University of Southern California Dissertations and Theses

Three essays on macro and labor finance

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Three essays on macro and labor finance

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Content THREE ESSAYS ON MACRO AND LABOR FINANCE by Zhao Zhang 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 (BUSINESS ADMINISTRATION) May 2023 Copyright 2023 Zhao Zhang Dedication For all those who have made or are currently making the world a better place. ii Acknowledgements I would like to thank my advisors: Mete Kilic, Vincenzo Quadrini, Rodney Ramcharan, Lukas Schmid, Selale Tuzel for their invaluable advice, unwavering support, and patience throughout my doctoral journey. I am also grateful to all the faculty members in the department of Finance and Business Economics, as well as my classmate, Reed Douglas, for their continuous support. Lastly, I would like to express my gratitude to my parents and my friends. Without their tremendous understanding and encouragement in the past few years, I could not have achieved this significant milestone in my life. iii TableofContents Dedication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Chapter 1: Inflation Heterogeneity and Household Financial Decisions: Evidence from Housing Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 A Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Inflation Heterogeneity and Two Types of Financial Markets . . . . . . . . . . . . . 6 1.3.2 A Toy Model and the Empirical Prediction . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2.1 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.2.2 Partial Equilibria and the Empirical Prediction . . . . . . . . . . . . . . . 9 1.4 The Empirical Setting and Preliminary Evidence . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.2 Inflation Heterogeneity Across Income Groups . . . . . . . . . . . . . . . . . . . . 11 1.4.3 Inflation Heterogeneity and Mortgage and Housing Markets . . . . . . . . . . . . . 12 1.4.3.1 The Conforming Mortgage Market . . . . . . . . . . . . . . . . . . . . . 13 1.4.3.2 Geographic Income Segregation and segmented Housing Markets . . . . 13 1.4.4 Evidence from Mortgage Borrowings . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4.5 Evidence from Home Ownership . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Identification using Exchange Rate Movements . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.5.1 Chinese Yuan Exchange Rate as The Instrumental Variable . . . . . . . . . . . . . . 18 1.5.1.1 The Relevance Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5.1.2 The Exclusion Restriction . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5.1.3 Evidence from the Instrumental Variable Approach . . . . . . . . . . . . 22 1.5.2 Chinese Yuan Exchange Rate Reform: A Quasi Natural Experiment . . . . . . . . . 24 1.5.2.1 RMB Exchange Rate Reform on July 21 2005 . . . . . . . . . . . . . . . . 24 1.5.2.2 Chinese Yuan Reform and the US Realized Inflation Heterogeneity . . . . 26 1.5.2.3 RMB Reform and the US Inflation Expectation Heterogeneity . . . . . . 27 1.5.2.4 Chinese Yuan Reform and US Housing Transactions . . . . . . . . . . . . 29 iv 1.6 Model and Counterfactual Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6.1 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6.1.1 Household’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.6.1.2 General Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.6.2 Calibration and Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1.6.3 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.6.4 Inflation Heterogeneity and Asset Prices . . . . . . . . . . . . . . . . . . . . . . . . 39 1.6.5 Inflation Heterogeneity and the Cross-sectional Home Ownership . . . . . . . . . 41 1.6.6 The Cross-sectional Dispersion in Welfare . . . . . . . . . . . . . . . . . . . . . . . 44 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.8 Appendix: Income Growth Spreads and Inflation Spreads . . . . . . . . . . . . . . . . . . . 47 1.9 Appendix: Income or Inflation? A Trade Exposure Channel . . . . . . . . . . . . . . . . . . 48 1.10 Appendix: Chinese Yuan Reform and the US Inflation . . . . . . . . . . . . . . . . . . . . . 50 1.11 Appendix: First Lien Mortgage or Home Equity Loan? . . . . . . . . . . . . . . . . . . . . . 52 Chapter 2: Talent Retention Risk and Corporate Investment . . . . . . . . . . . . . . . . . . . . . 75 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.2 CFO Survey Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.2.1 Surveys on Forgoing Corporate Investments . . . . . . . . . . . . . . . . . . . . . . 81 2.2.1.1 Kellogg CFO Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.2.1.2 Duke CFO Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.2.2 Surveys on CFOs’ Most Pressing Internal Risk Concerns . . . . . . . . . . . . . . . 82 2.2.2.1 Duke CFO Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.2.2.2 Deloitte CFO Signals™ Survey . . . . . . . . . . . . . . . . . . . . . . . . 82 2.3 A Simple On-The-Job Search Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.4 Data and Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.4.2 TRR Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.4.3 Descriptives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2.4.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2.4.4.1 Duke CFO Survey of Managerial Perceptions . . . . . . . . . . . . . . . . 89 2.4.4.2 Linkedin Workforce Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 90 2.5 Talent Retention Risk and Corporate Investment . . . . . . . . . . . . . . . . . . . . . . . . 91 2.5.1 Main Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 2.5.2 Robustness: TRR and Planned Investment . . . . . . . . . . . . . . . . . . . . . . . 93 2.5.3 Heterogeneous TRR Effects by Firms’ Tobin Q . . . . . . . . . . . . . . . . . . . . . 93 2.6 Where TRR Matters and Whose TRR Matters? . . . . . . . . . . . . . . . . . . . . . . . . . 94 2.6.1 TRR and New Capital Formation Industries . . . . . . . . . . . . . . . . . . . . . . 94 2.6.2 Manager vs. Non-managers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.7 Implications for Rising Investment-Q Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2.9 Appendix: Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 2.10 Appendix: Talent Turnover Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Chapter 3: Borrow from Employees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 3.2 Research Questions and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 3.2.1 "Borrow" from Employees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 v 3.2.2 Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.2.3 Research Design and Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.3 Data and Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 3.4 Wage and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 3.4.1 Wages Increased after Reforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 3.4.2 State Border Counties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 3.4.3 Decompose the Wage Staggered DiDs . . . . . . . . . . . . . . . . . . . . . . . . . 142 3.5 Firm Size, Labor Productivity, and Industry Aggregates . . . . . . . . . . . . . . . . . . . . 144 3.5.1 Number of Workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 3.5.2 Labor Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 3.5.3 Managerial Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 3.6 Household Consumption: Evidence from Housing . . . . . . . . . . . . . . . . . . . . . . . 152 3.6.1 Housing Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 3.6.2 Lower-income Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 3.6.3 Financially Constrained Households . . . . . . . . . . . . . . . . . . . . . . . . . . 156 3.7 A Framework for Policy Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 3.7.1 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 3.7.2 Firm’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 3.7.3 Employment, Wage, and Payday Frequency . . . . . . . . . . . . . . . . . . . . . . 161 3.7.4 Social Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 3.7.5 Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 3.7.6 Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 vi ListofTables 1.1 Mortgage Borrowing and Inflation Heterogeneity: RMB Appreciation as IV . . . . . . . . . 22 1.2 Calibration of the Baseline Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.3 Moments from the Data and the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.4 Inflation Heterogeneity and Rent and House Prices . . . . . . . . . . . . . . . . . . . . . . 40 1.5 Inflation Heterogeneity and Cross-sectional Housing Consumption . . . . . . . . . . . . . 42 1.6 Welfare Analysis by Household Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.7 The Distribution of Buyers’ Income Quintile and Locations’ Income Quintile . . . . . . . . 58 1.8 Mortgage Borrowing and Inflation Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . 60 1.9 Mortgage Borrowing and Inflation Heterogeneity: After the Financial Crisis . . . . . . . . 61 1.10 Mortgage Borrowing and Inflation Heterogeneity: Robustness of Inflation Definition . . . 62 1.11 Home Ownership and Inflation Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . 63 1.12 Home Ownership and Inflation Heterogeneity: After the Financial Crisis . . . . . . . . . . 64 1.13 Home Ownership and Inflation Heterogeneity: Robustness of Inflation Definition . . . . . 65 1.14 Correlation Between RMB Appreciation and US Inflation Gap . . . . . . . . . . . . . . . . 66 1.15 Home Ownership and Inflation Heterogeneity: RMB Appreciation as IV . . . . . . . . . . . 67 1.16 Inflation Expectation Heterogeneity and the 2005 Chinese Yuan Reform . . . . . . . . . . . 68 1.17 Household Expectation and the 2005 Chinese Yuan Reform . . . . . . . . . . . . . . . . . . 69 1.18 Mortgage Borrowing and the Chinese Yuan Reform . . . . . . . . . . . . . . . . . . . . . . 70 vii 1.19 Home Ownership within a Group and Inflation Heterogeneity . . . . . . . . . . . . . . . . 71 1.20 Detailed Distribution of Household Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1.21 Mortgage Borrowing and Inflation Heterogeneity: China Trade Exposure . . . . . . . . . . 72 1.22 Home Ownership and Inflation Heterogeneity: China Trade Exposure . . . . . . . . . . . . 73 1.23 Mortgage Lien Status and Inflation Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . 74 2.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 2.2 Validating the Talent Retention Risk Measure . . . . . . . . . . . . . . . . . . . . . . . . . 107 2.3 Talent Retention Risk and Investment Response . . . . . . . . . . . . . . . . . . . . . . . . 108 2.4 Robustness of Investment Response to TRR . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.5 Investment and Interaction of TRR and Q . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 2.6 Talent Retention Risk and Investment in Subsamples . . . . . . . . . . . . . . . . . . . . . 111 2.7 Decomposing TRR: Management vs. Non-Management . . . . . . . . . . . . . . . . . . . . 112 2.8 TRR and the Widening Investment-Q Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 2.8 TRR and the Widening Investment-Q Gap—Continued . . . . . . . . . . . . . . . . . . . . 117 2.9 Managers in our TRR measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 2.10 A Comprehensive Search for “Which Talent Matters” . . . . . . . . . . . . . . . . . . . . 121 2.11 Does TRR Lead to Talent Outflows? Evidence Across Industries . . . . . . . . . . . . . . . 122 2.12 Talent Retention Risk and Employee Turnover . . . . . . . . . . . . . . . . . . . . . . . . . 123 3.1 The Size of Half a Month Salary for a Median US Household and a Compustat Firm . . . . 133 3.2 State Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 3.3 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 3.4 Wage and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.5 Decompose the Wage Staggered DiDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 3.6 Number of Employees and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . 145 viii 3.7 Labor Productivity and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . 148 3.8 Capital Per Employee and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . 150 3.9 Officer Ratios and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . . . . 151 3.10 Home Ownership and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . . 154 3.11 Home Ownership and Payday Frequency Reforms: Lower Income and Financially Constrained Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 3.12 Wage and Payday Frequency Reforms: Weekly Paydays . . . . . . . . . . . . . . . . . . . . 165 3.13 Average Number of Employees and Payday Frequency Reforms . . . . . . . . . . . . . . . 166 3.14 Decompose Staggered DiDs: the Number of Workers . . . . . . . . . . . . . . . . . . . . . 167 3.15 Sales Per Worker and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . . . . . 168 3.16 Decompose Staggered DiDs: the Labor Productivity . . . . . . . . . . . . . . . . . . . . . . 169 3.17 Industry Characteristics and Payday Frequency Reforms . . . . . . . . . . . . . . . . . . . 170 3.18 Industry Characteristics and Payday Frequency Reforms: Border Counties . . . . . . . . . 170 3.19 Share of Clerks in All Employees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 3.20 Decompose Staggered DiDs: the Home Ownership . . . . . . . . . . . . . . . . . . . . . . 172 ix ListofFigures 1.1 Inflation Heterogeneity and Household Portfolio Allocation . . . . . . . . . . . . . . . . . 9 1.2 Mortgage Borrowing, Home Ownership, and Relative Inflation Spread . . . . . . . . . . . . 16 1.3 US Inflation Heterogeneity and Chinese Yuan Exchange Rate . . . . . . . . . . . . . . . . . 19 1.4 Chinese Yuan Exchange Rate Reform and US Realized Inflation Heterogeneity . . . . . . . 25 1.5 Chinese Yuan Exchange Rate Reform and US Household Expectation . . . . . . . . . . . . 28 1.6 Housing Transactions around the Chinese Yuan Reform . . . . . . . . . . . . . . . . . . . . 29 1.7 Heterogeneous Inflation and Household Portfolios . . . . . . . . . . . . . . . . . . . . . . . 38 1.8 House Size Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.9 US Dollar to Chinese Yuan Exchange Rate Around July 21 2005 . . . . . . . . . . . . . . . . 51 1.10 Import Price Indexes from China by Product Categories . . . . . . . . . . . . . . . . . . . . 52 1.11 Inflation Heterogeneity and Inflation Expectation Heterogeneity . . . . . . . . . . . . . . . 53 1.12 Inflation Heterogeneity and Mortgage Interest Rate Heterogeneity . . . . . . . . . . . . . . 54 1.13 The Distribution of Buyers’ Income Quintile and Locations’ Income Quintile . . . . . . . . 55 1.14 Household Portfolio by Income Quintiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 1.15 Inflation Heterogeneity and Inflation Expectation Heterogeneity . . . . . . . . . . . . . . . 57 1.16 Correlation Between Inflation Expectation Gap and Chinese Yuan Exchange Rate . . . . . 58 1.17 Accumulated Inflation by Metropolitan Areas . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.18 Relative Inflation Spreads and Income Growth Spreads . . . . . . . . . . . . . . . . . . . . 59 x 2.1 Talent Retention Concerns from the Duke CFO Survey . . . . . . . . . . . . . . . . . . . . 101 2.2 Talent Outflows from the LinkedIn Microdata . . . . . . . . . . . . . . . . . . . . . . . . . 102 2.3 Talent’s Time Spent on Job Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 2.4 Talent Retention Risk Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 2.5 Replicating Investment-Q Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 2.6 Top Chief Risk Concerns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 2.7 Measuring Talent Retention Risk: An Example . . . . . . . . . . . . . . . . . . . . . . . . . 124 2.8 Defining Skilled Labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 2.9 Talent Retention Concerns in Duke CFO Survey (Controlling for Firm Heterogeneity) . . . 126 3.1 An Example: Pay at the End of Each Month . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 3.2 An Example: Pay at the End of Each Semi-Month . . . . . . . . . . . . . . . . . . . . . . . 135 3.3 Wage Around the Payday Reforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 3.4 Number of Employees Around the Payday Reforms . . . . . . . . . . . . . . . . . . . . . . 146 3.5 Labor Productivity Around the Payday Reforms . . . . . . . . . . . . . . . . . . . . . . . . 149 3.6 Home Ownership Around the Payday Reforms . . . . . . . . . . . . . . . . . . . . . . . . . 153 3.7 State Border Counties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 xi Abstract The thesis contains three chapters. In the first chapter, I study the inflation heterogeneity across income groups. I find that households who experience a rise in inflation (relative to national inflation rates) increase their borrowing from the mortgage market and holdings of housing assets. These findings can be explained by households relocating their savings to markets where real returns are protected from relative inflation. A calibrated general equilibrium model suggests a smaller dispersion in home ownership between income groups but a greater dispersion in welfare due to inflation heterogeneity. In the second chapter, I study the effect of the risk of losing talent on corporate investment. I construct a firm-level measure of talent retention risk based on other firms’ job postings for skilled labor in the local labor market, which captures the outside options of the firm’s talent. Using this measure, we show that TRR reduces firm investment after controlling for Q, and effects are driven by retention risk for middle- managers but not other skilled labor, suggesting that managers are the core talent. In the last chapter, using state payday frequency reforms between the 1860s and the 1930s, I find that firms reduced employment after being required to pay employees more frequently, which reduced the amount of implicit borrowing from employees. However, the remaining employees were more productive and earned higher wages. Meanwhile, homeownership increased, especially those potentially financially constrained households, such as low-income minorities and females. xii Chapter1 InflationHeterogeneityandHouseholdFinancialDecisions: Evidence fromHousingMarkets 1.1 Introduction Households systematically experience different inflation rates because they persistently consume different baskets of products, whose prices evolve differently over time. In particular, a growing body of research shows that, since the 2000s, lower income households on average experience higher consumption infla- tion compared to higher income households (e.g., [81] and [76]). This inflation heterogeneity can create differences in real returns conditional on the same nominal investment position. The resulting real return heterogeneity should affect household savings and investment decisions. Beginning with [51], researchers have made a substantial effort to understand how national inflation transfers wealth between creditors and borrowers, impacts financial decisions, and affects real aggregates and asset prices. ∗ However, lim- ited attention is paid to the heterogeneity in inflation across households and its interactions with financial markets. This paper studies how inflation heterogeneity across different household groups affects financial deci- sions. When group-specific inflation rises (relative to national inflation), theory suggests that households dissave in markets in which real returns are eroded, and save more in markets in which real returns are ∗ For example, [49], [43], [57], and [31]. 1 protected from relative inflation spreads. I indeed empirically find that groups of households experiencing a rise in inflation relative to the national average inflation increase borrowing from the mortgage market and holdings of housing assets. To understand the consequences of inflation heterogeneity, I calibrate a general equilibrium model that features a cross-sectional relation between income and inflation and use the model to conduct counterfactual analyses. The model predicts a smaller dispersion in home ownership between income groups but a greater dispersion in welfare, as a result of inflation heterogeneity. Following [76], I measure relative inflation spreads as the difference between the group-specific infla- tion and the national average inflation, using the transaction-level Nielsen Consumer Panel data. Relative inflation spreads can alter real returns depending on the market structure. Standardized assets traded in centralized markets (e.g., stocks and bonds) are more likely to offer the same nominal return to all in- vestors and, thus, lead to differences in real returns due to cross-sectional inflation heterogeneity. Notably, the conforming mortgage market has been documented as highly standardized with little price hetero- geneity ([72]). In other markets, however, relative inflation spreads do not directly affect real returns. The most prominent example is the housing market. Conditional on owning a house, relative inflation spreads do not directly change the size and quality of the house, and therefore the utility flow from housing is unaf- fected. Furthermore, housing markets are segmented across income groups, which is known as geographic income segregation, documented by [101], [62], and [85]. Given this segmentation feature, nominal rent and house prices can potentially adjust for relative inflation spreads and shield the real returns away from the direct effect of inflation heterogeneity. Consider a scenario in which the relative inflation spread rises for a specific group of households. Real returns in centralized markets drop, which makes those markets less attractive places to save. Instead, households prefer to move their savings into the segmented housing markets in which real returns are protected from relative inflation spreads. Taking it one step further, households want to borrow from cen- tralized markets because of lowered real borrowing costs and invest in the segmented housing markets to 2 mitigate against relative inflation spreads. Therefore, it is reasonable to expect that inflation heterogeneity has a potent effect in mortgage-financed housing decisions because of the combination of a centralized and standardized mortgage liability and a segmented and real housing asset. Furthermore, home purchase and mortgage borrowing are the most prominent financial decisions that typical US households make. Finally, rich data with detailed information from the mortgage market facilitate the careful design of this study’s empirical investigations of the causal impact of inflation heterogeneity on household behavior. I first document the association between relative inflation spreads and mortgage activity in the data. Consistent with the above prediction, I find a positive correlation between relative inflation spreads and mortgage borrowing, using census tract by year level data from HMDA. In addition, using individual household-level data from American Community Survey, I also find that home ownership increases when relative inflation spreads rise. This indicates that the increase in mortgage borrowing is associated with actual home purchases by households in the corresponding group. All of the above results are robust in the subsample after the 2008-2009 financial crisis, which suggests that the housing boom and bust do not drive the documented patterns. Lastly, the results remain consistent for a battery of alternative inflation measures. To address endogeneity concerns, I employ two identification strategies. In particular, I use the Chi- nese Yuan (RMB) to US Dollar (USD) exchange rate as an instrumental variable for inflation heterogeneity across income groups and the 2005 Chinese Yuan reform as an unexpected shock. Both empirical strate- gies leverage the literature documenting that tradable goods constitute a more significant share in the consumption baskets of lower income households, and trade shocks have greater impacts on the prices of lower end products ([48], [32], [77]). As a result, exchange rate movements disproportionately affect the inflation rates of lower income households. † China is responsible for the largest share of US imports since 2007. Consistent with the previous literature, I document a positive and robust correlation between RMB † For example, [32] show that currency devaluation in Mexico increased the inflation rate for low-income households more. [77] find that the magnitude of the domestic price response is 5 times larger for product categories that cater to lower income households than for categories catering to higher income households. 3 appreciation against USD and US inflation heterogeneity across income groups. Using the appreciation of RMB against USD as an instrumental variable, I find that a one percentage point increase in relative inflation spreads leads to an increase in home ownership by nine percentage points. In addition, on 21 July 2005, China abandoned its fixed exchange rate system. ‡ RMB immediately appreciated by 2.1% against USD within one day, and further appreciated by nearly 20% against USD over the following year. The exact timing of this reform was unexpected by the market ([52]). I find that the unexpected RMB appreciation is associated with a widened gap in both realized inflation and inflation expectations between the low and high income US households. Moreover, there is no effect on income expectation and employment expectations. Consistent with previous findings, I document that mortgage borrowing by the low income households increased after the RMB reform. To conduct counterfactual analyses, I calibrate a model that captures the general equilibrium effects of inflation heterogeneity across income groups on asset prices, the cross-section of housing consumption, and household welfare. The model features an endowment economy that consists of overlapping genera- tions and heterogeneous income groups with idiosyncratic shocks. In the model, households endogenously make home ownership, savings, mortgage, and consumption decisions. The equilibrium national interest rate and segmented house prices are determined by market clear conditions. The model quantitatively matches the cross-sectional dispersion in home ownership, house price to income ratio, and house size differences between low income and high income households. Using the model, I then ask what would happen in the mortgage and housing markets in the absence of inflation heterogeneity. I find that higher relative inflation spreads push lower income households to borrow from the mortgage market and invest into segmented housing markets, which leads a smaller dispersion in home ownership across income groups. However, it also creates a thicker left tail distribution of housing consumption, i.e., some households that can not afford to buy a house are forced to rent a smaller one due ‡ From 1997 to 2005, the Chinese government maintained a peg of 8.27 RMB per USD. 4 to higher house prices in their segment. Lastly, the model suggests a larger dispersion in welfare across income groups. Lower income households are worse off because of lower real income and lower real return from savings, as housing assets can not fully mitigate the effect of relative inflation spreads. The paper is organized as follows: Section 2 discusses the related literature, Section 3 presents a con- ceptual framework and the prediction, Section 4 shows consistent empirical patterns from the data, Section 5 introduces two identification strategies, Section 6 calibrates a structural model for counter-factual anal- yses, and Section 7 concludes. 1.2 Literature This paper connects the growing literature on inflation heterogeneity across income groups to the lit- erature on inflation and household financial decisions. Powered by newly available granular household shopping data, [81], [76], and [7] show that lower income households systematically experience higher inflation levels between 2004 and 2015. [76] further finds a similar pattern exists in a longer period from 1955 to 2015 using the merged CEX-CPI data. Meanwhile, there is a rich body of studies on how household inflation experiences and expectations affect financial choices. Using data on inflation expectations from the Michigan Survey of Consumers, [87] reveal that differences in household inflation experiences strongly predict differences in inflation expectations, and higher experience-induced inflation expectations lead to more borrowing, especially from the mortgage market. [36] document that consumers update their infla- tion expectations from their grocery shopping experiences. [108] directly link survey data on quantitative inflation expectations to administrative data on income and wealth, and they document that households with higher inflation expectations consume more durable products like cars. My paper contributes to the literature by showing how the systematic inflation heterogeneity across income groups matters for house- hold financial decisions. I find households increase borrowing from the mortgage market and holdings 5 of housing assets to mitigate higher relative inflation by exploiting real return differences across markets caused by inflation heterogeneity. This paper also speaks to the literature on the interaction between inflation and financial markets. Because many debt-like financial contracts are written in nominal terms, inflation shocks lead to wealth transfer between creditors and borrowers, known as the Fisher channel ([51]). [43] measure the balance sheet’s inflation exposure of various groups of households and investors in the US. The differential bal- ance sheet exposure has real effects on the aggregate economy when households have different marginal propensities toward consumption, as discussed by [10]. On the production side, [80] and [57] show that unanticipated inflation changes firms’ real burden of debt and future investment and production deci- sions via a sticky leverage channel. [31] further consider the financial intermediation sector and find that higher inflation hurts intermediaries’ balance sheet, leading to a contraction in credit. My paper instead emphasizes a different scenario in which households intrinsically experience different inflation levels. I show that the differences in inflation levels can affect household financial decisions. I further argue that inflation heterogeneity matters for asset prices and the cross-sectional dispersion of housing consumption across income groups. 1.3 AConceptualFramework This section presents a conceptual framework to illustrate how inflation spreads (relative to the national inflation) can interact with different financial markets, change real returns, and therefore affect household financial decisions. 1.3.1 InflationHeterogeneityandTwoTypesofFinancialMarkets Households systematically experience different inflation levels because they persistently consume different baskets of products whose prices evolve differently over time. In particular, a growing body of research 6 shows that lower income households on average experience higher consumption inflation compared to higher income households since the 2000s (e.g., [81] and [76]). This inflation heterogeneity can lead to heterogeneity in real returns given the same nominal position, depending on the market structure. In this paper, conceptually, I classify financial markets into two groups based on whether real returns from those markets are directly affected by inflation heterogeneity or not. In the first category of financial markets, inflation heterogeneity directly creates differences in real returns. The first category includes centralized markets in which standardized assets are traded. Only one price exists for each asset at a given time. Conditional on the same nominal position, a standardized asset from a centralized market is more likely to offer the same nominal return to all households, regardless of the specific inflation processes that households face. Examples are bonds, stocks, and other publicly traded standardized financial instruments. Important to this paper, the conforming mortgage market has been documented as highly standardized with little price heterogeneity ([72]). In the second category of financial markets, real returns are not directly affected by inflation hetero- geneity. First, some assets in nature deliver real payoff flows. The most prominent example is the housing market. Conditional on owning a house, the real house size a person enjoys during each period will not be directly reduced or increased by his or her inflation spread, and therefore the utility flow from housing will be unaffected. Furthermore, housing markets are segmented across income groups, which is known as geographic income segregation, documented by [101], [62], and [85]. Given this segmentation feature, nominal rent and house prices can potentially adjust for relative inflation spreads and shield real returns away from the direct effect of inflation heterogeneity. 1.3.2 AToyModelandtheEmpiricalPrediction Motivated by the previous patterns, I explore the theoretical implications of inflation heterogeneity on household financial decisions in a simple partial equilibrium framework. 7 1.3.2.1 Environment Consider a household lives for two periods, receives nominal endowmentsw in the first period, and con- sumes retail good c t and housing service h t . The national inflation is assumed to be zero. The price of retail goods exogenously experiences a relative inflation spread π j between the first and second period. Household’s utility from a bundle of{c,h} is u(c,h)= c θ · h 1− θ 1− γ 1− γ The household can save via a centralized bond market and a segmented housing market. The cen- tralized bond market provides one-period nominal bonds with a risk-free returnR f . The household can also buy houses with the price ofP j in the first period, and the household is allowed to sell the house and consume using the home value in the second period. For simplicity, I assume rent r is determined in a competitive rental market, wherer =P · (R f − 1). § To maximize expected utility, the household chooses savingss in the bond market and house sizeh 2 in the housing market, as well as the first period retail consumption c 1 and rental house sizeh 1 . max c 1 ,h 1 ,s,h 2 =u(c 1 ,h 1 )+β · u(c 2 ,h 2 ) subject to budget constraints c 1 +r· h 1 =w− s− P · h 2 , e π j · c 2 =s· R f +P · h 2 8 Figure 1.1: Inflation Heterogeneity and Household Portfolio Allocation This figure shows the effect of relative inflation spreads π j on household’s savings choices in the housing market and the bond market. Figures (a) and (b) plot the scenario whenγ = 5. The x-axes of all subplots are relative inflation spreads π j in percentage points. The y-axes are also in percentage points, relative to the case when π j = 0. As π j rises, figures (a) shows that household savings in the housing market increase, meanwhile figure (b) shows that household savings (borrowing) in the bond market decrease (increases). 1.3.2.2 PartialEquilibriaandtheEmpiricalPrediction Figure ?? shows the effect of relative inflation spreads π j on household savings choices in the housing market and the bond market. Figures (a) and (b) plot the scenario in whichγ = 5. ¶ Asπ j rises, figure (a) shows that household savings in the housing market increase. Meanwhile, figure (b) shows that household savings in the bond market decrease. In combination, the household moves its portfolio from the bond market to the housing market. The intuition behind the above reallocation is that, whenπ j increases, the real value of the same nom- inal savings in the second period decreases. With the elasticity of intertemporal substitution 1 γ < 1, the household will save more in nominal terms to smooth real consumption in the second period. However, saving via the centralized bond market becomes less attractive, as real returns are reduced by higher rela- tive inflation spreads. Taking this point one step further, if possible, households seek to borrow from the bond market, because the real borrowing cost becomes lower. At the same time, segmented housing assets gain an advantage because the real return of owning a house is protected from relative inflation spreads. § I assume an exogenous housing price and no decapitation and property tax in this partial equilibrium toy model. These assumptions are relaxed in Section??. The competitive rental market assumption follows [73]. ¶ The assumption of a coefficient of relative risk aversion γ > 1 is typical in the macro-housing literature (e.g. [38] and [29]). 9 Conditional on owning a house, relative inflation spreads will not directly change the size and quality of the house, and therefore the utility flow from housing will be unaffected. ∥ Housing and mortgage markets are the ideal places to test the model’s prediction. First, the conforming mortgage market has been documented by the literature as centralized and standardized (more discussion in Section ??) and housing markets are real and segmented (more discussion in Section ??). Therefore, it is reasonable to expect that inflation heterogeneity has a potent effect in mortgage-financed housing decisions because of the combination of a centralized and standardized mortgage liability and a segmented and real housing asset. Second, housings (mortgages) are the largest assets (liabilities) for US households across all income quintiles (as indicated by Figure ??, Figure ??, and Figure ??), and home purchase and mortgage borrowing are the most prominent financial decisions that a typical household makes. Finally, rich data with detailed information from the mortgage market allow me to carefully design empirical investigations of the causal impact of inflation heterogeneity on household behavior. In sum, the model predicts that when relative inflation spreads rise, households borrow more from the mortgage market to finance their investments in the segmented housing market. When the relative inflation spread π j rises, households increase mortgage borrowing and housing investment. 1.4 TheEmpiricalSettingandPreliminaryEvidence This section presents the data, measures, and consistent empirical patterns with the conceptual framework discussed in Section??. The inflation heterogeneity can exist in many other cross-sectional dimensions. In this paper, I focus on the heterogeneity across the income distribution for empirical reasons (more discus- sion in Section ??). Consistent with the conceptual prediction, I find that households increase mortgage borrowings and housing investments, when they experience higher relative inflation spreads. ∥ Furthermore, in Section ??, I will use a general equilibrium model with endogenous house prices and segmented housing markets to show that nominal rent and house prices increase withπ j , which further shields housing real returns away from the direct effect of inflation heterogeneity. 10 1.4.1 Data This study uses the Nielsen Consumer Panel to estimate relative inflation spreads. Home Mortgage Dis- closure Act data (HMDA) and Zillow’s Assessor and Real Estate Database (ZTRAX) are used to measure household mortgage borrowing and housing transactions. I use the American Community Survey for individual-level home ownership, mortgage status, income, rent, home value, and geographic and demo- graphic characteristics. Michigan Surveys of Consumers are used to measure household inflation expec- tations. As the Nielsen Consumer Panel only starts from 2004, the sample period in this paper is between 2005 and 2019. 1.4.2 InflationHeterogeneityAcrossIncomeGroups Lower and higher income households spend differently not only across broad categories (food, energy, education, health, etc.), but also across quality ladders within a given product type. Using newly available granular household shopping data, a growing body of research shows a systematic and persistent inflation heterogeneity across income groups. In particular, [81] and [76] find that lower income households on average experience higher consumption inflation, compared to higher income households since the 2000s. The Nielsen Consumer Panel records consumption starting from 2004 for a rotating panel of about 40,000 households who are instructed to scan and input the price and quantity of any product they purchase that has a barcode, typically from retail stores. The Nielsen Consumer Panel data have detailed information on household characteristics such as income, age, and education. In the Nielsen Consumer Panel data, a productk is defined by its barcode, which allows me to compare the prices of the same product over two periods. Following the method used in [76], I calculate the year-to-year relative inflation spreads of an income group as: π j,t =Π n k=1 p j k,t p j k,t− 1 ! s j k,t− 1 +s j k,t 2 − π t , 11 wherej indexes income groups,k products, andt time;s j k,t is the spending share andp j k,t is the average price paid by the income groupj on productk in yeart. Note that the spending sharess j k,t are updated each year to better approximate the changes in consumption baskets.π t is the national average inflation across income groups estimated with the same method. Using the same method but aggregating consumption basket for each month rather than each year, I can also estimate the month-to-month relative inflation spread for income groupj. Alternative inflation measures are examined in Table ?? and?? as robustness checks. Micro-level survey data suggest that households have a consistent perception of inflation heterogeneity in their inflation expectations. This question is important as many studies demonstrate the crucial role that inflation expectation plays in household financial decisions; for example, [87], [108], and [36]. Plotting the average one year forward inflation expectation by household income groups, Figure ?? shows that the lower the income is, the higher the inflation expectations are, following a similar pattern of heterogeneity in realized inflation, as documented by [76] and [81]. ∗∗ 1.4.3 InflationHeterogeneityandMortgageandHousingMarkets In Section??, I group financial markets into two types based on how real returns are affected by inflation heterogeneity. I emphasize the mortgage market, especially conforming loans, as centralized and stan- dardized, in which real returns are directly changed by relative inflation spreads, and housing markets as segmented and real, in which real returns are protected from the direct impact of inflation heterogeneity. Consistent empirical evidence that supports the above classifications is discussed as follows. ∗∗ The same heterogeneity in inflation expectations across income groups is also documented by [35]. 12 1.4.3.1 TheConformingMortgageMarket Important to this paper, the mortgage market, especially the conforming mortgage market, has been doc- umented as highly standardized with little price heterogeneity ([72]). That is, nominal borrowing costs do not fully incorporate group-specific characteristics. I confirm that mortgage rates also do not adjust for relative inflation spreads across income groups using GSE conforming loan performance data. Figure?? and Figure?? plot relative inflation spreads and nominal mortgage rate spreads, with and without adjusting for predictable default risks, for each income quintile at each year. Default risks are predicted following [72]. If mortgage rates one-to-one reflect relative inflation spreads, we should expect a 45-degree line in both Figure ?? and Figure??. However, data suggest that, on average, relative mortgage rate spreads are only 0.17 percentage points higher when relative inflation spreads are 1 percentage point higher. This indicates that households experiencing higher relative inflation spreads pay a lower real mortgage rate than others. 1.4.3.2 GeographicIncomeSegregationandsegmentedHousingMarkets On the other hand, housing markets have been documented as segmented across income groups. There is a growing discussion on the increasing geographic income segregation; i.e., lower and higher income households increasingly live in different neighborhoods within a metropolitan area or a county, for exam- ple by [101]. Furthermore, this increasing geographic income segregation leads to different processes of nominal house prices across income groups, as shown by [62]. Consistent with the literature, I find that properties in low (high) income areas are more likely to be purchased by similarly low (high) income households, using mortgage level HMDA data between 2005 and 2019. For a given mortgage, HMDA allows me to identify the income quintile that the buyer belongs to and the income quintile of the average household in the census tract where the property is located. Figure ?? and Table?? display the distribution of buyers’ income quintiles by census tract income quintiles where 13 the properties are located. In the bottom income quintile census tract, 83% of properties are purchased by households from the bottom two income quintiles. In the top income quintile census tract, 82% of properties are purchased by households from the top two income quintiles. This segmentation shows that houses are segmented assets, as they are mostly held within similar income groups. 1.4.4 EvidencefromMortgageBorrowings To test whether higher relative inflation spreads can increase mortgage borrowing and housing invest- ments, as predicted in Section ??, I first run the following regression on a census tract by year panel constructed using the HMDA data: ln(Num k,j,c,t +1)=β · π j,t +γ · X k,j,c,t +ψ c,t +η k +ϵ k,j,c,t , (1.1) where Num k,j,c,t is the number of mortgages originated at census tract k in year t for home purchase purposes. The average borrower in census tractk belongs to income quintilej in yeart.π j,t is the relative inflation spread of the income quintile j in yeart. ψ c,t are the county by year fixed effects, and η k are the census tract fixed effects. X k,j,c,t are other control variables of census tractk, including the log of median income, Zillow home value index at the census tract, 1-year local housing market return, 5-year housing market return, 1-year local rent growth, and local rent level. By including year by county fixed effects, I compare a census tract with other census tracts in the same county in the same year, which allows nonparametrically absorbing county-level time-varying economic variations; for example, changes in local labor markets and local credit markets. Moreover, I also control for short-term and long-term interest rates and national inflation rates, and allow heterogeneous sensitivities to those variables across income groups. I use census tract fixed effects to control time-invariant census 14 tract level characteristics. 1-year and 5-year local housing market returns are used to capture the short- term momentum and the long-term reversal in local housing markets caused by either extrapolative beliefs ([8], and [83]) or improved home equity and relaxed collateral or liquidity constraints ([53]). Consistent with the prediction from Section??, Figure?? and Table?? show that, when experiencing higher relative inflation spreads, households in the corresponding income group increase mortgage bor- rowings for home purchase compared to the other households in the same county in the same year. This positive association between relative inflation spreads and mortgage borrowing is robust across various specifications. In column 5 of Table ??, an increase of one percentage point in the relative inflation spread is associated with a 0.09 increase in log one plus the number of mortgage borrowing by households. It is reasonable to suspect whether the above results are driven by the subprime mortgage crisis be- tween 2007 and 2009, either through a household demand channel as shown by [89, 88] or a financial system supply channel as shown by [100]. To address this question, I run the same specification using the subsample starting from 2010. The results are shown in Table ?? and are consistent with the full sample findings. 1.4.5 EvidencefromHomeOwnership Section ?? shows that housing markets are largely segmented in the sense that households in income quintilej typically buy properties at census tracts in the same or similar income quintile. However, it is still possible that buyers from very different income quintiles drive the increase in the number of mortgages that originated for home purchase purposes. To address this concern, I run the second regression using household-level American Community Survey data: Home Ownership i,j,k,c,t =β · π j,t +γ · X i,j,k,c,t +ψ c,t +η k +ϵ i,j,k,c,t (1.2) 15 Figure 1.2: Mortgage Borrowing, Home Ownership, and Relative Inflation Spread Figure (a) shows the correlation between the log of one plus the number of mortgages originated and relative inflation spreads at census tract by year level, using the specification ?? with data from HMDA. Figure (b) shows the correlation between home ownership and relative inflation spreads at household level, using the specification ?? with American Community Survey data. (a) (a) Mortgage Borrowing Data: HMDA (b) (b) Home Ownership Data: American Community Survey 16 where Home Ownership i,j,k,t is a dummy variable that equals one if householdi reports herself as a home- owner. π j,t is the relative inflation spread of the income quintile j that householdi belongs to in yeart. ψ c,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,c,t are other control variables, including the log of household income, PUMA home value level, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent level. I also control for short-term and long-term interest rates and national inflation rates and allow heterogeneous sensitivities to those variables across income groups. Figure?? and Table?? show that home ownership is also positively correlated with the relative infla- tion spread π j,t . A one percentage point increase in relative inflation spreads is associated with a three percentage point increase in home ownership in the corresponding income group. The same pattern holds using the subsample after the Financial crisis, both qualitatively and quantitatively, as shown in Table??. Taken together, the results from Table ?? and Table ?? are consistent with the prediction that house- holds increase mortgage borrowings to finance home purchases when relative inflation spreads rise. 1.5 IdentificationusingExchangeRateMovements Obviously, I should be careful to interpret the above results because of endogeneity concerns. For example, if a higher relative nominal income growth causes both a higher relative inflation and an increase in home purchase, the documented positive correlation between relative inflation spreads and housing investments are misleading and driven by an omitted variable problem. To address endogeneity concerns, I employ two identification strategies. In particular, I use the Chinese Yuan (RMB) to US Dollar (USD) exchange rate as an instrumental variable for US inflation heterogeneity across income groups and the 2005 Chinese Yuan reform as an unexpected shock. †† Both methods leverage the literature that documents the following: 1) tradable goods constitute a more significant share in the †† An example in the literature using exchange rate movements as instrumental variables is [14] 17 consumption baskets of lower income households and 2) trade shocks have greater impacts on the prices of lower end products (e.g. [48], [32], and [77]). As a result, exchange rate movements affect the price of consumption baskets of lower income households more than they do for higher income households. [32] show that the domestic currency devaluation in Mexico disproportionally increased the inflation rate for lower income households. China is responsible for the largest share of US imports since 2007. In 2017, the total US value of imports from China is $505 billion dollars, ‡‡ which is 3.8% of the $13,333 billion dollars total US personal spending. §§ Furthermore, [77] find that the US domestic prices respond more strongerly to the China trade shock in product categories that cater to lower income households. A one percentage point increase in China’s import penetration leads to a 4.3% (0.9%) decline in prices for a product targeting lower (higher) income households. 1.5.1 ChineseYuanExchangeRateasTheInstrumentalVariable I first use the appreciation of RMB against USD as an instrument for US inflation heterogeneity across income groups. The IV estimations are all consistent with the OLS estimations qualitatively and stronger quantitatively. The robust consistency suggests a causal effect of inflation heterogeneity on household mortgage and housing investments. 1.5.1.1 TheRelevanceCondition Motivated by the previous literature, I expect that the exchange rate movements of the RMB against USD will disproportionally affect the relative inflation spread of lower income US households. Indeed, I find that the relative inflation spread of the bottom income quintile shows the strongest and most positive correlation with RMB Appreciation against USD. Furthermore, the estimated correlations decline mono- tonically for higher income quintiles. Figure ?? shows this pattern by plotting the estimated coefficients ‡‡ Data source: United States Census Bureau §§ Data source: US Bureau of Economic Analysis 18 Figure 1.3: US Inflation Heterogeneity and Chinese Yuan Exchange Rate Figure (a) plots the coefficients of regressing relative inflation spreads on Chinese Yuan (RMB) Appreciation against US Dollar (USD) by income quintiles. The relative inflation spread of the bottom income quintile shows the strongest and most positive correlation with RMB against USD. The estimated correlations decline monotonically for higher income quintiles. Figure (b) reports the month-to-month RMB appreciation against USD and the difference in month- to-month inflation rates between the bottom income quintile and top income quintile US households. The correlation between RMB appreciation and the inflation gap is 0.45. (a) (a) Regression Coefficients of Relative Inflation Spreads on RMB Appreciation (b) (b) Correlation Between Inflation Gap and RMB Appre- ciation 19 of regressing relative inflation spreads on RMB appreciation against USD for each income quintile. Fur- thermore, Figure?? reports the month-to-month RMB appreciation against USD and the difference in the month-to-month inflation between the bottom income households and the top income households. The correlation between RMB appreciation and the inflation gap is 0.45. In addition, Figure?? shows the dif- ference in the 1-year forward inflation expectation between the bottom income households and the top income households from the Michigan Survey of Consumers. The correlation between RMB appreciation and the 1-year forward inflation expectation gap is 0.53. To formally test the relevance condition, I regress the time series of RMB appreciation on the inflation difference between the bottom and top income US households, Inflation Gap t =π 1,t − π 5,t : Inflation Gap t =β · RMB Appreciation t +γ · X t +ϵ t , where RMB Appreciation t is the month-to-month RMB appreciation against the US Dollar, π 1,t is the month-to-month relative inflation spread of US households in the bottom income quintile, and π 5,t is that of US households in the top income quintile. Column (1) in Table ?? confirms the positive correlation between RMB appreciation and the US inflation gap is statistically significant, with the F-statistic equal to 45.86. In column (2), I control for potentially co-moving variables such as aggregate inflation rates, fed funds rates, gas price changes, and dollar index changes. In column (3), I add month fixed effects to absorb seasonality, and in column (4), I add year as a control variable to capture the linear long-run trend. The positive correlation between RMB appreciation and the inflation gap remains robust among all specifications. 20 1.5.1.2 TheExclusionRestriction The identification assumption is that RMB appreciation against USD affects mortgage borrowing and hous- ing investments through and only through the inflation heterogeneity channel. Although there is no way to test the exclusion restriction perfectly, I try to address it in several steps. First, there are reasonable concerns about whether RMB appreciation can affect household incomes in a heterogeneous way and consequently change their mortgage and housing decisions. If lower income households were more likely to work in industries that face strong competition from China, RMB ap- preciation against USD can potentially affect their incomes to a greater extent. In Section ??, I test this alternative hypothesis using geographic variations in trade exposures to China. The effects of relative in- flation spreads on mortgage borrowing and housing investments are equally strong in counties both with low and high China trade exposures, which suggests that the alternative income channel hypothesis does not drive the results. Furthermore, it is also possible that RMB appreciation affects the US housing market through an in- terest rate channel. In the influential global saving glut speech, [18] proposes that excessive savings from developing countries, especially China, contribute to the low interest rate environment in the US. The appreciation of RMB might affect US interest rates by changing China’s foreign reserve and demand for US bonds, which could change US interest rates and affect low income US households and high income US households differently. In addition, exchange rate fluctuations can also be the results of US monetary policy shocks. Higher US domestic interest rates can make USD appreciate relative to other foreign curren- cies. The last two alternative channels can be eliminated by directly controlling short-term and long-term interest rates and allowing households to have different sensitivities towards the interest rate environment. The results are still robust and significant, both statistically and economically. 21 1.5.1.3 EvidencefromtheInstrumentalVariableApproach After validating the RMB appreciation against USD as an instrumental variable for US inflation hetero- geneity across income groups, I run a two-stage OLS regression following the baseline specification ??: Table 1.1: Mortgage Borrowing and Inflation Heterogeneity: RMB Appreciation as IV The second stage equation and the first stage in the IV specifications are ln(Num k,j,c,t +1)=β · ˆ π j,t +γ · X k,j,c,t +ψ c,t +η k +ϵ k,j,c,t , π j,t = ˜ β j· Zt + ˜ α, where k indexes census tract, t the year, Num k,j,c,t is the number of mortgages originated for home purchase at census tract k in year t recorded by HMDA. π j,t, the relative inflation spread of income quintile j in year t, is instrumented by Zt = RMB Appreciation t , which is the appreciation of Chinese Yuan relative to US Dollar over the past 12 months. ψ c,t are the county by year fixed effects, and η k are the census tract fixed effects. X k,j,c,t are other control variables of census tractk, including the log of median income, Zillow home value at the census tract, 1-year local housing market return, five-year hous- ing market return, 1-year local rent growth, and local rent index. I also control for short-term and long-term interest rates and national inflation rates and allow heterogeneous sensitivities to those variables across income groups. The sample period is from 2005 to 2019. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) (5) ln(Num + 1) d π j,t 0.115** 0.156*** 0.150* 0.195*** 0.175*** (0.0486) (0.0486) (0.0814) (0.0463) (0.0468) 1-Year Housing Ret 0.603*** 0.585*** 0.438*** 0.564*** (0.0975) (0.0978) (0.0762) (0.114) 5-Year Housing Ret -0.0105*** -0.0105*** -0.00832*** -0.0115*** (0.00214) (0.00215) (0.00173) (0.00291) 1-Year Rent Growth 0.0887*** (0.0291) Observations 660,015 592,313 592,313 592,313 348,801 R-squared 0.9017 0.9018 0.9039 0.9039 0.9037 Inflation Exposure Yes Yes Yes Interest Rate Curve Exposure Yes Yes County-Year Fixed Effects Yes Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 22 The first and second stage equations in the IV specification are ln(Num k,j,c,t +1)=β · ˆ π j,t +γ · X k,j,c,t +ψ c,t +η k +ϵ k,j,c,t , π j,t = ˜ β j · Z t +˜ α, wherek indexes census tract,t the year,Num k,j,c,t is the number of mortgages originated for home pur- chase at census tractk in yeart recorded by HMDA.π j,t , the relative inflation spread of income quintile j in yeart, is instrumented byZ t = RMB Appreciation t , which is the appreciation of RMB against USD over the past 12 months.ψ c,t are the county by year fixed effects, and η k are the census tract fixed effects. X k,j,c,t are other control variables of census tractk, including the log of median income, Zillow home value at the census tract, 1-year local housing market return, 5-year housing market return, 1-year local rent growth, and local rent index. I also control for short-term and long-term interest rates and national inflation rates and allow heterogeneous sensitivities to those variables across income groups. Under the identification condition[ ˜ β j · Z t · ϵ k,j,c,,t |X k,j,c,t ,ψ c,t ,η k ]=0 and relevance condition[ ˜ β j · Z t · π j,t |X k,j,c,t ,ψ c,t ,η k ]̸=0, the coefficient β gives the effect, causally induced by RMB appreciation, of a one percentage point increase in relative inflation spreads on the increase in log one plus the number of mortgages for an average census tract. The results are shown in Table??. In column (4), I find that a one percentage point increase in relative inflation spreads leads to a 0.175 increase in the log one plus the number of mortgages. The IV estimations are stronger than the OLS estimations in Section ??The estimated effect is economically large but still within the range of the literature’s estimations. For example [87] find a 1 pp increase in (birth cohort based) learning-from-experience inflation leads to a 35 percent increase in household mortgage borrowing. Table?? shows the effect on home ownership using the same instrumental variable design. I find that a one percentage point increase in relative inflation spreads leads to an increase in the home ownership 23 by nine percentage points. Similar to the findings on mortgage borrowing, the IV estimations are stronger than the OLS estimations in Section??. 1.5.2 ChineseYuanExchangeRateReform: AQuasiNaturalExperiment To further address other identification concerns, I exploit an unexpected reform of the Chinese exchange rate system in 2005, which led to an instant and persistent RMB appreciation against USD. I find that the unexpected RMB appreciation is associated with a widened gap in both realized inflation and infla- tion expectations between low and high income US households. Moreover, there is no effect on income expectation and employment expectations. Consistent with previous findings, I document that housing investments by low income households increased after the RMB reform. 1.5.2.1 RMBExchangeRateReformonJuly212005 From 1997 to 2005, the Chinese government maintained a peg of 8.27 RMB per USD. On 21 July 2005, China lifted the peg and moved to a managed float exchange rate system against a basket of major currencies. RMB immediately appreciated by 2.1% against USD within one day, and further appreciated by nearly 20% against USD by July 2008 (Figure ??). [52] show that the market was surprised by the reform. RMB suddenly appreciated against USD in both spot and forward markets. Analysts at Citigroup wrote, “The Chinese authorities had always said that they would make an announcement when no one was expecting it. In this regard, they have chosen well." ¶¶ Given the role of China as one of the largest US trading partners, the following RMB appreciation triggered many worries about high inflation in the US (Online Appendix: ??). 24 Figure 1.4: Chinese Yuan Exchange Rate Reform and US Realized Inflation Heterogeneity Figure?? plots the average month-to-month relative non-food inflation spreads by income quintiles. Figure ?? shows the widening inflation gap is statistically significant between the bottom income quintile and the top income quintile households. I regress the realized non-food inflation spreads π i,t of householdi on the interaction of income quintile dummies and a post dummy variable indicating the RMB reform on July 21, 2005. MSA-year-month fixed effects, household fixed effects, and income quintile by year fixed effects are included. -.5 0 .5 1 Relative Inflation Spread 2005m4 2005m7 2005m10 2006m1 2006m4 Year Bottom 20% Second 20% Third 20% Fourth 20% Top 20% (a) (a) Non-Food Goods Relative Inflation Spreads (b) (b) Difference Relative to the Top 20% Income Quintile 25 1.5.2.2 ChineseYuanReformandtheUSRealizedInflationHeterogeneity Based on the same arguments as in Section??, I expect the reform to have a greater impact on the inflation of lower income US households. Data suggest that the realized non-food inflation spreads of lower income US households rose after the Chinese Yuan reform. I use the Nielsen Consumer Panel data to estimate household level realized inflation, focusing on non-food retail products, for example general merchandise and health&beauty care, which are much more likely to be imported from China. Figure?? plots the time series of average realized non-food relative inflation spreads for each income quintile. To test whether the widened inflation heterogeneity is statistically significant, I regress the real- ized month-to-month relative inflation spreads on the interaction of income quintile dummies and a post dummy variable equal one after the RMB reform on July 21 2005. π i,j,m,t =α +β · Post t · Quintile i,j +h i +ψ m,t +η j,t +ϵ i,j,m,t , wherei indexes household,j income quintile,m metropolitan area, andt the year. To control for macro and local economy variations, I includeψ m,t MSA-year-month fixed effects. As a result, I compare the realized inflation changes of other income groups with the top income quintile within the same metropolitan area. I also control for h i household fixed effects and η j,t income quintile by year fixed effects. The results are presented in Figure ??, which shows that the bottom income quintile households experienced higher realized inflation for their non-food consumption baskets after the RMB reform on July 21 2005. The results are consistent with [32], who find that lower income Mexican households experienced higher inflation after Mexico’s currency devaluation. ¶¶ “Washington, Wall Street React to Chinese Yuan Revaluation," Wall Street Journal, July 21 2005. 26 1.5.2.3 RMBReformandtheUSInflationExpectationHeterogeneity Consistent with larger realized inflation spreads, I also find that the bottom income quintile US house- holds disproportionally increased their inflation expectation at the same time, using disaggregated monthly household interviews on inflation expectation from Michigan Surveys of Consumers from 2003 to 2007. Expectation i,m,t =β · Bottom i,m,t · Reform t +γ · X i,m,t +η · Z i,m,t +ψ m,t +ϵ i,m,t , where Expectation i,m,t is the inflation or income or employment expectation of survey participant i in year-montht at regionm, the dummy variable Bottom i,t equals one if the survey participant belongs to the bottom quintile, and Reform t is a dummy variable equal to one ift is after July 21, 2005.X i,m,t are the participants’ demographic characteristics, including income, gender fixed effects, education fixed effects, age fixed effects, and birth year fixed effects to account for potential cohort effects (i.e. [87]). Moreover, I also control forZ i,m,t , which are participants’ expectations of future income, unemployment, interest rate, and aggregate economy to make sure other expectations do not drive the result. ψ m,t are the region by year by month fixed effects to absorb any aggregate and local economy variations. The results are reported in Table ??. The bottom income quintile households had both higher 1-year and 5-year forward inflation expectations. However, this is no difference in income expectation, as shown in Columns (5)-(6), nor in other in macro economy expectations such as gas price, unemployment rate, and economy condition, as shown in Table??. The heterogeneity in inflation expectation responses to the RMB reform does not mean or require households to directly learn macro-economy news and update their beliefs accordingly. Instead, households can update their inflation expectation from their daily experience, such as grocery shopping, as shown by [36]. 27 Figure 1.5: Chinese Yuan Exchange Rate Reform and US Household Expectation Figures (a)-(d) plot differences in expectations for inflation, income, and unemployment between the bottom income quintile households and other households around the Chinese Yuan reform on July 21 2005. The exact specification is as follows: Expectation i,m,t =β · Bottom i,m,t · Reform t +γ · X i,m,t +η · Z i,m,t +ψ m,t +ϵ i,m,t , where Expectation i,m,t is the inflation, income, or employment expectation of survey participant i in year-month t at region m. Reform t is a dummy variable and equals one if year-month t is after the RMB Reform on July 21 2005. Bottom i,m,t equals one if the participanti belongs to the bottom income quintile. X i,m,t are the participant’s demographic characteristics, including income, gender fixed effects, education fixed effects, age fixed effects, and birth year fixed effects. ψ i,m,t are the region by year by month fixed effects to absorb any aggregate and local economy variations. Standard errors double clustered at the year-month level and birth year level. (a) (a) 1 Year Forward Inflation Expectation (b) (b) 5 Year Forward Inflation Expectation (c) (c) 1 Year Forward Income Expectation (d) (d) 1 Year Forward Unemployment Expec- tation 28 1.5.2.4 ChineseYuanReformandUSHousingTransactions Given that the RMB reform happened as a surprise to the market and created heterogeneous impacts on both inflation expectation and realized inflation of US households across income groups, I can use a stan- dard difference-in-differences approach to estimate its effect on household mortgage borrowing. Bottom income quintile households are regarded as the treated group, as the data suggest that the associated rise in both realized inflation spreads and inflation expectation spreads were strongest for them. Figure 1.6: Housing Transactions around the Chinese Yuan Reform This figure shows the estimated coefficients from the following regression at the monthly level. ln(Num z,k,j,t +1)=β · Bottom z · Reform t +γ · X z,k,j,t +ψ k,t +η z,t +ξ z,t +ϵ z,k,j,t whereNum z,k,j,t is the number of mortgages originated at zip codez in year-montht. Bottom z is a dummy variable and equals one if zip codez belongs to the bottom income quintile. Reform t is also a dummy variable and equals one if year-montht is after the RMB Reform in July 2005.ψ k,t are the county by year by month fixed effects, η z,t are the zip code by year fixed effects, and ξ z,t are the zip code by month fixed effects. X z,k,j,t are other control variables, including last month’s home value at the zip code and month-to-month local home value appreciation. Using county- by-year-by-month fixed effects, I can tightly control for any county-level time-varying macroeconomic variations. With zip code by year fixed effects, I can control for the long-run variations at the zip code level associated with the housing market boom and bust between 2003 and 2007. The zip code-by-month fixed effects are further used to control for seasonality variations in the zip code level housing markets. The sample period is from 2003 to 2007. Standard errors clustered at the county level and income quintile by year level . 29 Instead of using the annual data from HMDA and ACS, I use high-frequency real estate transactions data from ZTRAX. The relative higher frequency with monthly data can overcome the potential contami- nation because of the 2008-2009 financial crisis if using annual frequency data. ln(Num z,k,j,t +1)=β · Bottom z · Reform t +γ · X z,k,j,t +ψ k,t +η z,t +ξ z,t +ϵ z,k,j,t where Num z,k,j,t is the number of mortgage based housing transactions at zip code z in year-month t. Bottom z is a dummy variable and equals one if zip codez belongs to the bottom income quintile. Reform t is also a dummy variable and equals one if year-month t is after the RMB Reform in July 2005. ψ k,t are the county by year by month fixed effects, η z,t are the zip code by year fixed effects, ξ z,t are the zip code by month fixed effects. X z,k,j,t are other control variables, including last month’s home value at the zip code and month-to-month local home value appreciation. With county-by-year-by-month fixed effects, I can tightly control for any county-level time-varying macroeconomic variations. With zip code by year fixed effects, I can control for the long-run variations at the zip code level associated with the housing market boom and bust between 2003 and 2007. The zip code-by-month fixed effects are further used to control seasonality variations in the zip code level housing markets. The sample period is from 2003 to 2007, including two years before the RMB reform and two years after. The results are shown in Table?? and Figure??. Consistent with all previous findings, after the RMB reform in July 2005, the bottom income quintile households started to increase housing investments com- pared to the other households in the same county in the same year-month. Given the high frequency nature of this empirical design, the increase in mortgage borrowing can be interpreted as causally driven by the RMB reform and following widened inflation heterogeneity. I also control for the share of private labeled securitization (PLS) mortgages among all mortgages and the share of mortgages with misreported owner occupancy and second lien among all PLS mortgages, at the zip code by year-month level. The results are 30 robust to the additional controls, which suggests that the estimation is not driven by the subprime bubble documented by [89] and [61]. To isolate from the effect of Hurricane Katrina in August 2005, I exclude southern states including Mississippi, Louisiana, and Florida from the sample. 1.6 ModelandCounterfactualAnalyses As shown in previous sections, households respond to inflation heterogeneity by relocating their portfolios between the centralized mortgage market and segmented housing markets. In this section, I explore the theoretical implications of the systematic inflation heterogeneity across income groups on asset prices, the cross-sectional housing dispersion, and household welfare in a general equilibrium framework by comparing them to that of a counterfactual world without inflation heterogeneity. 1.6.1 Environment Consider an overlapping-generation endowment economy withJ (J = 2, low and high income) groups of households who live in I (I = 2, low and high income) islands with fixed housing supplies. Each group has a continuum of households with a measure of one. Each household lives for three equally long periods (young, middle age, and retirement), and receives a deterministic life stage labor income process with idiosyncratic shocks. The economy exhibits three financial markets: one centralized bond market, one segmented housing market in the low income island, and one segmented housing market in the high income island. All house- holds can save via the centralized bond market with a nominal risk-free interest rateR f,t . Meanwhile, only homeowners can borrow with the same nominal interest rate using their houses as collateral but be sub- jective to a maximum loan-to-value ratioη . Uncollateralized borrowing is not allowed. I assume there are two separate housing markets for low income households and high income households, based on the doc- umented increasing geographic income segregation (i.e., [101], [62], and [85]). To reproduce the realistic 31 mixture of households’ incomes and their housing locations, the two housing markets are not completely segmented. A small proportion of low income households can live in the high income island, and vice versa. Letλ j,i to be the fraction of households in groupj that lives in islandi, with P i∈I λ j,i = 1. In the background, there are competitive financial institutions who hold residential rental capital, as in [73]. The rental rate is determined by the competitive financial institutions such that it covers the interest payments, depreciation, and taxes, r i,t =P i,t · (R f,t +δ +τ − 1), wherer i,t is the rental price at islandi and timet,P i,t is the house price,δ is the depreciation rateδ , and τ is the property tax rateτ . 1.6.1.1 Household’sProblem At timet, a household in income groupj at agen receives nominal labor incomew j,t,n =w j · α n · ϵ j,t,n , wherew j is the average income for groupj,α n is the life stage labor efficiency to capture a deterministic life cycle income process, and e j,t,n represents the idiosyncratic stochastic shock to labor income every period. ∗∗∗ Households consumes retail goodsc and housing serviceh, and the utility from a bundle of{c,h} is ††† u(c,h)= c θ · h 1− θ 1− γ 1− γ . Households in groupj at agen have a specific basket of retail goods that they would like to consume. The nominal price of such basket isp j,n , which follows an exogenous relative inflation spread π j . To keep ∗∗∗ I assume that the nominal income growth process is uncorrelated with the relative inflation spread process. This assumption is consistent with the empirically near-zero correlation between group-income-growth-spread and relative inflation spread, as shown in the Online Appendix Section??. ††† I assume Cobb-Douglas utility function because households spend a relatively stable share of the nominal budget on housing services, as shown by [38] and [50]. 32 the economy stationary, the price of basket for each newly born generation is set to be p j,0 = 1. The national average inflation is assumed to be zero. Households maximize expected utility. At the young stage, household j in island i born at time t saves s j,i,t,0 via the centralized bond market. In addition, the household chooses a rental house with size h j,i,t,0 to live for the young stage. The household also needs to choose to rent or buy a house with size h j,i,t+1,1 = h j,i,t+2,2 in the local housing market to live for the coming middle age and retirement stages. This assumption is made to reduce the dimension of policy space and features the illiquidity of the housing market. Ifh j,i,t+1,1 is below a thresholdh min , the household must rent the property. Ifh j,i,t+1,1 is above the thresholdh min , the household must buy the property and become homeowners. Conditional on owning the property, the household is allowed to use it as collateral and borrow a mortgage from the centralized bond market with the nominal interest rate of R f,t but subject to a maximum loan-to-value ratioη . So, in the young stage, the household solves max s j,i,t,0 , h j,i,t,0 , h j,i,t+1,1 V j,i,t,0 =u(c j,i,t,0 ,h j,i,t,0 )+β · V j,i,t+1,1 (s j,i,t,0 ,h j,i,t+1,1 ) subject to the budget constraints c j,i,t,0 +r i,t · h j,i,t,0 =w j,i,t,0 − s j,i,t,0 − h j,i,t+1,1 · P i,t · 1(h j,i,t+1,1 ≥ h min ), 0≤ s j,i,t,0 +h j,i,t+1,1 · P i,t · η · 1(h j,i,t+1,1 ≥ h min ), where1(h j,i,t+1,1 ≥ h min ) is the indicator function for home owners. At the middle age stage, the household enjoys a housing service flow h j,i,t+1,1 based on the rental contract or home purchase contract she signed when young. Based on the nominal savings or borrowings 33 carried from the young stage and her realized labor income, the household chooses her savings or borrow- ingss j,i,t+1,1 for the retirement stage and her retail good consumption, whose price grows by an inflation rate ofπ j . The household solves max s j,i,t,1 V j,i,t+1,1 =u(c j,i,t+1,1 ,h j,i,t+1,1 )+β · V j,i,t+2,2 (s j,i,t+1,1 ,h j,i,t+1,1 ) subject to the budget constraints e π j · c j,i,t+1,1 +s j,i,t+1,1 +h j,i,t+1,1 · r i,t+1 · 1(h j,i,t+1,1 <h min ) =w j,i,t+1,1 +s j,i,t,0 · R f,t − h j,i,t+1,1 · P i,t+1 · (τ +δ )· 1(h j,i,t+1,1 ≥ h min ), 0≤ s j,i,t+1,1 +h j,i,t+1,1 · P i,t+1 · η · 1(h j,i,t+1,1 ≥ h min ), whereh j,i,t+1,1 · P i,t+1 · (τ +δ ) captures the cost of house depreciation and property tax as a home owner. At the retirement stage, the household does not make any active decisions. The household still enjoys the housing service flow h j,i,t+1,1 based on the rental contract or home purchase contract she signed when young. At the same time, the household spends on retail good consumption, whose price grows by an inflation rate of π j , financed by her realized labor income and all savings carried from the middle age stage including the home value. V j,i,t+2,2 =u(c j,i,t+2,2 ,h j,i,t+2,2 ) 34 subject to the budget constraints e 2·π j · c j,i,t+2,2 +h j,i,t+2,2 · r i,t+2 · 1(h j,i,t+2,2 <h min ) =w j,i,t+2,2 +s j,i,t+1,1 · R f,t+1 +h j,i,t+2,2 · P i,t+2 · (1− τ +δ )· 1(h j,i,t+2,2 ≥ h min ), h j,i,t+2,2 =h j,i,t+1,1 , 1.6.1.2 GeneralEquilibrium In equilibrium, given the prices{P i,t ,R f,t } and the distribution of idiosyncratic i.i.d. income shockϵ j,i,t,n , households in groupj on islandi solve their problems by choosing quantities{h j,i,t,0 ,h j,i,t,1 ,s j,i,t,0 ,s j,i,t,1 }. House priceP i,t adjusts to clear the housing market in islandi with fixed supplies: X j λ j,i · Z ϵ h j,i,t,0 (ϵ )+ Z ϵ h j,i,t,1 (ϵ )+ Z ϵ h j,i,t,2 (ϵ ) =H i The national risk free rate adjusts to clear the centralized bond (mortgage) market with the net supply of 0: X i X j λ j,i · Z ϵ s j,i,t,1 (ϵ )+ Z ϵ s j,i,t,2 (ϵ ) =0 1.6.2 CalibrationandNumericalResults For tractability, I assume the number of income groups J = 2 and the number of islands I = 2. There are a high income group and low income group in the economy as well as a high income island and a low income island. Households live through three life stages (young, middle age, retirement). They work during the first two life stages, representing ages 21–60, and are retired in the last life stage, representing ages 60–80. Each time period is selected as 20 years. 35 Table 1.2: Calibration of the Baseline Scenario High Income Low Income Source Literature Data Number of groupsJ: 2 ✓ Coefficient of relative risk aversion γ : 5 ✓ Discount factorβ : 0.96 ✓ Housing share in utilityθ j : 0.34 ✓ Relative Inflation Spread π j : -0.3pp 0.3pp ✓ Endowmentw j : 60,000 30,000 ✓ Population distributionλ j,− j : 0.2 ✓ Life-stage efficiency profile: 0.75, 1.31, 0.4 ✓ Idiosyncratic income volatilityσ 2 : 0.01 ✓ Housing depreciation rateδ : 0.02 ✓ Property tax rateτ : 0.01 ✓ Maximum loan-to-valueη : 0.8 ✓ Table?? summarizes the parameters used in calibration. Following [73], I assume 1) the subjective time discount factor,β , to be 0.96; 2) the relative risk aversion,γ , is 5; 3) the relative weight of housing in the utility function,θ , to be 0.33; 3) a maximum loan-to-value (LTV),η , at 80 percent; 4) a property tax rate, τ , at 1 percent; 5) a housing depreciation rate, δ , at 2 percent; 6) the life stage working efficiency, α n , to be 0.75 for the young period, 1.31, for the middle age, and 0.4 for the retirement age; and 7) idiosyncratic income volatilityσ 2 ϵ = 0.01. The total supplies of housing are 1 in both islands, with the average house size at 0.33. The minimal owner-occupied house size ish min = 0.3, which is around 90% of the average house size, as in [73]. The average annual incomes are calibrated to match the median annual income of the top 50% and bottom 50% income US households respectively. The share of low income households who live in the high income island is estimated based on the 2005 IRS tax return data. I setλ j,− j = 0.2, which implies that 80% of low income households live in the low income island and 20% of them live in the high income island, and the distribution is symmetric for high income households. To solve the model, I first numerically search the optimal savings decision for middle age households of groupi in timet, given their state variables including nominal savingss j,i,t+1,1 , housingh j,i,t+1,1 , income shocks ϵ j,i,t+1,1 , house price P i,t+1 , and national interest rate R f,t+1 . Then I use backward induction to 36 solve the optimal savingss j,i,t,0 and housing decisionsh j,i,t,0 for the young households, given state vari- ables including income shocksϵ j,i,t,0 , house priceP i,t , and national interest rateR f,t . Lastly, I numerically search in the price space{P j,t ,R f,t } until both the housing markets and the centralized bond market are cleared. Table 1.3: Moments from the Data and the Model This table compares moments estimated from the data and moments generated by the model. The fraction of homeowners and home value to income ratio are estimated using American Community Survey for both the low income group and high income group. The relative home size as percentages of the national average house size is estimated from US Census Bureau, American Housing Survey 2013. The real interest rate is the average difference between the nominal 30-year-fixed mortgage rate in the United States from Freddie Mac and the consumer prices inflation, from 2005 to 2019. The response in mortgage and & housing, rent, and house price to a 1 percentage point increase in relative inflation spreads π j is from the instrumental variable estimations. Data Model Home Ownership (High Income) 82% 79% Home Ownership (Low Income) 53% 49% Home Value to Income Ratio (High Income) 3.0 4.3 Home Value to Income Ratio (Low Income) 8.0 7.0 Home Size (High Income) 129% 121% Home Size (Low Income) 79% 80% Real Interest Rate 2.68% 2.23% Response in Mortgage & Housing per 1pp Increase inπ j Home Ownership 9.1 9.3 Response in Prices per 1pp Increase inπ j Rent 12.2 4.0 House Price 6.6 The model can generate comparable moments as what are estimated from the data. First, in the data, the fraction of homeowners from the American Community Survey is 82% for high income households and 53% for low income households. The model delivers very similar numbers, which are 79% and 49%, respectively. ‡‡‡ Second, the average home value to income ratio from the American Community Survey is 3.0 for high income households and 8.0 for low income households, which are 4.3 and 7.0 in the model, respectively. Third, the average house size as the percentages of the national average house size from the American Housing Survey is 129% for high income households and 79% for low income households, which ‡‡‡ In the simulated economy, I classify all households who consume a house size larger than the minimal owner house size as a home owner, regardless of their age. 37 are 121% and 80% in the model. Lastly, the real interest rate during the sample period of 2005 to 2019 is 2.68 pps, measured as the real 30-year-fixed rate mortgage average in the United States. The equilibrium interest rate in the model is 2.23 pps. 1.6.3 ComparativeStatics Figure 1.7: Heterogeneous Inflation and Household Portfolios The figures present the steady states for economies with different inflation heterogeneity scenarios. Figures (a) and (b) plot the differences in housing size choices and home ownership choices of low income households compared to high income households. Figure (c) shows the differences in house prices between the low income island and the high income island. Figure (d) shows the national equilibrium interest rate. The x-axes of all subplots are relative inflation spreads of low income households (thus -1× relative inflation spreads of high income households) in percentage points between -0.5pp and 0.5pp. The y-axes are also in percentage points. The general equilibrium model allows me to study counter-factual scenarios, comparing the baseline calibration to a world with no inflation heterogeneity across income groups. Figure ?? shows how the equi- librium household housing decisions and asset prices change with the inflation heterogeneity. Consistent with the empirical findings, households increase their investments in the housing assets, and consequently 38 home ownership. Intuitively, when relative inflation spreads increases, the real values of income and sav- ings in the future periods decrease. With the elasticity of intertemporal substitution 1 γ < 1, households would like to save more in nominal terms to smooth real consumption in future periods. But the real re- turn from the centralized bond market decreases because of the high relative inflation spreads. As a result, households moves their savings towards segmented housing assets, whose real returns are not directly affected by inflation heterogeneity. Notably, the instrumental variable estimations show that households increase home ownership by 9 percentage points in response to a one percentage point increase in the relative inflation spread. House- holds in the model show a sensitivity of 9.3 percent, which is covered by the empirically estimated range. 1.6.4 InflationHeterogeneityandAssetPrices The model suggests that inflation heterogeneity across income groups affect not only segment house prices and rent but also national interest rates. First of all, when the relative inflation spread π j rises, Figure?? (c) shows that the segment house price and rent increase, as households prefer to invest more in the segmented housing market, in which the housing supply is inelastic. Consistent with the model’s prediction, Table ?? further demonstrates that higher relative inflation spreads indeed lead to higher rent and house prices. Using the ACS data and the same empirical design as in Section??, I find that rent (house prices) increases by 12 percent (7 percent) in response to a one percentage point increase in the relative inflation spread. For comparison, the model predicts an increase by 4 percent. Furthermore, Figure?? (d) suggests that the national interest rate is higher in the scenario with inflation heterogeneity across income groups, compared to a counterfactual scenario without inflation heterogene- ity. If the relative inflation spread of the lower income households rises by 1pp from -0.5pp to 0.5pp, the national equilibrium interest rate will increase from 2.15pp to 2.25pp, by 5 percent. The resulting higher 39 Table 1.4: Inflation Heterogeneity and Rent and House Prices Price i,j,k,t =β · π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ i,j,k,t where Price i,j,k,t is the monthly rent or home value that householdi reports. π j,t is the relative inflation spread of the income quintilej that householdi belongs to in yeart. ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control interest rate term structure and national inflation rate and allow heterogeneous exposure to those variables across income groups. Columns (1) and (2) report the results from OLS, and columns (3) and (4) report the results from the 2SLS using RMB appreciation against US dollar as the instrument. The sample period is from 2005 to 2019. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) OLS OLS IV IV Rent Home Value Rent Home Value π j,t 0.0439*** 0.0285* 0.122*** 0.0661* (0.0118) (0.0157) (0.0257) (0.0391) 1-Year Housing Ret -0.00424 0.102*** -0.00369 0.102*** (0.00482) (0.0155) (0.00484) (0.0154) 1-Year Rent Growth 0.0392** -0.0717*** 0.0389** -0.0716*** (0.0166) (0.0161) (0.0169) (0.0160) Observations 2,722,445 5,995,590 2,722,445 5,995,590 R-squared 0.446 0.456 0.446 0.456 Inflation Exposure Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 40 interest rate can be explained by the sharp increase in mortgage borrowing demand from lower income households who choose to become homeowners because of higher relative inflation spreads. 1.6.5 InflationHeterogeneityandtheCross-sectionalHomeOwnership The model can also offer an estimation of how much of the cross-sectional home ownership dispersion can be contributed to or attenuated by the inflation heterogeneity across income groups under the model’s assumptions. The model suggests that the cross-sectional difference in home ownership by income groups is reduced by 33% compared to the difference in data, as higher relative inflation spreads encourage low income house- holds to hold more real estate. Meanwhile, the cross-sectional difference in owner-occupied house size by income groups is reduced by 49 percent compared to the difference in data, as low income households tend to buy bigger houses as well. Table ?? shows the average home ownership, owner-occupied house size, and renter-occupied house size by income groups under two scenarios with and without inflation heterogeneity across income. The reported house size is in the percentages of the average house size in the economy. However, the model also suggests that the increase in home ownership creates a thicker left tail distri- bution of housing consumption within the low income households. Renters with the bottom realized labor income are constrained by the minimal owner house size. Even if they want to, they can not afford the down payment, purchase a house, and save for future consumption. In fact, their housing consumption is crowded out by the higher house price, given that housing supply is inelastic. The 5th percentile of house size consumed within the low income group drops by 9.3 percent from 54% of the average house size to 50% of the average house size. Figure?? further demonstrates the increase in home ownership and the crowding out within the low income group when relative inflation spreads rise, by plotting the distributions of house size choices for 41 low income households in the low income island, low income households in the high income island, high income households in the low income island, high income households in the high income island. Figures (a) and (b) plot the scenarios with and without inflation heterogeneity across income distribution respec- tively. The red line indicates the minimal size of an owner occupied house. Compared to the no inflation heterogeneity counterfactual world, the share of homeowners increases for both low income households living in the low income island and low income households living in the high income island. At the same time, however, the fractions of low income renters living in a smaller house increase in both islands. Con- sistent with this crowding out within the group, the standard deviation of house size distribution for low income households increases from 16% to 21%. Empirical results also support the model’s predictions, as shown in Table ??. I find that, within an income group, the effects of relative inflation spreads on home ownership are much weaker for relatively lower income and young households. Within a group, relatively lower income and young households are more likely to be renters and can not afford the down payment of buying a house. In fact, a rise in relative inflation spreads reduces the home ownership of young and relatively lower income households within the group. Table 1.5: Inflation Heterogeneity and Cross-sectional Housing Consumption This table shows the average home ownership, owner-occupied house size, and renter-occupied house size by income groups under two scenarios with and without inflation heterogeneity across income. House size is in the percentages of the average house size in the economy. Model Data Inflation Heterogeneity Scenario Yes No Income Group Low High Low High Low High Home Ownership (%) 53 82 49 78 38 78 Owner House Size (%) 107 142 113 133 99 136 Renter House Size (%) 60 75 60 68 66 63 SD of House Size (Within, %) 21 28 16 28 5th Percentile House Size (Within, %) 50 77 54 79 42 Figure 1.8: House Size Choices The figures present the distributions of house size choices for low income households in the low income island, low income households in the high income island, high income households in the low income island, high income households in the high income island. Figures (a) and (b) plot the scenarios with and without inflation heterogeneity across income distribution respectively. The red line indicates the minimal size of an owner occupied house. (a) (a) With Inflation Heterogeneity (b) (b) Without Inflation Heterogeneity 43 1.6.6 TheCross-sectionalDispersioninWelfare Meanwhile, despite reducing the cross-sectional dispersion in home ownership, inflation heterogeneity increases the dispersion in welfare across income groups. Although being able to mitigate higher relative inflation spreads by using housing assets, welfare calculation suggests that households in the low income group unconditionally are worse off. First of all, low income households experience a drop in real labor income as a result of inflation heterogeneity. Second, even if owning a house, they need to pay a higher mortgage interest rate, and meanwhile, the nominal market value of rent rises less than one to one to their relative inflation, which means a lower real return even from the housing market, also as a result of inflation heterogeneity. Table?? compares households under two inflation heterogeneity scenarios. In the first scenario, rela- tive inflation spreads are zero for both high income households and low income households. In the second scenario, the relative inflation spread is 0.3pp for low income groups and -0.3pp for high income house- holds. I classify households into eight types based on their income groups and home ownership choices under the two inflation heterogeneity scenarios. The simulated economy includes 50% of high income households and 50% of low income households. Of the 50% low income households, 28.6% are always homeowners in both scenarios, 11.3% switch from renters to owners when relative inflation spreads rise, 10.1% of them remain renters, and none of them switch from renters to owners, which features their desire to invest in housing assets. All of the three types of low income households have lower expected utility in the scenario with inflation heterogeneity than in the scenario without inflation heterogeneity. Quantita- tively, low income households are worse off by the magnitude as if their consumption were reduced by 5%. Notably, the differences in equivalent consumption changes reported in Table ?? shall not be interpreted as the differences caused only by home ownership status. The three types of households are intrinsically not directly comparable, as they have different realized labor income, levels of wealth, and portfolios of 44 savings. Moreover, as shown in Table?? with in greater detail, they also tend to live in different locations (i.e., islands in the model), where housing prices are different. Table 1.6: Welfare Analysis by Household Types This table shows the distribution of households based on their home ownership status under two inflation heterogeneity scenarios. In the first scenario, relative inflation spreads are zero for both high income households and low income households. In the second scenario, the relative inflation spread is 0.3pp for low income groups and -0.3pp for high income households. Numbers reported in the fourth column are percentages of each type of households in the economy. Column 5 describes the equivalent consumption changes for each group if the economy moves from the first scenario without inflation heterogeneity to the second scenario with inflation heterogeneity. Homeowner Status in Inflation Heterogeneity Scenarios Income Group No Yes % in Population Equivalent Consumption Changes High Owner Owner 43.6 5.5% Owner Renter 4.5 6.0% Renter Owner 0 - Renter Renter 1.9 5.8% Low Owner Owner 28.6 -5.9% Owner Renter 0 - Renter Owner 11.3 -4.7% Renter Renter 10.1 -4.4% 1.7 Conclusion When group-specific inflation rises (relative to the national average), I find households increase borrow- ing from the centralized and standardized mortgage market and holdings of real and segmented housing assets. The same pattern holds if I use the Chinese Yuan to US Dollar exchange rate as exogenous shocks to relative inflation spreads for US households across income groups, leveraging that low-income house- holds consume more tradable goods in their baskets. The increase in mortgage borrowing and housing investment can be explained by that households relocate their savings to markets in which real returns are protected from relative inflation. A calibrated general equilibrium model suggests a smaller disper- sion in home ownership between income groups but a greater dispersion in welfare as a result of inflation heterogeneity. 45 Two interesting potential extensions are worth exploring. First, As households increase housing in- vestments to mitigate higher relative inflation, their portfolios become more fragile toward adverse shocks from the housing markets. Second, the geographic inflation heterogeneity across metropolitan areas is an even more salient phenomenon. Figure ?? shows that, since the 2000s, the accumulated inflation in San Francisco is 67 percentage points, while in Detroit is only 40 percentage points. Future studies can explore the geographic inflation heterogeneity and its interaction with the financial markets. 46 1.8 Appendix: IncomeGrowthSpreadsandInflationSpreads It is important to understand the correlation between inflation heterogeneity and nominal income growth heterogeneity. If the correlation is positive and close to one, inflation heterogeneity does not affect real income growth heterogeneity. If the correlation is small or close to zero, inflation heterogeneity also implies heterogeneity in real income growth rates. Figure?? suggests a small and negative correlation between relative nominal income growth spreads and relative inflation spreads, which means inflation heterogeneity is not offset by nominal income growth heterogeneity. To estimate annual relative spreads of nominal income growth for a given income quin- tile (compared to the national average), I use the Annual Social and Economic Supplement (ASES) of the Current Population Survey. ASES tracks the same households across two years, which allows me to first estimate the nominal income growth rate for a household and take the average for households within the same income quintile. To remove outliers, the sample is restricted between the 1st and 99th percentiles. Then I calculate the relative spreads of nominal income growth as the deviation from the national average nominal income growth in the same year. 47 1.9 Appendix: IncomeorInflation? ATradeExposureChannel The exclusion restriction for instruments could be violated if RMB appreciation affects not only inflation heterogeneity but also income heterogeneity between lower income households and higher income house- holds. If lower income households are more likely to work in industries with higher China trade exposure, such as manufacturing industries, RMB appreciation can potentially hurt the competitiveness of Chinese factories and benefit US firms as well as lower income households by improving their employment opportu- nities and incomes. The improved economic status can encourage home buying and mortgage borrowing, which could potentially explain the documented empirically in the previous sections. Although the above hypothesis sounds plausible, many will disagree. Notably, Alan Greenspan, the then chairman of the US Federal Reserve, said, “U.S. workers would not benefit from reduced Chinese competitiveness" and "Goods that were suddenly to become too expensive to import from China would then be imported from Malaysia, Indonesia, Bangladesh, or whoever is the next cheapest maker. South Carolina would definitely not be the next cheaper supplier of textiles..." §§§ One way to test this trade-income channel hypothesis is to check whether the effect of relative inflation spreads on mortgage borrowing is particularly stronger in counties with greater China trade exposure. Following [37] and their shared data from the authors’ website, I construct a measure of county-level employment exposure to China based on county-level employment compositions by industry as well as each industry’s exposure to Chinese competitions. Suppose RMB appreciation affects mortgage borrowing through the income channel. In that case, the effect should be stronger in counties with greater China trade exposure because their employment opportunities might be improved the most once local industries regain competitiveness thanks to the RMB appreciation and higher cost of importing from China. In the following test, I run the 2SLS IV regressions on the subsample with low China trade exposure counties and the subsample with high China trade exposure counties. §§§ "Greenspan’s Yuan Policy", the Wall Street Journal, May 23, 2005 48 Overall, the results do not support the hypothesis that RMB appreciation affects US household mort- gage borrowings through a trade-exposure-income channel. The results on mortgage borrowing with HMDA data are reported in Table??. Table?? shows the results on home ownership using ACS data. Con- sistent across various specification, the effects of relative inflation spreads on mortgage borrowing and home ownership are statistically significant in both low trade exposure and high trade exposure areas. If anything, the effect of the inflation heterogeneity seems to be slightly stronger in low China trade exposure counties, which is the opposite direction of the income hypothesis. 49 1.10 Appendix: ChineseYuanReformandtheUSInflation Right after the RMB reform on July 21, 2005, many practitioners in Wall Street believed RMB would con- tinue to appreciate. Jay Bryson, global economist for Wachovia Securities, “Will the yuan be 30 percent stronger vs. the dollar a year from now? I doubt that. Could it be 10 percent stronger? Yeah, that’s reasonable." ¶¶¶ How would the 2005 Chinese Yuan reform and the expectation of following RMB appreciation affect the inflation in the US? Allen Greenspan, then-chairman of Fed, expressed his concern about potential domestic inflation risk because of RMB appreciation. Mr. Greenspan said, “revaluation would amount to higher prices for consumers, as retailers passed the higher costs of Chines imports by raising prices," and “The effect will be a rise in domestic prices in the United States and, as a consequence of that, we will have other impacts." Consistent with the above concerns, Figure ?? shows that price indexes of imports from China start to increase after 2005 while they are previously decreasing before 2005. The response of US import price indexes to RMB appreciation is in line with the findings by [6]. ¶¶¶ “China Revalues Yuan", CNN, July 21, 2005. “Greenspan’s Yuan Policy", Wall Street Journal, May 23, 2005. 50 Figure 1.9: US Dollar to Chinese Yuan Exchange Rate Around July 21 2005 The blue line in figure (a) shows the daily exchange rate between US Dollar and the Chinese Yuan (RMB) between 2004 and 2006. Before July 21, 2005, RMB was pegged to USD with 8.27 RMB per USD. On 21 July, 2005, China lifted the peg and moved to a managed float exchange rate system against a basket of major currencies. RMB immediately appreciated by 2.1% against USD within one day. The orange line in figure (a) reports the daily Dollar Index. Figure (b) is from [52] and shows the spot and forward rates of USD/RMB around July 21, 2005. (a) (a) RMB Reform on July 21 2005 (2004 to 2006) (b) (b) Spot and Forward Rates of USD/RMB Source: [52] 51 Figure 1.10: Import Price Indexes from China by Product Categories Figure?? shows the price indexes of the top 10 product categories of US imports from China, based on disaggregated data from U.S. Import and Export Merchandise Trade Statistics following the methodology in [6]. The disaggregated US import data use a ten-digit classification of the Harmonized System and covers 12,499 product codes for goods imported from China, with monthly records of total value and unit price of each product code. The top 10 categories constitute about 80 percent of US total imports from China. 1.11 Appendix: FirstLienMortgageorHomeEquityLoan? In addition to home ownership, ACS asks households whether they have a first lien mortgage and whether they additionally have a home equity loan. Testing the response of mortgage borrowing on inflation het- erogeneity by lien types can further disentangle omitted contaminating factors that drive the overall mort- gage and housing market. The model in Section?? predicts that householdj will decrease savings in the national bond market to finance the investment in the housing market when relative inflation spreads rise. The prediction is consistent with taking a first lien mortgage to buy a house. However, the effect on a second lien loan or home equity loan is ambiguous. Because home equity loans not only can be used to buy real estate properties as first lien loans but also can be used to finance contemporaneous retail goods consumption ([1]), which means saving less, or to pay off standing debt ([41]), which means saving more in 52 the bond market. While as the model suggests, households will increase nominal savings via the housing market in total but borrow from the bond market when relative inflation spreads rise. Consistent with the model, Table ?? shows that relative inflation spreads π j are positively correlated with first-lien mortgage borrowing but negatively correlated with the second lien mortgage borrowing. A one percentage point increase in relative inflation spreads is associated with a four percentage point increase in having a first lien mortgage. The same pattern holds using the subsample starting from 2010. Figure 1.11: Inflation Heterogeneity and Inflation Expectation Heterogeneity Figure (a) reports the smoothed monthly average one-year forward inflation expectation by household income groups based on Michigan Surveys of Consumers. Figure (b) replicates the main finding from [76] and reports the average annual inflation rate across income groups using the Nielsen Consumer Panel data between 2005 and 2015. (a) (a) Inflation Expectation Heterogeneity (b) (b) Realized Inflation Heterogeneity 53 Figure 1.12: Inflation Heterogeneity and Mortgage Interest Rate Heterogeneity Figure (a) reports the correlation between relative inflation spreads and relative nominal mortgage interest rate spreads for each income quintile, using GSE conforming loan performance data. Both spreads are relative to the national average in the same year. Figure (b) reports the default risk adjusted nominal mortgage interest rate across income groups using GSE conforming loan performance data. Default risks are predicted following [72]. (a) (b) Nominal Mortgage Rate (Conforming Loans) (b) (b) Risk Adjusted Nominal Mortgage Rate (Conforming Loans) 54 Figure 1.13: The Distribution of Buyers’ Income Quintile and Locations’ Income Quintile This figure shows the percentage of mortgages borrowed by a household in income quintile i (left axis) to buy a property in a census tract that belongs to income quintilej (right axis) using mortgage level HMDA data between 2005 and 2017. 55 Figure 1.14: Household Portfolio by Income Quintiles Figure?? shows the percentages of each asset category in household balance sheets across income groups. Positive percentages represent net asset positions and negative percentages represent net liability positions. Percentages are calculated based on household net wealth. Data are from Survey of Consumer Finances. 56 Figure 1.15: Inflation Heterogeneity and Inflation Expectation Heterogeneity Figure (a) reports the share of homeowners across income groups, between 2005 and 2019. The y-axis is between 0 and 1. The x-axis is income quintile. Figure (b) reports the share of households having a mortgage conditional on being a home owner. (a) (a) Home Ownership across Income Quintiles (b) (b) Mortgage Status across Income Quintiles 57 Figure 1.16: Correlation Between Inflation Expectation Gap and Chinese Yuan Exchange Rate This figure reports the monthly 12-month Chinese Yuan (RMB) appreciation relative to the US Dollar and the differ- ence in the 3-month smoothed monthly 1-year forward inflation expectation between the bottom income quintile households and the top income quintile households based on the Michigan Survey of Consumers from 2005 through 2019. The correlation between RMB appreciation and the 1-year forward inflation expectation gap is 0.53. Table 1.7: The Distribution of Buyers’ Income Quintile and Locations’ Income Quintile This table reports that the percentage of mortgages in a census tract that belongs to income quintilej (columns) are taken by a buyer in income quintilei (rows), using mortgage-level HMDA data between 2005 and 2017. % Property Census Tract Income Quintile Buyer Income Quintile 1 2 3 4 5 1 65.93 45.18 15.84 7.98 2.69 2 17.39 28.69 38.85 13.45 6.02 3 8.83 13.53 26.18 30.63 10.79 4 5.00 8.27 12.30 35.52 23.68 5 2.85 4.33 6.83 12.41 56.81 Total 100 100 100 100 100 58 Figure 1.17: Accumulated Inflation by Metropolitan Areas Figure?? shows the accumulated increase in consumer price indexes since 2000 across major US metropolitan areas. The accumulated inflation in San Francisco increased by 67 percent, which in Detroit is only 40 percent. Data are from Bureau of Labor Statistics. 100.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 New York Atlanta Baltimore Boston Chicago Dallas Denver Detroit Houston Los Angeles Miami Minneapolis Philadelphia San Diego San Francisco Seattle St Louis Washington SanFransico=167 Detroit=140 Figure 1.18: Relative Inflation Spreads and Income Growth Spreads This figure reports the correlation between the relative nominal income growth spreads, estimated from the Annual Social and Economic Supplement (ASES) of the Current Population Survey, and relative inflation spreads, estimated from Nielsen Consumer Panel data, for US income quintiles between 2005 and 2019. 59 Table 1.8: Mortgage Borrowing and Inflation Heterogeneity ln(Num k,j,c,t +1)=β · π j,t +γ · X k,j,c,t +ψ c,t +η k +ϵ k,j,t where Num k,j,c,t is the number of mortgages originated at census tract k in year t. The average borrower in census tract k belongs to income quintilej in yeart.π j,t is the relative inflation spread of the income quintile j in yeart.ψ c,t are the county by year fixed effects, and η k are the census tract fixed effects. X k,j,c,t are other control variables of census tractk, including the log of median income, Zillow home value at the census tract, one-year local housing market return, 5-year housing market return, 1-year local rent growth, and local rent index. I also control for interest rate term structure and national inflation rate and allow heterogeneous sensitivity to those variables across income groups. The sample period is from 2005 to 2019. Column 5 has fewer observations because rent data have limited coverage. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) ln(Num + 1) π j,t 0.0709* 0.0840** 0.0615* 0.0933*** (0.0380) (0.0344) (0.0309) (0.0325) 1-Year Housing Ret 0.561*** 0.413*** 0.542*** (0.0947) (0.0740) (0.111) 5-Year Housing Ret -0.0106*** -0.00835*** -0.0117*** (0.00217) (0.00174) (0.00294) 1-Year Rent Growth 0.0864*** (0.0291) Observations 660,015 592,313 592,313 348,801 R-squared 0.897 0.899 0.903 0.912 Control Variables Yes Yes Yes Yes Inflation Exposure Yes Yes Interest Rate Curve Exposure Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 60 Table 1.9: Mortgage Borrowing and Inflation Heterogeneity: After the Financial Crisis ln(Num k,j,c,t +1)=β · π j,t +γ · X k,j,c,t +ψ c,t +η k +ϵ k,j,t where Num k,j,c,t is the number of mortgages originated at census tract k in year t. The average borrower in census tract k belongs to income quintilej in yeart. π j,t is the relative inflation spread of the income quintile j in yeart. ψ c,t are the county by year fixed effects, and η k are the census tract fixed effects. X k,j,c,t are other control variables of census tractk, including the log of median income, Zillow home value at the census tract, 1-year local housing market return, 5-year housing market return, 1-year local rent growth, and local rent index. I also control for interest rate term structure and national inflation rate and allow heterogeneous sensitivity to those variables across income groups. The sample period is from 2010 to 2019. Columns (2) and (5) have fewer observations because rent data have limited coverage. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) OLS OLS 2SLS 2SLS π j,t 0.0543** 0.0477* 0.103*** 0.113*** (0.0231) (0.0282) (0.0320) (0.0374) 1-Year Housing Ret 0.485*** 0.561*** 0.492*** 0.573*** (0.0704) (0.0769) (0.0699) (0.0759) 5-Year Housing Ret -0.00571*** -0.00751*** -0.00565*** -0.00739*** (0.00175) (0.00277) (0.00174) (0.00276) 1-Year Rent Growth 0.111*** 0.112*** (0.0306) (0.0307) Observations 413,315 255,640 413,315 255,640 R-squared 0.899 0.909 0.919 0.915 Inflation Exposure Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 61 Table 1.10: Mortgage Borrowing and Inflation Heterogeneity: Robustness of Inflation Definition ln(Num k,j,c,t +1)=β · π j,t +γ · X k,j,c,t +ψ c,t +η k +ϵ k,j,t where Num k,j,c,t is the number of mortgages originated at census tract k in year t. The average borrower in census tract k belongs to income quintilej in yeart. π j,t is the relative inflation spread of the income quintile j in yeart. ψ c,t are the county by year fixed effects, and η k are the census tract fixed effects. X k,j,c,t are other control variables of census tract k, including the log of median income, Zillow home value at the census tract, 1-year local housing market return, 5-year housing market return, 1-year local rent growth, and local rent index. I also control for interest rate term structure and national inflation rate and allow heterogeneous sensitivity to those variables across income groups. The sample period is from 2010 to 2019. Columns (1)-(5) compare the estimated coefficients of 5 versions of inflation index. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. ln(Num + 1) (1) (2) (3) (4) (5) Tornqvist Marshall Fisher Laspeyres Paasche π j,t 0.0935*** 0.0277** 0.0286** 0.0117 0.0387*** (0.0324) (0.0136) (0.0137) (0.00898) (0.0145) 1-Year Housing Ret 0.541*** 0.576*** 0.575*** 0.601*** 0.549*** (0.111) (0.112) (0.111) (0.113) (0.111) 5-Year Housing Ret -0.0117*** -0.0118*** -0.0118*** -0.0117*** -0.0119*** (0.00295) (0.00292) (0.00292) (0.00288) (0.00296) 1-Year Rent Growth 0.0874*** 0.0933*** 0.0933*** 0.0982*** 0.0907*** (0.0288) (0.0297) (0.0297) (0.0295) (0.0301) Observations 348,542 348,542 348,542 348,542 348,542 R-squared 0.897 0.897 0.897 0.897 0.897 Control Variables Yes Yes Yes Yes Yes Inflation Exposure Yes Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 62 Table 1.11: Home Ownership and Inflation Heterogeneity Home Ownership i,j,k,t =β · π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ k,t where Home Ownership i,j,k,t is a dummy variable that equals one if household i reports as a homeowner. π j,t is the relative inflation spread of the income quintile j that householdi belongs to in yeart.ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control interest rate term structure and national inflation rate and allow heterogeneous exposure to those variables across income groups. The sample period is from 2005 to 2019. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) Home Ownership π j,t 0.0270*** 0.0350*** 0.0334*** 0.0337*** (0.00646) (0.00633) (0.00703) (0.00706) 1-Year Housing Ret -0.0100 -0.00962 -0.00951 (0.00638) (0.00635) (0.00578) 1-Year Rent Growth -0.00497 (0.00884) Observations 9,677,676 8,872,562 8,872,562 8,833,397 R-squared 0.224 0.221 0.221 0.221 Control Variables Yes Yes Yes Yes Inflation Exposure Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 63 Table 1.12: Home Ownership and Inflation Heterogeneity: After the Financial Crisis Home Ownership i,j,k,t =β · π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ k,t where Home Ownership i,j,k,t is a dummy variable that equals one if household i reports as a homeowner. π j,t is the relative inflation spread of the income quintile j that householdi belongs to in yeart. ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control for interest rate term structure and national inflation rate and allow heterogeneous exposure to those variables across income groups. The sample period is from 2010 to 2019. Column 5 has fewer observations, because rent data have limited coverage. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. Home Ownership (1) (2) (3) (4) OLS OLS IV IV π j,t 0.0314*** 0.0317*** 0.0636*** 0.0639*** (0.00646) (0.00633) (0.00703) (0.00706) 1-Year Housing Ret -0.0101 -0.00975 -0.0101 -0.00977 (0.00834) (0.00737) (0.00830) (0.00734) 1-Year Rent Growth -0.00437 -0.00464 (0.00956) (0.00945) Observations 6,535,834 6,502,583 6,535,834 6,502,583 R-squared 0.218 0.218 0.218 0.218 Inflation Exposure Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 64 Table 1.13: Home Ownership and Inflation Heterogeneity: Robustness of Inflation Definition Home Ownership i,j,k,t =β · π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ k,t where Home Ownership i,j,k,t is a dummy variable that equals one if household i reports as a homeowner. π j,t is the relative inflation spread of the income quintile j that householdi belongs to in yeart. ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control for interest rate term structure and national inflation rate and allow heterogeneous exposure to those variables across income groups. The sample period is from 2010 to 2019. Columns (1)-(5) compare the estimated coefficients of 5 versions of inflation index. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. Home Ownership (1) (2) (3) (4) (5) Tornqvist Marshall Fisher Laspeyres Paasche π j,t 0.0337*** 0.0118*** 0.0118*** 0.0101*** 0.00624 (0.00706) (0.00331) (0.00333) (0.00277) (0.00403) 1-Year Housing Ret -0.00951 -0.0100* -0.0100* -0.00960 -0.0103* (0.00578) (0.00586) (0.00586) (0.00585) (0.00585) 1-Year Rent Growth -0.00497 -0.00557 -0.00555 -0.00457 -0.00637 (0.00884) (0.00883) (0.00883) (0.00883) (0.00894) Observations 8,833,397 8,833,397 8,833,397 8,833,397 8,833,397 R-squared 0.221 0.221 0.221 0.221 0.221 Control Variables Yes Yes Yes Yes Yes Inflation Exposure Yes Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 65 Table 1.14: Correlation Between RMB Appreciation and US Inflation Gap Inflation Gap t =β · RMB Appreciation t +γ · Xt +ϵ t, where Inflation Gap t is the difference of the month-to-month inflation spreads between bottom income quintile households and top income quintile households, and RMB Appreciation t is the month-to-month Chinese Yuan (RMB) appreciation against the US Dollar (USD). Column (1) shows that the positive correlation between RMB appreciation and the US inflation gap is statistically significant, with the F-statistic equal 45.86. In column (2), I control for potentially co-moving variables such as aggregate inflation rates, fed funds rates, gas price changes, and dollar index changes. In column (3), I add month fixed effects to absorb seasonality, and in column (4), I add year as a control variable to capture the linear long-run trend. Newey-West standard errors are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) Inflation Gap RMB Appreciation 0.0734*** 0.0731*** 0.0734*** 0.0731*** (0.0173) (0.0203) (0.0178) (0.0210) Observations 180 180 180 180 Controls Yes Yes Month Fixed Effects Yes Yes Newey-West Standard Errors Yes Yes Yes Yes Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 66 Table 1.15: Home Ownership and Inflation Heterogeneity: RMB Appreciation as IV The second stage equation and the first stage in the IV specifications are Home Ownership i,j,k,t =β · ˆ π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ i,j,k,t π j,t = ˜ β j· Zt + ˜ α, where Home Ownership i,j,k,t is a dummy variable that equals one if household i reports as a home owner. π j,t, the relative inflation spread of group j in yeart, is instrumented byZt = RMB Appreciation t , which is the appreciation of the Chinese Yuan relative to the US dollar over the past 12 months. ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control for interest rate term structure and national inflation rate and allow heterogeneous exposure to those variables across income groups. The sample period is from 2005 to 2019. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) Home Ownership d π j,t 0.0756*** 0.0800*** 0.0905*** 0.0909*** (0.0143) (0.0142) (0.0165) (0.0165) 1-Year Housing Ret -0.00914 -0.00914 -0.00931 -0.00926 (0.00626) (0.00626) (0.00571) 1-Year Rent Growth -0.00497 (0.00867) Observations 9,677,676 8,872,562 8,872,562 8,833,397 R-squared 0.224 0.221 0.221 0.221 Control Variables Yes Yes Yes Yes Inflation Exposure Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 67 Table 1.16: Inflation Expectation Heterogeneity and the 2005 Chinese Yuan Reform The regression uses the disaggregated monthly household expectation interviews from Michigan Surveys of Consumers from 2003 to 2007. Expectation i,m,t =β · Bottomi,t· Reformt +γ · Xi,m,t +η · Zi,m,t +ψ m,t +ϵ i,m,t, where Expectation i,m,t is the inflation or income expectation of survey participant i in year-montht at regionm, the dummy variable Bottomi,t equals one if the participanti is at the bottom income quintile, and Reformt is a dummy variable indicating whethert is after the 2005 July Chinse Yuan reform.Xi,m,t are the participants’ demographic characteristics, including income, gender fixed effects, education fixed effects, age fixed effects, and birth year fixed effects. Moreover, I also control for Zi,m,t , which are participants’ expectations of future unemployment and aggregate economy to make sure other expectations do not drive the result.ψ i,m,t are the region by year by month fixed effects to absorb any aggregate and local economy variations. Columns (1)-(2) show the results for 1-year forward inflation expectation. Columns (3)-(4) show results for 5-year forward inflation expectation. Columns (5)-(6) are income expectations. Standard errors double clustered at the year-month level and birth year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) (5) (6) 1 Year Inflation 5 Year Inflation Income Bottom· RMB Reform 0.167** 0.162** 0.118** 0.151*** 0.137 -0.0520 (0.0806) (0.0714) (0.0509) (0.0538) (0.631) (0.655) Constant 3.571*** 3.581*** 3.314*** 3.306*** 5.354*** 5.417*** (0.0259) (0.0228) (0.0143) (0.0152) (0.225) (0.228) Observations 24,244 23,578 23,942 23,348 26,009 25,195 R-squared 0.086 0.135 0.063 0.081 0.086 0.099 Demographic Controls Yes Yes Yes Yes Yes Yes Income Quintile-Year Fixed Effects Yes Yes Yes Yes Yes Yes Region-Year-Month Fixed Effects Yes Yes Yes Yes Yes Yes Macro Expectation Controls No Yes No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 68 Table 1.17: Household Expectation and the 2005 Chinese Yuan Reform The regression uses the disaggregated monthly household expectation interviews from Michigan Surveys of Consumers from 2003 to 2007. Expectation i,m,t =β · Bottomi,m,t· Reformt +γ · Xi,m,t +η · Zi,m,t +ψ m,t +ϵ i,m,t, where Expectation i,t is the householdi’s expectation of the future macro economy at year-montht, the dummy variable Bottomi,t equals one if the participanti is in the bottom income quintile, and Reformt is a dummy variable indicating whethert is after the 2005 July Chinse Yuan reform. Xi,m,t are the participant’s demographic characteristics, including income, gender fixed effects, education fixed effects, age fixed effects, and birth year fixed effects. ψ i,m,t are the region by year by month fixed effects to absorb any aggregate and local economy variations. Column (1) shows the results for future gas price and column (2) for the future unemployment rate. Columns (3)-(4) test the 1 and 5 year forward macro economy conditions, respectively. Standard errors double clustered at the year-month level and birth year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) Gas Price Unemployment Rate 1 Year Economy 5 Year Economy Bottom· RMB Reform 2.305 0.0211 -0.0453 0.00782 (2.613) (0.0452) (0.0495) (0.0529) Constant 52.81*** 2.629*** 2.986*** 3.137*** (1.259) (0.0166) (0.0169) (0.0182) Observations 19,042 26,754 25,206 25,967 R-squared 0.097 0.081 0.102 0.095 Demographic Controls Yes Yes Yes Yes Birth Year Fixed Effects Yes Yes Yes Yes Income Quintile-Year Fixed Effects Yes Yes Yes Yes Region-Year-Month Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 69 Table 1.18: Mortgage Borrowing and the Chinese Yuan Reform ln(Num k,c,t +1)=β · Bottom k · Reformt +γ · X k,c,t +ψ k,t +η k,t +ξ k,t +ϵ k,c,t whereNum k,c,t is the number of mortgages originated at zip codek in year-montht. Bottom k is a dummy variable and equals one if zip code k belongs to the bottom income quintile. Reformt is also a dummy variable and equals one if year-month t is after the RMB Reform in July 2005.ψ c,t are the county by year by month fixed effects, η k,t are the zip code by year fixed effects, andξ k,t are the zip code by month fixed effects. X k,c,t are other control variables, like last month’s home value at the zip code and one-year local home value appreciation. By including county-by-year-by-month fixed effects, I can tightly control for any county-level time-varying macroeconomic variations. With zip code by year fixed effects, I can control for the long-run variations at the zip code level associated with the housing market boom and bust between 2003 and 2007. The zip code-by-month fixed effects are further used to control seasonality variations in the zip code level housing markets. In columns (2) and (4), I control for the share of private labeled securitization (PLS) mortgages among all mortgages and the share of mortgages with misreported owner occupancy and second lien among all PLS mortgages at the zip code by month level. The sample period is from 2003 to 2007. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. log(Number + 1) (1) (2) (3) (4) Bottom Quintile· RMB Reform 0.0356** 0.0341** 0.0373** 0.0355** (0.0166) (0.0165) (0.0166) (0.0165) PLS Share -0.188*** -0.212*** (0.00995) (0.00910) Misreporting Share 0.0855*** 0.114*** (0.00622) (0.00722) Observations 402,982 402,982 402,982 402,982 R-squared 0.939 0.940 0.940 0.940 Control Variables Yes Yes Yes Yes ZipCode-Year Fixed Effects Yes Yes Yes Yes ZipCode-Month Fixed Effects Yes Yes Yes Yes Year-Month-County Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 70 Table 1.19: Home Ownership within a Group and Inflation Heterogeneity Home Ownership i,j,k,t =β · π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ k,t where Home Ownership i,j,k,t is a dummy variable that equals one if householdi reports as a homeowner. Higher is a dummy variable that equals one if householdi is at the top half of income distribution within groupj. Young is a dummy variable that equals one if household i is below 40 years ago. π j,t is the relative inflation spread of the income quintile j that household i belongs to in year t. ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control interest rate term structure and national inflation rate and allow heterogeneous exposure to those variables across income groups. The sample period is from 2005 to 2019. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) Home Ownership π j,t 0.0612*** 0.0711*** 0.0674*** 0.0679*** (0.0117) (0.0116) (0.0132) (0.0132) Higher 0.0322*** 0.0340*** 0.0342*** 0.0343*** (0.00330) (0.00321) (0.00326) (0.00327) π j,t· Higher 0.0150** 0.0192*** 0.0195*** 0.0193*** (0.00689) (0.00640) (0.00634) (0.00634) π j,t· Young -0.136*** -0.142*** -0.141*** -0.141*** (0.0276) (0.0278) (0.0278) (0.0278) 1-Year Housing Ret -0.0111* -0.0107* -0.00996* (0.00593) (0.00589) (0.00540) 1-Year Rent Growth -0.00898 (0.00769) Observations 9,677,676 8,872,562 8,872,562 8,833,397 R-squared 0.224 0.221 0.221 0.221 Control Variables Yes Yes Yes Yes Inflation Exposure Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 71 Table 1.20: Detailed Distribution of Household Types This table shows the detailed distribution of households based on their locations and their home ownership status under two inflation heterogeneity scenarios. In the first scenario, relative inflation spreads are zero for both high income households and low income households. In the second scenario, the relative inflation spread is 0.3pp for low income households and -0.3pp for high income households. Numbers reported are percentages of each type of household in the economy. Home Owner Status in Island Inflation Heterogeneity Scenarios High Income Low Income Income Group No Yes % % High Owner Owner 33.6 10.0 Owner Renter 4.6 0 Renter Owner 0 0 Renter Renter 1.9 0 Low Owner Owner 0 28.6 Owner Renter 0 0 Renter Owner 1.8 9.6 Renter Renter 8.2 1.9 Table 1.21: Mortgage Borrowing and Inflation Heterogeneity: China Trade Exposure The second stage equation and the first stage in the IV specifications are ln(Num k,j,c,t +1)=β · ˆ π j,t +γ · X k,j,c,t +ψ c,t +η k +ϵ k,j,c,t , π j,t = ˜ β j· Zt + ˜ α, wherek indexes census tract,t the year,Num k,j,c,t is the number of mortgages originated at census tractk in yeart recorded by HMDA.π j,t, the relative inflation spread of income quintile j in yeart, is instrumented byZt = RMB Appreciation t , which is the appreciation of the Chinese Yuan relative to the US dollar over the past 12 months. ψ c,t are the county by year fixed effects, andη k are the census tract fixed effects. X k,j,c,t are other control variables of census tractk, including the log of median income, Zillow home value at the census tract, 1-year local housing market return, 5-year housing market return, 1-year local rent growth, and local rent index. I also control for short-term and long-term interest rates and national inflation rate and allow heterogeneous sensitivities to those variables across income groups. The sample period is from 2005 to 2019. Columns (1) and (2) are run on the subsample of low China trade exposure counties, and Columns (3) and (4) are run on the subsample of high China trade exposure counties. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) Low Trade Exposure Low Trade Exposure High Trade Exposure High Trade Exposure d π j,t 0.213*** 0.197*** 0.180*** 0.155*** (0.0532) (0.0549) (0.0458) (0.0480) 1-Year Housing Ret 0.353*** 0.481*** 0.511*** 0.633*** (0.0636) (0.0904) (0.112) (0.165) 1-Year Rent Growth 0.0861* 0.0906** (0.0503) (0.0366) Observations 285,559 153,443 302,507 193,720 R-squared 0.904 0.906 0.908 0.910 Inflation Exposure Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 72 Table 1.22: Home Ownership and Inflation Heterogeneity: China Trade Exposure The second stage equation and the first stage in the IV specifications are Home Ownership i,j,k,t =β · ˆ π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ i,j,k,t π j,t = ˜ β j· Zt + ˜ α, where Home Ownership i,j,k,t is a dummy variable that equals one if household i reports as a home owner. π j,t, the relative inflation spread of group j in yeart, is instrumented byZt = RMB Appreciation t , which is the appreciation of the Chinese Yuan relative to the US dollar over the past 12 months. ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X i,j,k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control for interest rate term structure and national inflation rate and allow heterogeneous exposure to those variables across income groups. The sample period is from 2005 to 2019. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) Low Trade Exposure Low Trade Exposure High Trade Exposure High Trade Exposure d π j,t 0.0995*** 0.0995*** 0.0822*** 0.0831*** (0.0183) (0.0184) (0.0154) (0.0155) 1-Year Housing Ret -0.00836 -0.00958 -0.00954 -0.0101* (0.00708) (0.00729) (0.00657) (0.00595) 1-Year Rent Growth -0.00921 -0.00181 (0.00851) (0.0115) Observations 4,438,346 4,451,946 4,384,161 4,358,596 R-squared 0.252 0.243 0.251 0.244 Inflation Exposure Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 73 Table 1.23: Mortgage Lien Status and Inflation Heterogeneity Mortgage Lien i,j,k,t =β · π j,t +γ · X i,j,k,t +ψ k,t +η k +ϵ i,j,k,t where Mortgage Lien i,j,k,t is a dummy variable that equals one if householdi reports having a first lien or home equity mortgage. π j,t is the income-specific inflation of the income quintile j that householdi belongs to in yeart. ψ k,t are the county by year fixed effects, and η k are the public use micro area (PUMA) fixed effects. X k,t are other control variables, including the log of household income, PUMA home value index, 1-year PUMA home value appreciation, 1-year PUMA rent growth, and PUMA rent index. I also control interest rate term structure and national inflation rate and allow heterogeneous sensitivity to those variables across income groups. The sample period is from 2005 to 2019. Standard errors clustered at the county level and income quintile by year level are reported in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. 2005-2019 2010-2019 (1) (2) (3) (4) First Second (Home Equity) First Second (Home Equity) π j,t 0.0394*** -0.0234*** 0.0738*** -0.00711 (0.0105) (0.00525) -0.00627 (0.00782) 1-Year Housing Ret -0.00560 -0.00239 -0.00562 -0.00238 (0.00591) (0.00223) (0.00588) (0.00222) 1-Year Rent Growth -0.00538 0.00122 -0.00340 0.00128 (0.00543) (0.00384) (0.00542) (0.00383) Observations 8,872,562 8,833,397 6,535,834 6,502,583 R-squared 0.191 0.069 0.184 0.049 Inflation Exposure Yes Yes Yes Yes Interest Rate Curve Exposure Yes Yes Yes Yes County-by-Year Fixed Effects Yes Yes Yes Yes Census Tract Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 74 Chapter2 TalentRetentionRiskandCorporateInvestment Coauthored with AJ Chen and Miao Ben Zhang 2.1 Introduction “You can benchmark and mitigate operational risk, credit risk, market risk, and legal risk. But key-man risk is something else entirely.” - Chris Donegan, CEO of Invention Capital Associates ∗ Economists and policymakers have long been interested in understanding the forces that determine cor- porate investment. Recent surveys of CFOs show that talent concerns outweigh financial concerns and dominate corporate investment decisions in the 21st century ([75], Duke CFO Survey 2011). Moreover, executives frequently cite attracting and retaining skilled labor as a top challenge for internal risk manage- ment. † Despite the first-order importance of talent retention risk revealed by the surveys, little is known about how talent retention risk evolves over time, and how such evolution relates to recent patterns in corporate investment ([63]), likely due to challenges in measurement. In this paper, we construct the first measure of firms’ talent retention risk ( TRR) based on an on-the- job search framework. We define talent as occupations that require a college degree and 4-year working ∗ https://www.fm-magazine.com/news/2019/jan/how-to-manage-key-person-risk-201819925.html † See Section?? for a summary of several CFO surveys. 75 experience. ‡ In each local labor market (MSA), we compute the ratio of job postings for talent by other firms ( v) and the total employment of talent (e). Thisv-e ratio represents the abundance of an employed talent’s outside options. Variations in this ratio thus capture changes in the likelihood for the firm to lose a talent. For instance, an influx of job postings for financial managers by IT companies can increase the risk for a bank in the MSA to lose its financial managers. We define a firm’s TRR as the average v-e ratio across MSAs weighted by the firm’s talent presence in each MSA. Numerous studies have shown that turnovers of skilled labor are highly costly (e.g., [16]). TRR thus intuitively captures the average likelihood for the firm to lose a talent and pay the turnover cost. We next present evidence bolstering our interpretation that TRR indeed captures the risk for firms to lose talent. First, we access the microdata data of the Duke CFO Survey and show that a firm’s TRR is positively related to its CFO electing “attracting and retaining qualified employees” as the top three firm- specific concerns. This relation holds even after we control for firm and time fixed effects. This finding suggests that CFOs indeed perceive a greater challenge in talent retention when their talent’s outside options are more abundant, supporting our on-the-job search approach. Second, we access the LinkedIn microdata and show that a firm’s TRR strongly relates to talent outflows from the firm in the current and next year. This finding confirms that firms cannot fully hedge against TRR, and that TRR can indeed cause materialized talent loss to firms. Equipped with this measure, we study the impact of talent retention risk on corporate investment guided by a standard Q theory. In our framework, TRR can affect investment and Q through two channels. First, TRR reduces expected capital productivity which lowers both investment and marginal Q. Second, we hypothesize that TRR also increases adjustment costs for capital formation as suggested by prior literature ‡ Our definition suggests that about 5% of employees are talent in an average firm in our sample (see Table 1), consistent with prior findings ([11]). 76 and survey evidence. § For instance, the Duke CFO survey shows that the shortage of talent is the domi- nating reason for firms to bypass otherwise “positive net present value projects.” Interpreting the NPV as the value for installed capital, just like in the definition of Q, then talent shortage naturally represents the adjustment costs not accounted for in the NPV that led to the bypassing. It is well-known that adjustment cost can create a wedge between investment and Q, asI = 1 γ (Q− 1) in a standard Q theory whereγ is the quadratic adjustment cost parameter. Hence, TRR can dampen investment even after controlling for Q. We next present three empirical results supporting the predictions of our simple framework. First, we show that TRR significantly reduces next period investment in 2010-2018 even after controlling for Tobin’s Q, total Q that includes intangibles ([95]), other common predictors for investment, and fixed effects by firm and year. Firms in top quintile sorted by TRR have investment rate 1.3% lower than firms in the bottom quintile. We further conduct a battery of endogeneity assessments, and we show that this negative effect is not driven by firms’ endogenous choice of local labor market (i.e., an omitted variable concern) and other firms’ predatory job postings for talents (i.e., a reversal causality concern). These findings suggest that TRR can dampen investment beyond the influence of Q. Second, we present evidence that directly supports our model’s predicted relation for investment, Q and TRR. Our framework suggests thatI = 1 γ (Q− 1), which indicates that investment should be better characterized by an interaction between TRR and Q if TRR is indeed a source of capital adjustment cost. Consistent with this prediction, we show significant negative coefficient of interaction term no matter Q is measured as Tobin’s Q or total Q. Intuitively, these findings suggest that talent retention risk particularly dampens firm investment when the firm needs to growth at a faster pace. Third, we conduct a body of subsample analyses showing that the above effects of TRR are indeed stronger among firms that are likely to be constrained by talent during capital formation. Prior literature indicates that new investment projects rely more heavily on talent if they embody challenges that are § Prior studies on the nature of capital adjustment cost ([30] and [74]) and and on firm organization ([99] and [55]) suggest that talent is crucial for solving the tasks before projects are up-and-running such as team building and solving unusual tasks. 77 new to existing projects. Hence, talent can be a particularly important source of capital adjustment cost when new investment projects are different from firms’ existing projects. Consistent with this view, we show that the above effects of TRR alone and also the interaction effects of TRR and Q are both driven by firms in the new product innovation stage of life-cycle ([68]), firms in fast growing sectors ([33]), and firms engaging more in R&D. In addition, consistent with the survey evidence highlighting the shortage of middle managers as the core source of adjustment cost, we decompose our TRR measure based on management occupations and non-management occupations within our talent occupations. We show that our TRR results are driven primarily by management occupations. After establishing the role of TRR in affecting investment through capital adjustment cost, we study an important time-series implication of our findings. Seminal work by [63] shows that capital invest- ment by U.S. firms is lackluster despite high Tobin’s Q in the 21st century, resulting in a widening gap between actual investment and investment predicted by Q (investment-Qgap). Several recent studies have proposed explanations for this time-series phenomena including declining competition ([63]), rising in- tangibles ([63] and [33]), and measurement errors in discount rate for the Q calculation ([59]). We study the widening investment-Q gap through a standard Q theory, in which adjustment cost is the only source for the wedge between investment and Q. Hence, if TRR increases over time, the rising capital adjustment cost can dampen investment but not Q, resulting in a widening gap between them. We first present three time-series plots reflecting that firms are facing increasing challenges to retain their talent. First, we plot the time-series of our TRR measure, which shows that TRR increased sixfold from 2010 to 2018. Second, we show a rising percentage of CFOs electing talent retention as their top firm- specific concerns in the Duke CFO Surveys. Third, we plot a rising outflow rate of talent from incumbent employers in the LinkedIn data, suggesting that job-to-job moves by talent indeed increase in our sample period. The three plots present a unified message that firms are facing increasing challenges in retaining 78 their talent. Hence, they are indeed likely to face increasing adjust costs during the beginning period of capital formation. We next analyse whether the rising TRR can contribute to the widening investment-Q gap. We first confirm a widening investment-Q gap in our sample period of 2010-2018 following the empirical test of [63]. In particular, we regress investment on Tobin’s Q, firm controls, firm-fixed effects, and year dummies. We observe increasingly negative coefficients for the year dummies indicating that the investment-Q gap widened by about 3.6 percentage points over the past decade. Following the diagnose method by [63], we include TRR and the interaction of TRR and Tobin’s Q in the above regression, and we interpret the explanatory power by TRR through changes in the year dummy coefficients. We find that rising TRR explains 13 percent of the widening investment-Q gap in the overall sample. Yet, there are substantial heterogeneities across firms. TRR explains 27 percent of the widening investment-Q gap in fast-growing industries compared to zero percent in other industries; and the same pattern holds if we use Total Q instead of Tobin’s Q. TRR explains 20 percent in early-life-cycle firms compared to -4 percent in other firms; and TRR explains 24 percent in high-R&D firms compared to -8 percent in other firms. The numbers are similar if we consider the investment-Total Q gap. In summary, these results suggest that rising challenges of retaining talent explains a sizable fraction of the lackluster investment as compared to Q mainly in fast growing innovative firms. Our study relies on a central thesis of the organization capital literature that some intangible capital of a firm is embodied in the firm’s key talent ([99] and [46]). A large body of literature explored the implication of organization capital on firm valuation ([95], [45], [46], among others). [46] show theoretically and empirically that organization capital is riskier than physical capital because key talent can leave the firm during economic states with high stochastic discount factor. Motivated by survey evidence, we apply this thesis to explaining corporate investment. In particular, our empirical findings suggest that the inability 79 for firms to retain their talent plays an important role for understand the lackluster capital investment in the past decade. Our work also contributes to explaining the widening investment-Q gap in the 21st century discovered by [63]. [63] examine a large spectrum of potential explanations and show that accounting for intangible in the Q calculation only partially explains the puzzle. [33] develop a structural model that shows the interaction between rent and intangible explains a large fraction of the gap. More recently, [59] show that the actual discount rate adopted by firms are greater than asset market suggested, resulting in an overestimation of Q in the prior literature. We approach the investment-Q gap puzzle through a standard Q theory with quadratic adjustment cost. We show a battery of evidence along with the CFO survey results supporting that talent retention risk is a source of capital adjustment cost, and rising TRR explains a sizable fraction of the widening investment-Q gap. Finally, our measure of talent retention risk is related to the mobility of employees across firms. A large body of literature study the implications of labor mobility for firms ([44], [104], [78], among others). In particular, [78] shows that increases in state-level enforceability of non-compete agreements between firms boost up firm investment especially for firms with more skilled labor. [104] explores shocks to the mobility of skilled immigrant workers and shows that relaxing mobility constraints negatively influences firm value. While these studies based on policy shocks demonstrate the causation of labor mobility to firm investment and value, they cannot be used to understand time-series of changes in talent mobility nor the implications for the dynamics of corporate investment ([63]). Our study fills this void by constructing a talent retention risk measure based on an on-the-job search framework. Our measure helps us connect talent mobility to the wedge between investment and Q and demonstrate the importance of talent retention to the widening investment-Q gap in the past decade. 80 This paper is organized as following: Section ?? presents a simple Q theory framework connecting talent retention risk to firm investment and Q. Section ?? presents the data and measure for our firm- level talent retention risk. Section?? presents our main results of TRR on investment. Section?? presents a battery of subsample analysis results that are consistent with our framework. Section ?? presents the implication of rising TRR for explaining the widening investment-Q gap, and Section?? Concludes. 2.2 CFOSurveyEvidence In this section, we provide a brief summary of CFO surveys regarding “drivers for forgoing corporate investments” and regarding CFOs’ view on the most pressing concerns of internal risk management. 2.2.1 SurveysonForgoingCorporateInvestments 2.2.1.1 KelloggCFOSurvey An important study by [75] analyzes the 2003 Kellogg CFO survey about firms’ investment and cost of capital. A focal question asks the CFOs to choose how much they agree with the following two statements which we label as talent concerns and financial concerns for forgoing investment: • [Talent concerns:] “There are some (otherwise) good projects we cannot take due to limited access to capital markets. • [Financial concerns:] We cannot take all (otherwise) profitable projects due to limited resources in the form of limited qualified management and manpower. They show in their Figure 2 that 55% CFOs attribute forgoing otherwise profitable projects to talent con- cerns, while 39% CFOs attribute to financial concerns. ¶ ¶ Note that the percentages do not have to sum up to be one as CFOs can choose both options or neither of them. 81 2.2.1.2 DukeCFOSurvey Similarly, question 12 of the 2011 Q3 Duke CFO Survey asks “During normal economic times, does your company pursue all investment projects that you estimate will have positive net present value? [If No], what prevents you from pursuing all positive net present value projects?” Again, 58% CFOs view the lack of “management time and expertise” as the reason for bypassing oth- erwise valuable investment projects, while 43% CFOs attribute it to the lack of funding. 2.2.2 SurveysonCFOs’MostPressingInternalRiskConcerns 2.2.2.1 DukeCFOSurvey In the December 2019 Duke CFO Survey, for the question about "During the past quarter, which items have been the most pressing concerns for your company’s top management team?", among the total of 434 CFOs being interviewed, 195 of them chose "difficulty attracting/retaining qualified employees." In fact, talent retention is the number one concern, followed by "economic uncertainty," which is chosen by 154 CFOs. The same pattern appears in many other waves of surveys. For example, in the December 2018 Duke CFO Survey, talent retention is also the number one concern, chosen by 46.7% of CFOs, and is followed by "government policies", by 32.1%. Again, in the December 2017 Duke CFO Survey, talent retention is still the number one concern, chosen by 42.9% of CFOs, and is followed by "cost of benefits", by 33.6%, and "data security", by 31.7%. 2.2.2.2 DeloitteCFOSignals™Survey The 2022 2Q Deloitte CFO Signals survey has a total of 97 CFOs participating, with 72% from public compa- nies and 28% from privately held companies. The survey reports that "CFO’s top internal risk worries were again dominated by talent and concerns over retention" and "talent and retention are CFOs’ top internal 82 risks in 2Q 2022. Among the 97 CFOs, 37 of them choose "talent" as the keyword of internal risk worries. The CFOs express concerns over "getting the right talent to move technology investments forward" and "resource management as turnover increases and the rate for specialized roles increases." Another 37 of CFOs choose "retention" as the keyword of internal risk worries, indicating "loss of talent due to attrition" and "talent turnover." 2.3 ASimpleOn-The-JobSearchModel Consider an economy with infinitesimal firms and a total number of E employees with fixed supply (double check how many talent occupations go to unemployment and how many talent occupations are hired from non-employment.) An employee who searches job while employed pays a fixed search cost of c. ∥ Job searchers are expected to earn an expected present value ofx i from job-switching, wherex i follows a uniform distribution from 0 toX and is unobservable to the job posting firms. Assume s is the share of employees searching for jobs in the economy. We can solve for s from the following equilibrium condition: V sE x i − sc=0, (2.1) where V sE is the probability for the job searcher to get a job (as the hiring firms do not observe heterogeneity among job applicants), making V sE X the expected benefits of searching for a job. Because of the uniform distribution ofx i ,x ∗ i =s ∗ X captures the marginal benefit of the job searcher which should be the same as the job searching cost. We thus obtain that in the economy, there ares ∗ = q V E X c employees who search for jobs on the job. ∥ This can be the time spent on job hunting, fixed costs of subscribing to job posting websites, cost for help to update a resume, etc. Our intuition goes through if we include variable costs such as opportunity costs to the search cost. 83 A firm’s average probability of losing an employee depends on the distribution of its employees’ ex- pected benefits from job searching. For a representative firm with x i ranging uniformly between 0 and X, we knows ∗ share of its employ- ees have the incentive to search for jobs, resulting in an average probability ofp ∗ =s V sE = V E for the firm to lose an employee. For a firm with better employee pay and benefits, s s ∗ share of its employees find their x i worth the costc, resulting in an average probabilityp> V E . In this model, we assume job posting is exogenous. Hence, this is not a typical equilibrium OJS model where firms respond to employees’ willingness to search by posting more jobs. In a full fledged model, V should also be endogenous. In particular, a higherp ∗ will induce the firm to post more jobs to replace their lost employees, makingV a positive function ofp ∗ . We should thus solve for the optimalp ∗ as such. 2.4 DataandMeasure 2.4.1 Data This section describes the data used in the study. We compile several large-scale labor market datasets for the purpose of estimating firms’ exposures to talent retention risks. Our job posting data is derived from Burning Glass Technologies (BGT), which describes itself as “the world’s leading provider of real-time labor market data products and analysis” with data covering the near- universe of U.S. online posted job vacancies. BGT has one of the world’s largest real-time, proprietary databases of jobs and talent, with openings data collected from more than 50,000 sources (e.g., job boards, company websites, newspapers, and public agencies) on a daily basis. To date, BGT has more than one 84 billion deduplicated job postings and collects more than 3.4 million postings every day. Specifically, it uses a sophisticated deduplication system to collect and process job posts and parses the ads into a systematic and machine-readable form with detailed information covering title, occupation, employer firm name, industry, location, skills, qualifications, and other features. Our job posting data cover the electronic job postings in the U.S. from January 1, 2010 to December 31, 2018. The data has been used to examine the labor market in studies such as [67], [39], [21], [40], [25], and [2]. To acquire information about firm’s granular local employment information, we follow [27], [106], and [91] and rely on ReferenceUSA, a business directory dataset that spans both private and public business entities in the U.S. ReferenceUSA’s business data covers tens of millions of businesses – from Fortune 500 companies to small mom-and-pop stores. Detailed business information can be obtained to examine latitude and longitude, number of employees, estimated sales, location, credit rating, public/private, year established, among others. Relevant to our study, it covers detail firm’s establishment-level employment from 2007 to 2018. Our workforce dynamics data (inflow, outflow, and turnover) are obtained from Revelio Labs, a lead- ing provider of labor market analytics. The data provider continuously gathers unstructured data con- taining employees’ online profiles and resumes from various websites and social media platforms (such as LinkedIn). They absorb and standardize hundreds of millions of public employment records to create one the world’s first universal HR databases. To ensure reliable data are available for a large panel of firms, the data provider begins the dataset in 2008. The raw data contain more than 380 million online public profiles and resumes of employees from more than 5,000 public companies. In addition to the employment data, we use Duke CFO survey data to understand how financial ex- ecutives view the economy and prospects for their business, especially firm’s top concerns and planned 85 capital investments in our setting. The survey is designed to provide direct information on how U.S. com- panies are perceiving and reacting to the current economic environment. [60] describe how the survey is conducted and provide an overview of the survey results. We also combine several other standard firm-level data for our analysis. We use Standard and Poor’s Compustat database to obtain firm accounting and financial information. We also obtain firm segment in- formation from Compustat. Moreover, we acquire O*NET/OES data to identify occupational characteristics and employment classification, specifically, O*NET for occupational characteristics that helps categorize talent and OES for occupational employment by MSA/Industry. 2.4.2 TRRConstruction Conceptually, we use the labor market vacancy-to-employment (VE) ratio as a measure of firm level talent retention risk, which features the probability of a skilled employee being approached by other firms. VE ratio captures the labor market tightness for the job-to-job movements, as in [97] and [54]. For an employee searching for potential outside options, the chance of being successfully matched with a new job increases with the VE ratio. Meanwhile, from the firm’s perspective, the probability of its employees being poached by other employers also rises when the labor market is tight. We take a bottom-up approach to construct the firm-level VE ratio, i.e., talent retention risk (TRR). Within each firm, we first build a VE ratio for each occupation at each MSA and then calculate the average of the occupation-MSA level VE ratio into firm-level talent retention risk, weighted by the occupation employment shares within the firm. Figure ?? illustrates the detailed process using a hypothetical case of Tesla. In this hypothetical example, Tesla has two branches: one in San Francisco and another in Austin. For the financial manager occupation, ω share of financial managers is located in San Francisco, and 1− ω is located in Austin. In San Francisco, the talent retention risk of the financial manager is measured by its local VE ratio, where the denominator is the total number of financial managers in San Francisco from the 86 OES MSA-Occupation Employment Panel, and the numerator is the total number of job post for financial managers in San Francisco. To instrument the exogenous local demand for financial managers, we exclude the job posts from Tesla’s top 3 industries. The talent retention risk of financial managers for Tesla is the weighted average of the VE ratios for financial managers in San Francisco and Austin. The weights are ω and1− ω, respectively. Given the lack of data regarding firm-MSA-level occupation employment shares, we combine the estab- lishment data from ReferenceUSA with the industry-occupation matrix from the Bureau of Labor Statistics. For each firm, we observe the location, NAICS industry, and employment size for each of its establishments. Then, we estimate the number of employees by each SOC 5-digits occupation for each establishment by assuming the same employee occupation distribution within the same NAICS 4-digits industry. Next, we aggregate the establishment-occupation level employment size into a firm-MSA-occupation level employ- ment size panel. We drop those firm-MSA-occupation pairs if the firm has not previously posted any job for the given occupation at the given MSA. The lack of previous job posts is an indicator of the potential measurement error introduced by the imputation process using the BLS industry-occupation matrix. We covert BGT job post flows into a monthly stock with a law of motion that assumes a fixed daily job filling rate of 1%. To address the endogeneity concern that local competitors change job posting behaviors because of industry trends that also affect the firm of interest, we exclude all job posts from the firm’s top 3 industries when calculating the local occupation VE ratio. The talent retention risk measure constructed in this way is labeled as TRR hereafter. We also develop two additional versions of firm-level talent retention risks to further address other potential concerns. First, firms may strategically enter or exit MSAs with tight labor markets, and such entry and exit decisions can be correlated with other financial decisions. To fix the geographic employment distribution of a firm, we construct the Balanced TRR, which uses a restricted sample with MSA-firm pairs 87 that presents through our sample period. Second, unobserved variations in local economic environments could drive VE ratios and firm decisions. To capture the exogenous variations in talent retention risk that is uncorrelated local shocks, we use a Bartik-style instrument to measure local occupation VE ratios. Similar in the spirits of [12] and [22], we construct a Bartik VE ratio of a given occupation at a given MSA by the national VE ratio of the occupation after excluding the MSA. And the Bartik VE ratios are then aggregated into the firm-level Bartik TRR. 2.4.3 Descriptives Our analysis focus on the skilled occupations. We define an occupation as skilled if the occupations requir- ing a college degree & 4-year working experience in the O ∗ NET database of occupational characteristics and worker requirements information across the U.S. economy. Figure?? illustrates the occupation distri- bution of skilled labor used in our talent retention measure. Our sample period ranges from 2010 to 2018. We begin with the sample of Compustat firms that appear both in Refernece USA and BGT. We then eliminate observations that lack the data required to calculate the control variables. Our final sample contains 11,822 firm–year observations. The literature has developed multiple measures of Tobin’s q. In our setting, We compute Tobin’s Q following [63] as the market value of the firm divided by book assets. We also use total Q developed in [95] in our analysis, which incorporates capital stocks of both tangible and intangible capital. We also winsorize relevant variables by year at 1% and 99%. Table ?? shows the descriptive statistics. Notably, a talent in our sample has an average TRR of 4% (VE ratio). Following our definition, firms on average have about 5% skilled labor. Relative to average Compustat firms, our sample covers firms with similar investment and Q but with larger firm size. 88 2.4.4 Validation We consider an array of validation tests that illustrate that our primary TRR measure captures the risk of firm’s loss of talents. We show that our TRR can positively predict both the CFO perceived talent losing risk as well as the realized outflow of talent. In addition, we note that our TRR measure is derived using a combination of highly-granular labor market data, to ensure consistency with our theoretical foundation and ease of interpretation. 2.4.4.1 DukeCFOSurveyofManagerialPerceptions We validate TRR by first examining whether CFOs are more likely to view difficulty in attracting or re- taining qualified employees as the most pressing concerns when our TRR measure is high. TRR CFO perceived,i,t =β · TRR i,t + Firm FE+ Qurater FE+ϵ i,t . In Table??, we regress CFOs’ perceived talent retention risk on our TRR measure. The dependent variable TRR CFOperceived is an indicator variable equal one if the CFO includes “Difficulty attracting/retaining qualified employees" in the top 4 most pressing concerns. Our data structure allows us to include firm fixed effects, which absorb any firm-specific omitted variables, and quarter fixed effects. Standard errors are clustered at the firm level. Columns (1) and (2) in Panel A show that CFO’s perceived talent retention risk is positively correlated with our TRR measure. It provides evidence that our TRR measure captures the subjective risk of losing talent. Further, it suggests our TRR measure can have materialized effects on firm decisions, given the extensive evidence on the importance of executive’s belief in firm investment decisions, as shown by [56]. 89 2.4.4.2 LinkedinWorkforceDynamics To further validate our TRR as a measure of difficulty in attracting or retaining talent, we examine whether TRR leads to talent outflow based on the Revelio data. In Panel B of Table ??, we regress Log Outflow of Talent i,t+k =β · TRR i,t +γ · Emp i,t + Firm FE+ Year FEϵ i,t , where TRR i,t is the measured talent retention risk of firm i in yeart. Outflow of Talent i,t+k is the number of skilled employees who leave firm i in yeart+k,k∈{− 1,0,1,2}. Emp i,t is the log of the number of employees. We include firm fixed effects, which absorb any firm-specific omitted variables, and year fixed effects. Standard errors are clustered at the firm level. Columns (1)-(4) in Panel B of Table?? show that firms experience more talent outflow when TRR is high. A one standard deviation increase in TRR is associated with about a one percent increase in talent outflow. The predictive power is strongest contemporaneously and for the next year and declines as extending the forecast horizon. Most importantly, our TRR is uncorrelated with last year’s talent outflow, which suggests that our TRR measures the exogenous innovation of talent retention risk that is not reversely driven by the firm’s previous labor market performance. Moreover, Table?? shows that our TRR can predict talent outflow even if controlling for firm character- istics, including cash flow, firm size, age, Tobin’s Q, and employment. In addition, to address the potential concern that our TRR only captures the talent retention risk for the fasting growing industries, where on- line job posting is a more common practice, we regress talent outflow on the interaction term of TRR and fast-growing industry dummy, as defined by [33]. We find that our TRR measure predicts talent outflow in both fast-growing industries and other industries. Notably, the predictive power is equally strong as the interaction term of TRR and fast-growing industry dummy is not statistically significant. 90 Our validation provides useful insights that firms cannot stop talent exits when facing high TRR. In the following analysis, we will show that they actively hire to counteract talent loss due to the increasing TRR, which can be very costly, as shown by [23]. 2.5 TalentRetentionRiskandCorporateInvestment 2.5.1 MainFindings We first examine whether talent retention risk can affect corporate investment. The dependent variable in Table?? is a measure of firm’s capital investment scaled by property, plant and equipment (CAPX/PPEGT). All tests include firm and year fixed effects, and standard errors are clustered by firm. Following prior literature on investments, we include standard controls for all tests. Control variablesX i,t are Tobin’s Q, cash flow, firm size, and firm age. We control for firm size as smaller firms tend to be more volatile and to grow faster. The inclusion of firm size and age also proxy firm’s financial constraints. For example, [70] and [64] document that younger and more innovative firms face more financial constraints. The regression specification we estimate is as follows: CAPX i,t+1 /PPEGT i,t =βTRR i,t +X i,t +FirmFE+YearFE+ϵ i,t , whereCAPX i,t+1 /PPEGT i,t is the capital investment of firm i in yeart+1, andTRR i,t measures the talent retention risk in yeart. Columns (1)-(4) of Table ?? show that firms invest less when TRR is high. Column (1) shows our baseline model that does not includes any controls, and we find that firms are less likely to incur capital investments when they face higher talent retention risks. Column (2) adds the controls, and the coefficient estimate of TRR is significant at the 1% level with signs that reinforce the importance of talent in investment 91 decisions. Columns (3) includes Tobin’s Q as an additional control and presents consistent result, indicating that Tobin’s Q cannot explain the impact of TRR on capital investments. In Column 4, the documented negative coefficient is robust in specification controlling for total Q, which incorporates firm’s intangible capital following [95]. Overall, we provide evidence that capital in- vestments are dampened by TRR in the past decade. Our findings provide support that the risk of limited management and manpower may potentially explain the the missing investment, beyond the influence of Q. The above findings are not likely to be driven by endogeneity for the following reasons. First, we exclude all job posts from the firm’s top 3 industries when calculating local occupation VE ratios. This way addresses the potential omitted variable concern that local competitors change job posting behaviors because of industry trends that also affect the firm of interest. In other words, our TRR measure captures the local labor market competition from employers who do not compete with the firm of interest in the product markets. Furthermore, the decrease in capital investment can also be predicted by our Balanced TRR and Bartik TRR. The Balanced TRR addresses the concern that firms may strategically enter or exit MSAs with tight labor markets and invest accordingly. We construct the balanced TRR using a sample with only the MSA- firm pairs show up through our sample period to fix firms’ geographic employment distributions. Last, our Bartik TRR tries to exclude unobserved variations in local economic environments that could drive both VE ratios and firm decisions. We construct a Bartik VE ratio of a given occupation at a given MSA using the national VE ratio of the occupation after excluding the MSA. And the Bartik VE ratios are then aggregated into the firm-level Bartik TRR to capture the exogenous variations in talent retention risk unrelated to local economic conditions. 92 2.5.2 Robustness: TRRandPlannedInvestment Based on what CFOs actually say about their investment obstacles, we want to understand why do CFOs forgo profitable projects in practice. Importantly, future realized investment is a combination of manage- ment investment plans and unexpected shocks, which indicates the importance of examining how TRR affects the planned investments at the firm level. Our conceptual framework in Section ?? also relates planned investment to TRR. With our survey data, we are able to examine whether CFOs are concerned about TRR when doing capital budgeting. From Duke CFO Survey, we obtain planned investment. In Table??, we use the following regression specification: PlannedCAPX i,t =βTRR i,t +X i,t +FirmFE+YearFE+ϵ i,t By including firm fixed effects, our specification absorb any firm-specific omitted variables. We also include year fixed effects. Moreover, we also control for Tobin’s Q, cashflow, firm size, and age. Standard errors are clustered at firm level. Table ?? shows that our TRR measure also negatively predicts the CFO’s planned investment. The estimated coefficients are negative for all three versions of TRR and statistically significant for two of the three, noting that the sample size for the merged CFO survey data and TRR has only 353 observations. The result is also consistent with our finding that TRR is positively associated CFO’s perceived difficulty attracting and retaining qualified employees. 2.5.3 HeterogeneousTRREffectsbyFirms’TobinQ We examine the heterogeneous talent retention effects by firms’ Tobin’s Q. Our model in Section ?? predicts that high-Q firms are more sensitive towards the talent retention risk. Intuitively, high-Q firm’s investment 93 is more sensitive towards any changes in capital adjustment cost, which directly depends on firm’s stock of talent and indirectly on the talent retention risk. Consistent with the model, in Table ??, we find that capital investments by high-Q firms are dispro- portionately dampened by the rising talent retention concerns. And the negative interaction between TRR and firm’s Q is statistically significant. Moving from a firm with Tobin’s Q at the 10th percentile to a firm with Tobin’s Q at the 90th percentile, one percentage increase in TRR leads to a lower capital investment ratio by 2.5 percentage. Furthermore, the stronger effects of TRR on high-Q firms is robust to various measures of TRR and Q. Table?? shows the estimated interaction effects between Tobin’s Q and all our three measures of TRR are always statistically significant negative. Moreover, if we concern about whether Tobin’s Q is an accurate proxy for one additional unit of capital, the same results also hold if we use Total Q defined by [95]. 2.6 WhereTRRMattersandWhoseTRRMatters? 2.6.1 TRRandNewCapitalFormationIndustries Previous literature show that new capital investment of innovative firms may differ from their old capi- tal. Our theoretical framework on capital adjustment costs suggests that talent retention risk may affect investment of innovative firms more as the new capital formation process demands more talent inputs and managerial expertise. Thus, we hypothesize that TRR would increase adjustment costs for capital for- mation. To test this conjecture, we conduct a battery of subsample analysis on firms with differentiated exposure to new capital formation using three complementary approaches. First, new capital formation is the main theme in fast growing sectors, which likely involves more adjustment costs. The economic value that is generated by new ideas are more likely to be constrained by 94 talent during capital formation. We follow [33] to group fast-growing industries defined by Fama-French 5- sectors. Second, previous literature indicates that new investment projects depend significantly on talents if they involve challenges that are unique from existing projects. Viewing firms as a portfolio of products, [69] model a firm’s product life cycle with four stages: (1) Life1 - product innovation, (2) Life2 - process innovation, (3) Life3 - stability and maturity, and (4) Life 4 - product discontinuation. Empirically, they estimate the stages of a firm’s product portfolio as a four-element vector {Life1, Life2, Life3, Life4}. We use the Life1 stage to capture firm’s exposure to the life cycle of new capital formation. As a stage with products that have not established their positions in the product market space, Life1 capacity is risky and acquired before the outcome of product development is known. This stage involves the highest level of product uncertainties and likely requires the most decision-making and expert information from talents. Lastly, we conjecture that the effects of talent retention risks are likely to be stronger when firms are engaging actively in the R&D activities. The production process of new inventions and business ideas are argued to involve highly skilled personnel. Panel A in Table?? presents the results for fast-growing industries. In the left and right side panels, we demonstrate the analyses of the effects of TRR alone (the first two columns in the left side panel) and also the interaction effects (the other two columns in the right side panel). Consistent with our expectations, we find that the effects of TRR are indeed stronger among firms that are in those sectors with more new capital formation. Panel B in Table?? is based on firm life cycles. We use high-Life1 estimation from [69] as a measure of firms’ exposure to early product life cycle stage. We find that our findings of TRR are more pronounced in Life1 firms with more intensity of product innovation. Lastly, Panel C in Table ?? shows our findings based on firm’s RD activities. We continue to find that TRR dampens investments for innovative firms. Overall, our results provide support that talent can be a particularly significant source of capital adjustment cost when firms are involved in new capital formation. 95 2.6.2 Managervs. Non-managers It is important to examine which talent matters for corporate finance. We first focus on the talent retention risk for managers versus non-managers, as a large literature shows that managers are pivotal for firms, for example, [24] and [86]. Then we do a more comprehensive search for each occupation in SOC-2 digits to identify the crucial talents that matter for investment decisions. Using the same bottom-up approach, we estimate the management talent retention risk by first calcu- lating the VE ratios for each management occupation for a given firm in a given MSA and then aggregating them into a firm level TRR(mgmt) weighted by the employment shares. Our TRR(mgmt) mostly captures the retention risk for middle managers, which take the lion’s share of employment in the overall man- agement occupation. TRR(mgmt) does not measure and does not attempt to measure the risk of losing executives. Similarly, we construct a talent retention risk measure for all other non-management occupa- tions. Conceptually, the manager retention risk can be particularly important for the following reasons. First, [86] document a large effect of middle managers on team productivity. Middle managers can boost team productivity in many ways. For example, [71] document that a manager’s interpersonal skills can help to reduce employee turnover. [4] show middle managers can reallocate tasks inside a team to match with subordinates’ productivity. [65] analyze a theoretical framework where middle managers need to invest time and attention to better monitor their subordinates. However, both the reallocation and monitoring channels require information, skill, and practices that are firm-specific or even employee-specific, which can not be easily persevered within the firm upon the leaving of a manager ([26]). Moreover, the managerial loss can not be easily replaced by new hires, as many of the skills and traits are hard to observe ([5]), and it takes time for the newly hired managers to learn and develop the firm or employee-specific knowledge. Last but not least, the leaving of a good manager can trigger turnovers of other employees and lead to bigger loss of firm’s human capital ([86]). 96 To test the importance of manager retention risk on investment, we run the following regression: CAPX i,t+1 /PPEGT i,t =β · TRR i,o,t +X i,t +FirmFE+YearFE+ϵ i,t , whereCAPX i,t+1 /PPEGT i,t is the capital investment of firm i in yeart+1, andTRR i,t measures the overall talent retention risk of firm i in yeart, whileTRR(mgmt) i,t captures the retention risk specifically for managers, andTRR(nonmgmt) i,t for all other skilled occupations. Control variablesX i,t are tobin’s q, cash flow, firm size, and firm age. We include firm fixed effects, which absorb any firm-specific omitted variables, and year fixed effects. Standard errors are clustered at firm level. In Table??, we find that the manager retention risk negatively predicts a firm’s investment. However, the retention risk of non-management occupation appears not to affect firm’s investment decisions. The results confirm the specialty of middle managers’ roles. To further identify the importance of middle managers and which other occupations matter in firm’s investment decisions, we repeat our CAPX regression using alternative TRR based on each broad occupa- tion: CAPX i,t+1 /PPEGT i,t =β · TRR i,o,t +X i,t +FirmFE+YearFE+ϵ i,t , where CAPX i,t+1 /PPEGT i,t is the capital investment of firm i in year t+1, and TRR i,o,t measures the talent retention risk for occupationo of firm i in yeart. Control variablesX i,t are tobin’s q, cash flow, firm size, and firm age. We include firm fixed effects, which absorb any firm-specific omitted variables, and year fixed effects. Standard errors are clustered at firm level. When constructing the talent retention risk measures at SOC-2 digits level, we use the VE ratios of all corresponding SOC-5 digits occupations. We include both skilled and non-skilled labor to make sure the definition of skilled occupation does not drive our results. 97 Table?? shows that the retention risk of the management occupation still stands out as the strongest predictor of future investment. Most notably, the manager retention risk measure after excluding execu- tives is equally capable of predicting capital investment. This finding again demonstrates the importance of middle managers. Among the non-management occupations, we find the retention risk of the computer and mathematical occupation also negatively predict future investment. The result is consistent with the literature that stresses the growing importance of information technology in business decisions and performance ([28]). 2.7 ImplicationsforRisingInvestment-QGap In this section, we further investigate whether the rising challenge in retaining talent can be a reason for the widening investment-Q gap. Notably, our measure uses only the variation of job postings by other firms in the local labor market. Hence, it is less likely to be affected by the firm’s endogenous actions. Equipped with this measure, we provide three new empirical facts. We first follow [63] to estimate the widening investment-Q gap. Using their empirical specification, we estimate the year fixed effects in a firm investment regression after controlling for Q and other firm characteristics, including cash flow, firm size, and age: CAPX i,t+1 /PPEGT i,t = X t β t YearDummy t +αQ i,t +X i,t +FirmFE+ϵ i,t Consistent with their findings, we document an increasing divergence between investment and Q in the Panel A of Figure??. In Panel B, we show that the investment-Q Gap widened more for high-Q firms. 98 Next, we attempt to explain the widening investment-Q gap. Specifically, we examine how much rising TRR contributes to the widening investment-Q gap in the 2010s, by extending the [63]’s Model with TRR Control: CAPX i,t+1 /PPEGT i,t = X t γ t YearDummy t +ψTRR i,t +αQ i,t +X i,t +FirmFE+ϵ i,t In Table??, we show that our TRR measure can explain about 16% of the increase in the investment-Q gap between 2010 and 2017. As Tobin’s Q may overestimate Q because it does not account for intangible capital, we provide robustness tests using Total Q as an alternative in the bottom panel of Table??. Crouzet and Emberly (2022) argue that Total Q is not a sufficient statistic for CAPX. Nevertheless, we repeat our analyses using Total Q from Peters and Taylor (2017). Our results are generally consistent. Lastly, we find that the explanatory power from rising TRR on investment-Q gap mainly comes from high Q firms. And it does not matter whether we define high Q firms based on Tobin’s Q or Total Q or based on a dummy variable indicating fasting growing sectors. The stronger explanatory power for high-Q firms is not surprising, as we already show that our TRR cross-sectionally predicts firm investment much better for high-Q firms. However, the stronger explanatory power for high-Q firms is very important to explain the widening investment-Q gap, which we show is mostly driven by high-Q firms. 2.8 Conclusion Recent surveys of CFOs unveil that constraints in skilled labor are the dominant obstacle for corporate investment in the 21st century, and companies frequently highlight attracting and retaining skilled labor as a top challenge for internal risk management. In this paper, we construct the first measure of firms’ talent retention risk (TRR) based on an on-the-job search framework to capture changes in the likelihood for the firm to lose a talent. A battery of tests validate our TRR. First, we show that a firm’s TRR is 99 positively related to its CFO electing “attracting and retaining qualified employees” as the top three firm- specific concerns using Duke CFO survey. Second, we show that a firm’s TRR strongly relates to talent outflows using LinkedIn microdata. Equipped with this measure, we study the impact of talent retention risk on corporate investment. We hypothesize that TRR increases adjustment costs for capital formation as suggested by prior literature and survey evidence. We present empirical results supporting the predictions of our simple framework. First, we show that TRR significantly reduces next period investment in 2010-2018 even after controlling for Tobin’s Q, total Q that includes intangibles ([95]), other common predictors for investment, and fixed effects by firm and year. Second, we show significant negative coefficient of interaction term no matter Q is measured as Tobin’s Q or total Q. Intuitively, these findings suggest that talent retention risk par- ticularly dampens firm investment when the firm needs to accumulate capital at a faster pace. Third, we conduct a body of subsample analyses showing that the above effects of TRR are indeed stronger among firms that are likely to be constrained by talent during capital formation, for example firms in the new product innovation stage of life-cycle ([68]), firms in fast growing sectors ([33]), and firms engaging more in R&D. In addition, consistent with the survey evidence highlighting the shortage of middle managers as the core source of adjustment cost, we decompose our TRR measure based on management occupations and non-management occupations within our talent occupations. We show that our TRR results are driven primarily by management occupations. Last but not the least, we find that rising challenges of retaining talent explains a sizable fraction of the lackluster investment as compared to Q mainly in fast growing innovative firms. Our findings uncover new insights on how talent market dynamics affect firms’ invest- ment activities in the past decade and provide important implications on the role of adjustments costs in the capital formation process. We also believe our TRR measure can prove useful in other settings, which may have natural applications to other disciplines such as strategy and management. 100 Figure 2.1: Talent Retention Concerns from the Duke CFO Survey This figure plots the percentage of CFOs electing “attracting and retaining qualified employees” as the top firm- specific concerns using the microdata of the Duke CFO Survey. During 2008Q4-2014Q1, the survey asked CFOs to elect from about 10 options to answer “Whatarethetopthreeinternal,company-specificconcernsforyourcorporation? ” During 2015Q1-2019Q4, the survey asked CFOs to elect from about 18 options to answer “During the past quarter, which items have been the most pressing concerns for your company’s top management team? (Choose up to 4)” Both waves of survey include the option “attracting and retaining qualified employees.” The survey did not ask related questions during the interim quarters. Because the survey changed the question in 2014, we shift the percentage of CFOs electing “attracting and retaining qualified employees” in the first quarter of the later wave to align with the percentage in the last quarter of the earlier wave. The pattern is very similar if we control for firm heterogeneities across surveys (see the Internet Appendix Figure??). 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% CFOs viewing Attracting/Retaining Qualified Employees as a top concern 101 Figure 2.2: Talent Outflows from the LinkedIn Microdata This figure plots average outflows of talent using the LinkedIn Workforce Dynamics microdata. Talent is defined as occupations that require a college degree and 4-year working experience (see Section ??). The figure plots the coefficients of the year dummies in the following regression specification: log(Outflow of Talent i,t +1)= X t β t · Year Dummy t + Firm FE+ϵ i,t 102 Figure 2.3: Talent’s Time Spent on Job Search This figure plots the percent of a skilled worker’s time spent on job search in the American Time Use Survey database. See Section 3.3 for the definition of skilled occupations. 103 Figure 2.4: Talent Retention Risk Measure This figure plots average talent retention risk (TRR) measure in each Fama-French 5-sectors for each year from 2010 to 2018. See Section?? for the construction of firms’ TRR. 104 Figure 2.5: Replicating Investment-Q Gap This figure illustrates the gap between realized investment and the predicted investment from Tobin’s Q. Our esti- mation follows [63] by running the following specification using non-financial U.S. firms, Investment i,t+1 = X t β t · Year Dummy t +α · Q i,t +X i,t + Firm FE+ϵ i,t . Investment is the ratio of capital expenditures (CAPX) and lagged tangible asset (PPEGT).β t captures the change in Investment-Q Gap from starting year to yeart. Q i,t is Tobin’s Q in Panel A and total Q ([95]) in Panel B. Control variables include cash flow, size, age. Standard errors are clustered at firm level. PanelA:Tobin’sQ -.2 -.15 -.1 -.05 0 1980 1985 1990 1995 2000 2005 2010 2015 2020 PanelB:TotalQ -.2 -.15 -.1 -.05 0 1980 1985 1990 1995 2000 2005 2010 2015 2020 105 Table 2.1: Summary Statistics This table presents the summary statistics of the variables in our sample. Our sample includes all Compustat firms with talent retention risk (TRR) measure from 2010 to 2018. Section?? details the construction of the TRR measure. Share of Talent is the fraction of company employees in the talent occupations. Outflow is the natural logarithm of the number of talent leaving the firm in the year from the LinkedIn microdata. Turnover is the natural logarithm of the sum of number of talent leaving and joining the firm in the year. Planned Investment is the growth rate of the firm’s CAPX reported in the Duke CFO Survey. Investment is next year’s CAPX divided by this year’s PPEGT. Q is Tobin’s Q measured as the market value of the firm divided by book assets following [63]. Total Q includes intangible assets in the denominator and is obtained from [95]. Cashflow is the sum of income before extraordinary items (IB) and depreciation expense (DP) normalized by PPEGT. Size is the natural logarithm of total assets (AT). Age is the natural logarithm of firm age computed based on the first year the firm appears in the Compustat universe. Variable Mean SD Minimum Median Median Compustat Universe Maximum # obs. TRR 0.040 0.045 0.000 0.025 - 0.225 11,822 Share of Talent 0.049 0.040 0.000 0.040 - 0.211 11,824 Outflow (log) 3.279 1.682 0.000 3.284 - 8.981 10,344 Turnover (log) 4.077 1.696 0.000 4.097 - 9.867 10,344 Planned Investment 0.060 0.209 -0.750 0.044 - 1.200 438 Investment 0.120 0.112 0.000 0.088 0.085 0.836 11,824 Q 1.755 1.427 0.150 1.305 1.412 12.791 11,636 Total Q 1.227 1.594 -6.700 0.798 0.820 18.764 11,497 Cash Flow -0.028 2.430 -38.361 0.171 0.097 5.103 11,791 Size (log) 7.140 1.989 1.603 7.214 5.942 12.325 11,824 Age (log) 3.090 0.736 0.693 3.135 2.773 4.220 11,824 106 Table 2.2: Validating the Talent Retention Risk Measure This table presents results of two separate validation tests for our talent retention risk (TRR) measure using Duke CFO Survey microdata (in Panel A) and the LinkedIn microdata (in Panel B). Section ?? details the construction of the TRR measure. Panel A reports the regression of CFO’s perceived talent retention challenge on our TRR measure from 2015 to 2018 using the following specification: TRR CFO perceived,i,t =β · TRR i,t + Firm FE+ Qurater FE+ϵ i,t , where the dependent variable TRR CFO perceived,i,t is a dummy variable equals 1 if the CFO includes “Difficulty attract- ing/retaining qualified employees" in the top 4 most pressing concerns in the Duke CFO Survey. Standard errors are clustered at firm level. Panel B reports the results of regressing talent outflow on our TRR measure from 2010 to 2018 using the following specification, Log Outflow of Talent i,t+k =β · TRR i,t +γ · Log Emp i,t + Firm FE+ Year FE+ϵ i,t , where Log Outflow of Talent i,t+k is the natural logarithm of the number of talents who leave firm i in yeart+k plus 1,k∈{− 1,0,1,2}. Log Emp i,t is the natural logarithm of the number of employees. Standard errors are clustered at firm level. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Panel A: Does CFO Perceive Talent Retention Risk? TRR CFO perceived TRR 6.34 ∗∗ 7.86 ∗∗ (2.42) (3.42) Firm FE Yes Yes Quarter FE No Yes Observations 113 113 AdjustedR 2 0.32 0.25 Panel B: Does TRR Lead to Talent Outflows? Log Outflow of Talent t - 1 t t + 1 t+2 TRR 0.40 0.48 ∗∗ 0.54 ∗∗ 0.39 ∗ (0.26) (0.24) (0.23) (0.22) Log Emp 0.34 ∗∗∗ 0.47 ∗∗∗ 0.55 ∗∗∗ 0.47 ∗∗∗ (0.05) (0.05) (0.05) (0.05) Firm FE Yes Yes Yes Yes Year FE Yes Yes Yes Yes Observations 9721 9726 9730 9730 AdjustedR 2 0.91 0.92 0.92 0.92 107 Table 2.3: Talent Retention Risk and Investment Response This table reports the regression of firm future investment rate on the talent retention risk (TRR) measure in the following spefication: Investment i,t+1 =β · TRR i,t +X i,t + Firm FE+ Year FE+ϵ i,t , where Investment i,t+1 is next year’s CAPX divided by current PPEGT. Section?? details the construction of our TRR measure. Control variablesX i,t include Tobin’s Q, cash flow, firm size, and firm age. Standard errors are clustered at the firm level. Sample period is from 2010 to 2018. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) TRR -0.128 ∗∗ -0.143 ∗∗∗ -0.135 ∗∗∗ (0.052) (0.051) (0.050) Cashflow 0.004 ∗∗ 0.004 ∗∗ (0.002) (0.002) Size 0.007 0.015 ∗∗∗ (0.005) (0.005) Age -0.139 ∗∗∗ -0.114 ∗∗∗ (0.016) (0.016) Q 0.028 ∗∗∗ (0.002) Firm FE Yes Yes Yes Year FE Yes Yes Yes Observations 11623 11589 11413 AdjustedR 2 0.533 0.545 0.566 108 Table 2.4: Robustness of Investment Response to TRR This table reports the robustness check results for the investment response to talent retention risk (TRR) in Table ?? using an alternative measure of Q (in Column (2)), alternative measures of TRR (in Columns (3) and (4)) and an alternative investment measure (in Column (5)). See Table Table?? for the regression specification. TotalQ includes intangibles following [95]. BalancedTRR is an alternative TRR measure computed assuming that firms do reallocate talent across MSAs since their first year of appearance in our sample. Bartik TRR is an alternative TRR measure computed using a Bartik-instrumented job posting for talent in each MSA instead of the actual job posting for talent in the MSA. Planned Investment is CFO’s planned growth rate in capital expenditure using the data from the Duke CFO Survey instead of the realized future investment. Standard errors are clustered at the firm level. Sample period is from 2010 to 2018. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Baseline Total Q Balanced TRR Bartik TRR Planned Investment (1) (2) (3) (4) (5) TRR -0.135 ∗∗∗ -0.115 ∗∗ -0.106 ∗∗ -0.091 ∗∗ -1.497 ∗∗ (0.050) (0.053) (0.052) (0.038) (0.690) Q 0.028 ∗∗∗ 0.027 ∗∗∗ 0.028 ∗∗∗ 0.118 (0.002) (0.003) (0.002) (0.071) Cashflow 0.004 ∗∗ 0.003 ∗ 0.007 ∗∗∗ 0.004 ∗∗ -0.014 (0.002) (0.002) (0.002) (0.002) (0.057) Size 0.015 ∗∗∗ 0.002 0.017 ∗∗∗ 0.015 ∗∗∗ 0.010 (0.005) (0.005) (0.005) (0.005) (0.110) Age -0.114 ∗∗∗ -0.087 ∗∗∗ -0.088 ∗∗∗ -0.113 ∗∗∗ -0.314 (0.016) (0.015) (0.016) (0.016) (0.312) Total Q 0.032 ∗∗∗ (0.002) Firm FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes Observations 11413 11281 10080 11413 353 AdjustedR 2 0.566 0.587 0.530 0.565 0.192 109 Table 2.5: Investment and Interaction of TRR and Q This table reports the results of regressing firm future investment on an interacting of talent retention risk (TRR) and Q using the following regression specification: Investment i,t+1 =γ · TRR i,t × Q i,t +β · TRR i,t +θ · Q i,t +X i,t + Firm FE+ Year FE+ϵ i,t , where Investment i,t+1 is next year’s CAPX divided by current PPEGT. Section ?? details the construction of our baseline TRR measure. See Table ?? for definitions of Balanced TRR and Bartik TRR. Panel A reports results using Tobin’s Q while Panel B reports results using total Q from [95]. Control variablesX i,t include cash flow, firm size, and firm age. Standard errors are clustered at the firm level. Sample period is from 2010 to 2018. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Baseline TRR Balanced TRR Bartik TRR (1) (2) (3) PanelA:InteractingwithTobin’sQ TRR× Q -0.091 ∗∗∗ -0.095 ∗∗∗ -0.054 ∗∗ (0.029) (0.032) (0.021) TRR 0.051 0.076 0.016 (0.068) (0.070) (0.052) Q 0.032 ∗∗∗ 0.032 ∗∗∗ 0.031 ∗∗∗ (0.003) (0.004) (0.003) Cash Flow 0.004 ∗∗ 0.007 ∗∗∗ 0.004 ∗∗ (0.002) (0.002) (0.002) Size 0.017 ∗∗∗ 0.019 ∗∗∗ 0.017 ∗∗∗ (0.005) (0.005) (0.005) Age -0.110 ∗∗∗ -0.084 ∗∗∗ -0.110 ∗∗∗ (0.015) (0.016) (0.016) Observations 11,413 10,080 11,413 AdjustedR 2 0.567 0.532 0.567 PanelB:InteractingwithTotalQ TRR× Total Q -0.063 ∗∗∗ -0.082 ∗∗∗ -0.042 ∗∗∗ (0.023) (0.026) (0.014) TRR -0.025 0.008 -0.034 (0.061) (0.064) (0.043) Total Q 0.035 ∗∗∗ 0.036 ∗∗∗ 0.034 ∗∗∗ (0.002) (0.003) (0.002) Cash Flow 0.003 ∗ 0.004 ∗∗ 0.003 ∗ (0.002) (0.002) (0.002) Size 0.004 0.007 0.004 (0.005) (0.005) (0.005) Age -0.083 ∗∗∗ -0.072 ∗∗∗ -0.083 ∗∗∗ (0.015) (0.016) (0.015) Observations 11,281 9,969 11,281 AdjustedR 2 0.588 0.548 0.588 110 Table 2.6: Talent Retention Risk and Investment in Subsamples This table reports the regression of firm future investment rate on the talent retention risk (TRR) measure and the interaction between TRR and Tobin’s Q in three subsample analyses. Panel A uses subsample divided by fast growing sectors (IT and Healthcare) and other sectors (Consumer, Manufacturing, and Others) following [33]. Panel B uses firm product life-cycle measure from [68] and separates the sample into above average and below average product innovation life-cycle (life1) intensity. Panel C devide the sample into firms with and without positive R&D expense in Compustat. All regressions include firm and year fixed effects. Standard errors are clustered at the firm level. Sample period is from 2010 to 2018. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. PanelA:SubsamplebyIndustryGrowth Fast Growing Others (1) (2) (3) (4) TRR -0.254 ∗∗∗ -0.005 -0.016 0.046 (0.089) (0.111) (0.047) (0.081) TRR× Q -0.099 ∗∗∗ -0.039 (0.036) (0.036) Q 0.026 ∗∗∗ 0.032 ∗∗∗ 0.032 ∗∗∗ 0.034 ∗∗∗ (0.003) (0.004) (0.004) (0.004) Observations 3992 3992 7421 7421 AdjustedR 2 0.535 0.537 0.594 0.594 PanelB:SubsamplebyFirmProductLifeCycle High Product Innovation Stage Low Product Innovation Stage (1) (2) (3) (4) TRR -0.203 ∗∗∗ 0.004 0.013 0.001 (0.075) (0.097) (0.053) (0.102) TRR× Q -0.084 ∗∗∗ 0.009 (0.032) (0.050) Q 0.027 ∗∗∗ 0.031 ∗∗∗ 0.036 ∗∗∗ 0.035 ∗∗∗ (0.003) (0.004) (0.006) (0.007) Observations 5708 5708 5423 5423 AdjustedR 2 0.553 0.555 0.562 0.562 PanelC:SubsamplebyFirmR&DActivity Have R&D Do not have R&D (1) (2) (3) (4) TRR -0.206 ∗∗∗ 0.042 0.038 0.070 (0.069) (0.090) (0.060) (0.102) TRR× Q -0.107 ∗∗∗ -0.021 (0.033) (0.048) Q 0.028 ∗∗∗ 0.034 ∗∗∗ 0.029 ∗∗∗ 0.030 ∗∗∗ (0.003) (0.004) (0.004) (0.005) Observations 5689 5689 5696 5696 AdjustedR 2 0.555 0.558 0.588 0.588 111 Table 2.7: Decomposing TRR: Management vs. Non-Management This table reports our baseline investment regression in Table?? by decomposing TRR into retention risk for talent from the management occupations (SOC 2-digit code = 11) and talent from non-management occupations. See Table ?? for regression specifications. Standard errors are clustered at the firm level. Sample period is from 2010 to 2018. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) TRR -0.135 ∗∗∗ (0.050) TRR(mgmt) -0.145 ∗∗∗ -0.159 ∗∗∗ (0.039) (0.041) TRR(nonmgmt) -0.020 0.085 (0.071) (0.073) Q 0.028 ∗∗∗ 0.028 ∗∗∗ 0.028 ∗∗∗ 0.028 ∗∗∗ (0.002) (0.002) (0.002) (0.002) Cashflow 0.004 ∗∗ 0.004 ∗∗ 0.004 ∗∗ 0.004 ∗∗ (0.002) (0.002) (0.002) (0.002) Size 0.015 ∗∗∗ 0.015 ∗∗∗ 0.015 ∗∗∗ 0.015 ∗∗∗ (0.005) (0.005) (0.005) (0.005) Age -0.114 ∗∗∗ -0.114 ∗∗∗ -0.113 ∗∗∗ -0.113 ∗∗∗ (0.016) (0.016) (0.016) (0.015) Observations 11,413 11,413 11,412 11,412 AdjustedR 2 0.566 0.566 0.565 0.566 112 2.9 Appendix: ConceptualFramework This section presents a simple framework based on the standard Q theory to guide our empirical tests of TRR on firm investment. Consider a two-period investment model with convex adjustment costs. The firm is risk-neutral, max- imizes shareholder value att=0, and uses a zero discount rate for simplicity. At t = 0, the firm is endowed with k 0 physical capital. The firm decides investment I, and receives final payoff at t = 1. Importantly, the firm is also endowed with n 0 talent. Based on survey evidence, we assume that the firm cannot build up talent in short term. However, the firm may lose talent to other firms. At time t = 0, the firm observes job posting intensity in the local labor market which determines the probability p that each talent leaves the company after t = 0. Talent costs wage payment of w per unit. The production function Cobb-Douglas with respect to physical capital and talent: y t =a t k α t n 1− α t Capital accumulation follows: k 1 =(1− δ )k 0 +I 0 Talent changes due to job posting intensityp as: n 1 =(1− p)n 0 113 Crucial, we assume assume that talent affects the firm’s capital adjustment cost based on the CFO survey evidence and prior literature ([74]): C(I 0 ,k 0 )= ϕ (n 1 ) 2 I 0 k 0 2 k 0 The firm maximizes value at t=0 by choosingI 0 ,k 1 . max k 1 ,I 0 V 0 =y 0 − wn 0 − I 0 − C(I 0 ,k 0 )+E 0 [y 1 − wn 1 ] s.t. k 1 =(1− δ )k 0 +I 0 The Lagrangian is: L=a 0 k α 0 n 1− α 0 − wn 0 − I 0 − C(I 0 ,k 0 )+E 0 [a 1 k α 1 n 1− α 1 − wn 1 ]+q 0 [I 0 +(1− δ )k 0 − k 1 ] ∂L ∂I 0 =0⇐⇒q 0 =1+ϕ (n 1 )I 0 (2.2) ∂L ∂k 1 =0⇐⇒q 0 =α ¯a 1 n 1− α 1 (I 0 +(1− δ )k 0 ) α − 1 (2.3) From (1) and (2), we have: (1+ϕ (n 1 )I 0 )(I 0 +(1− δ )k 0 ) 1− α =α ¯a 1 n 1− α 1 114 Hence,I 0 is increasing inn 1 . ∗∗ The firm invest less if the talent retention risk p is higher. From equation (1), we see investment-q sensitivity is ∂I 0 ∂q 0 = 1 ϕ (n 1 ) which increases withn 1 and decreases withp. Hence ∂ 2 I 0 ∂q 0 ∂p = ϕ ′ (n 1 ) ϕ (n 1 ) 2 · n 0 <0 (2.4) An increase in talent retention riskp reduces investment more for firms with a higher q. 2.10 Appendix: TalentTurnoverCost Since TRR is a labor market risk, we expect to see firms’ direct reactions and responses in the labor market. More specifically, we examine whether firms actively hire to counteract talent loss due to the increasing TRR. Furthermore, we estimate the associated cost of talent turnover caused by TRR and compare the direct talent turnover cost with the decrease in capital investment. We argue that the direct talent turnover cost driven by the increase in TRR is sustantial part of the adjustment cost that firms have to pay. ∗∗ Take partial derivative of both sides with respect ton1, we have: (1− α )(1+ϕ (n1)I0)(I0 +(1− δ )k0) − α ∂I0 ∂n1 +(I0 +(1− δ )k0) 1− α ϕ (n1) ∂I0 ∂n1 +ϕ ′ (n1)I0 =α (1− α )¯a1n − α 1 Hence, ∂I0 ∂n1 = α (1− α )¯a1n − α 1 − ϕ ′ (n1)I0(I0 +(1− δ )k0) 1− α (1− α )(1+ϕ (n1)I0)(I0 +(1− δ )k0) − α +(I0 +(1− δ )k0) 1− α ϕ (n1) >0 Becauseϕ ′ (n1)<0. Given thatn1 =n0(1− p), ∂I0 ∂p =− ∂I0 ∂n1 <0 115 Table 2.8: TRR and the Widening Investment-Q Gap This table reports the contribution of TRR on the widening investment-Q gap. We follow [63] and estimate the widening investment-Q gap by running the following baseline specification: Investment i,t+1 = X t β t · Year Dummy t +α · Q i,t +X i,t + Firm FE+ϵ i,t . We next follow [63] and estimate the contribution of TRR on explaining the gap by including TRR into the baseline model, Investment i,t+1 = X t γ t · Year Dummy t +θ · TRR i,t × Q i,t +ψ · TRR i,t +α · Q i,t +X i,t + Firm FE+ϵ i,t . Following [63], the portion of investment-Q gap explain by the rising TRR is estimated by the difference between β 2017 andγ 2017 . Standard errors are clustered at the firm level. Sample period is from 2010 to 2018. Figure 2.6: Top Chief Risk Concerns This figure is generated by CFO Signals ™: 2Q 2022. Talent and retention dominated CFOs’ long list of internal worries this quarter. 116 Table 2.8: TRR and the Widening Investment-Q Gap—Continued PanelA:ExplainingInvestment-Tobin’sQGap Sample ∆ Gap 2010− 2017 : ∆ Gap 2010− 2017 : % TRR Explains Baseline Modelβ 2017 With TRR Controlγ 2017 (γ − β )/|β | All Firms -0.0361 -0.0315 13% (0.0033) (0.0039) Fast Growing Sectors -0.0454 -0.0330 27% (0.0067) (0.0082) Other Sectors -0.0318 -0.0317 0% (0.0035) (0.0040) High-Life1 Firms -0.0494 -0.0395 20% (0.0056) (0.0066) Low-Life1 Firms -0.0283 -0.0295 -4% (0.0042) (0.0049) R&D Firms -0.0431 -0.0326 24% (0.0051) (0.0062) Non-R&D Firms -0.0306 -0.0329 -8% (0.0041) (0.0047) PanelB:ExplainingInvestment-TotalQGap Sample ∆ Gap 2010− 2017 : ∆ Gap 2010− 2017 : % TRR Explains Baseline Model With TRR Control All Firms -0.0338 -0.0299 12% (0.0031) (0.0037) Fast Growing Sectors -0.0405 -0.0300 26% (0.0063) (0.0075) Other Sectors -0.0301 -0.0304 -1% (0.0034) (0.0038) High-Life1 Firms -0.0444 -0.0361 19% (0.0053) (0.0061) Low-Life1 Firms -0.0283 -0.0283 0% (0.0040) (0.0046) R&D Firms -0.0382 -0.0299 22% (0.0046) (0.0057) Non-R&D Firms -0.0302 -0.0319 -6% (0.0041) (0.0046) 117 We use the following specification: Y i,t+k =β · TRR i,t +X i,t + Firm FE+ Year FEϵ i,t , where TRR i,t is the measured talent retention risk of firm i in year t. Y i,t+k measures the job posting, talent inflow, and talent turnover of skilled employees for firm i in yeart+k,k∈{0,1}. X i,t is an array of firm characteristics including tobin’s q, cash flow, firm size, firm age, and log of number of employees. We include firm and year fixed effects, which absorb any firm-specific omitted variables. Standard errors are clustered at firm level. Table?? summarizes the influence of our TRR measure on firm’s job posting, talent inflow, and talent turnover in Columns (1)-(2), (3)-(4), and (5)-(6) respectively. First, we find the firms increase their job posting when TRR is high, which suggests that firm actively hire to counteract talent loss due to the increasing TRR. Second, we show that firms’ active hiring is effective in the sense that the number of talent inflow rises following the increase in job posting. However, the percentage increase in talent inflow is only a third of the percentage increase in job posting. The difference demonstrate the frictions in the process of hiring new talent. Last, we find the overall talent turnover increases dramatically in high TRR period. A one standard deviation increase in talent retention risk leads to 3 percent increase in the talent turnover. The effect is strong both in the same year and one year after. Many researchers have argued that losing and hiring new talents are very expensive, and the cost increases with the skill level, for example, [66], and [23]. Our back-of-envelope calculation shows that the talent turnovers associated with TRR are costly for firms and can explain about 10% of the decrease in capital investment. Table ?? implies that one standard deviation higher TRR increases talent turnover count by two persons for a median firm in our sample, with the median number of total talent turnover being 64. Assume that the cost per turnover is the average annual salary, and given the median wage of 118 skilled occupation is $140K in the sample, a one standard deviation increase in TRR raises turnover cost by $0.28M for a median firm. At the same time, the median of PPEGT is $755M, and a one standard deviation increase in TRR reduces CPAX by $2.9M. Our assumption is that the talent turnover cost as one year of salary is likely to be a lower bound in the literature. [23] show the personnel cost for interviewing job candidates is about ten times for managers or skilled workers with a vocational degree than for low-skilled occupations, especially in large firms. [17] also assumes that skilled labor is ten times more expensive to adjust than unskilled labor. Given that the average recruiting cost for low-skill occupations is 10.5 weeks of salary in [23], our estimation of the recruiting cost for skilled workers could be more than 105 weeks of salary, which is twice as large as what we assumed. Our back-of-envelope calculation aims to offer an approximation of direct adjustment cost associated with employee turnovers, which we find is about 10% of the decrease in capital investment. The overall ad- justment cost driven by TRR will be much larger, as the literature shows an interaction effect between labor and adjustment frictions, where employee turnover indirectly makes capital adjustment costlier ([47]). 119 Table 2.9: Managers in our TRR measure Manager Title Emp. Share Financial Managers 20% Sales Managers 14% Managers, All Other 14% Computer and Information Systems Managers 13% Construction Managers 9% Architectural and Engineering Managers 8% Marketing Managers 7% Transportation, Storage, and Distribution Managers 4% Human Resources Managers 4% Purchasing Managers 3% Natural Sciences Managers 2% Training and Development Managers 1% Compensation and Benefits Managers 1% ... ... 120 Table 2.10: A Comprehensive Search for “Which Talent Matters” We repeat our CAPX regression using alternative TRR based on each broad occupation. Sample period from 2010- 2018. CAPX i,t+1 /PPEGT i,t =β · TRR i,o,t +X i,t +FirmFE+YearFE+ϵ i,t , whereCAPX i,t+1 /PPEGT i,t is the capital investment of firm i in yeart+1, andTRR i,o,t measures the talent retention risk for occupationo of firm i in yeart. Control variablesX i,t are tobin’s q, cash flow, firm size, and firm age. We include firm fixed effects, which absorb any firm-specific omitted variables, and year fixed effects. Standard errors are clustered at firm level. SOC Talent Definition coef. s.e. 11-0000 Management -0.189*** (0.057) 11-0000 Management (ex. Executive) -0.182*** (0.056) 13-0000 Business and Financial Operations -0.112 (0.120) 15-0000 Computer and Mathematical -0.098** (0.044) 17-0000 Architecture and Engineering 0.019 (0.055) 19-0000 Life, Physical, and Social Science 0.044 (0.125) 21-0000 Community and Social Service 0.125 (0.376) 23-0000 Legal 0.067 (0.103) 25-0000 Educational Instruction and Library -0.101 (0.376) 27-0000 Arts, Design, Entertainment, Sports, and Media 0.009 (0.038) 29-0000 Healthcare Practitioners and Technical -0.088 (0.069) 31-0000 Healthcare Support -0.330 (0.452) 33-0000 Protective Service 0.133 (0.169) 35-0000 Food Preparation and Serving Related 0.457 (0.460) 37-0000 Building and Grounds Cleaning and Maintenance 0.215 (0.550) 39-0000 Personal Care and Service 0.270 (0.454) 41-0000 Sales and Related -0.066 (0.054) 43-0000 Office and Administrative Support -0.009 (0.191) 45-0000 Farming, Fishing, and Forestry 0.508 (2.212) 47-0000 Construction and Extraction 0.836* (0.450) 49-0000 Installation, Maintenance, and Repair -0.162 (0.178) 51-0000 Production 0.068 (0.241) 53-0000 Transportation and Material Moving -0.318 (0.225) 121 Table 2.11: Does TRR Lead to Talent Outflows? Evidence Across Industries Log Outflow of Talent t t t + 1 t+1 TRR 0.43 ∗ 0.59 ∗ 0.53 ∗∗ 0.61 ∗∗ (0.24) (0.31) (0.23) (0.29) TRR× Fast-growing -0.32 -0.12 (0.34) (0.35) Q -0.03 ∗∗∗ -0.03 ∗∗∗ 0.01 0.01 (0.01) (0.01) (0.01) (0.01) Cashflow 0.01 ∗∗ 0.01 ∗∗ 0.01 0.01 (0.01) (0.01) (0.01) (0.01) Size 0.29 ∗∗∗ 0.21 ∗∗∗ 0.38 ∗∗∗ 0.27 ∗∗∗ (0.03) (0.04) (0.03) (0.04) Age 0.28 ∗∗∗ 0.26 ∗∗∗ 0.12 0.09 (0.08) (0.08) (0.08) (0.08) Emp 0.20 ∗∗∗ 0.25 ∗∗∗ (0.06) (0.06) Observations 9603 9562 9607 9566 AdjustedR 2 0.92 0.92 0.92 0.92 122 Table 2.12: Talent Retention Risk and Employee Turnover Sample period from 2010-2018. Columns (1-2) Job Posting (t, t+1), Inflow (t, t+1), Total Turnover (t, t+1)) Y i,t+k =β · TRR i,t +X i,t + Firm FE+ Year FEϵ i,t , where TRR i,t is the measured talent retention risk of firm i in yeart. Y i,t+k measures the job posting, talent inflow, and talent turnover of skilled employees for firm i in yeart+k,k∈{0,1}. X i,t is an array of firm characteristics including tobin’s q, cash flow, firm size, firm age, and log of number of employees. We include firm and year fixed effects, which absorb any firm-specific omitted variables. Standard errors are clustered at firm level. Log Job Post for Talent Log Inflow of Talent Log Turnover of Talent t t+1 t t+1 t t+1 TRR 2.06 ∗∗∗ -0.21 0.61 ∗∗∗ 0.52 ∗∗ 0.69 ∗∗∗ 0.63 ∗∗∗ (0.38) (0.36) (0.21) (0.22) (0.20) (0.20) Q 0.01 0.08 ∗∗∗ 0.04 ∗∗∗ 0.08 ∗∗∗ 0.01 0.05 ∗∗∗ (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) Cashflow -0.00 -0.01 0.00 -0.00 0.01 -0.00 (0.00) (0.01) (0.00) (0.01) (0.00) (0.01) Size 0.13 ∗∗ 0.29 ∗∗∗ 0.29 ∗∗∗ 0.27 ∗∗∗ 0.26 ∗∗∗ 0.28 ∗∗∗ (0.05) (0.05) (0.04) (0.04) (0.04) (0.04) Age -0.02 0.18 -0.08 -0.06 0.06 0.01 (0.13) (0.13) (0.08) (0.08) (0.07) (0.08) Emp 0.68 ∗∗∗ 0.52 ∗∗∗ 0.21 ∗∗∗ 0.08 0.20 ∗∗∗ 0.15 ∗∗∗ (0.09) (0.09) (0.06) (0.05) (0.06) (0.06) Observations 9293 9293 9562 9566 9562 9566 AdjustedR 2 0.87 0.88 0.93 0.93 0.95 0.95 123 Figure 2.7: Measuring Talent Retention Risk: An Example This figure illustrates how we construction the measure of talent retention risk for a given firm. We first construct a talent retention risk measure for each occupation within a firm, and then aggregate the occupation talent retention risk into firm level risk using occupation employment share within the firm. In this hypothetical example, Tesla has two branches: one in San Francisco and another in Austin. For the financial manager occupation, ω share of financial managers locate in San Francisco, and 1− ω share locate in Austin. In San Francisco, the talent retention risk of financial manager is measured by the vacancy to employment ratio. The denominator is the total number of financial managers in San Francisco from the OES MSA-Occupation Employment Panel. The numerator is the total number of job post for financial managers in San Francisco. To instrument the exogenous local demand for financial managers, we exclude the job posts from Tesla’s top 3 industries. The talent retention risk of financial managers for Tesla is the weighted average of the vacancy to employment ratios for financial managers in San Francisco and Austin. The weights areω and1− ω respectively. Vacancy/Employment ---Financial Manager (Ex. Vacancy from Tesla’s top 3 industries) Vacancy/Employment ---Financial Manager (Ex. Vacancy from Tesla’s top 3 industries) San Francisco MSA Austin MSA Financial Managers in SF (−) Financial Managers in AUS 124 Figure 2.8: Defining Skilled Labor This figure illustrates the occupation distribution of skilled labor used in our talent retention measure. We define an occupation as skilled if the occupations requiring a college degree & 4-year working experience in the O ∗ NET database of occupational characteristics and worker requirements information across the U.S. economy. Occupation is defined at the 2010 SOC 2 digits level, and the occupation shares are from the OES National Employment Share database. Management Computer and Mathematical Business and Financial Operations Healthcare Practitioners and Technical Architecture and Engineering Arts, Design, Entertainment, Sports, and Media Life, Physical, and Social Science Transportation and Material Moving Legal 125 Figure 2.9: Talent Retention Concerns in Duke CFO Survey (Controlling for Firm Heterogeneity) This figure plots the percentage of CFOs electing “attracting and retaining qualified employees” as the top firm- specific concerns using the microdata of the Duke CFO Survey. During 2008Q4-2014Q1, the survey asked CFOs to elect from about 10 options to answer “Whatarethetopthreeinternal,company-specificconcernsforyourcorporation? ” During 2015Q1-2019Q4, the survey asked CFOs to elect from about 18 options to answer “During the past quarter, which items have been the most pressing concerns for your company’s top management team? (Choose up to 4)” Both waves of survey include the option “attracting and retaining qualified employees.” The survey did not answer related questions during the transitional interim quarters. Because the survey changed the question in 2014, we shift the percentage of CFOs electing “attracting and retaining qualified employees” in the first quarter of the later wave to align with the percentage in the last quarter of the earlier wave. In each period, we run the following regression to extract the coefficients of the time dummies, β t , Dummy i,t = X t β t YYYYQ t +Revenue i,t +Employment i,t +FE Industry× Ownership +ϵ i,t , whereDummy i,t equals one if the CFO elect “attracting and retaining qualified employees” and standard errors are clustered by industry and quarter. 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 126 Chapter3 BorrowfromEmployees The longer the interval between payments, therefore, the larger the loan which the workingman makes to his employer without interest. Robert Gildersleeve Paterson, 1917 3.1 Introduction Employees typically supply their labor to employers first and then get paid later. ∗ With a monthly payday schedule, there is, on average, a 15 day delay between labor being supplied and being compensated. As a result, firms equivalently borrow half a month’s salary from each employee every year by repeating the same short-term delays. The size of such borrowing is nontrivial. For a median US household in 2010, a half-month income is approximately 75 percent of cash-like savings. For a median Compustat firm, a half-month staff expense is about 21 percent of its cash and equivalents holdings. Similar payment delays between suppliers and customers provide important short-term liquidity for many firms and usually ∗ Only 2% to 5% of job postings on Indeed advertised signing bonuses (Konkel, 2022). [109] documents that even among executives at Standard Poor’s 1500 firms, only 12.0% of them received a signing bonus. [107] finds that 60% to 70% of a top 20 U.S. MBA program for the years 2002 to 2009 receive offers with signing bonuses. 127 require very high borrowing interest rates, as shown in the trade credit literature ([90] and [96]) † . This paper studies the labor “trade credit" between firms and their employees and its importance for both sides. In this paper, I ask the following questions. First, do wages adjust when the size of such implicit borrowing is exogenously changed? Second, what are the effects on firms and employees when the size of such implicit borrowing is changed? Third, how should we evaluate the social efficiency gains and losses resulting from implicit borrowing between firms and employees? In a frictionless competitive world, wages should fully compensate for the interest of such implicit borrowing. Any changes should only change the nominal wages and have no other real effects. However, with financial market frictions, if firms and workers face different interest rates, it is unclear which interest rate should be used to compensate for the implicit borrowing. Moreover, with labor market frictions as in [42], [98], and [3], firms and workers bargain to split the surplus from a job match, which can create wage compression and the borrowing interest may not be fully compensated. Moreover, wages are sticky, especially downwards, as documented by [19] and [79], which can also stop wages from correctly compensating for the implicit borrowing. This paper exploits a series of historical state regulation changes to study the labor “trade credit" be- tween firms and employees and answer the above questions. From the 1880s to the 1910s, 31 states passed payday frequency requirement laws that mandated wages to be paid at least semi-monthly or biweekly rather than monthly. Higher payday frequency reduces the amount of implicit borrowing from employees because the average delay between labor supply and compensation is shortened (Figure??). I use the his- torical censuses of manufacturers between the 1860s and 1930s to measure manufacturing establishments, the number of employees, wage expense, and labor productivity at the county-by-industry level. I use historical 1% population censuses between the 1900s and the 1930s to measure household consumption proxied by home ownership. † And also the following works by [20] and [34] 128 I begin by studying the changes in wages after states raised the payday frequency from monthly to at least semimonthly or biweekly. In a frictionless competitive world, wages should fully compensate for the interest from such implicit borrowing, and then higher payday frequency will cause a drop in nominal wages. Because the amount of implicit borrowing from employees is reduced with higher payday frequency, the wage compensation for such implicit borrowing is reduced correspondingly. Contrary to this neoclassical hypothesis that predicts a drop in wages, I find the average salaries increased by about 5.5 percent. To control for industry trends and location specificity, I include industry-by-year fixed effects, industry-by-state fixed effects, and county fixed effects. To address the endogeneity concern that some omitted variables affect both the state-level reforms and wages, I restrict the analysis to the border counties in each state, which are presumed to have similar economic conditions. Additional robustness analyses indicated that the estimated results are not driven by the potential bias discussed by [58] for staggered difference-in-differences. The rise in wages suggests that the payday frequency and hence the “implicit borrowing" from em- ployees may not be neutral. I further study other firm characteristics to understand the exact mechanisms that lead to higher wages. Using similar empirical specifications for the wage analysis, I find that firms reduced their employment size. The remained workers were, on average, more productive and operated more capital per worker. This evidence is consistent with higher payday frequency reforms reducing the amount of cheap borrowing from employees, which effectively raised the marginal labor cost for firms. In response, firms laid off lower-productivity workers, and wages rose as a result of higher marginal la- bor productivity. The results demonstrate that implicit borrowing from employees is important for firms. Exogenous shocks that restrict the amount of such borrowing have real impacts on firm decisions. The data do not support an alternative hypothesis where the higher payday frequency added an administrative burden on firms and caused changes in wages and employment. 129 On the household side, I find that reducing implicit borrowing by requiring higher payday frequency was beneficial overall to households, as shown by a rise in home ownership. The increase in home owner- ship was smaller for lower-income households, who faced the reduced firm labor demand for lower pro- ductivity workers. However, within lower-income households, those potentially more severely financially constrained benefited the most from the reforms. Being paid earlier and more frequently can potentially make them less reliant on expensive external credits ([15] and [102]). Given that the above results are estimated using historical data, I construct a stylized model to gen- eralize the economic intuitions for policy evaluations in today’s economy. In the model, higher payday frequency leads to a smaller employment size and raises the marginal productivity of labor, and there- fore wages rises as a result of Nash bargaining à la [42] and [92]. The relative magnitude of financial constraints that households and firms face determines whether reducing borrowing from employees by requiring higher payday frequency will be socially optimal or not. Intuitively, when households are more financially constrained, i.e., facing higher external borrowing rates or investment returns, reallocating the labor “trade credit" from firms to households can add value. When firms are more financially constrained, reallocating the labor “trade credit" away from firms destroys social efficiency because households value one additional dollar less than the firms do. One policy suggestion is that the payday frequency requirements should be firm and household spe- cific. First, higher payday frequency should target lower-income and financially constrained households, which value earlier wage payments the most. Indeed, many states protect manufacturing workers by requiring them to be paid more frequently as opposed to other professionals. Second, higher payday fre- quency is more appropriate for larger and non-growing firms that are not financially constrained or have lower returns from additional investments. These firm-specific requirements have not been implemented in any states yet. In short, firms should pay their employees more frequently when they are not financially constrained or have no good investment opportunities. 130 This paper directly speaks to a growing body of literature that studies the effect of payday frequency on household outcomes. [93] discussed a novel model with workers who have self-control problems and argued that wage pay should match the timing of workers’ consumption needs. [15] empirically showed that higher paycheck frequency results in less credit card borrowing. They theoretically proposed that higher paycheck frequency increases households’ investments in illiquid savings vehicles. To the best of my knowledge, my study is the first to study the effect of payday frequency on firms. Higher payday frequency raised the labor cost for firms and reduced their labor demand. I also find that higher payday frequency led to a rise in home ownership, which is consistent with the illiquid savings hypothesis that [15] conjectured. [102] studied the short-term wage dynamics of one firm around the 1886 reform in Mas- sachusetts, and they found that the average wage decreased within half a year after the reform. My paper differs by studying the population of manufacturing establishments using the censuses of manufacturers. Moreover, my research focuses on the long-term consequences of the reforms. This paper also contributes to the literature on trade credit. [90] noted that trade credit represents a substantial fraction of corporate liabilities. [96] showed that trade credit is important as a source of financ- ing, particularly for small firms. [20] proposed that trade credit can alleviate the asymmetric information problem between banks and firms. [34] demonstrated that the valuable relationship between customers and suppliers can help trade credit to overcome the limited contract enforceability problem and act as liq- uidity insurance. This paper is novel to studying the labor “trade credits" between firms and one of their most crucial suppliers: employees, which I show is vital for both firms and employees. Shocks to such labor “trade credits" can generate real impacts on both business decisions and household consumption. The rest of the paper is organized as follows. Section 2 discusses the research design, Section 3 describes the data, Section 4 shows the effects of payday frequency reforms on wages, Section 5 estimates the effects on firm employment and labor productivity, Section 6 displays the evidence on the household side, Section 7 presents a stylized model for policy evaluation, and Section 8 concludes. 131 3.2 ResearchQuestionsandDesign 3.2.1 "Borrow"fromEmployees Figure ?? illustrates how firms borrow from their employees when salaries get paid at the end of each month. Assume each month has 30 days. For the work on day 1, the payment comes 29 days after the employee supplies the labor. The firm borrows the salary of one day for 29 days. The interval between labor supply and wage payments becomes shorter starting on day 2. For the work on day 15, the payment comes 15 days after the employee supplies the labor. The firm borrows the salary of one day for 15 days. For the work on day 23, the payment comes seven days after the employee supplies the labor. The firm borrows the salary of one day for seven days. On average, the firm borrows a month’s salary for 15 days. Or, equivalently, the firm borrows half a month’s salary for 30 days. Each year, by repeating the same short-term borrowing pattern, the firm borrows half a month’s salary for 365 days. The size of such borrowing is nontrivial for a typical US household and a typical US firm. Table ?? reports the size of half a month’s salary for a typical median US household as a percentage of their liquid assets and the size of half a month’s salary expense for a US Compustat firm as percentage points of their liquid liabilities. For a median US household in 2010, a half-month income is approximately $1,960, which is about 4 percent of their total net worth, 7 percent of their home equity value, 75 percent of cash-like savings, and 115 percent of net liquid wealth. For a median Compustat firm, a half-month staff expense is $2 million, which is about 8 percent of net cash flow, 16 percent of accounts payable, 21 percent of cash and equivalents holdings, and 30 percent of debt in current liabilities. The ratios can be potentially greater for private firms, which are generally more financially constrained. This paper asks the following questions regarding this implicit borrowing from employees. First, do wages fully compensate for the interest of implicit borrowing? Second, what are the effects on firms and 132 Figure 3.1: An Example: Pay at the End of Each Month This figure illustrates how firms borrow from their employees when salaries get paid at the end of each month. Assume each month has 30 days. For the work on day 1, the payment comes 29 days after the employee supplies the labor. The firm borrows the salary of one day for 29 days. The interval between labor supply and wage payments becomes shorter starting on day 2. For the work on day 15, the payment comes 15 days after the employee supplies the labor. The firm borrows the salary of one day for 15 days. For the work on day 23, the payment comes seven days after the employee supplies the labor. The firm borrows the salary of one day for seven days. On average, the firm borrows a month’s salary for 15 days. Or, equivalently, the firm borrows half a month’s salary for 30 days. Table 3.1: The Size of Half a Month Salary for a Median US Household and a Compustat Firm This table reports the size of half a month’s salary for a typical median US household as a percentage of their liquid assets and the size of half a month’s salary expense for a US Compustat firm as a percentage of their liquid liabilities. The household’s balance sheet data are from [82]. For a median US household in 2010, the annual income is $47,040. A half-month income is approximately $1,960. The median net liquid wealth is $1,714. Cash, checking, savings, and money market mutual fund accounts are $ 2,640. The housing value net of mortgages is $29,000. The total net worth is $56,721. The firm balance sheet data are from Compustat, from 1950 to 2020. I excluded financial, utility, and public service firms. The median staff expense is $48 million. A half month staff expense is $2 million. The median net cash flow (ib plus dp) is $17 million. The median accounts payable (ap) is $13.5 million. The median cash and equivalents (che) is $8.5 million. Debt in current liabilities (dlc) is $3.8 million. A Median US Household % of Net Worth 4 % of Home Equity 7 % of Cash and Equivalents 75 % of Net Liquid Wealth 115 A Median Compustat Firm % of Net Cash Flow 8 % of Accounts Payable 16 % of Cash and Equivalents 21 % of Short Term Debt 30 133 employees if the size of such borrowing is changed? Third, how should we evaluate the social efficiency gains or losses because of such implicit borrowing? 3.2.2 PaydayFrequencyReforms This paper leverage a series of state regulation changes to answer the above questions. From the 1880s to the 1910s, 31 states passed payday frequency requirement laws that mandated wages to be paid at least semi-monthly or biweekly. ‡ For example, [94] documented that “Pennsylvania passed a law in 1887 to secure the semi-monthly payment of wages, and the act applied to ‘every individual, firm, association, or corporation employing wage workers, skilled or ordinary laborers, engaged at manual or clerical work, in the business of mining or manufacturing’". How does payday frequency relate to the implicit borrowing from employees? Generally speaking, higher payday frequency means smaller implicit borrowing from employees. Figure ?? illustrates the equivalent borrowing in a semi-monthly payday system. A firm borrows a quarter of a month’s salary for 365 days each year. Compared to Figure ??, the amount of implicit borrowing in the semi-monthly payday system is only half of the amount of borrowing in an alternative monthly payday system. This pattern can be extrapolated toward a broader range of payday frequency requirements. 3.2.3 ResearchDesignandHypotheses In this paper, I use payday frequency reforms as shocks that reduced the size of implicit borrowing from employees. With a staggered difference-in-differences design, I directly test how wages, firms, and house- holds responded to these shocks. ‡ Massachusetts (1886), Connecticut (1886), Virginia (1887), New Hampshire (1887), Pennsylvania (1887), West Virginia (1887), Maine (1887), Wisconsin (1889), New York (1890), Ohio (1891), Rhode Island (1891), Wyoming (1891), Iowa (1894), New Jersey (1896), Kentucky (1898), Arizona (1901), Maryland (1902), Hawaii (1903), Vermont (1906), Oklahoma (1909), Arkansas (1909), Missouri (1911), Louisiana (1912), Tennessee (1913), Illinois (1913), Michigan (1913), South Carolina (1914), Minnesota (1915), Kansas (1915), North Carolina (1915), Texas (1915). 134 Table 3.2: State Payday Frequency Reforms From the 1880s to 1910s, 31 states passed payday frequency requirement laws that mandated wages to be paid at least semi-monthly or biweekly. The exact years of the regulation changes are collected from [94]. Decades States 1880s Massachusetts, Connecticut, Virginia, New Hampshire, Pennsylvania, West Virginia, Maine, Wisconsin 1890s New York, Ohio, Rhode Island, Wyoming, Iowa, New Jersey, Kentucky 1900s Arizona, Maryland, Hawaii, Vermont, Oklahoma, Arkansas 1910s Missouri, Louisiana, Tennessee, Illinois, Michigan, South Carolina, Minnesota, Kansas, North Carolina, Texas Figure 3.2: An Example: Pay at the End of Each Semi-Month This figure illustrates how firms borrow from their employees when salaries get paid at the end of each semi-month. Assume each month has 30 days. For the work on day 1, the payment comes 14 days after the employee supplies the labor. The firm borrows the salary of one day for 14 days. The interval between labor supply and wage payments becomes shorter starting on day 2. For the work on day 15, the payment comes 0 days after the employee supplies the labor. The firm does not borrow the salary of that day. For the work on day 23, the payment comes seven days after the employee supplies the labor. The firm borrows the salary of one day for seven days. On average, the firm borrows a month’s salary for 7.5 days. Or, equivalently, the firm borrows a quarter of a month’s salary for 30 days. 135 In a frictionless world, such changes should only decrease wages but have no other real effects for the following reasons. First, if the labor market is perfectly competitive, wages should fully compensate for the value of interest from implicit borrowing. As the reforms lead to smaller “loan" amounts, the interest compensation part becomes smaller, and so does the wage. Second, firms and households should be able to use financial markets to smooth any changes in payment timing. The actual investment, production, and consumption should be independent of the payday frequency. Data did not support any of the above neoclassical hypotheses in the setting of state payday frequency reforms. I found that average wages rose after the reforms, whereas firm sizes shrunk in the number of employees. Lastly, households increased their housing consumption. 3.3 DataandDescriptiveStatistics I use the historical censuses of manufacturers between the 1860s and 1930s to measure firm responses. Every 10 years, the censuses of manufacturers published information about manufacturing establishments at the county-by-industry level. The censuses were digitized by [84] and can be downloaded from the author’s website. For the entire period, the censuses reported the number of employees, sales, wage ex- pense, cost of materials, value-added, and capital stock for each industry in a county. From 1890 onwards, the censuses started to distinguish between wage earners and salaried officials, which I use to proxy for managerial costs that could potentially arise because of higher payday frequency. To measure household consumption, I use the historical 1% population censuses between the 1900s and the 1930s from IPUMS data ([103]). The sample period is shorter than for the firms because the “home ownership" variable is only available from 1900 onwards. Home ownership is the only variable that can be used to proxy for household consumption during this sample period. Although housing consumption is only one item in the household consumption basket, it is arguably one of the most important. The censuses 136 also provide household-level demographic characteristics: literacy, race, and immigrant status. I use the three variables to proxy for financial constraints. Table ?? shows the descriptive statistics. The top panel reports the industry-by-county level aggre- gates from censuses of manufacturers from the 1860s to the 1930s. The variables include the number of establishments, workers, labor expense, sales, value-added, and capital stock. On average, there were 20 establishments and 447 workers for a given industry in a given county. The middle panel reports the characteristic of an average firm calculated based on the industry-by-county level aggregates. The av- erage establishment had 24 workers, and each earned a wage of 570 dollars. The bottom panel reports the household-level variables from the household censuses. About 47 percent of households owned their dwellings. 3.4 WageandPaydayFrequencyReforms In a perfectly competitive labor market, wages should fully compensate for all interest that occurs from the implicit borrowing between firms and employees. As higher payday frequency decreases the borrowing amount (Section ??), the average wage is expected to become lower after state-level payday regulations are passed. 3.4.1 WagesIncreasedafterReforms On the contrary, using the following regression, the results show that wages increased after reforms: ln(Wage) i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k , where Wage i,k,t is the average wage of a worker in industryi at countyk on yeart. Reform k,t is a dummy variable that equals one if year t is after the corresponding state passed a payday frequency regulation. 137 Table 3.3: Summary Statistics This table shows the descriptive statistics. The top panel reports the industry-by-county level aggregates from censuses of manufacturers from the 1860s to the 1930s. The variables include the number of establishments, the number of workers, labor expense, sales, value-added, and capital stock. The last four are all in dollars. The middle panel reports the characteristic of an average firm calculated based on the industry-by-county level aggregates. The variables include the number of workers, the average worker’s wage, the ratio of officers to workers, value added per worker, sales per worker, and capital per worker. The bottom panel reports the household-level variables from the household censuses from the 1900s to the 1930s. The variables include the dummy variables of home ownership, literacy, race, and immigrant status. N Mean SD P10 P50 P90 Industry-by-County Aggregates Number of Establishments 47080 19.58 43.87 2 6 41 Number of Workers 47071 446.99 1,331.54 7 62 911 Labor Expense 47061 329,635.17 1,086,452.02 2770 32335 606705 Sales 47061 1,884,185.11 6,496,686.90 13650 156000 3405285 Value Added 47042 859,473.76 2,891,974.70 7925 80057.5 1584063 Capital 42119 825,777.75 2,842,050.81 4400 59000 1504226 An Industry-by-County Average Firm Number of Workers 44084 23.53 45.93 1.833333 8.25 54.19048 Average Wage 43976 569.89 336.09 261 477.551 1100.073 Officer to Worker Ratio 26013 0.17 0.15 0 .1333333 .3688525 Value Added Per Worker 43957 1,625.41 1,423.59 540 1150 3238.294 Sales Per Worker 43976 3,581.61 4,204.88 955.9738 2165.917 7364.246 Capital Per Worker 42021 1,828.09 2,199.76 309.0909 1081.765 4115.385 Households Home Owner 476980 0.47 0.50 0 0 1 Literacy 481864 0.89 0.31 0 1 1 Nonwhite 481864 0.17 0.37 0 0 1 Immigrant 481864 0.32 0.47 0 0 1 138 Table 3.4: Wage and Payday Frequency Reforms ln(Wage) i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Wage i,k,t is the average wage of a worker in industryi at countyk on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry- by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by-county fixed effects are included. The sample period is from 1860 to 1930. Standard errors double clustered at the industry level and the state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. ln (Wage) Full Sample Border Counties (1) (2) (3) (4) Reform 0.0563*** 0.0535*** 0.0279** 0.0261** (0.0129) (0.0125) (0.0134) (0.0129) Observations 37,865 23,737 18,753 13,343 R-squared 0.847 0.884 0.842 0.881 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 139 Ind-Year FEs are the industry-by-year fixed effects, Ind-State FEs are industry-by-state fixed effects, and County FEs are county fixed effects. The results are reported in Table??. Columns (1) and (2) show the full sample estimations. In column (1), industry-by-state fixed effects and county fixed effects are included. Industry-by-county fixed effects are included in column (2). Standard errors are double clustered at the industry level and state-by-year level. The sample period is from 1860 to 1930. Unlike the neoclassical hypothesis that predicts a drop in wages, I find average wages increased by about 5.5 percent after states raised the payday frequency from monthly to at least semimonthly or bi- weekly. The results are robust to various combinations of fixed effects. If the increase in wages was caused by higher payday frequency, then we expect the effects to be stronger in states that require the payday frequency to be weekly rather than semimonthly or biweekly. The higher the payday frequency is, the smaller the amount of borrowing from employees. Table ?? columns (1) and (2) show that the increase in wages was indeed more significant in states that required a weekly payday schedule. Figure ?? shows the dynamics of wages around the state reforms. Prior to the reforms, there was no pre-trend in average wages. And after the reforms, the average wage rose by more than 5 percent. 3.4.2 StateBorderCounties To rule out potential omitted variables that drove labor wages other than the state payday frequency reforms, I restrict the above analysis to counties on state borders. The identification assumption is that neighbor counties share similar demographic and economic characteristics and only differ because they are located in different states. By comparing the same industry in two neighboring counties before and after the payday reforms, the estimated difference should be solely driven by the difference in regulations. Moreover, firms’ behaviors in border counties are affected by the state’s regulations, but the reverse is not 140 Figure 3.3: Wage Around the Payday Reforms Figure (a) visualizes the dynamics of the average wage around the state payday frequency reforms using the entire sample. Figure (b) shows the same coefficients using a smaller sample with only state border counties. Both figures are estimated from the following regression: ln(Wage) i,k,t =α + T X β T · Window T,k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Wage i,k,t is the average wage of a worker in industryi at countyk on yeart. Window T,k,t is a dummy variable that equals one if yeart is within the range ofT − 5 years andT +5 years after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects, Ind-State FEs are industry-by-state fixed effects, and County FEs are county fixed effects. The sample period is from 1860 to 1930. Standard errors are double clustered at the industry level and state-by-year level. The 95% confidence intervals are reported. -.05 0 .05 .1 Wage -20 -10 0 10 20 Wage and Payday Frequency Reform (a) (a) Full Sample -.05 0 .05 .1 Wage -20 -10 0 10 20 Wage and Payday Frequency Reform (b) (b) State Border Counties 141 likely to hold, given the small size of a county. Reverse causality is less of a concern when focusing on border counties. The results are reported in columns (3) and (4) of Table??. I find that average wages increased by about 2.6 percent after state payday reforms. Figure?? shows the dynamics of wages around the state reforms. Similarly, no pre-trend is detected. After the reforms, the average wage rose by more than 2.5 percent. 3.4.3 DecomposetheWageStaggeredDiDs As shown by [58], the estimated average treatment effects from a staggered DiDs design can be viewed as a weighted average of DiDs estimation from all possible combinations of treated and control groups. Furthermore, the staggered DiDs estimation can be biased when the treatment effects are time-varying. To address this concern, I randomly split the observations from the states without reforms (the control group) into four parts. Then I match each random control sub-sample with a sub-sample of states that passed their payday frequency regulation in the same decades. Next I independently estimate the treatment effects for each of the four sub-sample. In this way, the estimation for each sub-sample is free from the critiques from [58]. Because there is a 10-year gap between each census, this method ensures no differential treatment timing within each sub-sample from an empirical perspective. In other words, no earlier treated groups will be used as control groups for later treated groups. Table ?? reports the results for the four sub-samples. Columns (1)-(4) use states that passed payday regulations in the 1880s, 1890s, 1900s, and 1910s, respectively. All sub-sample estimations show increased wages after the payday frequency reforms were enacted. The estimated treatment effects are larger than the estimation from the staggered DiDs method. This difference in magnitudes is not too surprising, how- ever, as [58] demonstrated the estimation from staggered DiDs is the weighted average of the estimations from between the never treated and treated groups and the estimations from between the earlier treated and later treated groups, where the weights can be negative in various occasions. 142 Table 3.5: Decompose the Wage Staggered DiDs ln(Wage) i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Wage i,k,t is the average wage of a worker in industryi at countyk on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1)-(4) use states that passed payday regulations in the 1880s, 1890s, 1900s, and 1910s, respectively. All estimations include industry-by-county fixed effects. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, ln (Wage) 1880s 1890s 1900s 1910s (1) (2) (3) (4) Reform 0.147*** 0.133*** 0.103* 0.0642 (0.0474) (0.0451) (0.0614) (0.0592) Observations 7,126 8,364 527 3,934 R-squared 0.871 0.885 0.953 0.902 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-County Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 143 3.5 FirmSize,LaborProductivity,andIndustryAggregates How can we then explain the increase in wages after the regulations were enacted? After payday frequency reforms, I find that firms reduced their employment size. The remaining workers were more productive and operated more capital per worker. This evidence suggests that wages did not already fully compensate for the borrowing interest. After the payday frequency reforms, the amount of “cheap credit" per employee decreased. Firms laid off lower-productivity workers and replaced them with more capital. Overall, the results demonstrate that implicit borrowing from employees is an important financial source for firms. Further, exogenous shocks that restricted the amount of borrowing caused real changes in firm decisions. 3.5.1 NumberofWorkers Using the same empirical design for wages, I explored the effects of higher payday frequency on the number of workers employed. The results are reported in Table??. Despite the increase in wages, the industry-level employment size decreased by more than ten percent. The same pattern also holds for the average number of workers at an establishment (Table ??). Figure ?? shows the dynamics of employment size around the state reforms. Before the reforms, there was no pre-trend. After the reforms, the employment size dropped by more than 5 percent. The above finding is robust to the following robustness checks. First, the estimations of independent DiDs are always negative using each sub-sample of states that passed the regulation in the same decades (Table??). Second, the estimated effects are negative using only state border counties (Table ?? and Figure ??). The decrease in industry size was the most obvious in terms of employment. However, Table?? shows the industry became smaller in sales, value-added, total labor expense, and the number of establishments. The estimated effects are always negative, although sometimes not statistically significant, and similar patterns hold if using state border counties (Table??). 144 Table 3.6: Number of Employees and Payday Frequency Reforms ln(Emp) i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Emp i,k,t is the natural log of total number of workers in industryi at countyk on yeart. Reform k,t is a dummy variable equal to one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry-by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by-county fixed effects are included. The sample period is from 1860 to 1930. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. ln (Number of Employees) Full Sample Border Counties (1) (2) (3) (4) Reform -0.145*** -0.153** -0.145** -0.118 (0.0543) (0.0601) (0.0689) (0.0765) Constant 4.394*** 4.654*** 4.486*** 4.736*** (0.0215) (0.0264) (0.0293) (0.0356) Observations 37,882 23,751 18,765 13,354 R-squared 0.758 0.843 0.785 0.847 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 145 Figure 3.4: Number of Employees Around the Payday Reforms Figure (a) visualizes the dynamics of the total number of workers around the state payday frequency reforms using the full sample. Figure (b) shows the same coefficients using a smaller sample with only state border counties. Both figures are estimated from the following regression: ln(Emp) i,k,t =α + T X β T · Window T,k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Emp i,k,t is the natural log of total number of workers in industryi at countyk on yeart. Window T,k,t is a dummy variable that equals one if yeart is within the range ofT− 5 years andT +5 years after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects, Ind-State FEs are industry-by-state fixed effects, and County FEs are county fixed effects. The sample period is from 1860 to 1930. Standard errors are double clustered at the industry level and state-by-year level. The 95% confidence intervals are reported. -.2 0 .2 .4 Wage -20 -10 0 10 20 Number of Employees and Payday Frequency Reform (a) (a) Full Sample -.2 0 .2 .4 -20 -10 0 10 20 Number of Employees and Payday Frequency Reform (b) (b) State Border Counties 146 3.5.2 LaborProductivity Following the decrease in firm employment size, I find the value added per worker rose by more than 6 percent. The results are reported in Table ??. Figure ?? shows the dynamics of value-added per worker around the state reforms. Before the reforms, there was no pre-trend. After the reforms, the value added per worker rose by more than 5 percent. The above finding is robust to the following robustness checks. First, the estimations of independent DiDs are always positive using each sub-sample of states that passed the regulation in the same decades (Table??). Second, the estimated effects are positive using only state border counties (Table ??). Third, the same pattern also holds for the sales per worker (Table??). Table ?? and Figure ?? suggest that the higher labor productivity can be partially attributed to the increase in capital per employee. Before the reforms, there was no pre-trend. Moreover, right after the reforms, the capital per worker size rose by about 7 percent. The estimated increases are similar using the full sample and the smaller sub-sample with the border counties only. The above findings together suggest that after the payday frequency regulations were enacted, firms laid off and replaced lower-productivity workers with capital, which improved the productivity of the remaining workers. As a result, the average wage increased after the reforms. 3.5.3 ManagerialCost One potential concern is that the above patterns were driven by higher managerial costs rather than the decrease in the implicit borrowing from the employees. Some may argue that higher payday frequency is costly to implement, especially during the sample period. This higher operation cost could make it less profitable to keep a large workforce, which can explain the previous findings. If the payday frequency reforms caused an increase in administrative burden, we should expect the ratio of officers or clerks among all employees to rise because firms hire more managers to tackle the 147 Table 3.7: Labor Productivity and Payday Frequency Reforms Labor Productivity i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Labor Productivity i,k,t is the natural log of value added per worker in industry i at county k on year t. Reform k,t is a dummy variable equal to one if year t is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry-by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by-county fixed effects are included. The sample period is from 1860 to 1930. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Value Added Per Employee Full Sample Border Counties (1) (2) (3) (4) Reform 0.0830*** 0.0805*** 0.0581*** 0.0572*** (0.0162) (0.0154) (0.0188) (0.0182) Constant 7.140*** 7.160*** 7.096*** 7.143*** (0.00618) (0.00653) (0.00767) (0.00842) Observations 37,812 23,705 18,703 13,319 R-squared 0.802 0.852 0.800 0.848 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 148 Figure 3.5: Labor Productivity Around the Payday Reforms Figure (a) visualizes the dynamics of labor productivity around the state payday frequency reforms using the full sample. Figure (b) shows the same coefficients using a smaller sample with only state border counties. Both figures are estimated from the following regression: Y i,k,t =α + T X β T · Window T,k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k . In figure (a), Y is the natural log of value added per worker in industry i at countyk on yeart and is the natural log of capital per worker. In figure (b). Window T,k,t is a dummy variable that equals one if yeart is within the range of T − 5 years and T +5 years after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects, Ind-State FEs are industry-by-state fixed effects, and County FEs are county fixed effects. The sample period is from 1860 to 1930. Standard errors are double clustered at the industry level and state-by-year level. The 95% confidence intervals are reported. -.05 0 .05 .1 .15 Wage -20 -10 0 10 20 Labor Productivity and Payday Frequency Reform (a) (a) Value Added Per Worker -.2 -.1 0 .1 .2 -20 -10 0 10 20 Capital Per Employee and Payday Frequency Reform (b) (b) Capital Per Worker 149 Table 3.8: Capital Per Employee and Payday Frequency Reforms ln(Capital Per Employee i,k,t )=α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Capital Per Employee i,k,t is the capital per worker in industryi at countyk on yeart. Reform k,t is a dummy variable equal to one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry-by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by-county fixed effects are included. The sample period is from 1860 to 1930. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. ln (Capital Per Employee) Full Sample Border Counties (1) (2) (3) (4) Reform 0.0733*** 0.0691*** 0.0776** 0.0674** (0.0255) (0.0254) (0.0301) (0.0313) Constant 6.986*** 7.026*** 6.958*** 7.014*** (0.00818) (0.00970) (0.0105) (0.0124) Observations 34,586 21,807 17,668 12,492 R-squared 0.762 0.839 0.775 0.837 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 150 Table 3.9: Officer Ratios and Payday Frequency Reforms Officer Ratio i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Wage i,k,t is the average wage of a worker in industryi at countyk on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry by year fixed effects. Columns (1)-(4) use states that passed payday regulations in the 1880s, 1890s, 1900s, and 1910s, respectively. All estimations include industry by county fixed effects. Standard errors are double clustered at the industry level and state by year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Share of Officers Full Sample Border Counties (1) (2) (3) (4) Reform 0.00457 0.00328 0.00514 0.00466 (0.00485) (0.00433) (0.00763) (0.00723) Constant 0.160*** 0.163*** 0.151*** 0.156*** (0.00273) (0.00250) (0.00465) (0.00448) Observations 21,929 14,444 10,639 8,016 R-squared 0.749 0.804 0.768 0.805 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 151 administration tasks. This hypothesis can be directly tested using the censuses of manufacturers. The data not only report the number of total employees but also the number of officers and clerks. Table ?? does not show that the ratio of officers among total employees did not increase after the payday frequency reforms. In addition, Table?? shows that the ratio of clerks among total employees did not increase neither. The estimated coefficients are all very small and statistically indifferent from zero. Therefore, the data do not suggest that higher payday frequency substantially increased the administrative burden. 3.6 HouseholdConsumption: EvidencefromHousing In the previous section, I find that implicit borrowing from employees is important for firms. After payday frequency reforms that reduced the size of such borrowing, firms laid off lower-income workers, and the remaining workers experienced wage growth. A remaining question, then, is how the payday frequency reforms impacted households. The effects may not be homogeneous. After the reforms, I expect higher-income (productivity) households will in- crease their consumption, given their wage growth. However, the direction for lower-income households remain unclear. On the one hand, firms reduced the labor demand for lower-productivity workers. The decline in labor income can cause a decrease in household consumption. On the other hand, lower-income households can be more financially constrained, and they sometimes rely on expensive short-term credit from other financial sources to smooth consumption. Being paid earlier can make financially constrained and lower- income households less reliant on external credits ([15]). If the external financing cost is exceptionally high, the benefits from being paid earlier can dominate the decline in labor income. 152 Figure 3.6: Home Ownership Around the Payday Reforms Figure (a) visualizes the dynamics of the total number of workers around the state payday frequency reforms using the full sample. Figure (b) shows the same coefficients using a smaller sample with only the state border counties. Both figures are estimated from the following regression: Home Owner i,k,t =α + T X β T · Window T,k,t + Ind-Year FEs+ Occ-Year FEs+ County FEs+ϵ i,t,k where Home Owner i,k,t is a dummy variable equal to one if household i is a homeowner at county k on year t. Window T,k,t is a dummy variable that equals one if yeart is within the range ofT − 5 years andT +5 years after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects, Occ-Year FEs are the occupation-by-year fixed effects, and County FEs are county fixed effects. The sample period is from 1860 to 1930. Standard errors are double clustered at the industry level and state-by-year level. The 95% confidence intervals are reported. -.02 0 .02 .04 .06 Home Ownership -20 -10 0 10 20 Home Ownership and Payday Frequency Reform (a) (a) Full Sample -.02 0 .02 .04 .06 Home Ownership -20 -10 0 10 20 Home Ownership and Payday Frequency Reform (b) (b) State Border Counties 153 Table 3.10: Home Ownership and Payday Frequency Reforms Home Owner i,k,t =α +β · Reform k,t +γ · X i,k,t + Ind-Year FEs+ Occ-Year FEs+ County FEs+ϵ i,t,k , where Home Owner i,k,t is the a dummy variable that equals one if householdi owns her dwelling at countyk on year t. Reform k,t is a dummy variable that equals one if year t is after the corresponding state passed a payday frequency regulation. X i,k,t is a vector of household characteristics, including race, gender, and age. Ind-Year FEs are the industry-by-year fixed effects, Occ-Year FEs are the occupation-by-year fixed effects, and County FEs are county fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (2) and (4), region-by-year fixed effects are included. The sample period is from 1900 to 1930. Standard errors double clustered at the industry level and state by year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Home Ownership Full Sample Border Counties (1) (2) (3) (4) Reform 0.0208*** 0.0289*** 0.0235*** 0.0253*** (0.00373) (0.00500) (0.00835) (0.00754) Constant 0.457*** 0.454*** 0.440*** 0.440*** (0.00144) (0.00204) (0.00397) (0.00351) Observations 476,899 476,899 182,883 182,883 R-squared 0.231 0.232 0.241 0.242 Industry-Year Fixed Effects Yes Yes Yes Yes Occupation-Year Fixed Effects Yes Yes Yes Yes County Fixed Effects Yes Yes Yes Yes Region-Year Fixed Effects No Yes No Yes Demographic Controls Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 154 3.6.1 HousingConsumption I use home ownership as a proxy for household consumption. It is the only variable that proxies house- hold consumption in censuses before the 1930s. Nevertheless, housing consumption is one of the largest consumption categories for a typical US household. The results of the following regression show that, on average, home ownership increased after reforms: Home Owner i,k,t =α +β · Reform k,t +γ · X i,k,t + Ind-Year FEs+ Occ-Year FEs+ County FEs+ϵ i,t,k , where Home Owner i,k,t is the a dummy variable that equals one if householdi owns her dwelling at county k on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation. X i,k,t is a vector of household characteristics, including race, gender, and age. Ind-Year FEs are the industry-by-year fixed effects, Occ-Year FEs are the occupation-by-year fixed effects, and County FEs are county fixed effects. The sample period is from 1900 to 1930. Standard errors are double clustered at the industry level and state-by-year level. The results are reported in Table ??. Columns (1) and (2) show the full sample estimations. Figure ?? shows the dynamics of home ownership around the state reforms. Similarly, no pre-trend is detected. Furthermore, after the reforms, the average home ownership rose by about 2.5 percentage points. The increase in home ownership is robust to the following robustness checks. First, the estimations of independent DiDs are always positive using each sub-sample of states that passed a regulation in the same decade (Table??). Second, the estimated effects are positive using only state border counties (Table ?? and Figure??). 155 3.6.2 Lower-incomeHouseholds Although the previous results suggest that higher payday frequency was overall beneficial to the house- holds, we should not expect the effects to be equally strong for all households. As shown in the firm side analysis, firms reduced their employment size after the reforms, with the lower productivity workers po- tentially hurt the most by the decreased labor demand. Given the drop in labor income, lower-income households may experience less or even negative consumption growth. Columns (1) and (4) of Table?? confirmed that the increase in home ownership was smaller for lower- income households. After the payday frequency reforms, the home ownership of the bottom 50% income households increased by 1.6 percentage points (statistically significant at the 5% level). In contrast, the increase was 5.1 percentage points for the top 50% income households. 3.6.3 FinanciallyConstrainedHouseholds Nevertheless, the effects may not be the same even within the bottom 50% income households. If some households were financially constrained or had to smooth consumption using expensive external credit, the benefits from being paid earlier and more frequently could be enormous, depending on the exact bor- rowing interest rate they faced from external creditors. [102] documented that the reliance on short-term credit was common in the sample period: “Many factory workers... often resorted to buying groceries and other supplies on store accounts (using credit) at prices that were considerably higher than they would have been had they paid cash." Moreover, they showed that many financially constrained workers highly value being paid more fre- quently to reduce their reliance on short-term external credits, which were typically astonishingly expen- sive: "(Getpaid)weekly(enablesaman)topurchasehisnecessariesalittlecheaper,becausehecangetasmuch for a dollar cash as he could get for $1.20 or $1.25 on credit." 156 Table 3.11: Home Ownership and Payday Frequency Reforms: Lower Income and Financially Constrained Households Home Owner i,k,t =α +β · Reform k,t +γ · X i,k,t + Ind-Year FEs+ Occ-Year FEs+ County FEs+ϵ i,t,k , where Home Owner i,k,t is the a dummy variable that equals one if household i owns her dwelling at county k on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation.X i,k,t is a vector of household characteristics, including race, gender, and age. Ind-Year FEs are the industry-by-year fixed effects, Occ-Year FEs are the occupation-by-year fixed effects, and County FEs are county fixed effects. Columns (1)-(3) show the estimations using the full sample, and columns (4)-(6) show the estimations using the smaller sample with only state border counties. The sample period is from 1900 to 1930. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Home Ownership Full Sample Border Counties (1) (2) (3) (4) (5) (6) Reform 0.0510*** 0.0489*** 0.0502** 0.0458*** 0.0458*** 0.0457*** (0.0194) (0.0184) (0.0194) (0.0167) (0.0159) (0.0171) Reform· Low Income -0.0381** -0.0584*** -0.0398*** -0.0354*** -0.0559*** -0.0365*** (0.0150) (0.0121) (0.0150) (0.0110) (0.0101) (0.0119) Reform· Nonwhite -0.00928 -0.0134 (0.0130) (0.0187) Reform· Low Income· Nonwhite 0.0893*** 0.0831*** (0.0116) (0.0239) Reform· Female 0.00564 -0.000780 (0.00884) (0.0141) Reform· Low Income· Female 0.0580*** 0.0704*** (0.0205) (0.0208) Observations 476,899 476,899 476,899 182,883 182,883 182,883 R-squared 0.232 0.233 0.232 0.242 0.244 0.243 Industry-Year Fixed Effects Yes Yes Yes Yes Yes Yes Occupation-Year Fixed Effects Yes Yes Yes Yes Yes Yes County Fixed Effects Yes Yes Yes Yes Yes Yes Region-Year Fixed Effects Yes Yes Yes Yes Yes Yes Demographic Controls Yes Yes Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 157 We can use today’s payday loans to put the price of short-term credits into more concrete numbers. [105] documented that, for a typical payday loan, $15 to $30 in fees are charged on each $100 advanced. The implied annual interest rate ranges between 400% and 1000 %. The census data do not provide enough information to directly observe a household’s exact external borrowing cost. But two available demographic variables have been extensively shown to be related to higher credit cost and credit discrimination in the literature: gender and race. [9] showed a significant difference in the loan approval rate and the interest rate charged on approved loans for businesses owned by minority or white females and firms owned by white males. [13] show risk-equivalent Latinx/Black borrowers pay significantly higher interest rates on GSE-securitized and FHA-insured loans. Given the historical background, the credit discrimination against females and the minority could be much larger than what is documented today. Therefore, if anything, the benefits of being paid earlier and more fre- quently should be more valuable for female and nonwhite households. Columns (2)-(3) and (5)-(6) of Table?? confirmed that the increase in home ownership was much larger for lower-income female and nonwhite households compared to the white male lower-income households. After the payday frequency reforms, the home ownership of the nonwhite households in the bottom 50% income distribution increased by 5.0 percentage points, and the increase was 4.1 percentage points for the bottom 50% income female households. 3.7 AFrameworkforPolicyEvaluations The analysis using the census data between the 1860s and the 1930s shows that implicit borrowing is important for both firms and households. After states passed payday frequency regulations, firms reduced their employment, and the remaining workers earned higher wages. Households overall benefited from higher payday frequency, especially financially constrained households with higher external borrowing costs. 158 Given that the above results are estimated using historical data, the economy may have very differ- ent parameter settings than today’s economy. Therefore, I construct a stylized model to generalize the economic intuitions for policy evaluations in today’s economy. 3.7.1 Environment Consider a two-period economy with a representative firm and a representative worker. The firm has one unit of capital endowment and needs to hirel units of labor in both periods. The hiring decision is made at the beginning of the first period. The production process takes two periods, and the firm receives its sales revenue y at the end of the second period. The production function features decreasing marginal labor productivity: y =A· l α , whereα ∈(0,1) The firm pays a total wage of w for each unit of labor. Wage is determined by the standard Nash Bargaining between the firm and the household, à la [42], [92], and [3]. The firm and household split the surplus generated by one additional unit of labor. The equilibrium wagew is determined by w =β · ∂y ∂l +(1− β )· ¯w, (3.1) where ¯w is the household’s reservation wage,β is the household’s bargaining power, and ∂y ∂l is the marginal productivity of labor. I assume, exogenously by regulation,x∈(0, 1 2 ] of the wage shall be paid at the end of the first period, and1− x of the wage shall be paid at the end of the second period. Whenx= 1 2 , the regulation requires 159 wages to be paid semi-monthly if each period is a month in the model. Approximately, higherx maps into higher payday frequency. To pay the first period wage, the firm needs to pay an opportunity cost, r f . The opportunity cost can be interpreted as the borrowing interest rate or the alternative investment yield that the firm faces. The household prefers to be paid earlier because of an opportunity costr h . The opportunity cost can be similarly interpreted as the borrowing interest rate or the alternative investment yield that the household faces. 3.7.2 Firm’sProblem Assume shareholders of the representative firm are risk neutral and maximize its profit: max l A· l α − l· w· (1+x· r f ), wherex· r f is the firm’s cost to pay wages earlier. The first order condition is: ∂y ∂l =A· α · l α − 1 =w· (1+x· r f ) (3.2) Given wagew is also a function ofl, the firm’s labor demand can be solved from the first order condi- tion. Equation?? can be rewritten as A· α · l α − 1 1+x· r f =β · ∂y ∂l +(1− β )· ¯w, which is A· α · l α − 1 · 1 1+x· r f − β =(1− β )· ¯w. 160 The firm’s labor demand is given by: l = A· α · (1− β − β · x· r f ) (1− β )· ¯w· (1+x· r f ) 1 1− α . (3.3) 3.7.3 Employment,Wage,andPaydayFrequency The model generates consistent predictions, as I find empirically in the above sections. When the regulation requires higher payday frequency, firm labor demand decreases, and labor pro- ductivity rises. Proof: Equation?? implies thatl decreases asx increases. And Equation?? further shows that the marginal labor productivity ∂y ∂l is higher with smaller employment size. When the regulation requires higher payday frequency, the equilibrium wage increases. Proof: Nash bargaining in Equation?? determines that the equilibrium wage will be higher, given thanl decreases and labor’s marginal productivity rises whenx becomes larger. Intuitively, earlier paydays force the firm to incur opportunity costs of paying the first period wage. The marginal cost of hiring one unit of labor rises, discouraging the firm’s hiring. With a smaller employment size, the marginal productivity of labor increases, and the average wage rises because of Nash bargaining. 3.7.4 SocialWelfare Assume the representative firm is owned by the representative household, then define the total surplus of the economy as the sum of the firm’s profit, and the household’s total income (labor and financial): S =A· l α − l· w· (1+x· r f ) | {z } S f =firm’s profit + l· w· (1+x· r h ) | {z } S h =household’s total income , (3.4) wherex· r h is household’s benefit of being paid earlier. If households are sufficiently financially constrained whereas firms are not, higher payday frequency improves social welfare. 161 Proof: If firms are not financially constrained, to the limit of r f →0, Equation?? can be simplified as lim r f →0 S =A· l α +l· w· x· (r h − r f ) =A· l α · (1+α · x· (r h − r f )) ∝ A· α ¯w 1 1− α · (1+α · x· r h ). Clearly, the total surplus increases withx, and firm employment is unaffected. The benefits of earlier pay positively depend on the household’s financial constraint r h . If firms are sufficiently financially constrained whereas households are not, higher payday frequency decreases social welfare. Proof: If households are not financially constrained, to the limit of r h →0, Equation?? can be simpli- fied as lim r h →0 S =A· l α · (1+α · x· (r h − r f )) ∝l α · (1− α · x· r f ). Because higherx leads to lower employmentl, the total surplus decreases withx. The benefits of earlier pay negatively depend on the firm’s financial constraint r f . 3.7.5 Intuition The above analysis shows that the relative magnitude of the firm’s financial constraint and the household’s financial constraint is crucial to determining the welfare consequence of higher payday frequency. When the household is more financially constrained, the cost of external financing or the opportunity of external investment yield is higher for the household than for the firm. In this case, requiring higher 162 payday frequency will allocate internal “credit" from the firm to the worker. This reallocation improves efficiency because it can generate more wealth gain for the household than the value loss suffered by the firm. When the firm is more financially constrained, the cost of external financing or the opportunity of external investment yield is higher for the firm than for the household. In this case, requiring higher payday frequency will reallocate internal “credit" away from where the marginal value of one dollar is higher. Firms will reduce their employment, leading to lower production overall. 3.7.6 PolicyImplications The policy implication from the above framework is clear. When households are more financially con- strained, higher payday frequency is preferred. When firms are more financially constrained, higher pay- day frequency destroys social efficiency. Ideally, the payday frequency requirements should be firm and household specific, whereas the latter is partially true in reality. First, higher payday frequency should better target lower-income households, which are more financially constrained. Indeed, many states protect manufacturing workers by requir- ing them to be paid more frequently than other professionals. Second, higher payday frequency is more suitable for larger and non-growing firms, which are not as financially constrained as households or have lower returns from additional investments. These firm-specific requirements have not been implemented in any states yet. 3.8 Conclusion Employees typically supply labor to firms first and then get paid later. This paper shows that such implicit “trade credits" or “short-term borrowing" are important for both firms and employees. Using state payday frequency reforms between the 1860s and the 1930s, I find that firms decreased employment size after 163 being required to pay employees more frequently, which reduced the amount of borrowing from employ- ees. However, employees who were not laid off were more productive and earned higher wages. Despite decreased labor demand, households were better off, on average, as demonstrated by an increase in home ownership, especially those households that were severely financially constrained, such as the households of low-income minorities and women. Given this tradeoff between firms and employees, a stylized frame- work suggests that, when not financially constrained nor with no good investment opportunities, firms should pay their employees more frequently. This paper directly speaks to a growing body of literature that studies payday frequency by studying the effects on firms. This paper also contributes to the literature on trade credit by studying the labor “trade credits" between firms and one of their most crucial suppliers: employees. Figure 3.7: State Border Counties This figure maps the counties that are located at state borders. The border counties are shown in yellow. 164 Table 3.12: Wage and Payday Frequency Reforms: Weekly Paydays ln(Wage) i,k,t =α +β · Reform k,t · Weekly k + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Wage i,k,t is the average wage of a worker in industryi at countyk on yeart. Reform k,t is a dummy variable equal to one if yeart is after the corresponding state passed a payday frequency regulation.Weekly is also a dummy variable that equals one if state k requires payday frequency to be weekly. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry-by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by-county fixed effects are included. The sample period is from 1860 to 1930. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. ln (Wage) ln (Number of Employees) (1) (2) (3) (4) Reform 0.0457*** 0.0439*** -0.0106 -0.0359 (0.0134) (0.0128) (0.0308) (0.0290) Reform· Weekly 0.0290* 0.0260* -0.203*** -0.180*** (0.0150) (0.0149) (0.0452) (0.0487) Constant 6.175*** 6.206*** 2.224*** 2.290*** (0.00475) (0.00529) (0.0117) (0.0139) Observations 36,239 23,248 36,256 23,262 R-squared 0.831 0.878 0.741 0.839 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 165 Table 3.13: Average Number of Employees and Payday Frequency Reforms ln(Emp) i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Emp i,k,t is the natural log of the average number of workers of an establishment in industry i at county k on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry-by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by-county fixed effects are included. The sample period is from 1860 to 1930. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. VARIABLES ln (Number of Employees) Full Sample Border Counties (1) (2) (3) (4) Reform 0.0838** -0.101*** -0.0726* -0.0653 (0.0334) (0.0333) (0.0414) (0.0403) Constant 2.218*** 2.281*** 2.249*** 2.301*** (0.0121) (0.0139) (0.0164) (0.0181) Observations 36,256 23,262 18,364 13,163 R-squared 0.741 0.839 0.775 0.845 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 166 Table 3.14: Decompose Staggered DiDs: the Number of Workers ln(Emp) i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Emp i,k,t is the natural log of the average number of workers of an establishment in industry i at county k on yeart. Reform k,t is a dummy variable equal to one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1)-(4) use states that passed pay- day regulations in the 1880s, 1890s, 1900s, and 1910s, respectively. All estimations include industry-by-county fixed effects. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. ln (Number of Employees) 1880s 1890s 1900s 1910s (1) (2) (3) (4) Reform -0.194 -0.115 -0.392* -0.269 (0.185) (0.114) (0.228) (0.198) Constant 6.094*** 6.143*** 6.299*** 6.258*** (0.0301) (0.0190) (0.00682) (0.0115) Observations 7,126 8,364 527 3,934 R-squared 0.871 0.885 0.953 0.902 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-County Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 167 Table 3.15: Sales Per Worker and Payday Frequency Reforms Labor Productivity i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Labor Productivity i,k,t is the natural log of sales per worker in industry i at county k on year t. Reform k,t is a dummy variable equal to one if year t is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry-by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by- county fixed effects are included. The sample period is from 1860 to 1930. Standard errors are double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. VARIABLES Sales Per Employee Full Sample Border Counties (1) (2) (3) (4) Reform 0.0588*** 0.0604*** 0.0457*** 0.0462*** (0.0143) (0.0136) (0.0168) (0.0168) Constant 7.770*** 7.818*** 7.750*** 7.806*** (0.00558) (0.00625) (0.00709) (0.00816) Observations 37,812 23,705 18,703 13,319 R-squared 0.802 0.852 0.800 0.848 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 168 Table 3.16: Decompose Staggered DiDs: the Labor Productivity Labor Productivity i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Labor Productivity i,k,t is the natural log of the value add per worker in industry i at county k on year t. Reform k,t is a dummy variable equal to one if year t is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1)-(4) use states that passed payday regu- lations in the 1880s, 1890s, 1900s, and 1910s, respectively. All estimations include industry-by-county fixed effects. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Value Added Per Employee 1880s 1890s 1900s 1910s (1) (2) (3) (4) Reform 0.162** 0.103 0.0147 0.119 (0.0704) (0.0672) (0.0682) (0.0774) Constant 6.988*** 7.098*** 7.287*** 7.226*** (0.0451) (0.0284) (0.00874) (0.0153) Observations 7,109 8,355 527 3,930 R-squared 0.845 0.843 0.930 0.889 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-County Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 169 Table 3.17: Industry Characteristics and Payday Frequency Reforms Y i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k whereY i,k,t are characteristics of the industryi at countyk on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry- by-year fixed effects. Industry-by-state fixed effects and county fixed effects are included. All estimations include industry-by-county fixed effects. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) VARIABLES Sales Value Added Labor Expense Establishment Reform -0.0974* -0.0747 -0.0931* -0.0640 (0.0545) (0.0512) (0.0524) (0.0446) Constant 12.13*** 11.45*** 10.53*** 2.135*** (0.0212) (0.0199) (0.0203) (0.0168) Observations 36,332 36,272 36,240 36,352 R-squared 0.796 0.789 0.786 0.751 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes Yes Yes Yes County Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 3.18: Industry Characteristics and Payday Frequency Reforms: Border Counties Y i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k whereY i,k,t are characteristics of the industryi at countyk on yeart. Reform k,t is a dummy variable that equals one if yeart is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry- by-year fixed effects. Industry-by-state fixed effects and county fixed effects are included. All estimations include industry-by-county fixed effects. All estimations use only counties at state borders. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. (1) (2) (3) (4) VARIABLES Sales Value Added Labor Expense Establishment Reform -0.103 -0.0902 -0.112* -0.0665 (0.0700) (0.0661) (0.0665) (0.0495) Constant 12.21*** 11.54*** 10.63*** 2.209*** (0.0297) (0.0280) (0.0276) (0.0214) Observations 18,400 18,346 18,352 18,415 R-squared 0.815 0.808 0.806 0.774 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes Yes Yes Yes County Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 170 Table 3.19: Share of Clerks in All Employees Clerk Ratio i,k,t =α +β · Reform k,t + Ind-Year FEs+ Ind-State FEs+ County FEs+ϵ i,t,k where Clerk Ratio i,k,t is the ratio of clerks among all employees in industry i at county k on year t. Reform k,t is a dummy variable that equals one if year t is after the corresponding state passed a payday frequency regulation. Ind-Year FEs are the industry-by-year fixed effects. Columns (1) and (2) show the estimations using the full sample, and columns (3) and (4) show the estimations using the smaller sample with only state border counties. In columns (1) and (3), industry-by-state fixed effects and county fixed effects are included. In columns (2) and (4), industry-by- county fixed effects are included. The sample period is from 1860 to 1930. Standard errors double clustered at the industry level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Share of Clerks Full Sample Border Counties (1) (2) (3) (4) Reform 0.00598 0.00556 0.0111 0.0114 (0.00551) (0.00450) (0.00887) (0.00811) Constant 0.159*** 0.145*** 0.153*** 0.145*** (0.00296) (0.00274) (0.00535) (0.00537) Observations 11,284 5,422 5,052 3,120 R-squared 0.754 0.808 0.776 0.821 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-State Fixed Effects Yes No Yes No County Fixed Effects Yes No Yes No Industry-County Fixed Effects No Yes No Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 171 Table 3.20: Decompose Staggered DiDs: the Home Ownership Home Owner i,k,t =α +β · Reform k,t +γ · X i,k,t + Ind-Year FEs+ Occ-Year FEs+ County FEs+ϵ i,t,k , where Home Owner i,k,t is the a dummy variable that equals one if householdi owns her dwelling at countyk on year t. Reform k,t is a dummy variable that equals one if year t is after the corresponding state passed a payday frequency regulation. X i,k,t is a vector of household characteristics, including race, gender, and age. Ind-Year FEs are the industry-by-year fixed effects, Occ-Year FEs are the occupation-by-year fixed effects, and County FEs are county fixed effects. Columns (1)-(4) use states that passed payday regulations in the 1880s, 1890s, 1900s, and 1910s, respectively. All estimations include industry-by-county fixed effects. Standard errors double clustered at the indus- try level and state-by-year level are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ indicate significance at the 10%, 5%, and 1% level, respectively. Home Ownership Full Sample Border Counties 1900s 1910s 1900s 1910s (1) (2) (3) (4) Reform 0.100*** 0.0451*** 0.0620** 0.0224 (0.0211) (0.00891) (0.0289) (0.0144) Constant 0.419*** 0.452*** 0.447*** 0.435*** (0.00655) (0.00399) (0.00963) (0.00681) Observations 133,054 343,581 45,634 136,882 R-squared 0.245 0.238 0.288 0.247 Industry-Year Fixed Effects Yes Yes Yes Yes Industry-County Fixed Effects Yes Yes Yes Yes Clustered Standard Errors Yes Yes Yes Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 172 Bibliography [1] Chadi S Abdallah and William D Lastrapes. “Home equity lending and retail spending: Evidence from a natural experiment in Texas”. In: American Economic Journal: Macroeconomics 4.4 (2012), pp. 94–125. [2] Daron Acemoglu, David Autor, Jonathon Hazell, and Pascual Restrepo. “Artificial intelligence and jobs: evidence from online vacancies”. In: Journal of Labor Economics 40.S1 (2022), S293–S340. 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Abstract (if available)

Abstract The thesis contains three chapters.

In the first chapter, I study the inflation heterogeneity across income groups. I find that households who experience a rise in inflation (relative to national inflation rates) increase their borrowing from the mortgage market and holdings of housing assets. These findings can be explained by households relocating their savings to markets where real returns are protected from relative inflation. A calibrated general equilibrium model suggests a smaller dispersion in home ownership between income groups but a greater dispersion in welfare due to inflation heterogeneity.

In the second chapter, I study the effect of the risk of losing talent on corporate investment. I construct a firm-level measure of talent retention risk based on other firms’ job postings for skilled labor in the local labor market, which captures the outside options of the firm’s talent. Using this measure, we show that TRR reduces firm investment after controlling for Q, and effects are driven by retention risk for middle-managers but not other skilled labor, suggesting that managers are the core talent.

In the last chapter, using state payday frequency reforms between the 1860s and the 1930s, I find that firms reduced employment after being required to pay employees more frequently, which reduced the amount of implicit borrowing from employees. However, the remaining employees were more productive and earned higher wages. Meanwhile, homeownership increased, especially those potentially financially constrained households, such as low-income minorities and females.

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Creator Zhang, Zhao (author)

Core Title Three essays on macro and labor finance

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Degree Conferral Date 2023-05

Publication Date 03/29/2023

Defense Date 03/20/2023

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

Tag borrow from employees,inflation heterogeneity,mortgage and housing decision,OAI-PMH Harvest,talent retention risk

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Language English

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Advisor Ramcharan, Rodney (committee chair), Kilic, Mete (committee member), Kurlat, Pablo (committee member), Schmid, Lukas (committee member), Tuzel, Selale (committee member)

Creator Email zhang-z12@outlook.com,zhao.zhang@marshall.usc.edu

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