@prefix vivo: .
@prefix edm: .
@prefix ns0: .
@prefix dcterms: .
@prefix skos: .
vivo:departmentOrSchool "Arts, Faculty of"@en, "Vancouver School of Economics"@en ;
edm:dataProvider "DSpace"@en ;
ns0:degreeCampus "UBCV"@en ;
dcterms:creator "Mitra, Aruni"@en ;
dcterms:issued "2020-07-13T23:05:11Z"@en, "2020"@en ;
vivo:relatedDegree "Doctor of Philosophy - PhD"@en ;
ns0:degreeGrantor "University of British Columbia"@en ;
dcterms:description "For nearly four decades in the post-War United States, productivity rose during economic booms and fell in recessions. The first chapter of this thesis studies how increased labour market flexibility because of rapid de-unionization since the early 1980s can explain the sudden vanishing of this procyclicality of productivity, the so-called 'productivity puzzle'. Falling costs of hiring and firing workers, due to the decline in union power, prompted by firms to rely more on employment adjustment (extensive margin) instead of changing workers' effort through labour hoarding (intensive margin). High dependence on labour hoarding explains productivity's historical procyclicality, and its reduced importance in recent decades explains why productivity is now less procyclical. Increased hiring and firing of workers also imply a rise in the relative volatility of employment. I show that U.S. states and industries with a larger drop in union density experienced a deeper fall in the procyclicality of productivity and a larger increase in the relative volatility of employment. Simultaneous to the productivity puzzle in the mid-1980s, there were other important structural changes in the U.S. economy, namely, the rise of the service sector, increased use of intangible capital, more accommodative monetary policy, and the decline in the volatility of shocks during Great Moderation. The second chapter shows that none of these structural changes can explain the productivity puzzle. However, allowing the hiring cost to decline between pre- and post-1980s in an otherwise standard New Keynesian model with endogenous effort can match almost all the fall in cyclical productivity correlations and the rise in the relative volatility of employment. The third chapter characterizes the joint evolution of cross-sectional inequality in permanent income and consumption among parents and children in the U.S. We use a model of intra-family persistence across generations to estimate the parameters determining inequality of consumption and income within a generation. In accounting for cross-sectional dispersion, we find that idiosyncratic heterogeneity is quantitatively more important than inequality arising from family factors. This suggests that parents provide limited insurance against idiosyncratic life-cycle risk, even though the levels of permanent income and consumption exhibit significant persistence across generations."@en ;
edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/75154?expand=metadata"@en ;
skos:note "Essays on Dynamics of Household andFirm ChoicesbyAruni MitraB.Sc., University of Calcutta, 2012M.S., Indian Statistical Institute, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Economics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)July 2020c© Aruni Mitra 2020The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the dissertation titled:Essays on Dynamics of Household and Firm Choicessubmitted by Aruni Mitrain partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics.Examining Committee:Giovanni Gallipoli, Professor, Economics, UBCSupervisorMichael B. Devereux, Professor, Economics, UBCSupervisory Committee MemberHenry E. Siu, Professor, Economics, UBCUniversity ExaminerLorenzo Garlappi, Professor, Business Administration, UBCUniversity ExaminerThomas F. Crossley, European University InstituteExternal ExaminerAdditional Supervisory Committee Member:Florian Hoffmann, Associate Professor, Economics, UBCSupervisory Committee MemberiiAbstractFor nearly four decades in the post-War United States, productivity rose during economic boomsand fell in recessions. The first chapter of this thesis studies how increased labour market flexi-bility because of rapid de-unionization since the early 1980s can explain the sudden vanishing ofthis procyclicality of productivity, the so-called ‘productivity puzzle’. Falling costs of hiring andfiring workers, due to the decline in union power, prompted firms to rely more on employmentadjustment (extensive margin) instead of changing workers’ effort through labour hoarding (inten-sive margin). High dependence on labour hoarding explains productivity’s historical procyclicality,and its reduced importance in recent decades explains why productivity is now less procyclical.Increased hiring and firing of workers also imply a rise in the relative volatility of employment. Ishow that U.S. states and industries with a larger drop in union density experienced a deeper fallin the procyclicality of productivity and a larger increase in the relative volatility of employment.Simultaneous to the productivity puzzle in the mid-1980s, there were other important structuralchanges in the U.S. economy, namely, the rise of the service sector, increased use of intangiblecapital, more accommodative monetary policy, and the decline in the volatility of shocks duringGreat Moderation. The second chapter shows that none of these structural changes can explainthe productivity puzzle. However, allowing the hiring cost to decline between pre- and post-1980sin an otherwise standard New Keynesian model with endogenous effort can match almost all thefall in cyclical productivity correlations and the rise in the relative volatility of employment.The third chapter characterizes the joint evolution of cross-sectional inequality in permanentincome and consumption among parents and children in the U.S. We use a model of intra-family per-sistence across generations to estimate the parameters determining inequality of consumption andincome within a generation. In accounting for cross-sectional dispersion, we find that idiosyncraticheterogeneity is quantitatively more important than inequality arising from family factors. Thissuggests that parents provide limited insurance against idiosyncratic life-cycle risk, even thoughthe levels of permanent income and consumption exhibit significant persistence across generations.iiiLay SummaryMy dissertation consists of three chapters studying the business cycle dynamics of productivityand the evolution of intergenerational inequality in the United States. In the first chapter, I arguethat easier hiring and firing of workers due to the rapid decline in labour-union power can explainwhy productivity suddenly started to rise during recessions since the mid-1980s, after having risenduring economic booms for almost four decades. In the second chapter, I rule out structural changesthat occurred in the U.S. economy around the same time, like the rise of the service sector, theincreased use of intangible capital, or the change in monetary policy, as significant explanationsfor driving changes in productivity dynamics. The third chapter studies how inequality in incomeand consumption evolves over generations and finds that an overwhelming majority of the observedinequality cannot be explained by intra-family linkages.ivPrefaceChapters 2 and 3 of the thesis are pieces of original, unpublished and independent work. Chapter 4titled “Consumption and Income Inequality across Generations” is ongoing collaborative work withProfessor Giovanni Gallipoli (Vancouver School of Economics, University of British Columbia) andProfessor Hamish Low (Nuffield College, University of Oxford). I have been involved throughouteach stage of the research project: preparing data for statistical analysis, designing and executingthe estimation strategy, and writing and editing the manuscript.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The Productivity Puzzle and the Decline of Unions . . . . . . . . . . . . . . . . . 82.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 The Productivity Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Drop in Employment Adjustment Cost . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1 Vanishing Procyclicality of Factor Utilization Rate . . . . . . . . . . . . . . . 112.3.2 Changes in Response to Technology and Demand Shocks . . . . . . . . . . . 122.4 What Caused Employment Adjustment Cost to Drop . . . . . . . . . . . . . . . . . 142.4.1 Decline of Unions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.2 De-unionization: International Evidence . . . . . . . . . . . . . . . . . . . . 162.4.3 De-unionization: Evidence from U.S. States and Industries . . . . . . . . . . 172.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.6 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.7 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 The Productivity Puzzle: Evaluating Alternative Explanations . . . . . . . . . . 323.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35vi3.2.3 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.4 Equilibrium Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3.1 Structural Changes due to De-unionization . . . . . . . . . . . . . . . . . . . 403.3.2 Monetary Policy Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.3 Exogenous Shocks: Changes during Great Moderation . . . . . . . . . . . . . 413.3.4 Stationary Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4 Quantitative Performance of Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.4.1 Business Cycle Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.4.2 Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4.3 Robustness to Parameter Calibration . . . . . . . . . . . . . . . . . . . . . . 453.5 Other Plausible Explanations: Lack of Evidence . . . . . . . . . . . . . . . . . . . . 463.5.1 Vanishing Countercyclicality of Labour Quality . . . . . . . . . . . . . . . . 463.5.2 Rise of Service Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.5.3 Growing Share of Intangible Investment . . . . . . . . . . . . . . . . . . . . . 473.5.4 Aggregate versus Sectoral Shocks . . . . . . . . . . . . . . . . . . . . . . . . 483.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.7 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.8 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 Consumption and Income Inequality across Generations . . . . . . . . . . . . . . 624.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2 A Model of Intergenerational Inequality . . . . . . . . . . . . . . . . . . . . . . . . . 634.2.1 Cross-sectional Insurance and Intergenerational Smoothing . . . . . . . . . . 674.3 Identification, Estimation and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.3.1 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.3.2 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.4.1 Role of Parental Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . 744.4.2 Counterfactual Cross-sectional Distributions . . . . . . . . . . . . . . . . . . 764.5 The Evolution of Inequality across Generations . . . . . . . . . . . . . . . . . . . . . 764.6 Robustness and Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.6.1 Estimates by Child Birth-Cohort . . . . . . . . . . . . . . . . . . . . . . . . 794.6.2 Additional Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . . . . 794.6.3 An Alternative Model of Intergenerational Persistence . . . . . . . . . . . . . 814.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.8 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.9 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90vii5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93AppendicesA Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104A.1 Robustness to Choice of Filters and Datasets . . . . . . . . . . . . . . . . . . . . . . 104A.2 Evidence for De-unionization: A Difference-in-Difference Strategy . . . . . . . . . . 106A.3 Choice of SVAR Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.4 Impulse Response Functions from Time-Varying SVARs . . . . . . . . . . . . . . . . 110B Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115B.1 System of Log-Linearized Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 115B.2 Cyclical Moments of Capital and Factor Utilization . . . . . . . . . . . . . . . . . . 116B.3 Volatility of Monetary Policy Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . 118B.4 Data on Intellectual Property Products . . . . . . . . . . . . . . . . . . . . . . . . . 118B.5 Relative Importance of Sector-Specific Shocks . . . . . . . . . . . . . . . . . . . . . 119C Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121C.1 Derivation of the Consumption Process . . . . . . . . . . . . . . . . . . . . . . . . . 121C.1.1 CRRA Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122C.2 Data and Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123C.2.1 Imputation of Consumption Expenditure Data . . . . . . . . . . . . . . . . . 124C.3 Intergenerational Persistence: Reduced-Form Evidence . . . . . . . . . . . . . . . . 126C.3.1 The Evolution of Intergenerational Elasticities . . . . . . . . . . . . . . . . . 126C.3.2 Heterogeneity of Intergenerational Persistence . . . . . . . . . . . . . . . . . 128C.4 Empirical Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131C.5 Supplementary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132C.5.1 Role of Observable Characteristics in Intergenerational Persistence . . . . . . 132C.5.2 The Impact of Parental Factors on Inequality . . . . . . . . . . . . . . . . . 136C.6 Evolution of Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137C.7 Robustness and Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143C.7.1 Estimates by Child Birth-Cohort . . . . . . . . . . . . . . . . . . . . . . . . 143C.7.2 Estimates under Alternative Definitions of ‘Other Income’ . . . . . . . . . . 145C.7.3 Model using Panel Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146C.8 Random Walk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150C.8.1 Moment Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152C.8.2 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153C.8.3 Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153viiiList of Tables2.1 Reduction in Procyclicality of Factor Utilization Rate . . . . . . . . . . . . . . . . . 202.2 Reduction in Variance of Factor Utilization Rate . . . . . . . . . . . . . . . . . . . . 202.3 Labour Market Statistics from OECD Countries . . . . . . . . . . . . . . . . . . . . 213.1 Differences in Calibration between Pre- and Post-1984 . . . . . . . . . . . . . . . . . 513.2 Calibration of Time-Invariant Parameters . . . . . . . . . . . . . . . . . . . . . . . . 513.3 Changes in Business Cycle Moments due to De-unionization . . . . . . . . . . . . . . 523.4 Changes in Business Cycle Moments between Pre- and Post-1984 . . . . . . . . . . . 533.5 Robustness to Choice of γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.6 Robustness to Choice of φ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.7 Robustness to Choice of ψ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.8 Robustness to Changes in Nominal Rigidities . . . . . . . . . . . . . . . . . . . . . . 573.9 Labour Productivity Correlations in Manufacturing & Services . . . . . . . . . . . . 574.1 Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.2 Estimates: Intergenerational Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . 834.3 Estimates: Variances and Covariances of Idiosyncratic Components . . . . . . . . . . 844.4 Breaking Up Child Inequality: Parental versus Idiosyncratic Heterogeneity . . . . . . 854.5 Decomposition of Other Income: Intergenerational Elasticity Estimates . . . . . . . 854.6 Parental versus Idiosyncratic Heterogeneity: Role of Marital Selection . . . . . . . . 864.7 Steady-State versus Current Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . 864.8 Importance of Parents: Varying Persistence γ . . . . . . . . . . . . . . . . . . . . . . 874.9 Variances by Child-Cohort (Age: 30-40) . . . . . . . . . . . . . . . . . . . . . . . . . 874.10 Intergenerational Elasticity Estimates by Child Cohort (Age: 30-40) . . . . . . . . . 884.11 Robustness: Intergenerational Elasticity Estimates . . . . . . . . . . . . . . . . . . . 884.12 Robustness: Idiosyncratic Components . . . . . . . . . . . . . . . . . . . . . . . . . . 894.13 Robustness: Importance of Parents for Child Inequality . . . . . . . . . . . . . . . . 89A.1 Cyclical Correlation of Average Labour Productivity (Output per Hour) . . . . . . . 104A.2 Cyclical Volatility of Output, Hours & Employment . . . . . . . . . . . . . . . . . . 105A.3 Relative Cyclical Volatility of Hours & Employment . . . . . . . . . . . . . . . . . . 105A.4 Reduction in Procyclicality and Volatility of Factor/Capacity Utilization Rates . . . 105ixB.1 Components of Variance of Value Added Output Growth . . . . . . . . . . . . . . . 120B.2 Components of Variance of Labour Input Growth . . . . . . . . . . . . . . . . . . . . 120C.1 Estimates of Intergenerational Elasticities by Year . . . . . . . . . . . . . . . . . . . 128C.2 Persistence of Observable Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 132C.3 Variances for Parents and Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133C.4 Baseline Estimates: Intergenerational Elasticity . . . . . . . . . . . . . . . . . . . . . 133C.5 Baseline Estimates: Variances and Covariances of Idiosyncratic Components . . . . . 134C.6 Share of Child Inequality Explained by Parental Heterogeneity . . . . . . . . . . . . 135C.7 Baseline Estimates: Intergenerational Elasticity for Observables . . . . . . . . . . . . 135C.8 Mobility Matrix for Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136C.9 Intergenerational Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138C.10 Idiosyncratic Variances & Covariances . . . . . . . . . . . . . . . . . . . . . . . . . . 139C.11 Parental Importance by Child-Cohort (Age: 30-40) . . . . . . . . . . . . . . . . . . . 143C.12 Estimates by Child Cohort: Idiosyncratic Components (Age: 30-40) . . . . . . . . . 144C.13 Decomposition of Other Income: Idiosyncratic Components . . . . . . . . . . . . . . 145C.14 Estimated Variances of Components of Other Income . . . . . . . . . . . . . . . . . 146C.15 Transitory Shocks Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149C.16 Intergenerational Growth Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . 154C.17 Partial Insurance Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154C.18 Variances of Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155C.19 Growth Model Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156xList of Figures2.1 Vanishing Procyclicality of Productivity in the United States . . . . . . . . . . . . . 222.2 Cyclical Correlation of Labour Productivity with Job Flows . . . . . . . . . . . . . . 232.3 Relative Volatility of Hours & Employment over the Business Cycle . . . . . . . . . 232.4 Cyclical Volatility of Quarterly Growth Rates of Output, Hours & Employment . . . 232.5 Share of Part-time Employment in the U.S. (1968-2017) . . . . . . . . . . . . . . . . 242.6 Impulse Responses to Technology & Demand Shocks (LP, Hours & Output) . . . . . 252.7 Conditional Correlations of Labour Productivity with Hours . . . . . . . . . . . . . . 262.8 Size & Density of Labour Union Membership in the U.S. (1930-2014) . . . . . . . . . 262.9 De-unionization and Vanishing Procyclicality of Productivity . . . . . . . . . . . . . 272.10 Number of Work Stoppages involving 1000 or more workers in the U.S. (1947-2017) . 272.11 Cross-Industry Evidence for De-unionization: Productivity Correlation . . . . . . . . 282.12 Cross-Industry Evidence for De-unionization: Relative Volatility of Employment . . 282.13 De-unionization in U.S. States around 1984 . . . . . . . . . . . . . . . . . . . . . . . 292.14 Vanishing Procyclicality of Labour Productivity in U.S. States around 1984 . . . . . 292.15 Cross-State Evidence for De-unionization . . . . . . . . . . . . . . . . . . . . . . . . 302.16 Cross-State Evidence for De-unionization by Right-to-Work Status . . . . . . . . . . 302.17 Relative Volatility of Employment & Change in Labour Productivity Correlation . . 312.18 International Evidence for De-unionization . . . . . . . . . . . . . . . . . . . . . . . . 313.1 Model-implied Impulse Responses to Technology and Demand Shocks . . . . . . . . 583.2 Conditional Volatility of Hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.3 Conditional Volatility of Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . 593.4 Correlation of Labour Quality Index with Output . . . . . . . . . . . . . . . . . . . . 593.5 Share of Services in the U.S. (1947-2016) . . . . . . . . . . . . . . . . . . . . . . . . . 603.6 Changes in Share of Services Intermediate Input & Labour Productivity Correlation 603.7 Changes in Share of IPP in Total Capital Stock & Labour Productivity Correlation 613.8 Total Advertisement Spending as a Share of GDP in the U.S. (1919-2007) . . . . . . 614.1 Identification of Persistence and Dispersion Parameters . . . . . . . . . . . . . . . . 904.2 Baseline versus Counterfactual Probability Density Functions . . . . . . . . . . . . . 90A.1 Difference-in-Difference Effect of Union Density on Productivity Correlation . . . . . 107A.2 Difference-in-Difference Effect of Union Density on Relative Volatility of Employment107xiA.3 IRF of Per Capita Hours to Utilization-Adjusted TFP Shock . . . . . . . . . . . . . 109A.4 Dynamic Impulse Responses to Technology & Demand Shocks (LP, Hours & Output)110A.5 Difference in Impulse Responses between Pre- & Post-1984 (LP, Hours & Output) . 111A.6 Dynamic Impulse Responses to Technology & Demand Shocks (TFP & Hours) . . . 112A.7 Empirical Impulse Responses to Technology & Demand Shocks (TFP & Hours) . . . 113A.8 Difference in Impulse Responses between Pre- & Post-1984 (TFP & Hours) . . . . . 114B.1 Cyclical Correlations of Capital and Factor Utilization . . . . . . . . . . . . . . . . . 116B.2 Relative Volatility of Capital over the Business Cycle (1954-2010) . . . . . . . . . . . 117B.3 5-Year Rolling Standard Deviation of Romer-Romer Monetary Shock . . . . . . . . . 118B.4 Share of IPP in Total Non-Residential Capital Stock in the U.S. (1960-2016) . . . . 119C.1 Quality Assessment of Consumption Imputation . . . . . . . . . . . . . . . . . . . . 126C.2 Internal Fit of Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131C.3 Implication of γ and φ for Long Run Inequality (Age: 30-40) . . . . . . . . . . . . . 140C.4 Implication of γ and φ for Long Run Earnings & Consumption Inequality . . . . . . 142xiiAcknowledgementsI would like to express my deepest gratitude to my supervisor, Giovanni Gallipoli for his supportand advice throughout my doctoral studies. I am greatly indebted to Michael Devereux for hisinsightful comments and suggestions which have immensely enriched my learning experience. Ialso want to thank Paul Beaudry, who, even though not formally on my thesis committee, devoteda lot of time to discuss and shape my research in its early stages. Hamish Low, with whom achapter of this thesis is co-authored, has been a constant source of encouragement and motivation.I also thank him for inviting me for a research visit to the Institute for New Economic Thinkingat the University of Cambridge during my PhD. I am also indebted to Nicole Fortin, David Green,Florian Hoffmann, Thomas Lemieux, Jesse Perla, Henry Siu and other participants of the empiricaleconomics and macroeconomics brown-bag seminars at the Vancouver School of Economics (VSE)for their very useful feedback and discussions.I have been extremely fortunate to have some wonderful fellow students at VSE. Davide Alonzo,Anujit Chakraborty, Anand Chopra, Matthew Courchene, Tsenguun Enkhbaatar, Nicolas Franz-Pattillo, Arkadev Ghosh, Nadhanael GV, Da Kang, Neil Lloyd, David Macdonald, Bipasha Maity,Benjamin Milner, Ronit Mukherji, Adlai Newson, Mengying Wei and Michael Wiebe — they haveall helped me more than they know themselves.I want to thank Prithu Banerjee, Taylor Chapman, Amartya Dutta, Alexander Firanchuk, BertKramer and Jonathan Schmok — friends outside my PhD program, for their companionship thatkept me sane at various points of time during my six-year-long journey of doctoral studies. We hadsome wonderful time together.I would like to thank my professors at St. Xavier’s College and Indian Statistical Institute inKolkata, who had taught how to see the world around me through the lens of economics. Two ofmy teachers from high school days, Supriya Datta and Kalisadhan Mukherjee, both of whom passedaway last year, deserve special mention. Without their motivation, encouragement and nurturingof my young mind, I would not be where I am today.Finally, I thank my mother, who had given up her doctoral studies to raise me, and the memoryof my father, who would have been happy to see this thesis in print. Without their love, sacrificeand patience, this thesis would not be a reality.xiiiChapter 1IntroductionThis thesis studies the dynamics of household and firm choices. The following three chapters touchupon areas of business cycle dynamics of productivity as well as long-run evolution of economicinequality across generations. In particular, the first chapter studies the impact of the decline inthe power of labour unions in influencing firms’ hiring and firing decision, which in turn affects thebusiness cycle movements of productivity. The second chapter looks at a host of structural changesin the U.S. economy around the mid-1980s, and once again studies the impact of these significantregime-switches on the business cycle properties of productivity. Finally, the third chapter movesbeyond the short-run view of the economy at business cycle frequencies and instead looks at howeconomic inequality propagates through intra-family linkages across generations.Productivity, as measured by either the total value-added per worker or the total output pro-duced per hour worked or even the total factor productivity (TFP), rose during economic boomsand fell in recessions for about four decades after World War II. However, around the mid-1980s,this procyclicality of productivity suddenly started to vanish. Productivity has remained coun-tercyclical with employment and total hours worked and acyclical with output ever since. Thisphenomenon is known as the productivity puzzle (see McGrattan and Prescott, 2012).1 Chapter 2of this thesis argues that easier hiring and firing of workers due to the rapid decline in union powerfrom the early 1980s in the U.S., precipitated by President Reagan’s deregulation measures, canexplain this puzzle.When for some reason the hiring and firing of workers become easier, firms do not need torely on making their available workers change their effort level depending on economic slack orboom. They can instead simply fire workers in recessions and hire them back during better times.This means that an individual worker’s productivity does not need to fluctuate along the businesscycle when hiring and firing costs are low. This is a candidate theoretical explanation of the suddenvanishing procyclicality of productivity — the so-called reversal of the labour hoarding phenomenonthat was cited widely for the historical procyclicality of productivity since the 1940s. Chapter 2first provides empirical evidence for this channel of a drop in labour hoarding and then identifiesde-unionization in the U.S. as a potential reason for the decline in employment adjustment friction.There are two ways through which the reduced importance of labour hoarding is empirically1In popular media, the term productivity puzzle has recently been used in different contexts to mean a varietyof phenomena in the U.S. economy, e.g., the slow growth of productivity in recent years, the divergence betweenlabour productivity and real wage growth, etc. However, most of the academic literature recognizes the vanishingprocyclicality of productivity as the ‘productivity puzzle’, and it is in this sense that the term will be used in thisthesis.1made apparent. First, using a widely accepted decomposition of the TFP measure (see Fernald,2014) into a measure of factor utilization rate (which arguably measures the intensive margin offactor use) and a utilization-adjusted true productivity component, it is shown that the entire dropin procyclicality of TFP is driven by the decline in the explanatory power of the highly procyclicalfactor utilization component, while the true productivity dynamics changed very little. Secondly,following the strategy in Gal´ı and Gambetti (2009), a structural vector autoregression (SVAR)using productivity and per capita hours shows that it is not the changing relative importance ofthe technology versus demand shocks but the changing response of the U.S. economy to the sameshocks before and after the 1980s that led to the fall in productivity correlations with output andlabour input. In particular, it is shown that conditional on the same expansionary demand shockin the pre- and post-1984 eras, productivity rose much mildly in the post-1984 period. This canbe seen as indirect evidence of firms relying more on hiring new workers to meet the extra demandinstead of increasing the productivity (or effort) of its available workers due to the drop in hiringcost. Moreover, this enhanced hiring and firing also translate into larger volatility of employmentrelative to both output and the intensive margin of factor use at the same time as the productivitypuzzle.After considering a variety of reasons as to why hiring and firing costs can decline, e.g., theadvent of online job search, increased use of part-time or temporary workers, I settled for de-unionization as the most plausible channel.2 The de-unionization episode in the U.S. not onlylines up well in terms of the timing and speed of the productivity puzzle but it also aligns wellwith international evidence, e.g., Canada experienced neither de-unionization nor the productivitypuzzle, while the United Kingdom under Margaret Thatcher experienced both a decline in unionclout and the vanishing procyclicality of productivity. Using cross-sectional variation from 51 U.S.states and 17 industries, it is argued that sectors and regions which experienced a larger decline inthe fraction of unionized workers also witnessed a larger drop in the procyclicality of productivityand a bigger increase in the volatility of employment relative to that of output. Moreover, it is alsoshown how employment protection laws like the right-to-work laws in U.S. states interacts withthe de-unionization. In particular, those states which had these right-to-work laws understandablydid not get impacted by the de-unionization episode (as they were already pro-business) and hencedid not observe the productivity puzzle, while the entire effect of the decline of union power wasconcentrated in the non-right-to-work states.3The idea of a greater labour market flexibility in the last three decades in the U.S. as anexplanation for the vanishing procyclicality of productivity was first discussed in Gordon (2011),and most recently in Gal´ı and van Rens (2017). The key insight of the latter is that a decline inlabour market turnover, which reduced hiring frictions, can match the observed decline in labourproductivity correlations. However, Gal´ı and van Rens (2017) does not pinpoint any particular2See Stansbury and Summers (2020) for a survey of the changes in the U.S. economy that were brought about bythe rapid loss of workers’ bargaining power from the early 1980s.3Autor (2003) shows how in heavily unionized states hiring had become so difficult that it had to be outsourcedto temporary workers.2structural reason as to why the labour market turnover suddenly changed in the mid-1980s. Chapter2 investigates various structural changes in the labour market as possible candidates for the fallinghiring and firing frictions, and finds that de-unionization is the most likely channel.4Chapter 3 extends the understanding of the productivity puzzle by considering potential al-ternative explanations for the puzzle and quantifying the importance of the hiring cost channelidentified in Chapter 2 as a feasible explanation.McGrattan and Prescott (2012) propose that under-estimating the use of intangible capital isthe main channel for explaining the vanishing procyclicality of productivity. They argue that ifintangible capital is strongly procyclical but it is not included while measuring output, then themeasured procyclicality of productivity with value-added will be less. However, they do not presentany empirical fact regarding the increased use of intangible capital around the mid-1980s, ratherfocusing on the Great Recession period of the late 2000s. I do not find cross-industry evidencethat greater investment in intellectual property products (which is the closest measurable proxy forintangible capital) is correlated with a larger drop in productivity correlations in the mid-1980s.Moving beyond the narrative of mismeasurement in factor input (see Gal´ı and van Rens, 2017)or output (see McGrattan and Prescott, 2012), Barnichon (2010) shows that a large portion of therise in the correlation of labour productivity with unemployment is accounted for by the increas-ing volatility of technology shocks relative to demand shocks. The main argument is that sincetechnology shocks induce countercyclicality of productivity with labour input and demand shocksinduce procyclicality of productivity with labour input, the increasing relative importance of tech-nology shocks will help to explain the fall in unconditional correlations of productivity with hours.However, this explanation is insufficient for two reasons. First, the productivity correlations felleven conditional on a demand shock, whereas conditional on technological shock, the correlationof labour productivity increased slightly in the post-1984 period (as shown in Chapter 2). Thesechanges in the conditional correlations indicate that some form of structural change is required tofully explain the productivity puzzle. Second, the correlation of labour productivity with outputconditional on a technology shock has always been positive, and it increased further after the mid-1980s. Hence, the increasing importance of technology shocks cannot explain the falling correlationof output with productivity. Van Zandweghe (2010) performs a comparative study of the changesin technology and demand shocks on one hand and the structural change in the labour market onthe other. He concludes that since the productivity correlations conditional on both demand andsupply shocks have changed, it is more likely that change in labour market flexibility is the keyfactor behind the phenomenon. Through the lens of a New Keynesian model, featuring endogenouseffort choice and costly hiring of workers, I show in Chapter 3, that neither the reduced volatilityduring Great Moderation nor the changing relative importance of technology and demand shocks4The model in Gal´ı and van Rens (2017) predicts that productivity co-moves positively with both output andinputs in response to technology shocks. This is in stark contrast to the empirical finding in the post-War U.S.where labour input is negatively correlated with technology shocks (see for example Gal´ı and Gambetti (2009)). Akey element of the model in Chapter 3 will be to generate impulse responses to technology and demand shocks thatmimic the empirically observed ones.3can explain any notable part of the puzzle while allowing the hiring cost to fall by 67% to reflectthe decline in private-sector union density can generate almost the entire drop in productivitycorrelations and more than 80% of the increase in the relative volatility of employment.In contrast to studying demand and supply shocks, Garin, Pries, and Sims (2018) look atchanges in the contribution of sector-specific shocks relative to aggregate shock in the total volatilityof industrial production, and claim that the increasing importance of sectoral shocks have causeda drop in productivity correlations and also led to jobless recoveries.5 However, I show that theempirical finding of the increasing importance of sectoral shocks is not robust to the choice of thedataset, and there is reason to doubt that there has been a sudden increase in sectoral reallocationtowards more productive sectors since the mid-1980s. Relating jobless recoveries to the vanishingprocyclicality of productivity is also done by Berger (2016), whose model relies on heterogeneityin worker productivity. Crucially, in his model, firms know individual worker productivity andduring streamlining and restructuring in a recession they can lay off their least productive workers,thereby bringing up the average labour productivity. I show in Chapter 3 that while it is truethat firms indeed fire their least productive workers during recessions, this phenomenon has notincreased in intensity after the mid-1980s. So, rather than relying on selectively firing the lowproductivity workers, I find that firms have been hiring and firing all workers more frequently.Moreover, since the focus in Berger (2016) is only on the recovery part of the business cycle, thatmodel has trouble in generating the full magnitude of the drop in productivity correlations. Also,the impulse responses of employment to a TFP shock is positive in Berger’s modified Real BusinessCycles model, which goes against the empirical evidence and is corrected in the New Keynesianframework I consider.The link between the diminishing procyclicality of labour productivity and jobless recoveriescannot be overlooked. Even though jobless recoveries correspond to only a fraction of the entirebusiness cycle (namely, the post-recession recovery and not the pre-recession boom or the recessionitself), they are consistent with the falling correlation between productivity and labour input.However, jobless recoveries are at odds with the falling correlation between output and productivity.Hence, there is no a priori reason to try to explain these two phenomena of jobless recoveries andproductivity puzzle jointly. Nevertheless, it is natural to ask whether factors explaining one canalso explain other. Panovska (2017) runs a horse race among the different channels of explanationsfor jobless recoveries — (i) reallocation of resources across sectors (like in Groshen and Potter(2003), Garin, Pries, and Sims (2018) and others) or occupations (as highlighted by Jaimovichand Siu (2015)), (ii) expansionary overhang which leads to a restructuring in recessions, like inBerger (2016), (iii) shorter duration of recessions, as pointed out by Bachmann (2012), and (iv)structural changes in the economy, like those highlighted by Gal´ı and Gambetti (2009). Usinga VAR analysis, she finds that structural change in the economy is the most plausible channelexplaining jobless recoveries. Therefore, in this thesis, I will focus exclusively on the structural5The last three recessions in the U.S. (since the early 1990s recession) were characterized by recoveries whereoutput and productivity picked up (albeit at a slower pace than previous recessions) but labour input did not rise inthe initial recovery phase. This phenomenon has been termed as jobless recoveries.4changes in the economy to explain the productivity puzzle. Finally, Brault and Khan (2020) pointout changes in non-contemporaneous correlations of productivity with output and labour input,and argue that none of the theoretical explanations explored in the literature for the productivitypuzzle can explain these changes in non-contemporaneous correlations. Investigating this aspect ofcyclical productivity dynamics remains an agenda for future research.Unlike the first two chapters which deal with short-run business cycle dynamics of firms’ choicesregarding employment and labour effort, Chapter 4 addresses an issue of long-run dynamics in theeconomy, namely, the evolution of inequality across generations of households. It asks how muchof the observed cross-sectional inequality in earnings, other income sources (like transfers, wealthincome and spousal income) and consumption expenditure can be explained by intra-family inter-generational linkages.Parents influence their children’s life-cycle outcomes in many ways. Economists often quantifythese influences using measures of intergenerational persistence along dimensions of heterogeneitysuch as earnings, wealth, or consumption.6 The various channels of family influence are inter-relatedas parents can affect their children’s outcomes in complex ways: through choices about education,through the transmission of ability and preferences, by providing income-enhancing opportunities,as well as through inter-vivos and bequest transfers affecting wealth and consumption.7 Further,these mechanisms may be substitutes: investing in a child’s education to increase their earningspotential may imply lower transfers of wealth. This rich set of influences suggests that changes in ahousehold’s financial circumstances may induce intergenerational effects with empirically testableimplications. Unlike most previous studies, which looked at either income or consumption inisolation, and focused primarily on the intergenerational pass-through parameters, we develop aparsimonious model of the joint persistence of expenditures, earnings and other income and focusdirectly on understanding inequality. The co-dependence of these processes turns out to be of criticalimportance, as discussed in Alan, Browning, and Ejrnæs (2018). Our work has two main objectives:first, to examine the diverse ways parental influences shape children’s economic outcomes in a unifiedframework; second, to quantify how much of the inequality observed in a particular generation isdue to parental factors.To describe the influence of parental heterogeneity, we model intergenerationally linked house-holds that make consumption and saving choices in an environment where persistent shocks shapepermanent income. In our baseline model, we characterize the distribution of endogenous expendi-6Research linking family outcomes across generations often focuses on income and earnings persistence (for a sur-vey, see Aaronson and Mazumder, 2008). Related work documents the persistence of wealth (e.g., Charles and Hurst,2003), consumption (e.g. Waldkirch, Ng, and Cox, 2004; Charles, Danzinger, Li, and Schoeni, 2014; Bruze, 2016)and occupations (Corak and Piraino, 2010; Bello and Morchio, 2016). Boar (2017) documents parental behavioursconsistent with a precautionary motive geared to insure children against life-cycle risk.7For the role of transfers, see Daruich and Kozlowski (2016), Bolt, French, Maccuish, and ODea (2018) andAbbott, Gallipoli, Meghir, and Violante (2019). Restuccia and Urrutia (2004) and Lee and Seshadri (2019) examinethe role of investments at different stages of the life-cycle. Caucutt and Lochner (2019) highlight the impact ofcredit constraints in an environment with sequential parental investments. Gayle, Golan, and Soytas (2018) findthat human capital accumulation, nonlinear returns to hours worked, and parental time investments are key for theintergenerational correlation in earnings through their effects on fertility and the division of labour.5tures alongside a standard income process. The intergenerational linkages stem from intra-familypersistence of earned income as well as from savings and transfer decisions. Specifically, we allowparents to influence outcomes of children in three ways: through earned income, through othersources of income such as transfers, and through consumption.A key contribution of our analysis is to document the role of parental factors in explaininginequality in the next generation and to contrast the importance of family heterogeneity with theimpact of idiosyncratic variation which is independent of parents. The extent to which inequal-ity among parents is passed through to inequality among children depends on intergenerationalelasticities; however, the relative importance of family factors for inequality among children alsodepends on the magnitude of idiosyncratic (family-independent) variation. Hence, a decompositionof observed inequality requires estimates of intergenerational pass-through parameters, estimates ofinequality among parents and estimates of idiosyncratic heterogeneity. We use our model to jointlyestimate, through a method-of-moments approach, the parameters determining the importance ofthe different components of inequality.The model delivers moment restrictions on the variances of earnings, other income and con-sumption of parents and their adult children, and on their covariation across generations. We usethese moments to jointly estimate the parameters dictating intergenerational linkages, as well as theresponses of income and consumption to different shocks. Then, through the model, we quantifythe contribution of parental factors to children’s outcomes and overall cross-sectional inequality.For estimation, we employ data from the Panel Study of Income Dynamics (PSID) coveringbirth-cohorts of individuals born between the early 1950s and the late 1970s. We link households’income, expenditures and other family characteristics across generations in a long panel format.8 Toavoid the selection issues associated with women’s labour force participation, we focus on a sample offather-son pairs to characterize earnings persistence; however, we include women’s labour earningswithin our measure of other income. Since the availability of expenditure data varies across surveywaves, research on the consumption pass-through based on PSID data has used food expendituresfor the full-length sample or restricted attention to shorter periods for which extensive consumptionrecords are available.9 To account for these data limitations, in our baseline estimation we useinformation about the higher moments of measured food consumption going back to the late 1960s;then, in a set of robustness checks, we document the robustness of our findings by replicating theanalysis with imputed measures of total household outlays,10 and by restricting the sample periodto have detailed expenditure records for most categories.8The PSID initially recorded only housing and food-related expenditures. After 1999 more consumption categorieswere added to the survey; since 2005, the PSID expenditure data cover all the categories in the ConsumptionExpenditure Survey (CEX). The CEX started providing detailed data about multiple consumption categories at themicro-level in the 1980s, yet that data is unsuitable for intergenerational studies because individuals were followedfor a maximum of four quarters.9The former approach is that of Waldkirch, Ng, and Cox (2004). The latter route is taken by Charles, Danzinger,Li, and Schoeni (2014), who project average consumption expenditures of adult children for the years 2005-2009 onsimilar measures for their parents in the same years.10The imputation method (see Attanasio and Pistaferri, 2014) relies on the estimation of a demand system usingthe rich set of expenditures reported post-1999 in the PSID.6Our analysis also highlights a negative association between income inequality and economic mo-bility. This arises because greater income inequality in the kids’ generation is explained by strongerintergenerational pass-through channels. The finding is consistent with the empirical observationthat more unequal societies exhibit lower earnings mobility across generations, a relationship oftendubbed the ‘Great Gatsby’ curve (Krueger, 2012; Corak, 2013). The presence of a negative associ-ation between mobility and inequality does not, however, pin down the direction of causality (seeRauh, 2017; Comerford, Rodriguez Mora, and Watts, 2017; Kanbur, 2019). While higher persis-tence can lead to higher inequality (a channel which we explore directly), higher inequality itselfmight skew the distribution of economic opportunities and stifle long-term mobility. The negativecorrelation between inequality and intergenerational mobility also does not imply that a declinein mobility is necessary for the rise in inequality. We show that while inequality has increased inthe U.S. over the past few decades, mobility has remained roughly stationary, thereby implying arise in the idiosyncratic life-cycle shocks to the younger generation that cannot be attributed tointra-family linkages.Our semi-structural approach establishes that idiosyncratic life-cycle heterogeneity, rather thanparental economic circumstances, accounts for most of the observed cross-sectional inequality. How-ever, our statistical model remains silent about the underlying sources of these idiosyncratic het-erogeneities and intergenerational persistence. Endogenizing intergenerational linkages in a het-erogeneous agent framework to bring forth these underlying sources remains as work for futureresearch.7Chapter 2The Productivity Puzzle and theDecline of Unions2.1 IntroductionFor almost half a century after World War II, labour productivity was procyclical in the UnitedStates — it rose during economic booms and fell in recessions. However, since the mid-1980s,it became acyclical with output and countercyclical with total hours worked.11 Quite strikingly,during the recent Great Recession of the late 2000s, while output and hours took a downward turn,labour productivity stayed constant or even increased slightly over some quarters (Mulligan, 2011).This change in the cyclical correlations has been well documented and is often referred to as the‘labour productivity puzzle’ (McGrattan and Prescott, 2012).Typically, the explanation for procyclical labour productivity has been the phenomenon of‘labour hoarding ’12, whereby firms use their available workers less intensely during economic down-turns, and more intensely during booms. Since such changes in the intensity of factor utilizationcannot be observed in the changes of actual employment or labour hours, the measured labourproductivity, which is defined as output per hour worked, appears to be procyclical.13 Therefore,when the procyclicality of labour productivity started to diminish in the mid-1980s, a natural can-didate for an explanation was the vanishing procyclicality of factor utilization. Now, firms resortedto labour hoarding because it was costly for them to hire and fire workers along the business cycle.Therefore, any explanation for reduced labour hoarding should involve more flexible labour marketinstitutions which brings down the cost of employment adjustment. Such a reduction in labourmarket frictions can also explain the steady increase in the volatility of employment relative tothat of output since the mid-1980s. This chapter identifies rapid de-unionization since the early1980s as a key factor behind increased labour market flexibility in the U.S. that made hiring and11The level of correlation depends on the choice of the filtering process to extract the cyclical part from rawtime-series data, but the fall in productivity correlations is robust.12Biddle (2014) notes that the concept of ‘labour hoarding’, at least in its modern form, dates back to Okun (1962).Burnside, Eichenbaum, and Rebelo (1993) finds that a significant proportion of movements in standard productivitymeasures like the Solow residual are artefacts of labour hoarding behaviour. By the 1980s, the concept was beingregularly used as a standard textbook explanation for procyclical labour productivity (e.g., Dornbusch and Fischer,1981; Hamermesh and Rees, 1984). Paradoxically, it was around the same time that labour productivity startedbeing more countercyclical.13Real business cycle (RBC) models differ on the explanation of productivity procyclicality. They argue thatbusiness cycles are driven by procyclical technology shocks. In Section 2.3.2, I show evidence of negative response oflabour inputs to positive technology shocks, which militates against the RBC paradigm.8firing workers easier for firms. In a cross-section of U.S. states and industries, the magnitude of thedecline in union density is shown to be significantly correlated with the drop in labour productivitycorrelations and the rise in the relative volatility of employment. Other structural changes in thelabour market like the increased use of part-time workers and the rise in online job search marketdo not appear to have caused a drop in productivity correlations.Declining hiring costs should be accompanied by changes in how the economy responds todifferent types of shocks. For example, in response to a positive demand shock, firms can nowincrease their labour input by hiring more workers, and hence do not need to increase the intensityof labour utilization by as much. This would imply that the improvement in measured labourproductivity and total factor productivity (TFP) in response to a positive demand shock will besignificantly reduced. Using a time-varying structural VAR analysis, I show that this is indeed thecase.The rest of the chapter is organized as follows. Section 2.2 documents that the cyclical correla-tions of productivity with both output and labour input have decreased quite abruptly around themid-1980s in the U.S. After showing that this puzzling finding is robust to different data sources,the choice of de-trending methodology, and even the measure of labour input, I turn to explainthe puzzle in Section 2.3. I investigate the issue in two different ways. First, in Section 2.3.1, Idecompose productivity into factor utilization rate and utilization-adjusted productivity and showthat it is only the factor utilization component of measured productivity that has become morecountercyclical. Second, in Section 2.3.2, I show that the response of the aggregate U.S. economy totechnology and demand shocks have changed around the mid-1980s. Both these findings point to-wards a structural change in the labour market that made hiring and firing workers suddenly muchless costly. In Section 2.4, I consider the possible reasons for the drop in employment adjustmentcost and show that de-unionization is one structural change in the labour market that is consistentboth in terms of timing and speed with the productivity puzzle. Cross-sectional evidence fromU.S. states and industries, as well as international evidence from OECD countries, point towards adecline in union power as a major contributing factor towards higher labour market flexibility thatexplains the productivity puzzle. Finally, Section 2.5 concludes the chapter.2.2 The Productivity PuzzleThe productivity puzzle refers to the sudden vanishing of procyclicality of productivity around themid-1980s in the U.S. The existing literature on this puzzle has typically used average labourproductivity, defined as output per hour worked, as the measure of productivity. In Panels (a) and(b) of Figure 2.1, I corroborate that finding using quarterly data on output and hours worked forthe U.S. business sector from 1947 through 2017, sourced from the Labor Productivity and Costs(LPC) dataset of the Bureau of Labor Statistics (BLS). As an alternative measure of productivity, inPanels (c) and (d), I use TFP (unadjusted for factor utilization), sourced from Fernald (2014), and9find a remarkably similar pattern of a sudden drop in contemporaneous productivity correlations.14While I have used the Baxter and King (1999) bandpass filter to extract the cyclical component ofthe time-series variables in Figure 2.1, the finding is robust to the choice of the statistical filter.15These changes in productivity correlations have implications for the co-movement of produc-tivity with job flows over the business cycle. One can think of changes in employment as beingcomposed of an inflow of workers through job creation or vacancies, and outflow through job sep-arations. In fact, one can write employment growth ∆nt as the difference between job creationht and job destruction ft, ∆nt = ht − ft, implying Cov (∆nt, lpt) = Cov (ht, lpt) − Cov (ft, lpt),where lpt denotes cyclical component of labour productivity. Then it is natural to expect that job-creation or vacancy rate should become more countercyclical, and job-destruction or separationrate more procyclical after the 1980s. In other words, given that Cov (∆nt, lpt) has fallen, it mustbe composed of a drop in Cov (ht, lpt) and/or a rise in Cov (ft, lpt). Using different data sourceson job flows, I corroborate these conjectures in Figure 2.2.16From the above findings, it is clear that the sudden vanishing procyclicality of productivityaround the mid-1980s in the U.S. is not simply an artefact of a particular dataset, or a specificstatistical de-trending process, or the choice of the measure of productivity or labour input. Hav-ing established the empirical robustness of the so-called productivity puzzle, next I investigate itspotential cause.2.3 Drop in Employment Adjustment CostProcyclicality of measured productivity in the U.S. after World War II was traditionally explainedthrough labour hoarding by firms facing costly hiring and firing of workers. So a natural candidatefor explaining the vanishing procyclicality of productivity is a fall in employment adjustment cost.However, whether there has indeed been less factor hoarding after the mid-1980s remains an em-pirical question. In Section 2.3.1, I study the cyclical properties of factor utilization rate, which isa proxy measure for factor hoarding, and establish that factor hoarding has lost its importance inthe post-1980s U.S. In Section 2.3.2, I study the response of the aggregate U.S. economy to tech-nology and demand shocks in a structural VAR set-up. The changes in these responses between the14There is a difference in the levels of the correlations between the two alternative measures of productivity —while TFP has remained procyclical even after the drop, average labour productivity has become countercyclical withhours worked, and acyclical with output. The current thesis is not concerned with these level differences, but thesudden drop around the mid-1980s.15For the complete set of robustness checks for the choice of filters, see Panel A of Table A.1 in the Appendix.Using KLEMS data, provided by Jorgenson, Ho, and Samuels (2012), Panel B of the table shows that the drop inlabour productivity correlations is also robust to considering annual data for the aggregate U.S. economy. Data forthe non-farm business sector (not shown here) also produce the same correlation pattern. Findings are also robust tousing employment as the measure of labour input instead of total hours worked. Murali (2018) shows that the fall inproductivity correlations is also robust to using empirical mode decomposition method of calculating the momentsat different cyclical frequencies.16It is difficult to obtain data on economy-wide job destruction before the late 1970s. However, economy-widejob vacancy rate can be obtained using the monthly Help Wanted Index (HWI) from the Job Openings and LaborTurnover Survey (JOLTS) starting from 1951. Also, for the manufacturing sector, Davis, Faberman, and Haltiwanger(2006) have collected quarterly data on both job creation and destruction rates starting from 1947.10pre- and post-1984 periods further confirm the hypothesis that firms have resorted to less labourhoarding in recent decades.2.3.1 Vanishing Procyclicality of Factor Utilization RateCommonly used measures of productivity, like labour productivity and TFP, contain an implicitcomponent of factor utilization rate that can itself have cyclical correlations with output andlabour input measures like employment and total hours worked. For example, if labour is utilizedat a higher rate (by increasing labour effort) during economic booms than during recessions thenmeasured labour productivity will be more procyclical. This can be understood by simply studyinga production function with effective labour input, Y = AEα1Nα2 , where Y is the value-added,E is the effort or utilization rate of each worker N , and A is the utilization-adjusted productivitycomponent. Average labour productivity is defined as YN = AEα1Nα2−1, which is strictly increasingin E and weakly decreasing in N so long as α1 > 0 and α2 ≤ 1. In an economic downturn, whenfirms want to reduce the effective labour input, Eα1Nα2 , they face the option of either reducing thenumber of workers N , or decreasing the utilization rate E. When it is costly to adjust employment,firms mostly change effort. As an extreme example, when N is fixed over the business cycle dueto costly adjustment, all change in labour productivity is explained by changes in effort. Thus, asfirms increase E during booms and decrease it in recessions, labour productivity remains perfectlyprocyclical since measured productivity is increasing in E. As the cost of adjusting N falls, firmscan now rely on reducing N in recessions, thereby boosting labour productivity during economicdownturns since productivity is decreasing in N . Thus, lower hiring and firing cost makes measuredproductivity less procyclical.This argument of procyclical labour utilization was used to justify the procyclicality of TFPin the post-War U.S. economy. However, it remains to be established whether the drop in cyclicalproductivity correlations was driven by less factor hoarding or more countercyclical utilization-adjusted productivity. Using hours per worker as a proxy that is proportional to unobservedchanges in both labour effort and capital utilization, Basu, Fernald, and Kimball (2001) generateda composite factor utilization rate series and a utilization-adjusted TFP series. Studying thecyclical property of those series in Table 2.1, one can safely conclude that the drop in cyclicalcorrelations of measured productivity is driven by the factor utilization component of TFP, andnot the utilization-adjusted ‘true’ productivity component. As discussed above, factor utilizationcan become less procyclical if factor adjustment along the extensive margin over the business cyclebecomes more pervasive in comparison to changes in unobserved labour effort and work-week ofcapital.Notwithstanding the fall in procyclicality of factor utilization rate, utilization-adjusted TFP hashistorically been and continues to be much less procyclical than factor utilization. Hence, purely ina mechanical variance decomposition sense, if the relative contribution of factor utilization rate fallsin the total variability of aggregate TFP, measured productivity will become more countercyclical.Table 2.2 shows that the share of the total variation of TFP that is explained by the more procyclical11component of factor utilization rate has diminished sharply in the post-1984 period. Such a shifttowards greater relative importance of the extensive margin of factor adjustment can emanate froma drop in the cost of hiring and firing of factors of production, particularly labour.17Falling employment adjustment cost should imply a rise in the volatility of employment relativeto those of output and factor utilization. Panels (a) and (b) of Figure 2.3 show the dramaticrise in the volatility of hours and employment relative to that of output exactly at the time ofthe sudden drop in the productivity correlations. Finally, Panel (c) of Figure 2.3 shows howthe relative importance of employment (the extensive margin of labour adjustment) vis-a`-vis theintensive margin of factor utilization has progressively increased from around the same time. Thisrise in the relative volatilities of measured labour inputs happened immediately after the onsetof the so-called Great Moderation when the absolute volatilities of output and labour input fellprecipitously in the late 1970s. As is evident from Figure 2.4, even though the volatilities of output,hours and employment follow a similar time trend, the magnitude of reduction in volatility is largerfor output than for the labour inputs. This leads to the eventual increase in the volatility of labourinput relative to that of output.To summarize, the vanishing procyclicality and reduced volatility of factor utilization rate overthe business cycle, induced by a drop in employment adjustment cost, can not only explain the fallin measured productivity correlations but also the rise in relative volatility of employment.2.3.2 Changes in Response to Technology and Demand ShocksStructural changes in the labour market that make hiring and firing of workers easier for firmsshould have implications for how the economy responds to different types of shocks. In this section,I focus on such changes in the response of the aggregate U.S. economy to technology and demandshocks between the pre and post-1984 periods. I perform a time-varying structural vector auto-regression (SVAR) with labour productivity growth and per capita hours, as in Gal´ı and Gambetti(2009).18 There are two main advantages of this specification: first, it allows one to control for low-frequency movements in per capita hours without having to extract the cyclical component of hoursthrough any form of ad hoc time-series filtering, and second, it allows one to know the completedynamics of the impulse responses over the years so that it can be pinpointed as to exactly whenthe responses began to change.19 Since the current thesis focusses on documenting the changes inthe impulse responses during the mid-1980s, this method of time-varying SVAR is the most suitablefor the purpose. For a detailed discussion on the choice of SVAR specification and identification ofthe shocks, refer to Appendix A.3.17See Appendix Table A.4 for the robustness of these results using an alternative measure of capacity utilizationrate published by the Federal Reserve Board.18Chang and Hong (2006) criticize the use of labour productivity as a measure of productivity. They argue thatusing labour productivity instead of TFP mislabels changes in input mix (i.e., permanent changes in the capital-labourratio) as technology shocks. Hence, as a robustness check, I perform the same SVAR replacing labour productivitywith TFP.19In Figures A.4 and A.6, I show the dynamics of the impulse responses by year. This confirms the choice of 1984as the approximate year of the structural change, although no rigorous structural change test was performed.12Response to technology shock. Panels (a), (b) and (c) of Figure 2.6 respectively show theimpulse responses of per capita hours, per capita output and labour productivity to a positivetechnology shock separately for the pre-1983 (solid blue lines) and post-1984 (dashed red lines)periods. Of these, the only statistically significant difference between the two sub-periods is thechange in the impulse response of hours, as shown in Appendix Figure A.5. While I find thatper capita hours respond negatively on impact to a positive technology shock throughout thepost-War era, the negative response is much less intense and barely different from zero in thepost-1984 period.20 A common explanation provided for the diminished response of hours totechnology shocks is that the monetary policy conducted by the Federal Reserve became moreaccommodative of technology shocks to the economy. But what is most relevant in the contextof the productivity puzzle is that the muted negative response of hours to a positive technologyshock increases the productivity correlation with labour input. This acts as a counterforce to thevanishing procyclicality of productivity.Response to demand shock. In response to a positive demand shock, hours increased byroughly the same amount in the pre- and post-1984 periods, while the positive response of outputon impact was drastically muted after the mid-1980s. Since average labour productivity is nothingbut output per hour worked, the reduced response of output and a near-identical response of hoursimplies a muted response of labour productivity to a demand shock.21 A qualitatively similar resultis obtained when estimating the SVAR with TFP growth instead of labour productivity growth.While the impulse response of TFP remains positive albeit the reduction in magnitude (see Panel(d) of Appendix Figure A.7), the on-impact response of labour productivity turns negative after1984 (see Panel (f) of Figure 2.6). The muted response of productivity and an unchanged response ofhours to a demand shock imply that conditional on a demand shock, the correlation of productivitywith hours must drop in the post-1984 era. This is shown in Figure 2.7.The reduction in productivity correlation conditional on a demand shock proves that it is notthe case of changing composition of shocks to the U.S. economy that have induced the sudden fallin unconditional productivity correlation, rather there must have been deeper structural changesin the economy that caused firms to change output by a smaller magnitude when hit with the samedemand shock. An example of such a structural change is the decline in the labour adjustmentcost. Given a positive demand shock, when employment adjustment is less costly, a firm does notincrease the intensive margin of effort as much, which causes output and productivity to not riseas much for a given increase in employment and hours worked. This decreases the correlation ofproductivity with measured labour input.20Contrary to my findings, Gal´ı and Gambetti (2009) did not find a starkly muted response of hours conditional ona technology shock in the post-1984 period. This difference emanates from extending the post-1984 period with morerecent years of data — while they used data till 2005, my dataset extends till the fourth quarter of 2017. When TFPis used as the measure of productivity instead of labour productivity, a similar difference between the two sub-periodsin the initial response of hours emerges (see Panel (a) of Appendix Figures A.7 and A.8).21For statistical significance of the differences in the impulse responses between the two sub-periods, refer to Panels(d), (e) and (f) of Appendix Figure A.5.13In summary, while the change in response to demand shocks predicts decreasing procyclicalityof productivity, the change in response to technology shocks predicts just the opposite. How allthese opposing forces combine to generate the change in the unconditional correlation of produc-tivity with output and hours will be studied in Chapter 3. Nevertheless, the crucial finding isthat the unconditional correlation of productivity with output and hours fell not because of therising importance of technology shocks vis-a`-vis demand shocks (as claimed by Barnichon (2010))but because of a drop in the correlations conditional on demand shock, thereby pointing towardsstructural changes in the economy that made factor hoarding less relevant.2.4 What Caused Employment Adjustment Cost to DropThe reduced importance of factor utilization rate in measured productivity and the change in pro-ductivity correlation conditional on demand shocks establish that higher dependence on hiring andfiring of workers instead of the intensive margin of effort adjustment has caused the procyclicality ofproductivity to fall so drastically.22 However, what observable structural change in the labour mar-ket can bring about such a sudden drop in employment adjustment cost remains an open questionso far.One such possible cause of increasing employment turnover is the rise in online job-searchplatforms, which reduces the hiring cost by making it much easier to match workers and jobs.Moreover, the improved efficiency of online matching between specific worker and job types couldalso mean that firms need to terminate fewer workers who do not fit well with the job, therebyreducing the firing cost for firms. However, this is unlikely to have triggered the switch in theproductivity correlations in the mid-1980s because internet recruitment service providers did notbegin their journey until the mid-1990s.The increased use of temporary workers is another likely reason for the reduction in employmentadjustment cost. Jalo´n, Sosvilla-Rivero, and Herce (2017) argue that the countercyclicality of labourproductivity in Spain was driven by the 1984 legislative reform that increased the importance oftemporary workers in the Spanish economy. Daruich, Addario, and Saggio (2017) also study theimplications of a similar 2001-reform of lifting constraints on the employment of temporary contractworkers in Italy. For the U.S. it is difficult to ascertain the role of temporary workers in theincreased flexibility of labour markets due to lack of suitable data that dates back long enough, e.g.,employment data for the temporary help services industry from the Current Employment Statistics(CES) database of BLS dates back only till 1990. Although Carey and Hazelbaker (1986) showthat employment growth in the temporary help industry increased sharply immediately after the1982 recession, which lines up well with the timing of the switch in labour productivity correlations,Schreft and Singh (2003) show that temporary and part-time hiring and overtime — collectively22There could have been a similar drop in the cost of adjusting capital stock along the extensive margin along withor instead of a drop in the cost of hiring and firing workers. However, the proxy used here to measure the factorutilization rate is hours per worker, as advocated by Fernald (2014). Since it is empirically impossible to make adistinction between labour utilization (effort) and capital utilization rates, and because hours per worker is arguablya more direct proxy for labour effort, I will stick to only employment adjustment cost in this thesis.14known as ‘just-in-time hiring’ — has gained in importance only since the 1991 recession in the U.S.However, for the U.S., I study the time series of the share of part-time workers (see Figure 2.5) anddo not find any noticeable upsurge, if not an actual plateauing, in the share of part-time workersaround the mid-1980s.Gal´ı and van Rens (2017) claim that the main driver of falling labour market frictions in theU.S. labour market was the drop in job separation rate. They argue that because of a substantialdrop in the gross job destruction rate, firms need to hire much less new workers to maintain thelevel of employment. This reduced hiring activity implies lower cost of employment adjustment inequilibrium, thereby leading to more countercyclical productivity. While this channel of reductionin employment adjustment cost is certainly feasible for the U.S., a cursory glance at the interna-tional evidence from twelve other OECD countries, presented in Table 2.3, essentially refutes theclaim that change in job separation rate is a significant determinant of changes in productivitycorrelations.232.4.1 Decline of UnionsAn empirically identifiable labour market change that occurred in the U.S. almost around the sametime as the change in the productivity correlations is the decrease in size and influence of labourunions. In Figure 2.8 we see that union membership among working individuals (both in terms ofrates and absolute numbers) was rising in the U.S. until the early 1970s, after which it remained flatfor a decade (with falling rates for the private industries and increasing rates for the public sector),and started falling sharply since the early 1980s.24 To emphasize how dramatic the de-unionizationevent around the 1980s was, one can compare the growth rates in union density for 30 years beforeand after 1980. In the three decades preceding 1980, unionization rate remained almost constant,while between 1980 and 2010 it fell by roughly 50% in aggregate and by 67% in the private sector.One concern about de-unionization being the main driving force behind falling procyclicality ofproductivity is that union rates were already quite low in the U.S. even before 1980, roughly 20%of the workforce and so falling union rate should not matter much. Taschereau-Dumouchel (2017)argues that it is not so much the fraction of union-jobs but the presence of the political threat ofunionization that matters for labour market outcomes.Farber and Western (2002) argue that this stark reversal of unionization trend in the U.S. wasprecipitated by a fall in the annual number of union elections — a key channel of recruiting newunion members. The number of elections held fell by almost 50%, from about 8000 in 1980 to about23Of the countries considered, only Ireland experienced a notable decrease in the job separation rate along withdecreasing cyclical correlation of labour productivity. Nevertheless, Ireland also experienced a 21% drop in uniondensity, and hence the exact source of its vanishing procyclicality of productivity cannot be determined easily.24Consistent data on union density is available separately for the private sector only from 1973 onwards (see Hirschand Macpherson (2003)). Although unionization rate started falling from the early 1970s in the private sector, thede-unionization process accelerated from 1980: the average annual rate of decline in private-sector union density was2.4% between 1974 and 1979 compared to 6.6% between 1980 and 1985. Troy and Sheflin (1985) present data onprivate-sector union density in the U.S. between 1929 and 1972, and they also find an average annual de-unionizationrate of only 1.1% between 1950 and 1972. Therefore, it can be concluded that the decline of unions even in theprivate sector had a sharp acceleration starting from the early 1980s.154400 in 1985. The unfavourable political climate was precipitated by President Reagan’s strongstand against the air-traffic controllers’ strike of 1981,25 and the much-publicized appointment ofthe Reagan Labor Board in 1983. A change in the political climate regarding labour unions can alsomean that changes in union density might be an underestimate of the change in the real bargainingpower of unions. While it is difficult to directly measure the power of unions, one good proxy isto look at the number of work stoppages, which are usually organized by unions. From Figure2.10, one can see that large-scale work stoppages dropped by almost 90% of its pre-1980 level quitesuddenly within a couple of years. Thus, although the decline in union membership from the early1980s was a somewhat gradual process which might seem inconsistent as an explanation for thestrikingly rapid decline in the productivity correlations, union power seems to have declined morepromptly. Moreover, in Figure 2.9, I show that the timing and speed of de-unionization match wellwith that of the productivity puzzle.2.4.2 De-unionization: International EvidenceThe era of deregulation that began in the United States from the early 1980s had its parallel inother parts of the world.26 It is interesting to note as anecdotal evidence that the United Kingdom,which underwent a similar de-regulation episode under Margaret Thatcher, experienced both de-unionization and drop in procyclicality of productivity. On the other hand, countries like Canada,for which this drop in unionization is conspicuously absent (see Riddell (1993)), did not undergoa drop in cyclical correlations of productivity. In Table 2.3, I show that in most of the developedworld, de-unionization is strongly predictive of the loss in productivity procyclicality and a rise inthe volatility of employment relative to that of output.27 This evidence is consistent in spirit withGnocchi and Pappa (2009), who find that union coverage is one labour market rigidity that mostsignificantly affects business cycle statistics in a sample of 20 OECD countries.The evidence that de-unionization did not happen in all industrial countries highlights anotherimportant aspect of the phenomenon. It is natural to link de-unionization with other labour marketchanges happening at the same time as its potential cause. For example, Acemoglu, Aghion, andViolante (2001) and Dinlersoz and Greenwood (2016) argue that skill-biased technological changecan explain de-unionization in the U.S., and Ac¸ikgo¨z and Kaymak (2014) show that roughly 40%of the drop in unionization rates in the U.S. can be explained by the rise in the skill premium inwages. Further, Foll and Hartmann (2019) argues that routine task-biased technical change is notonly the driving force behind job market polarization but also de-unionization. However, since skill-biased or routine-biased technological change happened in most developed economies, the sudden25On August 5, 1981, Reagan fired more than 11,000 striking air traffic controllers who had ignored his order toreturn to work. This sweeping mass firing of federal employees sent a strong message to American business leadersthat they can hire and fire their workers much more easily.26De-regulation in the labour market can not only mean the decline in union power but also relaxation of employ-ment protection legislation (EPL). However, as shown in Table 2.3, I do not find any consistent pattern across OECDcountries that less stringent EPL translated into lower procyclicality of productivity.27Figure 2.18 shows the regression between changes in union density and the changes in labour productivitycorrelation in a cross-section of 13 developed economies.16trend reversal in union density in only a handful of these countries like the U.S. is likely to bemostly driven by political factors. Moreover, insofar as one believes that skill-biased technologicalchange from the 1980s was driven by IT capital use (due to high capital-skill complementarity inthe production process, e.g., as highlighted in Krusell, Ohanian, Rios-Rull, and Violante (2000)),one should find a significant correlation across industries between the rising share of IT capital andfalling productivity correlations. This is however not the case, as pointed out by Wang (2014).Therefore, while it could be the case that relatively slow-moving technological changes impactingthe labour market had some role to play in the de-unionization process, the episode of rapid fallin union power from the early 1980s is most likely to have been precipitated by political factorsthat are exogenous to labour market conditions. It is in this sense of exogeneity that the impactof de-unionization on the falling procyclicality of productivity (as shown in the next section usingcross-sectional variation from U.S. states and industries) can be thought as a causal channel.2.4.3 De-unionization: Evidence from U.S. States and IndustriesHaving established that in the aggregate U.S. economy, de-unionization since the early 1980s isconsistent, in terms of timing, with falling procyclicality of labour productivity, and rising volatilityof employment relative to that of output and factor utilization, I now use sectoral variation acrossU.S. states and industries to see if a larger magnitude of de-unionization is indeed correlated witha greater reduction in labour productivity correlation. In particular, I run the following cross-sectional regression:∆Corr (lpi, hi) = α+ β∆ ln (Union Density)i + εi, (2.1)where lpi and hi are the cyclical components of labour productivity and hours in industry or statei, and the time-difference ∆ denotes the difference between the pre- and post-1984 average values.28Figures 2.11 and 2.15 show a significant positive relationship between the degree of de-unionizationand the magnitude of the drop in productivity correlations across 17 U.S. industries and 51 U.S.states respectively. To avoid the result being driven by small industries or states, I weight theobservations with the average employment level in each industry or state.One concern while using cross-sectional variation in de-unionization in the above regression isthat union densities might not have fallen substantially within individual industries or states. Inother words, the fall in aggregate unionization rate might have been driven by employment shiftstowards less unionized sectors and regions, rather than de-unionization within them. This would beproblematic for identifying the slope coefficient in regression (2.1), because of lower cross-sectionalvariation in changes in union densities. However, a simple within-between decomposition29 ofaggregate de-unionization shows that nearly 88% of the fall in aggregate union density happened28I do not have data with simultaneous variation across states and industries, and so a single regression exploitingthat industry × state variation could not be performed.29Total change in union density, ∆u = Within-i change,∑17i=1 e¯i∆ui + Between-i change,∑17i=1 u¯i∆ei, where e¯i isthe average employment share and u¯i is the average union density in industry or state i.17within the 17 industries considered here between 1983 and 1991. Similarly, 91% of the total fallin the unionization rates in the U.S. between the pre- and post-1984 periods took place within thestates, and not through employment shifts towards less unionized states.For the state-level regression, there is an additional concern that in recent years many U.S. stateshave adopted right-to-work legislation promoting their “pro-business” outlook, thereby renderingthe labour unions a lot less powerful in those states. In that case, a decline in union density in theseright-to-work states should barely matter for explaining the drop in productivity correlations. InAppendix Figure 2.16, I show this is indeed the case, with only the so-called non-right-to-work statesdriving the positive relationship between de-unionization and drop in productivity correlation. Thisfinding of right-to-work law interacting with union power to determine productivity through changesin management practices resonates well with U.S. plant-level findings by Bloom, Brynjolfsson,Foster, Jarmin, Patnaik, Saporta-Eksten, and Van Reenen (2019).One alternative identification strategy to the one considered above, is to perform a difference-in-difference estimation a` la Card (1992). In that strategy, one assumes that the intensity of thede-unionization event is larger in industries with a higher initial proportion of unionized workers.Thus, instead of regressing the change in the productivity correlation on the change in the uniondensity, one simply regresses it on the pre-1984 level of union density:∆Corr (lpi, hi) = α+ β ln (Union Density)pre−1984i + εi (2.2)This method of identification also corroborates my finding that union density had a significant roleto play in the vanishing procyclicality of labour productivity and the rising volatility of employmentchanges relative to that of output.30The above cross-sectional evidence supports my claim that de-unionization is positively corre-lated with vanishing procyclicality of labour productivity, but it is still left to show that industrieswith a greater fall in productivity correlation experienced a larger increase in the volatility ofemployment (that is, the extensive margin of labour adjustment) relative to that of output and uti-lization (that is, the intensive margin of factor adjustment). Since utilization data is not availableat the industry level, I use hours per worker as a proxy for the measure of the intensive margin oflabour adjustment. From Figure 2.17 one can find a statistically significant negative relationshipbetween the change in labour productivity correlation on one hand and the relative volatility ofemployment on the other, across U.S. industries.31The negative correlation patterns in Panels (a) and (b) of Figure 2.17 are similar, but there isa subtle difference between the two scatter plots. A lot of the industries experienced a rise in thevolatility of employment relative to that of output, while very few experienced a similar rise in thevolatility of employment relative to that of hours per worker. This finding that the extensive marginof employment adjustment became less volatile relative to the intensive margin of changing hours30For details on the difference-in-difference strategy and the results based on that, refer to Appendix A.2.31As more direct evidence of the union channel, Figure 2.12 shows the negative correlation between larger declinesin the union density and the rising relative volatility of employment across U.S. industries.18per worker in almost all industries is an apparent aberration from what one would expect underfalling employment adjustment cost.32 This is particularly puzzling in light of the evidence in Panel(c) of Figure 2.3 that employment became increasingly more volatile relative to factor utilizationsince the 1980s. To understand why the dynamics of hours per worker and factor utilization mightvary, it is instructive to study the industry-level differences in the elasticity of output to hoursper worker. Basu, Fernald, and Kimball (2001) find that the responsiveness of output to hoursper worker is vastly different across industry-groups, e.g., the non-durables manufacturing sector isroughly 60% more responsive than the durables manufacturing industries, and more than thrice asresponsive as the service sector. The declining share of manufacturing in the U.S. can, therefore,explain the larger decline in the volatility of factor utilization at the aggregate level than withinindividual industries.2.5 ConclusionWhy did productivity suddenly start becoming less procyclical during the mid-1980s? This is theresearch question that this chapter tries to answer. A decomposition of measured productivityinto factor utilization and a utilization-adjusted productivity component reveals that the fall inproductivity correlations is driven by a lower dependence on factor hoarding. Changes in responsesof the U.S. economy to demand shocks also point towards some structural change that madeadjusting factors along the extensive margin less costly, thereby leading to firms relying less onfactor hoarding. I then identify a rapid decline in union power since the early-1980s as the keystructural change in the labour market that made hiring and firing of workers easier relative toeffort adjustment through labour hoarding. Using cross-sectional evidence from U.S. industriesand states, and also international evidence from OECD countries, it is argued that more intensede-unionization is associated with a deeper fall in the cyclical productivity correlations. Moreover,lower dependence on labour hoarding in the face of higher labour market flexibility is shown toimply rising relative volatility of employment, and this rise is also correlated with the fall in uniondensity and productivity correlations across U.S. industries. Understanding the role of labourmarket institutions like unions in influencing business cycle properties of aggregate macroeconomicvariables is the broad contribution of this chapter.32The post-1984 change in the volatility of employment relative to that of hours per worker is not very robust tothe choice of different datasets and time-series filters (see Table A.3 in Appendix). Regardless of the filter used, thevolatility of employment relative to hours per worker did not show any stark upward trend after the mid-1980s.192.6 TablesTable 2.1: Reduction in Procyclicality of Factor Utilization RateWith Output With HoursVariable & Filter Choice Pre 1983 Post 1984 Change Pre 1983 Post 1984 ChangePanel A: Quarterly Growth RateTFP 0.87 0.70 - 0.17 0.35 0.10 - 0.25Factor Utilization Rate 0.73 0.49 - 0.24 0.67 0.52 - 0.15Utilization-Adjusted TFP 0.10 0.25 +0.15 -0.40 -0.32 +0.08Panel B: Annual Growth RateTFP 0.88 0.69 - 0.19 0.49 0.29 - 0.20Factor Utilization Rate 0.87 0.62 - 0.25 0.75 0.61 - 0.15Utilization-Adjusted TFP -0.10 0.04 +0.14 -0.45 -0.34 +0.11Note: Data on quarterly and annual growth rates of TFP, factor utilization rate, utilization-adjusted TFP, outputand hours worked for the U.S. business sector are sourced from Fernald (2014). Since Fernald (2014) only providesthe growth rates of the three variables, robustness to other de-trending methods cannot be established.Table 2.2: Reduction in Variance of Factor Utilization RateVariancesVariable & Filter Choice 1948-1983 1984-2017Panel A: Quarterly Growth RateTotal Factor Productivity (TFP) 17.55 (100%) 5.89 (100%)Factor Utilization Rate 11.67 (66.5%) 1.64 (27.8%)Utilization-Adjusted TFP 5.88 (33.5%) 4.25 (72.2%)Panel B: Annual Growth RateTotal Factor Productivity (TFP) 4.56 (100%) 1.50 (100%)Factor Utilization Rate 3.79 (83.1%) 0.79 (52.7%)Utilization-Adjusted TFP 0.77 (16.9%) 0.71 (47.3%)Note: Data on quarterly and annual growth rates of TFP, factor utilization rate and utilization-adjusted TFP aresourced from Fernald (2014). Since Fernald (2014) only provides the growth rates of the three variables, robustnessto other de-trending methods cannot be established. Percentages in parentheses refer to the share of total variance ofTFP that is explained by each component. While calculating the variance of the components, the covariance term wasequally split, e.g., [V ar (Factor Utilization Rate) + Cov (Factor Utilization Rate, Utilization-Adjusted TFP)] is thevariance of factor utilization rate, and the variance of utilization-adjusted TFP is given by V ar (Utilization-Adjusted TFP)+Cov (Factor Utilization Rate, Utilization-Adjusted TFP).20Table 2.3: Labour Market Statistics from OECD Countries∆Correlation of Productivity ∆S.D.(Employment)S.D.(Output)Labour Market StructureCountry With Output With Hours ∆Union ∆Separation Rate ∆EPRCFrance -0.13 0.17 26% -54% 0% 1%U.S.A. -0.54 -0.62 32% -49% -24% 0%Australia -0.44 -0.48 73% -37% 4% 21%Austria -0.21 -0.16 -16% -32% No data -11%U.K. -0.39 -0.46 41% -28% 11% 16%Spain -1.37 -0.74 317% -24% -1% -34%Germany -0.04 -0.52 -10% -24% 41% 8%Ireland -0.44 -0.21 44% -21% -44% -2%Italy -0.09 -0.16 71% -4% 11% 0%Norway -0.35 -0.12 47% -3% 47% 0%Canada 0.01 0.09 -22% 2% 9% 0%Sweden 0.01 -0.03 59% 10% 84% -7%Finland -0.25 0.21 -9% 36% No data -22%Note: Countries are arranged in ascending order of union density changes. All changes are between the post andpre-1984 periods. Productivity is defined as real GDP per hour worked. De-trending of variables has been done usingthe HP-filter. Quarterly data on output and hours between 1960 and 2010 for all countries (except Spain) are takenfrom OECD Economic Outlook Database, collected by Ohanian and Raffo (2012). Annual data for Spain between1950 and 2017 is sourced from the Conference Board Total Economy Database. Union density data are sourced fromOECD Annual Trade Union Density Dataset. Since internationally comparable data on job flows are not availablebefore 1980s, changes in job separation rate are calculated as the difference between the average rate between 2002through 2007, and that between 1985 through 1990, as reported in Elsby, Hobijn, and Sahin (2015). Employmentprotection is the EPRC index from the OECD from 1985 to 2013. The index is very persistent over time, so changingthe end year of the sample would make very little difference.212.7 Figures-.20.2.4.6.8Corr (Labour Productivity, Output)1955 1965 1975 1985 1995 2005Year(a) Corr (Labour Productivity, Output)-.6-.4-.20.2Corr (Labour Productivity, Hours)1955 1965 1975 1985 1995 2005Year(b) Corr (Labour Productivity, Hours).5.6.7.8.9Corr (TFP, Output)1955 1965 1975 1985 1995 2005Year(c) Corr (TFP, Output)0.2.4.6.8Corr (TFP, Hours)1955 1965 1975 1985 1995 2005Year(d) Corr (TFP, Hours)Figure 2.1: Vanishing Procyclicality of Productivity in the United StatesNote: Output, hours and average labour productivity (output per hour worked) data for Panels (a) and (b) aresourced from the Labor Productivity and Costs quarterly dataset published by the Bureau of Labor Statistics for theU.S. business sector. Relevant data for Panels (c) and (d) are sourced from Fernald (2014), as modified by Ramey(2016). The measure of TFP is not adjusted for factor utilization. The Baxter and King (1999) bandpass filterbetween 6 and 32 quarters is used to filter all the variables. A centred rolling window of 15 years is used to calculatethe correlations. Findings are robust to alternative choice of filters and window-sizes.22-.20.2.4.6.8Corr. (Job Creation, Labour Productivity)1950 1960 1970 1980 1990 2000Year(a) Job Creation-.8-.6-.4-.20Corr. (Job Destruction, Labour Productivity)1950 1960 1970 1980 1990 2000Year(b) Job Destruction-.4-.20.2.4.6Corr. (Vacancy, Labour Productivity)1960 1970 1980 1990 2000 2010Year(c) Help Wanted IndexFigure 2.2: Cyclical Correlation of Labour Productivity with Job FlowsNote: Panels (a) and (b) correspond to the U.S. manufacturing sector (data from Davis, Faberman, and Haltiwanger(2006)), while Panel (c) is for the entire U.S. economy (data from the Job Openings and Labor Turnover Survey).The Baxter and King (1999) bandpass filter between 6 and 32 quarters is used to filter all the variables. A centredrolling window of 10 years is used to calculate the correlations. Findings are robust to alternative choice of filtersand window-sizes..7.8.911.11.2S.D.(Hours)/S.D.(Output)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(a) s.d.(Hours)s.d.(Output).6.7.8.91S.D.(Employment)/S.D.(Output)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(b) s.d.(Employment)s.d.(Output).6.7.8.911.1S.D.(Employment)/S.D.(Utilization)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(c) s.d.(Employment)s.d.(Utilization)Figure 2.3: Relative Volatility of Hours & Employment over the Business CycleNote: Data for hours, employment and output is sourced from the BLS-LPC quarterly dataset for the U.S. businesssector. Factor utilization data (in quarterly growth rates) is taken from Fernald (2014). The Christiano and Fitzgerald(2003) bandpass filter between 6 and 32 quarters have been used to extract the cyclical component of the variablesin Panels (a) and (b), while the annualized quarterly growth rate has been used in Panel (c). A centred rollingwindow of 15 years is used to calculate the second moments. Findings are robust to alternative choice of filters andwindow-sizes..006.008.01.012.014.016S.D.(Output)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(a) Output.004.006.008.01.012S.D.(Hours Worked)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(b) Hours.004.006.008.01S.D.(Employment)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(c) EmploymentFigure 2.4: Cyclical Volatility of Quarterly Growth Rates of Output, Hours & Employment2314161820Percentage of Part-Time Employment1970 1980 1990 2000 2010 2020YearFigure 2.5: Share of Part-time Employment in the U.S. (1968-2017)Note: Data is sourced from Labor Force Statistics (LFS) of the Current Population Survey (CPS). Part-timeemployment is defined as less than 35 hours of work per week.242 4 6 8 10 12 14 16 18 20-0.4-0.3-0.2-0.100.10.2(a) Technology Shock: Hours2 4 6 8 10 12 14 16 18 200.20.30.40.50.60.70.80.911.11.2(d) Demand Shock: Hours2 4 6 8 10 12 14 16 18 200.30.40.50.60.70.80.9(b) Technology Shock: Output2 4 6 8 10 12 14 16 18 200.20.40.60.811.21.4(e) Demand Shock: Output2 4 6 8 10 12 14 16 18 200.60.650.70.750.80.850.9(c) Technology Shock: Labour Productivity2 4 6 8 10 12 14 16 18 20-0.2-0.100.10.20.30.40.5(f) Demand Shock: Labour ProductivityFigure 2.6: Impulse Responses to Technology & Demand Shocks (LP, Hours & Output)Note: Impulse Response Functions (IRF’s) of per-capita hours, per-capita output and average labour productivityfrom a 2-variable (viz., labour productivity growth and per-capita hours) time-varying long-run SVAR. IRF’s for thepre-1984 period (1956-1983) are in blue, and the post-1984 (1984-2017) IRF’s are in red dashed lines. Data is sourcedfrom the Labor Productivity and Costs (LPC) quarterly dataset for the U.S. business sector, published by the Bureauof Labor Statistics (BLS).251960 1970 1980 1990 2000 2010-1-0.8-0.6-0.4-0.200.20.40.60.81Figure 2.7: Conditional Correlations of Labour Productivity with HoursNote: Time-varying correlations of per capita hours with labour productivity, conditional on technology shock (bluedashed line) and demand shock (red dotted line).05000100001500020000Union Membership (in thousand)510152025Union Density1930 1940 1950 1960 1970 1980 1990 2000 2010 2020YearUnion Density Union MembershipFigure 2.8: Size & Density of Labour Union Membership in the U.S. (1930-2014)Note: Figures represent the number and percentage of non-agricultural wage and salary employees who are unionmembers. Data before 1977 is sourced from Historical Tables published by the Bureau of Labor Statistics. Databetween 1977 and 1981 comes from May earnings files, and from 1983 onwards it comes from the Outgoing RotationGroup (ORG) earnings files of the Current Population Survey (CPS), collected by Hirsch and Macpherson (2003).Union coverage rates are slightly different from union membership rates but follow a similar time-trend.26-.20.2.4.6.8Corr (Output, Labour Productivity)10152025Union Density (%)1955 1965 1975 1985 1995 2005yearUnion Density Corr(y, lp)Figure 2.9: De-unionization and Vanishing Procyclicality of ProductivityNote: Union density, sourced from Hirsch and Macpherson (2003) and Historical Tables from the Bureau of LaborStatistics (BLS), refers to the percentage of non-farm wage and salary employees who are union members. Corr(y, lp)refers to a 15-year rolling window correlation between the Baxter and King (1999) filtered (between 6 and 32 quarters)business sector output and average labour productivity, sourced from the Labor Productivity and Costs quarterlydataset of the BLS.0100200300400500No. of work stoppages involving >1000 workers1940 1960 1980 2000 2020YearFigure 2.10: Number of Work Stoppages involving 1000 or more workers in the U.S. (1947-2017)Note: Data is sourced from the Economic News Release of the Bureau of Labor Statistics (BLS).27Slope = 0.014 [0.01]ConstructionReal EstateFinance & InsurancePost & CommunicationUtilitiesEducationHealthcarePublic AdministrationRetail TradeTransport & StorageOther ServicesAgricultureHotels & RestaurantsWholesale TradeDurable ManufacturingMiningNon-durable Manufacturing-1-.50.51Change in Labour Productivity Correlation with Hours-50 -40 -30 -20 -10 0% Change in Unionization Rate (1983-1991)R-squared = 0.17Figure 2.11: Cross-Industry Evidence for De-unionization: Productivity CorrelationNote: Data on industry-level unionization rates comes from the Current Population Survey (CPS), collected byHirsch and Macpherson (2003). Labour productivity is defined as real value added per hour worked. Annual industry-level data on value-added, hours and employment between 1947 and 2010 comes from KLEMS dataset, collected byJorgenson, Ho, and Samuels (2012). CPS industry codes for unionization and SIC industry codes in KLEMS werematched to create a consistent set of 17 U.S. industries. The Baxter and King (1999) bandpass filter between 2 and 8years have been used to de-trend the variables. Since industry-level union data is available only from 1983 onwards,and the CPS industry codes change from 1992, to minimize concordance error I have used the change between 1983and 1991 as the measure of change in union density. Size of the bubbles represent average industry employment level.The p-value of the slope coefficient using robust standard error is reported in parentheses.Retail TradeAgriculture, Forestry, Fishing and HuntingTransportation & StoragePublic Admin.EducationFinance & InsuranceMiningUtilitiesConstructionDurable ManufacturingWholesale TradeNondurable ManufacturingPost & CommunicationReal EstateHealthcareHotels & RestaurantsOther ServicesR-squared = 0.08Slope = -1.05 [0.03]-100-50050100% Change in Volatility of Employment Relative to Output-50 -40 -30 -20 -10 0% Change in Unionization Rate (1983-1991)Figure 2.12: Cross-Industry Evidence for De-unionization: Relative Volatility of EmploymentNote: Data on industry-level unionization rates comes from the Current Population Survey (CPS), collected byHirsch and Macpherson (2003). Labour productivity is defined as real value added per hour worked. Annual industry-level data on value-added, hours and employment between 1947 and 2010 comes from KLEMS dataset, collected byJorgenson, Ho, and Samuels (2012). CPS industry codes for unionization and SIC industry codes in KLEMS werematched to create a consistent set of 17 U.S. industries. The Baxter and King (1999) bandpass filter between 2 and 8years have been used to de-trend the variables. Since industry-level union data is available only from 1983 onwards,and the CPS industry codes change from 1992, to minimize concordance error I have used the change between 1983and 1991 as the measure of change in union density. Size of the bubbles represent average industry employment level.The p-value of the slope coefficient using robust standard error is reported in parentheses.28Figure 2.13: De-unionization in U.S. States around 1984Note: 49 U.S. states (Alaska and Hawaii are missing) are grouped into deciles, with lighter shades corresponding tolarger percentage of de-unionization around 1984.Figure 2.14: Vanishing Procyclicality of Labour Productivity in U.S. States around 1984Note: 49 U.S. states (Alaska and Hawaii are missing) are grouped into deciles, with lighter shades corresponding tolarger decrease in correlation between employment growth and output per worker growth in the pre- and post-1984periods.29ConnecticutCaliforniaNevadaMassachusettsRhode IslandNew Jersey HawaiiNew YorkD.C.MinnesotaAlaskaMaineIllinoisWisconsinMissouriVermontWashingtonMarylandNew MexicoNew HampshireN. DakotaKansasOregonAlabamaS. CarolinaKentuckyLouisianaS. DakotaIdahoUtahTennesseeVirginiaIowaArizonaMississippiIndianaW. VirginiaArkansasDelawareNebraskaWyomingMontanaOklahomaMichiganGeorgiaOhioTexasPennsylvaniaN. CarolinaFloridaColoradoR-squared = 0.34Slope = 0.012 [0.001]-1-.50.5Change in Labour Productivity Correlation with Employment-90 -80 -70 -60 -50 -40 -30 -20 -10% Change in Unionization RateFigure 2.15: Cross-State Evidence for De-unionizationNote: Data on state-level unionization rates comes from the Current Population Survey (CPS), collected by Hirschand Macpherson (2003). State-level data on real non-farm gross domestic product and total employment between1969 and 2010 is sourced from the Bureau of Economic Analysis (BEA). Since hours worked data is not available atthe state level, employment is used as the measure of labour input and labour productivity is defined as the state realnon-farm gross domestic product per worker. I use annual growth rate as the filter because the preferred Baxter andKing (1999) filter leads to 12 years of missing observations and leaves only 3 years of data before 1984. All changesin variables are calculated as the difference between the pre and post-1984 averages. Although observation for eachstate is weighted by its average employment in the regression, to improve readability I have not shown the weightshere through bubbles, rather made it explicit in Figures 2.13 and 2.14. The p-value of the slope coefficient usingrobust standard error is reported in parentheses.UtahTennesseeMississippiArizonaS. DakotaLouisianaAlabamaS. CarolinaIowaArkansasNebraskaVirginia TexasN. DakotaFloridaKansasNevadaWyomingGeorgiaN. CarolinaR-squared = 0.06Slope = 0.007 [0.30]-1-.50.5Change in Labour Productivity Correlation with Employment-90 -80 -70 -60 -50% Change in Unionization(a) Right-to-Work StatesIdahoKentuckyOregonW. VirginiaIndianaDelawareOklahomaMontanaMichiganWisconsin MaineAlaskaMinnesotaIllinoisMissouriOhioPennsylvaniaNew MexicoMarylandNew HampshireColoradoNew JerseyRhode IslandHawaiiNew YorkD.C.VermontConnecticutCaliforniaMassachusettsWashingtonR-squared = 0.26Slope = 0.011 [0.012]-.50.5Change in Labour Productivity Correlation with Employment-80 -60 -40 -20% Change in Unionization(b) Non Right-to-Work StatesFigure 2.16: Cross-State Evidence for De-unionization by Right-to-Work StatusNote: Categorization of states into Right-to-Work and Non-Right-to-Work has been done based on the status in1984. Other definitions are as in Figure 2.15.30ConstructionRecycling ManufacturingPost & TelecommunicationsMachineryFinanceUtilitiesFood, Beverages & TobaccoTextiles & LeatherMineralsWholesale TradeFuelsTransport EquipmentReal EstateElectrical & Optical EquipmentMetalsRubber & PlasticPaper, Pulp, Printing & PublishingWoodGovernmentHealth & Social WorkMiningEducationMotor VehiclesPrivate HouseholdsAgricultureRentingChemicalsTransport & StorageRetail TradeOther ServicesHotel & RestaurantR-squared = 0.64Slope = -0.81 [0.00]-1-.50.5Change in Labour Productivity Correlation with Hours-1 -.5 0 .5 1% Change in Relative Volatity of Employment to Output(a) Relative to Output VolatilityConstructionUtilitiesElectrical & Optical EquipmentPost & Telecommunications Recycling ManufacturingMachineryFinanceReal EstateTransport EquipmentFood, Beverages & TobaccoHealth & Social WorkWholesale TradeWoodTextiles & LeatherGovernmentMiningMineralsEducationTransport & StoragePaper, Pulp, Printing & PublishingChemicalsRubber & PlasticPrivate HouseholdsFuelsMetalsRetail TradeRentingHotels & RestaurantsMotor VehiclesAgricultureOther ServicesR-squared = 0.36Slope = -0.59 [0.00]-1-.50.5Change in Labour Productivity Correlation with Hours-1.5 -1 -.5 0 .5% Change in Relative Volatility of Employment to Hours Per Worker(b) Relative to Hours Per Worker VolatilityFigure 2.17: Relative Volatility of Employment & Change in Labour Productivity CorrelationNote: Data is for 31 U.S. industries from the annual KLEMS dataset, collected by Jorgenson, Ho, and Samuels(2012). The change in the second moments is the difference between their values in the post-1984 period (1984-2008)and the pre-1984 period (1959-1983). Regressions are weighted by the time-average of industry-level employment,depicted by the size of the bubbles. The p-value of the estimated slope using robust standard error is reported inparentheses. The Baxter and King (1999) bandpass filter between 2 and 8 years has been used to extract the cyclicalcomponent of the variables. Findings are robust to using other filters.FinlandSwedenCanadaSpainU.S.A.France NorwayItalyU.K.AustraliaIrelandAustriaGermanyR-squared = 0.35Slope = 0.72 [0.04]-.8-.6-.4-.20.2Change in Corr(Labour Productivity, Hours)-.6 -.4 -.2 0 .2 .4Change in Union DensityFigure 2.18: International Evidence for De-unionizationNote: All changes are between the pre- and post-1984 periods. Labour productivity is defined as real GDP perhour worked. De-trending of variables has been done using the HP-filter. Quarterly data on output and hoursbetween 1960 and 2010 for all countries (except Spain) are taken from OECD Economic Outlook Database, collectedby Ohanian and Raffo (2012). Annual data for Spain between 1950 and 2017 is sourced from the Conference BoardTotal Economy Database. Union density data are sourced from OECD Annual Trade Union Density Dataset. Theregression is weighted by the time-average of country-level employment, depicted by the size of the bubbles. Thep-value of the estimated slope using robust standard error is reported in parentheses.31Chapter 3The Productivity Puzzle: EvaluatingAlternative Explanations3.1 IntroductionWhat explains the sudden vanishing of the procyclicality of productivity in the mid-1980s in theU.S., or the so-called productivity puzzle? Chapter 2 provided an answer to this question — itis the increased labour market flexibility due to rapid de-unionization. However, along with thede-regulation of the economy under President Ronald Reagan, the mid-1980s was also a time ofother significant changes in the U.S. For example, the Federal Reserve under Paul Volcker mademonetary policy much more accommodative (not lower interest rates much in response to negativeoutput gaps) to curb inflation. There was a substantial decline in the importance of supply shocksfor the economy as the global crude oil price came down from its peak of about $104 in April1980 to about $22 per barrel in 1986 following conservation and insulation efforts after the IranianRevolution. The stabilization of monetary policy, as well as the favourable oil prices and otherstructural factors, led to a substantial drop in the aggregate volatility of the U.S. economy fromthe early 1980s — the so-called Great Moderation. Around the same time, the introduction ofIT capital in the workplace led to skill-biased technological change that had substantial impactson productivity. Simultaneously, intangible capital also started becoming more important in theproduction process. While the service sector’s share in total value-added was rising even beforethe 1980s, it was around the mid-1980s that the use of services as intermediate inputs in otherindustries picked up. The current chapter will investigate whether these changes in the shockshitting the U.S. economy and the structural changes in economic policy and production technologyhave a key role to play in explaining the productivity puzzle.The potential alternative explanations for the productivity puzzle will be assessed in two cate-gories: first, a subset of these explanations will be studied through the lens of a quantitative modelto ascertain the relative importance of these channels; and second, through separate empirical in-vestigation outside the model framework.33 The theoretical model will make explicit the relativequantitative importance of more accommodative monetary policy, reduced shock volatility in GreatModeration, lower hiring cost and higher bargaining power for firms due to de-unionization, andthe increased importance of technology shocks relative to demand shocks. The explanatory power33This has been done to keep the model simple and tractable without incorporating all the potential channels thatdid not have sufficient empirical evidence.32of other structural changes like the rise of the service sector, the increased relative importance ofsector-specific shocks as opposed to aggregate economy-wide shocks, the increased use of intangibleand IT capital, and the selective firing of least productive workers during recessions will be studiedseparately using a variety of data sources and empirical techniques.I use a New Keynesian model, with only two shocks (namely, a technology shock to TFP, anda demand shock to monetary policy), that incorporates endogenous movements in labour effort orutilization with costly hiring of workers by firms. The reason to rely on the standard New Keynesianframework is that it features nominal rigidities that help generate the negative response of labourinput to a positive technology shock.34 This is a key feature of the empirical impulse response oflabour input to technology shock (shown in Chapter 2) that is not captured by the RBC models thatare often used in the literature to study the productivity puzzle (e.g., see Gal´ı and van Rens (2017)and Berger (2016)). It is important to at least qualitatively get the correct sign of this impulseresponse because it informs us if the countercyclical response of hours was potentially driven merelyby stronger technology shocks (as argued in Barnichon (2010)). Similarly, the empirically observedpositive response of productivity to an expansionary demand shock is replicated in the model.The last chapter identified de-unionization as a potential reason for the increased hiring andfiring activities in the economy. This is not to claim that de-unionization is the only explanatoryfactor for falling employment adjustment cost. Acknowledging the possibility of multiple underlyingreasons behind increased labour market flexibility, the theoretical model in this chapter will beagnostic about the exact source of the fall in labour adjustment cost along the extensive margin.35The process of de-unionization will be captured through two parameter-changes in the model —one, the drop in the steady-state share hiring cost in total output, and a rise in the wage bargainingpower of firms. Changing each of these parameters one at a time, the model will be able to informwhich channel of the impact of de-unionization is relevant in explaining the productivity puzzle.Reasonable calibration of the model can generate almost the entire drop in productivity correlationsand more than 80% of the rise in relative volatility of employment. Almost all of the changes inthe correlations of productivity conditional on technology and demand shocks are also qualitativelymatched in the model simulations.The rest of the chapter is organized as follows. Section 3.2 proposes a dynamic stochasticgeneral equilibrium (DSGE) model featuring key elements of the empirical findings in Chapter 2 asdiscussed above. Section 3.3 then provides calibration of the model parameters, some of which areallowed to change between the pre- and post-1984 periods. Section 3.4 quantifies the performanceof the model in matching the changes in business cycle moments observed in the data. Different34This negative response of total hours worked or total employment to a positive technology shock can alternativelybe generated under the RBC framework, provided one allows for strong habit formation in household consumption.The reason to choose the New Keynesian framework is that it also allows one to study the impact of monetary policychange, whereas in an RBC economy there is no role of money.35In contrast, Zanetti (2007) shows that a standard New Keynesian monetary model with unionized labour marketcan explain European business cycle data much better than one with a competitive labour market, while Soskiceand Iversen (2000) and Alvarez and Shimer (2014) study in details the theoretical implications of a unionized labourmarket with minimum wages and job-rationing.33counterfactual scenarios are also discussed here. Section 3.5 then discusses the lack of empiricalevidence for a host of structural changes that could have potentially explained the productivitypuzzle. Finally, Section 3.6 summarizes the key conclusions of the chapter.3.2 ModelI will consider a New Keynesian model with two exogenous shocks — a technology shock to firmproductivity, and a monetary policy shock to the nominal interest rate. I will deviate from thetextbook model in two directions — first, I will explicitly consider both extensive and intensivemargins of labour input adjustment (namely, employment and effort), and second, I will consider thepresence of a convex cost of employment adjustment for firms. Crucially, the absence of adjustmentcost along the intensive margin of effort variation will lead firms to depend more on effort adjustmentwhen hiring costs are high. This drives the main result of vanishing procyclicality of effort, andconsequently of labour productivity, in the post-1984 era when hiring costs decreased significantly.3.2.1 HouseholdsI assume a large number of infinitely lived identical households in the economy, with each householdhaving a continuum of identical members represented by the unit interval. The household is therelevant decision unit for consumption and labour supply choices, and full consumption risk sharingis assumed within each household. Households seek to maximize the present value of lifetimeexpected utility, discounted at rate β ∈ (0, 1),E0∑∞t=0 βt [lnCt − χLt]subject to the per-period budget constraint,∫ 10 PitCitdi+QtDt ≤∫ 10 WjtNjtdj +Dt−1 + Πt.Here, Pit and Cit are the price and consumption of final good i, Wjt is the nominal wage paid atfirm j, Dt denotes the amount of one-period bonds purchased at price Qt, and Πt represents anylump-sum income including dividends from ownership of firms and government taxes and transfers.Household’s aggregate consumption bundle, Ct ≡(∫ 10 Cε−1εit di) εε−1is an index of the quantitiesconsumed of different types i of final goods, and is priced at Pt ≡(∫ 10 P1−εit di) 11−ε, with ε > 1being the Kimball aggregation parameter for the unit mass of final goods. The second term inthe period utility function represents disutility from effective labour supply Lt, which not onlydepends on the fraction Nt of household members who are employed but also the amount of effort,Et exerted by each employed member. More specifically, I assume the following functional formfor effective labour supply, Lt ≡(1+ζE1+φt1+ζ)Nt. The parameter χ > 0 measures the importanceof disutility from forgone leisure, while ζ ≥ 0 measures the importance of effort in that disutility34from working. The elasticity parameter φ ≥ 0 measures the degree of increasing marginal disutilityfrom exerting more effort.I make the simplifying assumption of constant hours per worker so that the only source ofintensive margin adjustment in labour supply is effort. More importantly, I assume that householdstake into account the endogenous impact of employment adjustment decisions on the level of effortexerted by each of its members.Consumption maximization for any given level of expenditure, PtCt is done by choosing theoptimal amount of consumption of each intermediate good, and the resulting demand function forgood i ∈ [0, 1] is given byCit =(PitPt)−εCt (3.1)The intertemporal optimality condition is given byQt = Et(PtPt+1Λt,t+1)(3.2)where Λt,t+k ≡ βk CtCt+k ∀t, k is the stochastic discount factor measuring the marginal rate of in-tertemporal substitution.3.2.2 FirmsI model the production side of the economy as a two-sector structure — final and intermediate goodssectors. Households supply labour only to firms in the intermediate goods sector who produce avariety of intermediate goods. Final goods firms do not employ labour, and effectively only re-package the intermediate goods and sell them in the market at a mark-up over marginal cost,subject to restrictions in the frequency of their price-setting decisions.Final GoodsA continuum of monopolistically competitive firms constitutes the final goods market, with eachfirm i ∈ [0, 1] producing a differentiated final good Yit according to the production function, Yit =Xit, where Xit is the quantity of the single intermediate good used by the final good firm i as aninput. In the absence of nominal rigidities, profit maximization leads to the following price-settingcondition for all t,Pit =(εε− 1)P It (3.3)where P It is the price of the intermediate good, and the factor(εε−1)is the optimal mark-upover the marginal cost of production. However, a` la Calvo (1983), I assume that final goodsfirms are precluded from setting their prices optimally in any period with probability θp ∈ [0, 1].This probability is independent both across firms, and of the time elapsed since the last nominaladjustment. This ensures that the fraction of firms changing their prices in any given period isa constant (1− θp), which can be interpreted as the degree of nominal flexibility in the economy.35Thus, the law of motion for the aggregate price level in the economy, Pt becomes a weighted averageof the optimally chosen price, P ∗t and the price that prevailed in the last period, Pt−1, with theweight being the probability of nominal adjustment:pt = θppt−1 + (1− θp) p∗t (3.4)where the lower case letters denote the natural logarithms of the corresponding upper case variables.Since all firms face an identical problem every period, the optimal price, P ∗t is the same across firms,and is given byp∗t = µp + (1− βθp)∞∑k=0(βθp)k Et(pIt+k)(3.5)where µp ≡ ln(−1). Combining equations (3.4) and (3.5), one can derive the inflation equationas follows:pipt = βEt(pipt+1)− λpµˆpt (3.6)where pipt ≡ pt − pt−1 is price inflation, λp ≡ (1−θp)(1−βθp)θp and µˆpt ≡ µpt − µp = pt − pIt − µp is thedeviation in logs of the average mark-up from its steady state value.36Intermediate GoodsEach perfectly competitive intermediate goods firm j ∈ [0, 1] faces the production function Y Ijt =At(EψjtNjt)(1−α), where At is the technology term common across all firms, the parameter ψ ∈(0, 1) measures the additional returns to effort over employment, and α ∈ (0, 1) denotes non-labour income share in the economy.37 In the calibration in Section 3.3, the parameters ψ andα are chosen such that they satisfy non-increasing returns to scale of the production function:(1− α) (1 + ψ) ≤ 1. The productivity term At has the following exogenous stochastic process: at ≡ln (At) = ρaat−1 +εat , where εat is a white noise process with variance σ2εa > 0. Since the productionfunction explicitly includes the factor utilization term, namely, effort Ejt, the productivity term Atshould be interpreted as the utilization-adjusted TFP.Labour MarketWorkers get separated from their jobs at intermediate goods firms at the exogenous gross rateof δ ∈ (0, 1), but every period t firm j hires back new workers Hjt ∀j, subject to a per-worker36See Gal´ı (2008) for derivation of equations (3.5) and (3.6).37One might be concerned that whatever is being labelled as ‘effort’ in the production function is in fact capital,the missing factor of production. In Appendix B.2, I contrast the cyclical properties of capital with that of factorutilization (which is a proxy for ‘effort’) and show how they evolved differently. This allays the identification concernof ‘effort’ being equivalent to capital. Empirically, it has so far been impossible to distinguish between capitalutilization and worker utilization rates, e.g., Fernald (2014) uses hours per worker as the proxy for both labour andcapital utilization, and the capacity utilization measure by the Federal Reserve is a combined measure of the intensivemargin of all factors of production. Given this lack of identification of the intensive and extensive margins of labourand capital separately, I do not include capital in the analysis because it would not be possible to separately identifytime-variation in capital adjustment cost and employment adjustment cost.36adjustment cost function, Gt = ΓHγt , with the parameters Γ and γ being strictly positive, andHt ≡∫ 10 Hjtdj denoting aggregate level of hiring. The assumption of a hiring cost as opposed toa firing cost is dictated by the simplicity of calibration. There is no reason to believe that thehiring and firing costs are symmetric, and this assumption should be relaxed in future research.Nevertheless, the motivation for this hiring cost is best summarized in Heckman, Page´s-Serra,Edwards, and Guidotti (2000): “...in the face of a positive shock firms may want to hire additionalworkers, but they will take into account that some workers may have to be fired in the future ifdemand turns down. This prospective cost acts as a hiring cost...” Moreover, more powerful unionscan make this hiring cost to rise for firms. This link between union density and hiring cost will becrucial later for the calibration of the model.38 However, there is no a priori reason to believe thatde-unionization could be the only reason for a decline in the hiring cost. As discussed in Chapter 2,increased use of temporary workers or the advent of online job-search platforms can also be thoughtof as potential determinants of hiring cost. Nonetheless, the presence of the job separation rateand the hiring by the firm implies that employment at firm j has the following law of motionNjt = (1− δ)Njt−1 +Hjt (3.7)Because of the presence of labour market frictions in the form of a hiring cost, wages and em-ployment may differ across firms, since they cannot be instantaneously arbitraged out by the freemovement of workers from low to high wage firms. Therefore, in what follows, the subscript j onwages and employment will signify this potential difference across firms. Faced with the commonhiring cost function, Gt and given the nominal wage Wjt, firm j’s optimal hiring policy is given bythe condition,MRPNjt =WjtPt+Gt − (1− δ)Et (Λt,t+1Gt+1) (3.8)where MRPNjt = (1− α) (1−ΨF ) PItPtY IjtNjtis the marginal revenue product of employment ex-pressed in terms of final goods. The non-zero term ΨF ≡ αψ1+φ−(1−α)ψ arises due to the endogenousresponse of effort to changes in employment. This condition implies that each period the firm hiresworkers up to the point where the marginal revenue from an additional employment equals thecost of that marginal worker, where the cost involves not only the wage and the hiring cost in thecurrent period, but also the discounted future savings from having to hire (1− δ) fewer workersin the following period. Solving equation (3.8) forward, one has the following expression for theaverage hiring cost,Gt = Et[ ∞∑k=0Λt,t+k (1− δ)k(MRPNjt+k − WjtPt+k)](3.9)38Freeman and Medoff (1982) highlight the substitution away from production workers towards other factors ofproduction in the presence of higher labour costs in unionized manufacturing.37For notational convenience in deriving the log-linearized version of equation (3.8) later on, I definethe net hiring cost as Bt ≡ Gt− (1− δ)Et (Λt,t+1Gt+1), such that equation (3.8) can be re-writtenasMRPNjt =WjtPt+Bt (3.10)I assume wages are negotiated and potentially adjusted every period through a Nash bargainingprocess between the intermediate goods firms and the households to split the total surplus generatedfrom an established employment relation. The surplus accruing to the firm j and the householdmembers who work at firm j are given by the following two equations respectively,SFjt = MRPNjt −WjtPt+ (1− δ)Et(Λt,t+1SFjt+1)(3.11)SHjt =WjtPt−MRSjt + (1− δ)Et(Λt,t+1SHjt+1)(3.12)where MRSjt =χCt1+ζ +ΨHP ItPtY IjtNjtis the household’s marginal rate of substitution between consump-tion and employment at firm j, or equivalently the marginal disutility of employment expressedin terms of the final goods bundle. The non-zero term ΨH ≡ ψ1+φ(1− (1+φ)WjtNjt(1+φ−ψ)PtCt)arises due tothe endogenous response of effort to changes in employment. It is interesting to note that profitmaximization by firms implies that the firm surplus SFjt equals the per worker hiring cost, Gt. Theaverage hiring cost can thus be interpreted as what the firm potentially saves from maintaining anexisting employment relation.Denoting the relative bargaining power of firms vis-a`-vis workers by the parameter ξ ∈ (0, 1),the Nash bargaining set-up solves the following problemmax{Wjt}(SFjt)ξ (SHjt)1−ξsubject to equations (3.11) and (3.12). The solution to the above bargaining problem impliesa constant share rule, ξSHjt = (1− ξ)SFjt, which translates to the equilibrium wage condition,WjtPt= ξMRSjt + (1− ξ)MRPNjt. Substituting for MRPNjt and MRSjt in the above wageequation, one can write the average Nash-bargained wage (upto a first order approximation) asWtPt= ξMRSt + (1− ξ)MRPNt (3.13)So far, I have assumed that firms can re-negotiate wages every period. However, this militatesagainst the empirical evidence of substantial nominal wage rigidities, e.g., the average frequencyof wage changes is often found to be more than one year. Incorporating Calvo-type nominal wagestickiness is quite straight-forward and does not alter the main intuition of the wage-setting processdiscussed here. In particular, I assume θw fraction of firms cannot re-optimize their nominal wagesin each period, thereby leading to the law of motion for average nominal wage, wt ≡∫ 10 wjtdjas wt = θwwt−1 + (1− θw)w∗t . In this set-up, the deviation between the actual average realwage (ωt ≡ wt − pt) and the average Nash-bargained wage under a counterfactual flexible wage38environment(ωtargett)drives the wage inflation in the economy.393.2.3 Monetary PolicyI assume a standard Taylor-type interest rate rule for the Central Bank,it = ρit−1 + (1− ρ) (φpipipt + φyyˆt) + φ∆y∆yˆt + νt (3.14)where it ≡ − lnQt is the nominal yield on a one-period riskless bond, ρ is the persistence inmonetary policy, yˆt is the logarithm of the period t output gap in the economy, and νt is theexogenous policy shifter. The monetary policy shock νt is assumed to follow an AR(1) process:νt = ρννt−1 + ενt , where the persistence parameter |ρν | < 1 and ενt is a white noise process withvariance σ2ν > 0. The degree to which the Central Bank accommodates exogenous shifts in produc-tivity partly determines the coefficient of the output gap in the Taylor rule. In particular, smallerthe parameter φy, the more accommodating is the monetary policy. Since I have already shownempirically that the response of hours and employment turned less countercyclical or sometimeseven procyclical after 1984, one can expect to see the parameter φy turning smaller in magnitude inthe later years. It should be noted that a countercyclical response of employment to a technologyshock is contingent on the monetary policy being not too accommodative.3.2.4 Equilibrium ConditionsI assume that hiring costs take the form of a bundle of final goods given by the same aggregationas the one defining the consumption index. This implies that the demand for each final good isgiven by Yit =(PitPt)−ε(Ct +GtHt). The goods market clearing condition is thus given byYt ≡(∫ 10Yε−1εit) εε−1= Ct +GtHt (3.15)The aggregate relation between final goods and intermediate input is given byXt ≡∫ 10Xitdj = Dpt Yt (3.16)where the chasm Dpt ≡∫ 10(PitPt)−εdi ≥ 1 between the quantities produced and consumed of thedifferent final goods arise due to the price dispersion caused by nominal rigidities. However, inthe neighbourhood of the zero-inflation steady state, Dpt ' 1, and hence the aggregate productionfunction can be approximated by the following condition,Yt = At(Eψt Nt)(1−α)(3.17)39For the system of log-linearized equations dictating the wage-setting process with nominal rigidity, refer toequations (B.11) through (B.13) in Appendix B.1.393.3 CalibrationHaving put in place a DSGE framework with endogenous effort choice and costly employmentadjustment, I now study the quantitative performance of that model.40 Specifically, I will calibratethe parameters of the model to reasonable values often estimated or assumed in the literature, andthen check whether structural changes in some of them between the pre and post-1984 periods cangenerate the empirically observed changes in the business cycle moments.A typical DSGE model, like the one presented above, contains a lot of parameters. For the easeof exposition, I discuss the calibration of the entire set of parameters in four groups: (i) parametersaffected by de-unionization, namely, the share of hiring cost in GDP, Θ and the wage bargainingpower, ξ; (ii) the accommodative stance of monetary policy, φy, which changed during the Volcker-era and had an impact on the economy’s response to technology shocks; (iii) parameters pertainingthe volatility of the exogenous shocks to technology and monetary policy, namely, σa and σν , whichdecreased during Great Moderation; and (iv) other parameters that I will consider to have remainedstationary over the period under study.3.3.1 Structural Changes due to De-unionizationA fall in hiring cost leading to a rise in the relative dependence on the extensive margin of labouradjustment is the key mechanism under study here. Denoting by Θ the steady-state share of totalhiring cost in real output, i.e., Θ ≡ G¯H¯Y¯, the main hypothesis can thus be captured by a decreasein Θ in the post-1984 period. I consider a fall in the share of the hiring cost in GDP from 3% inthe pre-1983 period to 1% in the post-1984 era. These magnitudes are in line with the estimatesof the hiring cost share by Silva and Toledo (2009) and used for calibration in Hagedorn andManovskii (2008). They estimate hiring cost to be roughly 4.5% of the average quarterly wage.Assuming average wage to be 67% of real output (which is nothing but the labour share in totalcompensation), the hiring cost as a share of GDP is calibrated to be 3% in the pre-1984 period.Now, union membership rate in private non-farm U.S. industries was about 21% in 1979 after whichtime it started falling sharply, and reached 1/3 of that value at roughly 7% by 2009. I, therefore,calibrate the hiring cost share in GDP in the post-1984 era as 1/3 of its pre-1984 value of 3%.41De-unionization not only affects the hiring cost of workers but also increases the bargainingpower of firms. Assuming equal bargaining power, i.e., ξ = 0.50, for calibration purposes, is thestandard in the literature. Felix and Hines Jr. (2009) find that workers in a fully unionized firmcapture roughly 54% of the benefits of lower state corporate income tax rates in the U.S., whichroughly indicates an equal bargaining power between workers and firms. Starting from an equal40For ease of exposition, I have collected in Appendix B.1 all the model equations with the variables being measuredin logarithms of deviations from their zero-inflation steady-state values.41Gal´ı and van Rens (2017) also consider a fall in the share of hiring cost from 3% to 1% of GDP, but theircalibration choice is motivated by the fall in the gross job separation rate. However, as argued in Appendix 2.4.2, thereduction in job separation rate appears to be an unlikely explanation for the fall in hiring costs when internationalevidence is taken into account. Moreover, data on quarterly job flows from Shimer (2012) show that job separationrate fell by only about 10% in the post-1984 era.40bargaining power between workers and firms in the pre-1983 period, I allow the parameter toincrease by 67% in the post-1984 period to 0.84, mirroring the fall in union density in the privatenonfarm business sector in the U.S.3.3.2 Monetary Policy ChangeTo capture the reduced response of hours on the impact of a technology shock in the post-1984period, it is crucial to allow for parameter φy, capturing the degree of accommodation of technologyshocks by the monetary policy, to fall in the post-1984 era. I use the values in Smets and Wouters(2007) who estimate the Taylor-rule parameters separately for two periods: 1966 through 1979,and 1984 through 2004, and find that φy decreased from 0.17 to 0.08 between the two periods.42As mentioned earlier, a more accommodative monetary policy counteracts the fall in productivitycorrelation with hours. In other words, the fall in productivity correlations would have been evenlarger had there been no structural change in the monetary policy.3.3.3 Exogenous Shocks: Changes during Great ModerationFor comparability to the literature, I will calibrate the persistences of the productivity and monetarypolicy shocks to values typically assumed in the literature. In particular, the persistence of thetechnology shock is assumed to be 0.90, following Gal´ı (2011), and that of the monetary shock isfixed at 0.50, following Gal´ı (2011) and Barnichon (2010). Accounting for the fall in volatility due toGreat Moderation, I calibrate the post-1984 standard deviation of the technology shock to be 70%of the pre-1983 value, and that of the monetary shock to be 50% of its corresponding pre-periodvalue. This choice of reductions of 30% and 50% in the standard deviations of the technology anddemand shocks is motivated by the findings in Barnichon (2010).43 Allowing for the shock variancesto change in a two-variable SVAR with labour productivity growth and unemployment, Barnichon(2010) finds these magnitudes of drops in the volatilities of technology and demand shocks aroundthe mid-1980s. The calibrated values for the volatilities in the two periods are reported in Table3.1.3.3.4 Stationary ParametersThe fourth set of parameters correspond to those which are quite standard in the literature andare arguably not likely to have changed significantly between the pre and post-1984 periods. Thecomplete list of these parameters and their calibrated values are presented in Table 3.2. Whilemost of the parameters are calibrated to some well-established estimates in the literature, the lastthree parameters in Table 3.2 are somewhat arbitrarily chosen because of lack of consensus in the42It should be noted that the positive response of productivity to an expansionary demand shock (i.e., a negativeTaylor-rule shock to the interest rate) is contingent on the monetary policy being not too accommodative. Thiscondition is maintained by the set of estimates in Smets and Wouters (2007).43As external evidence, in Appendix B.3 I show that the volatility of the monetary shock as measured by Romerand Romer (2004) empirically decreased by about 50%.41empirical literature — the curvature of the convex average hiring cost function (γ), the degree ofincreasing marginal disutility from higher effort (φ), and the additional curvature of effort in theproduction function (ψ). However, as a robustness check in Section 3.4.3, I show that assumingdifferent values for these three parameters do not significantly alter the main quantitative findingsfrom the model.The calibration of the production function parameters ψ and α needs attention. Supposeα = 0. Then the production function Yjt = AtEψjtNjt can be thought as a special case of astandard Cobb-Douglas production function with effective employment, E.N and capital K, Y˜jt ≡At (EjtNjt)ψK(1−ψ)jt , provided capital per worker,KjtNjtis held constant over the business cycle,since Y˜jt = Yjt(KjtNjt)1−ψ. This parameterization of the production function assumes short-runincreasing returns to effective labour, which is a standard feature of models trying to generateprocyclical movements of labour productivity in response to a demand shock.44 In this Cobb-Douglas representation, the parameter ψ has the natural interpretation of the labour share inaggregate production, and can, therefore, be calibrated to a value of 0.67. This route of calibrationhas been adopted in Barnichon (2010). However, the increasing returns to scale when α = 0 isinconsistent with the perfectly competitive nature of the intermediate goods firms considered here.As an alternative, one can interpret α as the share of non-labour inputs in the total factor cost ofproduction and can be calibrated to roughly 0.33.45 This leaves the calibration of ψ open withincertain limits — ψ cannot exceed 0.50 to avoid increasing returns to scale.3.4 Quantitative Performance of ModelHaving calibrated the model parameters separately for the pre and post-1984 sub-periods, I willnow examine how well the model can match the main phenomenon of vanishing procyclicality oflabour productivity, along with other changes in business cycle moments like the rising relativevolatility of employment, the falling procyclicality of real wages, etc.3.4.1 Business Cycle MomentsThere are multiple parameter changes in the calibration for the two sub-periods. It is thereforenatural to ask what role does each parameter change play in explaining the differences in thebusiness cycle moments. For that purpose, I will introduce the parameter changes in Table 3.1 oneat a time.44Gordon (1993) emphasizes the theoretical need for the presence of such increasing returns to labour for explainingbusiness cycle facts. Empirical works by Basu (1996), Basu, Fernald, and Kimball (2001) and others have confirmedincreasing returns to scale production functions, both for durable manufacturing and services industries.45The widely known empirically observed drop in the labour share of output or total compensation in the U.S.accelerated only from the early 2000s and therefore is not considered as a candidate for explaining the productivitypuzzle of the mid-1980s.42De-unionization. In Table 3.3, I first see how de-unionization alone performs in capturing thechanges in the moments. Column (1) reports the empirically observed changes in business cyclemoments between pre and post-1984 periods, while column (4) reports the total change explainedby de-unionization. However, since a fall in union density is captured by two parameter-changes,namely, a fall in the share of hiring cost in GDP, Θ and a rise in the firms’ bargaining power, ξ, I alsoshow the relative contribution of these two channels in the total effect of de-unionization in columns(2) and (3) respectively. Comparing columns (1) and (4) in Table 3.3 one can see that the parameterchanges attributed to de-unionization perform well in matching the empirically observed drop inproductivity correlations, both for unconditional correlations as well as conditional on technologyand demand shocks. For the relative volatility of employment, the baseline calibration of the modelcaptures more than 80% of the total rise in the data. Also, most of the changes in these momentscan be attributed to the change in the hiring cost parameter, which is the central mechanismdiscussed here.Finally, the cyclical properties of real wages have also changed in the U.S. around the sametime as the productivity puzzle and the Great Moderation. The model’s ability to capture thechanges in the cyclical wage correlations is primarily driven by the change in the bargaining powerparameter. This importance of the bargaining parameter in determining wage dynamics is notsurprising, given that the parameter directly enters the real wage equation (3.13). Regarding thevolatility of real wages, the current model predicts a fall in the post-1984 era. However, empiricalevidence on wage volatility has been mixed. Champagne, Kurmann, and Stewart (2017) discusshow average hourly wage volatility in the U.S. has diverged across different data sources: the LaborProductivity and Costs (LPC) program, the Current Population Survey (CPS), and the CurrentEmployment Statistics (CES). Supplements and irregular earnings of high-income workers, includedonly in the LPC, drive the rising volatility in LPC earnings as opposed to CPS and CES basedmeasures. One way to match the rising volatility of real wages (e.g., Champagne and Kurmann(2013) and Nucci and Riggi (2013)) in the current model would be to introduce real wage rigidityand let it decline in the post-1984 period.46 This can be done by introducing wage indexationto past inflation, or though endogenous real wage rigidity that depends on the size of the wagebargaining set in equilibrium. Lemieux, Macleod, and Parent (2009) discuss the rising importanceof performance wages in the U.S. economy, which can also help explain the rising wage volatility.These channels are however absent in the current version of the model and remain a task for futureresearch.Accommodative Monetary Policy. In Table 3.4, column (3) shows that more accommodativemonetary policy by the Federal Reserve cannot induce large changes in the productivity moments,46A real wage rigidity decline in the post-1984 period is not to be confused with increasing nominal wage rigidityduring the same period. Using Bayesian estimation, Smets and Wouters (2007) find nominal wage rigidity to havegone up after the mid-1980s, although the increase is not statistically significant. Under increasing nominal wagerigidity, firms cannot change wages as frequently as they want and need to rely on adjusting employment more. Thischannel of more employment adjustment further depresses the procyclicality of productivity and increases the relativeemployment volatility. This mechanism is highlighted in Gu and Prasad (2018).43and most of those changes go against the empirically observed direction of moment changes. Asargued in Section 2.3.2, allowing for a more accommodating monetary policy means that conditionalon a positive technology shock when the output gap increases, the contraction induced throughmonetary policy is less severe. This implies that with a lower φy, output and employment increasesmore in response to a given positive technology shock, thereby increasing the cyclical correlationof productivity with labour input. This corroborates the empirical finding in Section 2.3.2 thatthe negative impulse response of hours worked to a positive technology shock is somewhat mutedafter the mid-1980s. To summarize, in absence of the more accommodative stance of the FederalReserve under Volcker, the drop in productivity correlations would have been even more severe.Reduction in Shock Volatility. Column (4) of Table 3.4 shows that the model’s ability tomatch the changes in the business cycle moments is not contingent on the drop in volatilities ofthe exogenous shocks during Great Moderation. There are two aspects to this observation. First,a uniform reduction of volatilities of shocks per se cannot be expected to change the correlationbetween variables. In that sense, this finding is not surprising. However, in the calibration, thereduction in technology shock volatility was smaller than the fall in demand shock volatility. Thismechanically increases the importance of technology shock in the post-1984 period. Since technol-ogy shocks induce countercyclicality of productivity with labour input, this should explain part ofthe vanishing procyclicality of productivity. This mechanism was highlighted in Barnichon (2010).Nevertheless, one can see from column (4) that even this channel of non-uniformity in volatilityreduction could not explain any significant amount of the productivity puzzle.One of the main indicators that substantiated the role of increased flexibility in the labour mar-ket as the key driving factor behind the labour productivity puzzle was the drastic change in thecorrelations of productivity conditional on demand shocks. If it were merely the case of changingrelative importance of technology and demand shocks that explained the fall in the unconditionalproductivity correlations (as argued in Barnichon (2010)), then structural changes like the declineof hiring costs would not have been the significant channels for explaining the puzzle. The sub-stantial fall in the productivity correlations conditional on the monetary policy shock in the modelcorroborates that empirical finding.The finding that the fall in the productivity correlations conditional on a demand shock is drivingthe unconditional moments implies that demand shock should be the main source of variation foroutput and employment dynamics over the business cycle. This is empirically corroborated bythe dominance of non-technology shocks in explaining the total cyclical volatility of per capitahours in Figure 3.2. Since the only non-technology or demand shock in the model is the monetarypolicy shock, it is the dominant source of business cycle variation here. However, it should benoted that Smets and Wouters (2007) find that in the presence of a variety of demand shocks, e.g.,exogenous spending shock, risk premium shock, investment-specific technology shock, etc., the roleof monetary policy shock is quite limited in the cyclical variation of output. Thus, the predominantrole played by the monetary policy shock in this model should be thought as a consequence of the44loading of all variation due to various demand shocks onto a single monetary policy shock.3.4.2 Impulse Response FunctionsOne check for the quantitative validity of the model is to be able to generate impulse responsesthat are in line with the empirically observed ones. Figure 3.1 shows how the impulse response ofemployment rate to a positive technology shock (Panel (a)), and that of average labour productivityto a contractionary monetary policy shock (Panel (b)) have both become muted in the post-1984period. These changes in model-implied impulse responses are indeed qualitatively the same asthose observed empirically (discussed in Section 2.3.2).It is interesting to know what parameter changes in the model are driving the changes in theimpulse responses to shocks in the post-1984 period. While the muted negative response of em-ployment to technology shock is almost entirely driven by the fall in φy (which implies a moreaccommodative monetary policy in the post-1984 era), the reduced magnitude of the rise in pro-ductivity due to a contractionary monetary policy shock is caused by the fall in hiring cost Θ.These changes in impulse responses once again prove that the labour productivity puzzle cannotbe explained by the rise in the relative importance of technology shock (because the countercycli-cal property of technology shocks became muted post-1984), rather by structural changes in theeconomy that caused productivity to respond less to demand shocks over the business cycle.3.4.3 Robustness to Parameter CalibrationThe hiring cost function is taken to be quadratic in the baseline calibration of the model. However,there is no agreement in the literature as to the degree of convexity of the function. Mortensenand Nagypa´l (2007) find that in the presence of search frictions with linear vacancy posting costs,the matching function has an unemployment elasticity of 0.6. Interpreting employment adjustmentcosts as search frictions, a natural calibration for γ in the current model is therefore 0.6. On theother hand, Merz and Yashiv (2007) directly estimate the convexity of the average employmentadjustment cost and reports a value of 2.4. In Table 3.5, I show the robustness of the quantitativemodel predictions for different values of γ in this range.In the baseline calibration of the model, the degree of increasing marginal disutility from exertingmore effort, φ is taken to be 1 and the additional curvature of effort in the production function, ψis taken to be 0.5. Since there is no consensus in the literature regarding these values, in Tables3.6 and 3.7, I show the robustness of the model’s quantitative performance for alternative valuesof φ and ψ.Finally, the nominal rigidities in the baseline calibration has been assumed to have remainedconstant across the pre- and post-1984 periods. However, Smets and Wouters (2007) show thatthere has been a significant rise in the price rigidity for goods in the post-1984 period because ofthe reluctance of firms to change prices in an era of low inflation under the Great Moderation.Therefore, as a robustness check, I show in Table 3.8, that allowing for the price and nominal wage45rigidities to change between the two sub-periods according to the estimates in Smets and Wouters(2007) does not qualitatively alter the findings.3.5 Other Plausible Explanations: Lack of EvidenceHaving provided a coherent structural explanation for a host of changes that occurred in thecorrelation and volatility patterns of key economic variables around the mid-1980s in the U.S., Iwill now try to argue that some of the other plausible channels that have been explored in theliterature as potential explanations for the productivity puzzle do not hold up to closer empiricalscrutiny.3.5.1 Vanishing Countercyclicality of Labour QualityOne simple explanation for the increased countercyclicality of productivity could be that the firmsare selectively firing their least productive workers during recessions, and they are doing this moreintensely after the mid-1980s because of either a greater ability to measure individual workerproductivity (possibly due to the availability of better monitoring technology) or greater ease ofhiring and firing workers (possibly due to factors like de-unionization). Simply put, if firms firetheir least productive workers in recessions, the average productivity of the workers remaining inthe workforce automatically rises in bad times, driving the countercyclicality of productivity. Thischannel has been highlighted in Berger (2016). To ascertain whether this is indeed the case, Icompute the cyclical correlation of a measure of labour quality with business sector output. Themeasure of labour quality used is the Labour Quality Index constructed by Aaronson and Sullivan(2001) from 1979 onwards using CPS data on individual worker wage, sex, job experience andeducation, while the pre-1979 data is the annual BLS Multi-Factor Productivity estimate of labourcomposition interpolated by Fernald (2014) using the method outlined in Denton (1971). Plottingthe rolling window correlation of labour quality and output along the business cycle in Figure 3.4,I find that while it is true that labour quality rises in recessions (as manifested by the negativecyclical correlation of labour quality with output), there is no evidence that this phenomenon hasintensified in the post-1980s period (there is no discernible difference in the correlation before andafter the 1980s).47 This implies that the greater ease of hiring and firing workers did not translateinto a more selective firing of low-quality workers during recessions, rather more firing in generalof all workers (or the ‘average-quality representative’ worker).47Studying individual worker productivity from a large technology-based services company in the U.S. between 2006and 2010, Lazear, Shaw, and Stanton (2016) find that most of the increased productivity during the Great Recessionwas driven by an increased effort of the retained workers, and neither by the selective firing of least productive workersnor by hiring more productive new workers. Their finding corroborates the importance of the effort channel that ishighlighted in this thesis, as opposed to the labour quality channel.463.5.2 Rise of Service SectorThe rise of the service sector and the corresponding decline in the share of value-added and em-ployment for the manufacturing industries could have led to the fall in the labour productivitycorrelations.One possible channel is the so-called composition effect — if labour productivity in the servicesector is less correlated with output and hours (arguably due to more flexible work hours), then asimple compositional shift in the share of value-added or employment towards services can explainthe decline in the aggregate productivity correlations. However, the labour productivity correlationsin Table 3.9 clearly show that the two sectors had strikingly similar correlations even before themid-1980s, and both of them experienced a similar drop in labour productivity correlations overthe business cycle. Moreover, this compositional shift towards services has been too gradual (seePanels (a) and (b) of Figure 3.5) to explain the sudden drop in the productivity correlations. Thisrefutes the claim that a simple compositional shift towards a service economy was responsible forthe vanishing procyclicality of aggregate productivity.The second channel through which the rise of the service sector can contribute towards fallingaggregate productivity correlations is the substitution effect — if there is a larger share of servicesintermediate inputs in the economy then the labour productivity of all sectors will mimic that ofthe services sector.48 While there has indeed been an increase in the share of services intermediateinputs since the early 1980s (see Panel (c) of Figure 3.5), it is not the case that the manufacturingsector started to have similar productivity correlations as the service sector only after the increaseduse of services intermediate inputs. Moreover, looking at a cross-section of 31 U.S. industriesin Figure 3.6, I do not find any negative relationship between the rise in the share of servicesintermediate input usage and the change in the labour productivity correlations. Although allindustries, except agriculture, witnessed a rise in the share of services intermediate inputs in thepost-1984 period, this rise was not correlated with the industry-specific fall in the productivitycorrelations. All these pieces of evidence essentially refute both the composition effect and thesubstitution effect channels of the rise of the service sector as an explanation for the fall in labourproductivity correlations.3.5.3 Growing Share of Intangible InvestmentOne explanation that is provided in the literature for the drop in labour productivity correlations isthe mismeasurement of output (see McGrattan and Prescott (2012), henceforth MP). The argumentis that if a part of the output is not measured and if this omitted portion is more positively correlatedwith labour input than the measured part, then the measured labour productivity correlation canbe lower than the true one. MP argues that intangible capital is one such source of mismeasurementin output, and so the increased use of intangible capital in recent years can generate countercyclical48This idea of evolving input-output structure of the economy leading to switch in cyclicality of productivity canbe found in Huang, Liu, and Phaneuf (2004), who explain the switch in the cyclicality of real wages in the post-Warperiod.47labour productivity.For the argument to hold empirically, one needs intangible investment to rise markedly aroundthe mid-1980s. However, MP analyzes the U.S. business cycle only between 2004 and 2011. Never-theless, it is important to corroborate whether their explanation is supported by the data when thecorrect time-period is considered. Specifically, I want to check if the rise in intangible investmentacross U.S. industries around the mid-1980s is positively correlated with the magnitude of the fallin labour productivity correlations.McGrattan and Prescott (2012) defines intangible capital as the “...accumulated know-howfrom investing in research and development, brands, and organizations, which is for the most partexpensed by companies rather than capitalized.” Keeping this definition in mind, any empiricalmeasure of intangible investment is difficult to find, but the closest one can get in available data isto look at investment in intellectual property products (IPP).49 IPP contains research and devel-opment, computer software and databases, and other products like artistic originals.50 While IPPinvestment picked up in the late 1970s and early 1980s across almost all industries, I do not finda significant correlation between the rise in IPP capital share and the drop in labour productivitycorrelations in the cross-section (see Figure 3.7).3.5.4 Aggregate versus Sectoral ShocksAggregate productivity can be boosted through easier reallocation of factors of production acrossfirms and industries. There is a large literature discussing the inefficiency and lost productivitydue to factor misallocation (see, for example, Hsieh and Klenow (2009)). The basic intuition isthat when productive factors shift to firms or industries with higher marginal products of inputs,the overall economy generates more output with the same amount of inputs, even without anytechnological progress. Thus, if frictions impeding the efficient allocation of resources became lessimportant during economic downturns since the mid-1980s then measured productivity can becomeless procyclical. More flexible labour markets with lower frictions in hiring and firing (discussedabove in Section 2.3), and deeper financial markets aiding capital movement can contribute to suchcountercyclical reallocation of resources in the last three decades.In this context, Foster, Grim, and Haltiwanger (2016) find that downturns are indeed periodsof accelerated reallocation that is productivity-enhancing. However, they find that the intensity ofreallocation fell rather than rose for the Great Recession of 2007-08 and that the reallocation thatdid occur was less productivity-enhancing than in prior recessions. This casts doubt on the storyof productivity-enhancing sectoral reallocation during recessions for explaining the productivitypuzzle.49Advertisement spending is another type of intangible investment carried out by firms. Figure 3.8 shows thatthere has been no sudden increase in the share of advertising expenditure in total GDP of the U.S. economy aroundthe mid-1980s.50For a detailed discussion on the measure of IPP capital used, please refer to Appendix B.4. Wang (2014) considersinformation and communication technology (ICT) capital as the measure of intangible capital and finds no significantcorrelation across U.S. industries between the drop in the correlation of TFP with primary inputs and the rise inICT capital share.48Garin, Pries, and Sims (2018), however, differ from Foster, Grim, and Haltiwanger (2016).Using the finding in Foerster, Sarte, and Watson (2011) that sectoral reallocation shocks becamemore important for business cycles in the U.S. economy over the recent years, they claim that moreefficient reallocation in the post-1984 period has led to less procyclical productivity. Their claimhinges on separately identifying aggregate economy-wide shocks from sector-specific shocks51 andempirically finding that the volatility of aggregate shocks has shrunk drastically in the post-1984 era.They use monthly sectoral U.S. data from the Index of Industrial Production (IIP), which coversmostly the U.S. manufacturing sector only. I replicate the analysis using industry-level data fromvarious sources (like the BEA, the KLEMS, and the Current Employment Statistics (CES) data)that covers the entire U.S. economy. While there is considerable heterogeneity across datasetsin how much of the total variation in output and hours growth is explained by sectoral shocks,I find that, regardless of the dataset, the relative importance of sectoral shocks have increaseddramatically in the post-1984 period. However, this robustness is not maintained when the numberof industry classifications is large. For example, when the 31-industry classification from KLEMSdataset or the 20-industry classification from IIP data is considered, there is no clear pattern ofsectoral shocks becoming more important in the later decades.52Even if it is granted that reallocation of factors of production across different sectors of theeconomy has improved since the mid-1980s, it should be noted that sectoral measures of TFP andlabour productivity already take into account the intra-industry reallocation of resources. Since amajority of U.S. industries have individually experienced a decline in procyclicality of measuredproductivity (as shown in Chapter 2), intra-industry reallocation across firms has likely been moreimportant than inter-industry reallocation.53 Therefore, while there is certainly a predominanceof industry-specific shocks in the last three decades, there is reason to doubt that inter-industryreallocations have an important role to play in explaining the drop in aggregate productivity cor-relations.In this context, it is also important to note that sectoral labour reallocation is also oftencited as one of the major reasons for jobless recoveries after the last two recessions. This argumenttypically draws from the evidence in Groshen and Potter (2003) who argue that increased permanentrelocation of workers from some industries to others have stalled growth in jobs. Since joblessrecoveries tend to exacerbate the negative correlation between productivity and hours (althoughthey increase the correlation between productivity and output), it is important to consider thischannel of sectoral reallocation. However, Aaronson, Rissman, and Sullivan (2004) show thatGroshen and Potter’s findings are very sensitive to the exact period over which the measure ofreallocation is computed, the dating of business cycle turning points, and the weighting of theindustries. Using an alternative measure of sectoral reallocation developed by Rissman (1997) they51Aggregate shock is identified as the first principal component in the data on the sectoral growth rate of outputor employment. Refer to Appendix B.5 for details on the identification strategy.52See Appendix B.5 for details of analysis showing the relative importance of sector-specific shocks in the U.S.economy.53Wang (2014) also finds that individual industries have experienced a drop in procyclicality of procyclicality,whereas Molnarova (2020) opposes this claim.49show that reallocation of employment across industries has declined, not increased, over the pasttwo business cycles.To summarize, the evidence for increased inter-sectoral labour reallocation as an important ex-planation for either the vanishing procyclicality of labour productivity or jobless recoveries appearsto be less than convincing.3.6 ConclusionThis chapter shows that a standard New Keynesian model with endogenous effort choice in the faceof costly hiring of workers can not only generate the empirically observed changes in the businesscycle moments of output, employment and productivity with only a drop in hiring cost but alsoqualitatively match the changes in the impulse responses of these variables to technology anddemand shocks. It also points out the absence of empirical evidence for plausible explanations ofthe productivity puzzle. In particular, it shows that neither the rise of the service sector in terms ofvalue-added nor its use as intermediate input can explain the phenomenon. Moreover, the increaseduse of intangible capital, and the reduced variation of aggregate economy-wide shocks relative tosector-specific shocks that facilitate factor reallocation to more productive sectors during recessions,do not seem to have empirical validity as possible explanations for the productivity puzzle.Important policy implications like using a more accommodative monetary policy to generatemore jobs during recovery booms follow immediately from the quantitative analyses presented inthis chapter. Such a policy will also help in making productivity more procyclical again. However,there are potential downsides of too much accommodation of positive technology shocks by the mon-etary authority as it may lose its power to fight recessions by lowering interest rates further duringeconomic downturns. Therefore, there is a debate regarding whether maintaining countercyclicalproductivity, in the long run, is welfare-improving or not. Other immediate policy prescriptionslike short term work (STW) policies that encourage labour hoarding by firms during recessions canalso be envisaged. Giupponi and Landais (2018) show that such STW polices in Italy stabilizedemployment and brought small positive welfare gains during the Great Recession. Graves (2019)shows that in the United States firing taxes are more effective than hiring subsidies in stabilizingemployment along the business cycle. Further research is required to shed light on these welfareimplications of the productivity puzzle.503.7 TablesTable 3.1: Differences in Calibration between Pre- and Post-1984Parameter Meaning Pre-1984 Post-1984De-unionizationΘ Share of hiring cost in GDP 3% 1%ξ Wage Bargaining Power of Firms 0.50 0.84Monetary Policyφy Response to output gap 0.17 0.08Shocksσa Technology shock volatility 1.00 0.70σν Monetary shock volatility 0.53 0.27Table 3.2: Calibration of Time-Invariant ParametersParameter Value Calibrationβ 0.99 Real risk-free annual interest rate ' 3%ε 10.0 Mark-up over marginal cost ' 11%α 0.33 Share of non-labour input in total compensationθp 0.75 Calvo nominal rigidity; Gal´ı (2011)θw 0.75 Nominal wage rigidity; Gal´ı (2011)δ 0.10 Quarterly gross job separation rate; Shimer (2012)φpi 1.70 Taylor rule response to inflation; Smets and Wouters (2007)φ∆y 0.20 Taylor rule response to output gap growth; Smets and Wouters (2007)ρ 0.80 Persistence in monetary policy; Smets and Wouters (2007)ρa 0.90 Persistence of technology shock; Gal´ı (2011)ρν 0.50 Persistence of monetary policy shock; Gal´ı (2011), Barnichon (2010)γ 1.00 Quadratic hiring costφ 1.00 Increasing marginal disutility from effortψ 0.50 Additional curvature of effort in production function51Table 3.3: Changes in Business Cycle Moments due to De-unionizationChanges in Moments between Pre- & Post-1984 PeriodsBusiness Cycle Moments ModelData Hiring Cost: Θ Bargaining Power: ξ De-unionization: Θ, ξ(1) (2) (3) (4)Labour Productivity CorrelationsOutput: Corr (yt, lpt) -0.40 -0.54 -0.08 -0.58Employment: Corr (nt, lpt) -0.51 -0.35 -0.07 -0.38Hiring Flows: Corr (ht, lpt) -0.53 -0.48 -0.04 -0.50Relative Volatility of EmploymentOutput: s.d. (nt) /s.d. (yt) +46% +35% +6% +38%Conditional Corr (nt, lpt)Technology Shock -0.06 -0.06 -0.03 -0.07Demand Shock -1.24 -0.58 -0.10 -0.59Conditional Corr (yt, lpt)Technology Shock +0.19 -0.08 -0.01 -0.09Demand Shock -1.21 -0.89 -0.11 -0.91Real Wage CorrelationsOutput: Corr (yt, wt) -0.34 -0.06 -0.72 -0.41Employment: Corr (nt, wt) -0.34 -0.11 -0.77 -0.50Labour Productivity: Corr (lpt, wt) -0.10 -0.12 +0.13 +0.12Note: To maintain comparability with the existing literature, all moments have been calculated on quarterlyHodrick and Prescott (1997) filtered variables for both data and model-simulated series. Column (1) reports theempirically observed changes in the business cycle moments between the pre- and post-1984 periods. Column (2)reports the changes in the model-implied moments when only the hiring cost parameter Θ is allowed to drop from3% to 1%. Similarly, column (3) allows only the wage bargaining power parameter ξ to increase from 0.50 to 0.84.Column (4) combines the two parameter changes in columns (2) and (3).52Table 3.4: Changes in Business Cycle Moments between Pre- and Post-1984Changes in Moments between Pre- & Post-1984 PeriodsBusiness Cycle Moments ModelData De-unionization Monetary Policy: φy Shocks: σa,σν(1) (2) (3) (4)Labour Productivity CorrelationsOutput: Corr (yt, lpt) -0.40 -0.58 -0.01 +0.09Employment: Corr (nt, lpt) -0.51 -0.38 +0.03 -0.04Hiring Flows: Corr (ht, lpt) -0.53 -0.50 +0.05 -0.10Relative Volatility of EmploymentOutput: s.d. (nt) /s.d. (yt) +46% +38% -1% -2%Conditional Corr (nt, lpt)Technology Shock -0.06 -0.07 +0.05 0.00Demand Shock -1.24 -0.59 -0.01 0.00Conditional Corr (yt, lpt)Technology Shock +0.19 -0.09 +0.04 0.00Demand Shock -1.21 -0.91 -0.01 0.00Real Wage CorrelationsOutput: Corr (yt, wt) -0.34 -0.41 +0.02 -0.00Employment: Corr (nt, wt) -0.34 -0.50 +0.09 -0.16Labour Productivity: Corr (lpt, wt) -0.10 +0.12 -0.08 +0.15Note: To maintain comparability with the existing literature, all moments have been calculated on quarterlyHodrick-Prescott-filtered variables for both data and model-simulated series. Column (2) refers to the totaleffect of de-unionization by allowing the parameters Θ and ξ to change, same as column (4) in Table 3.3.Column (3) allows only the Taylor rule parameter φy to drop from 0.17 to 0.08. Similarly, column (4)corresponds to the changes in model-implied moments when only the volatilities of the shocks are allowed todecrease in the post-1984 period according to the calibration in Table 3.1.53Table 3.5: Robustness to Choice of γBusiness Cycle Moments Changes in Model Momentsγ = 0.6 Baseline, γ = 1 γ = 2.4(1) (2) (3)Labour Productivity CorrelationsOutput: Corr (yt, lpt) -0.44 -0.58 -0.64Employment: Corr (nt, lpt) -0.27 -0.38 -0.49Hiring Flows: Corr (ht, lpt) -0.44 -0.50 -0.45Relative Volatility of EmploymentOutput: s.d. (nt) /s.d. (yt) +28% +38% +66%Conditional Corr (nt, lpt)Technology Shock -0.07 -0.07 -0.05Demand Shock -0.37 -0.59 -0.74Conditional Corr (yt, lpt)Technology Shock -0.07 -0.09 -0.08Demand Shock -0.63 -0.91 -0.97Real Wage CorrelationsOutput: Corr (yt, wt) -0.29 -0.41 -0.65Employment: Corr (nt, wt) -0.37 -0.50 -0.76Labour Productivity: Corr (lpt, wt) +0.12 +0.12 +0.07Note: Columns (1) through (3) report changes in business cycle moments betweenpre- and post-1984 periods for alternative values of parameter, γ, denoting thedegree of convexity of the hiring cost function. All other parameters in the modelare fixed at the calibration values used in column (4) of Table 3.3, which correspondsto the total effect of de-unionization. To maintain comparability with the existingliterature, all moments have been calculated on quarterly Hodrick-Prescott-filteredvariables.54Table 3.6: Robustness to Choice of φBusiness Cycle Moments Changes in Model Momentsφ = 0.5 Baseline, φ = 1 φ = 1.5(1) (2) (3)Labour Productivity CorrelationsOutput: Corr (yt, lpt) -0.62 -0.58 -0.54Employment: Corr (nt, lpt) -0.42 -0.38 -0.35Hiring Flows: Corr (ht, lpt) -0.52 -0.50 -0.48Relative Volatility of EmploymentOutput: s.d. (nt) /s.d. (yt) +43% +38% +34%Conditional Corr (nt, lpt)Technology Shock -0.06 -0.07 -0.07Demand Shock -0.65 -0.59 -0.54Conditional Corr (yt, lpt)Technology Shock -0.09 -0.09 -0.09Demand Shock -0.97 -0.91 -0.85Real Wage CorrelationsOutput: Corr (yt, wt) -0.38 -0.41 -0.42Employment: Corr (nt, wt) -0.48 -0.50 -0.50Labour Productivity: Corr (lpt, wt) +0.08 +0.12 +0.15Note: Columns (1) through (3) report changes in business cycle moments betweenpre- and post-1984 periods for alternative values of parameter, φ, denoting the degreeof increasing marginal disutility from exerting more effort. All other parameters inthe model are fixed at the calibration values used in column (4) of Table 3.3, whichcorresponds to the total effect of de-unionization. To maintain comparability withthe existing literature, all moments have been calculated on quarterly Hodrick-Prescott-filtered variables.55Table 3.7: Robustness to Choice of ψBusiness Cycle Moments Changes in Model Momentsψ = 0.10 ψ = 0.25 Baseline, ψ = 0.50(1) (2) (3)Labour Productivity CorrelationsOutput: Corr (yt, lpt) -0.30 -0.46 -0.58Employment: Corr (nt, lpt) -0.19 -0.29 -0.38Hiring Flows: Corr (ht, lpt) -0.29 -0.43 -0.50Relative Volatility of EmploymentOutput: s.d. (nt) /s.d. (yt) +19% +28% +38%Conditional Corr (nt, lpt)Technology Shock -0.11 -0.08 -0.07Demand Shock -0.20 -0.43 -0.59Conditional Corr (yt, lpt)Technology Shock -0.02 -0.08 -0.09Demand Shock -0.33 -0.69 -0.91Real Wage CorrelationsOutput: Corr (yt, wt) -0.44 -0.43 -0.41Employment: Corr (nt, wt) -0.53 -0.51 -0.50Labour Productivity: Corr (lpt, wt) +0.27 +0.19 +0.12Note: Columns (1) through (3) report changes in business cycle moments between pre-and post-1984 periods for alternative values of parameter, ψ, denoting the additionalcurvature for effort in the production function. Given α = 0.33 in the baseline calibra-tion, ψ ∈ (0, 0.50] to ensure non-increasing returns to scale under perfect competitionamong intermediate goods firms. All other parameters in the model are fixed at the cal-ibration values used in column (4) of Table 3.3, which corresponds to the total effect ofde-unionization. To maintain comparability with the existing literature, all moments havebeen calculated on quarterly Hodrick-Prescott-filtered variables.56Table 3.8: Robustness to Changes in Nominal RigiditiesChanges in Moments due to De-unionizationBusiness Cycle Moments ModelData No change in rigidity Changes in θp & θw(1) (2) (3)Labour Productivity CorrelationsOutput: Corr (yt, lpt) -0.40 -0.58 -0.87Employment: Corr (nt, lpt) -0.51 -0.38 -0.43Hiring Flows: Corr (ht, lpt) -0.53 -0.50 -0.33Relative Volatility of EmploymentOutput: s.d. (nt) /s.d. (yt) +46% +38% +73%Conditional Corr (nt, lpt)Technology Shock -0.06 -0.07 -0.11Demand Shock -1.24 -0.59 -0.55Conditional Corr (yt, lpt)Technology Shock +0.19 -0.09 -0.17Demand Shock -1.21 -0.91 -0.90Real Wage CorrelationsOutput: Corr (yt, wt) -0.34 -0.41 -0.20Employment: Corr (nt, wt) -0.34 -0.50 -0.20Labour Productivity: Corr (lpt, wt) -0.10 +0.12 -0.24Note: Column (2) corresponds to θp = θw = 0.75 for both periods as in the baseline calibration. Column (3)corresponds to changing θp from 0.55 to 0.73, and θw from 0.65 to 0.74 between the pre- and post-1984 periods,along with the changes in Θ and ξ like in column (4) of Table 3.3.Table 3.9: Labour Productivity Correlations in Manufacturing & ServicesWith Output With HoursSector Pre-1983 Post-1984 Change Pre-1983 Post-1984 ChangeManufacturing 0.63 0.40 -0.23 -0.04 -0.30 -0.26Services 0.68 0.48 -0.20 -0.10 -0.59 -0.49Note: Data is sourced from annual KLEMS dataset between 1947 and 2010 by aggregatingindustry-level non-additive chained indices according to the cyclical expansion method developedin Cassing (1996). Results are robust to using annual sectoral dataset from BEA, compiled byHerrendorf, Herrington, and Valentinyi (2015).573.8 Figures-.6-.4-.20Impulse Response of Employment to Positive Technology Shock0 5 10 15 20Periods(a) Technology Shock: Employment-.50.5Impulse Response of Productivity to Expansionary Demand Shock0 5 10 15 20Periods(b) Demand Shock: Labour ProductivityFigure 3.1: Model-implied Impulse Responses to Technology and Demand ShocksNote: Model-generated Impluse Response Functions (IRF) for the pre-1984 period are in blue, and the post-1984IRF’s are in red dashed lines. Pre- and post-1984 calibrations of parameters correspond to all parameter changeslisted in Table 3.1.1960 1970 1980 1990 2000 20100.30.40.50.60.70.80.91(a) Labour Productivity1960 1970 1980 1990 2000 20100.30.40.50.60.70.80.9(b) Total Factor ProductivityFigure 3.2: Conditional Volatility of HoursNote: Time-varying standard deviations of per capita hours, conditional on technology shock (blue dashed line) anddemand shock (red dotted line). Measures of productivity are different in the two panels. Panels (a) and (b) usegrowth rates of labour productivity and TFP respectively, along with per capita hours as the two variables in theSVAR.581960 1970 1980 1990 2000 20100.30.40.50.60.70.8(a) Labour Productivity1960 1970 1980 1990 2000 20100.30.40.50.60.70.8(b) Total Factor ProductivityFigure 3.3: Conditional Volatility of ProductivityNote: Time-varying standard deviations of productivity, conditional on technology shock (blue dashed line) anddemand shock (red dotted line). Measures of productivity are different in the two panels. Panels (a) and (b) usegrowth rates of labour productivity and TFP respectively, along with per capita hours as the two variables in theSVAR.-1-.50.5Corr (Labour Quality Index, Output)1955 1965 1975 1985 1995 2005 2015YearFigure 3.4: Correlation of Labour Quality Index with OutputNote: Labour Quality Index is sourced from Fernald (2014). From 1979 onwards it is the one constructed byAaronson and Sullivan (2001). Pre-1979 data is interpolated annual BLS Multi Factor Productivity estimate oflabour composition using method in Denton (1971).59.72.74.76.78.8.82Share of Services Value Added1945 1955 1965 1975 1985 1995 2005Year(a) Output Share.6.65.7.75.8.85Share of Services in Total Hours Worked1945 1955 1965 1975 1985 1995 2005Year(b) Hours Share.4.5.6.7Share of Services Intermediate Inputs1945 1955 1965 1975 1985 1995 2005 2015Year(c) Intermediate Inputs ShareFigure 3.5: Share of Services in the U.S. (1947-2016)Note: Data for Panels (a) and (b) is sourced from KLEMS annual dataset. Data for Panel (c) is sourced from theannual input-output matrices published by BEA.ConstructionPost & Telecom.Financial IntermediationElectrical & Optical Equip.WoodMining & QuarryingMotor VehiclesSocial & Personal ServicesRenting of machine & equip.Transport & StorageRetail TradeCoke, Petroleum & Refined FuelRubber & PlasticsChemicalsPulp, Paper & PrintingHotels & RestaurantsPublic Admin. & DefenceHealthcareTextile & LeatherTransportUtilitiesMachineryRecyclingReal EstateFood, Beverages, TobaccoEducationNon-metallic MineralWholesale TradeBasic & Fabricated MetalAgricultureR-squared = 0.01Slope = 0.38 [0.59]-1-.50.51Change in Labour Productivity Correlation with Hours0 .1 .2 .3 .4% Change in Share of Services Intermediate InputsFigure 3.6: Changes in Share of Services Intermediate Input & Labour Productivity CorrelationNote: Data for labour productivity correlations and share of services intermediate inputs at the industry-level issourced from the annual KLEMS dataset. Time-changes refer to the difference between the average values in thepost-1984 (1984-2010) and the pre-1984 period (1969-1983). Regression is weighted by the time-average of totalhours worked in each industry, depicted by the size of the bubbles. The p-value of the estimated slope is reported inparentheses. The Baxter and King (1999) bandpass filter between 2 and 8 years has been used to extract the cyclicalcomponent of the variables. Result is robust to using other filters and time-horizons.60ConstructionUtilitiesRecycling ManufacturingMachineryPost & TelecommunicationFood, Beverages, TobaccoHealthcare & Social WorkEducationTextilesTransport EquipmentFinance, Insurance & Real EstateWood, Paper & PrintingChemicalsBasic & Fabricated MetalsRubber, Plastic, MineralsMiningTransport & Storage Retail TradeAgricultureHotels & RestaurantsWholesale TradeElec. Eqpmnt.FuelsCommunity, Personal Services & Pvt. HHsR-squared = 0.02Slope = -0.11 [0.64]-1-.50.51Change in Labour Productivity Correlation with Hours0 .5 1 1.5 2% Change in Share of IPP in Total Capital StockFigure 3.7: Changes in Share of IPP in Total Capital Stock & Labour Productivity CorrelationNote: Data for labour productivity correlations at the industry-level is sourced from the annual KLEMS dataset,and that for the IPP capital share is sourced from BEA. Industry codes from the two datasets were matched tocreate a consistent set of 24 U.S. industries. Time-changes refer to the difference between the average values in thepost-1984 (1984-2010) and the pre-1984 period (1969-1983). Regression is weighted by the time-average of industryemployment, depicted by the size of the bubbles. The p-value of the estimated slope is reported in parentheses. TheBaxter and King (1999) bandpass filter between 2 and 8 years has been used to extract the cyclical component ofthe variables. Result is robust to using other filters and time-horizons.11.522.53Total Advertisement Spending (% of GDP)1920 1940 1960 1980 2000YearFigure 3.8: Total Advertisement Spending as a Share of GDP in the U.S. (1919-2007)Note: Data on advertisement spending is maintained by Douglas A. Galbi at www.galbithink.org/ad-spending.htm61Chapter 4Consumption and Income Inequalityacross Generations4.1 IntroductionHow do parents impact the economic outcomes of their offspring? The current chapter tries to pro-vide a comprehensive understanding of the diverse channels of parental influence, namely, throughlabour earnings, other sources of income such as inter-vivos and bequest transfers and spousal in-come, and through consumption. It also quantifies how much of the observed economic inequalityin a particular generation is attributable to intra-family inter-generational linkages.We argue that since the various channels of transmission of parental characteristics are inter-linked (e.g., spending on a child’s education may be a substitute for income transfers in adulthood,etc.), it is important to consider the joint evolution of these different income sources and con-sumption expenditure. Crucially, this joint estimation strategy involving a system of momentconditions not only enables simultaneous estimation of cross-sectional inequality parameters andinter-generational persistence parameters but also allows for potentially non-trivial covariancesamong income sources and consumption. We find that intergenerational persistence is highest forlifetime earnings, with an elasticity around 0.23. In contrast, the inter-generational elasticity forother income is only 0.10 and mostly reflects persistence in spousal earnings. That is, men tend tomarry women who have similar economic outcomes as their mothers (as in Fernandez, Fogli, andOlivetti (2004)). Interestingly, other income has little effect on children’s earnings with an elastic-ity of 0.06 but we find evidence that higher parental earnings are associated with higher unearnedincome among kids, with a cross-elasticity of 0.21 in the baseline specification. Restricting these lat-ter cross-elasticities to zero leads to under-estimates of the importance of parents for consumptioninequality. We estimate a significant direct consumption pass-through, albeit a little weaker thanthe pass-through of earnings. Of course, consumption persistence operates also indirectly throughincome channels. Finally, we also find that persistence in observable characteristics accounts formost of the intergenerational pass-through. Taken together, our estimates of the intergenerationalpass-through are consistent with the view that persistence is largely driven by associations in life-time earnings of both spouses as well as tastes and preferences in consumption, with educationalattainment playing a crucial role.5454See Landersø and Heckman (2017) for evidence on the importance of education for intergenerational persistence.For a discussion of causal effects of parental education and income see, among others, Carneiro and Heckman (2003);Oreopoulos, Page, and Stevens (2006); Belley and Lochner (2007); Black and Devereux (2011); Holmlund, Lindahl,62The central question that we address in the debate on the role of family background for life-cycleoutcomes is whether observed within-generation inequality would be much different if heterogeneityamong parents were removed. Our model delivers a transparent setting to perform inequalityaccounting exercises and quantify the contribution of parental factors. These exercises consistentlyindicate that idiosyncratic heterogeneity over the life cycle, rather than family background, accountsfor the bulk of cross-sectional dispersion in earnings, income and expenditure. The largest impactof parental factors is on consumption inequality, as our baseline estimates imply that roughlyone-third of within-generation consumption inequality can be attributed to family characteristics.Further examination shows that the relatively larger role of family heterogeneity on consumptionfollows from the interaction of (i) cross-sectional insurance reducing the impact of idiosyncraticincome risk on expenditures, and (ii) the direct and indirect parental influences that are reflectedin consumption choices, notably the intergenerational transmission of saving propensities (highersavings rates for richer families) and marital sorting.We show that the historical evolution of consumption and earnings inequality is consistentwith stable intergenerational pass-through coefficients. This result helps reconcile the somewhatpuzzling observation of fairly stable intergenerational persistence (Hertz, 2007; Lee and Solon, 2009)in the face of growing inequality (Heathcote, Perri, and Violante, 2010; Attanasio and Pistaferri,2016). Our estimates show that growing parental disparities would not, all else equal, be sufficientto trigger significantly higher future inequality in the absence of much stronger inter-generationalelasticities.55The rest of the chapter is organized as follows. Section 4.2 outlines our benchmark consumptionmodel with intergenerational linkages. Section 4.3 discusses the identification of model parameters,outlines the estimation approach and describes the data from the Panel Study of Income Dynamics(PSID) that is used for estimation. Baseline estimates are discussed in Section 4.4, where we alsoreport the results of the counterfactual analysis of cross-sectional inequality. In Section 4.5 weexplore the implications of our estimates for the evolution of cross-sectional inequality. Section4.6 presents various robustness checks, including alternative approaches to the measurement ofconsumption expenditures and different model specifications. Section 4.7 concludes.4.2 A Model of Intergenerational InequalityWe develop an estimable consumption model of heterogeneous and intergenerationally linked house-holds. The model features multiple parent-child linkages and is designed to examine the jointbehaviour of earnings, other income and expenditures.To motivate these linkages, we begin by establishing stylized facts about the evolution of intra-family persistence in the U.S. over recent decades. In Appendix C.3.1 we report reduced-formand Plug (2011); Lefgren, Sims, and Lindquist (2012); Lee, Roys, and Seshadri (2014). Carneiro, Lopez Garcia,Salvanes, and Tominey (2015) show that the timing of parental income affects children education outcomes with theadvantage of having income occur in late adolescence rather than early childhood.55See Cordoba, Liu, and Ripoll (2016) for a dynastic model of long-run inequality and social mobility with endoge-nous fertility.63estimates of the intergenerational pass-through of earnings and consumption since 1990, obtainedusing the method popularized by Lee and Solon (2009) in their analysis of the gender-specificevolution of earnings persistence. Like those authors, we find little or no evidence of changes inthe intergenerational elasticity of labour earnings, with similar patterns holding for expenditures.56To corroborate this evidence, we also compute mobility matrices and intergenerational flows acrossquartiles of the distributions of earnings and expenditures.57 This analysis, shown in AppendixC.3.2, emphasizes that persistence is more intense at the tails of the distribution and that theinter-generational pass-through was remarkably stable over the past decades. These findings areconsistent with the evidence in Chetty, Hendren, Kline, Saez, and Turner (2014), who examine largeadministrative U.S. earning records and conclude that measures of “...intergenerational mobilityhave remained extremely stable for the 1971-1993 birth cohorts”. For these reasons, we maintainthe assumption of stationarity in the baseline analysis. However, among the robustness checksof Section 4.6, we explore potential cross-cohort differences in the cross-generation pass-throughparameters and the variances of the idiosyncratic risk processes.The building blocks of our analysis are the time series processes for earned and other incomeof parents and children, and a mechanism mapping them into distributions of family outcomes.Each household optimally chooses per-period consumption expenditures to maximize discountedexpected utility subject to a budget constraint.58 Households receive income from labour earningsof the head (the husband for couples in the PSID), as well as from ‘other income’ that includestransfer income and earnings of the spouse. Households also accrue income from asset returns, whichimplicitly depend on their consumption and saving decisions. We allow for each of labour earningsand other income to be individually linked across generations. Moreover, we let the income fromasset returns be part of a residual consumption shifter that can also be linked across generations.59While consumption is modelled as an optimal state-dependent choice, due to insufficient data wedo not impose the adding up required to satisfy a lifetime budget constraint. This would requiremore frequent and accurate data on the full set of expenditures, flows of asset income, inter-vivostransfers and bequests.Earnings and Other Income. We denote a time-period (a year) by t. Parent and child areidentified by superscripts p and k. A parent-child pair is denoted by the family subscript f . Head’searnings, other income and consumption expenditures (all logged) are denoted by e, n and c,respectively.Our baseline specification of the parents’ earning process has a canonical permanent-transitoryform. Specifically, it features a permanent individual fixed effect and an additive transitory shock56This is despite growing income and consumption inequality over this period (e.g. Aguiar and Bils, 2015).57Mobility matrices deliver the conditional probability of a child being placed in a certain quartile of the distributiongiven the quartile of his/her family.58This differs from approaches in which consumption expenditures were modelled as a stand-alone exogenousprocess.59The PSID does not report consistent wealth information before 1998. Therefore, we subsume unobserved incomefrom wealth within the residual consumption shifter terms.64component. The fixed effect measures lifetime average earnings and should not be thought of aspre-determined at the start of an individual’s life. Rather, as shocks accrue over the working life,earnings in any period can exceed, or fall below, the lifetime average. Hence, we use the fixed effectrepresentation as a way of summarising the lifetime resources available to a particular generation.In Section 4.6.3 we also consider robustness to an alternative model specification that focuses ongrowth rates. The latter allows for period-specific permanent innovations that are correlated acrossgenerations. We find no evidence in support of this alternative specification of parent-child linkages.In any year t the parent in family f has earnings epf,t equal to the sum of an individual fixed effectcomponent, e¯pf , and an independent mean zero transitory shock, ζpf,t, with variance σ2ζp . Similarly,the process for other income, npf,t, comprises a permanent component, n¯pf , and a transitory meanzero component, upf,t, with variance σ2up .epf,t = e¯pf + ζpf,t (4.1)npf,t = n¯pf + upf,t. (4.2)The income processes of children are also assumed to have a canonical permanent-transitorystructure; that is, ekf,t = e¯kf + ζkf,t and nkf,t = n¯kf +ukf,t (where ζkf,t and ukf,t are mean zero i.i.d. inno-vations with variances σ2ζkand σ2ukrespectively). Fixed effects are partly determined by parentalpermanent components but also depend on idiosyncratic random variables that are independent ofparents. For the children of family f this structure results in the following income components:ekf,t = γe¯pf + θn¯pf + δkf︸ ︷︷ ︸e¯kf+ζkf,t (4.3)nkf,t = ρn¯pf + λe¯pf + εkf︸ ︷︷ ︸n¯kf+ukf,t (4.4)where εkf and δkf are idiosyncratic permanent shocks with variances σ2εkand σ2δk, respectively.We allow for the most general dependence structure across generations: not only is there adirect channel from parental earnings to child earnings, and a direct channel from other income ofparents to other income of children, but there are also cross effects. Parental earnings can affectother income of children, and parental other income can affect earnings of children; that is, higherparental lifetime earnings can influence child earnings through the persistence parameter γ, butcan also change a child’s other income as captured by the parameter λ.Consumption. With the income processes in place, we solve the dynamic life-cycle problem thatdelivers consumption choices. When a household makes consumption decisions, it has knowledgeof its own permanent income, but does not know the value of future income shocks. Our approach65does not specify an altruistic motive and is agnostic about it.60 The consumption problem of amember of family f is given by:max{Cf,k}Tk=tEtT−t∑j=0βju(Cf,t+j)s.t. (4.5)Af,t+1 = (1 + r) (Af,t + Ef,t +Nf,t − Cf,t) ,where β is the discount factor, r is the real interest rate, Af,t is assets at the start of the period,Ef,t is the value of the household head’s labour earnings, and Nf,t is the value of other income.61Consumption at time t is the annuity value of lifetime resources. The approximate log-consumptionprocess62 for a parent can be represented as,cpf,t = qpf,t + e¯pf + n¯pf + α (r)(upf,t + ζpf,t).The term α (r) is an annuitization factor which tends to r/(1 + r) as the time horizon becomeslarger. The variable qpf,t denotes an idiosyncratic consumption shifter, subsuming unobserved in-come from savings as well as possible heterogeneity in preferences over the timing of consumption.Like other shifters of consumption, qpf,t comprises both a permanent and a transitory component sothat qpf,t = q¯pf + vpf,t. Combining these processes, the log-consumption of the parent can be writtenas:cpf,t = q¯pf + e¯pf + n¯pf + vpf,t + α(r)(upf,t + ζpf,t)(4.6)and analogously for the child. Parents affect the consumption of their children through familypersistence in both earnings and other income, as described in (4.3) and (4.4). In addition, weallow for a direct transmission channel through the consumption shifter q¯kf , which comprises aninherited component and a child-specific component: q¯kf = φq¯pf + ψkf . Substituting the intra-familytransmission mechanisms into the log-consumption process, we obtain:ckf,t = φq¯pf + (γ + λ) e¯pf + (ρ+ θ) n¯pf+ εkf + ψkf + δkf + vkf,t + α(r)(ukf,t + ζkf,t). (4.7)There are, therefore, three ways in which parents can affect the consumption process of theirchildren: (i) the earnings potential channel; (ii) the transfers and other income channel; and (iii)60For an analysis of altruistically linked households using PSID data see Altonji, Hayashi, and Kotlikoff (1992,1997).61In our baseline estimation we define other income as the sum of spousal earnings and total transfer income ofhusband and wife. In robustness checks we split other income into its two components and assess which one accountsfor most of the estimated persistence.62Appendix C.1 reports analytical solutions obtained by (i) assuming a quadratic utility function or (ii) a first-orderTaylor approximation of the Euler equation under CRRA utility.66inherited consumption shifters.4.2.1 Cross-sectional Insurance and Intergenerational SmoothingThe presence of an intergenerational correlation in the consumption shifter qf,t reflects the ac-crual of different family influences. In particular, heterogeneity in qf,t may capture family-specificconsumption preferences that shape saving behaviour. As we show in Appendix C.1, linear approx-imations of the Euler equation for general concave utility functions (say, CRRA) lead to omittedhigher-order preference terms being loaded onto the unobserved qf,t shifter.63 Accounting for theco-dependence between consumption propensities and income turns out to be quantitatively im-portant (see Alan, Browning, and Ejrnæs, 2018).64 In the estimation, we find evidence of strongnegative covariance between consumption shifters q¯f and measures of income. One interpretationof this negative correlation is that households with higher income tend to save proportionally more.This behaviour acts as a force towards reducing the cross-sectional dispersion of expenditures.The model suggests that two competing mechanisms shape the distribution of consumption.First, a dampening effect whereby the negative correlation of consumption and saving propensi-ties with income compresses the cross-sectional variance of household expenditures (see Blundell,Pistaferri, and Preston, 2008; Kaplan and Violante, 2010)). Second, an intra-family smoothingmechanism, whereby parents attempt to equalize marginal utilities of family members across gen-erations. This intergenerational smoothing has the effect of inflating inequality in both consumptionand income in the generation of children. Both mechanisms find support in our empirical analysis.Breaking Down Inequality. Equations (4.1) to (4.7) specify the complete set of conditionsthat characterize intergenerational dependence in this economy, linking earned income, non-earnedincome and consumption across generations. Once estimated, these relationships can be used tocharacterise inequality among parents and children, as well as to highlight how parental hetero-geneity translates into inequality among their children. Equations (4.1), (4.2) and (4.6) describethe processes (in levels) for parents and can be mapped into cross-sectional variances:Var(epf)= σ2e¯p (4.8)Var(npf)= σ2n¯p (4.9)Var(cpf)= σ2q¯p + σ2e¯p + σ2n¯p + 2 (σq¯p,e¯p + σq¯p,n¯p + σe¯p,n¯p) . (4.10)The latter equations highlight how consumption inequality among parents depends not only oninequality in earnings and other income, but also on their covariances. To the extent that insurance63Higher order preference terms may co-move with earnings e¯f and with other income n¯f . For example, if individ-uals with lower permanent income are credit-constrained, a precautionary saving motive might generate a negativecorrelation between qf,t and permanent income (see Caballe, 2016).64Alan, Browning, and Ejrnæs (2018) show that consumption responses to income shocks are heterogeneous andexhibit significant co-dependence with preference shifters and idiosyncratic properties of income.67implies that other income is negatively correlated with earnings, then consumption inequality maybe lower than earnings inequality.Similarly, equations (4.3), (4.4) and (4.7) describe the key processes (in levels) for children andhow inequality among children depends on inequality among parents:Var(ekf)= γ2σ2e¯p + θ2σ2n¯p + 2γθσe¯p,n¯p + σ2δk (4.11)Var(nkf)= ρ2σ2n¯p + λ2σ2e¯p + 2ρλσe¯p,n¯p + σ2εk (4.12)Var(ckf)= φ2σ2q¯p + (γ + λ)2 σ2e¯p + (ρ+ θ)2 σ2n¯p+2 [(γ + λ)φσq¯p,e¯p + (ρ+ θ)φσq¯p,n¯p + (ρ+ θ) (γ + λ)σe¯p,n¯p ]+σ2εk + σ2ψk + σ2δk + 2[σψk,εk + σψk,δk + σδk,εk]. (4.13)Earnings inequality among children changes with (i) the magnitude of earnings inequality amongparents (σ2e¯p) and (ii) the intensity of the intergenerational pass-through (γ). It is, therefore, clearthat the pass-through parameter alone is not sufficient to determine how much parents matterfor inequality in subsequent generations. For consumption, the first two rows of equation (4.13)describe how parental heterogeneity drives differences among their offspring: the first row capturesthe direct effects of inequality among parents being transmitted into inequality among children;the second row describes the covariances which may offset the direct effects. Finally, the last rowcaptures the drivers of inequality among children that are independent of parents.4.3 Identification, Estimation and DataTo identify and estimate the drivers of inequality among children, as captured in equations (4.11),(4.12) and (4.13), we focus on lifetime inequality and abstract from transitory components of incomeand consumption. We revisit the role of transitory components in Section 4.6 where we documentthe robustness of baseline estimates to the inclusion of yearly variation induced by transitoryshocks.654.3.1 IdentificationIdentification proceeds in three steps. First, we use cross-sectional moments for parents and iden-tify variances and covariances between their sources of income and consumption. Second, we usethese estimates, and inter-generational covariances, to recover parent-child persistence parame-ters. Lastly, information from the previous two steps is used alongside second moments from thecross-section of children to identify specific components driving inequality among children.65Transitory shocks cannot be identified separately from classical measurement error in the observed variables.Bound, Brown, Duncan, and Rodgers (1994) provide estimates of the proportion of variance in observed earningsthat can be attributed to measurement error. In the baseline specification we use time-averaged observations for across-section of individuals to mitigate concerns about classical measurement errors.68Cross-sectional Parameters for Parents. To identify parental dispersion parameters we useequations (4.8), (4.9), and:Cov(epf , npf)= σe¯p,n¯p . (4.14)These equations deliver σ2e¯p , σ2n¯p and σe¯p,n¯p . Then, using these estimates, σq¯p,e¯p and σq¯p,n¯p areidentified from:Cov(epf , cpf)= σ2e¯p + σq¯p,e¯p + σe¯p,n¯p (4.15)Cov(npf , cpf)= σ2n¯p + σq¯p,n¯p + σe¯p,n¯p . (4.16)Finally, equation (4.10) can be used to recover σ2q¯p .Intergenerational Persistence. The intergenerational elasticity parameters (γ, θ, ρ, λ, φ) areidentified using the cross-generation moments. After using equation (4.14) to recover σe¯p,n¯p andequation (4.8) to recover σ2e¯p , equations (4.17) and (4.20) jointly identify γ and θ. Similarly, ρ andλ are identified from (4.18) and (4.19). This leaves φ to be identified from equation (4.21).Cov(epf , ekf)= γσ2e¯p + θσe¯p,n¯p (4.17)Cov(npf , nkf)= ρσ2n¯p + λσe¯p,n¯p (4.18)Cov(epf , nkf)= ρσe¯p,n¯p + λσ2e¯p (4.19)Cov(npf , ekf)= γσe¯p,n¯p + θσ2n¯p (4.20)Cov(cpf , ckf)= φ(σ2q¯p + σq¯p,e¯p + σq¯p,n¯p)+ (γ + λ)(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ (ρ+ θ)(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(4.21)Cross-sectional Parameters for Children. Finally, we employ estimates from the previoussteps to identify children-specific dispersion parameters. The values of σ2δkand σ2εkare identifiedfrom (4.11) and (4.12), respectively. The remaining child specific parameters are identified fromthe covariances of income, earnings and consumption among children (see equations 4.22 through4.24 below) as well as from the variance of consumption in equation (4.13).Cov(ekf , nkf)= (ργ + θλ)σe¯p,n¯p + γλσ2e¯p + ρθσ2n¯p + σδk,εk (4.22)Cov(ekf , ckf)= γ (γ + λ)σ2e¯p + θ (θ + ρ)σ2n¯p + φγσq¯p,e¯p + φθσq¯p,n¯p+ [γ (ρ+ θ) + θ (γ + λ)]σe¯p,n¯p + σ2δk + σψk,δk + σδk,εk (4.23)Cov(nkf , ckf)= λ (γ + λ)σ2e¯p + ρ (θ + ρ)σ2n¯p + φλσq¯p,e¯p + φρσq¯p,n¯p+ [λ (ρ+ θ) + ρ (γ + λ)]σe¯p,n¯p + σ2εk + σδk,εk + σψk,εk (4.24)69Over-identifying Moments. The following four inter-generational moments can be used asover-identifying restrictions for the parameter estimates:Cov(epf , ckf)= (γ + λ)σ2e¯p + φσq¯p,e¯p + (ρ+ θ)σe¯p,n¯p (4.25)Cov(npf , ckf)= (ρ+ θ)σ2n¯p + φσq¯p,n¯p + (γ + λ)σe¯p,n¯p (4.26)Cov(cpf , ekf)= γ(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ θ(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(4.27)Cov(cpf , nkf)= λ(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ ρ(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(4.28)Identification: A Graphical Example. One insight of the identification argument is that wecan use elements of the covariance structure to jointly harness information about cross-sectionalinequality and covariation of permanent income across generations. To illustrate how this worksin practice, it helps to consider the relationships in Figure 4.1 where the y-axis measures theparental permanent earnings variance, σ2e¯p , and the x-axis represents the intergenerational earningspersistence, γ. To identify this pair of parameters we only use three empirical moments: V ar(epf ),Cov(epf , ekf ) and V ar(ekf ).From moment condition (4.8), the variance of parental earnings (σ2e¯p) is uniquely identified byVar(epf): its value is shown as the horizontal dashed line in Figure 4.1. The moment condition(4.11) captures the tradeoff between γ and σ2e¯p , holding constant other persistence and varianceparameters (i.e., θ, σ2n¯p , σe¯p,n¯p and σ2δk). This is plotted as the negatively sloped dotted line in Figure4.1. The intersection of the dotted line with the dashed line uniquely identifies the persistenceparameter, γ. However, our model features an additional restriction: the exact location of the pair(γ, σ2e¯p)needs to be consistent with the moment condition (4.17), imposing an additional tradeoffbetween the two parameters (shown by the solid line). That is, σ2e¯p and γ must be such that boththe solid and the dotted lines intersect the dashed line at a common location. One can verifythat the location where all three moment conditions hold in Figure 4.1 corresponds to the baselineparameter estimates presented in Section 4.4.4.3.2 EstimationWe estimate model parameters using a generalized method of moments that minimizes the sum ofsquared deviations between empirical and theoretical second moments. We use an equally weighteddistance metric because of the small sample biases associated with using a full variance-covariancematrix featuring higher-order moments (see Altonji and Segal, 1996). Data on earnings, otherincome and consumption is used to calculate the empirical moments, after removing time andbirth-cohort effects.66In Appendix C.5.1, we decompose the total variation in the baseline data into a component ex-plained by observable characteristics, like race, education, number of family members, employment66Empirical moments are constructed using the residuals of a log-linear regression of the variables on a full set ofyear and cohort dummies. This is done separately for the parent and child generations.70status, etc., and a residual component representing heterogeneity in unobservable factors. This ishelpful to establish whether the persistence and transmission of inequality across generations aredue to observable or unobservable characteristics of the parent-child pairs.4.3.3 DataWe use data from the Panel Study of Income Dynamics (PSID). This dataset is widely used inthe analysis of intergenerational persistence of economic outcomes because the offspring of originalsample members become part of the survey sample when they establish independent households.Using these data has also the advantage of making our analysis easily comparable to existing studiesbased on the PSID. We focus on the nationally representative sample of the PSID (from the SurveyResearch Centre, SRC) between 1967 and 2014, and exclude samples from the Survey of EconomicOpportunity (SEO), immigrant and Latino sub-populations. To avoid noise due to weak labourmarket attachment and variation in marital status, we sample married households with a malehead and at least 5 years of data.67 We also restrict the sample to families with non-negativelabour earnings and total income, that do no more than 5,840 hours of work in any year, and withwages at least half of the federal minimum wage. Finally, we select out households that experienceannual earnings growth of more than 400%. Baseline results focus on intergenerational linkagesbetween fathers and sons.68 For each generation, we consider income and expenditure from age25 onwards, with a maximum sample age of 65, to avoid issues related to retirement choices. Bydesign, the income and consumption information of parents refers to later stages of the life cycle.In our baseline sample of 760 unique father-son pairs, the average parental age is 47 years whilethat for the children is only 37 years. Further details about data and sampling restrictions are inAppendix C.2.Labour earnings data for the household head and his spouse are readily available for all surveywaves of the PSID. Data about transfers from public and private sources for the husband and thewife are also available for most years. In contrast, the consumption expenditure data can be sparse,and not presented as a single variable in the PSID. Expenditures on food are the only categorythat is observed almost consistently since the earliest 1968 wave, and we use food outlays as theconsumption measure for the baseline estimation. In Section 4.6, we examine the robustness of ourfindings to an alternative consumption measure, suggested by Attanasio and Pistaferri (2014), thatrelies on 11 major categories of consumption outlays that are reported from 1999 onwards. Thisapproach measures total consumption expenditure at the household level by estimating a simpledemand system using data for the years in which all 11 consumption expenditures were available inthe PSID; then, by inverting the demand system, one can recover total expenditures for the yearsbefore 1999. The method relies on the theory of consumer demand and two-stage budgeting: theallocation of resources spent in a given period over different commodities is assumed to depend67The restriction to married households is helpful but not inconsequential, as intergenerational insurance may comeinto play exactly at the time of relationship breakdown (Fisher and Low, 2015).68Our focus on father-son linkages also avoids the sample issues discussed in Hryshko and Manovskii (2019).71on relative prices, taste-shifters (demographic and socio-economic variables) and total expenditure.Details about the variables, their availability in the survey and the demand system estimationprocedure are reported in Appendix C.2. We adjust data on household-level expenditures throughthe OECD adult equivalence scale.4.4 ResultsTable 4.1 reports the variances of earnings, other income and consumption expenditures for parentsand children.69 These variances, along with the empirical moments reported in Appendix FigureC.2, are used in the baseline implementation to estimate intergenerational persistence parametersand the underlying variance-covariance structure of permanent income and consumption for eachgeneration. We summarize the within-sample fit of the model in Figure C.2 of Appendix C.4.The two lifetime income sources are much more dispersed than expenditures for both the gener-ations, indicating the presence of mechanisms that induce cross-sectional consumption smoothing.This may occur through both formal taxes and transfers and the heterogeneous saving and spend-ing behaviour of households. Amongst income sources, labour earnings of the male household headare less dispersed than other family income, which consists of transfer income and wife earnings.In Appendix Table C.14 we show that the higher dispersion of other income is due to the unevendistribution of transfer income; in contrast, spousal earnings are significantly less dispersed thantransfers in both generations. The relative magnitudes of head earnings and family consumptiondispersion reported in Table 4.1 are similar to those found in studies by Krueger and Perri (2006)and Attanasio and Pistaferri (2014). For a direct comparison with these studies that do not splitthe data into two generations, in Appendix Figure C.1 we show the evolution of cross-sectionalearnings and consumption inequality for the last four decades in the U.S.The age range used to calculate these variances is wider for parents than it is for children sinceparents are observed for a longer period in PSID data. Therefore, differences in the magnitude ofvariances of parents and children, shown in Table 4.1, do not imply a decline in income inequalityacross generations. Rather, these differences reflect shocks accruing at different stages of the life-cycle. Table 4.7 in Section 4.5 reports variances based on samples where the ages of both parentsand children are restricted between 30 and 40. These variances illustrate the evolution of inequalityacross generations, showing a relative increase in inequality among children that is consistent withthe well-established notion of increasing income U.S. inequality over the past decades. The agerestriction, however, substantially reduces the sample size, and in the baseline analysis, we usethe wider age range for parents to obtain more accurate estimates of parental permanent income.Since we do not observe children in the later part of their working lives, our estimates reflect howparental heterogeneity impacts dispersion among children in the earlier decades of their adult lives.69In Appendix Table C.3, we decompose each statistic into the variance due to observable characteristics of ageneration and the residual variance due to unobservable factors.72Intergenerational Elasticities. Table 4.2 reports estimates of intergenerational persistence pa-rameters. The elasticity is highest for earnings, with the pass-through γ estimated at 0.23; incontrast, the elasticity for other household income, ρ, is 0.10 and that for consumption, φ, is 0.15.It is important to emphasize that the significant covariation in idiosyncratic expenditure shifters qacross generations, captured by the parameter φ, contributes to consumption inequality over andabove any effects working through the earnings and other income channels. That is, family in-fluences on consumption expenditures build-up through three inter-dependent channels: earnings,other household income, and persistence in consumption and saving propensities.Higher parental earnings are associated with higher levels of other income among offspring, withthe cross-elasticity λ equal to 0.21: this positive covariation holds for both transfers and spousalearnings among children (see Table 4.5). On the other hand, other household income has littleeffect on children’s earnings, with the elasticity θ estimated to be small albeit statistically signifi-cant. Explicitly accounting for these cross-effects between different dimensions of intergenerationalpass-through (namely, male head earnings, wife earnings and transfer income) turns out to be an im-portant contribution of our approach over the standard reduced-form analysis of intergenerationalpersistence. As we show in Section 4.6, ignoring these cross-effects may lead to misleading inferenceabout the role of family influences for cross-sectional inequality in the children’s generation.In Appendix C.5.1, we show that all pass-through parameters in Table 4.2 are primarily drivenby intergenerational persistence in observable characteristics like race, employment status, edu-cational attainment, family structure, state of residence and so on. In particular, we documentthat education accounts for a large component of the earnings pass-through across generations,corroborating the evidence on this transmission channel in Landersø and Heckman (2017).70Permanent Income and Consumption. Table 4.3 reports estimates of the variances and co-variances of the permanent components of earnings, other income and consumption shifters.71 Theimportance of jointly estimating income and consumption processes becomes apparent when ex-amining these estimates. To illustrate how covariations are key to account for data patterns, wenote that the variance of the permanent consumption components, σq¯ is larger than that of perma-nent earnings in both generations; however, we know that consumption expenditures are much lessdispersed than earnings. This apparent discrepancy highlights the role of the negative covariationbetween permanent earnings and idiosyncratic consumption shifters. Estimates of this covarianceare -0.27 for the parents’ generation (see σe¯,q¯) and exhibit a similar magnitude in the child’s gen-eration. In addition, the permanent component of other income exhibits even stronger negativecovariation with lifetime consumption shifters (see σe¯,q¯). The negative covariation between thepermanent components of consumption and income mitigates the impact of income inequality onconsumption inequality; that is, the negative covariances compress the distribution of log consump-70Empirical support for this result can also be found in the mobility matrix of education in Appendix Table C.8.High persistence of education across generations might be due to unobserved ability, or to higher human capitalinvestments by parents with higher earnings (see Lefgren, Sims, and Lindquist, 2012).71In Appendix Table C.5 we report estimates of these parameters separately for cases where we use variation inthe outcome variables that are either explained by observable characteristics or left unexplained by them.73tion and drive its overall variance below the variance of income. Moreover, these estimates suggestthat higher-income families save proportionally more and have, on average, a lower propensity toconsume.72 Such traits are passed across generations, which reinforces their mitigating influenceon consumption dispersion.4.4.1 Role of Parental HeterogeneityThe quantitative importance of parental heterogeneity for offspring depends on three aspects: (i)intergenerational persistence, (ii) the level of inequality in the parents’ generation, and (iii) themagnitude of idiosyncratic heterogeneity among kids. We gauge the influence of parental factorsin two ways: first, we compute the share of earnings, income and consumption variances thatis explained by pre-determined parental heterogeneity; second, we show how the cross-sectionaldistributions of these outcomes change if differences in parental characteristics are removed.Variance Accounting. Table 4.4 summarizes the impact of parental heterogeneity on the vari-ance of children outcomes. Let Var[yk(p)] measure the offspring variance that is explained byparental factors for variable y ∈ {e, n, c}, while Var[yk] denotes the total cross-sectional variancein the kids’ generation. The ratio Var[yk(p)]Var[yk]quantifies the share of total variation attributed toparental heterogeneity.73Combining the estimates in Tables 4.2 and 4.3, we are able to break down the relative contribu-tions of parental and idiosyncratic heterogeneity to the cross-sectional dispersion of child outcomes(see Table 4.4). By far the largest impact of parental heterogeneity is on consumption dispersion,as it accounts for almost 30% of total variation among offspring. Parental factors account formuch less of the variation in income — 8% and 4% for earnings and other income, respectively.As discussed before, this is consistent with the observation that intergenerational transmission ofconsumption and saving behaviours, after accounting for the level of income, is an important chan-nel of intra-family persistence in consumption expenditures. Since the cross-sectional distributionof expenditures is more compressed than its counterparts for earnings and other income, parentalinfluences end up explaining a much larger share of this lower variance. Nevertheless, it is clearthat idiosyncratic heterogeneity accruing over the life cycle accounts for most of the dispersion ofincome and consumption outcomes in the younger generation.74Lastly, it is important to emphasize that a significant share of parental influence on consump-tion dispersion can only be identified if one allows for non-zero cross-elasticities λ and θ betweenearnings and other income in the two generations. Restricting these cross-elasticities to zero not72See Abbott and Gallipoli (2019) and Straub (2018) for recent evidence of high saving rates among the rich. Fan(2006) suggests that this maybe motivated by bequest motives. Dynan, Skinner, and Zeldes (2004) argue that othernon-bequest motives account for this excess savings.73For example, the contribution of parents in the cross-sectional earnings variance in the kids’ generation is givenby the ratioγ2σ2e¯p+θ2σ2n¯p+2γθσe¯p,n¯pσ2δk+γ2σ2e¯p+θ2σ2n¯p+2γθσe¯p,n¯p. For an illustration of all the calculations involved, see Appendix C.5.2.74In Appendix Table C.6, we document that most of the explanatory power of parental heterogeneity is dueto observable characteristics. In contrast, parental factors appear at most marginal in explaining unobservableheterogeneity in the younger generation.74only diminishes the quantitative contribution of parental heterogeneity to consumption dispersionbut also artificially boosts the parental importance for earnings heterogeneity. This highlightsagain the co-dependence of these processes and the biases that are introduced by ignoring it. Themechanism behind these biases is discussed in Section 4.6 where we re-estimate the model afterrestricting λ = θ = 0.Marital Selection. In the baseline model, other income is the sum of transfer income (bothpublic and private transfers) and spousal earnings. Table 4.5 reports estimates of intergenerationalpass-through elasticities under the restriction that other income consists only of transfers (column1) or spousal earnings (column 2).75 Focusing, in turn, on transfer or spousal income alone altersthe sample size because of missing values. Therefore, to aid comparison, we re-estimate the baselinemodel (with the broader measure of other income) on the sub-sample for which we have non-missingobservations for both transfers and wife’s earnings. We report the latter estimates in column (3).When only spousal earnings are used in estimation, all intergenerational elasticity estimatesare strongly significant and at least as large as their baseline counterparts. The point estimatesof intergenerational persistence for consumption shifters and other income are roughly 50% higherthan baseline results. In contrast, persistence parameters are low and very imprecisely estimatedin the specification featuring transfers alone. By removing transfer income, which is rather noisy,we effectively focus on the most significant and better-measured component of other householdincome.The fact that spousal earnings are rather persistent across parent-child pairs (with a ρ elasticityof 0.14) suggests that spousal sorting may partly depend on family traits and that maternal earningsmay play a role in female partner choices, especially for what pertains to wife’s labour marketparticipation and earnings. This is consistent with findings in Fernandez, Fogli, and Olivetti (2004),who document preference formation based on maternal characteristics.In Table 4.6 we break down children inequality into parental and idiosyncratic components forspecifications featuring spousal income only (Panel A) and transfer income only (Panel B), andcompare these to what we obtain for the baseline model estimated on the same sample (PanelC). It is instructive to notice that removing transfer measures marginally increases estimates offamily persistence on earnings of both spouses. This indicates that transfers somewhat confoundand offset parental influences on total household earnings. In part, these larger estimates are dueto the significantly lower variance of other income when noisy transfer measures are omitted. Incontrast, the contribution of family background to consumption dispersion is almost the same asin the baseline, suggesting that earnings and consumption elasticities are generally sufficient tocharacterize the dispersion of children expenditures.Even after shutting down direct family transfers, parental influences on consumption inequal-ity are estimated to be stronger than on household income, albeit the gap is smaller than in thebenchmark model. This suggests that family influences on expenditure operate through the trans-75In Table C.13 of the appendix we report the associated variance-covariance estimates.75mission of earning potential, rather than through direct transfers. Moreover, earning potential isincreased at the household level, as parents affect both the offspring’s earning ability and their mar-ital choices. It appears that marital selection, together with the ability to earn and the persistenceof consumption and saving behaviours, can account for most of the parental influences identified inthe baseline.4.4.2 Counterfactual Cross-sectional DistributionsAbsence of intergenerational transmission is equivalent to a setting with randomly matched parent-child pairs. A simple way of gauging the impact of family background in this setting is to plot theobserved and counterfactual cross-sectional distribution of each outcome in the children generation(top panels of Figure 4.2) and their local differences, (as measured by the histograms in the bottompanels of Figure 4.2). The histograms represent, for each interval of the domain, the probabilitymass of the actual distribution minus the corresponding mass in the counterfactual.76The counterfactual distributions are visibly less dispersed, with the strongest departure frombaseline observed for lifetime consumption. In all counterfactuals, much of the probability mass atthe lower tail is reshuffled towards the middle of the distribution, while the right tail also becomessomewhat less heavy. This suggests that the impact of parental heterogeneity is especially relevantat the bottom of the distributions, where it stretches the left tail of both income and consumption.These findings are in line with results in Table 4.4 and provide additional evidence that familyinfluences account for a comparatively larger share of consumption variation.4.5 The Evolution of Inequality across GenerationsThe magnitudes of the intergenerational pass-through parameters and the idiosyncratic variancesraise questions about the evolution of inequality across generations. A longer data panel would beideal to identify persistence across multiple generations, since the current span of PSID data covers,at most, the working life of children born between the 1950s and the early 1980s. This makes ithard to obtain direct estimates of the impact of grandparents on grandchildren and generationsfurther apart. However, under a stationarity assumption, one can examine the projected path ofinequality by computing a first-order approximation of the expected evolution of the variances ofincome and consumption starting from current levels.77To examine inequality across generations, we compute the long-run steady-state variances ofearnings, other income and consumption. These measures describe how dispersed income andconsumption would be if, all else equal, the baseline model were allowed sufficient time to convergeto its steady state. By comparing current variances to their steady-state values, one can tie changesin cross-sectional inequality to the intergenerational persistence of parental advantage. Since it is76Appendix C.5.2 describes how we measure the actual and counterfactual distributions. In the counterfactualcase, all parental channels are shut down. All exercises rely on estimates from Tables 4.2 and 4.3.77Stationarity implies holding {σ2δk , σ2ψk , σ2εk , σδk,εk , σψk,εk , σψk,δk} constant at their baseline values. Of course,large changes in structural parameters might mitigate or exacerbate the baseline scenario.76preferable to focus on individuals of similar age across generations and we do not observe childrenin the second half of their working lives, we restrict the age of both parents and children in oursample to be between 30 and 40.78A Vector Representation of the Model. Earnings, other income and consumption shiftersevolve through generations of family f according to the following vector autoregressive process:e¯ktfn¯ktfq¯ktf =γ θ 0λ ρ 00 0 φ .e¯kt−1fn¯kt−1fq¯kt−1f+δktfεktfψktf .The superscript {kt} identifies the tth generation of kids. Since k1 denotes the first generation ofkids, we define k0 to be the parents’ generation in our data, that is, x¯k0f ≡ x¯pf for any variablex ∈ {e, n, q}. The joint distribution of the covariance-stationary idiosyncratic shocks isδktfεktfψktf ∼ N000 , σ2δkσδk,εk σδk,ψkσδk,εk σ2εkσεk,ψkσδk,ψk σεk,ψk σ2ψk.Using parameter estimates, we simulate the VAR forward, iterating until convergence.79 Thisdelivers simulated data series for e¯ktf , n¯ktf , q¯ktf , δktf , εktf and ψktf . To obtain a series for log consump-tion, we use the relationship:cktf = φqkt−1f + (γ + λ) ekt−1f + (ρ+ θ)nkt−1f + δktf + εktf + ψktf ,for t ≥ 1. Having recovered the (log) series for the permanent components of earnings, otherincome, and consumption, we calculate their long-run variances and report them in column (3) ofTable 4.7.Current versus Long-Run Inequality. Comparing steady-state variances with those observedin data, we see that for earnings and consumption the inequality in the parents’ generation isthe lowest (see column 1 of Table 4.7), followed by that in the children’s generation (column 2 ofTable 4.7). Steady-state inequality is the largest, suggesting that the variance of lifetime earningsand consumption expenditures might rise further from current levels. For other income, inequalityin the children’s generation is lower than in their parents’ generation and slightly lower than itsvalue in the steady-state. The steady-state variances implied by the baseline model are not farabove what is measured in the children’s generation. This observation reflects the low value of theestimated pass-through parameter γ, meaning that predicted long-run inequality reflects primarilythe variance of idiosyncratic shocks.78Baseline estimates are based on a larger sample that includes observations for older parents.79Since we restrict the age range between 30 and 40 years, we re-estimate the baseline model on a smaller sample.The estimates are reported in column (1) of Tables 4.10 and C.12. The VAR is simulated for 100,000 generations.77To illustrate the quantitative importance of intergenerational elasticities in the long-run, were-estimate the baseline model using a constrained version of the GMM estimator where we holdconstant the earnings persistence γ at pre-determined values. By exogenously setting larger orsmaller values of γ, we can assess whether, and how much, steady-state inequality might deviatefrom its initial value. Table 4.8 shows that for counterfactually high values of γ, earnings inequalityin the children generation (column 4) can be substantially different from long-run model outcomes(column 5). Moreover, a trade-off between inter-generational persistence, γ (column 1) and idiosyn-cratic heterogeneity, σ2δk(column 2) is evident when explaining the total child variance (column4).80Despite a falling variance for idiosyncratic innovations, σ2δk, steady-state inequality in column5 increases with the magnitude of γ. Thus, the cross-generational persistence, rather than theinnovations variance, emerges as the key determinant of long-run inequality and as the main reasonfor the similarity of Var(ek)and Var (e∗).81These results emphasize that, without any increases in the underlying dispersion of idiosyn-cratic innovations, one would have to assume implausibly large values of the intergenerationalpass-through to induce significantly higher long-run inequality. It follows that intergenerationalpersistence dictates the proportional impact of parental heterogeneity on inequality. Further evi-dence of this is in the last column of Table 4.8, which documents how changes in γ lead to significantvariation in the contribution of parental factors to cross-sectional earnings inequality. A larger γamplifies the contribution of family background: the parental contribution to inequality swingswidely, between 1% and 12% (for values of γ between 0.1 and 0.4) even when steady-state earningsdispersion ̂V ar(e∗) barely changes.It is interesting to contrast the values in column 6 of Table 4.8 with baseline estimates of theimportance of parental factors in Table C.6, where the age range was not restricted. Restricting theage range over which parents’ income is measured implies that the importance of family backgrounddeclines from about 8% to 4% of total variation: that is, roughly half of the parental impact oninequality among children accrues by the time parents reach age 40.A final caveat for these results is that inference about the evolution of inequality is based onstationary parameter estimates. For this reason in Appendix C.6 we consider the implications ofchanges in structural parameter estimates on inequality going forward and we explore how inequalityevolves over subsequent generations (parent, child, grandchild) while converging to its steady-state80When intergenerational persistence γ is set to a higher value, the GMM estimator delivers a lower variance ofidiosyncratic heterogeneity (e.g., for earnings, lower σ2δk ) since the amount of cross-sectional inequality among childrenis fixed by what is observed in the data.81A striking feature of the GMM estimates in Table 4.8 is that the child variance remains constant and matchesexactly the empirically observed variance. On the other hand, the empirically observed parental variance is 0.199and none of the estimates matches this figure exactly. To understand this, consider the relevant moment conditions.At first glance, equation (4.8) suggests that the parental variance estimate should be independent of the choice of γ.However, the GMM tries to satisfy equation (4.17), which implies a direct trade-off between γ and V ar(ep). Thus,increasing γ tends to decrease V ar(ep). On the other hand, whatever the values for γ and V ar(ep), the empiricallyobserved value of V ar(ek) can always be matched exactly by choosing the free parameter σ2δk , which does not enterany other moment condition.78level.4.6 Robustness and ExtensionsTo assess the robustness of these findings we perform three types of sensitivity checks. We begin byexamining whether a specific cohort drives the baseline results. In the second round of checks, weestimate variants of the baseline model where we (i) restrict specific channels of intergenerationaltransmission, (ii) consider a sample of randomly matched parent-child pairs, (iii) employ alternativemeasures of expenditure, and (iv) target additional moments in the GMM estimation. Third, weestimate an alternative model of intergenerational persistence, specified in terms of growth ratesof the outcome variables. This allows one to draw inference about intergenerational persistence ofidiosyncratic innovations to income and consumption expenditures.4.6.1 Estimates by Child Birth-CohortAs a first check, we split observations by child birth-cohort. Grawe (2006) and Gouskova, Chiteji,and Stafford (2010) argue that life-cycle bias may be important when estimating intergenerationalpersistence. Since children from different birth cohorts are observed for varying lengths of theirlife-cycle in the PSID, we avoid life-cycle bias by restricting the age of parents and kids to bebetween 30 and 40 years.Table 4.9 shows the cross-sectional variances of economic outcomes for the parents and kidsfor different child birth-cohorts.82 Contrary to the estimates in Table 4.1 where we imposed noage restrictions, we find that controlling for the life-cycle bias through age restriction makes thedispersion of earnings higher in the child generation for all cohorts, consistent with the empiricalliterature documenting growing inequality in the U.S. over our sample period.Table 4.10 presents estimates of intergenerational pass-through parameters by children’s decadeof birth. The results are qualitatively similar to the baseline ones.83 The differences between es-timates of the intergenerational pass-through parameters for the 1960s and 1970s cohorts are notstatistically significant. In Appendix Table C.11 we consider whether the importance of parentalinfluence in explaining cross-sectional heterogeneity in the child generation varies by children co-horts. Contrasting the 1960s and 1970s cohorts, the contribution of parental heterogeneity changedonly for consumption, dropping from about 38% to 16%. However, cohort-specific sample sizes aresmall enough to suggest caution when comparing these shares.4.6.2 Additional Robustness ChecksNext, we perform four additional robustness checks. First, we estimate a restricted version of thebaseline model where we shut down cross-effects in intergenerational persistence; that is, we set λ82We do not report estimates for the 1950s cohort because the sample size for that cohort becomes too small andestimates are very noisy.83Some of the parameter estimates lose statistical significance, as the age restrictions result in a much smallersample, weakening the precision of the estimates.79and θ to zero. Second, we perform a placebo test where we randomly match parents and childrenand show that baseline estimates capture genuine intergenerational linkages rather than spuriouscorrelations. Third, we use imputed consumption expenditures, rather than food expenditure, tomeasure household outlays. Finally, we re-estimate the model using both cross-sectional and panelvariation: this extension increases the number of moments, as well as the number of parametersto estimate. The main results from these robustness checks are presented in Table 4.11, withadditional details in Appendix Table 4.12.Restricting Cross-Effects between Income SourcesWe consider a restricted version of the baseline model that does not allow for any effect from parentalearnings on other income of the children, nor from parent’s other income onto the child’s earnings,that is, imposing both λ and θ to be zero. Under these restrictions the point estimates of theparameters change significantly, overstating the importance of parents for earnings inequality amongchildren. Most of the difference from the baseline estimates can be attributed to the restriction thatλ = 0, as in the baseline model θ is already close to zero. By restricting λ to be zero, one effectivelydecreases its value below the positive baseline estimate. This mechanically pushes up the estimateof γ to guarantee a fairly constant value of (γ + λ), the total intergenerational persistence fromparental earnings to child outcomes. Hence, the exercise highlights the importance of allowing forcross-effects above and beyond the direct channels captured by γ and ρ when drawing inferenceabout pass-through parameters. Table 4.13 also illustrates that parental heterogeneity explainsmuch less of cross-sectional consumption dispersion when λ and θ are set to zero; this confirmsthat, while higher parental earnings have a positive direct impact on the earnings and expendituresof children, the consumption distribution is shaped by several other forces and ignoring the indirecteffects among different sources of income can lead to incorrect inference.Placebo Test: Random Matching of Parents and ChildrenOne might worry that spurious correlations in the data affect estimates of parent-child pass-throughparameters. To account for this possibility one can perform a placebo test using a sample in whichparents and children are randomly matched. Estimates based on this sample imply no role ofparental heterogeneity for inequality in the children’s generation, as seen in column (3) of Table4.13. The lack of significance in the randomly matched sample indicates that genuine familylinkages, rather than spurious correlations, drive baseline estimates.Alternative Measures of ExpenditureThe baseline analysis uses food expenditures as the consumption measure. This choice is dictatedby necessity as food consumption is available throughout the PSID sample. However, alternativecomponents of consumption might exhibit different intergenerational persistence. We examine theimportance of other expenditure categories in two ways. First, we impute total consumption using80the procedure suggested by Attanasio and Pistaferri (2014); this approach exploits rich consumptionexpenditure information available in the PSID after 1997 to approximate households’ outlays in theearlier years of the survey. We report results for this alternative consumption measure in column(4) of Tables 4.11, 4.13 and 4.12. Estimates based on this broader gauge of expenditures suggesta stronger role of parental heterogeneity for consumption dispersion among children, with roughlyhalf of the total dispersion due to family linkages.84In a second sensitivity exercise, we restrict the sample to the post-1997 period, when thereis no need for imputation of non-food consumption. Estimates from this smaller sample suggesta parental contribution to consumption inequality of roughly 24%, comparable to the baselineestimate based on food consumption alone.85 Inevitably, the smaller size of the post-1997 samplemakes estimates less precise.Additional Moments and Parameters: Panel VariationIn the baseline analysis, we average across yearly observations for each sample member and donot account for year-to-year individual variation. Time-averaging significantly reduces the impactof classical measurement error, but it also precludes identification of the variances of mean-zerotransitory shocks to earnings, income and consumption.86 Thus, accounting for panel variationintroduces extra parameters due to the need to estimate the variances and covariances of per-periodtransitory shocks. By the same token, this extra information introduces new moment restrictions.In Appendix C.7.3 we report the full set of moments and parameters. As shown in column (5)of Tables 4.11, 4.13 and 4.12, modelling period-specific variation makes little difference. However,standard errors are visibly inflated, as one would expect when measurement error becomes moresevere.4.6.3 An Alternative Model of Intergenerational PersistenceIn the baseline model specification, cross-sectional heterogeneity is partly inherited through in-tergenerational persistence of individual fixed effects in income and consumption. An alternativehypothesis is that these linkages may occur through persistence in growth rates. To examine thispossibility, we examine a model in which the permanent components of both earnings and other in-come are random walk processes (see for example, Blundell, Pistaferri, and Preston, 2008), and thecontemporaneous permanent innovations to these processes are correlated across parent-child pairs.Appendix C.8 presents details of this alternative model, along with the identification strategy andparameter estimates. We find little or no evidence of intergenerational persistence in permanentinnovations to earnings, other income and consumption expenditures.84Arguably, this higher estimate of the parental contribution to consumption inequality is an upper bound of thetrue value, as it may partly reflect latent persistence of observable characteristics used to impute consumption.85Estimates are not reported in the table and are available upon request.86When using panel variation, classical measurement error is indistinguishable from per-period transitory innova-tions. Estimates of variances and covariances of transitory shocks are presented in Table C.15.814.7 ConclusionThis chapter examines the importance of heterogeneity among parents for understanding incomeand consumption inequality. We estimate the intergenerational elasticities of earnings, other incomeand consumption and document their significance for the persistence of inequality across genera-tions. We find that the quantitative contribution of idiosyncratic life cycle shocks to inequality ismuch larger than the contribution of parental effects. This implies that families provide limitedinsurance against idiosyncratic life-cycle risk.In reaching this conclusion, we highlight the importance of jointly estimating the income andexpenditure processes, and of accounting for cross-effects between different sources of income andconsumption. As an example of these cross-effects, we document a negative covariation betweenpermanent income and consumption shifters, which suggests that higher-income families have alower average propensity to consume.Our estimates imply that intergenerational persistence is not by itself high enough to inducefurther large increases in inequality over time and across generations. This reiterates the prominentrole of idiosyncratic life-cycle risk, which diffuses and attenuates the impact of family backgroundon the cross-sectional distributions of life-cycle income and consumption.824.8 TablesTable 4.1: VariancesVariables Parent ChildEarnings 0.291 0.248Other Income 0.808 0.534Consumption 0.097 0.114Table 4.2: Estimates: Intergenerational ElasticitiesVariables Parameters Estimates(1)Earnings γ 0.230(0.027)Other Income ρ 0.100(0.023)e¯pf on nkf,t λ 0.206(0.032)n¯pf on ekf,t θ 0.055(0.019)Consumption Shifters φ 0.154(0.032)No. of Parent-Child Pairs N 760Note: Bootstrap standard errors (100 repetitions) in parentheses.Data is purged of year and birth-cohort effects. The average agefor parents in the sample is 47 years; that of children is 37 years.83Table 4.3: Estimates: Variances and Covariances of Idiosyncratic ComponentsParameters Estimates(1)Parental Outcomes: VariancesPermanent Earnings σ2e¯p 0.295(0.021)Permanent Other Income σ2n¯p 0.806( 0.06)Permanent Consumption Shifters σ2q¯p 1.031(0.065)Child Idiosyncratic Heterogeneity: VariancesPermanent Earnings σ2δk0.228(0.011)Permanent Other Income σ2εk0.511(0.043)Permanent Consumption Shifters σ2ψk0.730(0.056)Parental Outcomes: CovariancesConsumption Shifters & Earnings σq¯p,e¯p -0.271(0.024)Consumption Shifters & Other Income σq¯p,n¯p -0.818(0.061)Earnings and Other Income σe¯p,n¯p 0.070(0.013)Child Idiosyncratic Heterogeneity: CovariancesConsumption Shifters & Earnings σψk,δk -0.247(0.018)Consumption Shifters & Other Income σψk,εk -0.522(0.048)Earnings & Other Income σδk,εk 0.075(0.013)No. of Parent-Child Pairs N 760Note: Bootstrap standard errors (100 repetitions) in parentheses. Data is purged of year andbirth-cohort effects. The average age for parents in the sample is 47 years; that of children is 37years.84Table 4.4: Breaking Up Child Inequality: Parental versus Idiosyncratic HeterogeneityVariables Child Variance Variance due to Parents Idiosyncratic Variance(1) (2) (3)Earnings 0.248 0.020 (8.1%) 0.228 (91.9%)Other Income 0.534 0.024 (4.4%) 0.510 (95.6%)Consumption 0.114 0.034 (29.8%) 0.080 (70.2%)Note: Numbers obtained using parameter estimates from Tables 4.2 and 4.3.Table 4.5: Decomposition of Other Income: Intergenerational Elasticity EstimatesParameters Just Transfers Spouse Earnings Other Income(1) (2) (3)Earnings γ 0.239 0.275 0.254(0.050) (0.027) (0.032)Other Income ρ 0.031 0.142 0.097(0.046) (0.036) (0.033)e¯pf on nkf,t λ 0.107 0.232 0.184(0.073) (0.033) (0.045)n¯pf on ekf,t θ -0.007 0.144 0.086(0.017) (0.033) (0.027)Consumption Shifters φ 0.007 0.372 0.217(0.047) (0.047) (0.047)No. of Parent-Child Pairs N 459 459 459Note: Bootstrap standard errors (100 repetitions) reported in parentheses. Food expenditures used as a measure ofconsumption. Appendix Tables C.13 and C.14 present estimates of the corresponding variance-covariance parameters.85Table 4.6: Parental versus Idiosyncratic Heterogeneity: Role of Marital SelectionVariable Child Variance Variance due to Parents Idiosyncratic Variance(1) (2) (3)Panel AEarnings 0.229 0.033 (14.6%) 0.196 (85.4%)Wife Earnings 0.322 0.026 (8.1%) 0.296 (91.9%)Consumption 0.113 0.025 (22.5%) 0.088 (77.5%)Panel BEarnings 0.229 0.016 (7.1%) 0.213 (92.9%)Transfer Income 1.068 0.005 (0.4%) 1.063 (99.6%)Consumption 0.113 0.034 (30.3%) 0.079 (69.7%)Panel CEarnings 0.229 0.024 (10.7%) 0.205 (89.3%)Other Income 0.457 0.016 (3.5%) 0.441 (96.5%)Consumption 0.113 0.027 (24.2%) 0.086 (75.8%)Note: Panel A corresponds to the case where wife earnings is used as the measure of other income. PanelB uses transfer income of the male household head and his wife as the measure of other income. Panel Ccorresponds to the case where other income is defined as the sum of wife earnings and total transfer income.Numbers obtained using parameter estimates in column (2) of Tables 4.5 and C.13, based on sample of 459unique parent-child pairs in which both transfers and wife earnings are not missing.Table 4.7: Steady-State versus Current InequalityVariables Parental Child Steady-stateInequality Inequality Inequality(1) (2) (3)Earnings 0.199 0.251 0.255Other Income 0.845 0.669 0.676Consumption 0.097 0.118 0.127Note: Estimates based on sample of 336 unique parent-child pairs.Age restricted between 30 and 40 years.86Table 4.8: Importance of Parents: Varying Persistence γγ σ̂2δk̂V ar(ep) ̂V ar(ek) ̂V ar(e∗) γ2 ̂V ar(ep)̂V ar(ek)(1) (2) (3) (4) (5) (6)0.10 0.248 0.202 0.251 0.251 1.3%0.21 0.241 0.199 0.251 0.255 4.0%0.30 0.232 0.193 0.251 0.255 7.4%0.40 0.221 0.182 0.251 0.263 12.2%0.50 0.207 0.169 0.251 0.277 17.4%0.60 0.194 0.155 0.251 0.303 22.8%0.70 0.181 0.141 0.251 0.354 28.1%0.80 0.168 0.128 0.251 0.467 33.1%0.90 0.156 0.116 0.251 0.822 37.8%Note: Bold values refer to a specification with γ unconstrainedand estimated as part of the optimization. The age range for bothchildren and parents is between 30 and 40 years. Estimation arebased on 336 unique parent-child pairs for children born in the1960s and 1970s.Table 4.9: Variances by Child-Cohort (Age: 30-40)Variable Generation All Cohorts 1960s Cohort 1970s Cohort(1) (2) (3)Earnings Parent 0.199 0.172 0.225Child 0.251 0.243 0.259Other Income Parent 0.845 0.945 0.752Child 0.669 0.568 0.770Consumption Parent 0.097 0.112 0.081Child 0.118 0.100 0.13587Table 4.10: Intergenerational Elasticity Estimates by Child Cohort (Age: 30-40)Parameters All Cohorts 1960s Cohort 1970s Cohort(1) (2) (3)Earnings γ 0.209 0.251 0.191(0.069) (0.087) (0.106)Other Income ρ 0.041 -0.006 0.099(0.058) (0.068) (0.093)e¯pf on nkf,t λ 0.217 0.202 0.244(0.079) (0.131) ( 0.12)n¯pf on ekf,t θ 0.040 0.009 0.079(0.032) (0.046) (0.038)Consumption Shifters φ 0.075 -0.029 0.200(0.075) ( 0.09) (0.124)No. of Parent-Child Pairs N 336 166 170Note: Bootstrap standard errors (100 repetitions) in parentheses. Average parental ages in the threechild-cohorts are 35, 36 and 35 years. Average ages of the children are 35, 34 and 35 years respectively.‘All Cohorts’ refer to the combined sample of 1960s and 1970s child birth cohorts. Food expenditureis used as proxy measure of consumption. All columns use cross-sectional data variation, net of cohortand year effects. These estimates should be compared with those in column (1) of Appendix TableC.4 where all cohorts of children are combined.Table 4.11: Robustness: Intergenerational Elasticity EstimatesParameters Baseline λ = θ = 0 Random Match Imputation Panel Data(1) (2) (3) (4) (5)Earnings: γ 0.230 0.340 -0.018 0.257 0.294(0.029) ( 0.02) (0.028) (0.029) (0.041)Other Income: ρ 0.100 0.121 -0.039 0.096 0.095(0.029) (0.029) (0.025) (0.028) (0.045)e¯pf on nkf,t: λ 0.206 0 -0.007 0.236 0.107(0.038) (0) (0.035) (0.033) (0.060)n¯pf on ekf,t: θ 0.055 0 -0.015 0.052 0.066(0.017) (0) (0.023) (0.015) (0.035)Consumption Shifters: φ 0.154 0.109 -0.048 0.127 0.153(0.034) (0.032) (0.034) (0.033) (0.046)No. of Parent-Child Pairs: N 760 760 760 760 760Note: Bootstrap standard errors (100 repetitions) in parentheses. Year and cohort effects have beenremoved.88Table 4.12: Robustness: Idiosyncratic ComponentsParameters Baseline λ = θ = 0 Random Match Imputation Panel Data(1) (2) (3) (4) (5)Parental Outcomes: VariancesPermanent Earnings: σ2e¯p 0.295 0.289 0.291 0.291 0.289(0.018) (0.025) (0.022) ( 0.02) (0.015)Permanent Other Income: σ2n¯p 0.806 0.806 0.808 0.807 0.478(0.076) (0.074) (0.071) (0.072) (0.037)Permanent Consumption Shifters: σ2q¯p 1.031 1.053 1.032 0.861 0.689(0.081) ( 0.08) (0.073) ( 0.07) (0.044)Child Idiosyncratic Heterogeneity: VariancesPermanent Earnings: σ2δk0.228 0.214 0.247 0.224 0.208(0.013) (0.014) (0.015) (0.011) (0.013)Permanent Other Income σ2εk0.511 0.522 0.533 0.507 0.415(0.038) (0.046) (0.048) (0.036) (0.026)Permanent Consumption Shifters: σ2ψk0.730 0.741 0.752 0.573 0.584( 0.05) (0.063) (0.069) ( 0.04) (0.037)Parental Outcomes: CovariancesConsumption Shifters & Earnings: σq¯p,e¯p -0.271 -0.279 -0.263 -0.223 -0.258(0.021) (0.029) (0.028) (0.019) (0.022)Consumption Shifters & Other Income: σq¯p,n¯p -0.818 -0.833 -0.821 -0.769 -0.480(0.077) (0.076) (0.069) ( 0.07) (0.037)Earnings and Other Income: σe¯p,n¯p 0.070 0.086 0.067 0.068 0.058(0.015) (0.018) (0.017) (0.013) (0.012)Child Idiosyncratic Heterogeneity: CovariancesConsumption Shifters & Earnings: σψk,δk -0.247 -0.253 -0.263 -0.214 -0.212( 0.02) (0.024) (0.025) (0.016) ( 0.018)Consumption Shifters & Other Income: σψk,εk -0.522 -0.532 -0.542 -0.480 -0.398(0.041) ( 0.05) (0.055) (0.036) (0.029)Earnings & Other Income: σδk,εk 0.075 0.092 0.095 0.072 0.052(0.013) (0.017) (0.019) (0.012) (0.013)No. of Parent-Child Pairs: N 760 760 760 760 760Note: Bootstrap standard errors (100 repetitions) in parentheses. This table uses the same sample and model specification as Table4.11.Table 4.13: Robustness: Importance of Parents for Child InequalityVariables Baseline λ = θ = 0 Random Match Imputation Panel Data(1) (2) (3) (4) (5)Earnings 8.0 13.5 0.1 9.4 12.3Other Income 4.4 2.2 0.2 5.0 2.1Consumption 29.9 19.5 0.2 47.4 22.8Note: All numbers are percentages (%) and are based on parameter estimates inTables 4.11 and 4.12.894.9 FiguresFigure 4.1: Identification of Persistence and Dispersion ParametersFigure 4.2: Baseline versus Counterfactual Probability Density FunctionsNote: Top panels report density functions. Bottom panels report histograms of changes in local probability mass(the probability mass of the actual distribution minus the corresponding mass of the counterfactual).90Chapter 5ConclusionThis thesis looked at the dynamics of two different types of economic choices made by firms andhouseholds. First, it studied the short-run business cycle dynamics of how the frequency of hiringand firing of workers by firms influence whether productivity increases during economic boomsor busts. Second, it discussed the long-run dynamics of how economic inequality evolves acrossgenerations depending on household choices regarding educating children, intra-family transfers,consumption expenditure and so on.Chapter 2 argued that the sudden vanishing of the procyclicality of productivity in the U.S.around the mid-1980s (the so-called productivity puzzle) is driven by a sudden reduction in thecost of hiring and firing workers. To arrive at this conclusion, it was shown that the highly pro-cyclical factor utilization rate component of measured productivity became less important becauseof firms’ lower reliance on adjusting the intensive margin of factors of production. Since firms typ-ically depended on changing the intensity of factor use because of significant costs in the extensivemargin of factor adjustment, lower reliance on the former indicated a drop in the cost of the latter.Moreover, it was shown that given the same positive demand shock to the U.S. economy beforeand after the 1980s, productivity rose much less in the post-1980 period. This indicated that firmsare no longer increasing the intensity or productivity of its available workers but instead just hiringmore workers to meet the extra demand, thereby corroborating the story of falling hiring and firingcost of workers. Once the drop in employment adjustment cost was established as an explana-tion for the productivity puzzle, I identified rapid de-unionization as a significant determinant ofhiring and firing cost. In a cross-section of U.S. states and industries, it was shown that regionsand sectors which experienced a larger drop in union power also underwent a bigger move towardsmore countercyclical productivity, and larger volatility of employment changes relative to outputvolatility.While Chapter 2 showed that increased labour market flexibility due to rapid de-unionizationcan explain the productivity puzzle, the quantitative importance of that channel remained unex-plored. This quantitative exercise was particularly revealing because simultaneous to the episodeof de-unionization and the productivity puzzle in the 1980s, there was a host of other significantstructural changes in the U.S. economy, and it is important to ascertain the relative explanatorypower of each of these for the productivity puzzle. Chapter 3 fills precisely this gap in our under-standing of the productivity puzzle. It showed through the lens of a New Keynesian model that thechange in monetary policy stance by the Federal Reserve, the rising importance of technology shockvis-a`-vis demand shock, the rising wage bargaining power of firms due to a decline in the power of91labour unions, or the reduced volatility of shocks during Great Moderation has little to no influencein explaining the productivity puzzle. On the other hand, allowing the cost of hiring workers to fallby 67% between the pre- and post-1984 periods to reflect an equivalent drop in private-sector unionmembership in the U.S., was shown to be able to capture almost the entire drop in procyclicalityof productivity and more than half of the rise in the relative volatility of employment fluctuations.Moving beyond the model, using a variety of industry-level datasets, it was shown that the rise ofthe service sector in both value-added and intermediate input use, the increased use of intangiblecapital, or the rising importance of sector-specific shocks vis-a`-vis aggregate economy-wide shockshave no robust explanatory power for the productivity puzzle.Chapter 4 studied how cross-sectional inequality in economic outcomes amongst any givengeneration of individuals get transferred to the next generation through intra-family linkages inlabour earnings, other income and consumption expenditure. We first argued that inequality inthe offspring’s generation is determined not only by the strength of intergenerational persistencebut also by the amount of inequality that prevailed in the parents’ generation to begin with. Wefound that most of the observed inequality emanates from idiosyncratic life-cycle risk independentof parental effects. This finding is crucially determined by a moderately low (but significant) valueof intergenerational persistence, which further implies that long-run inequality will not grow muchthrough the family channel with currently observed values of persistence. Moreover, the need tojointly estimate the income and consumption processes allowing for potentially non-zero covariancesbetween the two was also highlighted. 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(2007): “A non-Walrasian labor market in a monetary model of the business cycle,”Journal of Economic Dynamics and Control, 31, 2413–2437.103Appendix AAppendix to Chapter 2A.1 Robustness to Choice of Filters and DatasetsIn this section, I will present the cyclical correlations and volatilities of different variables usingdifferent datasets and time-series filters. In particular, the three datasets considered here areas follows: (i) Labor Productivity and Costs (LPC) dataset published by the Bureau of LaborStatistics (BLS) that contains both quarterly and annual data on output, hours, employmentand labour productivity for the U.S. business sector; (ii) John G. Fernald’s TFP dataset whichcontains quarterly and annual data on growth rates of TFP, factor utilization rate and utilization-adjusted TFP for the U.S. business sector; and (iii) KLEMS dataset (compiled by Jorgenson, Hoand Samuels) that contains annual data on ouput, hours, employment, labour productivity andgrowth rate of TFP for the aggregate U.S. economy.Table A.1: Cyclical Correlation of Average Labour Productivity (Output per Hour)With Output With Hours With EmploymentDataset & Filter Choice Pre 1983 Post 1984 Change Pre 1983 Post 1984 Change Pre 1983 Post 1984 ChangePanel A: LPC DataHodrick-Prescott (λ=1600) 0.61 -0.01 -0.62 0.15 -0.53 -0.68 0.05 -0.59 -0.64BK-Bandpass: 6-32 Qtrs. 0.56 -0.03 -0.59 0.12 -0.53 -0.65 0.01 -0.58 -0.59Quarterly Growth Rate 0.71 0.53 -0.18 0.02 -0.34 -0.36 -0.02 -0.33 -0.314-Quarter Growth Rate 0.63 0.23 -0.40 0.08 -0.37 -0.45 -0.04 -0.37 -0.34Annual Growth Rate 0.64 0.16 -0.48 0.12 -0.40 -0.52 -0.03 -0.40 -0.37Panel B: KLEMS DataHodrick-Prescott (λ=6.25) 0.35 -0.02 -0.37 -0.22 -0.62 -0.40 -0.28 -0.60 -0.32BK-Bandpass: 2-8 Years 0.42 0.32 -0.10 -0.17 -0.52 -0.35 -0.33 -0.42 -0.10Annual Growth Rate 0.53 0.22 -0.31 -0.10 -0.32 -0.22 -0.14 -0.24 -0.10Since the TFP data is only available in growth rates, I could only use quarterly and annualgrowth rates as the filter for the analysis involving TFP. Apart from growth rates, I have consideredtwo other time-series filters that are regularly used for extracting business cycle dynamics frommacro-data — (i) Hodrick and Prescott (1997) filter, with the smoothing parameter being 1600for quarterly data and 6.25 for annual data, following Ravn and Uhlig (2002), and (ii) bandpassfilter, extracting the dynamics between 6 and 32 quarters or between 2 and 8 years for quarterly orannual data respectively. To compare the two sub-periods — before and after the mid-1980s, I havepresented all the moments in Tables A.1 through A.3 separately, and also indicated the statisticalsignificance of the difference between the two sub-periods.Note that in these tables there are two choices for the bandpass filter — (i) the Baxter andKing (1999) (BK) filter, and (ii) the Christiano and Fitzgerald (2003) (CF) filter. I use the BK104filter for any analysis involving correlations. This is because the BK filter, unlike the CF filter,does not introduce any time- or frequency-dependent phase shift in the filtered data (see Iacobucciand Noullez (2005)). While using the CF filter might introduce spurious correlations in the filtereddata, the BK filter distorts the amplitude or volatility of the extracted cycle. This prompts me touse the CF filter for the analysis involving cyclical volatility.Table A.2: Cyclical Volatility of Output, Hours & Employments.d.(Output) s.d.(Hours) s.d.(Employment)Dataset & Filter Choice Pre-1983 Post-1984 PostPrePre-1983 Post-1984 PostPrePre-1983 Post-1984 PostPrePanel A: LPC DataHodrick-Prescott (λ=1600) 2.42 1.41 0.58 1.95 1.66 0.80 1.61 1.38 0.85CF-Bandpass: 6-32 Quarters 2.33 1.36 0.58 1.88 1.46 0.78 1.53 1.14 0.744-Quarter Growth Rate 0.94 0.59 0.63 0.71 0.60 0.85 0.60 0.50 0.84Panel B: KLEMS DataHodrick-Prescott (λ=6.25) 1.68 0.94 0.56 1.59 1.18 0.74 1.38 0.91 0.66CF-Bandpass: 2-8 Years 1.65 1.02 0.62 1.56 1.13 0.72 1.34 0.85 0.63Annual Growth Rate 2.73 1.89 0.69 2.28 1.91 0.84 1.99 1.63 0.82Table A.3: Relative Cyclical Volatility of Hours & Employments.d.(Hours)s.d.(Output)s.d.(Employment)s.d.(Output)s.d.(Employment)s.d.(Hours/Worker)Dataset & Filter Choice Pre-1983 Post-1984 PostPrePre-1983 Post-1984 PostPrePre-1983 Post-1984 PostPrePanel A: LPC DataHodrick-Prescott (λ=1600) 0.80 1.18 1.47 0.67 0.98 1.46 2.99 3.17 1.06CF-Bandpass: 6-32 Quarters 0.81 1.08 1.33 0.66 0.84 1.28 3.13 2.71 0.874-Quarter Growth Rate 0.76 1.02 1.35 0.64 0.85 1.34 2.82 3.14 1.11Panel B: KLEMS DataHodrick-Prescott (λ=6.25) 0.95 1.26 1.33 0.82 0.97 1.19 3.50 2.73 0.78CF-Bandpass: 2-8 Years 0.95 1.11 1.17 0.82 0.83 1.02 3.28 2.47 0.75Annual Growth Rate 0.83 1.01 1.22 0.73 0.86 1.19 3.24 3.47 1.07In Table A.4, I show that the vanishing procyclicality volatility reduction of factor utilizationrate is not unique to using the hours per worker proxy used in Fernald (2014). The CapacityUtilization Rate published by the Federal Reserve Board (FRB) based on the Quarterly Surveyof Plant Capacity (QSPC) by the Census Bureau paints a very similar story. The QSPC asksplants to report both their current production and their full production capacity, defined as “themaximum level of production that this establishment could reasonably expect to attain under normaland realistic operating conditions fully utilizing the machinery and equipment in place”. While hoursper worker and the capacity utilization survey measure very different quantities, the correlationbetween the growth rates of factor utilization and capacity utilization rates is 0.73.Table A.4: Reduction in Procyclicality and Volatility of Factor/Capacity Utilization RatesCorr. with Output Corr. with Hours VarianceUtilization Rates Pre 1983 Post 1984 Change Pre 1983 Post 1984 Change Pre 1983 Post 1984 ChangeFactor (Fernald) 0.73 0.49 - 0.24 0.67 0.52 - 0.15 11.67 1.64 -85.9%Capacity (FRB) 0.86 0.61 - 0.25 0.89 0.64 - 0.25 8.28 4.73 -42.9%105A.2 Evidence for De-unionization: A Difference-in-DifferenceStrategyI will use sectoral variation across U.S. industries to see if de-unionization caused labour productiv-ity correlation to fall. To argue for this causal channel, I follow a difference-in-difference regressionstrategy similar to Card (1992). I consider a very simple structural model that explains the fallin employment adjustment cost in industry i, ∆Costi, as a function of the fraction of workersunionized in the industry prior to mid-1980s, Unionprei , and the change in correlation of labourproductivity with hours worked, ∆Corr (lpi, hi), as a function of that change in cost:∆Costi = a+ bUnionprei + ei (A.1)∆Corr (lpi, hi) = α+ β∆Costi + εi (A.2)The above system of structural equations can be combined to a reduced-form correlation changeequation:∆Corr (lpi, hi) = (α+ aβ) + bβUnionprei + (βei + εi)=⇒ ∆Corr (lpi, hi) ≡ β0 + β1Unionprei + ηi (A.3)Equation (A.3) can be interpreted as showing the impact on productivity correlations in differentindustries which were differentially impacted by de-unionization. In other words, if one thinks of thefall in union rates around the early 1980s as the treatment, then the intensity of treatment variedacross industries according to the pre-intervention level of union densities in those industries. Inparticular, an industry with a higher pre-intervention level of union density should be impactedmore by the de-unionization treatment, thereby leading to a larger fall in productivity correlations.As an extreme example, an industry with no unionization to begin with will experience no impactof the de-unionization event. Running the regression in equation (A.3) across 17 U.S. industries, Ifind a significant positive effect of union density on the fall in productivity correlation, as shownin Figure A.1. In order to avoid small industries driving the correlation pattern, I weighted theobservations by the pre-1983 average industry employment level.Finally, replacing the change in productivity correlations by the change in the relative volatilityof employment in equation (A.3), I find that industries with a larger pre-1984 level of union densityexperienced a larger increase (or a smaller decrease) in the volatility of employment relative to thatof output and hours per worker. This is shown in Figure A.2.106R-squared = 0.18Slope = 0.02 [0.09]Post & CommunicationTransport & StorageUtilitiesEducationRetail TradePublic AdministrationDurable ManufacturingConstructionNon-durable Manuf.MiningHealthcareWholesale TradeReal EstateOther ServicesHotels & RestaurantsAgricultureFinance & Insurance-1-.50.51Change in Labour Productivity Correlation with Hours0 20 40 60% of Unionized Workers (1983-1984)Figure A.1: Difference-in-Difference Effect of Union Density on Productivity CorrelationNote: Data on industry-level unionization rates comes from the Current Population Survey (CPS), collected byHirsch and Macpherson (2003). Labour productivity is defined as real value added per hour worked. Data on value-added, hours and employment comes from KLEMS dataset. CPS industry codes for unionization and SIC industrycodes for labour productivity were matched to create a consistent set of 17 U.S. industries. The Baxter and King(1999) bandpass filter between 2 and 8 years have been used to de-trend the variables. Change in productivitycorrelations is the difference in correlation between the post-1984 period (1984-2003) and the pre-1983 period (1964-1983). Since industry-level union data is available only from 1983 onwards, I have used the 2-year average of 1983 and1984 values as the measure of pre-1984 level of union density. Size of the bubbles represent pre-1983 average industryemployment level. The p-value of the slope coefficient using robust standard errors is reported in parentheses.Retail TradeAgricultureOther ServicesTransport & StorageUtilitiesDurable ManufacturingNon-durable ManufacturingEducationPublic AdministrationMiningConstructionPost & CommunicationReal EstateHotes & RestaurantsHealthcareWholesale TradeFinanceSlope = -1.65 [0.07]-100-50050100% Change in Relative Volatility of Employment to Output0 20 40 60% of Unionized Workers (1983-1984)R-squared = 0.18Relative to Output VolatilityR-squared = 0.16Slope = -1.29 [0.09]Retail TradeAgricultureHotels & RestaurantsOther ServicesMiningFinance & InsuranceReal EstateHealthcareWholesale TradeConstructionUtilitiesTransport & StorageEducationPost & CommunicationPublic AdministationNon-durable Manuf.Durable Manufacturing-150-100-50050% Change in Relative Volatility of Employment to HPW0 20 40 60% of Unionized Workers (1983-1984)Relative to Hours Per Worker VolatilityFigure A.2: Difference-in-Difference Effect of Union Density on Relative Volatility of EmploymentNote: Data on industry-level unionization rates comes from the Current Population Survey (CPS), collected byHirsch and Macpherson (2003). Labour productivity is defined as real value added per hour worked. Data on value-added, hours and employment comes from KLEMS dataset. CPS industry codes for unionization and SIC industrycodes for labour productivity were matched to create a consistent set of 17 U.S. industries. The Baxter and King(1999) bandpass filter between 2 and 8 years have been used to de-trend the variables. Change in productivitycorrelations is the difference in correlation between the post-1984 period (1984-2003) and the pre-1983 period (1964-1983). Since industry-level union data is available only from 1983 onwards, I have used the 2-year average of 1983 and1984 values as the measure of pre-1984 level of union density. Size of the bubbles represent pre-1983 average industryemployment level. The p-value of the slope coefficient using robust standard errors is reported in parentheses.107A.3 Choice of SVAR SpecificationThe seminal paper of Gal´ı (1999) showed that labour input responds negatively to technologyshocks on impact. In Gal´ı’s Vector Auto-Regression (VAR) specification, technology shocks wereidentified as the only shock that could change productivity in the long run.87 Since this findingwas at odds with the standard wisdom of a real business cycle model where technology shocks arepositively correlated with both output and hours input, a lot of criticism was generated againstthis finding.The main criticism of Gal´ı’s finding was that it was not robust to how the variables in the VAR,particularly the measure of labour input, were filtered.88Christiano, Eichenbaum, and Vigfusson(2003) show that filtering the measure of labour inputs by taking its growth rate generates thespurious negative impulse response of per capita hours to a positive technology shock. They arguethat per capita hours worked cannot be a non-stationary process, and hence differencing an alreadystationary time series creates the spurious negative correlation. In fact, when per capita hoursenters the SVAR in levels, instead of growth rates, technology shocks indeed become positivelycorrelated with hours. Nevertheless, it has since been argued that not controlling for low-frequencymovements in the labour input might introduce spurious correlations with productivity growth. Ahost of new VAR estimation techniques, like Threshold VAR by Ferraresi, Roventini, and Semmler(2016), and Bayesian estimation of Fractionally Integrated VAR by Doppelt and O’Hara (2018)— all corroborate that after controlling for low-frequency movements, hours per capita respondsnegatively to a technology shock on impact.I will use the technique in Gal´ı and Gambetti (2009) to control for the low-frequency movementsin per capita hours worked, and use the same identifying assumption as in Gal´ı (1999). Gal´ı andGambetti (2009) use a VAR model with time-varying coefficients and stochastic volatility of theinnovations. Defining xt ≡ [∆ (yt − nt) , nt], where yt and nt denote the (log) output and (log)hours in per capita terms, the reduced form VAR can be written as:xt = A0,t +A1,txt−1 +A2,txt−2 + ...+Ap,txt−p + ut (A.4)where A0,t is a vector of time-varying intercepts, Ai,t, i = 1, ..., p are matrices of time-varying coef-ficients, and the sequence of innovations {ut} follows a Gaussian white noise process (uncorrelatedwith all lages of xt) with zero mean and time-varying covariance matrix. Crucially, the presence of a87In a two-variable SVAR with productivity growth and per capita hours, the identifying assumption implies thatthe long run coefficient matrix is lower triangular, that is,(∆ (yt − nt)nt)=(C11(L) 0C21(L) C22(L))(εatενt), whereεat is the technology shock, and ενt is the non-technology or demand shock.88There were other criticisms as well. For example, Chang and Hong (2006) argue that TFP should be used insteadof labour productivity as the measure of productivity in the VAR to properly identify technological shocks. I havecompared the results obtained by using both these measures of productivity in details. Chari, Kehoe, and McGrattan(2008) argue that the use of long run restrictions in structural VAR to identify shocks, like Gal´ı’s identificationargument, is not helpful for developing business cycle theories in general. However, Francis, Owyang, Rousch,and DiCecio (2014) provide a flexible finite-horizon alternative to the long run restrictions, and corroborate Gal´ı’sconclusions.108time-varying intercept in equation A.4 absorbs the low-frequency co-movement between productiv-ity growth and per capita hours, thereby overcoming potential distortions in the VAR estimation.There are two main advantages of this specification: first, it allows one to control for low-frequencymovements in per capita hours without having to extract the cyclical component of hours throughany form of ad hoc time series filtering, and second, it allows one to know the complete dynamics ofthe impulse responses over the years so that it can be pin-pointed as to exactly when the responsesbegan to change. Nonetheless, this method of controlling for the low-frequency movements in percapita hours also generates a negative response of hours to a positive technology shock.As an alterantive to VAR specifications, which require strong identifying assumptions, I presentan alternative methodology, a` la Jorda (2005), of estimating the impulse response of hours tochanges in utilization-adjusted TFP. For this projection-type analysis, I run the regression specifi-cation used by Ramey (2016):ln (hourst/popt) = αh + βh∆ ln (uatfpt) + θh (L)Xt−1 + εt+h (A.5)βh: Response of hours at time t+ h to a technology shock at time t.Xt−1: One-period lagged values of growth rate of utilization-adjusted TFP (uatfp), log per capitahours, log real GDP per capita, log labour productivity, and log real stock prices per capita.εt+h is serially correlated, and so standard errors incorporate Newey-West correction.1984-20171950-1983-.20.2.4Impulse Response of Per Capita Hours0 5 10 15 20PeriodsFigure A.3: IRF of Per Capita Hours to Utilization-Adjusted TFP ShockNote: The solid blue and red lines are the impulse responses of per capita hours to one percent rise in utilization-adjusted TFP in the pre-1983 and post-1984 periods respectively. The corresponding dashed and dotted lines are the90 percent confidence intervals for the impulse responses. All data for the regression come from Ramey (2016).This methodology of a simple regression model with the shock being the explanatory variablenot only shows the negative correlation of hours and technology shock but also that the negativeresponse of hours became muted after the mid-1980s (see Figure A.3.)109A.4 Impulse Response Functions from Time-Varying SVARs-0.8-0.6-0.4-0.200.250.4101960197015 19801990200020 2010(a) Technology Shock: Hours00.5151.510 1960197015 198019902000201020(d) Demand Shock: Hours0.50.60.70.850.9110196015 197019801990200020 2010(b) Technology Shock: Labour Productivity-0.4-0.200.20.450.6101960197015 198019902000201020(e) Demand Shock: Labour Productivity-0.4-0.200.20.40.60.851101960197015 19801990200020 2010(c) Technology Shock: Output00.55119601.510 1970198015 19902000201020(f) Demand Shock: OutputFigure A.4: Dynamic Impulse Responses to Technology & Demand Shocks (LP, Hours & Output)Note: Impulse Response Functions (IRF’s) of per-capita hours, labour productivity and per-capita output from a2-variable (viz., labour productivity growth and per-capita hours) time-varying long-run SVAR. Data is sourced fromthe BLS-LPC quarterly dataset for the U.S. business sector.1102 4 6 8 10 12 14 16 18 20-0.200.20.40.60.811.2(a) Technology Shock: Hours2 4 6 8 10 12 14 16 18 20-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.4(d) Demand Shock: Hours2 4 6 8 10 12 14 16 18 20-0.5-0.4-0.3-0.2-0.100.10.2(b) Technology Shock: Labour Productivity2 4 6 8 10 12 14 16 18 20-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1(e) Demand Shock: Labour Productivity2 4 6 8 10 12 14 16 18 20-0.500.51(c) Technology Shock: Output2 4 6 8 10 12 14 16 18 20-1.2-1-0.8-0.6-0.4-0.200.2(f) Demand Shock: OutputFigure A.5: Difference in Impulse Responses between Pre- & Post-1984 (LP, Hours & Output)Note: Post-1984 impulse response minus pre-1984 impulse response of per-capita hours, labour productivity andper-capita output from a 2-variable (viz., labour productivity growth and per-capita hours) time-varying long-runSVAR. The solid line is the difference in the impulse responses between pre- and post-1984 periods. The dottedand dashed lines are the 95% and 90% confidence intervals of the difference respectively. Data is sourced from theBLS-LPC quarterly dataset for the U.S. business sector.111-1.2-1-0.8-0.6-0.45-0.200.21015196019701980199020 20002010(a) Technology Shock: Hours00.20.40.60.8511.21.410196015 197019801990200020 2010(c) Demand Shock: Hours-0.200.250.40.6100.8196015 197019801990200020 2010(b) Technology Shock: TFP00.250.40.610196015 197019801990200020 2010(d) Demand Shock: TFPFigure A.6: Dynamic Impulse Responses to Technology & Demand Shocks (TFP & Hours)Note: Impulse Response Functions (IRF’s) of per-capita hours and TFP from a 2-variable (viz., TFP growth andper-capita hours) time-varying long-run SVAR. Hours data is sourced from the BLS-LPC quarterly dataset, TFPdata is sourced from Fernald’s quarterly TFP series, and quarterly civilian non-institutional population (16 years ofage and older residing in the 51 U.S. states, who are not inmates of institutions, e.g., penal and mental facilities,homes for the aged, etc.) data is from the Employment Situation release of the BLS. All data correspond to the U.S.business sector.1122 4 6 8 10 12 14 16 18 20-0.5-0.4-0.3-0.2-0.10(a) Technology Shock: Hours2 4 6 8 10 12 14 16 18 200.10.20.30.40.50.60.70.80.91(c) Demand Shock: Hours2 4 6 8 10 12 14 16 18 200.30.350.40.450.50.550.60.650.70.750.8(b) Technology Shock: TFP2 4 6 8 10 12 14 16 18 200.10.20.30.40.50.6(d) Demand Shock: TFPFigure A.7: Empirical Impulse Responses to Technology & Demand Shocks (TFP & Hours)Note: Impluse Response Functions (IRF) for the pre-1984 period (1956-1983) are in blue, and the post-1984 (1984-2017) IRF’s are in red dashed lines. Hours data is sourced from the BLS-LPC quarterly dataset, both types of TFPdata are sourced from Fernald’s quarterly series, and quarterly civilian non-institutional population (16 years of ageand older residing in the 51 U.S. states, who are not inmates of institutions, e.g., penal and mental facilities, homesfor the aged, etc.) data is from the Employment Situation release of the BLS. All data correspond to the U.S. businesssector.1132 4 6 8 10 12 14 16 18 20-0.200.20.40.60.81(a) Technology Shock: Hours2 4 6 8 10 12 14 16 18 20-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5(c) Demand Shock: Hours2 4 6 8 10 12 14 16 18 20-0.2-0.100.10.20.30.40.50.6(b) Technology Shock: TFP2 4 6 8 10 12 14 16 18 20-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.2(d) Demand Shock: TFPFigure A.8: Difference in Impulse Responses between Pre- & Post-1984 (TFP & Hours)Note: Post-1984 impulse response minus pre-1984 impulse response of per-capita hours and TFP from a 2-variable(viz., TFP growth and per-capita hours) time-varying long-run SVAR. The solid line is the difference in the impulseresponses between pre- and post-1984 periods. The dotted and dashed lines are the 95% and 90% confidence intervalsof the difference respectively. Hours data is sourced from the BLS-LPC quarterly dataset, TFP data is sourced fromFernald’s quarterly TFP series, and quarterly civilian non-institutional population (16 years of age and older residingin the 51 U.S. states, who are not inmates of institutions, e.g., penal and mental facilities, homes for the aged, etc.)data is from the Employment Situation release of the BLS. All data correspond to the U.S. business sector.114Appendix BAppendix to Chapter 3B.1 System of Log-Linearized EquationsLog-linearizing the model around a zero-inflation ( p¯ = 0) steady-state with unit effort(E¯ = 1)andemployment rate, N¯ = 0.62, I get the following equations in log-deviation form, where the notationxˆt is used to denote the deviation of logarithm of the variable Xt from its logged steady-state valuex¯.yˆt = (1−Θ) cˆt + Θ(hˆt + gˆt)(B.1)yˆt = at + (1− α) (nˆt + ψeˆt) (B.2)nˆt = (1− δ) nˆt−1 + δhˆt (B.3)gˆt = γhˆt (B.4)cˆt = Et (cˆt+1)− rˆt (B.5)rˆt = iˆt − Et(pipt+1)(B.6)pipt = βEt(pipt+1)− λpµˆpt (B.7)µˆpt = (yˆt − nˆt)−[(1− Φ) ωˆt + Φbˆt](B.8)bˆt =11− β (1− δ) gˆt −β (1− δ)1− β (1− δ) [Et (gˆt+1)− rˆt] (B.9)m̂rst = κcˆt + (1− κ)[(yˆt − nˆt − µˆpt ) +ι1− ι (ωˆt + nˆt − cˆt)](B.10)ωˆt = ωˆt−1 + piwt − pipt (B.11)piwt = β (1− δ)Et(piwt+1)− λw (ωˆt − ωˆtargett ) (B.12)ωˆtargett = Υm̂rst + (1−Υ) (yˆt − nˆt − µˆpt ) (B.13)iˆt = ρˆit−1 + (1− ρ) (φpipipt + φyyˆt) + φ∆y∆yˆt + νt (B.14)eˆt =11 + φ(yˆt − nˆt − µˆpt − cˆt) (B.15)at = ρaat−1 + εat (B.16)νt = ρννt−1 + ενt (B.17)where Θ =Γ(δN¯)1+γY¯, Φ = B¯B¯+ W¯P¯, κ =(χ1+ζ).(C¯MRS), ι =(1+φ1+φ−ψ).(W¯ N¯P¯ C¯), Υ = ξ(MRSW¯P¯),λw =(1−θw)(1−βθw(1−δ))θw[1−(1−Υ)(1−Φ)] , and ωˆt = wˆt − pˆt. The parameters ζ and χ are calibrated to satisfy unit115effort in the steady-state (E¯ = 1) in a frictionless (no hiring cost) labour market. Furthermore, Itake W¯ N¯P¯ C¯= 1−α1−Θ .B.2 Cyclical Moments of Capital and Factor UtilizationThe model does not feature capital, rather includes only employment and effort. Since labour effortis not directly measurable in the data, one concern is that whatever is being labelled as ‘effort’in the model is essentially capital, the missing factor of production. Therefore, it is important todistinguish between the business cycle dynamics of effort and capital. Using factor utilization rateas an empirically measurable proxy for effort, I show below how the cyclical moments of factorutilization in the data is qualitatively consistent with those of effort in the model, and they aredifferent from those of capital.-.4-.20.2.4Corr. (Output, Capital)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(a) Corr.(Output,Capital).3.4.5.6.7.8Corr. (Output, Utilization)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(b) Corr.(Output,Utilization)-.20.2.4.6Corr. (Hours, Capital)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(c) Corr.(Hours,Capital).4.5.6.7.8Corr. (Hours, Utilization)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year(d) Corr.(Hours,Utilization)Figure B.1: Cyclical Correlations of Capital and Factor UtilizationNote: Data on quarterly growth rates of capital input, factor utilization, output and hours worked for the U.S.business sector are sourced from Fernald (2014). A centred rolling window of 15 years is used to calculate the secondmoments. Findings are robust to alternative choice of filters and window-sizes.Looking at Panels (b) and (d) in Figure B.1, one can see that exactly around the time when pro-ductivity started losing its procyclicality, factor utilization also became more countercyclical. This116fact was already presented in Table 2.1, where it was shown that the fall in aggregate TFP corre-lations with output and hours worked was driven by the reduced procyclicality of factor utilizationand not utilization-adjusted TFP. However, it is immediately clear from the cyclical correlations ofcapital in Panels (a) and (c) of Figure B.1 that capital became more procyclical around the mid-1980s unlike factor utilization. Now, if the model implied correlations of effort with output andemployment matches with those of factor utilization in the data then it can be argued that the roleplayed by effort in the model is not the same as that of capital. Under the baseline calibration ofthe model (corresponding to column (4) of Table 3.3), correlation of effort with labour productivityfell by 0.37, which is qualitatively similar to that of factor utilization..1.2.3.4.5.6S.D.(Capital)/S.D.(Output)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Years.d.(Capital)s.d.(Output)0.2.4.6.8SD.(Capital)/S.D.(Utilization)1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Years.d.(Capital)s.d.(Utilization)Figure B.2: Relative Volatility of Capital over the Business Cycle (1954-2010)Note: Data on quarterly growth rates of capital input, factor utilization and output for the U.S. business sector aresourced from Fernald (2014). A centred rolling window of 15 years is used to calculate the second moments. Findingsare robust to alternative choice of filters and window-sizes.The volatility of capital relative to that of output and factor utilization rises sharply since themid-1980s. It has already been shown that the relative volatility of employment has similarly rose.This further shows that the reliance on extensive margin of factor adjustment, for both labourand capital, has increased relative to the intensive margin of factor utilization. The model alsopredicts a substantial increase in the relative volatility of employment with respect to effort. Allthis evidence shows that the role of effort in the model is different from that of capital.117B.3 Volatility of Monetary Policy Shock0.511.55-Year Rolling Std. Dev. of Romer-Romer Shock1970 1980 1990 2000Year1971-2005.2.3.4.5.6.75-Year Rolling Std. Dev. of Romer-Romer Shock1970 1980 1990 2000Year1971-1977, 1984-2005Figure B.3: 5-Year Rolling Standard Deviation of Romer-Romer Monetary ShockNote: Ignoring the sudden jump in volatility in the monetary policy shock between 1977 and 1982 as seen in Panel(a), the average standard deviation in the 1984-2005 period is roughly half of the average standard deviation during1971-1977, as shown in Panel (b). Data for the Romer and Romer (2004) type monetary shock is sourced from Ramey(2016).B.4 Data on Intellectual Property ProductsI use the current-cost net capital stock of private non-residential fixed assets published by theBureau of Economic Analysis (BEA) at the industry-level from 1947 through 2016. The data isdisaggregated by asset type according to the classification by the National Income and ProductAccounts (NIPA) — there are three major categories, namely, (i) equipment, with 39 sub-types, (ii)structures, with 32 sub-types, and (iii) intellectual property products (IPP), with 25 sub-types. TheBEA typically does not include detailed estimates of different types of capital assets by industry inthe tables published in the Survey of Current Business or the Fixed Assets and Consumer Durablesvolume because their quality is significantly lower than that of the higher level aggregates in whichthey are included. Compared to these aggregates, the detailed estimates are more likely to be eitherbased on judgemental trends, on trends in the higher level aggregate, or on less reliable source data.Keeping this issue of data quality in mind, I will only use the share of aggregate IPP in total assetstock at the level of 24 U.S. industries. Below I present the time trend of the share of IPP in thetotal non-residential capital stock at current prices for the aggregate U.S. economy.118.06.08.1.12Share of IPP Capital in Total Asset1960 1970 1980 1990 2000 2010 2020YearFigure B.4: Share of IPP in Total Non-Residential Capital Stock in the U.S. (1960-2016)In order to give a clearer picture of what are the assets included under IPP, I provide below thecomplete list of NIPA asset-types that are categorized under IPP capital —A. Software: Prepackaged, custom, and own account softwareB. Research & Development : Pharmaceutical and medicine, other chemicals, semiconductor andother components, computers and peripheral equipment, communications equipment, navigationaland other instruments, other computer and electronics, motor vehicles and parts, aerospace prod-ucts and parts, and other manufacturing, scientific R&D services, software publishers, financial andreal estate services, computer systems design and related services, all other non-manufacturing, pri-vate universities and colleges, and other non-profit institutions.C. Artistic Originals: Theatrical movies, long-lived television programs, books, music, and otherentertainment originals.B.5 Relative Importance of Sector-Specific ShocksModel:Xi,t = λiFt + εi,tXi,t: Observed growth rate of value added output or labour input for sector i at time tFt: Principal component of sectoral growth rates common to all sectors at time tεi,t: Sector-specific growth rate for sector i at time tEstimation:Variance-covariance matrix of Xi,t, V ≡ ΓΛΓ′ (Eigenvalue-Eigenvector Decomposition)Ft = Xi,tΓ1, where Γ1 is the first eigenvector in Γ whose columns are sorted according to theordering of the eigenvalues in Λ. The variance of Ft is interpreted as the aggregate economy-widevolatility (indicated as ‘Common’ in Tables B.1 and B.2), while that of εi,t is the ‘Sectoral’ variance.119Table B.1: Components of Variance of Value Added Output GrowthPre-1983 Post-1984Dataset Common Sectoral Common SectoralBEA: 13 Sectors 92.93% 7.07% 68.30% 31.70%KLEMS: 10 Sectors 48.14% 51.86% 4.42% 95.58%KLEMS: 31 Sectors 17.96% 82.04% 5.15% 94.85%IIP: 8 Sectors 94.98% 5.02% 87.21% 12.79%IIP: 12 Sectors 70.89% 29.11% 31.49% 68.61%IIP: 20 Sectors 30.63% 69.37% 42.18% 57.82%Table B.2: Components of Variance of Labour Input GrowthPre-1983 Post-1984Dataset Common Sectoral Common SectoralCES: 14 Sectors 68.64% 31.36% 44.85% 55.15%BEA: 13 Sectors 92.31% 7.69% 74.61% 25.39%KLEMS: 10 Sectors 78.28% 21.72% 50.87% 49.13%KLEMS: 31 Sectors 89.36% 10.64% 91.14% 8.86%It should be noted that most of the rise in the relative importance of sector-specific variance wasdue to the drop in the variance of the common component, while the sectoral component remainedlargely constant between the pre and post-1984 periods. In other words, one can conclude thatthe drop in variance of output and labour inputs during the Great Moderation was mostly due tofalling volatility of the aggregate shocks rather than sectoral ones. However, this is not true whena 31-industry-split is considered — both the common and sectoral variances decline in that case.120Appendix CAppendix to Chapter 4C.1 Derivation of the Consumption ProcessIn this appendix we derive the analytical approximation of the optimal consumption processes.Assuming a quadratic utility function and β(1 + r) = 1, we solve the maximization problem (4.5)and derive consumption at time t as the annuity value of lifetime resources, as follows:Cf,t =r(1 + r)− (1 + r)−(T−t)Af,t + T−t∑j=0(11 + r)jEt (Ef,t+j) +T−t∑j=0(11 + r)jEt (Nf,t+j)To express consumption expenditure in terms of logs, we use a first order Taylor series approx-imation of the logarithm of each variable around unity. For any variable x, ln(x) ' ln(1) + x−11 =x−1.89 Using this approximate relationship x ' 1+ln(x), and denoting ln (Cf,t), ln (Af,t), ln (Ef,t)and ln (Nf,t) by cf,t, af,t, ef,t and nf,t respectively, and using the time-series processes we assumedfor af,t, ef,t and nf,t, we get,1 + cf,t ' (1 + e¯f ) + (1 + n¯f ) +r(1+r)−(1+r)−(T−t)(1 + af,t) +T−t∑j=0(11 + r)jEt (ζf,t+j) +T−t∑j=0(11 + r)jEt (uf,t+j)=⇒ cf,t ' 1 + r(1 + r)− (1 + r)−(T−t) [(1 + af,t) + (ζf,t + uf,t)] + e¯f + n¯fLet qf,t ≡ 1 + αt (r) (1 + af,t), with αt (r) = r(1+r)−(1+r)−(T−t) . Then we can write the approxi-mate log-consumption processes for an individual as:cf,t = qf,t + e¯f + n¯f + αt (r) (ζf,t + uf,t)For a large enough T relative to t, αt(r) can be approximated by α(r) =r1+r . Thus, forindividuals who are sufficiently away from their demise, we can approximate their log-consumption89This approximation holds only for values of x close to unity. Since in the empirical implementation of the model,we de-mean all the log variables (lnx), this approximation is valid.121as:cf,t = qf,t + e¯f + n¯f + α (r) (ζf,t + uf,t) (C.1)C.1.1 CRRA Utility FunctionRelaxing the assumption of a quadratic utility function, we can still arrive at the same log-consumption equation as (C.1) with a more general utility function, after a linear approximationof the Euler equation. For example, in the case of constant relative risk aversion (CRRA) utilityfunction, the Euler equation is given by C−τf,t = β (1 + r)Et(C−τf,t+1), where τ > 0 is the parametercapturing the degree of risk aversion as also the intertemporal elasticity of substitution. Maintain-ing the assumption β (1 + r) = 1, we get from the Euler equation Et[(Cf,t+1Cf,t)−τ]= 1. We definethe function h (gc) = (1 + gc)−τ , where gc =Cf,t+1Cf,t− 1 such that Et [h (gc)] = 1. A first orderTaylor series expansion of h (gc) around g∗c = 0 yields h (gc) ≈ 1 − τgc. Taking expectations onboth sides of this approximate equation, we get Et (gc) = 0, implying Cf,t = Et (Cf,t+1). This isexactly the same as the Euler equation that one obtains from quadratic utility function withoutany approximation. Now, since we did not derive explicitly the consumption expression from thisEuler equation in the paper, we provide the derivation here. Iterating forward the per-period bud-get constraint Af,t+1 = (1 + r) (Af,t + Yf,t − Cf,t) (where Yf,t = Ef,t + Nf,t) by one period andcombining it with the Euler equation Cf,t = Et (Cf,t+1), we get,(1 +11 + r)Cf,t = Af,t −(11 + r)2Et (Af,t+2) +[Yf,t +11 + rEt (Yf,t+1)]...⇒[1 +11 + r+(11 + r)2+ ...∞]Cf,t = Af,t − limk→∞(11 + r)kEt (Af,t+k) +∞∑j=0(11 + r)jEt (Yf,t+j)=⇒[1 + rr]Cf,t = Af,t +∞∑j=0(11 + r)jEt (Yf,t+j)=⇒ Cf,t = r1 + rAf,t + ∞∑j=0(11 + r)jEt (Yf,t+j)Note that in the above derivation we have assumed the No-Ponzi condition that prevents an individ-ual from continuously borrowing and rolling over his debt to future periods, limk→∞(11+r)kEt (Af,t+k) =0.122C.2 Data and SamplingThe Panel Study of Income Dynamics (PSID) is administered by the University of Michigan’sSurvey Research Center (SRC). This longitudinal survey began in 1968 with a national probabilitysample of almost 5,000 U.S. families. The sampled families were re-interviewed annually between1968 and 1997. After 1997 they were re-interviewed biennially. We focus our study only on the non-Latino, non-immigrant households within the SRC component of the PSID, and exclude those inthe Survey of Economic Opportunity (SEO) component where poor households were over-sampled.PSID data have been used by different authors for intergenerational analyses because, by design,this survey follows the children of original sample members when they become independent fromtheir original family. This allows to follow children from the original sample as they grow intoadulthood and become household heads themselves. To reduce noise due to weak labour marketparticipation and marital status, our main analysis for household heads focuses on observationsfor married male individuals between 25 and 65 years of age, who have at least 5 years of datain the PSID, have non-negative labour earnings and total family income, work for less than 5840hours annually, have wages greater than half of the federal minimum wage, and do not have annualearnings growth rates of more than 400 percent. Our analysis pertains to children born between1952 and 1981. To avoid over-representation of children who left their homes at a later stage of theirlives, the sample excludes children born before 1952 (that is, those children who were older than16 at the time of the first 1968 PSID interview). The first year in which child income is observedis 1977 (as reported in the 1978 interview) - the year in which the 1952 birth-cohort reached age25. Consequently, we can observe the 1952 cohort between ages 25 and 62, while the 1981 cohortcan only be observed between ages 25 and 33 years. Parents who are older than 65 are droppedfrom the analysis to avoid complications related to retirement decisions. In robustness checks, weconsider various alternative samples, e.g., restrict age range from 30 to 40 years for both parentsand children, and look at different cohorts of children separately. Our model estimates remainqualitatively similar under all these alternative samples.The labour earnings data for the male household head and his wife, and the total transferincome data for the couple are readily available for most survey rounds of the PSID. In contrast,the family consumption data is quite sparse across the survey years and not presented as a singlevariable in the PSID. Different consumption expenditure categories have to be suitably summedup (using appropriate weights depending on the frequency of consumption in a particular category,e.g., yearly, monthly, weekly, etc.) to arrive at an aggregate measure of consumption expenditure.There are 11 major categories of consumption variables, namely, (i) food, (ii) housing, (iii) child-care, (iv) education, (v) transportation, (vi) healthcare, (vii) recreation and entertainment, (viii)trips and vacation, (ix) clothing and apparel, (x) home repairs and maintenance, and (xi) householdfurnishings and equipment. Of these, food and housing are most consistently observed across theyears - expenditure on food is observed from the 1968 interview through the 2015 interview, barringonly 1973, 1988 and 1989. Housing expenditure is observed in all years except 1978, 1988 and 1989.Child-care expenditure data is available for 25 rounds of interview - 1970-1972 (3 interview years),1231976, 1977, 1979 and 1988-2015 (19 interview years). Education, transportation and health-careare only reported by the last 9 PSID interviews (biennially from 1999 through 2015). The rest ofthe categories from (vii) through (xi) are observed for only the last 6 interviews (biennially from2005 to 2015).The uneven availability of expenditure categories in different waves of the PSID suggests that asimple sum of the expenditure categories for different years would not provide an accurate approx-imation of total consumption because every year reports different subsets of consumption expendi-tures. There are two ways to account for this problem in the calculation of the total consumptionvariable: either take the measure of consumption to be equal to just the expenditure on food, themost consistently observed category (although that would ignore variation in the consumption ofnon-durable goods other than food); or impute the consumption of the missing categories.C.2.1 Imputation of Consumption Expenditure DataTo assess the quality of consumption survey data, Andreski, Li, Samancioglu, and Schoeni (2014)compare expenditure data from the Consumption Expenditure Survey (CEX) and the PSID. Theyfind that expenditures in individual categories of consumption may vary non-trivially across thetwo datasets, e.g., reported home repairs and maintenance expenditures are approximately twiceas large in the PSID as the are in the CEX, and the PSID home insurance expenditures are 40to 50 percent higher than their CEX counterparts. However, despite these inconsistencies withinindividual categories (due to differences in survey methodologies and sampling techniques), Li,Schoeni, Danziger, and Charles (2010) show that the average expenditure since 1999 in PSID andCEX have been fairly close to each other. Moreover, the consumption expenditures in the twodatasets vary in a similar way with observable household characteristics like age of household head,household size, educational attainment, marital status, race and home ownership. This averageconsistency between PSID and CEX data, as well as the fact that total consumption seems to beclose to the aggregate consumption estimates in the NIPA (National Income and Product Accounts)data, suggests that PSID expenditure data can be used to draw information about householdsconsumption behavior.Attanasio and Pistaferri (2014) (henceforth AP) suggest to impute consumption data for themissing consumption categories in the PSID before 1999 by using the more detailed data availablepost-1999. Their backward extrapolation is consistent with theories of consumer demand in thesense that the allocation of total resources spent in a given period over different commodities is madedependent on relative prices and taste-shifters, e.g., demographic and socio-economic variables.However, this specification implicitly assumes homotheticity of consumer preferences over differentcommodities. To relax that assumption, we include log total income in the imputation regressionas a control. We use this slightly modified approximated demand system to total consumptionexpenditures before 1999:ln (Nft) = Z′ftω + p′tpi + g(Fft;λ) + uft, (C.2)124where N is consumption net of food expenditure, Z are the socioeconomic controls (viz., dummiesfor age, education, marital status, race, state of residence, employment status, self-employment,head’s hours worked, homeownership, disability, family size, and the number of children in thehousehold) and total family income, p are the relative prices (the overall CPI and the CPIs for foodat home, food away from home, and rent), F is the total food expenditure (i.e., sum of food athome, food away from home, and food stamps) that is observed in the PSID consistently throughthe years, g(.) is a polynomial function, and u is the error term. The subscripts f and t denotesfamily identity and year respectively. This equation is estimated using data from the 1999-2015PSID waves, where the net consumption measure Nft is the sum of annualized expenditures onhome insurance, electricity, heating, water, other miscellaneous utilities, car insurance, car repairs,gasoline, parking, bus fares, taxi fares, other transportation, school tuition, other school expenses,child care, health insurance, out-of-pocket health, and rent. While performing the imputation weskip the consumption expenditure categories that were added to the PSID from the 2005 wave.This is done to keep the measure of consumption consistent over the years and to also maximizethe number of categories that can be used. Moreover, the categories added from the 2005 wave col-lectively constitute a very small fraction of total consumption. In the definition of net consumptionwe have excluded food expenditure to avoid endogeneity issues in the regression. The measure forrent equals the actual annual rent payments for renters and is imputed to 6% of the self-reportedhouse value (Flavin and Yamashita (2002)) for the homeowners.After estimating the logarithm of the net consumption equation by running a pooled OLSregression on equation (C.2), we construct a measure of imputed total consumption as followsCˆft = Fft + exp{Z ′ftωˆ + p′tpˆi + g(Fft; λˆ)}. (C.3)This measure is corrected for inflation by dividing it by the overall CPI. Finally the measure istransformed into adult-equivalent values using the OECD scale, (1 + 0.7(A− 1) + 0.5K), where Ais the number of adults and K the number of children in the household unit.A key question is how well the imputed consumption values match with the observed valuesduring the period when both data series are available. A natural choice for a measure of thegoodness of fit is the R2 of the regression (C.2), which is found to be 0.47. However, what we arereally interested in is matching the standard deviations of the observed and imputed series becausewe would be using only the second order moments of income and consumption for estimatingour model in Section 4.2. Like AP, we find that our imputed consumption series can match theobserved series quite closely in terms of standard deviation, and similarly well for a more generalnon-linear measure like the Gini coefficient. Figure C.1 presents the Gini coefficients (normalizedto their initial values in 2006) of the logs of imputed and actual consumption (in Panel C), and alsocompares the standard deviations of actual and imputed consumption with those of real incomeand labour earnings (in Panels A, B, and D). The top-coded values for total family income andthe household heads’ labour earnings in the PSID are replaced with the estimates obtained fromfitting a Pareto distribution to the upper tail of the corresponding distribution.125-.08-.06-.04-.020.02.041998 2000 2002 2004 2006 2008 2010 2012 2014 2016 SD log imputed consumptionSD log actual consumptionPanel A-.1-.050.051965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 SD log imputed consumptionSD log actual consumptionPanel B-.08-.06-.04-.020.021965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Gini, imputed consumption Gini, actual consumptionPanel C.3.4.5.6.7.81965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Predicted SD log consumption SD log actual consumptionSD log total incomeSD log labour earningsPanel DFigure C.1: Quality Assessment of Consumption ImputationNote: In Panels A, B and C, series are normalized to values in 2006 for ease of comparison.C.3 Intergenerational Persistence: Reduced-Form EvidenceIn this appendix, we present some reduced form evidence of the time trends and cross-sectionalheterogeneity of intergenerational persistence in earnings, as common in the literature, and alsoconsumption, which is more closely tied to welfare.C.3.1 The Evolution of Intergenerational ElasticitiesA natural way to measure the impact of parental economic circumstances on a child’s adult out-comes is to estimate the intergenerational elasticity of such outcomes. By definition, this elasticitymeasures the percentage change in the child’s variable following one percentage change in the cor-responding parental variable, and is obtained by regressing a logged measure of the child’s variableon its parental counterpart.We are interested in knowing the persistence in permanent earnings and consumption, but wedo not directly observe the long-term (permanent) earnings and consumption of any individual. Anadult child’s earnings are observed only over a limited range of ages. Hence we must proxy these life-cycle variables by some function of the current (yearly) variables that are actually observable.90 As90A simpler way of dealing with this issue is to take into account the relevant variable at a particular age (say 30)126in Lee and Solon (2009) we use adult children’s data for all the available years, along with a full setof age controls. We centre the child’s age around 40 years to minimise the bias from heterogeneityin growth rates, and interpret the estimated intergenerational elasticity as an average value assuccessive cohorts of children pass through age 40.91 In fact, these intergenerational elasticitiesat age 40 (for a given year) can be interpreted as an asymmetrical moving average of the cohort-specific elasticities for the cohorts of adult children who are observed for that particular year. It isasymmetrical because the older cohorts weigh more in a particular year’s estimate owing to the factthat cohorts enter as they turn 25 years of age but never leave till the end of the PSID dataset.92We also need to use a suitable proxy for the long-run parental variable serving as the principalregressor. Using the current measure of the parental variable would introduce an attenuation biasin the estimation of the long-term intergenerational elasticity of the child’s variable. As in Leeand Solon (2009), we use the average log annual value of the parental variable over the years whenthe child was between age 15 and 17 as a proxy for the long-run value of the parent’s process.We choose 15 years as the starting child age for a parental observation because our focus is onhow parental circumstances in the formative years affects outcomes.93 An alternative would havebeen to take the average of the parental variable (earnings or consumption) for the parents’ entirelifetime (till 65 years of age). This would confound a number of effects, in particular, the effect ofparental outcomes when children are at home with realisations of parental outcomes after childrenleft home. The latter contemporaneous pass-through may be important for consumption smoothingacross generations, but conceptually it is a different mechanism. A further issue with using theaverage over the entire lifetime is that this would impose that siblings born at different life-stagesof the parent face the same parental inputs. Obviously, the age of the parents of different childrenborn in a particular cohort will not be the same when the children reach the age range between 15and 17. Therefore, we also control for the age of the parental household head.We define the dependent variable ζfht as the outcome variable — earnings or consumption, ofthe child f born in year h observed in year t. We run the regression:ζfht = µDt + βtxfh + γapfh + δakfht + fht (C.4)The regressor, xfh is the average value of the parent’s outcome variable when the child f fromcohort h is between 15 and 17 years of age. As controls, we include year dummies Dt, and quarticsfor all children. This approach is adopted, for example, by Mayer and Lopoo (2005). The downside of conditioningon a specific age is that one has to throw out much valuable information (that is, all the data available for otherages). Moreover, transitory shocks occurring at the specific age may introduce some bias in the estimated parameter.91Classical measurement error in the dependent variable (here, the child variable) is usually not a problem. However,Haider and Solon (2006) shows that using current variables as a proxy for a child’s permanent (lifetime) earnings orincome may entail non-classical measurement error but the extent of the measurement error bias in the left-hand-sidevariable is the lowest if the current variable is measured at around age 40. So, we centre the child’s age around age40.92This asymmetry can be easily removed by making cohorts exit after a certain age, but that would lead to missingout on valuable information for those omitted cohorts. An alternative to this time-conditional estimation is toestimate cohort-specific elasticities using lifetime average of earnings (or consumption) for the adult children.93Data availability then implies that is the oldest cohort of children are those born in 1952, with available parentalobservations starting from 1967 (documented in the 1968 interview).127in the average parental age when the child is age 15-17 years, apfh, and also quartics in the ageof the child in year t, centred around 40 years (that is, a quartic in t − h − 40), akfht. The errorterm fht reflects factors like luck in labour and marriage markets, intergenerational transmissionof genetic traits and other environmental factors (see Peters (1992)). We allow the coefficient β tovary by year to capture the time variation in intergenerational persistence. It should be noted thatthe choice of the normalization age for akfht affects the point estimate of βt in each year but not thetime trend. In Table C.1 we report the actual year-specific estimates from 1990 through 2010. Wecan obtain estimates starting from 1977 onwards, but in earlier years of the PSID the average ageof the children samples is quite low, as we only observe independent children for very few years.This is problematic because one would have to rely on extremely short snapshots of early adulthoodto infer child outcomes. For this reason we only report point estimates of the elasticities from theyear 1990 onwards. This guarantees that the cross-section of children in any given year includes alarger number of individuals at later stages of their working life. This also guarantees that childrenpanels are longer, and hence less susceptible to initial conditions bias. It is interesting to note thatthe estimated elasticities lie in a fairly narrow range in the last 30 years. This absence of eithera positive or a negative trend is the basis of our time-stationary model of economic persistence inSection 4.2.Table C.1: Estimates of Intergenerational Elasticities by YearYear Head Earnings Total Consumption Food Consumption1990 0.30*** 0.48*** 0.25***1991 0.34*** 0.45*** 0.24***1992 0.29*** 0.47*** 0.27***1993 0.30*** 0.48*** 0.29***1994 0.29*** 0.49*** 0.25***1995 0.29*** 0.48*** 0.27***1996 0.25*** 0.45*** 0.25***1998 0.24*** 0.44*** 0.24***2000 0.30*** 0.45*** 0.25***2002 0.31*** 0.48*** 0.23***2004 0.29*** 0.41*** 0.19***2006 0.30*** 0.46*** 0.23***2008 0.35*** 0.47*** 0.26***2010 0.37*** 0.49*** 0.29***Note: ***, ** and * denote statistical significance at 1%, 5% and 10% levelsrespectively. Standard errors (not reported) are clustered at the level of the uniqueparent identity.C.3.2 Heterogeneity of Intergenerational PersistenceAn alternative way to study the extent of intergenerational economic persistence is through mobilitymatrices. Mobility matrices show the heterogeneity in intergenerational persistence across theincome or consumption distribution that is averaged out in the regression analysis above and the128GMM analysis later on. The basic idea is to study the probability that an adult child will fall intovarious quantiles in the income or consumption distribution, given the quantile in which the parentof that child belonged. If the probability of a child being placed in the same quartile as the parentis high, we say that intergenerational persistence is high for that quartile of the distribution. Ifthere were to be perfect intergenerational mobility then each cell in the mobility matrix would havea conditional probability of 25 percent, and on the other hand if there were perfect persistence inintergenerational well-being then all the diagonal cells would read 100 percent while the off-diagonalcells would have a zero probability.To accomplish the construction of such mobility matrices we first regress parental earnings (orconsumption) on the full set of year dummies and the quartic of parental age. The residuals fromthese regressions are then averaged across the years for each parent and these average residuals arefinally used to place each parent in one of the four quartiles of the parental distribution. Similarexercise with the adult children is performed, and finally the two quartile positions of the parentsand children are cross-tabulated. A cell ci,j in a mobility matrix at the intersection of the ith rowand the jth column ∀i, j = 1(1)4 is given byci,j = Prob [child ∈ Qc,i| parent ∈ Qp,j ]× 100where Qc,i denotes the ith quartile of the child distribution and Qp,j denotes the jth quartile of theparental distribution. One should note that the sum of each column in a mobility matrix must addup to 100. This is because the sum is essentially the integration of the conditional distribution forthe child over the entire range of that distribution. However, the sum of each row need not add upto 100.Mobility Matrix of Head EarningsPPPPPPPPPPChildParentQp,1 Qp,2 Qp,3 Qp,4Qc,1 45.98 27.88 17.29 9.56Qc,2 25.41 29.64 27.17 15.93Qc,3 19.75 24.80 30.44 23.10Qc,4 8.86 17.69 25.10 51.41129Mobility Matrix of Total ConsumptionPPPPPPPPPPChildParentQp,1 Qp,2 Qp,3 Qp,4Qc,1 53.02 27.79 9.75 4.95Qc,2 26.53 32.04 25.65 13.65Qc,3 16.28 26.51 35.40 23.55Qc,4 4.17 13.67 29.20 57.84Mobility Matrix of Food ConsumptionPPPPPPPPPPChildParentQp,1 Qp,2 Qp,3 Qp,4Qc,1 40.00 26.24 21.53 10.17Qc,2 27.03 30.19 20.26 20.75Qc,3 21.11 24.00 32.07 23.30Qc,4 11.86 19.57 26.14 45.78The mobility matrices for household head’s labour earnings, total family consumption and foodconsumption are provided above. There are two important observations to be made from the tables.First, the mobility matrix of labour earnings show more mobility than that of total consumption.This implies the presence of other channels of intra-family linkages in consumption that are overand above earnings. Note that this finding is consistent with the intergenerational elasticities above.The contributions of these different channels of persistence will be explicitly quantified in the morestructural model in Section 4.2. Secondly, there is a lot of heterogeneity in economic persistenceacross the conditional distributions, with the most persistence being observed at the two tails ofthe distributions, e.g., among children whose parents were in the lowest quartile of the parentaldistribution, at least about 39 percent are also in the lowest quartile. There is much more mobilityin the middle of the distributions.Mobility matrices, while good at highlighting distributional heterogeneity in intergenerationalpersistence, as such cannot provide a summary statistic for measuring the overall mobility in theeconomy. Using the fact that in the case of perfect persistence the mobility matrix is nothing butthe identity matrix of size m, where m is the number of quantiles used to construct the mobilitymatrix (in our case of quartiles, m = 4), (Shorrocks, 1978) provides a simple measure of the distanceof the estimated mobility matrix (M) from the identity matrix as follows:Normalized Trace Index, NTI = m−trace(M)m−1The NTI measure is 0.81 for the labour earnings transition matrix, while that for total consumptionexpenditure and food consumption stand lower at 0.74 and 0.84 respectively. This corroborates thehigher persistence of total consumption than earnings and food consumption.130C.4 Empirical MomentsThe GMM minimizes the distance between the empirical moments and the analytical momentsimplied by the statistical model. If the parameters were exactly identified then the GMM esti-mates would be nothing but the solution of the system of moment restrictions. However, withover-identification, the GMM becomes relevant in the sense that it minimizes the error from allover-identifying restrictions. Hence, it is important that we study the empirical moments which es-sentially gives the estimates via the GMM. Below we present the cross-sectional empirical momentsfor the baseline case along with the internal fit of the model.Figure C.2: Internal Fit of Baseline ModelNote: Both the data and the model estimates correspond to the baseline case where the raw data is purged of only birth-cohortand year fixed effects. The average age for parents is 47 years, while that for children is 37 years.131C.5 Supplementary ResultsC.5.1 Role of Observable Characteristics in Intergenerational PersistenceHow much of the intra-family linkages in earnings, other income and consumption can be explainedby observable characteristics of the two generations? Observables like race and educational attain-ment has long been argued to be significant determinants of intergenerational mobility.Table C.2: Persistence of Observable CharacteristicsObserved Variable PersistenceFamily Size 0.32State of Residence 0.71No. of Children 0.38Employment Status 0.86Race 0.98Education 0.50Table C.2 shows the high degree of persistence in a host of observable characteristics across thetwo generations in our sample. So a natural question to ask is — if the observables are themselvespersistent over generations, how do they influence the peristence in economic outcomes in turn.Below we address this question.Denoting the data matrix of the log of individual earnings, other income and consumption asyft, we proceed as follows:1. We regress the log of each outcome variable, yft, on a full set of year and cohort dummies,and denote estimated residuals as yˆ(1)ft . These are our baseline outcome measures.2. Next, we regress our baseline outcomes yˆ(1)ft on a set of observables xft. That is, we estimateleast square projections:94yˆ(1)ft = βxft + εft. (C.5)3. From the previous step we recover predicted values, as well as residuals. Specifically, wedefine:yˆ(2)ft ≡ βˆxft (C.6)andyˆ(3)ft ≡ εˆft (C.7)94The matrix of controls xft includes dummies for family size, number of children, state of residence, employmentstatus, race and education.132For each of the measures yˆ(i)ft we compute a set of variances and covariances. Each set ofsecond moments can then be used to separately estimate structural model parameters.4. We estimate the GMM model separately for each set of variance-covariance moments of yˆ(i)ft(i ∈ 1, 2, 3). This delivers different sets of parameter estimates. Comparing these estimates ishelpful to establish whether the transmission of inequality is due to observable or unobservablecomponents.Table C.3: Variances for Parents and ChildrenVariable Generation Baseline Observable Unobservable(1) (2) (3)Earnings Parent 0.291 0.093 0.182Child 0.248 0.057 0.177Other Income Parent 0.808 0.084 0.696Child 0.534 0.081 0.441Consumption Parent 0.097 0.024 0.066Child 0.114 0.024 0.087Table C.4: Baseline Estimates: Intergenerational ElasticityVariables Parameters Baseline Observable Unobservable(1) (2) (3)Earnings γ 0.230 0.339 0.109(0.027) (0.022) (0.027)Other Income ρ 0.100 0.248 0.021(0.023) (0.039) (0.029)e¯pf on nkf,t λ 0.206 0.255 0.060(0.032) (0.028) (0.038)n¯pf on ekf,t θ 0.055 0.111 0.003(0.019) (0.028) (0.017)Consumption Shifters φ 0.154 0.450 0.010(0.032) (0.042) (0.034)No. of Parent-Child Pairs N 760 760 760Note: Bootstrap standard errors (100 repetitions) in parentheses. Baseline refers to data thatis purged of year and birth cohort effects (viz., yˆ(1)ft in equation C.5). These data are thenregressed on various controls (namely, dummies for family size, state of residence, number ofchildren, employment status, race and education). Observable refers to the fitted values fromthis regression (viz., yˆ(2)ft in equation C.6), while Unobservable refers to its residual (viz., yˆ(3)ftin equation C.7). The average age for parents in the sample is 47 years; that of children is 37years.133Table C.3 reports the cross-sectional variances of earnings, other income and consumption forparents and for children. Columns 1-3 correspond to equations (C.5), (C.6) and (C.7): column1 reports the variance controlling only for time and cohort effects, as in equation equation (C.5);column 2 reports the fitted variance, defined as the variance explained by observables, as in equation(C.6); and column 3 reports the variance of the residual, equation (C.7).Table C.5: Baseline Estimates: Variances and Covariances of Idiosyncratic ComponentsParameters Baseline Observable Unobservable(1) (2) (3)Parental Outcomes: VariancesPermanent Earnings σ2e¯p 0.295 0.095 0.182(0.021) (0.006) (0.011)Permanent Other Income σ2n¯p 0.806 0.084 0.696( 0.06) ( 0.01) (0.059)Permanent Consumption Shifters σ2q¯p 1.031 0.196 0.789(0.065) (0.022) (0.064)Child Idiosyncratic Heterogeneity: VariancesPermanent Earnings σ2δk0.228 0.041 0.175(0.011) (0.002) ( 0.01)Permanent Other Income σ2εk0.511 0.062 0.440(0.043) (0.004) (0.031)Permanent Consumption Shifters σ2ψk0.730 0.104 0.584(0.056) (0.008) (0.039)Parental Outcomes: CovariancesConsumption Shifters & Earnings σq¯p,e¯p -0.271 -0.120 -0.120(0.024) ( 0.01) (0.016)Consumption Shifters & Other Income σq¯p,n¯p -0.818 -0.116 -0.669(0.061) (0.015) (0.062)Earnings and Other Income σe¯p,n¯p 0.070 0.059 -0.012(0.013) (0.007) (0.012)Child Idiosyncratic Heterogeneity: CovariancesConsumption Shifters & Earnings σψk,δk -0.247 -0.058 -0.165(0.018) (0.004) (0.016)Consumption Shifters & Other Income σψk,εk -0.522 -0.068 -0.430(0.048) (0.005) (0.034)Earnings & Other Income σδk,εk 0.075 0.031 0.036(0.013) (0.002) (0.013)No. of Parent-Child Pairs N 760 760 760Note: Bootstrap standard errors (100 repetitions) in parentheses. Baseline refers to data that is purged ofyear and birth cohort effects (viz., yˆ(1)ft in equation C.5). These data are then regressed on various controls(namely, dummies for family size, state of residence, number of children, employment status, race, and educa-tion). Observable refers to the fitted value from this regression (viz., yˆ(2)ft in equation C.6), while Unobservablerefers to its residual (viz., yˆ(3)ft in equation C.7).134Next, we use these variances and other covariances amongst the economic outcomes to esti-mate the parameters for intergenerational eslaticity (reported in Table C.4) and for the variance-covariance structure of the idiosyncratic shocks specific to a particular generation (reported in TableC.5). From Table C.4 is is clear that all pass-through parameters in the baseline estimation areprimarily driven by persistence in observables, while only earnings has some part that is explainedby unobservable factors that are linked across generations.Table C.6: Share of Child Inequality Explained by Parental HeterogeneityVariables Baseline Observable Unobservable(1) (2) (3)Earnings 8.0 28.7 1.2Other Income 4.4 23.4 0.2Consumption 29.9 32.8 5.6Note: Values represent the percentage share of cross-sectionalvariances for younger generation that is explained by parentalfactors. Numbers obtained using parameter estimates from Ta-bles C.4 and C.5.Role of EducationTable C.7: Baseline Estimates: Intergenerational Elasticity for ObservablesParameters Observable Education Other(2) (3) (4)Earnings γ 0.339 0.258 0.304(0.022) (0.035) (0.023)Other Income ρ 0.248 0.188 0.207(0.039) (0.027) ( 0.05)e¯pf on nkf,t λ 0.255 0.183 0.271(0.028) (0.018) (0.041)n¯pf on ekf,t θ 0.111 0.189 0.054(0.028) (0.033) (0.028)Consumption Shifters φ 0.450 0.410 0.354(0.042) (0.029) (0.062)No. of Parent-Child Pairs N 760 760 760Note: Bootstrap standard errors with 100 repetitions are reported in parentheses. Ob-servable refers to the total fitted value of the regression of the data (purged off of yearand birth cohort effects) on dummies for family size, state of residence, number of chil-dren, employment status, race and education. Education refers to the fitted value of theregression of the data on education only, while Other refers to the fitted value of theother observable control variables. The average age for parents is 47 years, while thatfor children is 37 years in the sample.135Table C.8: Mobility Matrix for EducationXXXXXXXXXXChildParent<12 years High School College Dropout College & above<12 years 21.83 4.93 0 0High School 40.47 39.95 19.27 7.80College Dropout 20.93 25.58 42.52 14.99College & above 16.77 29.54 38.21 77.20C.5.2 The Impact of Parental Factors on InequalityVariance Accounting Calculations. As reported in Section 4.4.1, the relative contributionof parental factors in the cross-sectional variance of earnings among their kids’ generation can becomputed as the ratioV ar[ek(p)]V ar [ek]=γ2σ2e¯p + θ2σ2n¯p + 2γθσe¯p,n¯pσ2δk+ γ2σ2e¯p + θ2σ2n¯p + 2γθσe¯p,n¯p. (C.8)Then, substituting the parameter estimates from Tables C.4 and C.5 in equation C.8, one canobtain the estimates in the first row of Table C.6. That is, we can write:γ2σ2e¯p + θ2σ2n¯p + 2γθσe¯p,n¯pσ2δk+ γ2σ2e¯p + θ2σ2n¯p + 2γθσe¯p,n¯p=(0.2302)(0.295) + (0.0552)(0.806) + 2(0.230)(0.055)(0.070)0.228 + (0.2302)(0.295) + (0.0552)(0.806) + 2(0.230)(0.055)(0.070)= 8.0%.Similarly, the contribution of parental factors to the cross-sectional variances of other incomeand consumption in the children’s generation is given by the ratios,V ar[nk(p)]V ar [nk](C.9)andV ar[ck(p)]V ar [ck](C.10)whereV ar[nk(p)]= ρ2σ2n¯p + λ2σ2e¯p + 2ρλσe¯p,n¯p (C.11)V ar[nk]= V ar[nk(p)]+ σ2εk (C.12)V ar[ck(p)]= φ2σ2q¯p + (γ + λ)2 σ2e¯p + (ρ+ θ)2 σ2n¯p+ 2 [(γ + λ)φσe¯p,q¯p + (ρ+ θ)φσn¯p,q¯p + (ρ+ θ) (γ + λ)σe¯p,n¯p ] (C.13)V ar[ck]= V ar[ck(p)]+ σ2εk + σ2ψk + σ2δk + 2(σψk,εk + σψk,δk + σδk,εk). (C.14)136Counterfactual Distributions. In order to compare the actual distribution of outcomes forchildren with the counterfactual distributions where parental effects are shut down, we assumethat the permanent parental and idiosyncratic child components of earnings, other income andconsumption jointly follow a Gaussian distribution in logarithms95:e¯pfn¯pfq¯pfδkfεkfψkf∼ N000000,σ2e¯p σe¯p,n¯p σe¯p,q¯p 0 0 0σe¯p,n¯p σ2n¯p σn¯p,q¯p 0 0 0σe¯p,q¯p σn¯p,q¯p σ2q¯p 0 0 00 0 0 σ2δkσδk,εk σδk,ψk0 0 0 σδk,εk σ2εkσψk,εk0 0 0 σψk,δk σψk,εk σ2ψkThen, by the property of a joint Normal distribution, any linear combination of the constituentrandom variables also follows a Normal distribution. For example, we can assume that the id-iosyncratic part of permanent child consumption,(εkf + ψkf + δkf), follows a Normal distributionwith zero mean and variance equal to σ2εk+ σ2ψk+ σ2δk+ 2(σψk,εk + σψk,δk + σδk,εk). Such childidiosyncratic components are by definition independent of any parental influence, and hence canbe used to generate the counterfactual distribution for the children. Now, since the logarithmicrandom variables follow the Gaussian distribution (by assumption), they will follow the Lognormaldistribution in their levels. Figure 4.2 reports the difference in the probability density functionswith and without parental influence.C.6 Evolution of InequalityWhat degree of persistence would generate, all else equal, growing dispersion across generations?To answer this question, one needs to derive a threshold value of persistence as a function of theinequality in that generation. In order to get a closed form expression for these threshold valuesof persistence, we shut down the cross-persistence terms, that is, restrict λ = θ = 0. With theseparameter restrictions, earnings evolve through generations of the same family according to:ek1 = γe¯p + δk1ek2 = γ2e¯p + γδk1 + δk2...ekt = γte¯p +t∑j=1γt−jδktwhere the superscript {kt} identifies the tth generation of kids. Since γ ∈ (0, 1), there exists a longrun stationary distribution for earnings. Assuming Var(δkt) = σ2δk∀t and Cov(δkt , δkt′ ) = 0 ∀t 6= t′,95The mean of the logarithmic variables are zero because we consider de-meaned variables net of year and cohortfixed effects.137the variance of the stationary distribution of e, denoted by Var(e∗), isVar(e∗) = limt→∞γ2tσ2e¯p + t∑j=1γ2(t−j)σ2δk = σ2δk1− γ2 (C.15)Similarly, one can derive the stationary variances for other income and consumption as,Var(n∗) =σ2εk1− ρ2 (C.16)Var(c∗) =σ2ψk1− φ2 +σ2δk1− γ2 +σ2εk1− ρ2 +2σδk,εk1− γρ +2σψk,εk1− φρ +2σψk,δk1− φγ . (C.17)Table C.9: Intergenerational ElasticitiesParameters Estimates(1)Earnings γ 0.279(0.048)Other Income ρ 0.020(0.041)Consumption Shifters φ 0.006(0.047)No. of Parent-Child Pairs N 403Note: Bootstrap standard errors (100 repetitions) in parentheses.Parental and child ages vary between 30 and 40. Parameters λ andθ are set to zero. Average parental age is 37 years, while averageage of children is 35. Food expenditures are used as a measure ofconsumption. Estimates use cross-sectional data variation net ofcohort and year effects.Plugging in estimated values for the parameters in equations (C.15) through (C.17),96 onecan identify the threshold values of the persistence parameters beyond which there will be risinginequality. Using equation (C.15), we identify the threshold value of γ above which the varianceof earnings would grow from the value estimated in the parents’ generation: this is the value ofγ such that Var(e∗) ≥ Var(ep). This threshold value of γ is given by γp ≡√1− σ2δkVar(ep) . Anyγ larger than γp implies growing earnings variance. Based on the parameter estimates in TablesC.9 and C.10, σ2δk= 0.246 > Var (ep) = 0.183, making γp an imaginary number. This essentiallyimplies that any non-negative value of γ would result in increasing earnings inequality from thelevel in the parents’ generation. Since our estimate of the current value of γ (= 0.279) is positive,the model implies that the earnings variance should become larger in the next generation k1. Infact, earnings variance in the child generation, Var(ek1)= 0.261 is larger than in the parents’ one,96Since we restrict the parameters λ = θ = 0, we need to re-estimate our baseline model with this additionalrestriction. Additionally, we restrict the age range between 30 and 40 years for both parents and kids, in order tofacilitate comparison of inequality across different generations in the same age range. These estimates are reportedin Tables C.9 and C.10.138Var (ep) = 0.183.Table C.10: Idiosyncratic Variances & CovariancesParameters Estimates(1)Parental Outcomes: Variances .Permanent Earnings σ2e¯p 0.183(0.012)Permanent Other Income σ2n¯p 0.877(0.128)Permanent Consumption Shifters σ2q¯p 0.956(0.134).Child Idiosyncratic Heterogeneity: Variances .Permanent Earnings σ2δk0.246(0.013)Permanent Other Income σ2εk0.630(0.038)Permanent Consumption Shifters σ2ψk0.848(0.037).Parental Outcomes: Covariances .Consumption Shifters & Earnings σq¯p,e¯p -0.122(0.029)Consumption Shifters & Other Income σq¯p,n¯p -0.841(0.126)Earnings and Other Income σe¯p,n¯p -0.000(0.025).Child Idiosyncratic Heterogeneity: Covariances .Consumption Shifters & Earnings σψk,δk -0.247(0.020)Consumption Shifters & Other Income σψk,εk -0.620(0.032)Earnings & Other Income σδk,εk 0.056(0.017)No. of Parent-Child Pairs N 403Note: Bootstrap standard errors (100 repetitions) in parentheses. This table uses thesame sample and model specification as Table C.9.Starting from the children generation, and using equation (C.15) again, we can find the thresholdvalue of γ above which the earnings variance after the child generation would be growing; that is,γk1 ≡√1− σ2δkVar(ek1)=√1− 0.2460.261= 0.24.This is plotted as the dashed vertical line in Figure C.3. Any value of γ to the right of thatvertical line implies growing earnings variance. Since our estimate of γ (= 0.279) lies to the139Figure C.3: Implication of γ and φ for Long Run Inequality (Age: 30-40)right of the new threshold γk1 , the threshold corresponding to the generation of grandchildren k2(denoted by the dotted vertical line in Figure C.3) will lie further to the right of γk1 ; one can repeatthese calculations over and over again.97 Eventually, the economy settles down at the stationarydistribution of earnings where the threshold is defined asγ∗ ≡√1− σ2δkVar(e∗)= 0.279,which is the estimated level of γ.We can perform a similar exercise for the evolution of the variance of consumption using equation(C.17). Instead of a single persistence parameter γ, as in the case of earnings, the variance ofconsumption is a function of three persistence parameters: γ, ρ and φ. To make interpretationeasier, we hold ρ constant at its estimated value and study the thresholds of γ and φ that implyincreasing or decreasing consumption variance. Equation (C.17) shows that Var(c∗) is a non-linear function of γ and φ. First we ask what combinations of γ and φ imply that the varianceof consumption is increasing across subsequent generations. For that we would like to plot thethreshold value,Var(cg) =σ2ψk1− φ2 +σ2δk1− γ2 +σ2εk1− ρ2 +2σδk,εk1− γρ +2σψk,εk1− φρ +2σψk,δk1− φγ ,97We find γk2 = 0.276, which is larger than γk1 but still slightly smaller than 0.279.140for each generation g = {p, k1, k2, ...} as a function of γ and φ, holding all other parameters constant.However, there is no combination of γ and φ in the economically meaningful range [0, 1] that satisfiesthe threshold value equation for Var (cp). Therefore, any point in the (γ, φ) ∈ [0, 1]2 space will implyrising consumption inequality from the parents’ generation. This finding is corroborated by thefact that Var(ck1)= 0.117 > Var (cp) = 0.09.Next, we plot the threshold starting from the children’s generation, denoted by the dashed ellipsein Figure C.3. Since the estimated point, labelled E∗, with values (γ, φ) = (0.28, 0.01), lies outsidethis ellipse, the grandchildren’s generation should have a larger consumption variance than thechildren’s generation. Indeed, plotting the corresponding threshold for the grandchild generation(denoted by the dotted ellipse in Figure C.3), we find that it lies outside that for the children withVar(ck2) = 0.124 > Var(ck1) = 0.117. These dynamics are replicated across generations until theeconomy settles at the stationary distribution of consumption which gives rise to the solid ellipticalthreshold of γ and φ in Figure C.3.98While the analysis above shows how the estimates of current parameter values help make senseof the evolution of earnings and consumption variances across generations, these hypothetical dy-namics are specific to the parameter estimates we feed into the model, which are in turn determinedby the raw data moments that we currently observe. For example, the dynamics of increasing earn-ings variance are contingent on whether our raw data imply Var(ep) < Var(ek). As an exampleof an alternative scenario, we use the estimates in column (2) of Tables 4.11 and 4.12 which doesnot restrict the age to be between 30 and 40 years, but keeps the λ = θ = 0 restriction. Relaxingour age restriction implies Var(ep) > Var(ek), so that the thresholds of γ approach the long runthreshold from the right, rather than from the left as in Figure C.3, suggesting decreasing earningsvariance across generations. Similarly, the dynamics of consumption and other income inequalityin the long run are also dictated by the empirically observed moments.Relaxing Age Restriction. We replicate the above analysis of inequality evolution using aparametrization of the model based on a sample without age restrictions. This means that therelevant parameter estimates are obtained from columns (2) of Tables 4.11 and 4.12.The threshold value of γ beyond which the earnings inequality is increasing in the parents’generation is given byγp ≡√1− σ2δkVar(ep)= 0.506,and is shown as the dot-dashed vertical line in Figure C.4. Since the estimate of the current value ofγ (= 0.340) lies to the left of that line, the model implies that the earnings variance should becomesmaller in the next generation k1. We corroborate this using equation (C.15) again to find thethreshold value of γ above which the earnings variance in the child generation should be growing.98The stationary locus for earnings (the solid vertical line) and that of consumption (the solid ellipse) intersect attwo points. One of those points, denoted by E∗, corresponds to the GMM point estimate of γ and φ. The otherintersection point cannot be an equilibrium of the model because the stationary locus for other income (not plottedhere) passes only through E∗.141We findγk1 ≡√1− σ2δkVar(ek1)= 0.367,which is less than γp. Once again the estimated value of γ = 0.340 lies to the left of this newthreshold γk1, and so the threshold corresponding to the generation of grandchildren k2 will liefurther to the left of γk1 , and so on. Eventually, the economy settles down at the stationarydistribution of earnings where the threshold is defined as γ∗ ≡√1− σ2δkVar(e∗) = 0.340, which is theestimated level of γ.Figure C.4: Implication of γ and φ for Long Run Earnings & Consumption InequalityWe again perform a similar exercise for the consumption variance using equation (C.17). Thevariance of consumption is a function of three persistence parameters: γ, ρ and φ. We hold ρconstant at its estimated value and study the thresholds of γ and φ that imply increasing ordecreasing consumption variance. First we ask what combinations of γ and φ imply that thevariance of consumption is increasing across generations. For that we plot the threshold valueVar(cp) =σ2ψk1− φ2 +σ2δk1− γ2 +σ2εk1− ρ2 +2σδk,εk1− γρ +2σψk,εk1− φρ +2σψk,δk1− φγ ,as a function of γ and φ. This is shown as the dot-dashed ellipse in Figure C.4. Any pointinside that ellipse implies the variance of consumption for the child generation is less than theirparents. Since the estimated point, labelled E∗, with values (γ, φ) = (0.340, 0.107), lies outsidethis ellipse, the children’s generation should have a larger consumption variance than the parental142generation. Indeed, plotting the corresponding threshold for the child generation, (denoted bythe outermost dashed ellipse in Figure C.4), we find that it lies outside that for the parents withVar(ck1) = 0.114 > Var(cp) = 0.096. However, our estimate values of (γ, φ) = (0.340, 0.107) lieinside the ellipse for the child generation. This means that the generation of grandchildren k2should exhibit lower consumption variance than the child generation k1, and therefore should havea threshold ellipse which lies inside that for the child generation. These dynamics are replicatedacross generations until the economy settles at the stationary distribution of consumption whichgives rise to the solid black elliptical threshold of γ and φ in Figure C.4.C.7 Robustness and ExtensionsIn this appendix we present additional empirical results for the different extensions and robustnesschecks of the baseline specification that we considered in Section 4.6.C.7.1 Estimates by Child Birth-CohortTable C.11: Parental Importance by Child-Cohort (Age: 30-40)Variables All Cohorts 1960s Cohort 1970s Cohort(1) (2) (3)Earnings 4.0 4.4 5.3Other Income 1.6 1.3 2.9Consumption 24.4 37.7 15.9Note: All numbers are percentages (%) and are based on parameterestimates in Tables 4.10 and C.12.143Table C.12: Estimates by Child Cohort: Idiosyncratic Components (Age: 30-40)Parameters All Cohorts 1960s Cohort 1970s Cohort(1) (2) (3)Parental Outcomes: VariancesPermanent Earnings σ2e¯p 0.199 0.172 0.225(0.019) (0.021) (0.026)Permanent Other Income σ2n¯p 0.845 0.945 0.752(0.105) ( 0.16) (0.157)Permanent Consumption Shifters σ2q¯p 0.911 0.977 0.840(0.115) (0.157) (0.153)Child Idiosyncratic Heterogeneity: VariancesPermanent Earnings σ2δk0.241 0.232 0.245(0.017) (0.021) (0.025)Permanent Other Income σ2εk0.658 0.561 0.747(0.067) ( 0.1) (0.162)Permanent Consumption Shifters σ2ψk0.869 0.816 0.900(0.075) (0.129) (0.196)Parental Outcomes: CovariancesConsumption Shifters & Earnings σq¯p,e¯p -0.126 -0.060 -0.187(0.037) (0.031) (0.041)Consumption Shifters & Other Income σq¯p,n¯p -0.798 -0.887 -0.711(0.106) (0.152) (0.149)Earnings and Other Income σe¯p,n¯p -0.006 -0.044 0.029(0.029) (0.029) (0.029)Child Idiosyncratic Heterogeneity: CovariancesConsumption Shifters & Earnings σψk,δk -0.232 -0.269 -0.189(0.028) (0.036) (0.039)Consumption Shifters & Other Income σψk,εk -0.654 -0.583 -0.714(0.069) (0.114) (0.181)Earnings & Other Income σδk,εk 0.047 0.078 0.013(0.025) (0.026) (0.044)No. of Parent-Child Pairs N 336 166 170Note: Bootstrap standard errors with 100 repetitions are reported in parentheses. This table uses the same sample andmodel specification as Table 4.10.144C.7.2 Estimates under Alternative Definitions of ‘Other Income’Table C.13: Decomposition of Other Income: Idiosyncratic ComponentsParameters Just Transfers Spouse Earnings Other Income(1) (2) (3)Parental Outcomes: VariancesPermanent Earnings σ2e¯p 0.287 0.295 0.295(0.027) (0.027) (0.027)Permanent Other Income σ2n¯p 1.297 0.294 0.459(0.128) (0.021) (0.041)Permanent Consumption Shifters σ2q¯p 1.504 0.502 0.650(0.132) (0.042) (0.055)Child Idiosyncratic Heterogeneity: VariancesPermanent Earnings σ2δk0.213 0.196 0.205(0.015) (0.011) (0.012)Permanent Other Income σ2εk1.063 0.296 0.441(0.085) (0.018) (0.038)Permanent Consumption Shifters σ2ψk1.292 0.460 0.589(0.096) (0.029) (0.042)Parental Outcomes: CovariancesConsumption Shifters & Earnings σq¯p,e¯p -0.225 -0.259 -0.247(0.042) (0.029) (0.026)Consumption Shifters & Other Income σq¯p,n¯p -1.314 -0.302 -0.458(0.125) (0.027) (0.045)Earnings and Other Income σe¯p,n¯p 0.044 0.063 0.051(0.035) (0.015) (0.017)Child Idiosyncratic Heterogeneity: CovariancesConsumption Shifters & Earnings σψk,δk -0.222 -0.199 -0.204(0.033) (0.017) (0.021)Consumption Shifters & Other Income σψk,εk -1.081 -0.289 -0.421(0.103) ( 0.02) (0.035)Earnings & Other Income σδk,εk 0.059 0.056 0.050(0.028) (0.014) (0.017)No. of Parent-Child Pairs N 459 459 459Note: Bootstrap standard errors with 100 repetitions are reported in parentheses. This table uses the same sample and modelspecification as Table 4.5.145Table C.14: Estimated Variances of Components of Other IncomeVariable Generation Just Transfers Spouse Earnings Other Income(1) (2) (3)Earnings Parent 0.287 0.295 0.295Child 0.229 0.229 0.229‘Other Income’ Component Parent 1.297 0.294 0.459Child 1.068 0.322 0.457Consumption Parent 0.098 0.094 0.096Child 0.113 0.113 0.113Note: This table uses parameter estimates from Tables 4.5 and C.13.C.7.3 Model using Panel DataIn this appendix we present the full set of moment conditions for the model using panel datavariation, and the identification strategy for all the parameters. We also report the estimates of thevariances of the transitory shocks, that were averaged out in the baseline specification with onlycross-sectional variation.Parent VarianceV ar(epf,t)= σ2e¯p + σ2ζp (C.18)V ar(npf,t)= σ2n¯p + σ2up (C.19)V ar(cpf,t)= σ2q¯p + σ2e¯p + σ2n¯p + σ2vp+ 2 (σq¯p,e¯p + σq¯p,n¯p + σe¯p,n¯p) + [f (r)]2 (σ2up + σ2ζp + 2σζp,up) (C.20)Child VarianceV ar(ekf,t)= γ2σ2e¯p + θ2σ2n¯p + σ2δk + σ2ζk + 2γθσe¯p,n¯p (C.21)V ar(nkf,t)= ρ2σ2n¯p + λ2σ2e¯p + σ2εk + σ2uk + 2ρλσe¯p,n¯p (C.22)V ar(ckf,t)= φ2σ2q¯p + (γ + λ)2 σ2e¯p + (ρ+ θ)2 σ2n¯p + σ2εk + σ2ψk + σ2δk+ 2 [(γ + λ)φσq¯p,e¯p + (ρ+ θ)φσq¯p,n¯p + (ρ+ θ) (γ + λ)σe¯p,n¯p ]+ 2[σψk,εk + σψk,δk + σδk,εk]+ σ2vk + [f (r)]2(σ2uk + σ2ζk + 2σζk,uk)(C.23)146Contemporaneous Parent CovarianceCov(epf,t, npf,t)= σe¯p,n¯p + σζp,up (C.24)Cov(epft, cpft)= σ2e¯p + σq¯p,e¯p + σe¯p,n¯p + f (r)(σ2ζp + σζp,up)(C.25)Cov(npf,t, cpf,t)= σ2n¯p + σq¯p,n¯p + σe¯p,n¯p + f (r)(σ2up + σζp,up)(C.26)Contemporaneous Child CovarianceCov(ekf,t, nkf,t)= (ργ + θλ)σe¯p,n¯p + γλσ2e¯p + ρθσ2n¯p + σδk,εk + σζk,uk (C.27)Cov(ekf,t, ckf,t)= γ (γ + λ)σ2e¯p + θ (θ + ρ)σ2n¯p + φγσq¯p,e¯p + φθσq¯p,n¯p+ [γ (ρ+ θ) + θ (γ + λ)]σe¯p,n¯p+ σ2δk + σψk,δk + σδk,εk + f (r)(σ2ζk + σζk,uk)(C.28)Cov(nkf,t, ckf,t)= λ (γ + λ)σ2e¯p + ρ (θ + ρ)σ2n¯p + φλσq¯p,e¯p + φρσq¯p,n¯p+ [λ (ρ+ θ) + ρ (γ + λ)]σe¯p,n¯p+ σ2εk + σψk,δk + σψk,εk + f (r)(σ2uk + σζk,uk)(C.29)Contemporaneous Cross-Generation CovarianceCov(epf,t, ekf,t)= γσ2e¯p + θσe¯p,n¯p (C.30)Cov(npf,t, nkf,t)= ρσ2n¯p + λσe¯p,n¯p (C.31)Cov(cpf,t, ckf,t)= φ(σ2q¯p + σq¯p,e¯p + σq¯p,n¯p)+ (γ + λ)(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ (ρ+ θ)(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(C.32)Cov(epf,t, nkf,t)= ρσe¯p,n¯p + λσ2e¯p (C.33)Cov(epf,t, ckf,t)= (γ + λ)σ2e¯p + φσq¯p,e¯p + (ρ+ θ)σe¯p,n¯p (C.34)Cov(npf,t, ekf,t)= γσe¯p,n¯p + θσ2n¯p (C.35)Cov(npf,t, ckf,t)= (ρ+ θ)σ2n¯p + φσq¯p,n¯p + (γ + λ)σe¯p,n¯p (C.36)Cov(cpf,t, ekf,t)= γ(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ θ(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(C.37)Cov(cpf,t, nkf,t)= λ(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ ρ(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(C.38)147Non-contemporaneous Covariances (lag 1) for ParentCov(epf,t, epf,t+1)= σ2e¯p (C.39)Cov(npf,t, npf,t+1)= σ2n¯p (C.40)Cov(cpf,t, cpf,t+1)= σ2q¯p + σ2e¯p + σ2n¯p + 2 (σq¯p,e¯p + σq¯p,n¯p + σe¯p,n¯p) (C.41)Cov(epf,t, npf,t+1)= σe¯p,n¯p (C.42)Cov(epf,t, cpf,t+1)= σ2e¯p + σq¯p,e¯p + σe¯p,n¯p (C.43)Cov(npf,t, epf,t+1)= σe¯p,n¯p (C.44)Cov(npf,t, cpf,t+1)= σ2n¯p + σq¯p,n¯p + σe¯p,n¯p (C.45)Cov(cpf,t, epf,t+1)= σ2e¯p + σq¯p,e¯p + σe¯p,n¯p (C.46)Cov(cpf,t, npf,t+1)= σ2n¯p + σq¯p,n¯p + σe¯p,n¯p (C.47)Non-contemporaneous Covariances (lag 1) for ChildCov(ekf,t, ekf,t+1)= γ2σ2e¯p + θ2σ2n¯p + 2γθσe¯p,n¯p + σ2δk (C.48)Cov(nkf,t, nkf,t+1)= ρ2σ2n¯p + λ2σ2e¯p + 2ρλσe¯p,n¯p + σ2εk (C.49)Cov(ckf,t, ckf,t+1)= φ2σ2q¯p + (γ + λ)2 σ2e¯p + (ρ+ θ)2 σ2n¯p + σ2εk + σ2ψk + σ2δk+ 2 [(γ + λ)φσq¯p,e¯p + (ρ+ θ)φσq¯p,n¯p + (ρ+ θ) (γ + λ)σe¯p,n¯p ]+ 2(σψk,εk + σψk,δk + σδk,εk)(C.50)Cov(ekf,t, nkf,t+1)= (ργ + θλ)σe¯p,n¯p + γλσ2e¯p + θρσ2n¯p + σδk,εk (C.51)Cov(ekf,t, ckf,t+1)= γ[(γ + λ)σ2e¯p + (θ + ρ)σe¯p,n¯p + φσq¯p,e¯p]+ σ2δk + σδk,εk + σψk,δk+ θ[(θ + ρ)σ2n¯p + (γ + λ)σe¯p,n¯p + φσq¯p,n¯p](C.52)Cov(nkf,t, ekf,t+1)= (ργ + θλ)σe¯p,n¯p + γλσ2e¯p + θρσ2n¯p + σδk,εk (C.53)Cov(nkf,t, ckf,t+1)= ρ[(γ + λ)σ2n¯p + φσq¯p,n¯p + (γ + λ)σe¯p,n¯p]+ σ2εk + σψk,εk + σδk,εk+ λ[(γ + λ)σ2e¯p + φσq¯p,e¯p + (θ + ρ)σe¯p,n¯p](C.54)Cov(ckf,t, ekf,t+1)= γ[(γ + λ)σ2e¯p + (θ + ρ)σe¯p,n¯p + φσq¯p,e¯p]+ σ2δk + σδk,εk + σψk,δk+ θ[(θ + ρ)σ2n¯p + (γ + λ)σe¯p,n¯p + φσq¯p,n¯p](C.55)Cov(ckf,t, nkf,t+1)= ρ[(γ + λ)σ2n¯p + φσq¯p,n¯p + (γ + λ)σe¯p,n¯p]+ σ2εk + σψk,εk + σδk,εk+ λ[(γ + λ)σ2e¯p + φσq¯p,e¯p + (θ + ρ)σe¯p,n¯p](C.56)148Cross-Generation Covariances: Parent at t & child at t+ 1Cov(epf,t, ekf,t+1)= γσ2e¯p + θσe¯p,n¯p (C.57)Cov(epf,t, nkf,t+1)= ρσe¯p,n¯p + λσ2e¯p (C.58)Cov(epf,t, ckf,t+1)= (γ + λ)σ2e¯p + φσq¯p,e¯p + (ρ+ θ)σe¯p,n¯p (C.59)Cov(npf,t, ekf,t+1)= γσe¯p,n¯p + θσ2n¯p (C.60)Cov(npf,t, nkf,t+1)= ρσ2n¯p + λσe¯p,n¯p (C.61)Cov(npf,t, ckf,t+1)= (ρ+ θ)σ2n¯p + φσq¯p,n¯p + (γ + λ)σe¯p,n¯p (C.62)Cov(cpf,t, ekf,t+1)= γ(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ θ(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(C.63)Cov(cpf,t, nkf,t+1)= λ(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ ρ(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(C.64)Cov(cpf,t, ckf,t+1)= φ(σ2q¯p + σq¯p,e¯p + σq¯p,n¯p)+ (γ + λ)(σ2e¯p + σq¯p,e¯p + σe¯p,n¯p)+ (ρ+ θ)(σ2n¯p + σq¯p,n¯p + σe¯p,n¯p)(C.65)Table C.15: Transitory Shocks EstimatesParameters Estimates(1)Parental Transitory Shocks .Earnings σ2ζp 0.095(0.006)Other Income σ2up 0.393(0.025)Consumption σ2vp 0.069(0.004)Earnings on Other Income σup,ζp -0.022(0.004).Child Transitory Shocks .Earnings σ2ζk0.097(0.006)Other Income σ2uk0.366(0.029)Consumption σ2vk0.086(0.006)Earnings on Other Income σuk,ζk 0.004(0.007)Note: Bootstrap standard errors (100 repetitions) inparentheses. This table uses the same sample and modelspecification as column (5) of Tables 4.11 and 4.12.149Identification There are 25 parameters to be identified from 48 equations. We will proceed withthe identification argument in the following three steps:(i) First, we identify 10 parameters linked to earnings, income and consumption processes for par-ents. Equations (C.39), (C.40), (C.18), (C.19), (C.42), (C.45), (C.46), (C.41), (C.24) and (C.20)can be considered sequentially to identify σ2e¯p , σ2n¯p , σ2ζp , σ2up , σe¯p,n¯p , σq¯p,n¯p , σq¯p,e¯p , σ2q¯p , σζp,up andσ2vp respectively.(ii) Next, we identify 5 parameters which denote intergenerational elasticities. Equations (C.30)and (C.37) can simultaneously identify γ and θ, while ρ and λ are identified from equations (C.31)and (C.38). Finally, φ is identified from equation (C.32).(iii) Lastly, the 10 parameters associated with the child’s earnings, income and consumption pro-cesses are identified. Equations (C.48), (C.49), (C.21), (C.22), (C.51), (C.54), (C.55), (C.50), (C.27)and (C.23) can be considered sequentially to identify σ2δk, σ2εk, σ2ζk, σ2uk, σδk,εk , σψk,εk , σψk,δk , σ2ψk,σζk,uk and σ2vkrespectively.C.8 Random Walk ModelIn this appendix, we posit an alternative to our baseline model of intergenerational persistencein individual fixed effects of income and consumption levels. We assume that the permanentcomponent of both head earnings and other income of the family is a random walk process, andexplore the extent of intergenerational persistence in the permanent innovations to these randomwalk components. Identification of intergenerational persistence in permanent life-cycle shocksinvolves calculating the growth rates of the outcome variables, which in turn implies that one canno longer identify the persistence in fixed effects, which are differenced out in growth rates.Under this alternative view of intergenerational persistence, the model equations describingearnings and other income are:epf,t = e¯pf + Ppf,t + upf,t (C.66)P pf,t = Ppf,t−1 + vpf,t (C.67)npf,t = n¯pf +Qpf,t + ζpf,t (C.68)Qpf,t = Qpf,t−1 + νpf,t (C.69)A similar set of equations for earnings and other income holds true for the children. In addition,we assume that intergenerational linkages follow:vkf,t = ρvpf,t + εkf,t150andνkf,t = λνpf,t + θkf,t.Time differencing the income equations over successive sample years delivers the following equa-tions:99∆2epf,t =(vpf,t + vpf,t−1)+ ∆2upf,t (C.70)∆2npf,t =(νpf,t + νpf,t−1)+ ∆2ζpf,t (C.71)∆2ekf,t = ρ(vpf,t + vpf,t−1)+(εkf,t + εkf,t)+ ∆2ukf,t (C.72)∆2nkf,t = λ(νpf,t + νpf,t−1)+(θkf,t + θkf,t)+ ∆2ζkf,t (C.73)In this setting, the growth rate of consumption depends on the transitory and permanent inno-vations to earnings and other income, as well as on consumption-specific transitory heterogeneity,just as in the well-known work of Blundell, Pistaferri, and Preston (2008):∆cjf,t = φejvjf,t + ψejujf,t + ψnjνjf,t + ψnjζjf,t + ξjf,t where j = {p, k}.The loading parameters of permanent innovations to earnings and other income in the consumptiongrowth equation are interpreted as inverse measures of consumption insurance. For example, whenφej is close to zero, permanent shocks to earnings have little or no effect on expenditure growth,which suggests the presence of effective consumption smoothing mechanisms. On the other hand,if φej is close to unity there is little insurance against innovations to permanent earnings. We alsoallow for the possibility of direct persistence in consumption growth so that ξkf,t = γξpf,t+χkf,t. Thisalternative model results in equations:∆2cpf,t = φep(vpf,t + vpf,t−1)+ φnp(νpf,t + νpf,t−1)+ ψep(upf,t + upf,t−1)+ ψnp(ζpf,t + ζpf,t−1)+(ξpf,t + ξpf,t−1)(C.74)∆2ckf,t = φek[ρ(vpf,t + vpf,t−1)+(εkf,t + εkf,t−1)]+ ψek(ukf,t + ukf,t−1)+ φnk[λ(νpf,t + νpf,t−1)+(θkf,t + θkf,t−1)]+ ψnk(ζkf,t + ζkf,t−1)+ γ(ξpf,t + ξpf,t−1)+(χkf,t + χkf,t−1)(C.75)99In equations (C.70) through (C.75), we use the notation ∆2xt ≡ xt−xt−2 to denote the two-year time differencefor any variable xt. Since PSID data are only available every two years after 1998, we consider two-year timedifferences throughout so as to use data from both pre and post 1998 interview rounds.151C.8.1 Moment ConditionsParent VarianceV ar(∆2epf,t)= 2(σ2vp + σ2up)(C.76)V ar(∆2npf,t)= 2(σ2νp + σ2ζp)(C.77)V ar(∆2cpf,t)= 2(φ2epσ2vp + φ2npσ2νp + ψ2epσ2up + ψ2npσ2ζp + σ2ξp)(C.78)Child VarianceV ar(∆2ekf,t)= 2(ρ2σ2vp + σ2uk + σ2εk)(C.79)V ar(∆2nkf,t)= 2(λ2σ2νp + σ2ζk + σ2θk)(C.80)V ar(∆2ckf,t)= 2(ρ2φ2ekσ2vp + φ2ekσ2εk + ψ2ekσ2uk)+ 2(λ2φ2nkσ2νp + φ2nkσ2θk + ψ2nkσ2ζk + γ2σ2ξp + σ2χk)(C.81)Contemporaneous Parent CovarianceCov(∆2epf,t,∆2cpf,t)= 2φepσ2vp + ψepσ2up (C.82)Cov(∆2npf,t,∆2cpf,t)= 2φnpσ2νp + ψnpσ2ζp (C.83)Contemporaneous Child CovarianceCov(∆2ekf,t,∆2ckf,t)= 2ρ2φekσ2vp + 2φekσ2εk + ψekσ2uk (C.84)Cov(∆2nkf,t,∆2ckf,t)= 2λ2φnkσ2νp + 2φnkσ2θk + ψnkσ2ζk (C.85)Contemporaneous Cross-Generation CovarianceCov(∆2epf,t,∆2ekf,t)= 2ρσ2vp (C.86)Cov(∆2npf,t,∆2nkf,t)= 2λσ2νp (C.87)Cov(∆2cpf,t,∆2ckf,t)= 2(ρφepφekσ2vp + λφnpφnkσ2νp + γσ2ξp)(C.88)Cov(∆2epf,t,∆2ckf,t)= 2ρφekσ2vp (C.89)Cov(∆2npf,t,∆2ckf,t)= 2λφnkσ2νp (C.90)Cov(∆2cpf,t,∆2ekf,t)= 2ρφepσ2vp (C.91)Cov(∆2cpf,t,∆2nkf,t)= 2λφnpσ2νp (C.92)152Non-contemporaneous Covariances (lag 2) for ParentCov(∆2epf,t,∆2epf,t+2)= −σ2up (C.93)Cov(∆2npf,t,∆2npf,t+2)= −σ2ζp (C.94)Cov(∆2cpf,t,∆2epf,t+2)= −ψepσ2up (C.95)Cov(∆2cpf,t,∆2npf,t+2)= −ψnpσ2ζp (C.96)Non-contemporaneous Covariances (lag 2) for ChildCov(∆2ekf,t,∆2ekf,t+2)= −σ2uk (C.97)Cov(∆2nkf,t,∆2nkf,t+2)= −σ2ζk (C.98)Cov(∆2ckf,t,∆2ekf,t+2)= −ψekσ2uk (C.99)Cov(∆2ckf,t,∆2nkf,t+2)= −ψnkσ2ζk (C.100)C.8.2 IdentificationThere are 21 parameters to be identified from 25 moment conditions. It is straightforward tosee the identification of σ2up , σ2ζp , ψep , ψnp , σ2uk, σ2ζk, ψek and ψnk from equations (C.93) through(C.100). Subsequently, σ2vp and σ2νp can be identified from equations (C.76) and (C.77). This allowsidentification of ρ and λ from equations (C.86) and (C.87); and consequently φek , φnk , φep and φnpfrom equations (C.89) through (C.92) respectively. Now, equations (C.78), (C.79) and (C.80) canidentify σ2ξp , σ2εkand σ2θkrespectively. Finally, γ is identified from equation (C.88), which leavesσ2χkto be identified from (C.81).C.8.3 EstimatesIn Table C.16, we present two sets of estimates for this random walk model. The first set is basedon imputed expenditure data; the second set is obtained using only directly observed food expendi-tures as a measure of consumption. Blundell, Pistaferri, and Preston (2008) point out that “...usingfood would provide an estimate of insurance that is ...higher than with imputed consumption data”and “...may give misleading evidence on the size and the stability of the insurance parameters.” Notsurprisingly, therefore, Table C.17 shows that we estimate higher value of consumption insurancewhen using food expenditures rather than imputed consumption data. Table C.16 shows that in-novations to earnings, other income and consumption display no statistically significant persistenceacross generations. With the caveat that first-differenced data can exacerbate measurement errorand reduce significance, we find no evidence of intergenerational linkages in the accrual rate ofpermanent innovations over the life-cycle.153Table C.16: Intergenerational Growth ElasticitiesParameters Imputed Food(1) (2)Earnings Growth ρ 0.241 0.256(0.161) (0.193)Other Income Growth λ 0.094 0.095(0.071) (0.059)Consumption Growth Shifter γ 0.009 0.047(0.048) (0.056)No. of Parent-Child Pairs N 760 760Note: Bootstrap standard errors (100 repetitions) in parentheses. Yearand cohort effects have been removed.Table C.17: Partial Insurance ParametersParameters Imputed Food(1) (2)ParentsPermanent Earnings φpe 0.230 0.104(0.037) (0.085)Permanent Other Income φpn 0.069 0.033(0.017) (0.025)Transitory Earnings ψpe 0.147 0.057(0.034) (0.094)Transitory Other Income ψpn 0.033 -0.047(0.042) (0.066)ChildrenPermanent Earnings φke 0.237 0.034(0.053) (0.102)Permanent Other Income φkn 0.127 0.076(0.021) (0.022)Transitory Earnings ψke 0.201 0.023(0.036) (0.067)Transitory Other Income ψkn 0.046 -0.042(0.025) (0.065)No. of Parent-Child Pairs N 760 760Note: Bootstrap standard errors (100 repetitions) in paren-theses. Data are purged of year and cohort effects.154Table C.18: Variances of ShocksParameters Imputed Food(1) (2)Parental ShocksTransitory Earnings σ2up 0.048 0.048(0.005) (0.004)Transitory Other Income σ2ζp 0.068 0.068(0.015) (0.016)Permanent Earnings σ2vp 0.033 0.033(0.004) (0.004)Permanent Other Income σ2νp 0.108 0.107(0.012) (0.013)Consumption Growth σ2ξp 0.017 0.070(0.001) (0.004)Child ShocksTransitory Earnings σ2uk0.048 0.049(0.005) (0.006)Transitory Other Income σ2ζk0.087 0.087(0.013) (0.013)Permanent Earnings σ2εk0.024 0.023(0.004) (0.005)Permanent Other Income σ2θk0.095 0.095(0.014) (0.015)Consumption Growth σ2χk0.016 0.088(0.001) (0.006)No. of Parent-Child Pairs N 760 760Note: Bootstrap standard errors (100 repetitions) in paren-theses. Data are purged of year and cohort effects.155Table C.19: Growth Model MomentsMoments Imputed Food(1) (2)V ar(∆2epf,t)0.161 0.161(0.009) (0.007)V ar(∆2npf,t)0.351 0.351(0.036) (0.036)V ar(∆2cpf,t)0.041 0.142(0.002) (0.007)V ar(∆2ekf,t)0.148 0.148( 0.01) (0.009)V ar(∆2nkf,t)0.366 0.366(0.033) (0.034)V ar(∆2ckf,t)0.042 0.177(0.001) (0.011)Cov(∆2epf,t∆2ekf,t)0.017 0.017(0.011) (0.012)Cov(∆2npf,t∆2nkf,t)0.020 0.020(0.014) (0.013)Cov(∆2cpf,t∆2ckf,t)0.001 0.007(0.002) (0.008)Cov(∆2epf,t∆2epf,t+2)-0.048 -0.048(0.005) (0.004)Cov(∆2npf,t∆2npf,t+2)-0.068 -0.068(0.015) (0.016)Cov(∆2ekf,t∆2ekf,t+2)-0.049 -0.049(0.005) (0.006)Cov(∆2nkf,t∆2nkf,t+2)-0.087 -0.087(0.013) (0.013)Cov(∆2epf,t∆2cpf,t)0.023 0.011(0.002) (0.003)Cov(∆2epf,t+2∆2cpf,t)-0.006 -0.002(0.002) (0.004)Cov(∆2npf,t∆2cpf,t)0.017 0.004(0.003) (0.003)Cov(∆2npf,t+2∆2cpf,t)-0.002 0.003(0.002) (0.005)Cov(∆2ekf,t∆2ckf,t)0.023 0.004(0.002) (0.003)Cov(∆2ekf,t+2∆2ckf,t)-0.008 0.000(0.002) (0.003)Cov(∆2nkf,t∆2ckf,t)0.028 0.010(0.003) (0.004)Cov(∆2nkf,t+2∆2ckf,t)-0.004 0.003(0.002) (0.005)Cov(∆2epf,t∆2ckf,t)-0.001 -0.003(0.004) (0.009)Cov(∆2npf,t∆2ckf,t)0.005 0.006(0.003) (0.006)Cov(∆2cpf,t∆2ekf,t)0.001 -0.003(0.003) (0.006)Cov(∆2cpf,t∆2nkf,t)-0.003 -0.002(0.008) (0.011)Note: These empirical moments are used to generatethe parameter estimates in Tables C.16, C.17 and C.18through GMM. Bootstrap standard errors are reportedin parentheses.156"@en ;
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vivo:dateIssued "2020-11"@en ;
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dcterms:publisher "University of British Columbia"@en ;
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dcterms:title "Essays on dynamics of household and firm choices"@en ;
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ns0:identifierURI "http://hdl.handle.net/2429/75154"@en .