University of Southern California Dissertations and Theses

Essays in macroeconomics

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Essays in macroeconomics

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Content Essays in Macroeconomics by Dongwook Kim A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2022 Copyright 2022 Dongwook Kim To my mother, Hongsook Kim and my wife, Nayoung Heo ii Acknowledgments I would like to express my gratitude to those who have made this five-year journey possible. I am indebted to my dissertation chair, Caroline Betts. This dissertation would not have been materialized without her guidance and support. I also owe much to Vincenzo Quadrini and Jeff Nugent for their many valuable comments and advice. I would like to thank David Zeke, Monica Morrlaco, Robert Dekle, and Pablo Kurlat for their helpful feedback. I am particularly grateful to Cheng Hsiao for offering me a three-year research assistantship. It was a privilege and honor to work for him. I would also like to thank Maria Prados, who pro- vided me with summer RAships and coauthorship. I am also thankful to my coauthor, Bada Han. I gratefully acknowledge the financial support I received from the Department of Eco- nomics and the Bank of Korea. A very special word of thanks goes to my parents. As a first-generation student, I never imagined I would pursue a Ph.D., much less do it in the United States. Without their endless love, none of this would have been possible. I am also grateful to my parents-in-law for their support. And to my son, Juho: It has been a great pleasure to watch you grow over the last three years. You are the best compliment that this journey has given me. Thank you. My final thanks are reserved for my beloved wife, Nayoung, who has stood by me through all my travails. Her support, encouragement, and love are without comparison. For that, I am eternally thankful. iii Table of Contents Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii 1 Misallocation in Korean Manufacturing Sector 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Theoretical Framework and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Misallocation over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.1 Evolution of productivity dispersion . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.2 Correlated distortions and efficiency gains . . . . . . . . . . . . . . . . . . . . 14 1.4 The patterns of misallocation by firm size . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4.1 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4.2 Misallocation by firm size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.3 Efficient and actual plant size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4.4 Plant age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.5 Mismeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5.1 Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 iv 1.5.2 Data and specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.6.1 Risk premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.6.2 Financial intermediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.6.3 Capital flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2 Size-dependent Policy and Firm Dynamics 42 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.2 Empirical evidence : Evidence from removing SSR in Korea . . . . . . . . . . . . . . 45 2.2.1 Small-scale reservation policies in Korea . . . . . . . . . . . . . . . . . . . . . 45 2.2.2 Data and specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2.3 Regression results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.3.1 The GVX model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.3.3 Aggregate implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3 International Reserve Accumulation: Balancing Private Inflows with Public Outflows 68 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.2 Empirical Regularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2.1 General Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2.2 Reserve Accumulation and "Extra" Capital Inflows . . . . . . . . . . . . . . . 81 3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.3.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.3.2 Solving the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 v 3.4 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 3.4.1 The Model with Heterogeneous Agents . . . . . . . . . . . . . . . . . . . . . . 121 3.4.2 The Infinite Horizon Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 3.4.3 Endogenous Direct Investments and Capital Price . . . . . . . . . . . . . . . 131 3.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Bibliography 138 A Appendix to Chapter 1 147 A.1 Misallocation over time (No trimmed case) . . . . . . . . . . . . . . . . . . . . . . . . 147 A.2 Misallocation over time with percentile ratios . . . . . . . . . . . . . . . . . . . . . . 147 A.3 Misallocation by firm size (alternative measure) . . . . . . . . . . . . . . . . . . . . . 147 A.4 What happened to small firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 A.5 Mismeasurement (No trimmed case) . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 B Appendix to Chapter 3 152 B.1 List of Countries and Omitted Figures and Tables . . . . . . . . . . . . . . . . . . . . 152 B.1.1 List of Countries used in Regressions . . . . . . . . . . . . . . . . . . . . . . . 152 B.1.2 Omitted Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 B.1.3 Omitted Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 B.2 Omitted Algebras and Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 B.2.1 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 B.2.2 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 B.2.3 Derivation of the Optimal Tax . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 B.2.4 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 B.2.5 Proof of Corollary 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 B.2.6 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 B.2.7 Proof of Proposition 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 B.2.8 Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 vi B.3 Other Mircofoundations of Frictions on Capital Outflows . . . . . . . . . . . . . . . 163 B.4 Reserve Accumulation of Saving Glut EMEs . . . . . . . . . . . . . . . . . . . . . . . 165 B.5 Capital Outflows Restrictions in EMEs . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 vii List of Tables 1.1 Percent of plants, actual vs. efficient size . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2 Percent of plants, actual vs. efficient size . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3 Average age of plants, actual vs. efficient size . . . . . . . . . . . . . . . . . . . . . . . 26 1.4 Average age of plants, actual vs. efficient size . . . . . . . . . . . . . . . . . . . . . . . 28 1.5 Estimate Measurement Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.6 Firm-level volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.7 Effects of FDI on misallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.1 The number of SSR products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2 Impact of de-reservation on a establishment’s outcomes . . . . . . . . . . . . . . . . 51 2.3 Parameter values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.4 Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.5 Aggregate and productivity effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.6 Output accounted for by different ability (%) . . . . . . . . . . . . . . . . . . . . . . . 65 2.7 Size distribution effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.1 Reserve outflows and extra capital inflows . . . . . . . . . . . . . . . . . . . . . . . . 84 3.2 The U.S Treasury’s Foreign Exchange Report . . . . . . . . . . . . . . . . . . . . . . . 119 A.1 Relative mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 A.2 Overproduction (%) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 A.3 Estimate Measurement Error (No trimming) . . . . . . . . . . . . . . . . . . . . . . . 151 viii B.1 Correlations with reserve flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 ix List of Figures 1.1 Distributions of TFPQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Distributions of TFPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Distributions of MRPK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Distributions of MRPL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 Dispersion over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Correlated distortions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.7 Allocative efficiency and gains from reallocation . . . . . . . . . . . . . . . . . . . . 16 1.8 Decomposition of overall variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.9 Within-group variations by quintiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.10 Plant size distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.11 Proportion of outstanding loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.12 Growth rate of loans receivable, domestic banks . . . . . . . . . . . . . . . . . . . . . 38 1.13 FDI inflows and TFPR dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.1 SSR share in manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.2 SSR share in SMEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.3 Size distribution of establishments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1 Reserve Accumulation of EMEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.2 NFA ex-IR and International Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3 External Liability and Asset of EMEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 x 3.4 Private External Assets and Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.5 Current Account and Reserve Accumulation . . . . . . . . . . . . . . . . . . . . . . . 81 3.6 Reserves and FDI & Equity Liability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.7 Reserve Outflows and Extra Capital Inflows on Selected EMEs . . . . . . . . . . . . . 83 3.8 Comparative statics of the households decision . . . . . . . . . . . . . . . . . . . . . 101 3.9 Decentralized Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.10 Reserve accumulation without capital control . . . . . . . . . . . . . . . . . . . . . . 108 3.11 Passive Reserve Accumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.12 Reserve Accumulation and Currency Manipulation . . . . . . . . . . . . . . . . . . . 120 3.13 Flow of Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.14 Reserve Depletion during Sudden Stops . . . . . . . . . . . . . . . . . . . . . . . . . . 129 A.1 Dispersion over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 A.2 Percentile ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 A.3 Decomposition of overall variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 A.4 Within-group variations by quintiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 B.1 Reserve Outflows and Extra Capital Inflows . . . . . . . . . . . . . . . . . . . . . . . . 153 B.2 External Asset Structure and GDP per capita . . . . . . . . . . . . . . . . . . . . . . . 154 B.3 Capital Outflow Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 xi Abstract This dissertation consists of three independent essays in macroeconomics. In all the essays, I focus on the context of South Korea. The first essay studies misallocation over time in Korea’s manufacturing sector. Using the confidential Korean establishment-level data, I explore the patterns of misallocation across dif- ferent sizes and ages. I find that the overall misallocation in Korea and its negative effects in- creased substantially over time. The main culprit behind such increased misallocation was dis- tortions in the capital markets. Moreover, the decomposition of the overall dispersion reveals that it was small and young firms that suffered most from the distortions. These firms were unable to utilize inputs as much as they needed, limiting their ability to expand. Lastly, I show that the extent of mismeasurement was moderate, which provides more concrete evidence of the increased misallocation. In the second essay, I study the effects of size-dependent policies (SDPs) both empirically and structurally in the context of Korean manufacturing sector. On the empirical side, I focus on the effects of the removal of small-scale reservations policy, which restricts the new entry of large firms into certain products. Using a Difference-in-Difference design, I find that elim- inating this regulation had positive effects on firm outcomes. Motivated by these findings, I investigate the quantitative effects of general SDPs. By calibrating a model to plant size distri- butions in Korea, I show that such policies have substantial negative effects on the aggregate economy. The key mechanism of this policy is the misallocation of talents: it reallocates re- sources from productive (large) to unproductive (small) firms, resulting in allocative efficiency xii losses. The third essay (joint with Bada Han) provides a novel theory of international reserve accu- mulation of Emerging Market Economies. Motivated by empirical findings we document, we view reserve accumulation as capital outflows by the public sector, which supplements less- than-optimal outflows by the private sector. In our model, EMEs face a probability of future sudden reversals in capital inflows (sudden stops). When a country receives large inflows in the form of direct or equity portfolio investment, the country should invest abroad to maintain macroeconomic balance and prepare for sudden stops. If the private sector is unable to invest abroad sufficiently due to restrictions on capital outflows, the public sector may come in to in- crease gross outflows in the form of reserves. Furthermore, our theory has implications for the debate over currency manipulation. xiii Chapter 1 Misallocation in Korean Manufacturing Sector 1.1 Introduction Why are some countries so rich and others so poor? Research has shown that one of the important factors in determining cross-country differences in living standards is allocative ef- ficiency. Poor countries generally do not use their inputs efficiently and thus fail to maximize their growth. In fact, efficient allocation is crucial to economic growth. Allocative efficiency is also imperative to explain a country’s growth over time. Better resource allocation itself is a source of economic growth. In their seminal paper, Hsieh and Klenow (2009) not only show that such misallocation impedes a country’s growth but they also present a practical methodology to measure the degree of misallocation. In this paper, I study misallocation 1 over time in Korea’s manufacturing sector. South Korea is an interesting case for studying the dynamics of misallocation because Korea has not only developed into a high-income economy in a short period but has also experienced massive 1 Klenow defines misallocation as follows: “Misallocation exists if a social planner could implement budget- neutral targeted taxes and subsidies to induce the reallocation of inputs across activities (e.g., across products, firms or occupations) in a way that would increase the welfare of a representative agent.” 1 crises that have transformed the economy. This suggests that Korea has experienced substan- tial reallocation. Rich panel data on the manufacturing sector also allows me to analyze such misallocation in terms of individual firm characteristics. I explore the patterns of misallocation across different firm sizes and ages. To provide more concrete evidence of misallocation, I use a newly developed method to exploit the longitudinal nature of the microdata, and thus I detect the extent of mismeasurement. I highlight two main findings. First, the overall misallocation in Korea and its negative effects have increased over time. Specifically, the revenue productivity (TFPR) dispersion, which is a measure of misallocation, began to rise in 2003, reaching its peak in 2013. The thickened right tail of the TFPR distribution implies that more firms confronted barriers to expanding their capacity. The main culprit behind such increased misallocation is distortions in the capital markets. While the dispersion in the labor market fluctuated only slightly, the dispersion in the capital markets sharply increased and still remained high. This shows that firms used fewer capital inputs than their optimal, which impeded their expansion. The negative effects of the increased misallocation on the economy can be gauged by the de- gree of “correlated distortions” and counterfactual efficiency gains. The correlated distortions mean more productive firms face higher taxes, implying the negative effects are large. Such distortions shot up during the Asian financial crisis and reached a peak in 2009. Moreover, the potential gains from reallocation rose greatly from 76.9% in the 1990s to 127.9% in the 2010s. Such gains suggest that, if the economy maintained the same level of allocative efficiency as in the 1990s, the aggregate productivity in the 2010s would have increased by 66.3%. My second finding is that it was small and young firms that suffered most from the distor- tions. The decomposition across different sized firms shows that it was mainly the within-group component, not the between-group, that caused the productivity dispersion. In fact, in gener- ating the aggregate variations, the dispersion within the same size group (e.g., among small or large firms) is more important than that of different groups. Further, to see whether small or large firms suffered more from the distortions, I divide the within-group variation into quintiles 2 by firm size. The results show that small firms had the highest variation compared to the other groups. Also, their variation showed a rapid increase over time. These observations imply that the misallocation worsened particularly among the small firms. The comparison between the (counterfactual) “efficient” sizes and the actual sizes shows that, among small firms, the share of the firms that needed to expand increased. In fact, the small firms employed fewer inputs, and thus they were smaller than they should have been. Repeating the exercise on a firm’s age reveals that young firms tend to face larger barriers to ex- pansion. Specifically, when the misallocation was substantial, much younger firms were unable to utilize as many inputs as they wanted. These findings rely on the assumption that the measured differences in productivity reflect the true values. If the measurement of revenue and inputs is poor, however, the greater dis- persion may not be evidence of misallocation. In fact, mismeasurement also can cause gaps in productivity. I employ a useful diagnostic by Bils et al. (2017) to resolve such error. The results show that the amount of mismeasurement in the Korean manufacturing survey is mod- erate compared to that of other countries. Moreover, the extent of the error was actually low when the misallocation was high. Therefore, these results provide more robust evidence of the increased misallocation. The remainder of the paper is organized as follows. Section 1.2 explains the theoretical framework and data that I use to measure misallocation. Section 1.3 shows misallocation over time. Specifically, we show how misallocation has evolved depending on different productivity measures. Section 1.4 discusses the patterns of misallocation by firm size by focusing on the differences between the efficient size and the actual size. Then, Section 1.5 deals with the is- sues of measurement errors in determining misallocation. In Section 1.6, I discuss reasons to suspect misallocation. Section 1.7 concludes. 3 Related Literature This paper is related mainly to two strands of literature. First, this paper relates to the literature 2 that studies misallocation and aggregate productivity. An early con- tribution is the seminal Hsieh and Klenow (2009), showing resource misallocation can lower aggregate productivity. They provide the first empirical method to measure misallocation by analyzing microdata from the U.S., India, and China. Restuccia and Rogerson (2008) analyze misallocation from hypothetical policy distortions by calibrating their model to US data. While such an "indirect approach" to studying the importance of misallocation is useful for quantify- ing the effects of misallocation, it does not allow for the identification of the underlying sources 3 of the distortions. Using panel data from China, David and Venkateswaran (2019) develop a method to disentangle sources of capital misallocation. These studies have mainly focused on differences in the extent of misallocation across countries. This paper, unlike the others, focuses on the evolution of misallocation using Korean panel data. Specifically, this research examines how the distributions of various productivity mea- sures, such as capital and labor productivity, have changed over time. With this information, we can understand which types of firms were affected most by the distortions. This emphasis on the dynamics of misallocation is similar to that of Gopinath et al. (2017), who show that in- creased capital inflows worsened capital misallocation in Spain. Chen and Irarrazabal (2015) study the role of allocative efficiency during Chile’s period of growth following the crisis of the early 1980s. In doing so, they decompose misallocation across plants of different productivity. This paper adopts the decomposition of misallocation, yet it focuses on misallocation across plants of different sizes. This paper also has relevant to studies on the measurement of misallocation. Studies on misallocation using cross-sectional data are susceptible to measurement error. Thus, to pro- vide concrete evidence of misallocation, mismeasurement (Bils et al., 2021) or misspecification 2 Restuccia and Rogerson (2017) provide a comprehensive review of the literature. See also Hopenhayn (2014) and Buera et al. (2015). 3 The examples of potential sources of misallocation are financial frictions(e.g., Moll, 2014; Midrigan and Xu, 2014; Buera et al., 2011), size-dependent regulations(e.g., Guner et al., 2008), and adjustment costs(e.g., Asker et al., 2014). 4 (Haltiwanger et al., 2018) should be considered. One notable article is Rotemberg and White (2021), who provide direct evidence of measurement error. They describe the considerable dif- ferences between the raw data a plant reports and the cleaned data the Census provides, em- phasizing the importance of trimming in measuring misallocation. Bils et al. (2021) assess the extent of additive measurement error (or overhead costs) in measuring distortions by exploiting the advantages of panel data. This paper also uses the diagnostic by Bils et al. (2017) 4 and thus evaluates whether the observed dispersions reflect misallocation. Lastly, this paper is closely related to Kim et al. (2017) and Oh (2016b), who study the mis- allocation in Korea using Hsieh and Klenow’s framework. I add to this in two ways. First, while they use cross-sectional data to measure misallocation, this paper exploits the advantages of panel data. Specifically, this allows me to examine the issues of measurement errors and the potential sources of the increased misallocation. Second, this paper focuses on the patterns and evolution of misallocation by firm size. It provides not only which types of firms in terms of size suffered most from the distortions but also in which direction the misallocation worsened within the same size group. 1.2 Theoretical Framework and Data In this section, I briefly introduce the framework proposed by Hsieh and Klenow (2009) (HK framework, hereafter) to measure misallocation. Then, I discuss the data and the measurement of the main variables. 1.2.1 Theoretical Framework The HK framework posits a standard model of monopolistic competition with heteroge- neous firms (Melitz, 2003). In an industry s, each firm ( i ) differs in its productivity, A si . Firms 4 In this earlier version, they use a simple regression approach to infer the extent of mismeasurement. They note that this approach works well except in cases where the error is large. I adopt this approach because it provides direct information on the extent of mismeasurement. 5 produce with a Cobb-Douglas aggregate of capital and labor. The key assumption is that they face firm-specific (idiosyncratic) distortions: τ Y ,si is the distortion to the marginal product of capital and labor, and τ K ,si is the distortion to the marginal product of capital relative to la- bor. On the demand side, they face a CES demand curve, resulting in curvature in a revenue function. Here, I focus on the main results of the model 5 . Misallocation measures From the profit maximization problem, we can see that the firm’s marginal revenue products of labor and capital (MRPL and MRPK, respectively) are propor- tional to the revenue per worker and the revenue-capital ratio, respectively : MRPL si = (1−α s ) σ− 1 σ P si Y si L si = w· 1 1−τ Y ,si . (1.1) MRPK si =α s σ− 1 σ P si Y si K si = R· 1+τ K ,si 1−τ Y ,si (1.2) It is noteworthy that they are also proportional to the product of the factor price and func- tions of one or both distortions. Absent distortions, both measures should be equated across firms. Hsieh and Klenow distinguish two types of productivity measures: T F PQ si = A si = Y si K α s si L 1−α s si (1.3) T F PR si = P si A si = P si Y si K α s si L 1−α s si = σ σ− 1 ( MRPK si α s ) α s ( MRPL si 1−α s ) 1−α s (1.4) where TFPQ is a quantity-based measure of TFP (“physical productivity”) and TFPR is a revenue- based measure of TFP (“revenue productivity”). This distinction is important in measuring mis- allocation. In Equation 1.4, as noted, marginal revenue products of labor and capital would be equalized in the absence of distortions, implying that TFPR does not vary. In the efficient benchmark, while TFPQ differs across the plants (A si ), TFPR remains constant. 5 I relegate a complete description of the model economy to the Appendix. 6 Therefore, TFPR dispersion within an industry is evidence of misallocation as well as the existence of firm-specific distortions. Specifically, a plant’s high TFPR signs that the plant con- fronts barriers that raise its marginal products of capital and labor, rendering the plant smaller than optimal. In the next section, we will use the TFPR dispersion as the main measure of mis- allocation. Aggregate efficiency Here, we show how the firm-specific distortions affect aggregate TFP . First, the sectoral TFP is derived as follows: T F P s (= T F PQ s )= h X i (A si · T F PR s T F PR si ) σ−1 i 1 σ−1 (1.5) where T F PR s is a geometric average of the average marginal revenue products of labor and capital in the sector. In computing the sectoral values, value-added is used as a weight. This equation shows that a plant’s distortion (T F PR si ) relative to its sectoral mean determines the sectoral TFP . Moreover, if there exist “correlated distortions” , which means the positive correla- tion between productivity and distortion, the negative effects of the distortion will be larger 6 . In the absence of distortions, T F PR si = T F PR s . Thus, the efficient sectoral TFP is the average of each plant’s TFPQ, T F P e f f s = h P i (A si ) σ−1 i 1 σ−1 . Bils et al. (2017) further decompose the sectoral TFP in this way: T F P s = h 1 N s N s X i ( A si ˜ A s ) σ−1 ( T F PR si T F PR s ) 1−σ ) i 1 σ−1 | {z } AE s =Allocative Efficiency × h 1 N s N s X i ( A si ¯ A s ) σ−1 i 1 σ−1 | {z } PD s =Productivity Dispersion × N 1 σ−1 s |{z} Variety × ¯ A s |{z} Ave. Productivity (1.6) where ˜ A s is the power mean of idiosyncratic productivities, N 1 1−σ s · T F P e f f s , and ¯ A s is the geo- metric mean of idiosyncratic productivities, Q (A si ) 1 N s . If the allocative efficiency ( AE s ) is close to one, it means that there is no variation in the distortions across firms within an industry. Meanwhile, the higher the productivity dispersion (PD s ), the greater the sectoral TFP . 6 This issue is discussed in details in Section 1.4. 7 Lastly, we compute the counterfactual efficiency gains from reallocation by comparing the actual sectoral TFP to the efficient one. After calculating the ratio of these two values, we ag- greagate this ratio across sectors with the CD aggregator (θ s ) in this fashion: Y Y e f f = Y s £ T F P s T F P e f f s ¤ θ s = h X i ( A si T F P e f f s · T F PR s T F PR si ) σ−1 i θ s σ−1 . (1.7) 1.2.2 Data I use the Mining and Manufacturing Survey (MMS) conducted by Statistics Korea, Korea’s official national statistical organization. Midrigan and Xu (2014) and Asturias et al. (2017) have also used this data set. This annual survey is a panel that covers all mining and manufacturing plants in Korea with at least five employees until 2007 and ten employees after 2008. For consis- tency, I only consider plants with ten or more workers. Although this survey was firstly carried out in 1968, the data are only available from 1992. Then, I use the MMS data from 1992 through 2019 which is sufficient to analyze the dynamics of allocative efficiency. The MMS has detailed information on outputs and inputs at the plant level, which is suit- able for this paper. The main variables are value-added, labor costs, and capital stock. For outputs, I use value-added rather than gross output following Hsieh and Klenow (2009). In this survey, value-added is defined as the total revenue net of spending on intermediate inputs such as raw materials and electricity costs. For labor inputs, I construct labor compensation by sum- ming up wages, benefits, and employee pension. Compared to the number of workers, this compensation is better to capture the quality of labor. Capital is constructed as the average of the opening and closing book value of capital. The survey provides seven different types of capital. Following Oh (2016b), I only consider three types of capital: buildings and structures, machinery and equipment, and vehicles and ships. To compute the real values, I constructed deflators for each type of capital using gross capital formation in national accounts provided by the Bank of Korea. The total (real) capital stock is the sum of the real values of the three types of capital. I drop plants with missing or negative 8 values of any of the main variables required to construct productivity measures. In addition to the main variables, the MMS contains firm age (the self-reported year of birth), location, and intermediate inputs. One challenge is that there were four revisions in the Korean Standard Industry Classifica- tion (KSIC) during the sample period. KSIC Rev. 6 is for 1992-1997, Rev. 8 for 1998-2006, Rev. 9 for 2007-2015, and Rev. 10 for 2016-2019. KSIC Rev. 6 and 8 are comparable to the ISIC Rev. 3, and KSIC Rev. 9 and 10 correspond to the ISIC Rev. 4. To construct panel data, I use the KSIC Rev. 9 as the baseline and then use the correspondence tables to link the different classifica- tions to the baseline. While the industry specification is based on a five-digit KSIC code, I use four-digit level industries as the main unit of industry analysis. Since this analysis focuses on the manufacturing sector, I drop the plants in the mining industries. On average, there were 175 industries in the manufacturing sector every year. To calculate resource misallocation, in addition to key variables from data, we need to as- sume parameters: the rental price of capital, the elasticity of substitution, and sectoral factor shares. The rental price of capital without individual wedges is set to R = 0.10 following Hsieh and Klenow (2009) as the sum of a real interest rate and a depreciation rate. The capital price that a firm faces is the rental price multiplied by an individual capital wedge. Thus, what de- termines the dispersion of capital is not the common rental price but the individual wedge. Another key parameter is the elasticity of substitution because the hypothetical efficiency gains are closely associated with this elasticity. While there is considerable variation in the estimates of this elasticity, following Hsieh and Klenow (2009), I set it equal to three. There are a couple of ways how to compute the sectoral factor shares. For example, Hsieh and Klenow (2009) apply U.S. shares as the benchmark to the cases of India and China. This is under the assumption that the U.S. is the most undistorted economy. However, instead of using the U.S. data, I compute the sectoral factor shares in each industry directly from the data. Since I use Cobb Douglas production function at the industry level, the capital share in each industry is computed as one minus its labor share. The labor share is the ratio of the labor compensation, 9 the sum of wages and other benefits, to value-added for each industry. To reflect the fact that the technology evolves across industries over time as well as within an industry at a time, I compute the factor shares for each industry and year. I trim the 1% tails of plant productivity and distortions in each year to make the results robust to outliers. After trimming the sample, I recalculate the sectoral shares to compute pro- ductivity measures. 1.3 Misallocation over time In this section, I show how the misallocation in the Korean manufacturing sector has evolved over time. I first present the evolution of various productivity measures. Then, I discuss their correlations to show how much the misallocation depresses the total productivity. Lastly, I quantify the potential gains of allocative efficiency by reallocation. 1.3.1 Evolution of productivity dispersion To characterize the dynamics of allocative efficiency, I choose the years 1993, 2003, and 2013 from the whole sample (see the appendix for more detail). As I discuss below, the misallocation began to rise in 2003, reaching its peak in 2013. Therefore, these years are useful to understand the evolution. Figure 1.1 plots the distribution of TFPQ. As discussed, under normality assumption, a greater variance of TFPQ increases aggregate productivity. This is because more productive firms will produce more, and thus be weighted more heavily in the calculation of TFP . In this figure, the dispersion of TFPQ increased by 2013, implying that the evolution of TFPQ contributed to a higher TFP . After its peak in 2013, it decreased a bit. Meanwhile, the means of TFPQ slightly moved to the right, which indicates the average productivity of the economy increased. An- other thing to note is that the distribution of TFPQ became a fat right tail. This was still true even after 2013, when the dispersion started to decrease. It demonstrates that the share of more 10 productive firms increased. As long as the reallocation of inputs works well, they contribute to the growth of aggregate productivity. To better understand the dynamics of TFPQ, whether highly productive firms were entrants or incumbents matters. At the current stage, however, we cannot identify it. We will discuss this entry-exit issue later. Figure 1.2 shows the distribution of TFPR for the same years. Unlike TFPQ, a higher variance of TFPR leads to lower aggregate productivity. Ideally, if there were no distortions, we would have a degenerate distribution because firms in the same sector will have the same marginal products. Thus, the presence of TFPR dispersion indicates the resources are not allocated ef- ficiently. Figure 1.2 clearly shows that the dispersion of TFPR increased over time. The right tail of the distribution significantly thickened, implying that more plants confronted barriers in expanding their output. Thus, they were smaller than optimal. This trend is consistent with the fact that the misallocation increased. The thickness in the right tail is also verified by right skewness. The skewness of the distribution in 1993 was 0.66, but in 2019 it increased to 1.1. The left tail, on the other hand, did not change significantly. It suggests that less efficient firms did not exit the sample. Next, I present how the misallocation in both capital and labor markets evolved. As seen in Figure 1.3 and Figure 1.4, the main culprit behind the higher TFPR dispersion seems to be capital because the distribution of the marginal revenue products of capital has also a fat right tail. Compared to TFPR, the changes in the right tails are more pronounced. This implies that more plants faced difficulty using more capital. That is, capital market distortions were severe in the economy. Note that, unlike TFPR, even in 2019 the right skewness remained. On the other hand, the distribution of MRPL, which shows the misallocation in the labor market, has a left fat tail. It suggests that many plants hired more workers than optimal. In sum, the distributions of MRPK and MRPL indicate that, since firms that wanted to expand had obstacles to utilizing more capital, they had to substitute labor for capital. This led them to use more labor than optimal. 11 Figure 1.1: Distributions of TFPQ Note: This figure shows the distribution of TFPQ, log( A si M 1 σ−1 s / ¯ A s ), for 1993, 2003, and 2013. Figure 1.2: Distributions of TFPR Note: This figure shows the distribution of TFPR, log( T F RP si /T F PR s ), for 1993, 2003, and 2013. 12 Figure 1.3: Distributions of MRPK Note: This figure shows the distribution of MRPK, log( MRPK si /MRPK s ), for 1993, 2003, and 2013. Figure 1.4: Distributions of MRPL Note: This figure shows the distribution of MRPL, log( MRPL si /MRPL s ), for 1993, 2003, and 2013. 13 Figure 1.5: Dispersion over time Note: Dispersion is the standard deviation of productivity measures. Specifi- cally, it is the weighted average of each sector’s standard deviation. Value-added is used for the sectoral weight. I display standard deviations of the above productivity measures over the entire sample pe- riod (see Figure 1.5). The standard deviations simply summarize the dispersion of productivity. As discussed, dispersions of TFPR and MRPK follow a very similar trend. After the Asian finan- cial crisis in 1997, the trend started to rise in 2003 and peaked in 2013. Although it decreased a bit thereafter, the level of dispersion still remained high compared to the 1990s. While the capi- tal dispersion increased from 1993 (0.94) to 2019 (1.23) by about 30 percent, the labor dispersion rose during the same period by a modest 15 percent. 1.3.2 Correlated distortions and efficiency gains In addition to the increased productivity dispersion, another important aspect is the corre- lation between the distortions and productivity. The analysis in Restuccia and Rogerson (2008) found that misallocation has large negative effects on the economy if the distortions that a firm 14 faces are positively associated with its productivity. That is, “correlated distortions” mean more productive firms are systematically taxed and less productive firms are systemically subsidized. Such correlated distortions have larger impacts. If the distortions are purely random, on the other hand, its effect is not that costly. One way to check this relationship is to compute the correlation between a firm’s TFPR and TFPQ. This correlation is also related to an alternative measure of misallocation in Bartelsman et al. (2013). They focus on the covariance between firm size and productivity. Absent any wedges, a more productive firm will produce more. Chen and Irarrazabal (2015) show that this covariance has a one-to-one relation with the covariance of TFPR and TFPQ. Thus, the corre- lation between revenue and physical productivity is suggestive of misallocation in a different way. Figure 1.6 depicts the path of this correlation. From 1992 to 1997, the correlation remained fairly static at approximately 0.69. However, after a dramatic increase during the Asian financial crisis, it showed an upward trend and reached a peak of 0.78 in 2009. Compared to the 1990s, the correlation increased by about 10%. Thereafter, it went up and down only slightly. The increased correlation implies that the economy also experienced the correlated distortions. The more productive a firm is, the more (implicit) taxes it pays. Accordingly, the negative effects of misallocation on total factor productivity became more noticeable. Another exercise using the HK method is to compute counterfactual gains from equalizing TFPR (See Equation 1.7). As discussed earlier, without any distortions, firms in the same indus- try should have the same marginal products. From this intuition, one can estimate the extent of the gains from equalizing their marginal products. As Hsieh and Klenow (2009) noted, these gains could be overstated due to model misspecifications or measurement errors. The exercise shows that the potential gains from reallocation, averaged across years, increased from 76.9% in the 1990s to 127.9% in the 2010s (see Figure 1.7). If the resources were efficiently allocated in the 2010s, aggregate manufacturing productivity would have increased by 126%. 15 Figure 1.6: Correlated distortions Note: The correlated distortions are the correlation between each plant’s logTFPQ and logTFPR. Figure 1.7: Allocative efficiency and gains from reallocation Note: The figure shows the % allocative efficiency and its gains from hypothet- ical reallocation. If allocative efficiency is close to 100, there is no variation in the distortions across plants within the same industry. The counterfactual gains are computed by comparing the actual TFP to the efficient one. 16 1.4 The patterns of misallocation by firm size In this section, I explore the patterns of misallocation across different firm sizes. The overall trend of the misallocation is discussed in the previous section. However, to better understand what is behind this, we need to investigate how firms of different sizes contribute to resource allocation for two reasons. First, from a policy perspective, we need to know which types of firms use inputs inefficiently and firm size is a simple criterion to design a relevant policy to enhance allocative efficiency. Second, the gap between small and large firms is rapidly growing. One of the driving forces behind this change may be the misallocation by firm size. 1.4.1 Decomposition Following Chen and Irarrazabal (2015), as well as Calligaris et al. (2018), I decompose TFPR dispersion into within and between-group components. I divide the firms in the sample into five groups (quintiles) according to their value-added in each industry and year. Therefore, the decomposition of industry-level TFPR dispersion is as follows: V ar s (log T F PR si )= 1 M s Q X q N q X i (log T F PR sqi − log T F PR s ) 2 | {z } overall variation = 1 M s Q X q N q V ar (log T F PR si ) q | {z } within-group component + 1 M s Q X q N q (log T F PR sq − log T F PR s ) 2 | {z } between-group where q is the quintiles of firm size (value-added); log T F PR sqi is the logT F PR for plant i belongs to the qth quintile in the industry s; log T F PR s is the mean of logT F PR for the industry s; and log T F PR sq is the mean of logT F PR for the qth quintile and the industry s. After computing these components in each industry, I weighted them using each indus- try’s value-added to determine aggregate level variation. From this decomposition, we can see which component drove the increase in misallocation. If the within-group component is large, 17 for example, the variations of the firms in the same size group are important. In this case, what matters is the differences not between small and large firms but among firms of the same size. I also compute each quintile’s variations to identify which size group is the impetus behind the increase in misallocation. For this decomposition, I drop the observations if the number of plants in an industry is less than ten. In the sample, 1,257 plants are dropped, but the findings in the previous do not change. 1.4.2 Misallocation by firm size The decomposition shows that the within-group variation mainly caused the aggregate vari- ation (Figure 1.8). The share of within-group variation, averaged across years, was approxi- mately 96%. The between-group variation only made up a small part. As discussed, it sug- gests that, in generating the aggregate dispersion, the productivity dispersion in the same size group is more important than that of different groups. Also, while the between-group com- ponent remained fairly unchanged over time, the within-group component moved in tandem with the variance of TFPR. It demonstrates that the variation in the same size group completely drove the aggregate trend. Considering the fact that the gap between small and large firms has widened, this result is somewhat contrary to the expectation that the between-group variation dominates. To further understand what happened in the within-group variation, I divide it into quin- tiles according to firm size and then compute each quintile’s TFPR dispersion (Figure 1.9). The first thing to note from this figure is that the bottom quintile (small firms) not only had the highest TFPR variance over the entire period but also showed a rapid increase relative to the other groups. In the 1990s, the differences between the quintiles were not big and the disper- sions fluctuated only slightly. However, after 2000, the variances of the different groups began to diverge. The TFPR variance of the smallest firm group almost doubled from 1996 to 2013. The top quintile (large firms), on the other hand, showed low volatility by increasing 64% in the 18 same period. A notable finding for the largest firm group is that there were significant rises in its dispersion after the Asian financial crisis and the Great Recession. The analysis above showed that the misallocation worsened particularly among the small firm group, rather than between small and large firms. In fact, in the past, small firms did not clearly show the differences in revenue productivity. However, after 2000, their differences in productivity became greater. Two interpretations behind this phenomenon are probable. First, among the bottom quintile (small firms), the share of higher TFPR firms increased, implying that the small firms were unable to utilize inputs due to some frictions. Second, the portion of lower TFPR firms rose. This suggests that unproductive small firms which should have exited remained in the market possibly due to government subsidies. Figure 1.8: Decomposition of overall variance Note: This figure shows the variance of TFPR, var(log( T F RP si /T F PR s )), and its within-group and between-group components. Plants are divided into five groups according to their value-added in each industry and year. 19 Figure 1.9: Within-group variations by quintiles Note: This figure shows each quintile’s TFPR variance. Plants are divided into five groups (quintiles) according to their value-added in each industry and year. Bottom (top) quintile is the small (large) plant group. 1.4.3 Efficient and actual plant size We can investigate which interpretation is more reliable by comparing the “efficient” plant sizes to the actual sizes. As noted above, size is defined as a plant’s value-added. The efficient plant size is computed by replacing idiosyncratic wedges with industry-level wedges. Therefore, each firm’s TFPR is equalized to its industry’s TFPR. That is, to figure out the efficient size, we do not need to remove all of the distortions. As long as the plants in the same industry face the same level of wedges, the resource allocation is efficient and mirrors what the social planner achieves. Then, we can evaluate if a plant should contract or expand to reach its most efficient level. This information is crucial in understanding what happened within the small firm group. If the actual size is smaller than its efficient size, for instance, it means they faced some barriers to expanding their output. I begin by presenting findings from the entire sample period. Table 1.1 shows the percent- age of plants that need to contract or expand according to their size group. To make a con- 20 sistent comparison with the previous subsection, a plant size group is determined according to its value-added in each industry and year. The rows are actual plant size quintiles, and the columns are bins of efficient size relative to actual size. For example, 0%-50% means the plant should shrink by half or more, and 200%+ indicates that the plant should at least double. The key finding is the positive size-TFPR relation, which is also observed in other studies on misal- location in India and China. That is, the larger a plant size, the higher the share of the plants that need to expand. For example, the proportion of the plants that are smaller than the op- timal within the largest firm group (the top quintile) is 13.3%, while that of the smallest group (the bottom quintile) is 10.7%. Table 1.1: Percent of plants, actual vs. efficient size 1992-2019 Shrink Expand Size Quintile 0-50 50-100 100-200 200+ Shrink Expand Bottom (Small) 5.9 3.5 3.4 7.3 9.4 10.7 Second 4.5 3.8 4.0 7.8 8.3 11.7 Third 4.0 3.9 4.1 8.0 7.8 12.1 Fourth 3.5 3.9 4.3 8.3 7.4 12.6 Top (Large) 2.8 3.8 4.6 8.8 6.5 13.3 Notes: Plants are divided into five groups according to their value-added in each industry and year. The efficient level of each plant’s output is calculated by assum- ing TFPR are equalized within an industry. The entries are the percent of plants. Next, I do the same exercise for two periods when the productivity dispersion was low and high. The TFPR dispersion was low from 1992 to 1997 (Period 1), while it was high from 2008 to 2014 (Period 2). By comparing outcomes in the two periods, we can figure out in which direction the misallocation worsened among the small firms. Table 1.2 presents the percentage of plants in Periods 1 and 2. It is notable that, among the small firms (the bottom quantile), the share of plants that need to expand slightly increased (10.4%→ 11.2%). Specifically, the share of plants 21 that should at least double in size shot up (6.1%→ 8.2%). These changes also happened among the second quantile. It implies that the small firms were not able to utilize inputs as much as they needed. This means they were smaller than the optimal. The remaining quintiles changed only slightly. Another thing to note is that the shares of both 0%-50% and 200%+ increased in the large firm group, implying the differences between the efficient sizes and the actual sizes rose. We can interpret this as the technology gap among the large firms increased. It is also imperative to see how the entire size distributions evolved. I compare the efficient and actual size distributions in 1993, when TFPR dispersion was low, and in 2013, when it was high. It is clear that there were more mid-sized firms in both years compared to the efficient distribution (Figure 1.10). It suggests that some firms were larger than their optimal sizes due to (implicit) subsidies and other firms were smaller due to taxes. In fact, the economy needed more firms, both small and large firms, to increase allocative efficiency. It is noteworthy that the efficient size distribution in 2013 was more dispersed than that in 1993. The standard deviation of plant size (value-added) increased from 1.8 in 1993 to 2.2 in 2013. The actual distribution, however, remained basically unchanged as the standard deviation in both years was approx- imately 1.2. Although the economy should have moved to where there were more small and large firms to achieve efficient allocation, it failed to respond and maintained the status quo. Meanwhile, the average plant size increased from 1993 to 2013. This increase in average es- tablishment size was accompanied by an increase in GDP per capita in the same period. This pattern is consistent with the findings from Bento and Restuccia (2021), which show a positive relationship between average plant size and GDP per capita in the manufacturing sector. In addition to this exercise on efficient firm size, I look at how the relative mean of TFPR in each industry evolved and how the share of overproduction changed to see what was behind the growing misallocation among the small firms. I relegate the outcomes of these exercises to the appendix. All of these exercises reveal that, compared to the 1990s, the small firms struggled to use inputs efficiently. Therefore, they were unable to expand, and thus smaller than they should have been. 22 Figure 1.10: Plant size distributions Notes: Size is value-added. The efficient level of each plant’s output is calculated by assuming TFPR are equalized within an industry. 23 Table 1.2: Percent of plants, actual vs. efficient size (a) When misallocation was low 1992-1997 Shrink Expand Size Quintile 0-50 50-100 100-200 200+ Shrink Expand Bottom (Small) 5.6 4.3 4.3 6.1 9.9 10.4 Second 4.3 4.1 4.5 7.1 8.4 11.6 Third 3.9 3.9 4.4 7.8 7.8 12.2 Fourth 3.4 4.0 4.3 8.3 7.4 12.6 Top(Large) 2.5 4.0 4.9 8.5 6.5 13.4 (b) When misallocation was high 2008-2014 Shrink Expand Size Quintile 0-50 50-100 100-200 200+ Shrink Expand Bottom (Small) 5.9 3.0 3.0 8.2 8.9 11.2 Second 4.5 3.6 3.6 8.2 8.2 11.8 Third 4.0 3.8 4.0 8.1 7.9 12.1 Fourth 3.7 3.8 4.2 8.3 7.5 12.5 Top (Large) 2.9 3.7 4.4 8.9 6.6 13.2 Notes: Plants are divided into five groups according to their value-added in each industry and year. The efficient level of each plant’s output is calculated by assuming TFPR are equalized within an industry. The entries are the percent of plants. 24 1.4.4 Plant age The dynamics of misallocation are also characterized by a plant’s age, the life cycle of a plant. A well-known fact in the United States is that older establishments are typically more produc- tive and larger. However, Hsieh and Klenow (2014) find that this positive relation between age and productivity/size is relatively weak in both Mexico and India. The reason is that misalloca- tion largely causes the differences in productivity distributions. Since more productive firms in these countries face higher taxes or factor prices, small firms have less incentive to grow. This dynamic decision on investment and growth affects the distribution of productivity, generating a weak relation between firm age and productivity. Therefore, to better understand the mis- allocation over time, it is crucial to study whether young or old firms suffer more from such distortions. Measurement When analyzing a firm’s life cycle, measuring a firm’s age from raw data can be tricky. This is because the self-reported years of establishment in the data are imperfect. The plants often reported conflicting years. In fact, for the 275,877 plants in the sample, there are 416,645 years that match those plants. This means that each plant provided at least two or three different years. As a result, it is difficult to consistently track the plant’s performance. To avoid this critical drawback, I estimate a firm’s age based on its first appearance in the data. That is, since the panel data provide a unique identifier for each plant over the years, I can determine when a plant first appeared, and track when it exited or survived. Instead of using imperfect information, with this approach, age can be computed consistently. However, we need to remedy this approach’s shortcomings. First, there is an issue with the observations in the first year of the survey, 1992. Since the data started in 1992, all plants in that year first appeared, and thus they were considered as an age of zero. Clearly, this is not true be- cause most firms had existed before the survey started. Therefore, this method underestimates their ages. To overcome this problem, as long as a plant provided the same answer across the survey, I use the self-reported year of establishment. Another limitation is that the data only in- 25 clude plants with more than ten employees. If it takes a long time for a new firm to grow above this threshold, this approach could be an issue. Since all firms generally experience similar life cycles, the effects of this limitation will be minimal. Plant age The goal of this subsection is to investigate which firms suffer more from the distor- tions in terms of age. After dividing the sample according to the efficient sizes and the actual sizes as I did in the previous subsection, I compute the average age of plants that are in the same category (Table 1.3). The rows and columns mean the same as in Table 10. The entries here are the average ages. For example, 4.8 years in the bottom quintile (last column) indicates that the average age of plants in the quintile is 4.8 years. As shown in the last column of Table 1.3, plant age is positively correlated to plant size. Old firms are larger, and young firms are smaller. One interesting finding is that, in the same size group, a plant that needs to expand more is younger. For example, in the bottom quintile (small firm group), the (average) age of plants that need Table 1.3: Average age of plants, actual vs. efficient size 1992-2019 Shrink Expand Size Quintile 0-50 50-100 100-200 200+ (Average) Bottom (Small) 5.8 5.1 4.7 3.8 4.8 Second 7.0 6.2 5.9 5.1 5.9 Third 8.0 7.4 7.0 6.0 6.9 Fourth 9.1 8.8 8.6 7.4 8.2 Top (Large) 11.9 12.0 12.0 10.4 11.3 (Average) 8.3 7.9 7.7 6.5 7.4 Notes: Plants are divided into five groups according to their value-added in each industry and year. The efficient level of each plant’s output is calcu- lated by assuming TFPR are equalized within an industry. The entries are the average age across plants in the same bin. 26 to shrink by half or more is 5.8 years. On the other hand, the age of plants that should at least double in size is 3.8 years. This relation happens across all groups. It suggests that young firms tend to face higher barriers to expanding, and thus they use fewer inputs than their optimal. Next, I do the same exercise for Periods 1 and 2 as previously defined. This exercise is to see which firms particularly suffered when the misallocation worsened. Table 1.4 presents the average age of plants in each period. One thing to note is that the average age (8.4) in Period 2 (2008 – 2014) is generally higher than that (5.8) of Period 1 (1992 – 1997) because Period 2 is almost 15 years from Period 1. Therefore, it would be desirable to utilize an age relative to the overall average age in the sample. I consider how young a plant is compared to the average age. I find that when the misallocation was high (Period 2), among the first and second quintiles (small firms), the plants that need to expand were younger compared to Period 1. For example, within the bottom quintile, the plants that should at least double were 4.1 years younger than the average age. This was 3.1 in Period 1. That is, much younger firms were placed in a situation where they were unable to employ as many inputs as they wanted. In sum, the exercises on a firm’s age revealed that it was young firms that confronted the most barriers to hiring more workers and raising more capital. Therefore, they ended up be- ing smaller than their optimal sizes. This indicates that the inputs were misallocated among young firms. Moreover, when the misallocation was high, this pattern was reinforced. That is, it became increasingly difficult for relatively young firms to expand their production. 27 Table 1.4: Average age of plants, actual vs. efficient size (a) When misallocation was low 1992-2019 Shrink Expand Size Quintile 0-50 50-100 100-200 200+ (Average) Bottom (Small) 4.3 3.8 3.3 2.7 3.5 Second 5.5 5.1 4.6 3.8 4.6 Third 6.4 6.0 5.4 4.4 5.3 Fourth 7.1 6.9 6.7 5.5 6.3 Top (Large) 9.9 9.9 9.8 8.2 9.1 (Average) 6.7 6.3 6.0 4.9 5.8 (b) When misallocation was high 1992-2019 Shrink Expand Size Quintile 0-50 50-100 100-200 200+ (Average) Bottom (Small) 6.5 5.8 5.3 4.3 5.3 Second 7.6 7.0 6.9 5.8 6.6 Third 8.8 8.3 8.1 7.1 7.9 Fourth 10.0 9.8 9.9 8.7 9.4 Top (Large) 12.8 13.3 13.3 11.9 12.6 (Average) 9.1 8.8 8.7 7.6 8.4 Notes: Plants are divided into five groups according to their value-added in each industry and year. The efficient level of each plant’s output is calculated by assuming TFPR are equalized within an industry. The entries are the average age across plants in the same bin. 28 1.5 Mismeasurement Studies on misallocation using cross-sectional data are susceptible to measurement error. They assume that differences in measured average products reflect differences in true values. From this assumption, we interpret the dispersion in measured TFPR as evidence of misallo- cation as we did in the previous sections. However, the mismeasurement in value-added and inputs also causes gaps in the productivity measures. Thus, the dispersion, though it is often assumed to be evidence of misallocation, may in fact be evidence of measurement error. If so, the increased misallocation may simply suggest that the mismeasurement problem worsened. This is why we need to examine measurement issues. Panel data provide a way of detecting mismeasurement. In this section, I introduce the method proposed by Bils et al. (2017) and address measurement issues. 1.5.1 Intuition Bils et al. (2017) propose a method to quantify the extent to which measured average prod- ucts imply true marginal products in the presence of measurement error. Their main argument is that revenue changes are less sensitive to input changes when average products are overstated by the error. To compute these changes, one needs consecutive observations of a plant: panel data. Using this method, they show that the correction of measurement error reduces potential gains from reallocation by 20% for Indian manufacturing and by 60% for the U.S. Other studies, including those by David and Venkateswaran (2019), Bai et al. (2019), and Adamopoulos et al. (2022), have applied their method to detecting mismeasurement in Chinese firm and farm-level data. The intuition of this method is as follows: Absent mismeasurement, if a firm has high TFPR, it means that the firm is facing barriers to utilizing more inputs, and thus it is smaller than opti- mal. Then, an increase in inputs would lead to higher revenue. This relation holds regardless of whether TFPR is high or low. In fact, revenue growth is proportional to input growth across all 29 the plants. If there are any mismeasurements in inputs and revenue, however, this relation no longer holds. For example, assume that a firm has high TFPR because of overstated revenue or understated inputs, not because of the distortions it faces. Then, since its true TFPR is smaller than its measured TFPR, its revenue growth is less responsive to its input growth. The higher the TFPR relative to the true distortion, the lower the revenue growth relative to the input growth. Therefore, by computing the elasticity of revenue with respect to inputs over time, we can infer the extent of mismeasurement. One caveat is that this method is based on two assumptions regarding the form and distri- bution of the error for identification. First, they assume that the error in revenue and inputs are an additive form. This is why this method can be interpreted as a tool to detect overhead costs. Since they focus on these purely additive errors, the estimates should be viewed as a con- servative assessment of mismeasurement. Second, they assume that the error is orthogonal to the true marginal products. This is a key restriction to identifying the error in the data. This restriction means that the amount of errors is not associated with a plant’s productivity. 1.5.2 Data and specifications From this intuition, they regress revenue growth on input growth, TFPR, and the interac- tion of input growth and TFPR across plants. I adopt this approach and estimate the following model: ∆ ˆ R i t =β 1 ln(T F PR) i t +β 2 ∆ ˆ I i t +β 3 ln(T F PR) i t ·∆ ˆ I i t + D st +ϵ i t (1.8) where∆R is the (annual) growth rate of each plant’s measured value-added; lnT F PR is the aver- age logT F PR for the current and previous year;∆I is the growth rate of (measured) inputs; and D is a full set of sector-year fixed effects Here, ∆I is constructed as the growth rate of composite inputs,∆I=α∆K+ 1−α∆L, whereα is the capital share of industry; L is labor compensation; and K is capital stocks. Labor compensation is the sum of wages, pensions, and other benefits. 30 Capital stocks include the three types of capital that were used previously. These variables are nominal values. The variable of interest is the coefficient on the interaction term ( β 3 ). As discussed, if the revenue growth is less responsive to the input growth for high TFPR plants, which is evidence of mismeasurement, this coefficient is negative. Specifically, Bils et al. (2017) show that we can identify an estimate of the share of the dispersion in TFPR that is due to the true variation,λ, from the regression coefficients ( λ= 1+ β 3 β 2 ). In fact, we can decompose the TFPR variation into the true variation and the variation from the measurement error. Here,λ shows the amount of true variation in generating the misallocation. For instance, ifλ is close to one, it means that the measurement error is minimal. This is because most variations in TFPR are due to variations in the distortions. I estimate this equation using OLS, clustering standard errors at the plant level. To imple- ment this regression, the sample needs to be modified. First, since the growth rates of value- added and inputs are needed, I drop all the observations that appear only one time. Second, following the original paper, the 1% tails of both growth rates are trimmed to make the results robust to outliers. I also list the regression results without trimming in the appendix. 1.5.3 Results The first column of Table 1.5 reports the results of the baseline regression over the entire sample period. The coefficients of interest, which are β 2 (Input growth) andβ 3 (Interaction), are significant and have the expected signs. ˆ β 2 is 0.36, implying that a one percentage point increase in the input growth, evaluated at the mean lnTFPR, is associated with a 0.36 percentage point increase in the growth of value-added. The key coefficient, the implied λ, is 0.748. Hence, 74.8% of the variation in TFPR is due to the true distortions, and the remaining 25.2% is due to the measurement error. This amount of mismeasurement is relatively moderate compared to that of other countries. Bils et al. (2017) show that the λs for the U.S. and India are 0.229 and 0.547, respectively, which suggests that the error is 77.1% and 45.3%. Therefore, the Korean 31 manufacturing sector seems to have a low level of mismeasurement. Although there was a relatively small amount of the error, one may say that mismeasure- ment is time-varying. For example, the extent of the error was particularly high when the mis- allocation worsened. In this case, the measured distortions would overestimate the negative effects of the misallocation. To resolve this issue, I break the entire sample into two periods. One is when the dispersion was low (1992-2002), and the other is when it was high (2003-2019). If the estimated mismeasurement was significantly greater in the second period, the increased misallocation may have been caused by the measurement error. However, the results are fairly consistent across sub-periods, as shown in Columns (2) and (3). In both regressions, the coefficients of interest are significant and have the expected signs. While the estimatedλ is 0.704 in the first period, it is 0.761 in the second. Like the regression using the entire sample, the extent of the measurement error is approximately 25%. In fact, the estimated λ rose slightly in the latter period when the misallocation increased. This implies that mismeasurement decreased during this period. Thus, the increased misallocation cannot be explained by the measurement error. I also check whether or not the results are robust if I weigh the observations with their shares of value-added relative to the total value-added. Columns (4) - (6) correspond to Columns (1) - (3) in terms of the sample period. The overall findings are similar compared to when there are no weights. For example, in Column (4), ˆ β 2 and ˆ β 3 are highly significant. The estimated λ is 0.874, implying that the true distortions explain 87.4% of the TFPR variations. In fact, the degree of mismeasurement decreases. For the estimation of the two sub-periods, the estimatedλ are 0.906 and 0.831, respectively. Although we have lowerλ in the second period, the amount of the estimated errors is quite low. Moreover, the results are robust when I use all the observations without trimming (See Appendix). In sum, these regression analyses show that the productivity dispersion was mainly driven by distortions rather than measurement error typically conceived. Also, the extent of mismea- surement seems to be low compared to other countries. This result is comparable to that of 32 Dong and Hsieh (2021)’s exercise. They also study the extent of (capital) measurement error in the Korean manufacturing sector. They find that the variance of error constitutes approximately 20% of the variance of capital measures. Table 1.5: Estimate Measurement Error Dep. Variable: Value-added Growth (1) (2) (3) (4) (5) (6) 1992-2019 1992-2003 2004-2019 1992-2019 1992-2003 2004-2019 Average TFPR 0.00303** -0.00923** -0.00124 -0.0149* -0.0299* -0.0000146 (1.97) (-2.42) (-0.65) (-1.95) (-1.93) (-0.00) Input Growth 0.360*** 0.350*** 0.379*** 0.356*** 0.331*** 0.404*** (85.18) (55.34) (64.12) (16.80) (11.83) (13.03) Average TFPR -0.0906*** -0.104*** -0.0907*** -0.0450*** -0.0311+ -0.0684*** x Input Growth (-35.32) (-21.76) (-28.89) (-3.52) (-1.59) (-4.46) ˆ λ 0.748 0.704 0.761 0.874 0.906 0.831 Plant fixed effects Yes Yes Yes Yes Yes Yes Year fixed effects Yes Yes Yes Yes Yes Yes Observations 937,385 339,550 597,835 937,385 339,550 597,835 Adj. R-sq 0.0897 0.0937 0.0723 0.0949 0.0975 0.0853 Notes: Average TFPR is the average TFPR in logs for the current and previous years. In Columns (4)-(6), the plant’s value-added is used as a weight. Reported in brackets are the corresponding t statistics. Standard errors are clustered at the plant level. +, *, ** and *** indicate statistical significance at the 15%, 10%, 5%, and 1% levels, respectively. 33 1.6 Discussion In this section, I briefly discuss the potential sources of the increased misallocation. Fo- cusing on the fact that capital misallocation is the main culprit, I relate the increase in misal- location in Korea to risk premium, financial intermediation, and capital flows. In addition, the prevalent size-dependent policies and the great presence of large firms may be other candidates behind the misallocation. 1.6.1 Risk premium Recent research has investigated the link between business cycle volatility (macroeconomic risk) and resource misallocation (firm-level dispersion). David et al. (2021) find that dispersion in firm-level risk premia can account for a substantial portion of the measured MPK dispersion 7 . Since the aggregate risk should be incorporated into the model, this framework requires a departure from the canonical Hsieh and Klenow (2009). To illustrate it, assume a standard neo- classical theory of investment. From the Euler equation, we can derive the following equation for expected MPK: E t [MPK i ,t+1 ]=α t +β i t λ t (1.9) where the common risk-free user cost (α t ) is the sum of risk-free rate and the depreciation rate (α t ≡ r f t +δ) and the firm-specific risk premium ( β i t λ t ) is the product of the riskiness of the firm (the firm’s beta, β i t ) and the market price of that risk (λ t ). In fact, it shows that firms equate their expected MPK to the cost of capital. From this, the variance of expected MPK is σ 2 E t [MPK i ,t+1 ] =σ 2 β i t λ 2 t . (1.10) 7 In this sense, if the wedges generated by risk premia are the source of productivity dispersion, “misallocation” may be efficient. 34 This equation shows that the extent to which risk considerations lead to MPK dispersion is increasing in the variation in risk exposure and the price of risk, implying an important role of differences in risk premia in explaining the dispersion. To examine whether the risk premia contributed to the increased (capital) misallocation in Korea, I first compute the simple measure of firm-level risk. I follow Comin and Philippon (2005), who compute firm-level volatility using real measures, such as capital expenditures or sales. Similar to Section 1.4, I divide the sample (1992-2019) into two sub-periods to see how the firm-level risk changed. One (Period 1) is when the dispersion is low (1992-2005), and the other (Period 2) is when it was high (2006-2019). Then, I compare the firm-level volatility be- tween the two periods. If the measured firm-level risk was greater in the second period, risk considerations may explain the increase in capital misallocation. The firm-level volatility is estimated as follows. First, I compute a growth rate of (real) capital for each plant,γ i t . Real capital is computed in the same way as Section 1.2. Then, for Periods 1 and 2, each plant’s standard deviation of the growth rate is computed,σ 1 i andσ 2 i : σ j i = h 1 T j X t∈T j (γ i t − ¯ γ j i ) 2 i 1/2 j= 1,2, (1.11) where ¯ γ j i is the average of the growth rates in each period. Here,σ j i measures a firm’s risk. Then, by taking the mean across plants in each period, mean(σ i ), we can examine how firm-level risks changed in the aggregate level between the two periods. Table 1.6 shows the results of this exercise. The average firm-level risks in the economy (mean(σ i )) increased from 0.77 in Period 1 to 0.83 in Period 2, implying that the overall risk premia increased. Given that capital misallocation became worse in Period 2, this may be at- tributable to the increase in risk premia. In fact, higher firm-level volatility leads to more vari- ance in M(R)PK dispersion. In this case, the observed variation in productivity measures may be an efficient outcome, not evidence of distortions. 35 Table 1.6: Firm-level volatility Period MRPK dispersion mean(σ i ) Number of plants Period 1 (1992-2005) 0.99 (Low) 0.77 5,652 Period 2 (2005-2019) 1.21 (High) 0.83 10,245 Notes: MRPK disperion, a measure of capital misallocation, is the standard devia- tion of each plant’s MRPK. mean(σ i ) is the mean of each plant’s risk (σ i ), showing the average firm-level risks in each period. This finding raises a new question: what factors contributed to increased firm-level volatil- ity? Or, why have firms become more exposed to aggregate risks (business cycles)? This is be- yond the scope of this paper, yet previous studies explore the potential explanations. The prob- able culprits are product competition, research and development (R&D) activity, and financial development. One thing to note is the coverage of plants in each period (sample selection). Since this exercise requires a consecutive observation for each plant, I drop the plants that do not meet this requirement. 1.6.2 Financial intermediation Studies have shown that small firms are more constrained in their access to finance than large firms (Ayyagari et al., 2017). They also rely on banks for credit more than large firms do. In Section 1.4, we find that the increase in misallocation is related to both the capital markets and small firms. In this regard, we may link the two observations together by examining what happened in financial markets when misallocation increased. Due to data limitations, I focus on how the credit for firms and households has evolved. There were changes in agents’ (firms and households) financing patterns and banks’ lending behavior after the Asian financial crisis. Figure 1.11 shows the proportion of outstanding loans (from depository institutions) for private non-financial corporations and households. Before 36 the crisis, the banks’ main debtor was private firms. Their share was around 65 percent. After the crisis, however, it dropped dramatically to below 50 percent. On the other hand, there was a significant increase in the share of loans for households. It shot up from 32% (1998) to 57% (2005). This pattern is also observed in the growth rate of lending from domestic banks (Fig- ure 1.12). The lending for households including mortgage loans grew significantly by approxi- mately 40 % in the early 2000s. While the business loans have fluctuated greatly, the household loans have shown a steady increase. These two figures indicate that banks have focused on lending to households rather than firms. With the financial development, large firms can get access to other funding such as cor- porate debts. However, small firms rely heavily on banks for credit. Thus, such changes in lend- ing behavior would negatively affect the credit conditions of small firms, implying that they faced tighter credit constraints. In the sense that the misallocation worsened disproportion- ately among small firms, tightened credit constraints may be a prominent source of misalloca- tion. This discussion is related to studies on “credit-less recoveries” (e.g. Calvo et al., 2006; Abiad et al., 2011). Credit-less recoveries, often known as “Phoenix Miracles” , occur when output re- covers quickly from a collapse but credit does not. Understanding these phenomena is impor- tant from a policy perspective. At the aggregate level, Korea did not experience a credit-less recovery from the Asian financial crisis. Specifically, it showed no drop in private sector credit while output dropped to 7 percent (Ayyagari et al., 2021). Although the total private credit did not decrease, as previously stated, its composition changed significantly. It may be called a firm credit-less recovery. 37 Figure 1.11: Proportion of outstanding loans Note: The provider of loans is depository institutions. Private corporation is private non-financial corporations. Household includes households and NPISHs. Due to changes in SNA, the series have been modified from 2006. Source: Flow of funds, Bank of Korea Figure 1.12: Growth rate of loans receivable, domestic banks Note: Growth rate (quarter) is year-over-year. Data on loans receivable is from balance sheets of domestic banks. Source: FISIS, FSS 38 1.6.3 Capital flows The impact of increased capital inflows on misallocation is controversial. Gopinath et al. (2017) show that an increase in the dispersion of the MRPK in Spain was associated with large capital flows. They argue that the increased inflows were directed to less productive (and large) firms due to size-dependent borrowing constraints. Bau and Matray (2020), however, find that foreign capital liberalization reduces capital misallocation in India. High MRPK firms were able to increase their performance by gaining access to foreign capital. Therefore, the effects of in- creased financial flows on misallocation hinge on which firms (productive or unproductive) are the main recipients. Korea is an interesting case to study the relationship between misallocation and FDI inflows. In 1996, after joining the OECD, Korea started to take liberalization steps on FDI (SaKong and Koh, 2010). After that, FDI into Korea increased dramatically. During the Asian financial crisis, the government opened capital markets extensively by allowing friendly and hostile M&As to promote foreign capital. As result, the ratio of M&A in total FDI shot up from 1.1% in 1995 to 45.6% in 2005. Figure 1.13 shows these changes in FDI as well as TFPR dispersion. Before 2000 the two series moved in tandem (correlation: 0.90). After that, however, while FDI was on a decreasing trend, TFPR dispersion steadily increased (correlation: -0.34). To examine this relationship more thoroughly, I run industry-level panel regressions of the dispersions on FDI as follows: Di sp st =α +β F D I st GDP t + δ t + δ s + ϵ st . (1.12) Specifically, dependent variables are TFPR and MRPK dispersion (standard deviation) of an industry s. Independent variables are industry-level FDI inflows (to GDP) and two fixed effects (year and industry). Due to data limitations, an industry is defined as a three-digit level (83 industries). The sample period is from 1992 through 2019. Table 1.7 reports the results. The 39 Figure 1.13: FDI inflows and TFPR dispersion Note: FDI is inward FDI inflows divided by Korea’s GDP . TFPR dispersion is the (value-added weighted) standard deviation of industries’ TFPR. Source: BOP , Bank of Korea Table 1.7: Effects of FDI on misallocation (1) (2) Variables TFPR dispersion MRPK dispersion FDI to GDP -0.02* -0.11** (0.04) (0.05) Constant 0.59*** 0.95*** (0.00) (0.01) Industry fixed effects Yes Yes Year fixed effects Yes Yes Number of industries 83 83 Observations 2,127 2,127 Adj. R-sq 0.29 0.26 Notes: Reported in brackets are the clustered standard errors. *, ** and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. 40 estimates indicate that the FDI inflows are negatively associated with misallocation, implying that the increased flow lowers the productivity dispersion. One unit increase in FDI to GDP ratio correlates with a 0.02 decrease in TFPR dispersion (Column 1) and a 0.11 decrease in MRPK dispersion (Column 2). The negative effects are greater and more statistically significant with capital market distortions as expected. These results suggest that the gradual decrease in capital inflows to Korea may be associated with the increased (capital) misallocation. 1.7 Conclusion In this paper, I investigate the dynamics of misallocation in Korea’s manufacturing sector. Using rich panel data on the manufacturing sector, I analyze such misallocation in terms of individual firm characteristics from 1992 through 2019. Specifically, I explore the patterns of misallocation across different firm sizes and ages. It is crucial to examine these patterns in order to better understand what is behind the overall misallocation trend. I find that the overall misallocation in Korea and its negative consequences have increased over time. Capital market distortions were the main cause of the increased misallocation. The thickened right tail of the TFPR distribution suggests that more firms confronted barriers to expanding their capacity. In particular, they were particularly unable to utilize capital and thus smaller than optimal. Moreover, the distortions had the greatest impact on small and young firms. The decomposition of the overall dispersion reveals that the misallocation worsened particularly within the small firm group. In terms of plant age, it was young plants that faced the most barriers to expanding their capacities. Previous studies on misallocation are susceptible to mismeasurement. With poor measure- ment, the dispersion in measured TFPR may not be evidence of misallocation. To deal with this issue, I employ a useful diagnostic by Bils et al. (2017), which provides the proportion of true variations in measured variations. The results show that the amount of mismeasurement in the Korean manufacturing survey is relatively moderate compared to that of other countries. 41 Chapter 2 Size-dependent Policy and Firm Dynamics 2.1 Introduction Government policies to support small and medium-sized enterprises (SMEs) are widespread in developed countries as well as in developing. They are commonly justified by the important role of SMEs in generating employment and their lack of access to finance. These policies are size-dependent policies (SDPs) because they depend on firm 1 size. In this sense, in addition to promoting small firms, restricting large firms is also included in SDPs. Although they are popular among policymakers, empirical and quantitative studies on their effects are scarce. In this paper, I study the effects of size-dependent policies both empirically and structurally. On the empirical side, I focus on one specific policy in Korea: Small-scale reservations. This was a unique policy of restriction on firm size. It restricted the new entry of large firms in certain products by law. In fact, several products in the manufacturing sector were reserved for pro- duction by SMEs. Using plant-level microdata, I investigate how this policy affected firm per- formance. On the structural side, I concentrate on the more general size-dependent policies. In doing so, I use the framework suggested by Guner et al. (2008) to analyze how the SDPs affect the aggregate economy. It is a simple framework to evaluate policy distortions that depend on 1 In this paper, I use firm, plant, and establishment interchangeably. Unless otherwise specified, they mean the same thing (establishment). 42 establishment size. By calibrating the model to the plant size distribution in Korea, I quantify the effects of SDPs on aggregate variables, productivity, and size distribution. The main contribution of this paper is twofold. First, I find empirically that the removal of the SSR industries had positive effects on firm outcomes. The policy was first implemented in 1979 and began to de-reserve in 1994. This policy was non-trivial because the proportion of SSR industries in the manufacturing sector was approximately 20% at its peak in terms of value- added. Since the manufacturing survey that I use started in 1992, I focus on the de-reservation of this policy. Following Martin et al. (2017), which study the effects of de-reservation in India, I employ a Difference-in-Difference design with the two-way fixed effects. Specifically, the de- reservation was associated with a significant increase in both the labor productivity and the per-employee wage. Second, motivated by this empirical evidence, I investigate the quantitative effects of SDPs on the aggregate economy. While the empirical exercise only deals with the production side, the quantification analysis helps to evaluate the aggregate effects of these types of policies. In this analysis, I consider more general SDPs, including tax treatments and financial benefits, rather than the SSR policy, which is the most restrictive size-dependent policy. Guner et al. (2008)’s model is parsimonious yet powerful enough to capture the aggregate effects of SDPs. Then, for the quantification, the model is calibrated to capture the aspects of the Korean economy, which has a high fraction of small firms. The SDPs are modeled as a tax that is applied to capital services above a certain level. The tax rates are hypothetically set to be equal to 15% and 40%., which corresponds to a lower average firm size by five and ten percent, respectively. Using this hypothetical tax on large plants, the counterfactual effects of this policy on the aggregate economy are investigated. The negative effects of size-dependent policy on aggregate variables are sizeable. Notably, with the implementation of a 15% tax rate, aggregate output decreases by 4.2%. If the tax rate increase to 40%, output loss also rises to 9.3%. Such a large loss is because large and productive firms should pay additional costs on capital, resulting in lower demand for capital services. In addition to output, this policy reduces aggregate consumption 43 and TFP significantly. The main mechanism through which restrictions on capital use affect the aggregate econ- omy is the misallocation of talents, i.e., the distortion of occupational choices. In fact, with this policy, resources in the economy are reallocated from productive (large) firms to unproductive (small) firms. The fractions of total output accounted for by managers with different abilities clearly show this distortion. In the benchmark, while the top quintile (highest 20%) explains 78.4% of total output, the bottom quintile (lowest 20%) only accounts for 2.3%. When the re- strictions are imposed, however, each quintile’s fraction of output increases only except for the upper 20%. Moreover, the restrictions on capital use cause the new entry of small (marginal) firms. This is because general equilibrium effects via wage kick in. A decrease in capital demand leads to a decrease in labor demand for constrained firms, and thus the equilibrium wage fall. Specifically, the wage decreases by 3.7% (8.3%) with a 15% (40%) tax rate, implying that a worker’s incentive to remain as a worker decreases. Therefore, the number of establishments increases rises. This phenomenon eventually leads to high fractions of small firms. It indicates that the prevalence of policies to support small firms may explain why small firms comprise the majority. Lastly, the findings from the quantitative analysis are consistent with empirical evidence. In the model, output per worker decreases by 3.7% (8.3%) with a 15% (40%) tax rate. This lower la- bor productivity is related to the aforementioned general equilibrium effects, lower equilibrium wage. This implies that the size-dependent policy drives lower labor productivity. It is consis- tent with our empirical evidence on the SSR policy, which shows the removal of the restriction increased the labor productivity of the treated firms. Therefore, the results from the structural model reconcile with the empirical findings, suggesting the mechanisms of SSR policy. The remainder of this paper is organized as follows. Section 2 explains the small-scale reser- vation policies in Korea and empirically analyzes their impacts on firm performance. Section 3 discusses the model and calibration. Then, we present our quantitative findings. Section 4 concludes. 44 2.2 Empirical evidence : Evidence from removing SSR in Korea In this section, I empirically analyze the effects of small-scale reservations in Korea. First, I provide an overview 2 of this policy. Then, I conduct an empirical analysis of how removing this policy affected a firm’s performance. 2.2.1 Small-scale reservation policies in Korea The small-scale reservation (SSR, hereafter) policy was first implemented in 1979. The goal of this policy was to secure business opportunities for small and medium enterprise owners. Before this policy was implemented, the Korean government’s industrial policy mainly focused on the promotion of large firms. In the 1970s, for instance, South Korea started the HCI (Heavy Chemical and Industry) drive. The key players of the HCI drive were the chaebol, a large in- dustrial conglomerate in Korea. Such policy favoring large firms, though it contributed to faster economic growth, led to their disproportionate presence regardless of their productivity. To re- duce widened gaps between small and large firms, in the 1980s, the government implemented a series of policies to support SMEs, including the SSR policy. The SSR policy was legally enforceable according to the “ Act on the protection of the busi- ness sphere of small and medium enterprises and promotion of their cooperation.” The gov- ernment was able to designate an industry as SSR when it contributes to the improvement of industrial structure if the industry is managed by SME. There were broadly three criteria for the designation (See Lee, 2015). One example is that an industry, in which SMEs are producing high-quality products, can be reserved for SMEs if large companies can monopolize it using their bargaining power. The Act specified that large firms are unable to “acquire, initiate, or ex- pand” their business in the SSR industries. If they violate this entry restriction, they had to be punished by imprisonment or a fine. This policy applied exclusively to the manufacturing sector. When the SSR policy was ini- 2 The main reference is Lee and Lee (2004) and Lee (2015). 45 tiated in 1979, 23 products were reserved. Table (2.1) shows how many products were newly- reserved and de-reserved over time. After that, the number of products increased and peaked at 237 products in 1989. There were 14 categories of products, including the metal industry, fine chemical industry, and machinery industry. For example, the products included pressure accumulators, welding machines, and unslaked lime. Table 2.1: The number of SSR products Year 1979 1983 1984 1989 1994 1995 1997 2001 2004 2005 2006 Newly-reserved 23 80 104 49 - - - - - - - De-reserve - - 2 17 58 45 47 43 8 19 18 Total 23 103 205 237 179 134 88 45 37 18 0 Despite the relatively small number of the designated products, the SSR industries’ share was not negligible. Figure (2.1) shows the proportion of the SSR industries in the entire man- ufacturing sector. In terms of value-added, their share was 7.5% in 1984, but it began to rise, reaching its peak at 18.6% in 1992. Similarly, for the number of employees and plants, the pro- portion also peaked early in the 1990s. As the de-reservation started in 1994, their share plunged by approximately 20 percentage points. We also gauge the importance of the SSR industries among small and medium-sized enterprises (See Figure (2.2)). The trend was similar to the pre- vious case. For example, the proportion of the establishments producing the SSR products in the total SMEs decreased from 25.7% in 1990 to 2.7% in 2006. As South Korea moved to liberalize import markets in the early 1990s, there were growing concerns about the effectiveness of the SSR policy. Since the regulation was not able to enforce against foreign firms, domestic large firms claimed to be disadvantaged in the SSR industry. Moreover, the WTO recommended the repeal of this policy (Chun et al., 2018). As a result, large- scale de-reservation started from 1994 to 1997 (150 products). Accordingly, as shown in Figures 46 Figure 2.1: SSR share in manufacturing Note: The share is the proportion of SSR industries in the manufacturing sector. Source: Lee (2015) Figure 2.2: SSR share in SMEs Note:The share is the proportion of SSR industries in the SMEs. Source: Lee (2015) 47 (2.1) and (2.2), the portion of the SSR industries decreased dramatically. In 2000, the Regulatory Reform Committee recommended that all the remaining industries should be removed if there were no specific reasons. Therefore, the last products were removed from the list in 2006. Interestingly, the SSR policy was restored in 2011 under different norms. This revival was due to widespread concerns about widening gaps between small and large firms after the Global financial crisis. This policy is different from the preceding one in several ways. First, the des- ignation is done by not the government but the Korea Commission for Corporate Partnership, which consists of both private and public agents. Second, while the previous policy applied only to the manufacturing sector, the current one also covers the service sector. Lastly, this policy only lasts three years. 2.2.2 Data and specification Data The main dataset I use is the Mining and Manufacturing Survey (MMS) conducted by Statis- tics Korea, Korea’s official national statistical organization. This annual survey is a panel that covers all mining and manufacturing establishments in South Korea with at least five employ- ees. The MMS, though it was first carried out in 1968, is only available since 1992. After 2007, the survey only covers plants that hire more than ten employees. Then, to capture the charac- teristics of plant size distribution in Korea, which has higher fractions of small firms, I use the data from 1992 through 2006 (15 years). This data set has detailed information on outputs and inputs at a plant level. For instance, sales, the number of employees, and (tangible) fixed assets of each plant are available. One thing to note is that the basic unit of observation is an establishment. Therefore, I was not able to distinguish different plants within one firm, implying that a small subsidiary of a large firm is considered as SMEs as well. This can be justified by the fact that the majority of firms have a single establishment. Data on the dates and list of de-reservation are available from the website of the Korea Min- 48 istry of Government Legislation. Specifically, this information is from the attached table in the Presidential Decree of the Act. In this table, an SSR industry is provided in terms of a five-digit KSIC (the Korean Standard Industry Classification) code. Therefore, I match the SSR industries to the MMS data at the five-digit level. During the sample period, there was a revision of the KSIC. KSIC Rev. 6 is for 1992-1997 and Rev. 8 for 1998-2006. Since the reservation data is based on KSCI Rev. 6, I use a correspondence table to link the Rev. 8 to the Rev. 6. Specification The goal of this exercise is to investigate the effects of the SSR policy on a firm’s perfor- mance. The main data set, however, is only available from 1992. As discussed, the large-scale de-reservation began in 1994. As a result, rather than focusing on the implementation of the policy, I analyze how the removal of the SSR affects a plant’s performance. Specifically, following Martin et al. (2017), which study the effects of de-reservation in India, I start with a Difference- in-Difference equation of the following form for establishment i in year t: Outcome i t =β Der eser v i t +α i +δ t +ϵ i t . (2.1) Here, Outcome i t is the outcome variable of interest. It consists of the logs of sales, labor compensation, the stocks of tangible fixed assets, and labor productivity. Labor compensation is the sum of wages and other benefits. Labor productivity is the (real) sales over the number of employees. I deflate these variables to measure the changes in real values. Sales are deflated by the producer price index of the manufacturing sector. Labor compensation and fixed assets are also deflated by the consumer price index and the GDP deflator for fixed assets (private sector), respectively. Der eser v i t is an indicator variable equal to one if the industry has been de-reserved. As discussed, there were two waves of dismantling the SSR policy. The first wave includes the removal in 1994, 1995, and 1997. The second is from 2001. Since the MMS covers the annual 49 values of a plant, we need to consider when the de-reservation started within the year. For the cases in 1995 and 1996, it was the beginning of the year. Also, for the 1994 and 2001 reforms, the industries were removed from the list in September. For these cases, I consider that the reforms happened in that year. However, after 2004, they were dismantled in December. As a result, the treated year is the next year of the reforms. Due to this restriction, I mainly focus on the first wave. α i andδ t are plant and year fixed effects, respectively. α i controls for time-invariant plant-level heterogeneity. δ t is used to control for aggregate fluctuations. Standard errors are clustered at the establishment level. The coefficient of interest is β, which captures the effects of the reform.β> 0 implies that a firm’s performance increases after the removal of the SSR regulation. This estimation is based on the two-way fixed effects difference-in-difference framework. The identification relies on the different timing of de-reservation. Specifically, as Martin et al. (2017) show, after controlling for both year and plant fixed effects, β can be identified by a combination of products becoming de-reserved and plants switching into making (de)reserved products. In this exercise, however, since the MMS does not provide the information about multiple products that an establishment produces, I am not able to differentiate the above two channels. I can only observe changes in a plant’s industry code, which is determined by its main product. Therefore, I consider that a multiproduct plant is treated only if its main product is re- moved from the list. Moreover, I include all establishments in the sample as long as they are observed in a row. This is because these establishments help to identify the secular time trend. 2.2.3 Regression results I estimate Equation (2.1) to study how de-reservation affected a firm’s performance. Ta- ble (2.2) reports the results. The estimates indicate that the removal of the SSR industries had positive effects on firm outcomes. Specifically, the de-reservation was associated with a sig- nificant increase in both the labor productivity and the per-employee wage. Here, the labor productivity is computed as (real) sales over the number of employees. The wage per employee 50 is the (real) labor compensation divided by the number. The coefficients on them suggest that the removal led to a 1.3 percent increase in the productivity and a 0.9 percent increase in the av- erage wage, respectively. Moreover, sales and tangible fixed assets in both real terms increased after de-reservation. On the other hand, the effects of the removal on labor (the number of employees) were not significant. Related to this, one thing to note is the data’s restriction on the number of employees. The MMS only covers plants with more than five employees. Yet the majority of plants were concentrated under the threshold. With the manufacturing survey, it was hard to capture this aspect entirely. In sum, we find empirically that removing the SSR regulation was associated with the better performance of the treated plants. With the DID setting, we can interpret that they showed an increased outcome compared to the rest of the plants. In particular, the labor productivity was highly improved. These findings are robust even if I tried different timings of the removal as discussed below. Table 2.2: Impact of de-reservation on a establishment’s outcomes log(sales) log(Y/L) log(wage) log(K) log(labor) Dereserv 0.0119** 0.0128*** 0.00916*** 0.0122* -0.000873 (2.32) (3.66) (4.16) (1.90) (-0.27) Plant fixed effects Yes Yes Yes Yes Yes Year fixed effects Yes Yes Yes Yes Yes Observations 471,541 471,541 471,541 471,541 471,541 Adj. R-sq 0.0635 0.138 0.0946 0.00376 0.0271 Notes: Reported in brackets are the corresponding t statistics. Standard errors are clus- tered at the plant level. +, *, ** and *** indicate statistical significance at the 15%, 10%, 5%, and 1% levels, respectively. 51 2.3 Quantitative Analysis In this section, I study the quantitative effects of SDPs on the aggregate economy. In the pre- vious section, I find that the removal of small-scale reservations improved firm performances, in particular labor productivity. It suggests that the SSR policy was not effective. Yet this empir- ical analysis focuses only on the production side. Therefore, the quantification exercise helps to not only explain these empirical findings but also gauge the aggregate effects of these types of policies. Also, the SSR policy that regulates an entry of a firm is the most restrictive size- dependent policy. However, other SDPs, including tax treatments and financial benefits, are more prevalent across countries. Here I would like to consider a more general policy. For these purposes, I use the model from Guner et al. (2008) (GVX model, hereafter), which studies the macroeconomic implications of SDPs. Since I do not focus on SDPs’ interactions with other frictions such as financial constraints, this GVX model is parsimonious yet powerful enough to capture the aggregate effects of SDPs. The key challenge in this quantification is to calibrate the model to capture the aspects of the Korean economy because it has a high fraction of small firms. I also refer to Oh (2016a), which conducts similar exercises using Korean data. 2.3.1 The GVX model The GVX model is a simple one-sector model, which is based on the Lucas (1978) span-of- control framework. This framework can capture firm size distributions in the reality. The Lucas model endogenously determines the number of managers and the size of each manager. Also, it assumes heterogeneous manager ability, which generates the realistic size distributions. Since this model is static, we can interpret it as the long-run distributions of firms. In fact, we study the effects of SDPs by comparing two different steady-states. First, I describe the GVX model without any distortions. Then, I add to the model the restrictions on capital services. 52 A distortion-free economy There is a representative household with a continuum of members of total size, L t , which grows at g L . Its members differ in their managerial ability z (∈ [0, ¯ z]) with a density function f (z). Production A manager of type z hires capital k and labor n to maximize its profit π(z,W,R)= max k,n n z 1−γ A(k ν n 1−ν ) γ −W n− Rk o (2.2) whereγ is the span of control parameter measuring the returns to scale;ν is the capital share parameter; and W and R are the rental prices for labor and capital services, respectively. The term A accounts for exogenous productivity growth at g A . From two first-order conditions of Equation (2.2), we have the factor demand functions: n d =Ω z R −νγ 1−γ W νγ−1 1−γ (2.3) k d =Φ z R γ(1−ν)−1 1−γ W γ(ν−1) 1−γ (2.4) whereΩ andΦ are a constant. One thing to note is that these demand functions are linear to a manager’s ability, z. This implies that firm size is perfectly associated with firm productivity. Another feature of the Lucas model is that, given the factor prices, all managers have a common capital-labor ratio, h: h≡ k n = ν 1−ν W R . (2.5) Household problem The household problem is to choose sequences of consumption and next period’s capital under a budget constraint to maximize the sum of discounted utilities, P β t L t log(C t /L t ). Its income depends on the occupational choice, which allocates each mem- ber into a worker or a manager. While a worker earns the fixed W , a manager’s profit ( π(z,W,R)) 53 depends on her ability. As Equations (2.3) and (2.4) suggest, the profit function is strictly in- creasing (linear) in z. As a result, there exists a threshold ˆ z that a member who has z< (>) ˆ z become a worker (a manager). Therefore, the budget constraint is: C t + K t+1 = I t ( ˆ z t ,W t ,R t ) L t + R t K t + K t (1−δ) (2.6) where the per capital income (I t ) is W t F ( ˆ z t )+ ´ ¯ z ˆ z π(z,W t ,R t )f (z)d z, andδ is the depreciation rate. The solution is characterized by both the standard Euler equation : 1 C t /L t =β (1+ R t+1 −δ) 1 C t+1 /L t+1 , (2.7) and W t =π( ˆ z t ,W t ,R t ), which means that a marginal manager with ˆ z t earns the same income as a worker. Equilibrium In this economy, there are three markets: labor services, capital services, and goods. In the equilibrium, all these markets clear. For the market for labor, total labor demand is: N d t = L t ˆ ¯ z ˆ z t n(z,W t ,R t )f (z)d z (2.8) where n(z,W t ,R t ) is the demand of a manager with z. Total labor supply is the volume of workers, N s t ≡ L t F ( ˆ z t ). The market for capital services is also defied in the same way. Letting y(z,W t ,R t ) be the output by a manager with z, the goods’ market is cleared by: L t ˆ ¯ z ˆ z t y(z,W t ,R t )f (z)d z= C t + K t+1 − K t +δK t . (2.9) Formally, a competitive equilibrium is characterized by a set of sequences {C t ,K t+1 , ˆ z t ,W t ,R t } such that (1) given the factor prices {W t ,R t }, the sequences {C t ,K t+1 , ˆ z t } solve the household problem; (2) the labor and capital services markets clear for all t; and (3) the market for goods clears for all t. 54 As discussed, we focus on the equilibrium in a steady state. Along a balanced growth path, both the rental rate of capital (R) and the ability threshold ( ˆ z) are constant. One thing to note is that, absent any restrictions, this competitive equilibrium is Pareto optimal. Restrictions on capital services Now, restrictions on capital use are added to the distortion-free model. Following Guner et al. (2008), the restriction is modeled as implicit taxes that are applied to the capital use above a certain level, ¯ k. In fact, if a firm wants to demand capital above this threshold, it should pay an additional marginal cost (τ) on the differences between k and ¯ k. Therefore, for an establish- ment under this restriction, its profit maximization problem (previously, Equation (2.2)) takes on the following form: π(z,W,R;τ, ¯ k)= max k,n n z 1−γ A(k ν n 1−ν ) γ −W n− R(1+τ)k+ Rτ ¯ k. o (2.10) This equation clearly shows that large firms face R(1+τ) as capital costs, while small firms have the same R as before. More precisely, there are three types of plants. First, unconstrained plants (k d < ¯ k) solve the same problem. Second, there are plants that demand the given level of capital (k d = ¯ k). They exist because of the difference between the two marginal costs (R and R(1+τ)), implying that their (original) marginal products of capital are between them. Lastly, constrained plants (k d > ¯ k) face higher marginal costs and thus reduce their size. As shown in Equation (2.4), demands for capital service are linear to managerial ability. Thus, there exist other thresholds (z − and z + ) that divide managers into the above three groups. In fact, z − and z + are directly solved from Equation (2.4): z − = ¯ kΦ −1 R γ(1−ν)−1 γ−1 W γ(ν−1) γ−1 and z + = ¯ kΦ −1 (R(1+τ)) γ(1−ν)−1 γ−1 W γ(ν−1) γ−1 . Then, if a manager has z< z − (> z + ), he is unconstrained (con- strained). If his ability z is located between the thresholds, his capital is fixed at ¯ k. It is also crucial to consider how the taxes collected are distributed. Yet, since we focus on the effects of the policy, simply assume that the taxes are transferred to the household in a lump-sum fashion (X t ). Thus, the modified household budget constraint is: 55 C t + K t+1 = I t ( ˆ z t ,W t ,R t ;τ, ¯ k) L t + R t K t + K t (1−δ) + X t . (2.11) The competitive equilibrium is defined in a similar way to the distortion-free case. Discussion on modeling SDPs Size-dependent policies come in multiple forms. For instance, a country may restrict the production of large firms or encourage the production of SMEs via taxes or subsidies. Therefore, the way we model SDPs can have different implications. Taken from the seminal work by Guner et al. (2008), these policies are modeled as (implicit) taxes on capital use that become effective above a threshold. In addition to the restrictions on capital use, they consider taxes on labor use as well as subsidies on input use. As noted in Section 2, the criteria for SME eligibility have changed over time in South Korea. In the 1990s, SMEs were defined by the number of employees and total assets. These two re- quirements must be met. From this perspective, we may model SDPs in several ways. Currently, a threshold on capital use is exogenously given. This modeling is only related to total assets. To mimic the exact criteria that were in place, we need the threshold on labor use as well. Then, when a plant satisfies the two conditions, they are considered unconstrained. The goal of this exercise, however, is to consider the macroeconomic effects of SDPs rather than measure their exact magnitude. In addition to Guner et al. (2008), for instance, Restuccia and Rogerson (2008) use hypothetical firm-specific taxes and subsidies to study how misallocation impacts aggre- gate TFP . Similarly, this exercise on the effects of SDPs can be viewed as a simplified version. 2.3.2 Calibration In this subsection, I calibrate the model and evaluate its performance along with a plant size distribution. Guner et al. (2008) calibrate the distortion-free benchmark of their model to the US econ- omy. They use data pertaining to the US because it is considered a relatively undistorted econ- omy. Specifically, they focus on replicating both aggregate and cross-sectional aspects. Then, 56 using this calibrated model, they conduct counterfactual exercises with the taxes reducing the average plant size by 10 or 20 percent. This is because there are no empirical counterparts to these policies. These hypothetical exercises, however, are useful in that it is relatively simple to compare average firm size across countries. Bento and Restuccia (2021) show a positive rela- tionship between average plant size and GDP per capita in the manufacturing sector. Therefore, by determining how small a country’s plant size is relative to that of the US, we can estimate the effects of the size-dependent policy. My exercise is different from theirs in two ways. First, I calibrate the model to capture the plant size distribution in Korea. Compared to the US, Korea has a large fraction of small firms, resulting in smaller average plant size. For instance, while the US’s average was 17.09 from the paper, that of Korea was only 10.9 in 1993. One may insist that we can estimate Korea’s implied tax rate by comparing the two average sizes. The purpose of this calibration, however, is to study the aggregate effects and mechanisms of SDPs not to back out the tax rates. Moreover, as Oh (2016a) noted, it is hard to reproduce this aspect of Korean firm size with the GVX parameters. Even if we assume the tax rate is higher than 100%, it is difficult to replicate the small average size due to Korea’s loose SME eligibility. Since the Korean economy is not considered an undis- torted case, this exercise can be interpreted as an evaluation of the effects of SDPs when they worsen. Second, the size distribution of plants under the SSR regulation can be an empirical coun- terpart. This is similar to the approach of Garcia-Santana and Pijoan-Mas (2014) in analyzing India’s small-scale reservation policy. They calibrate the upper bound of capital to reproduce the proportion of capital in the sectors employed by the SSR firms. Similarly, the Korea’s policy can be used to investigate the effects of the specific SDP . One way of thinking of it is to compare the SSR industries to the entire manufacturing sector, though this requires the assumption that the only difference is driven by the policy. For instance, we can gauge the effects of this policy on firm size distributions (or, average firm sizes) by comparing the two sectors, the treated and control sector. For this reason, I choose the year 1993, which is the year right before the pro- 57 cess of de-reservation started. Since we focus on a steady-state equilibrium, we assume that the Korean economy was at the equilibrium in that year. Parameters The parameters are divided into two categories (See Table (2.3)). The first cate- gory includes the parameters adopted directly from Guner et al. (2008). Such parameters are related to the general features of an economy. For example, the share of capital ratio in total output is 0.32 (See Table (2.4)). To reproduce this value, they calibrate the depreciation rate (δ) and the discount rate (β). Such assignment can be legitimate since we consider the long-run steady-state equilibrium. Long-run growth rates (g L , g ) are used in the same way. The second category includes the calibrated parameters to mimic the plant size distribution in Korea. The main targets related to the distribution are the average plant size and the fraction of plants over the number of employees (See Table (2.4)). These values are from the 1993 Census on Establishments conducted by Statistics Korea. Unlike the manufacturing survey which only covers establishments with more than five employees, this census annually surveys establish- ments with one or more employees that are doing business in Korea. Therefore, it is suitable to capture a high proportion of small firms. Specifically, I use the manufacturing sector as a benchmark to make better compassion with the SSR policy. In 1993, while the fraction of large firms (> 100 employees) was only 1.6 %, the plants with one to nine employees took up 80 %. The two key parameters that determine the distribution are returns to scale (γ) and disper- sion in the ability (σ). The span-of-control parameter governs firm size distributions as well as the importance of capital. Specifically, as Guner et al. (2008) discuss, it determines not only the sensitivity of firm size to changes in factor prices but also the size of the smallest and the average size. The higherγ, the larger the average plant size. Therefore, to reproduce the Korean average size, we need a lower value relative to the US. In the Indian case, Garcia-Santana and Pijoan-Mas (2014) choose 0.57 and 0.58 to match the small average size. Korea’s size is between the two extreme cases, and thus we assign 0.652. The dispersion of the managerial ability (σ) is another important parameter to determine 58 size distributions. Guner et al. (2008) assume that the ability follows the (truncated) log-normal distribution, which reflects the fat left tail. In the log-normal case, the higher dispersion ( σ) generates the fatter left tail. For the fraction of plants with less than ten employees, there is a great difference between the US (70.7%) and Korea (80.0%). As a result, the dispersion increased to 2.81. Moreover, to replicate the portion at the top, the parameters related to the highest ability (z max , f max ) are chosen. The final numbers are listed in Table (2.3). The policy parameters include the threshold of capital and the tax rates. The threshold of capital ( ¯ k) is set to be mean capital use in the distortion-free case like Guner et al. (2008) did. The tax rates (τ) are hypothetically set to be equal to 15% and 40%. Each rate corresponds to a lower average firm size by five and ten percent, respectively. As discussed, this counterfactual exercise, which is similar to that of Oh (2016a), can be interpreted as an evaluation of the effects of SDPs when they become more severe. Table 2.3: Parameter values Parameter Value Parameter Value (1) assigned parameters (2) calibrated parameters Population growth (g L ) 0.011 Returns to scale (γ) 0.652 Productivity growth (g ) 0.0255 Importance of capital (ν) 0.45 Depreciation rate (δ) 0.04 Dispersion in log-managerial ability (σ) 2.81 Discount factor (β) 0.9357 Highest managerial ability level (z max ) 5,884.2 Mean log-managerial ability (µ) -0.367 Mass highest ability level (f max ) 0.00138 Notes: Productivity growth (g ) is computed from 1+ g≡ (1+ g A ) 1 1−νγ . Results Table (2.4) shows the results of this calibration. First, the average size (10.7) from the model matches well the target size (10.9). Second, the fraction of establishments over the num- ber of employees also captures the actual size distribution. Figure (2.3) shows graphically the overall fit of the size distributions. Although there are small gaps in the medium-sized groups 59 (20-99 employees), it reproduces both the smallest and the largest proportions well. The share of employment, however, is difficult to replicate from the calibration. For instance, although the large firms’ share of employment (+100 employees) is 48.6%, the model generates only ap- proximately half of the values (27.1%). This is because the main focus of this calibration is the fraction of small firms, not the share of employment. It may be resolved if the Pareto distribu- tion is used to describe the top firms, rather than the truncated distribution. Yet this is not the primary target, and thus I leave it for future work. Table 2.4: Targets Statistics Data Model Statistics Data Model Mean Size 10.9 10.7 Aggregate capital share 0.32 0.29 Capital to output ratio 2.3 2.2 % of establishements at Share of employment at 0-9 employees 80.0 81.6 0-9 employees 17.3 23.1 10-19 9.5 8.1 10-19 9.1 10.5 20-49 6.8 5.5 20-49 14.9 15.7 50-99 2.1 3.2 50-99 10.0 23.6 100+ 1.6 1.6 100+ 48.6 27.1 Notes: The data on establishments is from the 1993 Census on Establishments. 60 Figure 2.3: Size distribution of establishments Note: The data on establishments is from the 1993 Census on Establishments. 61 2.3.3 Aggregate implications Now I describe the quantitative results and explore the aggregate implications of SDPs. In doing so, we compare the steady-state of the distortion-free economy with that of a distorted economy. Specifically, applying hypothetical taxes rates to large plants, I examine how this policy affects the aggregate variables, productivity, and size distributions. Aggregates The negative effects of size-dependent policy on aggregate variables are sizeable. Table (2.5) summarizes the main findings for aggregate variables. As noted, 15% (40%) tax rate on capital use leads to a reduction in average establishment size of 5% (11%) across steady states (Row 1). Notably, with a 15% tax rate, aggregate output decreases by 4.2%. If the tax rate increase to 40%, output loss also rises to 9.3%. Such loss is because large and productive firms should pay additional costs on capital, and thus they reduce the demand for capital service. Thus, the aggregate capital plunges by 13.2% (26.5%) from the 15% (40%) tax rate. Accordingly, aggregate consumption decreases by 2.4% (5.8%), implying a considerable welfare loss. To understand the mechanism through which restrictions on capital use affect the aggregate economy, it is imperative to investigate how occupational choice is distorted. A decrease in cap- ital demand leads to a decrease in labor demand for constrained firms. Since their presence in the economy is large, reduced demand for labor results in lower equilibrium wages. Specifically, the wages decrease by 3.7% (8.3%) with a 15% (40%) tax rate. For workers, this means that their incentives to remain as workers decrease. Therefore, a threshold ( ˆ z) on the occupational choice between a worker and a manager falls, implying that the number of establishments increases rises (See Table (2.5)). One thing to note is that these new entrants are marginal managers (i.e., subsistence entrepreneurship). That is why the aggregate variables deteriorate despite the in- creased entry. 62 Table 2.5: Aggregate and productivity effects Statistics Benchmark τ = 15% τ = 40% Average plant size 100 95 89 (1) Aggregate variables Aggregate output 100 95.8 90.7 Capital 100 86.8 73.5 Consumption 100 97.6 94.2 Threshold on occupational choice ( ˆ z) 100 92.5 85.0 Number of establishments 100 105.2 111.0 (2) Productivity and TFP Output per worker 100 96.3 91.7 Output per establishment 100 91.1 81.7 Output per efficient unit 100 95.4 89.9 Average managerial quality 100 95.5 90.9 Aggregate TFP 100 97.3 93.2 Notes: This table reports aggregate and productivity effects of restricting large plants via taxes on capital services. 63 Productivity The SDPs also lower labor productivity. We compute the productivity in three different ways: (1) output per worker, (2) output per establishment, and (3) output per efficiency unit. They are measured as follows: (1) ´ ˆ z y(z,W,R)f (z)d z 1− F ( ˆ z) , (2) ´ ˆ z y(z,W,R)f (z)d z F ( ˆ z)+ ´ ˆ z z f (z)d z , (3) ´ ˆ z z f (z)d z 1− F ( ˆ z) . (2.12) As shown in Table (2.5), all the three measures drop. Output per worker and average man- agerial ability decrease by approximately 5% (10%) with a 15% (40%) tax rate. The fall in output per establishment is more pronounced as it decreases by 8.9% (18.3%). This is because of the aforementioned increase in small firms. The fact that the size-dependent policy drives lower labor productivity is consistent with our empirical evidence on the SSR policy. In the previous section, removing the SSR policy increased the labor productivity of the treated firms. In the model, the restriction on capital affects output per worker through the general equilibrium ef- fects, i.e., the changes in wages. In equilibrium, each plant’s output per worker is expressed as W (1−ν)γ . Therefore, lower output per worker stems from the lower equilibrium wages. The aggregate total factor productivity (TFP) also drops. The TFP is computed as follows: T F P = Y K νγ (N+Z ) 1−νγ where Z ≡ L ´ ¯ z ˆ z z f (z)d z. The 15% (40%) tax rate reduce the TFP by 2.7% (6.8%). This reduction in TFP is due to the reallocation of talents. In fact, the policy distorts the occupational choice, implying that resources in the economy are reallocated from productive (large) firms to unproductive (small) firms. Such misallocation causes aggregate productivity losses. More precisely, Table (2.5) presents how the size-dependent taxes distort talent allocation. In fact, it shows the fractions of total output accounted for by managers with different abili- ties. In the benchmark, while the top quintile (highest 20%) explains 78.4% of total output, the bottom quintile (lowest 20%) only accounts for 2.3%, demonstrating the great presence of large firms. When the restrictions are imposed, each quintile’s fraction of output increases only ex- cept for the upper 20%. For instance, with a 40% tax, the top quintile’s proportion drops by 3.5 64 percent points. Yet that of the remaining groups expands. This clearly illustrates the realloca- tion of resources from productive managers to unproductive. Table 2.6: Output accounted for by different ability (%) Economy Lowest 20% Next 20% Next 20% Next 20% Upper 20% Benckmark 2.3 3.2 5.4 10.7 78.4 τ = 15% 2.3 3.6 5.6 11.5 77.0 τ = 40% 2.5 3.8 6.2 12.6 74.9 Notes: This table reports the fraction of output accounted for by managers at differ- ent quintiles of the ability distribution. Size distributions Now we explore how plant size distributions respond to the SDPs (See Ta- ble (2.7). First of all, as discussed, the taxes result in lower average sizes. The coefficient of variation (CV), which is defined as standard deviation over mean, measures the dispersion in establishment size. It falls from 2.47 (Benchmark) to 2.44 (15%) or 2.37 (40%), implying that the dispersion in size decreases. This reflects the reduction of large plants due to the restrictions. The proportion of managers at the threshold ( ¯ k) increases as the size-dependent taxes are implemented. As a tax rate increases (15%→ 40%), their proportion also rises (3.3%→ 6.8%). Furthermore, with the taxes, the share of total output accounted for by these plants increases to 3.3% (15%) or 6.8% (40%). This means that they choose not to use capital at a higher price but to reduce their sizes, which undermines allocative efficiency. Lastly, Table (2.7) also shows the changes in the fraction of establishments over the number of employees under the restrictions on size. For relatively large plants (> 20 employees), their fraction falls. The proportion of small establishments (10-19 employees), however, rises signif- icantly. This rise is attributable to the fact that the unconstrained firms expand as input prices fall. 65 Table 2.7: Size distribution effects Statistics Benchmark τ = 15% τ = 40% Mean size 10.7 10.2 9.6 Coefficient of variation 2.47 2.44 2.37 % distorted (k≥ ¯ k) 17.3 17.0 16.7 % distorted (k> ¯ k) 17.3 13.7 10.0 % distorted (k= ¯ k) 0.0 3.3 6.8 Size distribution (% of establishments at) 0-9 employees 81.6 81.4 80.9 10-19 8.1 9.2 10.7 20-49 5.5 5.0 4.5 50-99 3.2 2.9 2.5 100+ 1.6 1.5 1.5 Notes: This table reports the results on the distribution of estab- lishment size due to taxes on capital use. 66 2.4 Conclusion In this paper, I investigate both empirically and structurally the effects of size-dependent policies. I find empirically that eliminating SSR industries had positive effects on firm out- comes. By law, this policy prevented large firms from entering particular markets. In fact, only SMEs can produce these products. Using the manufacturing survey, I investigate how this pol- icy affected firm performance. Specifically, I use a Difference-in-Difference design with the two-way fixed effects. The results show that the removal of this restriction was correlated with a significant increase in both the labor productivity and the per-employee wage. In addition to this empirical analysis, I study the quantitative implications of SDPs on the aggregate economy. I use the GVX model and calibrate it to capture the aspects of the Korean economy, which has a significant proportion of small firms. The SDPs are modeled as a tax that is applied to capital services. Such policies have substantial negative effects on the aggregate economy. They reduce output, consumption, and TFP . The key mechanism of this policy is the misallocation of talents, i.e., the distortion of occupational choices. In fact, this policy reallo- cates resources in the economy from productive (large) to unproductive (small) firms. Such misallocation causes aggregate productivity losses. 67 Chapter 3 International Reserve Accumulation: Balancing Private Inflows with Public Outflows 3.1 Introduction The massive international reserve 1 accumulation in Emerging Market Economies (EMEs) since the mid-1990s has been one of the most debatable issues in international macroeco- nomics. One widely accepted view is that EMEs have accumulated reserves as a buffer against sudden stops 2 in the future: this is “Precautionary view.” Among emerging market policymak- ers, reserve accumulation has been a favored policy instrument against sudden stops. Despite its popularity in practice, theoretically, the exact mechanism through which reserve accumu- lation serves as the precautionary purpose has yet to be addressed. Absent a theory of reserve accumulation in the precautionary view, it is hard to answer the following questions: What is the optimal accumulation of reserves for EMEs? How is it related to other policies such as mon- 0 Joint Work with Bada Han 1 Throughout this paper, we use reserve and international reserve interchangeably. 2 Sudden stop is defined as sudden reversal or stop of capital inflows to an EME. This results in the country’s currency depreciation and balance sheet deterioration. 68 etary policy? Is the role of reserves substitutable by capital controls? In this paper, we suggest a novel mechanism of how reserve accumulation serves the goal in the precautionary view. We view reserve accumulation as the capital outflow by public sectors, facing large capital inflows. Let us think of the following scenario. Imagine the sudden surge of capital inflows in the forms of foreign direct investment or equity portfolio investment. This will worsen the country’s capital account and thus its current account as well. Generally, we would expect that, in equilibrium, there may be corresponding outflows, or the increased inflows may crowd out other forms of capital inflows. Let us further assume that, even after crowding out, the total inflows are still sizeable. Then, the country needs to make capital outflows to maintain its macroeconomic balance. If capital outflows are frictionless, it is done by private sectors. If they are not able to invest abroad sufficiently due to restrictions on capital outflows, however, parts of overseas investments should be done by the public sectors. Such outflows are reserve accumulation: the direct investment inflows cause “floods of foreign currency liquidity", and thus central banks in EMEs accumulate reserves to “pump out" the liquidity. The main contribution of this paper is to suggest a new theoretical model, which formally il- lustrates the ideas in the scenario above. Although our main contribution lies in the new theory, our model is motivated by the empirical regularities we uncover in this paper. Our strategy to found empirical regularities is to look at the evolution of the structures of external liabilities and assets. As it is documented in Lane and Milesi-Ferretti (2007) and Bénétrix et al. (2015), there have been structural changes in the size and the composition of external liabilities and assets of EMEs for the last 30 years. We link these changes to reserve accumulations. Similarly, we ana- lyze the gross flows rather than focus on the net flows following the lessons from some influen- tial papers such as Forbes and Warnock (2012) or Bruno and Shin (2015). Broadly speaking, the empirical regularities we found are 1) both of “inflows” and “stocks” of direct investment and equity portfolio investment are strongly and positively correlated with both of “outflows” and “stocks” of international reserve, 2) reserve outflows (accumulations) are also strongly and pos- itively correlated to current account surplus, and 3) reserve outflows are positively correlated to 69 private sector capital outflows. The patterns described so far hold in both cross-country data and individual country time-series data. To summarize our empirical findings more simply, both reserve outflows and private sector capital outflows increase when EMEs receive more di- rect investment or equity portfolio investment capital inflows, or have higher current account surpluses. Based on the empirical regularities, we construct a three-period model to explain the facts qualitatively. Our modeling strategy is to put minimal ingredients into the baseline model in the capital control literature. The baseline model is the Fisherian deflation model (e.g. Bianchi, 2011; Korinek, 2018; Jeanne and Korinek, 2019). The class of the models captures the features of sudden stop in a simple way, and more importantly, private saving and borrowing in the model are inefficient due to the pecuniary externality, with which we can design a planning problem of the optimal reserve accumulation. The two ingredients added to the baseline model are 1) imperfect capital mobility for both debt inflows and debt outflows, and 2) gross capital flows including direct investments. We model the imperfect capital mobility in the idea of limited participation following Fanelli and Straub (2020) for debt capital inflows, and then model the imperfect mobility for the private sector debt outflows in a similar fashion. Our specification is an EME needs to rely on inter- national financial intermediaries (IFIs) and the IFIs ask for more fees for the intermediations facing higher demands of overseas investment intermediation from the EME 3 . In this environ- ment, more overseas investments by private sectors lead to lower returns to the economy, but the private sector agents do not take account of it. Direct investments in our model are similar to equity portfolio investments or merger and acquisition in the reality. Foreign direct investors purchase claims on the capital. In such environments, receiving direct investments instead of debt inflows makes the EMEs more robust to possible sudden stops in the future. However, when the direct investment in- 3 We model in such a way to have a clean result. Our view is there are different sources of inefficiencies in private sector capital outflows from EMEs. We discuss this in Section 3 and suggest a different microfoundation in the appendix. 70 flows are beyond a certain level, the EME needs to save abroad since more direct investments mean more capital returns to the foreign investors in the future; it is better than external debt, but still a different form of external liability. The problem is private sectors cannot make enough capital outflows (overseas investments) by themselves and it is done inefficiently. Furthermore, the economy may be subject to insufficient net foreign assets to prepare for sudden stops, and the frictions on the capital outflows make it worse. As a result, in the absence of reserve accu- mulation, the excessive direct investment flows cause inefficient domestic currency apprecia- tions and equivalently domestic consumption booms. Therefore, the social planner in the EME is incentivized to accumulate reserves to generate capital outflows as reactions to the massive capital inflows. In our model, there is no particular structure except for the two new ingredients. Unlike preceding papers, we do not need any particular structures in the model such as longer matu- rity in the external debt than reserves, the existence of long-term project 4 or constantly binding credit constraint. Furthermore, reserve accumulation in our model is a reaction to direct in- vestment inflows and hence it is a function of direct investment and equity portfolio capital inflows. Hence, we can easily explain our empirical regularities of the relationship between di- rect investment external liability and reserve accumulation; once we posit direct investment inflows to EMEs as given, we can explain much of the increases in reserve holdings of EMEs since the mid-1990s and why some EMEs hold more reserves than others. In addition, the role of reserve accumulation in our paper is unique because the function of reserve accumulation is to supplement insufficient capital outflows by private sectors. In contrast to a few other papers, the reserve management policy - accumulating and depleting reserves - in our model cannot be perfectly replaced by other policy tools such as capital controls. Our model also provides important implications about the debate of “currency manipula- tion”: Do some EMEs depreciate their currencies to boost their exports? While we cannot fully answer the question, our model implies that the amount of reserve holding is not a good litmus 4 This is required in the papers where the reserve is modeled in the structures of Diamond and Dybvig banking model 71 for the test of currency manipulation. Reserve accumulation in our model is a passive reaction to direct investment type capital inflows. In terms of currency valuation, the interventions to accumulate reserves prevent domestic currency appreciation so as to keep the current account balance from getting worse due to the capital inflows: but, there is no intention to depreciate the currency to boost exports. Moreover, reserve accumulation in our model looks like a man- aged floating exchange rate regime in the sense that the policy limits the currency appreciations although it is not an object itself. Hence we link the reserve accumulation to the managed float- ing literature initiated by Calvo and Reinhart (2002). Related Literature Our paper is related to several strands of literature in international macroe- conomics. First and foremost, our paper relates to the literature that studies the reserve accu- mulation of EMEs. The main objective of the literature is to find why EMEs hold large amounts of costly reserves. While there are a few different approaches, the literature broadly falls into two different views: The mercantilist view and the precautionary view. The mercantilist view argues that reserve accumulation is a byproduct of exchange rate policies to boost exports by depreciating local currencies. Early works in the literature include Dooley et al. (2004), and there have been a few notable recent papers of similar ideas (e.g. Korinek and Serven, 2016; Choi and Taylor, 2017). On the other hand, the precautionary view pays attention to the his- torical fact that most EMEs began building their stocks of reserves after experiencing financial crises, in particular after the East Asian crisis in 1997. The papers in this view argue that EMEs have accumulated reserves believing that the reserves will protect them against sudden stops. Earlier works on this explanation include Aizenman and Lee (2007), which analyzes the macro- prudential role of reserves in the framework of the Diamond-Dybvig model, and Jeanne and Ranciere (2011), which quantify the optimal reserve holding by assuming reserve is a sort of Arrow-Debreu security. More recently, Bianchi et al. (2018) show how reserves can help EMEs with reducing roll-over risks of external sovereign debts 5 . A recent work that shares similar in- 5 Other papers that studied reserve accumulation in the precautionary view are Durdu et al. (2009), Obstfeld et al. (2010), Aizenman (2011), Hur and Kondo (2016), Shousha (2017), and Bocola and Lorenzoni (2020). 72 sights with ours is Jeanne and Sandri (2020). The paper introduces a model where EME policy authorities accumulate reserves to complement insufficient capital outflows by private sectors and to generate enough capital outflows (having more liquid foreign assets) that stabilize do- mestic debt prices from volatile capital flows. We contribute to this literature by proposing a novel theory of reserve accumulation from the precautionary view 6 . We show that in environ- ments where there are frictions on capital outflows, EME policy authorities facing large capital inflows are incentivized to accumulate reserves, and it is not based on any mechanism in pre- ceding papers. Although we share some insights with Jeanne and Sandri (2020), we construct our model using different micro-foundation of frictions on capital outflows, and we link reserve accumulation to the types of direct investment or equity portfolio inflows, which we will discuss more below. Our work is also related to the papers investigating the positive correlations between FDI ex- ternal liabilities and official reserve assets. The positive correlation between direct investment inflows and reserve accumulation is documented in Dooley et al. (2004). The paper argues that EMEs depreciate their currencies to attract direct investments so as to utilize otherwise waste- ful resources in the economy, such as labor. Matsumoto (2022) and Wang (2019) share similar ideas with Dooley et al. (2004). They introduce a small open economy model where EMEs ac- cumulate reserves to have more FDI to the economy. While these papers interpret the observed correlations with the mercantilist view, we provide another way of looking at the same fact. It is from the point of the precautionary view 7 . Furthermore, our model can explain empirical regularities, which papers listed above might have difficulties explaining: positive correlations between FDI inflows and reserve outflows in a short run 8 , and positive correlations between eq- 6 We do not include the mercantilist view-related ingredients in our model. In the formalization of the mer- cantilism view, it is required to model externalities in export sectors, which cannot be verified easily. It is often documented that the correlation between reserve accumulation and export growth is low for many EMEs, which contradicts the prediction from the mercantilism view (BIS, 2019). 7 However, we also showed that reserve accumulation attracts more direct investments in an extension of the baseline model. 8 In Appendix, we show the positive correlation between FDI and international reserve is also clear in the flow data in the frequency in quarter or year. This is problematic in the explanation of the mercantilism view since the policymakers do not necessarily react to capital flows in such short runs; it usually takes several years for direct investors to decide which country to invest. 73 uity portfolio investments inflows and reserve accumulation, which resembles the correlations between direct investments and reserve accumulation. In our model, the reserve accumulation is an almost linear function of capital inflows in the form of direct investment or equity portfolio investment 9 , and thus those empirical facts are explained by the model. This paper also adds to the nascent literature that studies the effectiveness of foreign ex- change market interventions under imperfect capital mobility. Gabaix and Maggiori (2015) show how limits to the arbitrage in global asset markets - UIP violation - can explain important puzzles in the exchange rate literature. They also show interventions in the foreign exchange market should be effective and can be welfare-improving. Cavallino (2019) build a continuous- time New Keynesian general equilibrium model that analyzes foreign exchange market inter- vention, using almost the same specification as Gabaix and Maggiori (2015). From a slightly different micro-foundation, Fanelli and Straub (2020) derives general principles of foreign ex- change market interventions. 10 To model limited arbitrage in a foreign exchange market, we mostly follow Fanelli and Straub (2020) but extend their modeling technique to private capital outflows from EMEs. Our new insights are that EME policy authorities might intervene not just to manage spreads on the borrowing rates but also to supplement insufficient overseas invest- ments by private sectors in the EME. We also incorporate the idea of imperfect capital mobility into a sudden stop model and show how policy authorities can use foreign exchange market intervention to prepare for sudden stops in the future. Besides, our paper is related to capital control literature. After the Global Financial Crisis, there has been an eruption of the capital control literature; notable works are Bianchi (2011), Farhi and Werning (2014), and Bianchi and Mendoza (2018). Recently, a few papers analyze the relationship between capital control and reserve accumulation. Acharya and Krishnamurthy 9 In addition, the approaches in Matsumoto (2022) and Wang (2019) cannot clearly explain why EMEs rely on reserve accumulation to attract more foreign direct investments rather than use other seemingly more efficient tools. For instance, simple tax cuts on the profits of foreign direct investors probably are more efficient than re- serve accumulation. Another difficulty in the approaches of those papers is that some exogenous factors such as geographic location might be dominant in determining FDI. Therefore, with this view alone, we will not see such clear positive correlations between FDI liabilities and reserve assets. 10 For other papers that analyzed foreign exchange market intervention, see Basu et al. (2016), Chang (2018) and Amador et al. (2020). 74 (2018) and Jeanne (2016) argue that capital control is a complement to reserve accumulation policy in terms of financial stability since the capital control eliminates the possible moral haz- ard of private agents when central banks hold reserves. Arce et al. (2019) and Davis et al. (2021) show that reserve accumulation and capital control are perfect substitutes with each other in environments where collateral constraints on private sectors are always binding and yields on the reserves are the same as the borrowing rates. We do not precisely identify the relation of capital control to reserve accumulation, but our analytical results imply the role of the reserve cannot be perfectly replaced by capital control since policy authorities accumulate reserves to generate additional capital outflows. Lastly, we contribute to the fear of floating literature. Since the famous paper Calvo and Reinhart (2002), it has been widely known that many EMEs in fact manage their exchange rates rather than let the exchange rates float. More recently, Levy-Yeyati et al. (2013) document the pattern of foreign exchange market interventions in EMEs, which suggests the EMEs intervene in the market to prevent their currencies from appreciating rather than depreciate the curren- cies. The authors interpret the pattern as evidence that EMEs manage their exchange rates to expedite capital accumulation in their countries. However, our model shows that reserve accu- mulation amid substantial capital inflows would look like interventions to avoid appreciation of the currency, but the purpose of the intervention is at preventing sudden stops and more efficient foreign liquid asset accumulation. Layout The rest of the paper is organized as follows. Section 3.2 illustrates stylized facts about reserve accumulation, which motivate our model. Section 3.3 introduces the model. The model explains the stylized facts in Section 3.2 and provides new insights related to reserve accumu- lation. In Section 3.4, we suggest three extensions of the baseline model in Section 3.3. We confirm that our key insights will survive or even become stronger in the more general environ- ments. Section 3.5 concludes and discusses avenues for future researchers. 75 3.2 Empirical Regularities As a first step, we find empirical regularities that will provide a guide to build our model of reserve accumulation. We aim at finding out what macro variables co-move with reserve ac- cumulation and what macroeconomic conditions can explain different reserve holdings across EMEs. We first document the general facts regarding the reserve accumulation of EMEs since the mid-1990s. Then, we focus on how different types of capital flows are associated with re- serve accumulation. 3.2.1 General Facts This subsection introduces general facts about international reserves. Readers familiar with the literature or readers who might want to focus on the key insight may skip this subsection. Reserve accumulation and the evolution of national wealth of EMEs As it is widely known, EMEs began accumulating massive amounts of reserves since the mid-90s. By the end of the ’80s, the levels of reserve holdings of most EMEs were around 5% of GDP . As in Figure 3.1, the level began rising from the mid-90s and the accumulation was escalated from the late 90s, which approximately corresponds to the East Asian crisis in 1997. The “rally” for having more reserves had been kept until the Global Financial Crisis in 2008 and after the crisis, the pace of reserve accumulation has become slow down. The pattern of increasing reserve holdings from the late 90s to the beginning of the crisis in 2008 is very consistent across different EMEs, but nevertheless the level of reserve holding varies along with a region and a country. Looking at Figure 3.1, it seems that Asian EMEs tend to hold more reserves; particularly Thailand and Malaysia holding reserves by the amounts of 30-40% of GDP . Most EMEs in Latin America and East Europe, as of 2017, are holding reserves by the amounts of 10-20% of GDP , but some EMEs there hold reserves comparable to or even more than the levels of the East Asian EMEs; Peru, Russia and Bulgaria. 76 Figure 3.1: Reserve Accumulation of EMEs Source: IMF BOP/IIP Now, we look at such rapid increases of the reserve holdings along with the evolution of ex- ternal liabilities and assets of EMEs; hence, along with the national “wealth” of the EMEs in the terminology in Lane and Milesi-Ferretti (2007). In terms of the Net Foreign Assets (NFAs), how reserve accumulation changes NFAs of EMEs is not clear as shown in Figure 3.2 below. Clearly, EMEs holding more reserves have more external liabilities and hence here we have no support- ive evidence of positive effects of reserve accumulation on NFAs. In the earlier literature, such ambiguous effects of reserve accumulation on NFA and the low returns to reserve compared with the borrowing rates of EMEs altogether raised a doubt on the precautionary motivation of reserve accumulation. For example, Rodrik (2006) stated that reserve accumulations seem to expedite the borrowing of private agents in EMEs, and therefore the NFAs of the EMEs might not increase enough to compensate the cost of reserves. More recently, Korinek (2018) insinu- ated that the Ricardian equivalence mechanism might work in a way of undoing the effects of reserve accumulation 11 . However, while there have been no vivid changes in the net position, there have been no- table changes in the gross positions. First of all, as it was documented in Lane and Milesi- Ferretti (2007) and Bénétrix et al. (2015), there was a shift of a way of external financing of EMEs: from debt financing to foreign direct investment (FDI) or equity portfolio investment; hence to the equity type financing. To put it another way, the high growth of the gross liabili- 11 Another important criticism on the precautionary view of reserve accumulation is Alfaro and Kanczuk (2009). 77 Figure 3.2: NFA ex-IR and International Reserves Note: Average ratios of NFA ex-Reserves and Reserves to GDP , 2011-17 Source : IMF BOP/IIP ties of EMEs was mostly attributable to direct investments and equity portfolio investments. As Figure 3.3-a indicates, the external debts scaled by GDP had slowly declined from the late 90s to 2006 and have remained at similar levels since then. On the other hand, FDI and portfolio eq- uity liabilities have increased sharply and become the main component of external liability. It is noteworthy that the periods external debt to GDP ratios decreased roughly match the periods when the pace of reserve accumulation of EMEs was at its peak. Second, as in Figure 3.3-b, ex- ternal assets held by private sectors in EMEs have also increased and its trend is very similar to the reserve assets. In the aggregation over EMEs in the sample, reserve assets of public sectors and external assets of private sectors closely co-moved until the early 2010s and interestingly, the two different external assets have diverged since then; external assets of private sectors, de- nominated by GDP , have rapidly increased while the official reserve holdings have been stable. In the appendix, we discuss possible reasons for the divergence between private external assets and public external assets - official international reserves -, but the focus in this paper is on the 78 Figure 3.3: External Liability and Asset of EMEs (a) External Liability (by type) (b) External Asset (by agent) Note: All values are the summation across the sample countries. (a) Debt liability includes debt portfolio investment liability and other investment liability. Source : IMF BOP/IIP , External Wealth of Nations Database periods EMEs rapidly increased the stocks of their reserve holdings. During the periods EMEs increased their reserve holdings, external assets of private sectors also increased. Weakly positive correlations between external assets of private sectors and official reserve assets As we saw in Figure 3.3-b, external assets held by private sectors in EMEs increased even during the time official reserve holdings were increasing. Here we look at the relationship between reserve assets and the private sector external assets in the cross-country data. Figure 3.4 presents a positive correlation between external assets of private sectors and reserve assets of public sectors. The correlation is low, but even such a weakly positive correlation is opposite to a prediction from the Ricardian equivalence mechanism; private agents expect reserve assets of public sectors will be ultimately given to them in the future, and thus the reserve accumula- tion incentivizes the private agents to have less foreign assets. In the next section, we provide a rationale behind the positive correlations. Also, in the appendix, we discuss other related facts such as the recent divergence between private sector external assets and official reserve assets in Figure 3.3-a. 79 Figure 3.4: Private External Assets and Reserves Note: All values are averaged over 2013-2017. Source : IMF BOP/IIP Positive correlations between current account surplus and reserve outflows Another impor- tant macroeconomic variable that comoves with reserve accumulation is the current account. What we found is that EMEs tend to accumulate more reserves facing larger current account surpluses, as evidenced in Figure 3.5 below. Looking at Figure 3.5, one might wonder whether the reserve accumulation causes the current account surplus or the current account surplus causes the reserve accumulation. Careful empirical analysis may find which causality results in the correlations in Figure 3.5 and few papers documented they found reserve accumulations improve the current accounts 12 . Empirical identification of precise causalities is beyond the scope of this paper, but our model shows the causality in either direction: reserve accumula- tion improves the current accounts and more (less) current account surplus (deficit) also causes more reserve accumulation. 12 See Bayoumi et al. (2015) and Choi and Taylor (2017). 80 Figure 3.5: Current Account and Reserve Accumulation Note: All values are averaged over 1998-2007. Source: IMF BOP/IIP 3.2.2 Reserve Accumulation and "Extra" Capital Inflows In this subsection, we provide key empirical facts on the relationship between reserve out- flows and equity-type capital inflows. Based on this relationship, we define "extra" capital in- flows and present how it is related to reserve accumulation. Positive correlations between reserve outflows and FDI & equity portfolio investment inflows As evidenced in Figure 3.6-a, the FDI liabilities of the EMEs are positively associated with re- serve holdings of the EMEs 13 . Equity portfolio investment liability is a relatively small part of the total external liability. But, we can still see clear positive correlations between the total eq- uity type liabilities - the summation of FDI liabilities and equity portfolio investment liabilities - and the reserve assets in Figure 3.6-b. In addition to the close relationship in the stock variables, another interest is to see how 13 As we discussed in the last section, Matsumoto (2022) and Wang (2019) also reported the strong positive correlations between the FDI external liabilities and reserve assets. 81 Figure 3.6: Reserves and FDI & Equity Liability (a) Reserves and FDI (b) Reserves and FDI & Equity Note: All values are averaged over 2013-2017. Source : IMF BOP/IIP different types of capital inflows are related to reserve outflows. We run a simple panel regres- sion 14 and relegate the details of this regression to the appendix. The key results are that the equity type capital inflows, particularly equity portfolio investment inflows, is more correlated to reserve outflows. Furthermore, the positive correlations between the equity type inflows - FDI and equity portfolio - and reserve outflows become larger in the sample period of 2003-07 when EMEs were rapidly increasing their reserve holdings. Highly positive correlations between “extra” capital inflows and reserve outflows Finally, we define a measure of extra capital flows that summarizes the information from the empirical findings above. The extra capital inflow we define is seemingly unnatural, but interesting corre- lations between the external inflows and reserve outflows are observed in the data. We denote the extra capital inflows by EC I . Then we define EC I= Net Inflows of F D I & E qui t y Por t f ol i o +Cur r ent Account B al ance 14 Our regression analysis must be plagued by possible endogeneity and cross-sectional dependence in the data. However, we emphasize that this is a step to find suggestive evidence to help us with building a new model. 82 Then surprisingly, as in Figure 3.7 below, the crude measure of the extra capital inflows exhibits strong comovements with reserve outflows. For the selected six EMEs, the reserve accumula- tions move “in tandem” with the extra capital inflows. Figures of other EMEs are relegated to the appendix. Figure 3.7: Reserve Outflows and Extra Capital Inflows on Selected EMEs Note: All values are scaled by GDP . Source : IMF BOP/IIP To test the comovements in a different way, we regress reserve outflows on the extra capital inflows. Table 3.1 reports the results from the regressions. Table 3.1 reaffirms the relationship in Figure 3.7. A one percentage point increase in the extra capital inflows-to-GDP is associated with a 0.27-0.62 percentage point increase in reserve outflows-to-GDP , depending on the sam- ple periods and specifications. However, the positive coefficients may just result from the ac- counting identity; the current account balance must be almost identical to the capital account balance. To check it, we define the extra capital inflows differently; we replace the net FDI & eq- uity portfolio investment inflows with the net debt inflows, naming them EC I 2. Then it turns 83 out that the measure with the equity type flows has larger coefficients and more explanatory power - higher R 2 - than the measure with debt flows. As we expect, the difference between the two measures becomes larger in the sample period of 2003-07. Table 3.1: Reserve outflows and extra capital inflows (a) Extra capital inflows Reserve outflows-to-GDP (Whole sample) (2003-2007) VARIABLES (1) (2) (3) (4) ECI to GDP 0.33*** 0.27*** 0.62*** 0.42*** (0.071) (0.052) (0.113) (0.066) Constant 0.01*** 0.01 0.01*** 0.02*** (0.001) (0.005) (0.003) (0.005) Observations 560 560 140 140 R-squared 0.163 0.245 0.334 0.363 Number of Country 28 28 28 28 Country FE YES YES YES YES Year FE NO YES NO YES (b) Alternative extra capital inflows Reserve outflows-to-GDP (Whole sample) (2003-2007) VARIABLES (1) (2) (3) (4) ECI2 to GDP 0.21*** 0.15*** 0.14 0.12 (0.075) (0.047) (0.152) (0.072) Constant 0.02*** 0.01** 0.03*** 0.03*** (0.000) (0.005) (0.001) (0.006) Observations 560 560 140 140 R-squared 0.077 0.160 0.025 0.098 Number of Country 28 28 28 28 Country FE YES YES YES YES Year FE NO YES NO YES Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Note: In each table, column (1) and (2) show the results with the whole sample (1998-2017) and column (3) and (4) with 2003-2007. Source: IMF BOP/IIP What kind of rationale behind the strong comovements between the two series? Let’s imag- 84 ine an EME receiving large amounts of capital inflows in the forms of direct investment or equity portfolio. Without any changes in the EME, the large capital inflows will cause domestic cur- rency appreciations, which might incentivize private agents to invest abroad. However, if some frictions prevent the agents from investing abroad and it is desirable for the policy authorities to suppress the currency appreciation, the policy authorities do intervene and generate capital outflows by themselves. Of course, the outflows by the policy authorities are in the correspond- ing amounts of the excessive capital inflows. Another way of thinking of the relationship is that reserve outflows move as it would be done by private sectors 15 . The figures and the regres- sion exercise imply that reserve outflows are made when EMEs receive capital inflows. Those tremendous capital inflows cause excessive resources and it obviously incentivizes the decen- tralized agents to invest abroad. In other words, if there is no friction on private capital outflows, the capital outflows by private agents will look like reserve outflows in Figure 3.7. The ideas of the discussion here will be materialized in the model of the following sections. 3.3 Model In this section, we present our model to explain why EMEs accumulate reserves. Of course, we also aim at capturing the empirical patterns that we highlighted in the last section. Since the mechanism in the model is novel, we adopt a “minimum ingredients” strategy so that we can derive a few “pen and paper” analytical results that map the model to the empirical regu- larities. The minimum ingredients are 1) capital inflows in the form of direct investment, and 2) imperfect capital mobility for both capital inflows and outflows. We plug in these two into the framework of the small economy version of Fisherian deflation model, which was developed to model currency crises in the context of pecuniary externality 16 . Though we discuss key assumptions below, some readers may wonder how our key results 15 Such comovements only exist for EMEs. In most AEs, central banks do nothing with reserves. Some EMEs such as Japan frequently intervene in the market, such tight comovements are not observed. 16 For more details of Fisherian deflation model, see Mendoza (2010) and Korinek and Mendoza (2014). 85 change as we bring the model to a more general environment. In the next section, we will introduce three extensions of the baseline model, in which our key results and insights survive, and the key mechanism can be even more powerful. 3.3.1 Model Setup We consider a small open economy that last three periods, t = 0, 1, 2. There are two do- mestic agents in our model: households and the social planner. On the other side, there are two international investors: international financial intermediations who intermediate capital inflows (outflows) to (from) the small open economy and direct investors who purchase the do- mestic capitals in the small open economy in period 0. The small open economy faces a credit constraint only in period 1 17 , which may or may not bind depending on the states. Thus, for precautionary purposes, the social planner accumulates reserves in period 0 when there is no concern over the binding credit constraint 18 . Production To model direct investments, while keeping the simplicity, we assume that both tradable and nontradable goods are produced by AK technology. That is, there are two different capitals, namely K T ,K N . K T ,K N are capitals to produce tradable goods and nontradable goods respectively. Two different kinds of capital cannot be converted from one to another and, more importantly, there is no capital accumulation or depreciation. Such a “semi-production” econ- omy is a useful modeling technique to allow direct investments in the model while keeping the only necessary ingredients. We denote output of sector j at time t by y j t ; therefore y j t = A j t K j where A j t is the TFP of sector j at time t. Throughout this section, we do not allow direct in- vestors to purchase the nontradable goods sector capitals. Then it is convenient to drop the 17 This is same as Korinek and Sandri (2016). We can put the credit constraint in period 0. But, it makes it harder to solve the model, without providing any extra insight. 18 Remember the level of reserves of EMEs soared from the late 1990s to the mid 2000s. Considering many EMEs experienced or witnessed the currency crises around the mid 1990s, it is reasonable to think that policy authorities in EMEs during the time had a fear of currency crisis in the future, which is captured by the occasionally binding credit constraint in our model. 86 upperscript j and let y T t = A t K 19 . We set y N 0 = y N 1 = y N 2 , but y T 0 < y T 1 < y T 2 (hence A 0 < A 1 < A 2 ) so that households need to borrow against higher outputs in the future. It is to investigate how reserve accumulation in our model is linked to the precautionary motivation 20 . Households The overall utility of the representative household is given by U= u(c T 0 ,c N 0 )+E 0 £ βu(c T 1 ,c N 1 )+β 2 u(c T 2 ,c N 2 ) ¤ where the utility function u(c T t , c N t )= ln ³ ¡ c T t ¢ α ¡ c N t ¢ 1−α ´ . Following the tradition,α and 1−α are the shares of tradable goods and nontradable goods respectively, andβ is the discount rate. For simplicity, we use log-utility function. The households enter period 0 with some legacy debts d 0 , d 1 , d 2 , which the households have to repay in each period respectively. This is not necessary for us to derive desired results. The seemingly ad-hoc assumption is to match our model to the empirical findings in the last section: although the total outstanding external debt to GDP ratio has declined, surely EMEs have had substantial external debts 21 . Given the output streams and the legacy debts, households determine their borrowing or saving of tradable goods. Since there is no saving technology domestically, for the households to save they must invest abroad. The households’ saving decision will be discussed in detail in the paragraphs of overseas investments. Throughout this paper, we use households’ saving, lending abroad and overseas investments interchangeably. We denote borrowing (saving) of households at time t by b t+1 ; b t+1 < 0 corresponds to a borrowing and naturally b t+1 > 0 corre- 19 In fact, in terms of nontradable goods the economy is same as an endowment economy. In the next section, we will look at an extension where direct investors purchase capitals in nontradable goods sector. 20 However, we note that even with a decreasing output stream of y T 0 > y T 1 > y T 2 , the model generates positive amounts of reserve accumulation and the amounts of reserve accumulation can potentially be larger. 21 Such drawback arises because our model is a representative agent model. In the next section, we will examine an extension to heterogeneous agents setup. It turns out that the heterogeneous agent extension matches the empirical findings better and prove our key insight survives in the new environment. However, as one expects it makes it harder to solve the model and poses few challenges. 87 sponds to a saving. Direct investments Direct investment inflows into the economy are novel and one of the most important elements in our model. A group of papers in the international trade literature ana- lyzed foreign direct investments 22 . However, we analyze direct investments from a different re- search question and therefore we model direct investments in a different structure rather than follow the traditions in the international trade literature. In other words, we take some aspects of foreign direct investments depending on our purpose although the related environments look too barren or unnatural. We will discuss more details below and here we just explain the direct investments in the model rather than discuss it. There is a direct investor interested in the tradable goods sector capitals in the economy. At the beginning of period 0, the direct investor determines how much capital she will purchase depending on technological features from which we abstract. Here purchasing capitals means to buy claims on the returns to the capital like equities in the reality. One can imagine direct investments in our model as a merger and acquisition process. Regarding the price of the capital, we assume the price is determined through a bargaining process, again similarly as like a merger and acquisition process in the reality. We assume that direct investors value the capitals higher than domestic households, which imply the equilib- rium price of capital is higher than the valuation of households. Letθ be the share of capitals sold to the direct investor among the measure 1 unit of capital: thus among the total returns of A t K ,θA t K belongs to the direct investors and remaining returns for households. Also, let’s denote the price of capital by Q 0 , which is determined through the bargaining process. Then we have Q 0 > 2 X t=0 M h 0,t A t where M h 0,t is the stochastic discount factor of households; hence, M h 0,t =β t E u T t u T 0 and u T t is the marginal utility of tradable goods consumption in period t. Then direct investment capital in- 22 See the excellent survey by Antras and Yeaple (2013). 88 flows in period 0 is Q 0 θK . When we simulate our model for the purpose of the illustration of the model outcomes, we may assume that some direct investors buy the claims on the capital returns in period 0 and 1. In such a case, the “average” capital price will be Q 0 > 2 X t=0 M h 0,t A t (1−σ· 1 t=2 ) whereσ is the measure of the direct investors who purchase the capital claims only in period 0 and 1, and 1 is an identity function. This minor change gives a little more realistic description and accordingly more realistic numerical results. Of course, this does not seriously change our results or significantly affect our insights 23 . In illustrating our analytical results, we mostly letσ be zero, and otherwise will be noted in figures of numerical results. International Financial Intermediation and household overseas investment We haven’t ex- plicitly solved the model, but can easily envision that large amounts of direct investment in- flows induce households to save. Since there is no available saving technology, households must invest abroad to transfer their incomes to the future. In the reality, there should be dif- ferent sources of frictions on overseas investments, which we cannot include all in our model. Regarding the importance and simplicity, we focus on frictions about intermediations done by global investment banks. Below we will separately discuss how we can derive similar results with other similar specifications but under similar spirits. Reflecting on the fact that much of overseas investments are intermediated by international financial intermediaries (IFIs), we assume that any overseas investment by households must be intermediated by IFIs. There is a continuum of IFIs and they have a heterogeneous opera- tion cost to intermediate 24 . Following Fanelli and Straub (2020), let the fixed cost be uniformly 23 Another way of understanding the minor modification is some direct investors quit the EME at the end of period 1. 24 Global banks in this context indicate that international investment banks operating in multiple countries. In fact, almost all renowned global banks such as JP Morgan, HSBC, and etc. have branches in major cities in most EMEs and do important roles in both capital inflows and outflows. In this context, the cost can be understood to 89 distributed on IFIs. That is, if there exists a continuum of IFIs, labeled by j ∈ [0,∞), then IFI j pays a cost of j . Further, we assume that IFIs of measure χ can manage the assets by the amount ofγχ. If the equilibrium intermediation fee is determined by the marginal cost of the intermediation, then it implies γχ= b 1 (3.1) And furthermore, the return facing households, say r t+1 , is r t+1 = r ∗ −Γ s b t+1 (3.2) whereΓ s =γ −1 and r ∗ is direct return to the overseas investment before paying the intermedi- ation fee 25 . As a result, r t+1 < r ∗ since b t+1 > 0. Furthermore, the gross return to the overseas investment b t+1 will be decomposed as below. b t+1 ¡ 1+ r ∗ ¢ = b t+1 (1+ r t+1 ) | {z } r etur ns to househol d s − 1 2 Γ s b 2 t+1 | {z } r etur ns to I F I s − 1 2 Γ s b 2 t+1 | {z } tot al f i xed cost s (3.3) The return to financial experts 1 2 Γ s b 2 t+1 is a sort of rent to IFIs and it represents a cost of overseas investment, which is not taken account by households. run these branches or offices in EMEs; e.g., costs to hire and train new people in the EMEs. Also, the participation of a new IFI can be both of entrance of new IFI (extensive margin) or more operation of an incumbent IFI (intensive margin). 25 We implicitly make two assumptions. First, the heterogeneous fixed cost is the cost in terms of tradable goods; each expert must pay tradable goods to participate. This is for simplicity and tractability. However, much of such cost following overseas investment in reality is the costs denominated by foreign currencies; for example, costs to manage branches in foreign countries. Second, the only available option to invest abroad is a fixed income security that pays a net return at the rate of r ∗ . This is surely counterfactual, but incorporating portfolio decision problem into our model will be overly complicated. 90 International Financial Intermediation and household borrowing The friction on capital outflows described above is a version of imperfect capital mobility, which has been popularized since the influential work by Gabaix and Maggiori (2015) 26 . The feature in the paper is the break-down of interest parities so that exchange rates are determined by capital flows and accordingly foreign exchange market intervention becomes effective by changing the spreads. For the borrowing of households and the borrowing rates determination, we adopt results in Fanelli and Straub (2020). The key idea is that limited participation arises due to participation costs. If an EME borrows more, the EME attracts more IFIs into the bond market by paying higher rates; IFIs with higher participation costs need to join the market. That is, −b t+1 = 1 Γ b ¡ r t+1 −r ∗ ¢ (3.4) Hence, the amount of capital inflow in the debt form linearly increases in the spread r t+1 −r ∗ . Rearranging the equation (4) yields a similar form with (2) r t+1 = r ∗ −Γ b b t+1 (3.5) Credit constraint Households face a credit constraint in period 1. That is, − b 2 ≤φ ¡ y T 1 (1−θ)+ p 1 y N 1 ¢ (3.6) The credit constraint is just the same as the collateral constraint in the recent capital control literature (e.g., Bianchi (2011); Korinek (2018)) where the collateral is GDP 27 . The idea of the standard specification of credit constraint in EMEs is that the borrowers in an EME may default on their external borrowing, but in such cases, international investors can take some properties 26 Other papers sharing a similar framework are Basu et al. (2016) and Cavallino (2019) 27 Some readers might wonder how the credit constraint can coexist with the limited participation. To handle the issue, we can conceptually decompose the borrowing process. In the first step, whether the credit constraint binds or not is determined by the realized states. If it turns out that the constraint binds, the amount of borrowing and the borrowing rates by the equation (5) and the credit constraint in (3.7). 91 in the country, which prevents a default of the EME. Since the international investors cannot fully utilize the properties in the EME, the international investors should discount the values of the collateral. We add one property to this standard form. In our model,φ is stochastic 28 . More formally, φ(ω) depends on the realized stateω. It is frequently argued that an important driver of sudden stops is a change in the amount of funds that international investors are willing to provide for a given amount of collateral, i.e. changes in the leverage parameterφ. A few theoretical works in macro-finance, such as Geanakopolos (2008) document such pro-cyclical leverage ratios as a general feature of financial markets, and more recently Arce et al. (2019) have a similar feature with ours. It isn’t necessary, but for convenience and tractability, we assumeφ has a support of an interval, and further its CDF and PDF are both continuous. An additional note about the credit constraint in (3.7) is that it captures the infimum of the cost of sudden stop. Notice that disruption of consumption smoothing by drops of the consumption is the only cost of sudden stop. This is counter-factual; many of sudden stops accompany significant falls in output 29 . Furthermore, Nakamura et al. (2013) document that the negative impacts of a financial crisis on output may last much longer than expected in a standard model. In this regard, the conditions under which the social planner in our model is incentivized to accumulate reserves can be interpreted as “sufficient” conditions in the sense that it is socially desirable to accumulate reserves with the infimum cost of sudden stop. Social planner The social planner accumulates international reserves in period 0 when there is no concern over the binding credit constraint. To finance the accumulation of reserves, the planner imposes lump-sum taxes by the amount of T units of tradable goods. With the revenue from the tax, the planner purchases foreign bonds in period 0, which will earn 1+r units of 28 The exogenous change of theφ mostly reflects “global financial shocks” changes in global financial market conditions. Like Shin (2012), Bruno and Shin (2015), and Agrippino and Rey (2019), the change in global financial market conditions, which may stem from center economics, would cause changes in risk appetites of international investors. For example, when the conditions in global financial market become worsen, the risk appetite of the investors will be lower (risk-off), and therefore the investors will ask EMEs to provide more collaterals. 29 See Basu et al. (2016). 92 tradable goods in period 1 per one unit of the bond. Accordingly, the dynamics of international reserves holding is given by T ¡ 1+ r ¢ = R 1 Discussion of assumptions Direct investments The description of FDI in our model is much different from international trade literature. This is because the features we want to look at in this paper are different from the literature. In the classical small open economy model where net capital flows are captured by debt flows, external borrowing or lending is determined by the Euler equation of the rep- resentative agent. The final decision is made by the agents in the small open economy. In contrast, it is not clear who makes the final decision of direct investment or equity portfolio investment; the final decision can be made by foreign investors. If there is no capital control, the capital inflows or equity portfolio investments are not necessarily aligned with the optimal- ity conditions of domestic agents: capital inflows can be much more than what the small open economy needs to finance current deficits and pay back external debts on the maturity date. We model direct investment inflows as an almost exogenous variable, but we can endog- enize the direct investment along with the capital price that direct investors pay. In the next section, we introduce an extension where the amounts of direct investments and the price of the capital are endogenous. We found that the social planner will accumulate more reserves in the new environment. Intuitively, more reserve accumulation derives down the capital price through lower marginal utilities in the future. In our model, the direct investors never undo their investment during sudden stops. This reflects the idea that the direct investments are more stable than other capital flows. However, few papers such as Ostry et al. (2011) document that certain FDI can outflow during sudden stops. Similarly, it is also argued that irreversible ’greenfield’ FDI is actually small parts of the total. Considering all these points, it is more realistic to think that some FDI is partly reversible. But, throughout this paper, we maintain the common view that FDIs are more stable than oth- 93 ers. Letting FDI outflow during sudden stops will give us a similar result with Jeanne and Sandri (2020). Overseas investment To the best of our knowledge, the only preceding paper in the interna- tional reserve literature that includes capital outflows of private sectors is Jeanne and Sandri (2020). In fact, almost all papers in the emerging market economy literature focus on capital inflows (or net inflows while assuming that EMEs have negative net foreign asset positions) 30 . However, thanks to the few influential empirical papers such as Forbes and Warnock (2012) and Broner et al. (2013), now the importance of analysis of gross flows is widely recognized. We also believe capital outflows of EMEs are really important, but unfortunately we still have a scant theory about private capital outflows from EMEs. Since we nearly have no giant on which we can stand, we borrow some modeling tools from recent papers assuming imperfect capital mo- bility and describe frictions of private overseas investment in the simplest way that gives us a clean result. To model frictions on capital outflows of private sectors, we assume that all the overseas investments are intermediated by global investment banks. Of course, it is extreme, but also reflects reality. It is true that domestic banks in EMEs often need assistance from global in- vestment banks when they invest abroad, probably due to the lack of expertise. For instance, sovereign wealth funds or national pension funds are often advised by global investment banks for overseas investments. In the appendix, we documents that the profit growth of branches of global banks in Korea is positively correlated with the growth of overseas investment in Korea, which suggests that much of the overseas investments are directly or indirectly intermediated by the global banks. However, we do not want to limit the frictions on capital outflows to rent extractions to foreign banks. Actually, another important cost about capital outflows might be capital “migra- tions” for the purpose of tax evasion or improper concealment of assets, especially for EMEs 30 An exception is a strand of papers that interpreted the global imbalance as a result heterogeneous financial development between developed and developing countries. See Caballero et al. (2008), Mendoza et al. (2009) and Maggiori (2017) 94 with low quality institutions. The fear of such capital migration would have been a reason be- hind strict capital control measures on outflows, as documented in Fernández et al. (2016). In the appendix, we document the relative strict controls on the outflows than inflows, and illus- trate the evolution of the regulations in Korea, as an example. 31 Accordingly, we also provide an- other setup where domestic financial experts extract rents from households and conceal some of them. The result is a little different, but we can still maintain our key insights. 32 We also abstract from the portfolio decision of overseas investment; the only available op- tion is a short-term fixed income security. Allowing different securities of different risk profiles does not alter our qualitative result, but may strengthen the quantitative performance of the model because households may underestimate the cost of risk-taking in the portfolio decision. 3.3.2 Solving the Model Now we solve the model. First, we will solve the household problem in decentralized equi- librium, and then solve for the solution of the social planner who accumulate reserves or control capital flows. Decentralized Equilibrium First we illustrate the household decisions. Then, a simple comparative statics is introduced to highlight how decisions of the households are related to direct investment inflows and re- serve accumulation, and how the relationship changes along with the measure of imperfect capital mobility,Γ. Next, we introduce our first analytical result, which proves the existence of pecuniary externality in our model and shows how the externality depends on the frictions on capital outflows. Finally, based on the comparative statics and the analytical result, we illustrate 31 If the controls on capital outflows strictly limit the physical amounts of capital, to reflect such features in the model, we can set an arbitrary limit on b s or it can be understood as a case ofΓ s =∞ when the limit on b s is zero. 32 The concealment in the appendix is still the concealment by asset managers. Another important case for EMEs is the concealment by customers, not managers. Our sense is it should be almost identical to the case of asset managers, but simply the negative marginal impacts not in the consideration by other people are much larger. In our model, it can be understood as a case of a largeΓ s . 95 how the benefit of direct investment inflows is greatly reduced. Utility maximization of households We derive the solution of households via backward in- duction. In the last period, by construction, there is no dynamic decision of households. House- holds consume all the available tradable and non-tradable goods after paying back all the debts and receiving remaining reserves from the planner. As we will show later, in our three period model, the social planner depletes all the reserves in period 1 regardless of the realization of φ, which corresponds to our intuition. However, the social planner might not deplete all the reserves once we make the model more dynamic; the number of periods is equal to or larger than 4. It is more formally stated and discussed in the subsection of the planning problem. Of course, the main conclusion and insights from the model are not affected by the reserve deple- tion decision. Back to the household problem, since all the reserves are depleted in period 1, the consumption of the households is as below. c T 2 = (1−θ) y T 2 + b 2 (1+ r 2 )− d 2 , c N 2 = y N 2 In period 1, the households take the states of the economy as given and solve the utility maximization problem. It is important to note that the states include φ. As we emphasized earlier,φ is a random variable whose value is determined at the beginning of period 1. A difficult question is “what would be a good distribution ofφ that resembles the reality?” To materialize an idea of a disaster, it seems a positively skewed distribution would be good, i.e., its pdf has a left-leaning curve. Here, we only assume that the distribution has a support on an interval of positive real numbers. That is, the support ofφ is h φ,φ i whereφ> 0 and ¯ φ<∞. Also, we suppose it is nicely well-defined so that we don’t have any trouble in using calculus. The utility maximization is formally defined as below. 96 max c T t , c N t , b t u ¡ c T 0 , c N 0 ¢ +E £ βu ¡ c T 1 , c N 1 ¢ +β 2 u ¡ c T 2 , c N 2 ¢¤ sub j ect to c T 0 = (1−θ) y T 0 + p 0 y N 0 −p 0 c N 0 −b 1 −T+Q 0 θk− d 0 c T 1 = (1−θ) y T 1 + p 1 y N 1 + b 1 (1+ r 1 )+ R−p 1 c N 1 −b 2 − d 1 c T 2 = (1−θ) y T 2 + p 2 y N 2 + b 2 (1+ r 2 )−p 2 c N 2 − d 2 −b 2 ≤ φ(y T 1 (1−θ)+ p 1 y N 1 ) where u(c T t , c N t )= ln ³ ¡ c T t ¢ α ¡ c N t ¢ 1−α ´ and R= T (1+ ¯ r ). Market clearing conditions will be given by the pricing functions. p t = µ 1−α α ¶ Ã c T t c N t ! and r t =−Γ j b t + r ∗ wher e j= b, s If the credit constraint doesn’t bind, i.e., the realizedφ is high enough, then the household determines its consumption of tradable goods according to her Euler equation. The amount of borrowing in period 1 is determined by −b 2 = −β(1+ r 2 ) ¡ (1−θ) y T 1 + b 1 (1+ r 1 )+ R− d 1 ¢ + (1−θ) y T 2 − d 2 (1+ r 2 ) ¡ 1+β ¢ (3.7) The interest rate r 2 is accordingly determined by r 2 = −Γ b b 2 + r ∗ . Plugging in the pricing func- tion into (3.7) yields −b 2 = −ζ 1 + q ζ 2 1 −4 ¡ 1+β ¢ Γ ¡ β(1+ r ∗ ) ¡ (1−θ) y T 1 + b 1 (1+ r 1 )+ R− d 1 ¢ −(1−θ) y T 2 − d 2 ¢ 2 ¡ 1+β ¢ Γ (3.8) whereζ 1 = (1+ r ∗ ) ¡ 1+β ¢ +βΓ ¡ (1−θ) y T 1 + b 1 (1+ r 1 )+ R− d 1 ¢ . If the credit constraint binds, the consumption of tradable goods will be determined by the credit constraint. Plugging in the budget constraint into the credit constraint equation, we can 97 derive 3334 − b 2 = Ã 1 1−φ ¡ 1−α α ¢ ! µ φ µ (1−θ) y T 1 + 1−α α ¡ (1−θ) y T 1 + b 1 (1+ r 1 )− d 1 + R ¢ ¶¶ (3.9) r 2 = r ∗ + Ã Γ b 1−φ ¡ 1−α α ¢ ! µ φ µ (1−θ) y T 1 + 1−α α ¡ (1−θ) y T 1 + b 1 (1+ r 1 )− d 1 + R ¢ ¶¶ (3.10) Sinceφ has a support of an interval, we can derive a formula of the cut-off ofφ, below which the credit constraint binds, given other states and the reserve. We can obtain φ c = −b 2 1 α (1−θ) y T 1 + 1−α α (b 1 (1+ r 1 )+ R− d 1 − b 2 ) (3.11) where−b 2 is determined by (3.8). We now turn to the period 0 optimization problem. Since there is no credit constraint, triv- ially the solution is the Euler equation. By denoting the marginal utility of good x in period t as u x t , u T 0 (b 1 , ;)=β(1+ r 1 ) Ã ˆ φ c φ u T 1 ¡ b 1 , b 2,c , ; ¢ dF φ + ˆ φ φ c u T 1 ¡ b 1 , b 2,u , ; ¢ dF φ ! (3.12) where b 2,c is determined by (3.9), while b 2,u is determined by (3.8). Comparative statics of the households decision Although we cannot solve for b 1 more ex- plicitly, it is easy to see the key characteristics of the b 1 as a function ofθ and R. We can easily show ∂b 1 ∂θ > 0, ∂b 1 ∂R 1 < 0 33 To have a unique equilibrium, we need a condition φ ¡ 1−α α ¢ < 1. Here, it is easily satisfied since the credit constraint only binds for low values ofφ. The parametric restriction is imposed to make sure households cannot increase the limit in the credit constraint just by consuming more. Such parametric restrictions are usual in a small open economy model with a credit constraint including asset price (Korinek (2018)). 34 The equation (10) implies that the borrowing rate r 2 is low during sudden stop. This is a little unsatisfactory since the spread often soars during sudden stop. This can be corrected by lettingΓ b as a function ofφ andΓ ′ b < 0 or similarly assuming r ∗ is a decreasing function ofφ. However, since the counterfactual does not seriously affect our key insight and the modifications make the model complicated without providing extra insights, we keep Γ b and r ∗ as constants. 98 It is straightforward that b 1 increases inθ since more capital purchase by direct investors in pe- riod 0 induces more excess tradable goods to save for the future 35 . Similarly, b 1 decreases in the amounts of reserve accumulation because households borrow more or save less as resources are transferred from the current period to future periods through the reserve accumulation. In addition to these comparative statics, it is important to notice that the marginal impacts of direct investments and reserve accumulation on the borrowing (saving) vary with the value ofΓ b (Γ s ): the absolute values of ∂b 1 ∂θ and ∂b 1 ∂R depend onΓ. We first look at the dependence of ∂b 1 ∂θ onΓ. If b 1 > 0, more direct investments increase the saving and therefore lower the interest rates facing the households; recall r t =−Γ s b t + r ∗ if b 1 > 0 36 . Hence, the “second” effect works in a way of reducing the saving. To see it more clearly, let’s invoke the implicit function theorem to the Euler equation. Then we can see db 1 dθ = u ′′ 0 ¡ y T 0 +Q 0 θk ¢ +β(1+ r 1 ) y T 1 E 0 h u ′′ 1 i ¡ u ′′ 0 −βΓ s E 0 £ u ′ 1 ¤ −β(1+ r 1 ) ¢ E 0 h u ′′ 1 (1+ r ∗ −2Γ s b 1 ) ³ 1− ∂b 2 ∂θ ´i (3.13) where u ′′ t = ∂u t ∂c T t . It is little cumbersome to show it formally, but we can easily see| db 1 dθ | decrease inΓ s . To an extreme, asΓ s →∞, db 1 dθ → 0. Obviously, forΓ s →∞, any positive saving derives down the gross yield to zero, and therefore households don’t save in any amount; they consume all the tradable goods. To summarize, massive direct investments in period 0 incentivize house- holds to save so much for the consumption smoothing, but severe friction on capital outflows (highΓ s ) hinder the households from investing abroad to transfer extra resources to the future periods. The friction on capital outflows by households is the key to understanding the motiva- tion of reserve accumulation in our model. Direct investments or equity portfolio investments, which are not necessarily in line with optimal consumption smoothing of the households, give households more resource than needed to consume now and if households cannot save (invest abroad) to reallocate the resources enough or it is done inefficiently, the social planner needs 35 Recall the budget constraint in period 0, c T 0 + p 0 c N 0 = (1−θ) y T 0 + p 0 y N 0 −b 1 −T+Q 0 θk− d 0 36 The effect is opposite for b 1 < 0 since direct investments reduce borrowing and it lowers the borrowing rates. Here, we only look at b 1 > 0 because it is a more empirically relevant case and that is the case in which central banks are likely to accumulate reserves. 99 to supplement (or substitute for) the insufficient savings by households. Next we look at the relationship betweenΓ and ∂b 1 ∂R . As with direct investments, reserve accumulation affects the borrowing (saving) rates through the changes in borrowing (saving) itself. When households borrow, the households face higher interest rates as they borrow more responding to reserve accumulation; therefore the households will borrow less. On the contrary, when households save, the less savings due to reserve accumulation drive up the yields facing the households, which results in more savings. To summarize, the changes in the interest rates also make the borrowing and saving less sensitive to reserve accumulation: hence, the Ricardian equivalence is broken. This is illustrated in Figure 3.8 and the equation (14) below. db 1 dR 1 = −u ′′ 0 +β(1+ r 1 )E 0 h u ′′ 1 ³ (1+ ¯ r )− ∂b 2 ∂R ´i u ′′ 0 −β(1+ r 1 )E 0 h u ′′ 1 ³ 1+ r ∗ −2Γ j b 1 − ∂b 2 ∂b 1 ´i −E 0 £ βu ′ 1 Γ j ¤ (3.14) where u ′′ t = ∂u t ∂c T t . Obviously, higherΓ suppresses the responsiveness of the borrowing (saving) to the reserve accumulation. These comparative statics are important in deriving our key results, which we will derive in the next subsection. Considering its importance, we highlight the comparative statics in the following remark. Remark 1. More frictions on capital flows, higher Γ, make the saving and borrowing by house- holds less responsive to reserve accumulation and to direct investments as well if households save. In analytical forms, ∂b 1 ∂θ > 0, ∂b 1 ∂R < 0 ∂ 2 b 1 ∂θ∂Γ s < 0, ∂ 2 b 1 ∂R∂Γ > 0 Pecuniary externalities Before we move on to the subsection of the planning problem, we in- troduce our first analytical result. We can easily notice the amount of borrowing and saving in 100 Figure 3.8: Comparative statics of the households decision the Euler equation (12) is not necessarily socially optimal. b 1 will impact the interest rates r 1 , r 2 , and p 1 , and households do not take account of it. The externalities arise because agents do not take account of the impact of their action on the prices and such externalities are often named as pecuniary externality 37 . We here note that there are two different sources of pecuniary exter- nalities; one through the real exchange rate in period 1 (p 1 ), and the other one through interest rates in period 0, 1 (r 1 , r 2 ). Interestingly, when households borrow, both externalities work in the same way, whereas the two different externalities work in the opposite way from each other when households save. In the same way as the models in the capital control literature, house- holds do not consider the effects of their decision on the real exchange rate in the future, which creates overborrowing (Bianchi (2011)). At the same time, more borrowing by the households also creates another source of overborrowing; more borrowing by households pushes up the interest rate on the borrowing. On the contrary, when households save more (higher b 1 > 0), it pushes down the yields on the saving, but it also makes the economy better prepared for a 37 For a more detailed discussion of pecuniary externality, see Dávila and Korinek (2018) 101 possible crisis in the next period. Consequently, higher saving by households creates two dif- ferent externalities working in the opposite ways in terms of the distance between the saving by households and the socially optimal saving. Whether the saving decision by households will be “undersaving” or “oversaving” in the eye of the social planner is itself indeterministic and depends on the state of the economy and values of important parameters; the distribution ofφ andΓ s . We formally state these results in the following lemma. The formal proof is relegated to the appendix B. Lemma 1. Assumeφ c >φ andΓ s ,Γ b > 0. b h t be the solution of (12), and b sp t be the solution by a social planner . 1) If b h t < 0, then b h t 0, then there always existsγ 0 ∈ (0,∞] such that forΓ s ∈ ¡ 0,γ 0 ¢ b h t b sp t Proof) See the Appendix B. Lemma 1 illustrates two (or three) different externalities from capital flows and when we are more likely to have undersaving or oversaving by households. First, as long as pr ob ¡ φ<φ c ¢ > 0 38 , any borrowing by households has an externality of tightening the credit constraint in pe- riod 1. The borrowing of households will lower the real exchange rate in period 1, p 1 , which is included in the credit constraint−b 2 ≤φ ¡ (1−θ) y T 1 + p 1 y N 1 ¢ ; obviously, more borrowing will re- duce the tradable consumption in period 1, and thereby resulting in lower real exchange rates. Second, any borrowing or lending abroad results in extra costs of capital flows, of which house- holds do not take account. Recall that r t =−Γ j b t + r ∗ and one unit of borrowing or lending gives b 1 (1+ r 1 ) in period 1. Differentiating b 1 (1+ r 1 (b 1 )) with respect to b 1 gives d (b 1 (1+ r 1 (b 1 ))) db 1 = 1+ r ∗ − 2Γ j b 1 = 1+ r 1 (b 1 )−Γ j b 1 38 We assumed that the support ofφ is ³ 0,φ ´ , the condition is equivalent to b 2 < 0. 102 Obviously, households are price takers and hence they only consider 1+ r 1 as a cost (return) to their borrowing (lending). Thus, any borrowing or lending by households leaves a term that is not in the calculation of the households: the second externality through borrowing rates or returns to overseas investments. Here it is important to note that the term−Γ j b 1 is positive for b 1 < 0 while it is negative for b 1 > 0. These different signs show reasons why we always have b h t b sp t for b h t > 0 only ifΓ s is large enough. If households borrow abroad, additional borrowing raises the borrowing rate. Hence less borrowing, which leaves more resources for period 1, is desirable in terms of both the borrowing rates and the prepa- ration for sudden stops in period 1. In contrast, once the borrowing alters to lending due to direct investment inflows, additional lending increases the marginal cost of overseas invest- ments, equivalently lowers returns to the lending. This makes more lending by households undesirable for the social planner, while it still makes the economy better prepared for possi- ble sudden stops in the next period. Thus the saving creates two externalities that work in the opposite direction from each other; the negative externality of lower returns, and the positive externality of less probable and less severe sudden stops. Of course, the negative externality increases in the measure of the frictions on oversea lending. Therefore the socially optimal overseas investments are lower than the investments by households forΓ s large enough and vice versa. Direct investment inflows and decentralized equilibrium The comparative statics above im- ply how the equilibrium without intervention by the social planner might change. To discuss the change, we need to see the problem facing the economy. Since we assumed y T 2 > y T 1 > y T 0 , the optimum for the households is to borrow against larger outputs in the future. However, borrowing creates two externalities as discussed above. Those externalities hinder households from “transferring” resources from the future to the present. The direct investment inflows provide a better way of external financing for the households with the problems described above. Capital inflows in the form of direct investment are free 103 from concerns about the externalities, or at least are better in terms of the externalities as we discussed in the last section; for example, the required return is less sensitive to the amount of capital inflows than debt inflows. However, the friction imposed on capital outflows, Γ s , gives a new challenge for the households. For direct investments inflows above a certain level, households need to save; they need to lend tradable goods abroad. Previously, they needed to bring the resources from the future to the present for the purpose of consumption smoothing, but now they need to reallocate the extra resources in the present to the future, again for the consumption smoothing. However, ifΓ s is non-negligible more saving by households leads to lower returns, which in turn lead to insufficient saving and inefficient consumption boom accordingly. Figure 3.9 below shows how the decentralized equilibrium changes along with direct invest- ment inflows, parameter θ in the model. As one can easily envision from the comparative stat- ics, more capital inflows cause higher tradable goods consumption in period 0, so higher real exchange rates. Despite the inefficient consumption booms in period 0, the direct investment inflows make the economy more robust to sudden stop: lower probability of binding credit constraint and less tight constraint for givenφ. Hence, as it is commonly argued, external fi- nancing in the forms of direct investments or equity portfolio investments is better in terms of macro-prudence in our model. However, the gain is strictly diminishing in the friction of capital ouflows. Figure 3.9 vividly indicates that magnitudes of the decline of the sudden stop probability pr ob ¡ φ<φ c ¢ rapidly decrease inΓ s . For an extremely largeΓ s , it is observed that the probability of sudden stop against direct investment inflows exhibits “U-shaped” curve: For direct investment flows above a certain level, the economy becomes more vulnerable to sudden stop as more direct investment capitals inflow 39 . Such an efficiency arises because households cannot save enough by themselves due to the friction underlying overseas investments. 39 We can see the relationship between sudden stop and direct investment more explicitly through− ∂b 2 ∂θ | φ<φ c . − ∂b 2 ∂θ | φ<φ c=φ − 1 α y T 1 + ¡ 1−α α ¢ (1−2Γ s ) db 1 dθ 1−φ ¡ 1−α α ¢ . The first term in the derivative − 1 α y T 1 is less collateral in period 1; since the claim on the capital was sold to foreigners, it cannot be used as pledged collaterals. The second term is effect from more saving from period 0. More tradable goods saved for period 1 raise the real exchange rate so as to ease the credit constraint. 104 Figure 3.9: Decentralized Equilibrium Note: As a benchmark, the parameter values for our numerical results are as follows: lower bound of bor- rowing rate(r ∗ )=0.05, interest rate on reserves( ¯ r )=0.01, weight on tradables(α)=0.35, discount factor (β)= 0.94, distribution of credit coefficient=Beta(1.5,5), wedges in UIP( Γ s = 0.2,Γ b =0.25), endowment stream( y T 0 =0.8, y T 1 =1, y T 2 =1.5, y N T =1), legacy debts(d 0 =0.1, d 1 =0.2, d 2 =0.1). To summarize, the economy suffers from the inefficiency of overseas lending by households, which generates extra costs of the lending,−Γ j b 1 . In another aspect, the low returns signifi- cantly dampen the benefit of direct investment flows in terms of the macro-prudence. It will be introduced and analyzed in details, but the analytics so far already hint what would be the role of the social planner: Since agents in private sectors cannot save enough and it is done inefficiently, the planner invests instead of the private agents. Equilibrium with Social Planner Now we solve for the solution of the planning problem. First, we will derive the solution of a social planner without capital controls and then derive the optimal reserve accumulation with 105 capital controls. Next, we will introduce a proposition that gives an implication of “currency manipulation.” Reserve accumulation without capital control To solve for the reserve accumulation in pe- riod 0, we first need to solve for the reserve depletion in period 1. As one easily expects, the so- cial planner, regardless of whether the credit constraint binds or not, depletes all the reserves. It apparently looks natural, but it is actually a little unsatisfactory considering the fact that many EMEs during sudden stops did not deplete much of their reserves: fear of losing reserve (Aizen- man and Sun, 2012). A few recent theoretical papers explicitly showed that in their environ- ments a social planner never depletes all the reserves during a sudden stop or other crises look- ing alike; Bocola and Lorenzoni (2020). However, once we extend our model to a more dynamic version, i.e., the number of periods larger than 3, we can have similar results. The intuition is as follows. If the social planner facing an ongoing sudden stop expects that the crisis might be recurrent in the near future, then the social planner leaves a part of the reserves for a possible crisis in the future. A more detailed analysis is in the next section. Given that the social planner will deplete all the reserves in period 1, we can formulate the planning problem as below. max R V = u ¡ c T 0 , y N 0 ¢ +E 0 £ βu ¡ c T 1 , y N 1 ¢ +β 2 u ¡ c T 2 , y N 2 ¢¤ sub j ect to −b 1 = the solution of (3.12) −b 2 =        φ ¡ (1−θ)y T 1 + 1−α α ¡ (1−θ)y T 1 +b 1 (1+r 1 )−d 1 +R ¢¢ 1−φ ¡ 1−α α ¢ i f φ∈ h φ,φ c i −ζ 1 + q ζ 2 1 −4(1+β)Γ ¡ β(1+r ∗ ) ¡ (1−θ)y T 1 +b 1 (1+r 1 )+R−d 1 ¢ −(1−θ)y T 2 −d 2 ¢ 2(1+β)Γ i f φ∈ h φ c ,φ i c T 0 = (1−θ) y T 0 + p 0 y N 0 −p 0 c N 0 −b 1 −T+Q 0 θk− d 0 c T 1 = (1−θ) y T 1 + p 1 y N 1 + b 1 (1+ r 1 )+ R−p 1 c N 1 −b 2 − d 1 c T 2 = (1−θ) y T 2 + p 2 y N 2 + b 2 (1+ r 2 )−p 2 c N 2 − d 2 r t = −Γb t + r ∗ 106 where u(c T t , c N t )= ln ³ ¡ c T t ¢ α ¡ c N t ¢ 1−α ´ and R= T (1+ ¯ r ). Then deriving the first-order condition and rearranging the equation yields the proposition 1. Proposition 1. The optimal reserve accumulation at t=0 is characterized by If b h 1 < 0 βΓ b E £ u T 1 ¤ b 1 db 1 dR ∗ 1 | {z } Hi g her r 1 + £ u T 0 −β ¡ 1+ r ¢ E £ u T 1 ¤¤ | {z } Consumpti on W ed g e at r = β d w 1 dR ∗ 1       ˆ φ c φ d (−b 2 ) d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ | {z } M ar g i nal V alue o f Bor r owi ng −βΓ b E · u T 2 b 2 db 2 d w 1 ¸ | {z } Lower r 2       (3.15) If b h 1 > 0 £ u T 0 −β ¡ 1+ r ¢ E £ u T 1 ¤¤ | {z } Consumpti on W ed g e at r = β d w 1 dR ∗ 1       ˆ φ c φ d (−b 2 ) d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ | {z } M ar g i nal V alue o f Bor r owi ng −βΓ b E · u T 2 b 2 db 2 d w 1 ¸ | {z } Lower r 2       −βΓ s E £ u T 1 ¤ b 1 db s 1 dR ∗ 1 | {z } Hi g her r 1 (3.16) where w 1 = R ∗ 1 + b 1 (1+ r 1 ) and d w 1 dR ∗ 1 = ∂w 1 ∂R + ∂w 1 ∂b 1 db dR = 1+ ¡ 1+ r ∗ − 2Γ j b 1 ¢ db 1 dR Proof) See the Appendix B. The proposition above well illustrates what determines the optimal reserve accumulation. The terms in the LHS are the marginal costs of reserve accumulation and the terms in the RHS are the benefits. The term u T 0 −β ¡ 1+ r ¢ E £ u T 1 ¤ in the LHS indicates the cost of reserve accu- mulation due to low returns to reserve, in terms of utility 40 . The two terms in the RHS are the benefits from higher wealth in period 1 41 . Because of the imperfect capital mobility in both of capital inflows and outflows, reserve accumulation raises the wealth in the future, which in turn helps with sudden stops and drives down expected borrowing rates in period 1 42 . 40 As long as r< r 1 , u T 0 −β ¡ 1+ r ¢ E £ u T 1 ¤ is positive; hence positive marginal cost. 41 Please notice that this excludes the direct investments. The term wealth can be understood as net foreign currency liquidity. 42 Throughout this paper, we implicitly assume b 2 | φ>φ c< 0. That is, households still want to borrow in period 1. 107 An interesting term isβΓ j E £ u T 1 ¤ b 1 db 1 dR ∗ 1 . The term is in LHS in equation (15) whereas it is in RHS in equation (16): the term is a marginal cost when b 1 < 0, but it is a marginal benefit when b 1 > 0. This is related to the mechanism of how reserve accumulation works. When households borrow, the Ricardian equivalence breaks down due to higher borrowing rates; hence db 1 dR >−1. On the contrary, the Ricardian equivalence breaks down due to higher yields for households when the households save. Thus the changes in the interest rates driven by reserve accumula- tion are the costs when households borrow, but are benefits when households save. It naturally implies that we are more likely to have an interior solution, i.e., positive reserve accumulation when households save rather than borrow. Figure 3.10 below illustrates this point. Figure 3.10: Reserve accumulation without capital control Note: All the parameter values are the same as the benchmark except for distribution of credit coefficient(=Beta(1.2,5)). However, if direct investment inflows in period 0 is so overwhelming; i.e., θ is large enough, it is possible to have b 2 | φ>φ c> 0 under the reserve accumulation. This might be relevant to some EMEs with large amounts of external assets comparing with the external debts. However, it is a little difficult to interpret the results in such a case. We relegate the analysis of the case of b 2 | φ>φ c> 0 to the appendix C. Also notice that we likely to have b 2 | φ>φ c> 0 when the planner optimally accumulates reserves. Otherwise, very lowΓ s and large θ are required to generate b 2 | φ>φ c> 0. 108 As we stated in the last subsection, b 1 increases in direct investment which is measured byθ, and as b 1 increases, the optimal reserve accumulation increases as well. Moreover, forθ such that b 1 < 0, the optimal reserve accumulation is not to accumulate reserve. Of course, our model is stylized and thus we should not think of the results quantitatively. However, the results in proposition 1 and Figure 3.10 highlight deficiencies of reserve accumulation as a macro- prudential policy tool in an environment where agents borrow from outside of the economy. As noted in lemma 1, when households borrow, the economy suffers from the overborrowing problem. Since reserve accumulation always incentivizes households to borrow more if the households borrow in the absence of reserve accumulation, the reserve accumulation calls a side effect: the economy suffers even more from the overborrowing. This is similar to a few preceding papers that documented the moral hazard from reserve accumulation (Acharya and Krishnamurthy (2018)) 43 . Furthermore, once we extend the model to a more dynamic version as we will see in the next section, the reserve accumulation policy is not time-consistent. Al- together it implies that reserve accumulation in our model and similar models using imperfect capital mobility suffer from the usual side effects of ex-ante bail-out policies: Moral hazard and Time-inconsistency. However, once we model reserve accumulation as a policy to supplement insufficient overseas investments by private sectors the deficiencies will be lessened because less saving by households is desirable at least in terms of the returns to the saving. Reserve accumulation with capital control Now we analyze the reserve accumulation in an environment where the social planner has control over the capital flows. Since there are two different types of capital flows - direct investment and debt instrument - in our model, we sep- arately look at the two different capital controls 44 . 43 Same as our paper, the moral hazard in those papers is slightly different from the traditional concept of moral hazard because of the absence of agency problem. 44 Throughout this subsection, we assume that the capital control is perfect; the social planner can compute the optimal tax or subsidy to the different capital flows and can impose it perfectly. This is obviously counterfactual. In reality, the capital control is imperfect due to incomplete information or any other reasons and furthermore cannot be imposed perfectly. To cover those realistic features is obviously beyond the coverage of this paper. For a formal analysis of the leakage of capital control, see Bengui and Bianchi (2018). 109 Capital controls over debt flows Suppose the social planner can tax or subsidize (hence negative tax) debt instruments type capital flows, i.e., b t+1 . As it is well known in the capital control literature, the optimal tax can achieve the same equilibrium where the social planner directly chooses the capital flow. Because this is well known and analyzed in the literature, we do not discuss it further and introduce the optimal tax on the debt type capital flows. The optimal tax is characterized as below. τ b = 1 u T 0 β[ ˆ φ c φ − db 2 db 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ − ˆ φ φ Γb 1 u T 1 −βΓb 2 db 2 db 1 u T 2 dF φ ] (3.17) As one can easily see, the optimal tax increases in the externalities from borrowing or saving of households 45 . Now we present the two equations that characterize the equilibrium where the social plan- ner optimally accumulates reserve and tax (or choose borrowing or saving). Assuming an inte- rior solution, which is not always, the equilibrium is characterized by the two equations. − u T 0 +βu T 1 ¡ 1+ r ∗ − 2Γ s b sp 1 ¢ +β ˆ φ c φ ¡ −u T 1 +βu T 2 (1+ r 2 ) ¢ db 2 d w 1 ¡ 1+ r ∗ − 2Γ s b sp 1 ¢ = 0 (3.18) − u T 0 +βu T 1 ¡ 1+ r ¢ +β ˆ φ c φ ¡ −u T 1 +βu T 2 (1+ r 2 ) ¢ db 2 d w 1 ¡ 1+ r ¢ = 0 (3.19) where w 1 = b 1 (1+ r 1 )+ R 1 and b 2 is characterized in equation (3.8), (3.9). It is straightforward that we can solve for b sp 1 once we assume an interior solution for both of b sp 1 and R 1 . Equation (18) and (19) give us b sp 1 = r ∗ − r 2Γ s (3.20) See in equation (19), for b sp 1 > 0, b sp 1 → 0 asΓ s →∞. On the contrary, b sp 1 →∞ asΓ s → 0, 45 Some papers named such taxation ’Pigouvian taxation’ . See Jeanne and Korinek (2019). Also, please notice that there are multiple policy instruments that achieve the same equilibrium. For deeper discussions, see Benigno et al. (2016). 110 which is a contradiction. The contradiction implies that we cannot have an interior solution forΓ s small enough. More broadly, the reserve accumulation increases inΓ s , while overseas investments are chosen by the social planner decrease inΓ s . This is intuitive and corresponds to our main message throughout this paper. The social planner accumulates reserves since households cannot lend abroad enough by themselves.Γ s is the measure of the friction on the private capital outflows and therefore the results above are straightforward. b sp 1 > 0 in equation (20) since r ∗ > r . This implies that R ∗ = 0 if b sp 1 < 0. The result of no reserve accumulation when the social planner chooses to borrow is also important and inter- esting analytics. In this paper, we aim at explaining why EMEs choose reserve accumulation as a macroprudential policy tool against sudden stop. For this purpose, suggesting mechanisms of how reserve accumulation works against sudden stop is not enough: It is a necessary con- dition, but not a sufficient condition. If there are multiple policy options, we need to explain why reserve accumulation is chosen over others and what is the unique role of it. Equation (20) already answers those questions. Although the social planner optimally subsidizes invest- ments by households, which is unrealistic since such taxation or subsidy is never perfect in the reality, the social planner would like to accumulate reserves forΓ s large enough. IfΓ s is large, the marginal benefit of overseas investment rapidly falls, and therefore beyond a certain level, the planner accumulates reserves to have more foreign assets. On the contrary, when the social planner optimally chooses to borrow, the capital control always dominates the reserve accumu- lation. Recall that the function of reserve accumulation is to raise net foreign currency external assets. In this regard, the taxation on external borrowing is always better than the reserve accu- mulation since the reserve accumulation works by raising the borrowing rates; it gives a penalty to the borrowers. Then it is obvious to see why taxing external borrowings is better than the reserve accumulation. The capital control lowers the borrowing rates whereas the reserve ac- cumulation raises the rates 46 . We summarize these findings in the second proposition. 46 Few theoretical papers (David and Venkateswaran (2019); and Arce et al. (2019)) documented the equivalence between reserve accumulation and capital controls based on the assumption that the credit constraints are always binding. However, these papers also assumed that the returns to reserve are the same as the borrowing rates, which is counterfactual. 111 Proposition 2. Suppose the planner optimally taxes or subsidies debt capital flows, then 1. b sp t+1 = b t+1 (τ t ) 2. If b sp t+1 < 0 and b sp 1 = b t+1 then R ∗ = 0 3. If b sp t+1 > 0 and b sp 1 = b t+1 then we may have R ∗ > 0 Proof) See the Appendix B. We can formulate the proposition in a different way, which gives us a corollary. It restates that the capital control on debt flows always dominates reserve accumulation for the borrowing, but reserve accumulation can be more efficient than the saving 47 . Corollary 1. Let V 0 (R) is the value function of the planner with the optimal reserve accumulation at t=0. Similarly, define V 0 (τ). Then, V 0 (τ)> V 0 (R) if b sp 1 < 0. On the contrary, if b sp 1 > 0, then we may have V 0 (R)> V 0 (τ) for r high enough orΓ s high enough. Proof) See the Appendix B. Capital controls over direct invesment flows If reserve accumulation is a reaction to di- rect investment flows beyond a level above which households are forced to save in an inefficient way, one easy solution would be to limit the direct investments themselves. For example, EME governments may ban foreign investors from buying domestic assets or set a cap, above which foreign investors cannot buy more. Regardless of the difficulties in implementing these reg- ulations, it is hard to analyze the optimal control over direct investment flows in this paper. Direct investment flows are viewed better than debt flows not just because it is more stable, but 47 The proposition and corollary also explain another puzzle about international reserve accumulation. One puzzle about international reserve is why central banks in EMEs limit the compositions of their reserves to certain safe assets such as US treasury bonds. Because of the low returns to these assets, sovereign wealth funds, whose portfolios accommodate more risky assets were expected to replace international reserves by central banks to a substantial extent. However, most of the external assets held by the public sector in EMEs are still international reserve. Proposition 2 suggests that the sovereign wealth funds are probably subject to the same frictions with private sectors. If sovereign wealth funds need to rely on foreign banks to make overseas investments, they must be subject to the same restriction (Γ s ). Also, the inefficiencies of domestic financial sectors or low quality institutions may matter in a similar way; for example, corruption in the sovereign wealth funds. In other words, although the social planner chooses how much to save and invest abroad, the social planner still faces the same constraint and thereby being incentivized to accumulate reserves. 112 also there might be some technological spill-over effects. Such unobservable positive effects might be the same for equity portfolio investments; for example, it promotes the development of domestic stock markets. Those externalities may exist or not, and moreover, the quantitative importance is hard to measure. Since these are beyond the scope of our paper, we mute all these channels, through which the capital inflows positively impact EMEs. Interestingly, even without those externalities, it turns out that the social planner in our model economy wants to receive direct investments to some extent, which provides incentives to accumulate reserves. To make the problem simple, let’s suppose that the social planner can chooseθ. Further, assume that the capital is priced by the stochastic discount factors of households. That is Q 0 = 2 X t=0 Ã β t A t u T t u T 0 ! Hence there is no extra gain from direct investments in terms of price. Letθ ∗ beθ chosen by the social planner. Then FOC ofθ ∗ is as follows. E · −βΓ j b 1 u T 1 db 1 dθ −β 2 Γ b b 2 u T 2 db 2 dθ ¸ | {z } C hang es i n r 1 ,r 2 − ˆ φ c φ db 2 dθ ¡ u T 1 −β(1+ r 2 )u T 2 ¢ | {z } M ar g i nal V alue o f Bor r owi ng + dQ 0 dθ u T 0 | {z } C hang e i n Q 0 = 0 (3.21) We interpret the equation (21) after introducing our second lemma driven from the equation (21). Lemma 2. Suppose ∂b 2 ∂θ | φ<φ c< 0 but E h u T 2 b 2 ∂b 2 ∂θ i < 0. Then withθ=θ ∗ ,b h 1 > 0. Proof) It it obvious that all the three terms in equation (21) are positive under b h 1 < 0. If b 1 > 0, then the first term E h −βΓ j b 1 u T 1 db 1 dθ i is negative. Therefore, for the equation (21) to hold, b h 1 must be positive. To give some intuition to equation (21) and lemma 2, first notice that all the terms in equa- tion (21) are related to the externalities from borrowing or saving by households. Any borrowing or saving by households affects interest rates and real exchange rates in the future, of which the 113 households do not take account. Since direct investments change b 1 , it generates the same ex- ternalities as well through the changes in b 1 . The first and second term are related to changes in r 1 and r 2 respectively, and the last term is the changes in borrowing under sudden stops through real exchange rates in the collateral constraint 48 . As stated in lemma 1 and the comparative statics in the last section, it is always b h 1 0. Then it is straightforward that more direct investment is beneficial since it lessens the overborrowing problem: Receiving more direct investment flows is desirable for the social planner as long as the economy is in the state of overborrowing. To give more eco- nomic interpretation, our model EME “transfers” resources from the future to the present for the consumption smoothing. However, because of the imperfect capital mobilities and credit constraint, the economy has trouble having transfer resources from the future. Direct invest- ments do provide another way of transferring the resources while circumventing the frictions in the external borrowings. As a result, it is optimal to allow direct investors to purchase domestic capitals at least until the borrowing in the form of debt alters to a saving. How is it related to reserve accumulation? The social planner in our model does not limit direct investments until households begin lending abroad. Also, we know that we may have the optimal reserve accumulation at positive amounts when households save. Hence if the social planner can do both reserve accumulation and control of direct investments, the social planner is likely to accumulate reserves. It is more likely if we add some positive externalities from direct investments, which we do not consider in this paper. Reserve accumulation and currency manipulation In this subsection, we characterize the optimal reserve accumulation more specifically as a function of direct investment capital inflows. It uncovers the nature of the reserve accumulation as a macroprudential policy tool against sudden stop and vividly maps our model to the empir- ical finding in section 2. In addition, the new proposition will provide important implications 48 Full characterization of ∂b 2 ∂θ | φ<φ c and conditions to guarantee the assumptions in lemma 1 are in appendix 114 for the policy debate of currency manipulation. As a first step, we denote b 1 = b 1 (θ,R). That is, b 1 is a function ofθ and R. From Remark 1, we know ∂b 1 ∂θ > 0 and ∂b 1 ∂R < 0. And recall the FOC of reserve accumulation without capital control. £ u T 0 −β ¡ 1+ r ¢ E £ u T 1 ¤¤ = β d w 1 dR ∗ 1 " ˆ φ c φ d (−b 2 ) d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ −βΓ b E · u T 2 b 2 db 2 d w 1 ¸ # −βΓ s E £ u T 1 ¤ b 1 db 1 dR ∗ 1 (3.22) Rearranging the equation (22) and using u T 0 −β(1+ r 1 )E £ u T 1 ¤ = 0 give us · r ∗ −r−Γ s b 1 (θ) µ 1− db 1 (θ) dR 1 ¶¸ E £ u T 1 ¤ = d w 1 dR ∗ 1 " ˆ φ c φ d (−b 2 ) d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ −βΓ b E · u T 2 b 2 db 2 d w 1 ¸ # (3.23) See the LHS in the equation (23) decreases inθ. However, the RHS is always positive as long as b 2 < 0 49 . We can think of the LHS as adjusted marginal costs and RHS as adjusted marginal benefits accordingly. Now define θ c such that the LHS in equation (23) is zero. That is r ∗ −r−Γ s b 1 ¡ θ c ¢ µ 1− db 1 (θ c ) dR 1 ¶ = 0 (3.24) Atθ=θ c , the social planner must accumulate reserves because the marginal cost is zero while the marginal benefit is positive. Thus θ c is a cut-off of direct investment above which the so- cial planner must accumulate reserves. Along with a few other related analytical results, we introduce our third proposition. Proposition 3. (Passive Reserve Accumulation) Let Q 0 = Q and define θ c such that r ∗ − r = Γ s b 1 (θ c ) ³ 1− db 1(θ c ) dR 1 ´ . Then we have 1) There existsδ 0 such that forθ>θ c −δ 0 , R ∗ 1 > 0 and R ∗ 1 increases inθ 49 If b 2 is negative in any state, then it is negative in all the states. The only stochastic variable isφ. Once the decision is to borrow, lowerφ only yields lower borrowing. 115 2) R ∗ 1 = (Q 0 − A 0 )(θ−θ c )K+b 1 (θ c ,0)− b 1 ¡ θ,R ∗ 1 ¢ + c T 0 (θ c ,0)− c T 0 ¡ θ,R ∗ 1 ¢ 3) b 1 (θ c ,0)> b 1 ¡ θ,R ∗ 1 ¢ 4) There exists δ 1 such that c T 0 (θ c ,0)− c T 0 ¡ θ,R ∗ 1 ¢ > 0 for θ ∈ (θ,θ+δ 1 ). Therefore, for θ ∈ (θ c ,θ c +δ 1 ), R ∗ 1 > (Q 0 − A 0 )(θ−θ c )K . Proof) See the Appendix B. Broadly speaking, the proposition 3 illustrates the existence of the cut-off and the amounts of reserve accumulation are bounded below by (Q 0 − A 0 )(θ−θ c )K . Now assume thatδ is small and b 1 (θ c ,0)− b 1 (θ,R ∗ )≃ 0 then we have R ∗ 1 ≃ (Q 0 − A 0 ) ¡ θ−θ c ¢ K (3.25) More importantly, the real exchange rate in period 0 becomes almost invariant toθ. More for- mally, define p 0 = µ 1−α α ¶ y T 0 + (Q 0 − A 0 )θK− d 0 + b 1 (θ)− R (θ) y N 0 (3.26) ≃ µ 1−α α ¶ y T 0 + (Q 0 − A 0 )θ c K− d 0 + b 1 (θ c ) y N 0 Then p 0 is almost invariant toθ∈ (θ c ,1). In other words, because the social planner absorbs the extra liquidity from direct investments by accumulating more reserves, the real exchange rate turns out to be almost “invariant” to direct investment capital inflows. Figure 3.11 illustrates such “passive” reserve accumulations and invariant real exchange rates under the passive re- serve accumulation. To explain more, the social planner facing direct investment flows above a certain level “passively” absorbs the extra inflows beyond the level: The reserve accumulation increases by the almost same amount of the increase in direct investments. We explain more about such a passive reserve accumulation and following invariant real exchange rates in the discussion of currency manipulation below. Before we move on to the discussion, we restate the findings in the remark 2. 116 Remark 2. For direct investments inflows beyond a certain level, 1) the social planner must accumulate reserves, and 2) for direct investments more than the level, the planner absorbs the extra inflows by accumulating reserves and thereby making the real exchange rates almost invariant to the capital inflows. Figure 3.11: Passive Reserve Accumulation Note: A 0.1 unit ofθ approximately corresponds to the inflow in the amount of the 9.5% of GDP . All the parameter values are the same as the benchmark except for distribution of credit coefficient(=Beta(1.2,5)). Remark 2 and Figure 3.11 map our model to the empirical regularities in Section 2. The key finding in Section 2 is the close relationship between reserve accumulation and extra capital inflows that we defined as a summation of current account surplus and net inflows of direct investment and equity portfolio investment. The equation (25) is the theoretical counterpart 117 to the empirical regularity. Furthermore, once we posit the direct investment capital flows and equity portfolio flows as given, we can explain the evolution of international reserve holding of EMEs for the last two decades: as more direct investment and equity portfolio capitals flow into EMEs, many of the EMEs absorb the capital inflows by accumulating reserves. Also, we can ex- plain much of the cross country difference of reserve holdings: The more direct investments or equity portfolio investments EMEs receive, the more reserves the EMEs accumulate. The model predicts that EMEs with more direct investment or equity portfolio external liabilities accumu- late more reserves as we saw in the data in section 2 50 . Another important parameter to explain the reserve accumulation isΓ s . The model predicts lowerΓ s induces more reserve accumula- tion. Unfortunately, we have no clear idea of what determinesΓ s or the empirical counterpart of the parameter. Despite such difficulty, it seems that the recent divergence between private sector external assets and official reserves in EMEs, which we showed in section 2, is a result of less friction on overseas investment by the private sectors: that is, lowerΓ s . For more discussion and related empirical findings, we relegate it to the appendix. Discussion of currency manipulation Reserve accumulation is often viewed as evidence that some EMEs depreciate their currencies to boost their exports, and such one side interventions to depreciate domestic currencies are often called “currency manipulation.” For example, one of the criteria that the US treasury examines to judge whether an EME is manipulating their currency value is the amounts of reserve accumulation; detailed information is in Table 3.2 below. In the literature, it has been often argued that international reserve holdings at extraordinary large amounts cannot be justified by the precautionary view and therefore the large amounts of reserves are a byproduct of the export-oriented growth strategy; for example, some East Asian countries such as China, Thailand, or Malaysia. The underlying idea is that reserve holdings 50 The EMEs holding reserves more than 40% of GDP , such as Malaysia, Thailand or Bulgaria also have sizable direct investment and equity portfolio investment external liabilities. 118 Table 3.2: The U.S Treasury’s Foreign Exchange Report Each country reports shall contain: (1) country's bilateral trade balance with the United States (2) country's current account balance as a percentage of its GDP ... (4) country's foreign exchange reserves as a percentage of its short-term debt (5) country's foreign exchange reserves as a percentage of its GDP Enhanced analysis shall include: (1) a significant bilateral trade surplus with the United States (2) a material current account surplus (3) engaged in persistent one-sided intervention in the foreign exchange market Source: Section 701 of the Trade Facilitation and Trade Enforcement Act of 2015 in such countries seem to be much more than needed for a precautionary purpose. Here we argue that the simple international reserve to GDP ratio is not a correct measure to identify a currency manipulation. If the apparent excessive reserve accumulation is caused by massive capital inflows, then the purpose of the reserve accumulation can be precautionary. Of course, we do not analyze or discuss the currency manipulation itself or try to examine whether certain EMEs manipulate their currencies in the spirit of mercantilism. We only aim at explaining why amounts of accumulated reserves are not a good “litmus” to test currency manipulation. 51 The empirical facts about reserve accumulation that we find in section 2 and proposition 3 altogether imply that EMEs facing massive capital inflows make corresponding capital outflows in the form of reserves to maintain the macroeconomic balance. The purpose of reserve accu- mulation is to reallocate the resources from capital inflows so as to minimize the inefficiencies of capital outflows by private sectors and be better prepared for possible sudden stops in the future. All the motivation of reserve accumulation lies in the precautionary purpose. The social planner in our model does not have an idea of mercantilism since we do not put any ingredients related to the mercantilism, such as positive externalities from export sectors. Figure 3.12 below well illustrates it. First, in the absence of reserve accumulation, the di- rect investment flows generate consumption booms. As θ increases, the households’ saving 51 For the theoretical exploration of currency manipulation, see Hassan et al. (2019). For empirical studies, see Dominguez (2019). 119 increases, but not enough due to falling returns for the households, which appreciates the real exchange rate through more tradable goods consumption. Therefore, although the direct in- vestments lower the probability of sudden stop, it falls slowly as the households cannot invest abroad enough. On the contrary, when the social planner accumulates reserves, more capital outflows are made and it keeps tradable goods consumption constant and hence real exchange as well. More importantly, thanks to the more overseas investments, the sudden stop probabil- ity falls much faster. As a result, the equilibrium with reserve accumulation is similar to little or no friction on capital outflows; that is, a very small Γ s . Figure 3.12: Reserve Accumulation and Currency Manipulation Note: All the parameter values are the same as the benchmark except for distribution of credit coefficient(=Beta(1.2,5)). In this regard, reserve accumulation is a way to “restore” the macroeconomic balance under little direct investment inflows or to achieve the balance under frictionless capital outflows. The real exchange rate might be a target for the planner since it measures over-consumption in the present, but the purpose of the intervention is to prevent “appreciations” of the currency, not to “depreciate” the currency. The current account ( y T 0 − c T 0 ) neither improves or becomes worsen 120 as more reserves are accumulated, as opposed to a common prediction from the mercantilism view. Such patterns of reserve accumulation in our model correspond to observations in Levy- Yeyati (2008) and Levy-Yeyati et al. (2013), which document that foreign exchange market in- terventions seem to aim at limiting domestic currency appreciations. Also, the patterns are in the same line with the famous finding in Calvo and Reinhart (2002) so-called “Fear of Float- ing” in a sense that real exchange rates in our model economy may look somehow managed in the eyes of outsiders to the economy. However, the motivation for reserve accumulation in our model lies in the precautionary purpose as it is designed so. Therefore, our model reconciles the precautionary view of reserve accumulation with empirical findings in the managed float literature. Back to our discussion of currency manipulation, our theory implies that evidence supporting the managed float exchange regime does not necessarily support the mercantilist view and the evidence can be aligned with the precautionary view. 3.4 Extensions In the last section, we maintained the simplest structures in the models to make the model tractable. In this section, we introduce three extensions of the baseline model. In each ex- tension, strong assumptions in the baseline model are alleviated and it turns out that our key insights and results survive in the more general environments. 3.4.1 The Model with Heterogeneous Agents We introduce a heterogeneous agents model. Our goal in the model is to show how our main results in the representative agent model can survive in the new heterogeneous agents model rather than solve the heterogeneous model fully. We borrow some features from Korinek and Sandri (2016). The environments of productions, international financial intermediations (IFIs), and direct 121 investors are same as the baseline model. However, there are two heterogeneous agents in the small open economy: Borrower and Saver. We may think that savers are the group who receives direct investments; hence they sold their tradable goods capitals to foreign direct investors. The savers need to lend their tradable goods to the borrowers or invest abroad. Similarly, the bor- rowers can borrow from either IFIs or the savers. We denote the total borrowing of the borrowers by b b t+1 and similarly the total saving of the savers by b s t+1 . To differentiate the borrowings from IFIs from the total borrowings, we let b b ∗ t+1 be the borrowing from IFIs. Similarly, we define the overseas investment by the savers as b s ∗ t+1 . The social planner issues their own bonds to accumulate reserves. Let’s denote it by b g t+1 . Similarly with b b ∗ t+1 , define b g ∗ t+1 . The market clearing condition of the domestic funds market is as below. b b t+1 − b b ∗ t+1 + b g t+1 − b g ∗ t+1 + b s t+1 − b s ∗ t+1 = 0 (3.27) That is, the total demand for the tradable goods borrowing in the domestic market is b b t+1 − b b ∗ t+1 + b g t+1 − b g ∗ t+1 , while b s t+1 − b s ∗ t+1 is the supply from the savers in the domestic market. The description of flows of funds is provided in Figure 3.13 below. Figure 3.13: Flow of Funds To clear the market, we need one more market clearing condition, by which borrowers 122 (savers) are indifferent between borrowing from IFIs and savers (lending abroad and lending to the borrowers). To have the condition, let’s assume that the yields from investing abroad without the fee to IFIs are higher than the borrowing rates. The net returns to the savers are characterized in the same way, but now r t+1 =−Γ s b s ∗ t+1 + r ∗∗ (3.28) Similarly, for the borrowing rates from IFIs, r t+1 =−Γ b ³ b b ∗ t+1 + b g ∗ t+1 ´ + r ∗ (3.29) Since b b ∗ t+1 < 0 and b s ∗ t+1 > 0, for the market to be cleared, we need r ∗∗ > r ∗52 . In period 1, the credit constraint can bind and it is as follows. −b b ∗ t+1 ≤φ t ¡ (1−θ t ) y T t + p t y N t ¢ (3.30) That is, the amount of the total external debt by the borrowers is constrained by the aggre- gate GDP . The credit constraint does not include b g ∗ t+1 since the social planner does not borrow abroad when the credit constraint binds 53 . Furthermore, during a sudden stop, nontradable goods are really cheap so that savers dispose of all their assets abroad to consume more non- tradable good; the retrenchment in Forbes and Warnock (2012). 54 Hence, we can imagine that from period 1, the different groups of the agents merge into one big family so that the model backs to the representative agent model. The return to reserves, b g t+1 is low at r < r ∗ . Thus, the planner has to collect tax from the agents to pay the extra interest rates, r t+1 − r . We assume the tax is imposed optimally so that it 52 The r ∗ is the required rate for an economy who have nearly do external debt in terms of gross. Hence it must be low. 53 It is different in a more dynamic version of the model as it is explained in the next subsection. 54 Such a nice retrenchment does not strictly hold in the reality due to risk hedging motives or low confidence of the savers about the economy. 123 does not make any extra terms in the first order condition of the reserve accumulation, which we introduce below. It turns out to be optimal to impose the tax on the savers under reasonable parameter values. Taking all the changes, we derive the first-order condition for the optimal reserve accumu- lation in period 0 55 . βΓ b E h u b 1,T i b b ∗ 1 d(b b ∗ 1 + b g ∗ 1 ) dR 1 | {z } Hi g her r 1 + £ u s 0,T −β ¡ 1+ r ¢ E £ u s 1,T ¤¤ | {z } Consumpti on W ed g e at r = d w 1 dR 1       X i=b,s ˆ φ c φ β d ¡ −b i 2 ¢ d w 1 ³ u i 1,T −β(1+ r 2 )u i 2,T ´ dF φ | {z } M ar g i nal V alue o f Bor r owi ng −βΓ b E " u i 2,T b i 2 db i 2 d w 1 # | {z } Lower r 2       −βΓ s E £ u s 1,T ¤ b s ∗ 1 db s ∗ 1 dR 1 | {z } Hi g her r 1 (3.31) where w 1 =−b g∗ 1 ¡ 1+ r ¢ + ³ b b ∗ t+1 + b g ∗ t+1 + b s ∗ t+1 ´ (1+ r 1 ), R 1 =−b g 1 , and d w 1 dR 1 = ¡ r 1 − r ¢ db g ∗ 1 dR 1 + (1+ r 1 ) Ã db b ∗ 1 dR 1 + db s ∗ 1 dR 1 ! − ³ b b ∗ t+1 + b g ∗ t+1 + b s ∗ t+1 ´ Ã Γ b Ã db b ∗ 1 dR 1 + db g ∗ 1 dR 1 !! . From (27), we see b b t+1 + b g t+1 + b s t+1 = b b ∗ t+1 + b g ∗ t+1 + b s ∗ t+1 . Then d w 1 dR 1 = ¡ 1+ r ¢ + (1+ r 1 ) Ã −1+ db b 1 dR 1 + db s 1 dR 1 ! − ³ b b ∗ t+1 + b g ∗ t+1 + b s ∗ t+1 ´ Ã Γ b Ã db b ∗ 1 dR 1 + db g ∗ 1 dR 1 !! (3.32) See db j 1 dR 1 > 0 for j= s,b. Therefore, forΓ b ,Γ s large enough, d w 1 dR 1 > 0. The mechanism of how re- serve accumulation improves the net foreign asset position is analogous to the baseline model. Since it raises the borrowing rates and therefore returns to the savers as well, the interventions to accumulate reserves discourage the borrowing, but encourage the saving. As one might expect, the mechanism in proposition 1 and proposition 3 applies. As direct 55 We assume the planner assign equal weights to each of the borrower and the saver. 124 investment capitals inflows, −b b ∗ 1 decreases, but−b s ∗ 1 increases. It reduces marginal costs of reserve accumulation while raising the benefits. Therefore, we have the following proposition. Proposition 4. The optimal reserve accumulation in the heterogeneous agents model is charac- terized as follows. 1) It is characterized by the first-order condition " r ∗∗ −r−Γ s b s ∗ 1 (θ)+Γ s b s ∗ 1 db s ∗ 1 (θ) dR 1 # E £ u s 1,T ¤ +Γ b b b ∗ 1 (θ) d(b b ∗ 1 (θ)+ b g ∗ 1 ) dR 1 E h u b 1,T i = d w 1 dR 1 " X i=b,s ˆ φ c φ β d ¡ −b i 2 ¢ d w 1 ³ u i 1,T −β(1+ r 2 )u i 2,T ´ dF φ −βΓ b E " u i 2,T b i 2 db i 2 d w 1 ## (3.33) 2) There existδ such that forθ>θ c −δ, R ∗ 1 > 0 and R ∗ 1 increases inθ 3) There existsδ 1 such that R ∗ 1 > (Q 0 − A 0 )(θ−θ c )K forθ∈ (θ c ,θ c +δ 1 ). Proof) See the discussion above. Proposition 4 is analogous to proposition 3. Therefore, our analytics and insights in the baseline model survive and hold in the heterogeneous agents model. As one might expect, more direct investment capital inflows - higher θ - make more borrowers switch to savers and the increase in the share of savers in the economy force the planner to accumulate more reserves. 3.4.2 The Infinite Horizon Model We illustrate an infinite horizon model as an extension of the baseline model. Same as the heterogeneous model, we aim at proving that our key insights survive in the new environment. In addition, we introduce analytical results about reserve depletions during sudden stop and the time-inconsistency of reserve management policy. The economy is populated by a continuum of identical, infinitely-lived households of mea- sure unity with preferences given by: E 0 ½ ∞ X t=0 β t u (c t ) ¾ (3.34) 125 where c t = f ¡ c T t ,c N t ¢ . Vector of endowments given by y y≡ ¡ y T , y N ¢ ∈ Y ⊆ R 2 ++ follows a first- order Markov process. The social planner taxes households by the amount T to accumulate reserves; of course, the planner grants subsidies when decumulating reserves. Using notations in the baseline model, the budget constraint of household is as below. b t+1 + c T t + p t c N t + T t = b t (1+ r t )+Q t (θ t −θ t−1 )K T + (1−θ t ) y T t + p t y N t (3.35) whereθ t is the share of foreign investors in domestic capital markets. For simplicity, we assume that the capital price is determined through the same bargaining process in the baseline model. We assume thatθ t is time-variant, but deterministic. Same as the three period model, the household faces the credit constraint, but now in every period. That is 56 , − b t+1 ≤φ y t ¡ (1−θ t ) y T t + p t y N t ¢ +φ R R t+1 (3.36) where φ t follows a stochastic process 57 . Following Shousha (2017), we assume that holding reserves of R t+1 can relax the credit constraint by the amount of φ R R t+1 58 . The idea behind the new assumption is that holding reserves gives EMEs a better reputation or it can be used as a collateral as US treasury billls are used as collaterals in the repo market in the reality. φ R ∈ (0,1) 59 and unlikeφ y t , it is constant because the collateral value of reserves composed of safe assets is highly invariant to global financial conditions. The social planner accumulates reserves in the same way with the baseline model. Again, 56 I R t is the amount of reserves after goverment depletes its reserves. 57 We don’t specifiy the process of φ t , but the process ofφ t should include some hazardous events. In this sense, φ t can follow a first-order Markov process whose Markov chain includes disaster states described in Barro (2006). More generally,φ t can be the summation of a “normal” AR(1) process and a compound Poisson process, which delivers a negative random shock with a certain probability in every period. 58 For the mechanism of how liquid financial assets can works as a collateral, see Gottardi et al. (2017) and Parlatore (2019) 59 Theoretically, it is not impossible to haveφ R > 1 as it is in Shousha (2017). However, we exclude such a case because of legal structures on the reserves. As it is noted in Alfaro and Kanczuk (2009), which rejected the idea that reserves can be used as collateral, under the Foreign Sovereign Immunities Act of 1976 of the United States and similar laws in other countries, central bank assets, including international reserves, are usually protected against attachment. This means that reserves can be accepted as collateral only if EME governments are willing to pledge as such. Although it is highly unrealistic to think EMEs will default leaving so much reserves behind, we restrictφ R to be smaller than 1. 126 we define w t ≡ b t (1+ r t )+ R t . This is net foreign asset position in terms of liquid assets. Then the problem of the planner is formulated as follows. V ¡ w, y,φ,θ ¢ = max R ′ u ¡ c T , y N ¢ +βE £ V ′ ¡ w ′ , y ′ ,φ ′ ,θ ′ ¢¤ s. t. c T = (1−θ) y T +Q(θ−θ −1 )K T −b ′ + b(1+ r (b))+ R(1+ r )−R ′ b ′ =        solution of the credit constraint i f φ≤φ c solution of the euler equation i f φ>φ c We find that it is convenient to formulate the valuation in the following way. V ¡ w, y,φ,θ ¢ = max R ′ u ¡ c T , y N ¢ +βE £ u ¡ c ′ T , y ′ N ¢ +V ′′ ¡ b ′′ ,R ′′ , y ′′ ,φ ′′ ,θ ′′ ¢¤ Notice that we substituted b ′′ ,R ′′ for w ′′ . Assuming the credit constraint does not bind, the first order condition is µ r ∗ − r−Γb ′ db ′ dR ′ ¶ E £ u ′ T ¤ = d w ′ dR ′ · Pr ¡ φ ′ ≤φ ′c ¢ E φ ′ ≤φ ′c · ∂b ′′ c ∂w ′ µ −u ′ T +β ∂V ′′ ∂b ′′ c ¶¸ + Pr ¡ φ ′ >φ ′c ¢ E φ ′ >φ ′c · ∂b ′′ u ∂w ′ µ −u ′ T +β ∂V ′′ ∂b ′′ u ¶¸¸ (3.37) where db ′ dR ′ = ∂b ′ ∂R ′ + ∂b ′ ∂R ′′ ∂R ′′ ∂R ′ and d w ′ dR ′ = ∂w ′ ∂R ′ + ∂w ′ ∂b ′ db ′ dR ′ = 1+ ¡ 1+ r ∗ − 2Γ j ¢ db ′ dR ′ . It is easy to notice that equation (37) is analogous to equation (15), (16) in the baseline model. Once we replace V ′′ with u ′′ T , it is identical to equation (15), (16). Another difference is ∂b ′ ∂R ′′ ∂R ′′ ∂R ′ in db ′ dR ′ = ∂b ′ ∂R ′ + ∂b ′ ∂R ′′ ∂R ′′ ∂R ′ . This term emerges due to the time-inconsistency we will discuss below. Overall, the reserve accumulation in (37) is much analogous to the one in proposition 3. There exists a cut- off of direct investment above which the social planner always wants to accumulate reserves, and as more direct investment capital inflows, the planner passively accumulates reserves to 127 maintain the macroeconomic balance and thereby making the economy more prudential to sudden stops in the future. Reserve depletion during sudden stops and the Time-inconsistency First, we characterize the reserve depletion by the social planner during sudden stop. Using equation (37), we can easily derive the first-order condition of reserve depletion. That is βΓb ′ E £ u ′ T ¤ db ′ dR ′ + £ u T −β ¡ 1+ r ¢ E £ u ′ T ¤¤ + £ u T −β ¡ 1+ r ′ ¢ E £ u ′ T ¤¤ db ′ dR ′ = d w ′ dR ′ · Pr ¡ φ ′ ≤φ ′c ¢ βE φ ′ ≤φ ′c · ∂b ′′ c ∂w ′ µ −u ′ T +β ∂V ′′ ∂b ′′ c ¶¸ + Pr ¡ φ ′ >φ ′c ¢ βE φ ′ >φ ′c · ∂b ′′ u ∂w ′ µ −u ′ T +β ∂V ′′ ∂b ′′ u ¶¸¸ (3.38) The equation (38) is identical to the equation (37) except for £ u T −β ¡ 1+ r ′ ¢ E £ u ′ T ¤¤ db ′ dR ′ . For our convenience, define Λ ¡ r ¢ ≡ u T −β ¡ 1+ r ¢ E £ u ′ T ¤ andΛ ¡ r ′ ¢ ≡ u T −β ¡ 1+ r ′ ¢ E £ u ′ T ¤ . Then both Λ ¡ r ¢ andΛ ¡ r ′ ¢ decrease in R ′ . See ∂c ′ T ∂R ′ =−1− ∂b ∂R ′ ′ < 0 since 0<− ∂b ∂R ′ ′ ≈φ y ∂p ∂R ′ y N +φ R <φ R < 1. Hence, holding reserves (less depletion) reduces the current consumptions - hence, higher wedges in the consumptions -, but leaves more resources for the future. With these comparative statics, we characterize the reserve depletions during sudden stop in the proposition 4. Proposition 5. Suppose the EME is under a sudden stop crisis. That is,φ<φ c . Then the reserve holding under the sudden stop R ′ has following comparative statics. 1) R ′ increases inφ. That is, ∂R ′ ∂φ > 0. 2) Both of H ¡ φ ′ ¢ and G ¡ φ ′ ¢ are the CDFs ofφ ′ , and H ¡ φ ′ ¢ < G ¡ φ ′ ¢ . Then R ′ is larger under H ¡ φ ′ ¢ than G ¡ φ ′ ¢ . Proof) See the Appendix B. The interpretation of lemma 3 is straightforward. If the ongoing crisis is more severe, more reserves are depleted (less reserve holding). If the crisis becomes more persistent, i.e.,φ ′ be- 128 comes smaller in all the states, givenφ, then the less reserves are depleted (more reserve hold- ing). To explain more, during a sudden stop, the planner decides whether to deplete reserves to grant it to households or hold it to use as collateral. Since we assumeφ R < 1, reserve depletion gives more liquidity so as to raise current consumption of tradable goods, while the depletion leaves fewer resources for the future. Hence holding reserves is a sort of auxiliary policy, which is painful now, but desirable for the preparation for the possible crisis in the future. The use of reserve during sudden stops are described in Figure 3.14 below. The use of reserve in Figure corresponds to the empirical findings in (Aizenman and Sun, 2012) that EMEs during the Global Financial Crisis hesitated to deplete reserves, and similar patterns of using reserves during 2013 tapering tantrum and recent market turmoil in Brazil and Chile 60 . Figure 3.14: Reserve Depletion during Sudden Stops Proposition 5 tells us that there is some discretion for the planner to use reserves during sudden stops. It implies that using reserves is a particular bail-out policy under discretion. A usual side effect from such ex-ante interventions with discretion is time-inconsistency. As one might expect, the bail-out in lemma 3 is not time-consistent. Furthermore, it turns out that 60 The central banks in Barzil and Chile announced that they will lend reserves to the domestic banks and will recover the reserves by the time they announce. 129 reserve management policy - both reserve accumulation and depletion - is in general time- inconsistent. We introduce the following proposition. Lemma 3. (Time-inconsistency) Denote a state in period t+k byω t+k . Define © T ∗ t+k (ω t+k ) ª 0≤k≤∞ as the reserve management policy function of the planner . Similarly, let © T ∗∗ t+k (ω t+k ) ª 0≤k≤∞ be the reserve management policy function of the planner with a commitment power . Then, T ∗ t+k (ω t+k )̸= T ∗∗ t+k (ω t+k ). Proof) See the Appendix B. Therefore the reserve management policy is time-inconsistent in both of accumulation and depletion. The reserve management in the future will impact the borrowing or saving by house- holds today, but the planner without commitment power has no way to enforce the future plan- ner to take account of such an effect. Lemma 3 above only tells us that the reserve management in general is not time-consistent. It does not suggest a “direction” of the inconsistency: is it underaccumulation or overaccumu- lation? or underdepletion or overdepletion? Unfortunately, we have no clear-cut answers to these questions. We have such ambiguous results because the direction of externality is not deterministic. If the EME suffers from overborrowing or undersaving, promising more accu- mulations and less depletions during sudden stops is time-consistent so that the households borrow less or save more responding to higher marginal utilities in the future. On the contrary, if the EME is under oversaving by the households, then it should be time-consistent to promise less accumulations and more depletions since it brings down the saving today through lower marginal utilities in the future. Since whether the EME is in a state of oversaving or undersaving varies along with time and state, it is not trivial to find the directions of the time-inconsistency. Although it would be an interesting theoretical point, we do not analyze further as it is not our main focus in this paper. 130 3.4.3 Endogenous Direct Investments and Capital Price Finally, we look at the extension where the direct investment and capital price are endoge- nous. Same as the last two extensions, we describe our new environment and then show why our key results do not change rather than solve the model fully. In the reality, direct investment in an EME depends on various factors such as locations, natural resources, or macroeconomic stabilities. Obviously, still we cannot reflect all the realistic features. We simply assume that the direct investment is an increasing function of the profitability of the investment. First, define π T = P 2 t=0 M t 0 A t Q 0 where M t 0 is the discount factor of the investor. π T is the gross return rate to the direct invest- ment in the tradable goods sector capital. Then we can assume θQ 0 K T = F T (π T ) (3.39) Hence, how much direct investors purchase the tradable goods capitals depends on the prof- itability. Of course, we assume F ′ > 0. We also endogenize the capital price. To model the capital price, we can posit that the do- mestic capital market is perfectly competitive. Then the capital price must be Q 0 = 2 X t=0 β t u T t u T 0 A t = A 0 + A 1 1+ r 1 +E · A 2 (1+ r 1 )(1+ r 2 ) ¸ We can easily see the reserve accumulation will impact the capital price through the changes in the interest rates; the borrowing rates and returns to the saving are the linear functions of the borrowing and saving, which are changed by reserve accumulation. Then from previous sections, once b 1 > 0 we expect r 1 increases in reserve accumulation, while r 2 changes in the 131 opposite ways to the reserve accumulation, depending on whether the credit constraint binds or not. However, with plausible parameter values, we can expect the effect through r 1 domi- nates. Hence, we reasonably conjectures ∂Q 0 ∂R 1 < 0 Then of course,θ increases in reserve accumulation R 1 because the lower capital price boosts the profitability of the direct investment. It provides two opposite different implications of reserve accumulations. First, the reserve accumulation by the social planner would have a sort of self-multiplication effect. As we saw in the last section, reserve accumulation increases in the amounts of direct investment. Here the reserve accumulation attracts more direct investments which in turn calls for more reserve ac- cumulation. Second, in the other way, reserve accumulation discounts the capital price, which is unfavorable for the EME. However, such negative impacts, which might be small, could be offset by possible positive effects, which we abstract in our model. For example, any knowledge spillover effects can be probably more than offsetting the negative impacts. Overall, although it is hard to make a strong assumption since the environment in our model is not rich enough, the optimal reserve accumulation could rise once we let the direct investment and the capital price be endogenous. Another strict restriction imposed in our model is that we exclude direct investments in the nontradable goods sector. Now we allow the investments in the nontradable goods capital. Let’s denote the share of foreign direct investors in the domestic tradable goods and nontrad- able gods capital markets byθ T andθ N respectively. Direct investors interested in holding K N also decide their investments based on the expected profitability. The crucial difference is the investors convert the returns of nontradable goods to tradable goods 61 . Hence the expected 61 Such assumption is common in the local currency sovereign debt literature. 132 profitability of the nontradable goods capital investments is π N =E 0   P 2 t=0 M t 0 p t A t p 0 Q 0   Notice that the expected profit increases in the expected appreciation E h p t>0 p 0 i . Also, from pre- vious results, we can notice d (E[ p t/p 0 ]) dR 1 > 0 f or t= 1,2 Intuitively, the reserve accumulation has effects of increasing net foreign assets in the future, which raise the price of the nontradable goods prices in the future, but lowers the price in the present. Therefore, the direct investment in nontradable goods sector increases in the reserve accumulation. This is the mechanism examined in handful papers that studied the relationship between foreign direct investment and reserve accumulation. Matsumoto (2019) argued that EMEs ac- cumulate reserves to attract more direct investments. In contrast, we provide the causality in the opposite direction: direct investments cause reserve accumulations. However, we also have a similar mechanism with Matsumoto (2018). Reserve accumulation causes the currency de- preciation, while promising appreciations in the future, and therefore it is more profitable to invest in the EME. But, we do not believe that EMEs accumulate reserves to attract direct in- vestments as we discussed in the literature review section 62 . More plausible scenario is that EMEs facing lots of direct investment capital inflows make corresponding outflows in the form of reserve and the reserve accumulation again attracts more direct investments, which calls for even more reserve accumulation. 62 Another difficulty in the explanation that reserve is accumulated to attract direct investments through cur- rency depreciation is a possibility that EME policy authorities may depreciate their currency in the future to dilute “real liabilities” measured in foreign currencies. If currency valuations are truly important in making direct invest- ment decisions, such a time-inconsistent incentive to depreciate currency in the future must significantly impugn the direct investors’ interest so as to make the reserve accumulation less useful policy to attract direct investments. Such an ex-ante desire to depreciate currency is widely studied in the local currency sovereign debt literature; see Du et al. (2016), Engel and Park (2018), and Perez and Ottonello (2019). These papers concluded that desires to dilute local currency significantly limit the gain from local currency sovereign debts. 133 We close this section summarizing our findings in the claim below. Claim. Once we endogenize direct investment and the capital price, and allow nontradable goods sector capital investment as above, we have following properties. 1) Reserve accumulation makes it more profitable for foreign direct investors to purchase domestic capitals since it discounts the current capital price through lower domestic interest rates or lower real exchange rates. 2) Therefore, reserve accumulation may attract more direct investments, which in turn in- centives EMEs to accumulate even more reserves. As a result, we have a sort of loop mechanism, by which magnifies both of direct investment inflows and reserve outflows. 3.5 Concluding Remarks In this paper, we provide a novel theory of reserve accumulation of EME. Our view of the reserves accumulation of EMEs is that it is the capital outflows by public sectors to supple- ment insufficient capital outflows by private sectors. When an EME receives excessively large amounts of capital inflows in the form of direct investment or equity portfolio investment, the EME needs to invest abroad to maintain the macroeconomic balance. If private sectors in the EME have a problem making overseas investments enough due to some reasons such as re- liance on foreign financial intermediations for the overseas investment, policy authorities in the EME need to invest abroad instead of the inefficient private sectors. Therefore, policy au- thorities accumulate reserves to pump out excessive foreign currency liquidity from the certain types of capital inflows. Our theory is motivated by empirical regularities we found. We found that reserve accumu- lation of EMEs is positively and strongly correlated with 1) capital inflows in the types of direct investment and equity portfolio investment, 2) current account surpluses and 3) capital out- flows by private sectors. Furthermore, the extra capital inflows we defined as the summation of current account surplus and net direct investment and equity portfolio investment inflows 134 show highly positive correlations with reserve accumulation. To describe the empirical facts we found, both reserve outflows and private sector capital outflows increase when EMEs receive more direct investment or equity portfolio investment capital inflows, or have higher current account surpluses. Motivated by the facts, we construct a tractable three period model. Our model is built on the framework of Fisherian deflation model developed in the capital control literature. Into the framework, we incorporated imperfect capital mobility for both debt capital inflows and debt capital outflows, and direct investment capital inflows. The imperfect capital mobility allows us to overcome the Ricardian equivalence critique on reserve accumulation. However, reserve accumulation turns out to be an inefficient policy tool in environments where private agents borrow abroad; the Ricardian equivalence is broken due to higher borrowing rates and there- fore it is very costly. However, when EMEs receive large amounts of direct investment inflows so that the decision of the private agents alters from borrowing abroad to saving abroad, the efficiency of reserve accumulation is dramatically raised. Because more overseas investments by the private sectors create more negative externality from it, less investment by the private agents responding to reserve accumulation is beneficial to the economy. Moreover, the reserve accumulation is not substitutable by capital controls - subsidies or taxes on overseas invest- ment when saving abroad - once the intertemporal maximization of the private agents is to save, whereas it is it perfectly substitutable if the decision is to borrow 63 . This result is driven in our simple model, but our key insights survive or even become stronger although we generalize our environments in several different ways. Our model also provides important implications about ongoing debates of the currency ma- nipulation. In our model, when EMEs receive direct investment capital flows beyond a certain level, the EMEs passively accumulate reserves by the amounts of the direct investment flows above the level. In terms of the currency valuation, the intervention to accumulate reserves works in a way of preventing the currencies from appreciating although it is not an object it- 63 Again, we note that this result is assuming the capital control is perfectly efficient, which is not in the reality. Hence, the capital control should not be a perfect substitute for reserve accumulation in the reality. 135 self. Such patterns correspond to the empirical findings in Levy-Yeyati et al. (2013); EMEs in- tervene in the foreign exchange market to prevent currency appreciation, not to depreciate the currency. The intervention to discourage the currency appreciation is much different from de- scriptions in a common criticism on the reserve accumulation that EMEs accumulate reserves to depreciate their currencies to boost their exports. Moreover, our model predicts that EMEs receiving excessively large amounts of capital inflows can accumulate seemingly excessive re- serves. Therefore, our model implies that the amount of reserve holding is not a good litmus for the test of currency manipulation. In this paper, we used a tractable three period model and abstracted from important fea- tures in the reality to clarify our novel key insights. One obvious way of developing the idea in this paper is to construct a medium scale DSGE model embedded with our key ideas. In richer environments with production technology or more sophisticated modeling of direct in- vestment, we can try to quantify the optimal reserve accumulation and compare the outcomes from the DSGE model to the actual levels of reserve holding in EMEs. Another direction in which we can develop the ideas in this paper is to search more for private overseas investment in EMEs. To the best of our knowledge, our paper is the first in modeling frictions on overseas investment in EMEs and we adopted a way of giving us a nice and tractable result. Although studies of external assets of EMEs are very scant in the literature, external assets of EMEs except for international reserves are not negligible any more and we need to understand it more prop- erly. Deeper understanding of EMEs’ overseas investment will certainly give important impli- cations about reserve accumulation and of course, it can be important for the understanding of international monetary system as well 64 . Lastly, it will be also interesting to extend our model to incorporate the mercantilist view. In our model, large capital inflows in the form of direct investment or equity portfolio investment generate domestic booms in consumptions, but no changes in production since the model economy is de-facto an endowment economy. However, in a richer environment with different sectors with production technologies, domestic currency 64 Recently, Horn et al. 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Manuscript, Columbia University. 146 Appendix A Appendix to Chapter 1 A.1 Misallocation over time (No trimmed case) In Chapter 1, I trim the 1% tails of plant TFPQ and TFPR in each year to make the results robust to outliers. As Rotemberg and White (2021), this trimming may be critical to determine the degree of misallocation. Figure A.1 shows the results of two cases (no trim and the benchmark) on TFPR and MRPK. Although there are some differences between the two cases, the overall trends are similar. A.2 Misallocation over time with percentile ratios As an alternative measure, Figure A.2 shows the percentile ratios of TFPR and MRPK. This figure veri- fies the findings in Chapter 1. In fact, the increased dispersion was related to the tails of the distributions. A.3 Misallocation by firm size (alternative measure) In Chapter 1 (Section 4), using firm value-added as firm size, I find that 1) the within-group compo- nent dominated the total variations, and 2) the small firm group showed a rapid increase. These results may be sensitive to different measures of firm size. Thus, as a robustness check, I repeat the same exer- cise with an alternative measure of firm size, sales. As Figures A.3 and A.4 show, the results in Chapter 1 are consistent if sales are used as firm size. 147 Figure A.1: Dispersion over time Note: Dispersion is the standard deviation of productivity measures. Solid (dashed-) lines are the results of the benchmark (no-trim) case. Figure A.2: Percentile ratios Note: This figure shows the 90:10 percentile ratio and the 75:25 ratio of log(TFPR) and log(MRPK). Solid (dashed-) lines are the 90:10 (75:25) percentile ratio. 148 Figure A.3: Decomposition of overall variance Note: This figure shows the variance of TFPR, var(log( T F RP si /T F PR s )), and its within-group and between-group components. Plants are divided into five groups according to their sales in each industry and year. Figure A.4: Within-group variations by quintiles Note: This figure shows each quintile’s TFPR variance. Plants are divided into five groups (quintiles) according to their sales in each industry and year. Bot- tom (top) quintile is the small (large) plant group. 149 A.4 What happened to small firms In Chapter 1 (Section 4), I compare the efficient plant sizes to the actual sizes to understand in which direction the misallocation worsened within small firm group. Here, I explore the same question with different measures: relative mean of TFPR and overproduction. Both exercises confirm the findings in Chapter 1 that small firms were unable to use inputs as much as they wanted. Table A.1 shows the relative mean of log(TFPR) by firm size quintile. The mean of the bottom group (small firms) increased gradually, implying that more small firms faced barriers to expanding their capac- ities. Following Kim et al. (2017), I compute the "overproduction" ratio (Table A.2) by firm size quintile. This ratio is the proportion of plants whose TFPR is lower than their industry mean. This table also shows that the share decreased continuously among small firms (bottom quintile). Table A.1: Relative mean Size Quintile Bottom Second Third Fourth Top 1992 - 1999 0.92 0.93 1.04 1.04 1.05 2000 - 2009 0.97 1.02 1.00 1.02 0.99 2011 - 2019 1.02 1.02 0.98 1.01 0.98 Notes: Plants are divided into five groups according to their value-added in each industry and year. Table A.2: Overproduction (%) Size Quintile Bottom Second Third Fourth Top 1992 - 1999 61.5 54.7 50.9 48.4 45.5 2000 - 2009 60.1 55.8 53.6 52.0 48.4 2011 - 2019 56.3 56.0 56.2 55.3 51.9 Notes: Plants are divided into five groups according to their value-added in each industry and year. 150 A.5 Mismeasurement (No trimmed case) Table A.3 reports the results of the regression in Chapter 1 (Section 5) when the observations are not trimmed. Compared to the finding in Section 5, the amount of mismeasurement increases slightly. As Column (1) shows, 61.0% of the variation in TFPR is due to the true distortions while it is 74.8% with trimming data. Although there is a slight difference, the main finding remains the same. Moreover, when I repeat the same exercise with sub-periods, the estimated λ rose (mismeasurement fell) in the latter period when the misallocation increased. Table A.3: Estimate Measurement Error (No trimming) Dep. Variable: Value-added Growth (1) (2) (3) (4) (5) (6) 1992-2019 1992-2003 2004-2019 1992-2019 1992-2003 2004-2019 Average TFPR -0.0255*** -0.0395** -0.0361*** -0.00911 0.0378 -0.0461+ (-3.77) (-1.98) (-6.93) (-0.42) (0.82) (-1.62) Input Growth 0.132** 0.568*** 0.0316* 0.614*** 0.782*** 0.133+ (2.04) (5.43) (1.65) (4.58) (5.10) (1.55) Average TFPR -0.0513* -0.277*** -0.00652 -0.240*** -0.337*** -0.0420 × Input Growth (-1.71) (-4.34) (-0.74) (-4.11) (-3.21) (-1.21) ˆ λ 0.610 0.512 0.793 0.608 0.569 0.683 Plant fixed effects Yes Yes Yes Yes Yes Yes Year fixed effects Yes Yes Yes Yes Yes Yes Observations 972,758 352,006 620,752 972,758 352,006 620,752 Adj. R-sq 0.0589 0.253 0.0220 0.367 0.530 0.0430 Notes: Average TFPR is the average TFPR in logs for the current and previous years. In Columns (4)- (6), the plant’s value-added is used as a weight. Reported in brackets are the corresponding t statistics. Standard errors are clustered at the plant level. +, *, ** and *** indicate statistical significance at the 15%, 10%, 5%, and 1% levels, respectively. 151 Appendix B Appendix to Chapter 3 B.1 List of Countries and Omitted Figures and Tables B.1.1 List of Countries used in Regressions Argentina, Bolivia, Brazil, Bulgaria, Chile, Colombia, Croatia, Czech Republic, Guatemala, India, In- donesia, Kazakhstan, Korea, Malaysia, Mexico, Mongolia, Pakistan, Paraguay, Peru, Philippines, Poland, Romania, Russia, South Africa, Thailand, Turkey, Uruguay, Vietnam (28 EMEs) B.1.2 Omitted Figures Figure B.1 plots the change in the reserve outflows-to-GDP and extra capital inflows-to-GDP for all the sample countries during the period 1998-2017. As discussed, for most sample countries, the two series show strong co-movement. Figure B.2 plots per capital GDP and the ratio of reserve asset to total external assets during the period 2013-2017. This Figure shows a negative association between the two variables. That is, the country with higher GDP per capita tends to have less international reserves of the total external assets. The relation might be explained by the following reasons. First, developed countries generally have more efficient financial systems, which suggests their institutional quality is superior enough to generate private capital outflows. Second, in the course of growth, an EME can reduce the reliance on public capital outflows. Korea is a good example in this regard. In 2003, the ratio of reserves to the total external assets in Korea 152 was 60.1%. But, it has decreased to about 40% recently. On the flip side, it means the portion of private external assets has increased as we discussed in Chapter 3. This divergence between the private and public outflows may be caused by structural changes in private sector’s overseas investment such as improved access to foreign financial assets due to technological advances. Figure B.1: Reserve Outflows and Extra Capital Inflows Note: All values are scaled by GDP . Source : IMF BOP/IIP B.1.3 Omitted Tables Here, we list the regression results discussed in Chapter 3. A difficulty in our regression analysis is that our sample periods include both of the periods of reserve accumulation and the periods of reserve depletion. We want to exclude the periods of sudden stops such as the crises in Latin America in 2002 or other periods alike because we want to see how reserve “accumulation” is associated with different types of capital inflows; during a sudden stop, we should see reserve depletion with falling debt capital inflows 153 Figure B.2: External Asset Structure and GDP per capita Note: Y axis (RS_TOT) is defined as the ratio of reserve assets to the total external assets. X axis (GDP per capita) is dollar value. All values are averaged over 2013-2017. Source : IMF BOP/IIP and relatively stable FDI inflows, which might cause positive correlations of reserve outflows with debt inflows, but negative correlations with FDI inflows. To handle the issue, we opt to run regressions in the sample period of 2003-07. This is to avoid the periods of the crises in the sample period 12 . The results of the regressions are provided in Table A.1 be- low, with the results of the whole sample periods, 1998-2017. As we expected, almost all the coefficients of capital inflows are positive and significant regardless of our choice of sample periods. First, the co- efficients of the equity portfolio are larger than the others and moreover the largenesses are statistically significant. Second, once we trim down the sample period to 2003-07, the coefficients of direct invest- ment inflows become larger while the coefficients of debt inflows become smaller or insignificant. 1 The currency crises in Malaysia and Indonesia in 1999, the sovereign debt crisis in Argentina in 2002 that propagated to other Latin America countries, and obviously the Global Financial Crisis in 2008 along with its sub- sequent turbulent periods such as tapering tantrum in 2013. 2 Furthermore, 2003-07 was the time under the mood of the great moderation except for the subprime mort- gage default in 2007, which was yet to propagate to emerging markets. 154 Table B.1: Correlations with reserve flows (a) The whole sample period (1998-2017) Reserve outflows-to-GDP VARIABLES (1) (2) (3) FDI inflows 0.27*** (0.090) EQ inflows 0.82*** (0.186) DT inflows 0.31*** (0.083) Current account 0.26*** 0.16** 0.25*** (0.047) (0.060) (0.055) Constant 0.01* 0.01*** 0.01*** (0.003) (0.001) (0.001) Observations 140 140 140 R-squared 0.204 0.192 0.264 Number of Country 28 28 28 (b) The sample period of 2003-2007 Reserve outflows-to-GDP VARIABLES (1) (2) (3) FDI inflows 0.60*** (0.061) EQ inflows 1.33*** (0.111) DT inflows 0.25*** (0.036) Current account 0.42*** 0.31*** 0.31*** (0.032) (0.030) (0.046) Constant 0.02*** 0.04*** 0.04*** (0.003) (0.001) (0.001) Observations 140 140 140 R-squared 0.247 0.306 0.209 Number of Country 28 28 28 Driscoll and Kraay (1998) standard errors *** p<0.01, ** p<0.05, * p<0.1 Note: Panel Regressions with country and year fixed effects. All dependent variables are scaled by GDP . Source: IMF BOP/IIP 155 B.2 Omitted Algebras and Proofs B.2.1 Proof of Lemma 1 First, we show the the object function of the social planner is concave in b 1 . Define V ≡ u ¡ c T 0 , y N 0 ¢ +E 0 £ βu ¡ c T 1 , y N 1 ¢ +β 2 u ¡ c T 2 , y N 2 ¢¤ . Then taking the derivative of V with repect to b 1 gives us dV db 1 = −u T 0 +β ˆ φ φ · ¡ 1+ r ∗ −2Γ j b 1 ¢ µ 1− db 2 d w 1 ¶¸ u T 1 dF φ +β 2 ˆ φ φ · ¡ 1+ r ∗ −2Γ j b 1 ¢ db 2 d w 1 ¡ 1+ r ∗ −2Γ b b 2 ¢ ¸ u T 2 dF φ (B.1) where w 1 = b 1 (1+ r 1 ) because we have no reserve accumulation yet. Since the social planner can choose b 2 forφ∈ ³ φ,φ c ´ whereφ c is the cut-off for the social planner, the equation (B.1) changes to dV db 1 = −u T 0 +β ˆ φ φ ¡ 1+ r ∗ −2Γ j b 1 ¢ u T 1 dF φ + (B.2) β 2 ˆ φ c φ ¡ 1+ r ∗ −2Γ j b 1 ¢ db 2 d w 1 £ −u T 1 + ¡ 1+ r ∗ −2Γ b b 2 ¢ u T 2 ¤ dF φ It is easy to seeβ ´ φ φ ¡ 1+ r ∗ −2Γ j b 1 ¢ u T 1 dF φ is decreasing in b 1 since the return to the saving is derceasing (increasing borrowing rates in the borrowing). Hence, the first and second terms in the equation (B.2) decreases in b 1 . In the third term, from (9) we can check db 2 d w 1 < 0 and| db 2 d w 1 | is decreasing in b 1 . φ c obviously decreases in b 1 . Since b 2 | φ<φ c decreases in b 1 , we can immediately see u T 1 −(1+ r ∗ −2Γ b b 2 )u T 2 decreases in b 1 for allφ∈ ³ φ,φ c ´ . Therefore, all the terms are decreasing in b 1 . It implies d 2 V db 2 1 < 0. Now we show the claims in the lemma. First, we show b h 1 < b sp 1 if b h 1 < 0. To show b pr i v 1 < b sp 1 , we first derive the first order condition of b 1 for the social planner. b sp 1 is char- 156 acterized as below −u T 0 +β ˆ φ φ · ¡ 1+ r ∗ −2Γ b b 1 ¢ µ 1− db 2 d w 1 ¶¸ u T 1 dF φ β 2 ˆ φ φ · ¡ 1+ r ∗ −2Γ b b 2 ¢ db 2 d w 1 ¡ 1+ r ∗ −2Γ b b 1 ¢ ¸ u T 2 dF φ =0 (B.3) where w 1 = b 1 (1+ r 1 )+ R 1 . This can be represented by −u T 0 +β ˆ φ φ (1+ r 1 )u T 1 −Γ b b 1 u T 1 dF φ − ¡ 1+ r ∗ −2Γ b b 1 ¢ β ˆ φ φ db 2 d w 1 ¡ u T 1 −β(1+ r 2 −Γ b b 2 )u T 2 ¢ dF φ = 0 (B.4) Suppose b 1 = b pr i v 1 and b 2 = b pr i v 2 . Then we have u T 0 =β ´ φ φ (1+ r 1 )u T 1 dF φ and also u T 1 =β(1+ r 2 )u T 2 i f φ>φ c . This gives us −β ˆ φ φ Γ b b 1 u T 1 +β 2 ¡ 1+ r ∗ −2Γ b b 1 ¢ ˆ φ φ db 2 d w 1 Γ b b 2 u T 2 dF φ −β ¡ 1+ r ∗ −2Γ b b 1 ¢ ˆ φ c φ db 2 d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ > 0 (B.5) Ifφ∈ [φ,φ c ), then u T 1 −β(1+ r 2 )u T 2 > 0. Absolutely the remaining terms are all positive. It implies that b h 1 0, then there always exists γ 0 ∈ (0,∞] such that forΓ s ∈ ¡ 0,γ 0 ¢ b h t b sp t . Since b h 1 > 0,we replaceΓ b withΓ s in front of b 1 in equation (B.2). This gives us dV db 1 = −β ˆ φ φ Γ s b 1 u T 1 +β 2 ¡ 1+ r ∗ −2Γ s b 1 ¢ ˆ φ φ db 2 d w 1 Γ b b 2 u T 2 dF φ −β ¡ 1+ r ∗ −2Γ s b 1 ¢ ˆ φ c φ db 2 d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ (B.6) First, notices dV db 1 is continuous inΓ s as long as b 1 > 0. All the variables are continuous and the mappings 157 in dV db 1 are continuous as well. Then we show lim Γ s↓0 dV db 1 > 0 and lim Γ s↑∞ dV db 1 > 0 These properties come from lim Γ s↓0 Γ s b 1 = lim Γ s↑∞ Γ s b 1 = 0. lim Γ s↓0 Γ s b 1 = 0 is obvious. lim Γ s↑∞ Γ s b 1 = 0 can be easily shown by a contradiction. If lim Γ s↑∞ Γ s b 1 ̸= 0, then the gross return must be zero. Then the households can be better off by letting b 1 = 0. IfΓ s b 1 = 0, then the equation (B.6) will be dV db 1 = β 2 ¡ 1+ r ∗ ¢ ˆ φ φ db 2 d w 1 Γ b b 2 u T 2 dF φ −β ¡ 1+ r ∗ ¢ ˆ φ c φ db 2 d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ > 0 (B.7) It proves there always existsγ 0 ∈ (0,∞] such that forΓ s ∈ ¡ 0,γ 0 ¢ b h t b sp t . To show it, it is enough to show we may have dV db 1 < 0 for someΓ s by again the continuity of dV db 1 inΓ s . In equation (B.6), we can manipulate the distribution ofφ and relative values of y T 1 and y T s so thatφ c →φ and−b 2 is small enougn to haveβ ´ φ φ Γ s b 1 u T 1 >β 2 (1+ r ∗ −2Γ s b 1 ) ´ φ φ db 2 d w 1 Γ b b 2 u T 2 dF φ . This holds as long asΓ s b 1 > 0, and we showed dV db 1 < 0 for someΓ s . This completes the proof. B.2.2 Proof of Proposition 1 In the same way we did in the proof of lemma 1, we let b 1 and b 2 as functions of R 1 . Taking a derivative with respect to R 1 gives us dV db 1 = £ −u T 0 +β ¡ 1+ r ¢ E £ u T 1 ¤¤ + db 1 dR 1 Ã u T 0 − ¡ 1+ r ∗ −2Γ j b 1 ¢ β ˆ φ φ u T 1 dF φ ! +β µ db 1 dR 1 ¡ 1+ r ∗ −2Γ j b 1 ¢ + ¡ 1+ r ¢ ¶ˆ φ φ · db 2 d w 1 ¡ u T 1 −β ¡ 1+ r ∗ −2Γ b b 2 ¢ u T 2 ¢ ¸ dF φ + dφ c dR 1 £¡ βu ¡ c T 1 ¡ b 2 ¡ φ c+ ¢¢¢ +β 2 u ¡ c T 2 ¡ b 2 ¡ φ c+ ¢¢¢¢ − ¡ βu ¡ c T 1 ¡ b 2 ¡ φ c− ¢¢¢ +β 2 u ¡ c T 2 ¡ b 2 ¡ φ c− ¢¢¢¢¤ We knowβu ¡ c T 1 ¡ b 2 ¡ φ c+ ¢¢¢ +β 2 u ¡ c T 2 ¡ b 2 ¡ φ c+ ¢¢¢ =βu ¡ c T 1 ¡ b 2 ¡ φ c− ¢¢¢ +β 2 u ¡ c T 2 ¡ b 2 ¡ φ c− ¢¢¢ . Also we know u T 0 −β(1+ r 1 )E £ u T 1 ¤ = 0 and u T 1 −β(1+ r 2 )E £ u T 2 ¤ = 0 forφ∈ ³ φ c ,φ ´ . Taking all of these and letting d w 1 dR 1 = db 1 dR 1 ¡ 1+ r ∗ −2Γ j b 1 ¢ + ¡ 1+ r ¢ gives the equation (15), (16). 158 B.2.3 Derivation of the Optimal Tax First, we show the borrowing of decentralized households under the optimal taxation is same as the direct choice of the social planner. The Euler equation of the households under the taxation will be u T 0 (b 1 ,;)=β(1+ r 1 )(1+τ d ) Ã ˆ φ c φ u T 1 ¡ b 1 ,b 2,c ,; ¢ dF φ + ˆ φ φ c u T 1 ¡ b 1 ,b 2,u ,; ¢ dF φ ! (B.8) The solution of the planning isτ d such that the equation (B.8) is ex-post identical to the equation (B.6), which characterizes the borrowing determined by the government. Of course, it implies b pr i v 1 (τ d )= b sp 1 . Ignoring the term r 1 τ d , solving forτ d such that the equation (B.8) is same as the equation (B.6) yields the characterization of the optimal taxation in the equation (B.8). 0 B.2.4 Proof of Proposition 2 The first statement in the proposition follows from the definition of the optimal tax. To prove the second and third statements, rewrting the first order conditions in the equations (18),(19) are as below − u T 0 +βu T 1 ¡ 1+ r ∗ − 2Γ s b sp 1 ¢ +β ˆ φ c φ ¡ −u T 1 +βu T 2 (1+ r 2 ) ¢ db 2 d w 1 ¡ 1+ r ∗ − 2Γ s b sp 1 ¢ = 0 (B.9) − u T 0 +βu T 1 ¡ 1+ r ¢ +β ˆ φ c φ ¡ −u T 1 +βu T 2 (1+ r 2 ) ¢ db 2 d w 1 ¡ 1+ r ¢ +η= 0 (B.10) whereη is the multiplier of the non-zero constraint of reserve accumulation. If b sp 1 < 0, then 1+r ∗ −2Γ s b sp 1 > 1+r . It impliesη> 0. Hence, if If b sp t+1 < 0 and b sp 1 = b t+1 then R ∗ = 0 If b sp 1 > 0, then we may have 1+ r ∗ − 2Γ s b sp 1 = 1+ r . It implies b sp 1 = r ∗ − r 2Γ s Then the optimal reserve accumulation is R 1 = w 1 − r ∗ − r 2Γ s 159 where w 1 is the optimal net foreign liquid assets chosen by the social planner. The social planner problem of choosing b 1 and R 1 can be understood the two steps where the plan- ner firstly chooses w 1 and then choose how to compose w 1 with b 1 and R 1 . As one might expect, for b 1 < r ∗ −r 2Γ s b 1 is always more efficient. For b 1 > r ∗ −r 2Γ s vice versa. B.2.5 Proof of Corollary 1 We formulate the problem to the problem the social planner determine the optimal w 1 and then compare b 1 and R 1 . For the planner who only use the optimal taxation b sp 1 ¡ 1+ r ∗ −Γ j b sp 1 ¢ = w 1 (B.11) For the planner who only use the reserve accumulation b h 1 ³ 1+ r ∗ −Γ j b h 1 ´ + R 1 = w 1 (B.12) where j= b, s. Assume that w 1 < 0. Then obviously b 1 < 0 in the both of equations (B.11) and (B.12), and b h 1 r , it is always better to reduce R 1 and raise (reduce) b h 1 ¡ −b h 1 ¢ . It implies V (τ)> V (R) if b sp 1 < 0. Next now assume w 1 > 0. Let’s compute the return to the two different policies. For the optimal taxation policy in equation (B.11) r 1 = 1+ r ∗ −Γ s b sp 1 Similarly, we can compute the return to the EME in equation (17). Denote the return byb r 1 b r 1 = R 1 / ¡ 1+ r ¢ R 1 / ¡ 1+ r ¢ + b h 1 r+ b h 1 R 1 / ¡ 1+ r ¢ + b h 1 , ³ r ∗ −Γ s b h 1 ´ For the same w 1 , b h 1 r 1 . This completes the proof. 160 B.2.6 Proof of Proposition 3 To prove the second statement we make a reasonable assumption Assumption A1 . Let the LHS of equation (23) be h L (b 1 (θ,R (θ)),θ,R (θ)) and the the RHS be h R (b 1 (θ,R (θ)),θ,R (θ)). Then we assume 1. | dh L dθ | R =| ∂h L ∂θ + ∂h L ∂b 1 ∂b 1 ∂θ |>| dh R dθ | R =| ∂h R ∂θ + ∂h R ∂b 1 ∂b 1 ∂θ | 2. ∂h L ∂b 1 ∂b 1 ∂R 1 + ∂h L ∂R 1 > 0 To see why the assumption A1 can easily hold, first see dh L dθ , dh R dθ < 0. Then b 1 chages the LHS directly, but affetct RHS through b 2 ,which makes the RHS less responsive to b 1 . The second inequality easily holds for most of the parameter values including some exterme values. Now we prove the statements in the proposition. To show the first statement, recall that we have dh L dθ , dh R dθ < 0. Withθ= ˜ θ, h L (b 1 ,θ)= 0, while h R > 0 since b 2 < 0 for allφ. It implies that atθ= ˜ θ R ∗ 1 > 0. Since ∂b 1 ∂θ > 0, R ∗ 1 > 0 for allθ> ˜ θ. Then we need to show there existsδ> 0 such that R ∗ 1 > 0θ∈ ¡ ˜ θ−δ, ˜ θ ¢ . See both h L and h R are continuous inθ and R 1 . For δ small enough, h L ¡ b 1 ¡ ˜ θ−δ,0 ¢ , ˜ θ−δ,0 ¢ is positive, but smaller than h R by the continuity of h L and h R . It implies R ∗ 1 > 0θ∈ ¡ ˜ θ−δ, ˜ θ ¢ . Second statement can easily follow from the assumption. Envoking the envelope condition yields ∂h L ∂θ + ∂h L ∂b 1 µ ∂b 1 dθ + ∂b 1 dR dR 1 dθ ¶ + ∂h L ∂R 1 dR 1 dθ = ∂h R ∂θ + ∂h R ∂b 1 µ ∂b 1 dθ + ∂b 1 ∂R dR 1 dθ ¶ + ∂h R ∂R 1 dR 1 dθ Then we must have dR 1 dθ > 0 under the assumption A1. Lastly, we prove the third and forth statements in the proposition. The resource constraints in trad- able goods are c T 0 (θ,R 1 )+ b 1 (θ,R 1 )+ R 1 = (1−θ) y T 0 +Q 0 θK c T 0 ¡ ˜ θ,0 ¢ + b 1 ¡ ˜ θ,0 ¢ = ¡ 1− ˜ θ ¢ y T 0 +Q 0 ˜ θK Since (1−θ) y T 0 +Q 0 θK= y T 0 + (Q 0 − A 0 )θK , we have R= (Q 0 − A 0 ) ¡ θ− ˜ θ ¢ K+ c T 0 ¡ ˜ θ,0 ¢ − c T 0 (θ,R 1 )+ b 1 ¡ ˜ θ,0 ¢ − b 1 (θ,R 1 ) 161 We know, by definition, r ∗ −r−Γ s b 1 (θ,R 1 ) ³ 1− db 1 (θ,R 1 ) dR 1 ´ > 0 and r ∗ −r−Γ s b 1 ¡ ˜ θ,0 ¢ ³ 1− db 1 ¡ ˜ θ,0 ¢ dR 1 ´ = 0. It implies b 1 ¡ ˜ θ,0 ¢ > b 1 (θ,R 1 ) To show the last statement, notice that ∂c T 0 ∂θ > 0, ∂c T 0 ∂R 1 < 0 and c T 0 ¡ ˜ θ,R ∗ 1 ¡ ˜ θ ¢¢ < c T 0 (θ,0). Thus we have c T 0 ¡ ˜ θ,R ∗ 1 ¡ ˜ θ ¢¢ < c T 0 ¡ ˜ θ,0 ¢ . If ∂c T 0 ∂θ + ∂c T 0 ∂R 1 dR 1 dθ < 0, then it is obvious. Even if ∂c T 0 ∂θ + ∂c T 0 ∂R 1 dR 1 dθ > 0, there always exists δ> 0 such that c T 0 ¡ ˜ θ+δ,R ∗ 1 ¡ ˜ θ+δ ¢¢ < c T 0 (θ,0). This completes the proof. B.2.7 Proof of Proposition 5 Recall the equation (38) βΓ b b ′ E £ u ′ T ¤ db ′ dR ′ + £ u T −β ¡ 1+ r ¢ E £ u ′ T ¤¤ + £ u T −β ¡ 1+ r ′ ¢ E £ u ′ T ¤¤ db ′ dR ′ = d w ′ dR ′ · Pr ¡ φ ′ ≤φ ′c ¢ βE φ ′ ≤φ ′c · ∂b ′′ c ∂w ′ µ −u ′ T +β ∂V ′′ ∂b ′′ c ¶¸ + Pr ¡ φ ′ >φ ′c ¢ βE φ ′ >φ ′c · ∂b ′′ u ∂w ′ µ −u ′ T +β ∂V ′′ ∂b ′′ u ¶¸¸ Let Pr ¡ φ ′ ≤φ ′c ¢ βE φ ′ ≤φ ′c h ∂b ′′ c ∂w ′ ³ −u ′ T +β ∂V ′′ ∂b ′′ c ´i ≡Θ c and Pr ¡ φ ′ >φ ′c ¢ βE φ ′ >φ ′c h ∂b ′′ u ∂w ′ ³ −u ′ T +β ∂V ′′ ∂b ′′ u ´i ≡Θ u . It is easy to see both ofΘ c andΘ u decreases in w 1 . To show the first statement, notice that for a lower φ,| db ′ dR ′ | becomes larger and hence smaller d w ′ dR ′ . Also u T −β ¡ 1+ r ¢ E £ u ′ T ¤ and u T −β ¡ 1+ r ′ ¢ E £ u ′ T ¤ become larger as well. WhetherΓ b b ′ E £ u ′ T ¤ db ′ dR ′ increases by the assumption. Given w 1 ,Θ c andΘ u are invariant, and w 1 increases for smallerφ, which makes the falls inΘ c andΘ u . Therefore, for smaller φ<φ c , the marginal costs are higher, but the marginal benefits are lower. Hence, the optimal plan is to accumulate less reserves (deplete more reserves). That is, ∂R ′ ∂φ | φ<φ c> 0. Next, we prove the second statement. Suppose that there happens a left shitf of the pdf ofφ ′ such that ˜ Pr ¡ φ ′ < a ¢ < Pr ¡ φ ′ < a ¢ for all a∈ (0,1) where ˜ Pr ob is the cdf of the new distribution. Then ob- viously, the RHS increases in the new distribution. In the LHS, onlyE £ u ′ T ¤ rises due to expected tighter credit constraint. Since we assumeβ ¡ 1+ r ¢ >−β ¡ 1+ r ∗ − 2Γ b b ′ ¢ db ′ dR ′ , the LHS falls. To restore the balance between the LHS and RHS, we need higher R 1 . This is as desired. 162 B.2.8 Proof of Lemma 3 Suppose the credit constraint does not bind in the stateω t . Then b h t+1 (ω t ) is determined by the euler equation u T t ¡ b h t+1 ¢ =β(1+ r t+1 )E £ u T t+1 ¡ b h t+1 ,T ∗ t+1 ¢¤ . More formally, b h t+1 is a functinonal of the fuction T ∗ t+1 (ω t+1 ). We know, in general V (t) b t+1 ̸= 0, and of coure it is not in the optimality conditions of the social planner. B.3 Other Mircofoundations of Frictions on Capital Outflows We introduce results with different microfoundations of frictions on private capital outflows. We consider the case where overseas investments are intermediated by domestic financial experts, and the case the intermediation is done by the domestic financial experts but the experts conceal parts of their income from the intermediation fees. Now we assume that there is a continuum of domestic financial experts and they face heterogeneous participation costs, same as the IFIs in Chapter 3. For the households who are not financial experts, the decision is same as the model in Chapter 3. The difference is now the rents 1 2 Γ s b 2 1 back to the households since the financial experts belong to the family of households. Without going through all the necessary steps, we introduce the condition for the optimal reserve accumulation. £ u T 0 −β ¡ 1+ r ¢ E £ u T 1 ¤¤ | {z } Consumpti on W ed g e at r = d w 1 dR ∗ 1 β       ˆ φ c φ d (−b 2 ) d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ | {z } M ar g i nal V alue o f Bor r owi ng −βΓ b E · u T 2 b 2 db 2 d w 1 ¸ | {z } Lower r 2       (B.13) The main difference is the term −βΓ s E £ u T 1 ¤ b 1 db 1 dR ∗ 1 vanishes since the rents from the intermediation belong to the households. Also notice that the saving b h 1 by the decentralized households is always short of the optimum for the planner because the households do not take account of the negative externalities 163 from the insufficient wealth in the next period; the terms in the RHS in the equation (B.13), but the term of negative externality of additional saving βΓ s E £ u T 1 ¤ b 1 disappers; the decreasing return to the saving is mere a result from increasing marginal costs. Therefore, in the new environment where the intermediation is done by domestic financial experts who face increasing cost of the intermediation, the amount of reserve accumulation, assuming all the states are equal, is strictly smaller than when the intermediation is done by foreign parties. Additionally let’s assume that the financial experts conceal parts of the incomes of the rents; i.e., they conceal parts of the profits of the intermediation 1 2 Γ s b 2 1 ; denote it asπ. For the simplicity, we consider the case all the rents 1 2 Γ s b 2 1 are concealed and the experts invest the concealed incomes in the assets that bear no interest. The experts conceal the rents in the period 1 and consume the rents in the period 2 regardless of the states in the period 1. Then the concealment results in “inefficient resource allocations across time”; it reduces the tradable goods resources in the period 1 by 1 2 Γ s b 2 1 while it raises the resources in the period 2 by the same amount; it is inefficient because the economy in the period 1 needs to bor- row against the outputs in the period 2. Again, we just introduce the optimality condition of reserve accumulation as below. £ u T 0 −β ¡ 1+ r ¢ E £ u T 1 ¤¤ | {z } Consumpti on W ed g e at r =β ˆ φ c φ d w 1 dR ∗ 1 d (−b 2 ) d w 1 ¡ u T 1 −β(1+ r 2 )u T 2 ¢ dF φ | {z } M ar g i nal V alue o f Bor r owi ng −β 2 Γ b E · u T 2 b 2 µ ∂b 2 ∂w 1 d w 1 dR 1 + ∂b 2 ∂π dπ dR 1 ¶¸ | {z } − Lower r 2 βΓ s b 1 db s 1 dR ∗ 1 ¡ E £ u T 1 ¤ −βE £ u T 2 ¤¢ | {z } Loss due to concealment s (B.14) where db 2 dR ∗ 1 = ∂b 2 ∂w 1 d w 1 dR 1 + ∂b 2 ∂π dπ dR 1 . SeeE £ u T 1 ¤ −βE £ u T 2 ¤ > 0 sinceE £ u T 1 ¤ −β(1+ r 2 )E £ u T 2 ¤ ≥ 0. The con- cealment makes two changes to the optimality condition in the baseline model;βΓ b E h u T 2 b 2 ∂b 2 ∂π dπ dR 1 i and βΓ s b 1 db s 1 dR ∗ 1 ¡ E £ u T 1 ¤ −βE £ u T 2 ¤¢ . First, the concealment generates inefficient income streams and it is cap- tured by βΓ b E h u T 2 b 2 ∂b 2 ∂π dπ dR 1 i . The economy needs more resources in the period 1 to lessen the costs of sudden stop and reduce the inefficient borrowing from IFIs, but the concealments worsen the prob- lem; it adds some resouces to the period 2 whereas it reduces equivalent resources in periods 1 and thus the households need to borrow even more. As a result, the reserve accumulation reduces the costs 164 of the concealments by replacing the private overseas investments. Second, since the concealed assets are invested inefficiently, the replacement of private overseas investments by the reserve accumulation is beneficial as it is shown in the term βΓ s b 1 db s 1 dR ∗ 1 ¡ E £ u T 1 ¤ −βE £ u T 2 ¤¢ . Consequently, introducing overseas concealments by domestic financial experts worsen the problems of overseas investments by private sec- tors and accordingly raises the benefits of reserve accumulation, which substitutes for the undesirable investments by households. The optimal reserve accumulation in the equation (B.14) must be higher than the equation (B.13) but it is hard to predict that the reserve accumulation is higher or lower than baseline model in Chapter 3. Our conjecture is that it might be still lower than the the baseline model. However, introducing cases where households conceal their assets for themselves or other costs of the concealments undo the lower reserve accumulation. B.4 Reserve Accumulation of Saving Glut EMEs In this section in the appendix, we remove one assumption that we have kept throughout this paper. Now we assume that our model EME saves even in period 1. We can think of an EME experiencing rapid aging or saving excessively due to some reasons 3 . In the data, some EMEs, in particular East Asian EMEs, have sizably positive net foreign asset positions. We show how our model can explain reserve accumulation in such EMEs. To model EMEs that save in period 1, we assume y T 0 > (1−θ) y T 1 > (1−θ)(1−σ) y T 2 . Hence, we can posit b 1 ,b 2 > 0 and therefore there is no chance of sudden stop in period 1 4 . Interestingly, the plan- ner in the EME might be incentivized to accumulate reserves even when b 2 > 0. The optimal reserve accumulation in period 1 is characterized by r ∗ −r−Γ s b 2 µ 1− db 2 dR 2 ¶ = 0 (B.15) The equation (B.15) does not necessarily hold, but it holds if R 2 > 0. On the contrary, if equation (B.15) does not hold, we have R 2 = 0. As one might expect, db 2 dR 2 is almost invariant to R 2 . Then, conditioning 3 For example, low financial development in certain EMEs lead the EMEs to save excessively. See Caballero et al. (2008), Mendoza et al. (2009) and Maggiori (2017). 4 It might be little extreme and such results stem from our modeling of sudden stop 165 on R 2 > 0, the equation (B.20) almost pins down b 2 . The intuition behind this results is rather straight- forward. The return to private overseas investments (for the planner, not for the households) decrease in the investment amounts and it implies that the return to the investment beyond a certain level is even below the return to the reserve. Hence, the planner chooses reserve accumulation by a mean of national saving. Now we characterize the reserve accumulation in period 0, while accommodating the results in equa- tion (B.15). The optimal reserve accumulation is characterized by the equation (B.16) below. · r ∗ −r−Γ s b 1 (θ) µ 1− µ ∂b 1 (θ) ∂R 1 + ∂b 1 (θ) ∂R 2 dR 2 dR 1 ¶¶¸ E £ u T 1 ¤ = − d w 1 dR ∗ 1 βΓ s E · u T 2 b 2 db 2 d w 1 ¸ (B.16) See the RHS is negative and as we saw in equation (B.15), b 2 is almost fixed once we have R 2 > 0. Once the value of RHS is highly invariant, then we need to have invariant LHS as well: the RHS pins down b 1 in the LHS; let’s denote it as b c 1 . It implies that for EMEs to need external assets more than b c 1 , the extra de- mands for external assets beyond b c 1 is absorbed by reserve accumulation. To understand it, think of an EME that has current account surpluses and receive lots of direct investments. The EME needs to accu- mulate external assets, but accumulating external assets by private sectors accompanies nonnegligible inefficiencies. As we have repeated throughout this paper, in such a case the planner accumulate reserve to replace the inefficient overseas investment by private sectors. Hence, passive capital inflows (direct investments or equity portfolio investments) to such EMEs generate seemingly excessive reserve accu- mulation. Although we cannot make a strong claim because our model is not suitable for quantitative analysis, the result in this section potentially explain why some East Asian EMEs with high net positive foreign asset positions, for example Malaysia, Thailand, and China, hold high levels of international re- serves from 30 to 40 percent of GDP . 166 B.5 Capital Outflows Restrictions in EMEs Compared to capital inflow restrictions, the discussion on capital outflow restriction in EMEs is scarce. However, in reality, the restrictions on capital outflow in EMEs are stricter than capital inflow. To show how capital outflow restrictions have changed, we exploit capital control measures constructed by Fernández et al. (2016). Figure B.3a presents the evolution of capital control restrictions on both inflows and outflows for our sample countries. The two series show strong co-movement over time. Remarkably, EMEs have maintained higher levels of capital outflow restrictions than capital inflow. This suggests that residents in EMEs would have more difficulty investing abroad. Fernández et al. (2016) also note that this pattern of strict outflow restrictions is more noticeable for EMEs than advanced economies. Figure B.3b shows how capital outflow restrictions in EMEs evolve by major asset classes. The outflow controls on money market instruments, which include bonds with a maturity of one year or less, have maintained a relatively high level. As an example, we will illustrate the evolution of the regulations on capital flows in Korea. The capi- tal outflow indicator shows that Korea imposed relatively strict restrictions on capital outflows by 2004. 5 While there were some relaxations on capital control in the 1980s, outward investment by residents in Korea was strictly controlled by the government. For instance, domestic residents were not permitted to purchase foreign securities. Starting in 1995, residents were allowed to freely purchase and hold for- eign currency only up to USD 10 thousand per year per individual. For outward FDI, there were a list of investment areas that had to be reviewed by the government and the quantification conditions such as self-financing. After Korea’s accession to the OECD, from the late 1990s, regulations on capital transac- tions were gradually reduced. To deal with a continued trade surplus and support the competitiveness of Korean firms, the government encouraged domestic firms and residents to invest abroad. For example, the investment restriction per project was abolished and the maximum investment amount by individ- ual investors raised to USD 10 million in 2005. 5 From 1998 to 2004, the overall capital outflow control index is 0.64 on average. In 2005 it decreased to 0.2. Then, the average index from 2006 to 2017 is 0.11. For an inflow index, it shows a similar trend to the outflow index. However, as discussed, the average inflow index is 0.51 before 2004, which shows that outflow restrictions were stricter then. 167 Figure B.3: Capital Outflow Restrictions (a) Inflows and Outflows Restrictions (b) Outflows Restrictions (by asset class) Note: A higher value means strict restrictions. All values are averaged across the sample countries. Source: Capital Control Measures: A New Dataset, Fernandez et al. (2016) 168

Abstract (if available)

Abstract This dissertation consists of three independent essays in macroeconomics. In all the essays, I focus on the context of South Korea.
The first essay studies misallocation over time in Korea’s manufacturing sector. Using the confidential Korean establishment-level data, I explore the patterns of misallocation across different sizes and ages. I find that the overall misallocation in Korea and its negative effects increased substantially over time. The main culprit behind such increased misallocation was distortions in the capital markets. Moreover, the decomposition of the overall dispersion reveals that it was small and young firms that suffered most from the distortions. These firms were unable to utilize inputs as much as they needed, limiting their ability to expand. Lastly, I show that the extent of mismeasurement was moderate, which provides more concrete evidence of the increased misallocation.
In the second essay, I study the effects of size-dependent policies (SDPs) both empirically and structurally in the context of Korean manufacturing sector. On the empirical side, I focus on the effects of the removal of small-scale reservations policy, which restricts the new entry of large firms into certain products. Using a Difference-in-Difference design, I find that eliminating this regulation had positive effects on firm outcomes. Motivated by these findings, I investigate the quantitative effects of general SDPs. By calibrating a model to plant size distributions in Korea, I show that such policies have substantial negative effects on the aggregate economy. The key mechanism of this policy is the misallocation of talents: it reallocates resources from productive (large) to unproductive (small) firms, resulting in allocative efficiency losses.
The third essay (joint with Bada Han) provides a novel theory of international reserve accumulation of Emerging Market Economies. Motivated by empirical findings we document, we view reserve accumulation as capital outflows by the public sector, which supplements less-than-optimal outflows by the private sector. In our model, EMEs face a probability of future sudden reversals in capital inflows (sudden stops). When a country receives large inflows in the form of direct or equity portfolio investment, the country should invest abroad to maintain macroeconomic balance and prepare for sudden stops. If the private sector is unable to invest abroad sufficiently due to restrictions on capital outflows, the public sector may come in to increase gross outflows in the form of reserves. Furthermore, our theory has implications for the debate over currency manipulation.

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Creator Kim, Dongwook (author)

Core Title Essays in macroeconomics

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Degree Conferral Date 2022-08

Publication Date 08/02/2022

Defense Date 05/26/2022

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

Tag capital flows,firm dynamics,international reserves,misallocation,OAI-PMH Harvest,productivity

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Betts, Caroline Marie (committee chair), Nugent, Jeff (committee member), Quadrini, Vincenzo (committee member)

Creator Email dwkim.econ@gmail.com,kim235@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111375979

Unique identifier UC111375979

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Document Type Dissertation

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Source 20220802-usctheses-batch-966 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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