s F OC on k s : q t (1 t ) =A t f 0 (k s;t ) [1 + +g(z s;t )] Giv en q t , tak e deriv ativ es on b oth side with resp ect to : A[1 + +g(z s )]f 00 (k s ) @k s @ +Ag 0 (z s )f 0 (k s ) @z s @k s @k @ =q (C.1) By SOE’s F OC on z s : Ag 0 (z s )f 0 (k s ) +Ag 00 (z s )f(k s ) @z @k = 0 with g 00 (z s )< 0, g 0 (z s )> 0 andf 0 (z s )> 0, then: @z @k > 0 substitute out @z @k in equation C.1 and rearrange it: q = (1 +)Af 00 (k s ) @k @ + Ag(z s )f 00 (k s )Ag 0 (z s )f 0 (k s ) g 0 (z s )f 0 (k s ) g 00 (z s )f(k) @k @ Notice that under assumption I 1 2 and 1 2 , the second term in the brac k et is less than 0 Ag(z s )f 00 (k s )Ag 0 (z s )f 0 (k s ) g 0 (z s )f 0 (k s ) g 00 (z s )f(k s ) = A g 00 (z s )f(k s ) g(z s )f 00 (k s )g 00 (z s )f(k s ) (g 0 (z s )f 0 (k s )) 2 =Af 00 (k s )(1 +) + A g 00 (z s )f(k s ) (k s z s ) 2 2 (1 2) (1 2 )< 0 Hence, w e ha v e: @k @ > 0. By F OC on k s : f 0 (k s ) [1 + +g(z s )] = 1 t R g 0 (z s )f(k s ) 168 tak e deriv ativ es on b oth side with resp ect to and with R = 1 : f 0 (k s )g 0 (z s )(1)g 00 (z s )f 0 (k s ) @z s @ =f 00 (k s ) [1 + +g(z s )] @k s @ +g 0 (z s ) (1)f 0 (k s ) @k s @ f(k s ) Hence: if f 0 (k) f(k) @k @ > 1 1 , it m ust b e true that @zs @ > 0. Th us, an increase in go v ernmen t subsidy increase SOE’s in v estmen t in capital k s and in tangible go o ds z s . By mark et clearing condition in lab or mark et: =k p +k s +z p +z s substitute out k p and k s : = q A s z 1 s 1 + (1 + ~ B)q A p z 1 p ! 1 +z p +z s substitute out q and (1 +B)q using F OCs on z : = 1 1 (1 +) s z 1 s + 1 1 z s + (1 +) p [1 +(z p +z s )]z 1 p + [1 +(z p +z s )]z p tak e deriv ativ es with resp ect to on b oth side: 0 = 1 1 (1 +)(1 ) s z s + 1 1 + (1 +) p z 1 p + z p | {z } s @z s @ + (1 +) p [1 +(z p +z s )](1 )z p + + (1 +) p z 1 p + z p | {z } p @z p @ + 1 (1) 2 (1 +) s z 1 s + z s | {z } q = s @z s @ + p @z p @ + q rearrange it: @z p @ = s p @z s @ + q p As q > 0, s > 0, p > 0 and @zs @ > 0, it m ust b e true that @zp @ < 0. T o summarize: an increase in : 1. raise in v estmen t in capital and in tangible go o ds among state-o wned en terprise 2. reduce in v estmen t in capital and in tangible go o ds among priv ate-o wned en terprise 169 C.2 Additional Empirical Results C.2.1 Sample Construction Details I constructed a panel data sample for Chinese man ufacturing rms from 2003 to 2011. Data used in this pap er are tak en from three sources: 1) Chinese Ann ual Surv ey of Man ufacturing (ASM). This dataset includes rms with ann ual sales greater than 5 million RMB (appro ximately $800,000) 1 ; 2) P aten t activities from China’s State In tellectual Prop ert y Oce (SIPO); and 3) P aten t citations and claims data from Go ogle P aten t. The ASM con tains detailed rm-lev el balanced sheet infor- mation suc h as output, emplo ymen t, exp ort, xed capital, comp ensation (w age paid and w elfare pro vided) and etc. Eac h Chinese rm has a unique iden tifying n um b er whic h enables me to link rm o v ertime 2 . SIPO pro vides detailed information on rm’s application date, gran t date, n um b er of applicators in a giv en paten t, applier’s information (rm name and lo cation) and paten t’s tec h- nology domain. Those paten t activities are link ed to rm’s data b y the metho dology prop osed in He et al. (2016). Ho w ev er, SIPO do es not pro vide a qualied citation data, whic h is crucial to measure rm’s paten t qualit y . T o o v ercome this, I matc h the citation data in Go ogle P aten t to eac h SIPO paten t. The citation data not only con tains applican ts citation, but also co v ers citation made b y examiners and paten t ocers. The inclusion of examiner citations pro vides a b etter measuremen t for paten t qualities. Go ogle P aten t also pro vides information of the time and tec hnology domain when a paten t is cited. This enables me to adjust paten t citation based on its time windo w and tec hnology eld. After suc h adjustmen t, w e can compare dieren t paten ts o v er time and tec hnology domains. Unqualied observ ations in the merged sample are dropp ed according to criteria suggested b y Cai and Liu (2009) and F eenstra (2013). Those criteria include dropping observ ations that: 1) missing k ey v ariables suc h as total assets, net v alue of xed asset, sales and the gross v alue of rm output 3 ; 2) ha ving few er than 8 w ork ers; 3) with ann ual sale less than 5 million RMB; 4) in v alid establishmen t time (op en mon th greater than 12 or less than 1, birth y ear later than surv ey y ear or earlier than 1700); and 5) conicting on nancial data (liquid asset greater than total asset; total xed asset greater than total asset; negativ e v alues in debt, subsidies, R&D, input and sales rev- en ue etc). I also delete rms with name "trading compan y" or "imp orting and exp orting compan y" follo wing Y u (2015). Firms that op erate less than three consecutiv e y ears are also dropp ed out of the sample. The nal merged sample con tains 2,162,066 observ ations with 235,299 rms from p erio d 1998-2013. Among those rms, only 30,712 of them ha v e led at least one paten t during our sample p erio d. Firms in our sample applied 1,298,068 paten ts from y ear 1998 to y ear 2013, consisting of 454,680 in v en tion paten ts, 396,635 utilit y mo del paten ts and 273,406 industrial design paten ts. T able 1 lists basic summary statistics of our merged sample. Column (1) and (3) lists n um b er of rms in our sample and n um b er of paten tees p er y ear (I de- ne a rm as paten tee if it has applied once during that y ear). Column (2) and (4) sho ws p ercen tage of state-o wned rms (SOE) in our sample and as paten tees. F ollo wing Song and Hsieh (2015), SOE are dened as rms either registered as SOEs, or its con trolling shareholders are state go v ernmen t. P ercen tage of SOEs are decreasing through y ears b y priv atization. Still SOEs are more lik ely le 1 After 2010, the ASM only con tains rms with ann ual sales greater than 20 million RMB (appro ximately $3,200,000) 2 As some of those id n um b ers are missing or c hanged in some y ears, follo wing Brandt et al (2012), I also link rm b y fuzzy matc hing with its names, legal p erson, telephone and lo cation. 3 output data are missing in y ear 2004. I appro ximate output data b y using an accoun ting equation: output equals sale’s rev en ue min us in v en tory at b eginning and plus in v en tory at the end of y ear 170 T able C.1: Summary Statistics for Merged Sample Merged Sample NBS Ann ual Y ear No. of rms % of SOE No. of paten tee % of SOE P aten t app P aten t app (1) (2) (3) (4) (5) (6) 1998 60,664 34% 1,244 45% 5,339 6,317 1999 70,576 32% 1,704 41% 8,642 7,884 2000 81,685 30% 2,282 41% 11,549 11,819 2001 98,788 25% 2,901 36% 16,270 15,339 2002 120,631 22% 4,267 34% 26,928 21,297 2003 149,276 20% 5,568 32% 38,574 31,382 2004 229,644 16% 6,826 27% 47,746 42,318 2005 217,636 16% 7,373 27% 63,719 55,271 2006 209,084 17% 8,460 27% 74,653 69,009 2007 194,716 15% 9,022 24% 86,109 95,905 2008 173,310 9% 10,315 18% 103,135 122,076 2009 150,578 11% 9,076 19% 107,480 166,762 2010 125,827 13% 6,320 22% 82,351 198,890 2011 95,345 16% 7,723 26% 137,432 265,612 2012 96,081 16% 7,847 27% 157,287 327,116 2013 93,470 16% 7,548 27% 154,264 359,791 paten ts then priv ate o wned en terprise. T o assess the qualit y of the matc hed sample, I compare the n um b er of paten t application at the aggregate lev el. Column (5) lists the aggregated n um b er of paten t application in the merged sample and column (6) sho ws the ann ual paten t applications b y medium-to-large rms rep orted b y NBS’s China Statistical Y earb o ok. The n um b er are close b efore y ear 2010. Num b er of paten ts and rms drop considerably after 2010, as AMS readjust its surv ey sample. Ho w ev er, the trend are still closer during the sample p erio d. This suggesting the merged sample are represen tativ e in terms of capturing trend of paten t application b y medium-to-large rms. 171 T able C.2: Economic and Inno v ation A ctivit y of Firms By Industries Financial Constrain ts Inno v ation A ctivit y industry N. Firm V A F C score SA index Prob( ^ FC > 0) % paten tee P aten t In v en tion R&D (1) (2) (3) (4) (5) (6) (7) (8) (9) mining 8874 9.591 0.393 -3.045 0.924 0.029 2514 1431 0.276 fo o d 15579 9.801 0.139 -2.889 0.837 0.083 1982 910 0.470 b ev erage 3066 10.016 0.455 -3.120 0.876 0.190 2655 304 0.851 textile 17463 9.793 0.349 -2.849 0.917 0.042 940 400 0.346 w earing 8745 9.583 0.381 -2.826 0.919 0.030 824 126 0.287 leather 4268 9.696 0.244 -2.816 0.901 0.039 2675 198 0.338 w o o d 3396 9.600 0.555 -2.752 0.931 0.052 1208 145 0.210 furniture 2345 9.573 0.423 -2.816 0.937 0.104 1211 92 0.415 pap er 5869 9.657 0.289 -2.887 0.918 0.046 605 308 0.243 prin ting 3995 9.153 0.169 -3.118 0.694 0.054 123 74 0.289 media 2129 9.526 0.276 -2.876 0.922 0.142 2530 144 0.516 p etroleum 1569 10.312 0.280 -2.854 0.873 0.098 717 664 0.607 c hemincal 14802 9.826 0.170 -2.942 0.883 0.152 1786 1153 0.884 pharmaceutical 3831 10.200 0.843 -3.055 0.806 0.414 1645 1607 2.549 fabricated metal 1159 10.302 0.146 -2.805 0.895 0.112 911 641 0.714 rubb er and plastics 11108 9.535 0.442 -2.860 0.931 0.113 696 303 0.434 other non-metallic 16808 9.675 0.445 -2.954 0.898 0.069 1587 1478 0.377 basic metal 20400 9.867 0.104 -2.858 0.816 0.109 2375 1293 0.412 mac hinery and equipmen t 23828 9.692 0.320 -3.041 0.908 0.234 1875 1383 0.983 transp ort 8093 10.135 0.383 -3.017 0.912 0.224 9183 4026 1.358 electrical 11678 9.890 0.083 -2.924 0.752 0.256 12028 5489 1.130 computer 5184 10.186 0.245 -2.896 0.825 0.337 38850 37624 2.355 other man u 6949 9.526 1.241 -2.915 0.929 0.202 2212 727 1.307 utilit y 7598 9.468 0.020 -3.324 0.465 0.057 21523 9675 0.315 Note: Column (2) rep orts the mean of log real v alue added. Column (3) and (4) rep orts the mean of F C score and SA index. The calculation of these t w o nancial constrain ts measuremen ts are stated in section 3.3. Column (5) are the p ercen tage rms that b eing nancially constrained based on F C measuremen t. Column (6) rep orts p ercen tage paten tees in eac h industry . Column (7) is the total paten t sto c k and Column (8) is the total n um b er of in v en tion paten t sto c k. Column (9) rep orts the mean of log R&D input, deated b y input deator. R&D data is only a v ailable from y ear 2005 to y ear 2007 and y ear 2010. C.2.2 A dditional Mediation Analysis 172 T able C.3: Mediation Analysis - All sample y ears c 0 b a ab Condence In terv al INE% P anel A: P aten t Application In terest Rate 0:0368 0:0116 0:0169 0:0002 [0:0004; 0:0000] 0:0024 (0:0087) (0:0028) (0:0083) (0:0001) Subsidies 0:0368 0:1539 0:0676 0:0104 [0:0090; 0:0118] 0:1280 (0:0087) (0:0086) (0:0029) (0:0007) Skill Lev el 0:0368 1:1312 0:0628 0:0710 [0:0673; 0:0748] 0:8744 (0:0087) (0:0176) (0:0014) (0:0019) P anel B: P aten t Application to Capital Ratio In terest Rate 0:0095 0:0114 0:0004 0:0000 [0:0000; 0:0000] 0:0004 (0:0018) (0:0028) (0:0017) (0:00002) Subsidies 0:0095 0:1583 0:0057 0:0009 [0:0007; 0:0011] 0:0877 (0:0018) (0:0086) (0:0006) (0:0001) Skill Lev el 0:0095 0:1479 0:0635 0:0094 [0:0088; 0:0100] 0:9128 (0:0018) (0:0036) (0:0014) (0:0003) Note: Descriptiv e statistics for the merged AMS-P aten t sample from y ear 2003 to y ear 2011. Exclude all foreign o wned rms, rms that c hanged o wnership more than t wice and rms that op erates less than 3 consecutiv e y ears. Skill ratio data is only a v ailable in y ear 2004. R&D data is only a v ailable in y ear 2010 and from y ear 2005 to y ear 2007. See section 4.2.2 for the construction of eac h v ariable 173

Abstract (if available)

Abstract This dissertation studies firms' innovation activities and their impact on aggregate outcomes such as aggregate growth, firm size distribution, firm entry and exit, and productivity disparities between different types of firms. ❧ Chapter 2 investigates the role of financial constraints in shaping innovation quality and firm-growth dynamics through heterogeneous innovation. I build a unique data-set combining patent activities with the operating data of private Chinese manufacturing firms and show a strong negative relationship between the severity of financial constraints and a) firm growth, b) innovation intensity, and c) innovation quality. Based on these empirical regularities, I build a tractable endogenous growth model in which a multi-product firm invests in heterogeneous innovation in the face of imperfect financial markets. Tighter financial constraints cause firms to undertake more low-quality innovation, which yields temporary payoffs but no longer-term productivity improvements. This lowers firm and aggregate growth rates. The quantitative model suggests financial frictions reduce incumbents' R&D investment by 19.94% on average and slows aggregate annual productivity growth by 10.2 percent (0.4 percentage point annually). ❧ Chapter 3, I use a firm's and stock trader's investment behavior to infer agents' uncertainty about the future. In particular, I develop a general equilibrium model with traders endowed with differentiated beliefs on TFP shocks. We study qualitatively how dispersed beliefs will be gathered in the stock market and to what extend that aggregated information would influence a firm's investment behavior. Next, I use the observed relationship between investment, stock prices and innovation in TFP to measure the information and its precision firm received. I find a moderate degree of learning from a firm's own private signal but no learning from the stock market. Our empirical work also shows that the existence of noise traders generate a huge noise in the public signal firm receive. And such noise inhibits information transmission between imperfectly informed traders and firms. ❧ Chapter 4 empirically analyze the determinants of the observed innovation and productivity disparity between state-owned firms (SOE) and private-owned firms (POE) before and after 2009-2010 China's fiscal stimulus policy. It documents an enlarging disparity in innovation activities between SOEs and POEs after the financial crisis. Empirically, the difference in subsidies and skill levels can explain as high as 90 percent of the observed variation in patent application between SOEs and POEs. In the pre-2009 sample, subsidies can only explain 9.3 percent of the observed difference in patent applications. However, it can tell 24 percent of the observed difference in patent applications in the post-2009 sample. In addition, the observed difference in productivity growth between SOEs and POEs after the 2009-2010 fiscal stimulus policy can be attributed to an increase in subsidies SOEs received. Moreover, 31.4 percent of subsidies' impact on productivity growth can be explained by the rise in SOEs' granted patents.

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Creator Cao, Yu (author)

Core Title Essays on firm investment, innovation and productivity

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 05/05/2020

Defense Date 05/05/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag firm dynamics,innovation,intangible investment,OAI-PMH Harvest,productivity

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Betts, Caroline (committee chair), David, Joel (committee member), Quadrini, Vincenzo (committee member), Zeke, David (committee member)

Creator Email cyu812@usc.edu,yucao0301@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-298005

Unique identifier UC11663433

Identifier etd-CaoYu-8430.pdf (filename),usctheses-c89-298005 (legacy record id)

Legacy Identifier etd-CaoYu-8430.pdf

Dmrecord 298005

Document Type Dissertation

Rights Cao, Yu

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA