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Essays in applied microeconomics Molnár, Tímea Laura 2017

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Essays in Applied MicroeconomicsbyT´ımea Laura Molna´rB.A. and M.A.,Corvinus University of Budapest, 2010M.A., Central European University, 2011A 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)August 2017c© T´ımea Laura Molna´r 2017AbstractThe first chapter studies parents’ intra-household time and resource allocation, focusing on parentalquality time, and the implications for early childhood development. I develop a model that explainsthe “parental time-education gradient” puzzle, and I confirm its predictions, exploiting exogenous,drastic daycare price decrease in Quebec. I find that as daycare becomes cheaper, parents increasetime devoted to their children, at the expense of home production and leisure, while consuming moreof home production market goods (eating out, domestic help), and child market goods (daycare,games and toys); the time reallocation is larger for higher-educated parents. The estimated structuralparameters uncover the pivotal role of complementarity (substitutability) between time and marketgoods in child human capital (home) production, and suggest a time efficiency advantage in non-market activities for higher-educated parents. I use them to assess how universal daycare shapes skillgaps in early childhood. My findings point to differential parental investment and time efficiency asimportant mechanisms behind widening skill gaps in early childhood.The second chapter measures the causal impact of academic redshirting—the practice of postpon-ing school entry of an age-eligible child—on student achievement and mental health. I use Hungarianadministrative testscore data for 2008-2014, and an instrumental variable framework. The institutionalfeature I exploit is a school-readiness evaluation, compulsory for potentially redshirted children bornbefore January 1st. I compare children born around this cutoff and find that (1) although there arelarge student achievement gains for all, disadvantaged boys benefit the most from redshirting—andonly they benefit in terms of mental health; (2) the positive effects of higher school-starting age aredriven by absolute, rather than within-class relative age advantage.The third chapter studies how closely private insurers’ payment schedules follow Medicare’s, ex-ploiting institutional changes in Medicare’s payments and dramatic bunching in markups over Medicarerates. We find that, although Medicare’s rates are influential, 25 percent of physician services, rep-resenting 45 percent of spending, deviate from this benchmark. Heterogeneity in the pervasivenessand direction of deviations reveals that the private market coordinates around Medicare’s pricing forsimplicity but innovates when sufficient value is at stake.iiLay SummaryMy dissertation consists of three chapters in family economics and child development, economics ofeducation and health economics. First, I investigate how parents choose the amount of quality timespent with their children, and why higher-educated parents spend more. I propose and confirm themechanism of higher-educated parents being more efficient in translating time with their children intochild human capital. Second, I measure the causal impact of academic redshirting on student achieve-ment and mental health. Redshirting is the practice of postponing school entry of an age-eligible,but potentially not school-ready child. I show that disadvantaged boys are the main beneficiaries ofthis practice. Third, we study to what extent US private insurers benchmark to the correspondingMedicare price, when negotiating on how much to pay to doctors for a given medical service. In ourdata, 75% of physician services, representing 55% of spending, are directly linked to Medicare.iiiPrefaceChapters 2 and 3 are original, unpublished and independent work by the author, T´ımea Laura Molna´r.Chapter 4, forthcoming in the Journal of Health Economics, is a joint work with Professor JeffreyClemens (UCSD and NBER) and Professor Joshua Gottlieb (UBC and NBER). Chapter 3 was ap-proved by the UBC Human Ethics Research Board under the name “Insurer-Physician Pricing Rela-tionships” and project number H1302021. I have been involved throughout each stage of the research:preparing data, designing the empirical method, carrying out estimation, developing the economicmodel, and organizing and presenting results.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 How Do Mothers Manage? Universal Daycare, Child Skill Formation, and theParental Time-Education Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Institutional Background and Available Evidence . . . . . . . . . . . . . . . . . . . . 162.4 Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Data, Measurement and Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . 232.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.7 Discussion of Alternative Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.8 Income and Substitution Effects: The German Experiment . . . . . . . . . . . . . . . 352.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.10 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.11 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Returns to Starting School Later: Academic Redshirting vs. Lucky Date of Birth 483.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2 Institutional Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.4 Data and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.7 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.8 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82vTable of Contents4 Do Health Insurers Innovate? Evidence from the Anatomy of Physician Payments 844.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.2 Medical Pricing Institutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.3 Medical Pricing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.4 Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.5 Baseline Benchmarking Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.6 How Do Private Payments Deviate from Medicare? . . . . . . . . . . . . . . . . . . . 974.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.8 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.9 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111AppendicesA Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120A.1 Solving the Utility Maximization Problem . . . . . . . . . . . . . . . . . . . . . . . . 120A.2 Solving the Expenditure Minimization Problem . . . . . . . . . . . . . . . . . . . . . 121A.3 Comparative Statics for the Marshallian Demands . . . . . . . . . . . . . . . . . . . . 122A.4 Discussion of Alternative Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128A.5 Appendix Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129A.6 Appendix Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139A.7 Robustness of Confidence Intervals to Small # of Clusters . . . . . . . . . . . . . . . 144A.8 Details on Daycare Price Imputation . . . . . . . . . . . . . . . . . . . . . . . . . . . 145A.9 Details on the Propensity Score Estimation . . . . . . . . . . . . . . . . . . . . . . . . 146A.10 Robustness of the Structural Parameter Estimates . . . . . . . . . . . . . . . . . . . . 148A.11 Details on the Policy Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149B Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150B.1 Additional Institutional Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150B.2 Appendix Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150C Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154C.1 Conceptual Framework: Contracting Under Complexity . . . . . . . . . . . . . . . . . 154C.2 Additional Detail on Implied Conversion Factors . . . . . . . . . . . . . . . . . . . . . 155C.3 Estimation in Changes and Threats to Identification . . . . . . . . . . . . . . . . . . . 160C.4 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169viList of Tables2.1 Effect of a Daycare Price Decrease on Daycare Use (Extensive Margin) and MaternalLabor Supply (Both Margins); Policy Impact for All and by Education . . . . . . . . 392.2 Effect of a Daycare Price Decrease on Reading to the Child; Policy Impact for All andby Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.3 Effect of a Daycare Price Decrease on Mother’s and Father’s Child Time and HomeProduction Time Use; Policy Impact for All and by Education . . . . . . . . . . . . . 402.4 Effect of a Daycare Price Decrease on Mother’s Time Use; Policy Impact for All and byEducation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.5 Effect of a Daycare Price Decrease on Food Expenditures (%); Policy Impact for Alland by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.6 Effect of a Daycare Price Decrease on Child Good and Home Production Good Expen-ditures (%); Policy Impact for All and by Education . . . . . . . . . . . . . . . . . . . 412.7 Estimation of Structural Parameters - Child Human Capital Production . . . . . . . . 422.8 Estimation of Structural Parameters - Home Production . . . . . . . . . . . . . . . . . 422.9 Documenting the Behavioral Skill Gap between High-status and Low-status Childrenover Ages 0-11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.10 Effect of a Daycare Price Increase on Public Daycare Use, Mother’s Labor Supply, andMother’s Time Allocation on Work, Children, Home Production and Hobbies; PolicyImpact by the Propensity of Using Public Daycare in the Absence of the Policy . . . 433.1 Predicted Path into Primary School in Hungary, by Month of Birth . . . . . . . . . . . 703.2 The Fraction of Boys and Children with Different Parental Education, by Month ofBirth and School Starting Age, Administrative Data Grade 6 . . . . . . . . . . . . . . 703.3 The Fraction of Children with Different Developmental Obstacles born between Septem-ber and May by School Starting Age, Survey Data . . . . . . . . . . . . . . . . . . . . 713.4 The Effect of Quarter of Birth - First-stage Results on School Entry Delay, with full setof interactions by Gender and Parental Education, Administrative Data, Grades 6/8/10 723.5 The Effect of Quarter of Birth - First-stage Results on School Entry Delay, with full setof interactions by Gender and Parental Education, Survey Data . . . . . . . . . . . . . 733.6 Academic Redshirting and Involuntary Delay, Average Characteristics of Compliers,Administrative Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.7 The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Resultson 6th/8th/10th-grade Mathematics testscore, with full set of interactions by Genderand Parental Education, Administrative Data, Grades 6/8/10 . . . . . . . . . . . . . . 753.8 The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Resultson 6th/8th/10th-grade Reading testscore, with full set of interactions by Gender andParental Education, Administrative Data, Grades 6/8/10 . . . . . . . . . . . . . . . . 763.9 The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Resultson the Probability of Repeating a Grade by 6th/10th-grade, with full set of interactionsby Gender and Parental Education, Administrative Data, Grades 6/8/10 . . . . . . . . 77viiList of Tables3.10 The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Resultson 10th-grade Secondary School Track Choice, with full set of interactions by Genderand Parental Education, Administrative Data, Grade 10 . . . . . . . . . . . . . . . . . 783.11 The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Resultson Mental Health Outcomes at grade 8, with full set of interactions by Gender andParental Education, Survey Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.12 First-stage Results on School Entry Delay (Starting School at 7) and the Change inRelative Rank in Class, Administrative Data, Grades 6 . . . . . . . . . . . . . . . . . . 803.13 OLS and IV Estimates of the Effect of Involuntary School Entry Delay (Starting Schoolat 7) and the Relative Rank in Class on Mathematics Score, Administrative Data Grade 6 814.1 Summary Statistics by Physician Group . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.2 Services Priced According to Common Implied Conversion Factors . . . . . . . . . . . 1014.3 Firm Size and Implied Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . 1024.4 Estimating Medicare Benchmarking Using RVU Changes . . . . . . . . . . . . . . . . 1024.5 Medicare Benchmarking by Firm Size . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.6 Public-Private Payment Links Across Service Categories . . . . . . . . . . . . . . . . . 1034.7 Medicare Benchmarking by Betos Category . . . . . . . . . . . . . . . . . . . . . . . . 1044.8 In What Direction Does BCBS Adjust Its Payments for the Various Service Categories? 104A.1 Effect of a Daycare Price Decrease on Daycare Use (Extensive Margin); Policy Impactfor All and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129A.2 Effect of a Daycare Price Decrease on daycare use (Intensive Margin); Policy Impactfor All and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130A.3 Effect of a Daycare Price Decrease on Mother’s Working Propensity and daycare use;Policy Impact for All and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . 130A.4 Effect of a Daycare Price Decrease on Parents’ Labor Supply (Extensive and IntensiveMargin); Policy Impact for All and by Education . . . . . . . . . . . . . . . . . . . . 131A.5 Effect of a Daycare Price Decrease on Parents’ Labor Supply (Extensive Margin); PolicyImpact for All and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131A.6 Effect of a Daycare Price Decrease on Parents’ Labor Supply (Intensive Margin); PolicyImpact for All and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132A.7 Effect of a Daycare Price Decrease on Mother’s Child Time; Policy Impact for All andby Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132A.8 Effect of a Daycare Price Decrease on Mother’s Home Production Time; Policy Impactfor All and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133A.9 Effect of a Daycare Price Decrease on Father’s Child Time; Policy Impact for All andby Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133A.10 Effect of a Daycare Price Decrease on Father’s Home Production Time; Policy Impactfor All and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134A.11 Effect of a Daycare Price Decrease on Father’s Time Use; Policy Impact for All and byEducation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134A.12 Effect of a Daycare Price Decrease on Mother’s Labor Supply (Both Margins) by thePropensity of Mother’s Working in the Absence of the Policy and by Education, Census 135A.13 Effect of a Daycare Price Decrease on Mother’s Labor Supply (Both Margins) by thePropensity of Mother’s Working in the Absence of the Policy and by Education, LFS . 135A.14 Effect of a Daycare Price Decrease on Mother’s Labor Supply (Extensive Margin) andAny daycare use; Policy Impact by the Propensity of Mother’s Working in the Absenceof the Policy and by Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136viiiList of TablesA.15 Effect of a Daycare Price Decrease on Reading Propensity and Child Time; PolicyImpact by the Propensity of Mother’s Working in the Absence of the Policy and byEducation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136A.16 Effect of a Daycare Price Decrease on Home Production and Leisure Time; PolicyImpact by the Propensity of Mother’s Working in the Absence of the Policy and byEducation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A.17 Effect of a Daycare Price Decrease on Maternal Mental Health and Parenting Scores;Policy Impact by the Propensity of Mother’s Working in the Absence of the Policy andby Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A.18 Effect of a Daycare Price Decrease on Child Outcomes; Policy Impact by the Propensityof Mother’s Working in the Absence of the Policy and by Education . . . . . . . . . . 138A.19 Effect of a Daycare Price Decrease on Household Expenditures; Policy Impact by thePropensity of Mother’s Working in the Absence of the Policy . . . . . . . . . . . . . . 138A.20 Alternative Confidence Bounds for Selected Outcome Variables in the NLSCY . . . . . 144A.21 Alternative Confidence Bounds for Selected Outcome Variables in the Census . . . . . 144A.22 Alternative Confidence Bounds for Selected Outcome Variables in the GSS . . . . . . 145A.23 Alternative Confidence Bounds for Selected Outcome Variables in the LFS . . . . . . . 145A.24 Details on the Propensity Score Estimation, for High- and Low-Educated Families . . 147A.25 Robustness of the Parameter Estimates for Different Values of βK and ρX . . . . . . 148A.26 Robustness of the Parameter Estimates for Different Values of βH . . . . . . . . . . . 148A.27 Underlying Means of Daycare and Parental Time for Policy Simulation, No DaycarePolicy in Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149A.28 Policy Impacts on Daycare and Parental Time for Policy Simulation, Ages 3-4 . . . . . 149A.29 Summary Table of No-Policy, Actual and Counterfactual Levels of Child Human Capitalfor Higher- and Lower-Educated Parents’ Children in Policy Simulation . . . . . . . . 149B.1 Details of Sample Selection, Administrative Data . . . . . . . . . . . . . . . . . . . . . 150B.2 Distribution, Fraction of Children Entering School at age 7 and Average Years Spentin child care, by Month of Birth and child care Entry Age . . . . . . . . . . . . . . . . 151B.3 The Effect of Quarter of Birth - Detailed First-stage Results on School Entry Delay andits Interactions by Gender and Parental Education, Administrative Data, Grades 6/8/10152B.4 The Effect of Quarter of Birth - Detailed First-stage Results on School Entry Delay andits Interactions by Gender and Parental Education, Survey Data . . . . . . . . . . . . 153B.5 Descriptive Statistics of Class Size, Relative Rank and Fraction of Summer-Born Chil-dren in Class in All Schools and Non-sorting Schools, Children born in a 3-monthwindow around June 1st, Administrative Data Grade 6 . . . . . . . . . . . . . . . . . . 153B.6 Descriptive Statistics of the Fraction of Within-Class Sum-of-Squares, All Schools andNon-sorting Schools, Children born in a 3-month window around June 1st, Administra-tive Data Grade 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153C.1 Data Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157C.2 Alternative Measures of Pricing According to Common Implicit Conversion Factors . . 158C.3 Firm Size and Implied Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . 159C.4 Medicare Benchmarking by Betos Category . . . . . . . . . . . . . . . . . . . . . . . . 160C.5 Other Years’ Estimates of Benchmarking Using RVU Changes . . . . . . . . . . . . . . 163C.6 Dollar-Weighted Estimates of Benchmarking Using RVU Changes . . . . . . . . . . . . 164C.7 Checks for the Relevance of Active Contract Negotiations . . . . . . . . . . . . . . . . 165C.8 Public-Private Payment Links Across Service Categories . . . . . . . . . . . . . . . . . 166C.9 Medicare Benchmarking by Firm Size . . . . . . . . . . . . . . . . . . . . . . . . . . . 167ixList of TablesC.10 Estimating Medicare Benchmarking Using RVU Changes: Colorado . . . . . . . . . . 171C.11 Supply Elasticity Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172C.12 Estimating Medicare Benchmarking for Out-of-Network Payments Using RVU Changes 172C.13 Dollar-Weighted Estimates of Medicare Benchmarking for Out-of-Network PaymentsUsing RVU Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173C.14 Out-of-Network Services Priced According to Common Implied Conversion Factors . . 174xList of Figures2.1 Trends in Quebec and the Rest-of-Canada in Maternal Employment (Both Margins) . 442.2 Trends in Quebec and the Rest-of-Canada in Regulated (Institutional Daycare Use) . 442.3 Estimated Policy Impacts by Propensity of the Mother Working in the Absence of thePolicy, with a 95% Confidence Band, for High-Educated Mothers (Linear Model) . . . 452.4 Estimated Policy Impacts by Propensity of the Mother Working in the Absence of thePolicy, with a 95% Confidence Band, for Low-Educated Mothers (Linear Model) . . . 462.5 Counterfactuals on the Child Human Capital Gap When Policy Implemented at Age 2.5 473.1 Fraction of Children who Started School at the Age of 7 and Average MathematicsTestscores, by Month of Birth and child care Starting Age . . . . . . . . . . . . . . . . 823.2 Histogram of Number of Peers in Class, of Relative Age Rank (%) in Class, and ofFraction of Summer-born Peers in Class; Administrative Data Grade 6 . . . . . . . . . 834.1 Raw Payments For Illustrative Physician Groups . . . . . . . . . . . . . . . . . . . . . 1054.2 Benchmarking Estimates Based on Price Changes . . . . . . . . . . . . . . . . . . . . . 1064.3 Estimating Multiple Years’ RVU Updates Simultaneously . . . . . . . . . . . . . . . . 1074.4 Frequency of Benchmarking and Physician Group Size . . . . . . . . . . . . . . . . . . 1074.5 Deviations from Medicare Benchmark by Service Category . . . . . . . . . . . . . . . . 108A.1 Estimated Difference between Quebec and the Rest-of-Canada across Years, with a 95%Confidence Band, for All and by Education, NLSCY . . . . . . . . . . . . . . . . . . . 139A.2 Estimated Difference between Quebec and the Rest-of-Canada across Years, with a 95%Confidence Band, for All and by Education, GSS Time Use Diary and Census . . . . . 140A.3 Estimated Difference between Quebec and the Rest-of-Canada across Years, with a 95%Confidence Band, for All and by Having Children Aged 0-4, SHS . . . . . . . . . . . . 141A.4 Estimated Policy Impacts by Propensity with a 95% Confidence Band, for High-EducatedMothers (Quadratic Model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142A.5 Estimated Policy Impacts by Propensity with a 95% Confidence Band, for Low-EducatedMothers (Quadratic Model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143A.6 Predicted Propensity of Mother Working in the Absence of the Policy . . . . . . . . . 146C.1 Examples of Updates to Individual Services . . . . . . . . . . . . . . . . . . . . . . . . 156C.2 Distribution of ICFs by Firm Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157C.3 Strength of Public Private Payment Relationships . . . . . . . . . . . . . . . . . . . . 168C.4 Benchmarking Estimates Based on Price Changes Across Services . . . . . . . . . . . . 169C.5 Raw Payments For Illustrative Physician Group: Colorado . . . . . . . . . . . . . . . . 174C.6 Validating Bunching-Based Benchmarking Measure: Colorado . . . . . . . . . . . . . . 175C.7 Short-Run Supply Responses to Medicare Price Changes . . . . . . . . . . . . . . . . . 175xiAcknowledgementsI would like to express my deepest gratitude to Kevin Milligan, Nicole Fortin, and Joshua Gottliebfor their invaluable support, excellent guidance, and infinite patience throughout my years at UBC.They were extremely generous with their time and encouragement, and taught me how to be a bettereconomist and researcher. I also want to thank David Green and Vadim Marmer, who, even thoughnot formally on my committee, still devoted a lot of time towards helping me with modeling andeconometric theory. Ga´bor Ke´zdi (CEU) taught me the foundations of empirical research, providedessential conceptual suggestions to improve this thesis, and has had a life-long impact on me and mycareer. I am also indebted to Matilde Bombardini, Patrick Francois, Florian Hoffmann, Hiro Kasahara,Thomas Lemieux, Jamie McCasland and Marit Rehavi (UBC), Irene Botosaru (SFU), Hedvig Horva´th(UCL), and Pe´ter Hudomiet (RAND) for very useful suggestions and discussions at different stagesof my doctoral studies. Finally, I have had many extremely talented and encouraging fellow studentsat UBC, such as Oscar Becerra, Anujit Chakraborty, Thomas Cornwall, Alix Duhaime-Ross, AlastairFraser, Coral Gonzales, Brad Hackinen, Nouri Najjar, Adlai Newson, Jutong Pan, Pierluca Pannella,Rogerio Santarrosa, Daniel Shack, Iain Snoddy, Lori Timmins, Ruoying Wang, and Tzu-Ting Yang.All aforementioned helped me more than they can imagine.Most of the analysis in the first chapter was completed at the UBC Research Data Centre, whereCheryl Fu, Lee Grenon and Wendy Kei provided invaluable help with the data.Regarding data access to the second chapter, I would like to thank members of the Economicsof Education Research Unit at the Hungarian Academy of Sciences, Institute of Economics, especiallyGa´bor Kertesi, Ga´bor Ke´zdi, Zolta´n Hermann and Melinda Tir, for providing me the datasets of theHungarian National Assessment of Basic Competences, the Hungarian Life Course Survey, KIR-Statand the Local Government Treasury Dataset, and for helping with the data. My thanks go to Ga´borKertesi for providing me the municipality-level demography dataset for Hungary.Regarding the third chapter, I and co-authors Jeffrey Clemens and Joshua Gottlieb, are gratefulto Luisa Franzini, Cecilia Ganduglia-Cazaban, Osama Mikhail, and the UTSPH/BCBSTX PaymentSystems and Policies Research Program at the University of Texas School of Public Health for dataaccess, and for their extensive assistance in navigating the BCBSTX claims data. We thank SSHRC,Jon Skinner and the Dartmouth Institute for support, and Victor Saldarriaga and Andrew Vogt forexcellent research assistance. We are grateful to Leila Agha, Liran Einav, Je Emerson, Amy Finkelstein,John Friedman, Matt Gentzkow, R.B. Harris, David Laibson, Neale Mahoney, Matt Panhans, MariaPolyakova, Jon Skinner, and Ashley Swanson for helpful comments.Finally, I thank my parents, my sister, and best friends Zsuzsi, Adlai and Miklo´s for theirunconditional love, guidance, and encouragement throughout my life.xiiChapter 1IntroductionThis thesis consists of three chapters in applied microeconomics. These chapters touch upon areasof family economics and early childhood development, economics of education and health economics.They all exploit some unique institutional feature or policy change of major economic sectors—thelabor market, the educational and health systems—shaping incentives, to identify the causal impacton families’ or firms’ behavior, primarily focusing on disadvantaged members of the population.The first chapter asks: what drives parents’ child time allocation choices, and why do these differacross education groups? I focus on parental quality time, and the implications for early childhooddevelopment and skill gaps. From a Beckerian point of view it is puzzling why higher-educated parentsspend more time with their children, despite their less time spent on home production and leisure,and their higher opportunity cost of time in non-market activities. This cross-sectional observation,called the “parental time-education gradient” puzzle—documented by Guryan, Hurst and Kearney(2008)—is the starting point of this chapter.1 To resolve it, I examine parents’ time and marketgood responses to a shock to the opportunity cost of their time, by exploiting a drastic and exogenousuniversal daycare price decrease in Quebec in 1997. I ask whether different substitutability possibilitiesbetween time and market goods in child human capital and home production can explain parents’ timechoices both cross-sectionally and in response to the shock. I also ask whether heterogeneous timeefficiency in non-market activities by education can explain differential responses across educationgroups. Looking at parents’ responses to a price change helps to rule out competing explanations forthe cross-sectional observation, since alternative models predict responses the data rejects.Examining responses to a daycare price change also has immediate policy implications: govern-ments in many countries subsidize the labor market reintegration of mothers with young children, inpart responding to concerns about gender inequality within the household and on the labor market.However, a question arises whether these policies—such as providing direct daycare subsidies, tax cred-its or tax deductions to eligible daycare expenses—crowd out or reinforce parental investments in childhuman capital formation, other than daycare, such as parental quality time. Differential responsesby education have important implications for whether policies should target low-education familiesto “level the playing field”2, or rather should be universal. To the extent that parental quality time1Early references to this puzzle are Hill and Stafford (1974) or Leibowitz (1974).2Evidence on the impact of universal or large-scale daycare programs is inconclusive on the mean impact on childoutcomes. The results of Havnes and Mogstad (2015) suggest that the effects of subsidized daycare vary systematicallyacross the outcome distribution, and that disadvantaged children of are the primary beneficiaries. An example of targeteddaycare policy is the one implemented exactly in Quebec: the contribution for a subsidized daycare place recently changedfrom being universal to a system of a basic contribution plus an additional contribution, the latter adjusted by familyincome. As of January 1, 2016, the basic contribution is $7.55 per day, per child, and the additional contribution is0 below a family income of $50,000, then it increases gradually up to $13.15 per day, corresponding to $158,820. Theadditional contribution is reduced by 50% for second, and by 100% for third and additional children. Additional detailscan be found at http://www.budget.finances.gouv.qc.ca/Budget/outils/garde en.asp.1Chapter 1. Introductionand skill-enhancing resources contribute to child skill formation, differential time allocation choicesshape skill gaps in early childhood between children of higher- and lower-educated parents. Parentaltime investment behavior and the extent policies might influence them have important implications forequality of opportunity, given the high correlation between early childhood human capital and adultoutcomes on the one hand, and the increasing consequences of accident of birth on the other.3I have three contributions. First, the theoretical contribution is extending the classic Beckerianframework of child skill formation with time efficiency differences across education-groups in non-market activities, and allowing for differential substitutability between time and market goods in childhuman capital and home production. Second, motivated by the predictions of the model, I offer a newset of reduced-form results on parental time and household expenditures using exogenous daycare pricevariation. Using the same moments in the data, I estimate the model’s structural parameters on thesubstitutability between time and market goods in child human capital and home production, and onthe between-education-group heterogeneity in non-market time efficiency. Third, I test the behavioralskill gap between children of higher- and lower-educated parents in the first five years of life; using thestructural estimates and parents’ observed choices, I assess how universal daycare shapes the gap.I find that as daycare becomes cheaper, mothers are more likely to work and they supply morehours on the market. At the same time, both mothers and fathers increase time devoted to theirchildren, at the expense of home production time, while consuming more of home production marketgoods (eating out in a restaurant and hiring domestic help), and child market goods (daycare, games,books and toys). I find the time reallocation to be larger for higher-educated parents, having completedsome post-secondary education. I use the model to estimate structural parameters, which uncoverthe pivotal role of complementarity between time and market goods in child skill formation, andsubstitutability in home production. In addition, they suggest a time efficiency advantage in non-market activities for higher-educated parents, outweighing their higher opportunity cost of time.My findings on differential parental time responses link to the literature on human capital gapsin early childhood. There is evidence on significant cognitive, noncognitive (also called behavioral ordevelopmental)4 and health gaps between high- and low-educated parents’ children, opening up earlyand widening over ages.5 Although the literature on these gaps often uses the label ‘early childhood’,3Chetty et al. (2011) document that kindergarten test scores are associated with better adult outcomes on a widerange, such as earnings at age 27, college attendance, home ownership, and retirement savings. Chetty et al. (2014) showevidence that although rank-based mobility measures remained stable for children born between 1971 and 1993, sinceincome inequality increased, the “birth lottery” has larger consequences today.4Noncognitive or behavioral skills, such as temperament, persistence, self-discipline, adaptability, reliability, etc., haveonly recently attracted economists’ interest, in explaining general educational/ labor market outcomes (e.g. Rubinsteinand Heckman (2001), Osborne et al. (2001), Heckman et al. (2006), Borghans et al. (2008), Deming (2015)), labor marketreturns to particular personality traits (e.g. Osborne (2005), Mueller and Plug (2006), Heineck and Anger (2010)) orthe probability of dropping out of school (Coneus et al., 2011). This research indicates that noncognitive skills play asignificant, increasing role in the labor outcome process; e.g. Deming (2015) shows the link between jobs’ social skillrequirements and wage growth since 1980. Additionally, there is a growing literature on the technology of human capitalformation, including noncognitive skills (e.g. Cunha et al. (2006), Heckman and Cunha (2007)). The policy implicationargued by this research area is to invest in young disadvantaged children, as there is no efficiency-equity trade-off of suchinvestments and consequences of the accident of birth could be alleviated (Heckman and Masterov (2007)).5Fryer and Levitt document that the Black-White achievement gap increases on average by 10 percent of a standarddeviation per school year in the first three grades (Fryer and Levitt (2004), Fryer and Levitt (2006)), and rule out geneticdifferences across races to account for the gap (Fryer and Levitt, 2013). Cunha et al. (2006) and Carneiro et al. (2005)show an 8 and a 6 percentage points increase in the Peabody Individual Achievement Test (PIAT) mathematics score2Chapter 1. Introductionthe majority of this evidence relies on children aged five or older. I test the noncognitive gap in the first3-4 years of life, often labeled as the ‘critical period’ in child development. I find the largest wideningbetween children aged 0-2 and 3-4 years old. I find that bedtime reading, maternal (mental) healthand positive parenting practices are more important transmission mechanisms from socio-economicbackground to behavioral scores than are daycare time or maternal work. These results motivate thechosen age range and justify the focus on parental time in this chapter.My findings point to parental investment as one important mechanism behind widening skill gapsin early childhood. In this area of research there is more evidence on health gaps6, than there is oncognitive/non-cognitive skill gaps. According to Heckman and Cunha (2007), binding family incomeconstraints in early childhood lead to underinvestment in skills relative to the case of perfect creditmarkets, and variation in parental environment and initial endowment are the main reasons behindwidening skill gaps. Buttressing the importance of parental environment, I find that higher-educatedmothers most likely to be drawn (back) into the labor market increase time spent with their childrenthe most, and decrease home production and leisure time the most. Also, they invest more in reading,parenting and—if depression score is an adequate measure of health investments,—also in their ownmental health. Consistent with these larger investments, the behavioral outcomes of these mothers’children deteriorated less, or even improved after the introduction of the Quebec Daycare Policy.There is a literature in early childhood development on whether parents invest in a reinforcingor a compensatory manner; however, with respect to the child’s initial endowment. Rosenzweig andWolpin (1988) find that children with better health endowments are more likely to be breastfed, Dataret al. (2010) find that breastfeeding, nursery school enrollment and maternal time increase with birthweight and Aizer and Cunha (2012) find that the degree of reinforcement increases with family size.Less educated mothers are found to invest in a reinforcing, while more educated ones in a compensatorymanner (Hsin, 2012), although the literature is inconclusive about the mechanisms at play. My resultsin the first chapter indicate that high-educated parents invest in a compensatory manner with respectto the mother’s labor supply, with their time efficiency advantage being the underlying mechanism.The second chapter focuses on the impact of academic redshirting on student achievement andmental health, and its motivation stems from the literature on school entry delay and school startingage. There are two main practices to delay school entry by a year: one is compliance with the schoolenrollment cutoff date, the other is the practice of postponing an age-eligible, but potentially non-school-ready child’s school entry – called academic redshirting. In this chapter I measure the causalimpact of starting school a year older, using Hungarian data for years 2008-2014, and exploiting twodiscontinuity points in month of birth in an instrumental variable framework.gap between ages 5 and 13, between children from families in the lowest and highest income quartile and between Blacksand Whites, respectively. Case et al. (2002) and Currie and Stabile (2003) provide evidence on the steepening health- status gradient by age for the United States and Canada, respectively. Cunha et al. (2006) document a 4 percentagepoint increase in the anti-social behavioral score gap between both poor and rich children and between Black and Whitechildren aged 4-12. These gaps disappear when controlling for family structure, maternal education or maternal ability,measured by the AFQT-score; although there are no formal tests shown on the significance or the shape of the gap.6Case et al. (2002) document that poor children with a chronic condition have worse health than rich children witha chronic condition. Additionally, by ruling out mechanisms operating through health insurance, health at birth andgenetics, they find that income buffers children from adverse effects of chronic conditions and this buffering effect iscumulative. According to Currie and Stabile (2003), the worsening health-status gradient is more likely due to the higherarrival rate of shocks, rather than the lower recovery rate for low-status children.3Chapter 1. IntroductionTo the best of my knowledge, mine is the first attempt to measure the causal impact of redshirtingon child outcomes, using a natural experimental design. The main institutional feature I exploit is aschool-readiness evaluation in the Hungarian educational system, compulsory for potentially redshirtedchildren born before January 1st. By comparing children born around January 1st, I measure thecombined impact of age and boosted human capital due to redshirting, for complier children who mightor might not have struggled with school-readiness problems. By comparing children born around theJune 1st school enrollment cutoff date, I measure the sole age impact of starting school a year olderfor the complier children who, by definition, did not struggle with any school-readiness problems.I provide three further contributions. First, I show the impact on broader cognitive and differentnoncognitive child outcomes, than shown previously. Using Hungarian administrative testscore datafor 2008-2014, I show the impact on mathematics and reading testscores at grades 6, 8 and 10, graderepetition by grades 6, 8 and 10, and secondary school track choice. Using Hungarian survey data for2008, I show the impact on mental stability measures at grade 8, measured by anxiety and exhaustion.I present the impact by the interaction between gender and parental education; an angle that has beenignored by the majority of the reviewed literature. Second, I contribute to the literature on academicredshirting also by relating the propensity of being redshirted to birth shocks, family shocks, andhealth/developmental obstacles in early childhood. Third, exploiting natural variation in the fractionof summer-born children in class and month of birth, I disentangle absolute and relative age effects ofstarting school a year older due to compliance with the school enrollment cutoff date.Studies in the existing literature identify the impact of school starting age primarily using schoolenrollment cutoff dates. For instance, Elder and Lubotsky (2009) exploit variation in kindergartenentrance age stemming from two sources: the distribution of birth dates throughout the calendar yearamong those who comply with their state’s school enrollment cutoff date, and differences across statesin cutoff dates among children born on the same day but living in different states. Puhani and Weber(2007) use a similar identification strategy for Germany. I measure both the causal impact of startingschool later using the school enrollment cutoff date, and the causal impact of academic redshirting.The relevant literature focuses primarily on the effect of school starting age on student achieve-ment test results in kindergarten and at grades 4, 6 and 8. Additionally, there is some evidence ongrade repetition of first grade, secondary school track choice after grade 6, IQ measured at the age of18 and earnings at the beginning of the labor market history. Noncognitive and prosocial outcomes arealso considered, as persistence, stability and hyperactivity at ages 8, and 11 and teenage pregnancy.The literature on testscores shows consistently across countries that children who entered schoolat a higher age–due to the school enrollment cutoff date–perform better on achievement tests. Puhaniand Weber (2007) provide evidence for Germany, Kollo and Hamori (2011) for Hungary, Fredrikssonand Ockert (2006) for Sweden, McEwan and Shapiro (2008) for Chile, Elder and Lubotsky (2009) forthe United States and Crawford et al. (2007) for England. The range of the impact on standardizedtestscores is found to be between 0.2 and 0.5 standard deviations, with generally decreasing impactsacross grades 4 to 8 and larger effects for boys and disadvantaged children.7 The similarly positive7Puhani and Weber (2007) present evidence that entering the German primary school system at the age of 7 insteadof 6 increases 6th-grade reading testscores by 40 percent of a standard deviation. Kollo and Hamori (2011) show that theeffects are larger for disadvantaged children. They find very large effects for student achievement in grade 4 (80 percent4Chapter 1. Introductioneffects on grade repetition and secondary school track choice are documented by McEwan and Shapiro(2008) and Puhani and Weber (2007); entering school a year older is found to decrease the chanceof repeating first grade by 2 percentage points and to increase the probability of attending the mostadvanced school track by 12 percentage points.8 In contrast, Black et al. (2011) find a small positiveeffect of starting school younger on IQ scores at the age of 18. Regarding the noncognitive outcomes,Evans et al. (2010) show that older children have a significantly lower incidence of Attention DeficitHyperactivity Disorder (ADHD) diagnosis and treatment, Muhlenweg et al. (2012) present Germanevidence that school starting age has a stable positive effect on persistence, a short-run negative impacton hyperactivity, and a long-run effect on being more adaptable to change, while Fortin et al. (2015)find that being young in class aggravates an underlying propensity toward inattentive or hyperactivebehaviour, that is more prevalent for boys. Black et al. (2011) present Norwegian evidence thatchildren starting school at a younger age have a larger probability of teenage pregnancy and a short-run advantage in earnings (although disappearing by age the age of 30). Using extensive Danishdata on mental health outcomes, Dee and Sievertsen (2015) find that starting school a year oldersubstantially reduces inattention/hyperactivity at the age of 7, and the effect persists to the age of 11.I show the impact on broader cognitive (up to grade 10) and different noncognitive child outcomes (asanxiety and exhaustion), and by the interaction between gender and parental education.Similarly to school starting age, relative age effects (separately) are found to be positively relatedto various dimensions of educational success.9 However, this literature on relative age effects does notanswer the question whether relative age effects remain important beyond school starting age, thatcan be of interest of both parents and policy makers. In the last part of the chapter, exploiting naturalvariation in the fraction of summer-born children in class and month of birth, I find the positive effectsof higher school entry age to be driven by absolute, rather than within-class relative age effects. Theresults suggest that entering primary school a year later matters because it makes the child older inabsolute terms, rather than making the child older relative to her classmates at the time of the test.The third chapter, joint work with Jeffrey Clemens and Joshua Gottlieb, studies how closelyprivate insurers’ payment schedules follow that of Medicare’s. One of private health insurers’ uniqueroles in the United States is to negotiate physician payment rates on their customers’ behalf. Doprivate insurers’ payment schedules differ from that of Medicare, their public sector counterpart, or isthe ostensibly prominent private sector a mirage? We investigate the frequency with which privatelynegotiated payments deviate from the public sector benchmark using two empirical approaches. Theof a standard deviation), while 25-40 percent for student achievement in grade 8 for children whose mother finished atmost primary school. The same effects for children whose mother received a tertiary degree are 0.3 and 0.2 standarddeviations, respectively. They find substantially higher effects for reading, than for mathematics testscore. McEwanand Shapiro (2008) find that starting school one year later leads to a more than 30 percent increase in 4th-grade and8th-grade standardized testscores. They show that entering primary school one year older increases 4th-grade testscoresby 0.29 standard deviations in mathematics and 0.38 standard deviations in language. Elder and Lubotsky (2009) findevidence that entering kindergarten one year older leads to a 53 (83) percentage point increase in reading (mathematics)testscores during the fall of kindergarten. However, these effects fade away, faster for disadvantaged children.8In a similar study, Muhlenweg and Puhani (2010) find that early school entrants are only 2/3 as likely to enterGymnasium (the academic school track in Germany) as older entrants.9Dhuey and Lipscomb (2010) present evidence from the United States that an additional month of relative agedecreases the probability of receiving special education by 2-5 percent; Dhuey and Lipscomb (2008) find that the oldeststudents are 4-11 percent more likely to be high school leaders (and presumably enjoy the wage premium attached tohigh school leadership); Bedard and Dhuey (2006) show the effect of relative age on testscore across the OECD-countries.5Chapter 1. Introductionfirst exploits changes in Medicare’s payment rates and the second exploits dramatic bunching inmarkups over Medicare rates. Although Medicare’s rates are influential, we find that prices for 25percent of physician services, representing 45 percent of spending, deviate from this benchmark.To understand private insurers’ objectives, we examine heterogeneity in the pervasiveness anddirection of deviations they make from the Medicare benchmark. We show that the Medicare-benchmarked share is high for services provided by small physician groups. It is low for capital-intensive care, for which Medicare’s average-cost reimbursements deviate most from marginal cost.When relative prices deviate from Medicare’s, they adjust towards the marginal costs of treatment.One plausible interpretation of these findings emphasizes the complexity of the insurer-physiciancontracting environment. To manage the tension between gains from fine-tuning payments and costsfrom making contracts complex, insurers may draw on Medicare’s relative value scale for the purposeof contract simplification, while strategically adapting their contracts where the value is highest. Thisview is consistent with the heterogeneity we observe: the benefits of fine-tuning payments will tend tobe largest within contracts with large physician groups and for the capital-intensive services for whichMedicare’s average cost payments deviate most from marginal cost. Complementary interpretationsmay highlight the relevance of large firms’ bargaining power. The information content of the relativevalue scale on which Medicare’s payments rely can also be interpreted as a knowledge standard or,more generally, as a public good.Our results are of potential interest to analyses of two broader contexts. Learning how pricesare set in health care—a sector comprising 18 percent of the economy—is essential for understandingmacroeconomic price-setting dynamics. The service sector in general (Nakamura and Steinsson, 2008),and medical care in particular (Bils and Klenow, 2004), have especially sticky prices. We provideevidence on how this stickiness arises.10 Consistent with the evidence provided by Anderson et al.,(forthcoming) from retail, the complexity of physician contracting may explain both the long durationof these prices and the public-private linkages we identify.Public polices’ residual influence on private firms is relevant in a wide range of contexts. Out-side of the health care context, labor contracts sometimes benchmark wage rates to the statutoryminimum.11 Within the health sector, Medicare has been found to shape aspects of private players’behavior in the pharmaceutical, hospital, and physician marketplaces (Duggan and Scott Morton,2006; Alpert et al., 2013; White, 2013; Clemens and Gottlieb, 2017). The forces we investigate herediffer conceptually from those that our prior work uncovered, including the analysis of Clemens andGottlieb (2017) on physician payments. Clemens and Gottlieb (2017) assess how incentives and out-side options lead to Medicare’s influence on physicians’ bargaining positions. Our research emphasizesthe Medicare payment model’s role as an “industry standard.” This role stems in part from the in-formation contained in the Medicare payment model’s estimates of services’ relative input costs. Ouranalysis provides insights into the overall pervasiveness of benchmarking against Medicare’s relativecost schedule and into the types of contracts in which customization is most prevalent.10In particular, our empirical evidence supports price-setting mechanisms with the flavour of Christiano et al. (2005)or Smets and Wouters (2003, 2007).11A publicly posted contract template of the United Food and Commercial Workers Union (2002), for example, includesthe requirement that “At no time during the life of this Agreement will any of the bagger/carry-out rates be less thantwenty-five ($0.25) cents an hour above the Federal minimum wage.”6Chapter 2How Do Mothers Manage? UniversalDaycare, Child Skill Formation, andthe Parental Time-Education Puzzle2.1 IntroductionA mother working full-time today spends more time with her children than non-working mothers didin 1960, and today’s non-working mother spends less time on housework than working mothers spentin 1960.12 Highly-educated working mothers today devote on average 2 hours more per week to workand 1.7 hours more to their children than lower-educated working mothers do, at the expense of theirhome production and leisure time.13 Parental time investments in early childhood are crucial; forinstance, reading to the child an extra day per week in the first ten years of life was shown to increasereading testscores by more than 40 percent at the age of 11.14 In this chapter I ask: what drivesparents’ child time allocation choices, and why do these allocations differ across education groups?The classic Beckerian framework suggests that higher-educated parents, similarly to their lesstime spent on home production and leisure, should spend less time with their children, since theirnon-market activities have higher opportunity costs. However, previous research finds the opposite,leading to a “parental time-education gradient” puzzle, documented by Guryan, Hurst and Kearney(2008). In this chapter I develop a model of intra-household time and resource allocation that explainsthis puzzle. It also offers a mechanism based on heterogeneous time efficiency in non-market activities,that leads higher-educated parents to respond differently to price shocks.In my model setup parents derive utility from three commodities: child human capital, homeproduction goods and leisure goods. These commodities are produced from time and a market good,12Based on time use diary data compiled on 16 industrialized countries by Gauthier et al. (2004); see Table 1 formarried or co-habitating women between ages 20 and 49, with at least one child under the age of 5.13Based on data from the Canadian General Social Survey - Time Use Diary (1998), for working women below 50 intwo-parent households, having at least one child aged 0-4; low-educated denotes having at most a high school degree.14Using data from the NLSY’79, Price (2012) accounts for parents’ endogenous reading behavior by using birth orderas an instrument, exploiting the empirical observation that first-born children are read to more often. In an earlierpaper (Price, 2008), based on the American Time Use Survey, he provides evidence that first-born children receive morequality time from both the father and the mother—by approximately 20 and 25 minutes—per day at each age, thando second-born children at the same age. Using both the birth order instrument and a propensity score approach ondata from the Longitudinal Study of Australian Children, Kalb and van Ours (2014) find that being read to at the ageof 4 and 5 regularly has significant positive effects on the reading and cognitive skills of children up to an age of 10 or11: reading 3-5 (6-7) days per week increases a cognitive skill index by half a (almost one) standard deviation. Usingdata from the Fragile Families and Child Wellbeing Study and a propensity score approach, Hale et al. (2011) find apositive relationship between language-based bedtime routines and nighttime sleep duration, general health and verbaltest scores, and a negative relationship with behavior problems (anxious, withdrawn, and aggressive behaviors).72.1. Introductionwith constant elasticity of substitution (CES) production functions; and they are assumed to differ inhow easily time can be substituted for the market good in their production processes. By assumingthat parents use daycare while the mother is working, I link daycare price to the opportunity cost ofthe mother’s time in non-market activities. This framework maps structural parameters into optimalallocations, gives an explanation to the parental time-education puzzle and generates a rich set ofpredictions on responses to a shock to the opportunity cost of time. To account for differentialresponses by education, I allow for heterogeneity in the efficiency of parents’ time in child humancapital and home production. The model predicts that less expensive daycare induces mothers towork more, to use more daycare and to purchase more market goods, with their time response inparenting and home production depending on the complementarity or substitutability between timeand market goods in child human capital and home production. Higher-educated parents are predictedto change their time allocation more, if they have a time efficiency advantage in non-market activitiesthat outweighs their larger opportunity cost of time in non-market activities.I confirm the model’s predictions, by exploiting exogenous daycare price drop in Quebec (1997).I use data from the National Longitudinal Survey of Children and Youth (NLSCY), the Labor ForceSurvey (LFS), the Survey of Household Spending (SHS) and the Canadian Time Use Diary and Censusdatasets, on parents with children aged 0-4. I present new evidence on the total effect of an uncom-pensated daycare price change on parents’ time allocation at home, on their home production- andchild-related market good expenditures, and on their reading practices. I also exploit the Thuringiandaycare policy change (2006) and data from the German Socio-Economic Panel (GSOEP) to estimatethe impact of a compensated daycare price change and a pure income shock on parents’ time allocation,with the aim of disentangling income and substitution effects. I use the model to estimate structuralparameters, with which I am able to assess how universal daycare shapes skill gaps in early childhood.I confirm existing evidence on the Quebec daycare policy change on large maternal labor supplyand daycare use responses, and find that these are driven primarily by higher-educated mothers un-likely to work in the absence of the policy. I also find that as daycare becomes cheaper, (1) parentsincrease time devoted to their children, at the expense of their home production and leisure time, whileconsuming more of home production market goods (eating out, domestic help), and child market goods(daycare, child games and toys); (2) the time reallocation is larger for higher-educated parents.The first set of reduced-form findings (1) on time and market good expenditures generate partic-ular implications for the signs of the substitution parameters, and uncover the pivotal role of substi-tutability and complementarity between time and market goods: parents substitute their time awayfrom activities where time is substitutable with market goods (home production) to activities wheretime is complementary to market goods (child human capital production). These findings are consis-tent with available evidence: Aguiar and Hurst (2007), using scanner and time use data, find that timeand money for home production and shopping are highly substitutable. Cunha et al. (2010) find thatlagged human capital and investment inputs in child human capital production are complementary.The second set of reduced-form findings (2) on differential time responses imply, through the lensof the model, that higher-educated parents’ time is more efficient—has a higher marginal return—inchild human capital and home production, compared to lower-educated parents’ time. These findings82.2. Modelare also consistent with empirical evidence. Kalil et al. (2012) show that higher-educated motherschoose activities that most fit their child’s current developmental needs15; Hoff (2003) shows thathearing more advanced speech at home is one reason behind higher-educated parents’ children havingmore advanced language skills16; Weisleder and Fernald (2013) find large variation in child-directedspeech by parental education, and argue that children exposed to it become more efficient in processingfamiliar words in real time, and have larger expressive vocabularies by the age of two.The rest of the chapter is organized as follows. Section 2.2 develops the model, presents itstestable implications and discusses alternative models (alternative to differences in time efficiencyin non-market activities by education). Section 2.3 provides the institutional details of the QuebecDaycare Policy (1997). Section 2.4 presents the estimation approach and section 2.5 describes thedata. Section 2.6 presents and discusses the results on the total impact of a daycare price change,the structural parameter estimation and the policy simulation on early childhood skill gaps. Section2.7 discusses alternative models–alternative to time efficiency differences across education groups–,along with their predictions, that are not supported by the data. Section 2.8 disentangles income andsubstitution effects directly, by estimating the impact of a compensated daycare price change usingthe Thuringian Daycare Policy (2006-2010). Section 2.9 concludes.2.2 ModelThe model is inspired by the setup of time allocation outlined in words by Guryan et al. (2008). Thefollowing elements are taken from their setup: households derive utility from a home-produced good,a leisure good, and well-cared-for children. As in Becker (1965), these goods are produced from timeand a general market good. Following Aguiar and Hurst (2007), the goods can be classified based onthe elasticity of substitution between time and the market good in their production processes. Guryanet al. (2008), without formalizing this setup, discuss how optimal cross-sectional choices might changewith wages, the opportunity cost of time. They suggest that such a framework can be extended byheterogeneity of preferences or time productivity according to some measure of earnings potential.However, they did not investigate parents’ time reallocation responses to a shock to the opportunitycost of their time, neither did they distinguish between competing explanations for the parental time-education puzzle. My theoretical contribution is to formalize this setup, and to derive the model’sexplanation both for the puzzle—the cross-sectional observation on choices—, and parental timereallocation responses to daycare price changes (linked to the opportunity cost of mothers’ time).Parents’ time reallocation in response to daycare price changes is crucial not only for identificationpurposes, but it also allows us to separately test the explanations Guryan et al. (2008) provide for thecross-sectional observation. They propose the following explanations of why higher-educated parentsspend more time with their child(ren): (1) children’s human capital is a luxury good (with higherincome elasticity than home production or leisure); (2) the substitution of time and market goods in15For instance, they spend most of their times reading and problem-solving while their child is in preschool, but shiftto management of their children’s lives outside the home while their child is in middle school.16Speech at home is measured by number/length of utterances, word tokens/types, and topic-continuing replies.92.2. Modelproducing children’s human capital is perceived to be lower for higher-educated parents; (3) higher-educated parents have a higher preference for their children’s human capital; (4) returns to investmentin children’s human capital is higher for higher educated parents. Using my model I am able togenerate testable predictions for each of these four competing mechanisms, and I show that only (4)provides predictions on the parental time and daycare use responses that are consistent with the data.In this section first I present the model and the Marshallian demands. Then, I describe theestimation approach of the structural parameters, using the demands and exploiting exogenous daycareprice variation from the Quebec policy change. Lastly, I discuss the model’s reduced-form predictions.2.2.1 The Setup of the ModelConsider a model of the household that abstracts from bargaining and fertility decisions. Supposea household has one child and derives utility from three commodities: child human capital K, homeproduction goods H and leisure goods L, according to the following Cobb-Douglas utility function:U = βK logK + βH logH + βL logL. (2.1)For simplicity, I impose the following normalization: βK + βH + βL = 1.Commodities K, H and L are produced from time T and market good X with CES productionfunctions, where ρj is the substitution parameter between T and X, for j = K,H,L:K =[(γKTK)ρK +XρKK] 1ρK ; H =[(γHTH)ρH +XρHH] 1ρH ; L =[γLTρLL +XρLL] 1ρL . (2.2)Negative values of ρ imply complementarity between inputs, values of ρ between 0 and 1 imply sub-stitutability between inputs, with the Leontief and perfect substitution being the limiting cases. TKis parents’ time investments in child human capital, while XK includes daycare time D and all otherchild goods B (including child books, games and toys), in a nested CES with substitution parameterρX : XK = [BρX +DρX ]1ρX ; D has a price of m, while B, XH and XL have unit price. TH is time spenton home production, while XH includes, e.g., domestic help, laundry/cleaning services, pre-preparedmeals and food inputs. L can be thought of as leisure experience, produced from XL (say, movietickets or books) and leisure time. The total household time for category j is produced from time ofthe mother (M) and the father (F ), in a nested CES with substitution parameter ρTj :Tj =[(TMj)ρTj+(TFj)ρTj] 1ρTj for j = K,H,L.Mothers and fathers work to be able to buy the market goods and earn wage wM and wF , respectively.Higher- and lower-educated households differ by their time efficiency in child human capital,home production, and leisure production. The time efficiency parameters γK ,γH and γL are related tothe marginal product of time investment in non-market activities, and conceptually are closely relatedto the marginal productivity of work at home as in Gronau (1977). These parameters are allowed to102.2. Modeldepend on years of schooling S and a good-specific error εj : γj = Υ(S, εj), for j = K,H,L, where,after the parametrization of Υ, δj will represent the dependence (the coefficient) of γj on S. I allowfor the efficiency in transforming time into child human capital, home production and leisure goods todiffer by education. Specifically, I allow for the possibility that a higher-educated parent’s unit of time,on average, produces a different amount of commodity output, than does a lower-educated parent’sunit of time. Note that these parameters are linked to the marginal product of time input in the non-market production of K, H and L, but are not linked to market productivity, captured by the wagew. I discuss and show formally in Section 2.7 that alternative models only with differing preferencesor substitution parameters by education, or allowing daycare quality to decrease contemporaneouslywith the price decrease, all generate predictions that are not supported by the data.The structural parameters to be estimated are the substitution parameters between time andmarket goods in producing child human capital (ρK) and producing the home production good (ρH),and δK and δH , that show the dependency of time efficiency on schooling.The constraints households face incorporate the assumptions that (i) the parents use daycarewhile the mother is working (thus, D = TMW ), (ii) parents hire a nanny while enjoying leisure timetogether, and (iii) there is no overlap between any two time-use categories: e.g. during home productiontime the child might be around the parents, but is not the primary focus of their attention. Formally,the household maximizes utility in (2.1) with respect to B,XH , XL bought by the household andtime use allocations TW , TK , TH , TL of both the mother (M) and the father (F ), subject to the timeconstraints T iW + TiK + TiH + TiL = T¯ for i = M,F and the household budget constraintB +XH +XL +mTMW + nTML = IM + IF . (2.3)In (2.3) m denotes hourly daycare price, TMW denotes the mother’s time spent on work, n denotes thehourly nanny cost, IM = wMTMW and IF = wFTFW denote the mother’s and the father’s labor income,respectively, and T¯ denotes total time available to each member of the household.I make three simplifying assumptions, justified by the data, to keep the model tractable andsimple. First, by forcing households to use daycare while the mother is working, the model makesdaycare cost m part of the mother’s, but not the father’s opportunity cost of time17; in addition, Iassume that fathers supply labor full-time inelastically, thus IF = τF T¯wF , where τF is the fraction ofT¯ spent on work by fathers. As will be shown later, fathers’ labor supply is unresponsive to a daycareprice change. Second, I abstract from any bargaining and time reallocation between the mother andthe father after a daycare price change, and assume that the mother spends a constant θK and θHfraction of total household time on the children and home production, respectively.18 As will be shownlater, mothers’ and fathers’ time use responses move not only in parallel after a change in the price17This can be seen by rearranging the budget constraint as B + XH + XL +(mM − w) (TMK + TMH + TML ) +mF(TFK + TFH + TFL)+ nTML =(wM −m) T¯ + wF T¯ .18 Note that since at the solutionθj1−θj =(wM−mwF) 1ρTj−1 , this assumption implies that(wM−mwF) 1ρTj−1 is constant. Aslightly stricter assumption is that τFwFw−mM is constant, that will be only used for recovering structural parameters.112.2. Modelof daycare, but their time weights in child human capital and home production are approximatelyconstant. Since any further extension complicates the solution of the model without adding importantinsights, θK and θH is considered as constant. Finally, I assume positive assortative matching onwages: ∂IF∂wM> 0, despite that the father’s labor income IF is assumed to be unrelated to m.Let α denote the fraction of XK of other child market goods (than daycare), so that αXK = B.Then the household budget constraint (2.3) can be re-arranged in terms of the mother’s variables:αXK +XH +XL +(wM −m) θKTK + (wM −m) θHTH + (wM −m+ n) 12TL =(wM −m) T¯ + IF ,(2.4)where(wM −m) T¯ denotes the household’s total income (the income the household would receive inthe hypothetical situation of the mother spending all her time on working). From (2.4) the opportunitycosts (denoted by oj) of the mother’s different time use categories can be defined as: oK = oH = wM−mand oL = wM −m+ n. To ease notation, from now on the mother’s wage wM will be denoted by w.2.2.2 The Solution of the ModelAs derived in the Appendix, the Marshallian demand for child goods and child time are:X∗K =1αβKI1 +((w−m)θKαγK) ρKρK−1and T ∗K =βKI ((w −m) θK)1ρK−1 (αγK)ρK1−ρK1 +((w−m)θKαγK) ρKρK−1, (2.5)while the Marshallian demands for home production H and leisure L are:X∗j =βjI1 +(ojθjγj) ρjρj−1and T ∗j =βjI (ojθj)1ρj−1 γρj1−ρjj1 +(ojθjγj) ρjρj−1, (2.6)where I = T¯ (w −m) + IF is the potential household income, and the oj-s are defined above.The Marshallian demands depend on schooling through the wage w and time efficiency γj . Thisdelivers an important contribution of this model: total differentiation of optimal cross-sectional choicesand optimal responses with respect to schooling leads to a decomposition into two key channels: a wagechannel and a time efficiency channel; generally, these two channels move into the opposite direction.Some other models of daycare and labor supply incorporate daycare expenditures as a fixed costpaid by the household if the mother is working, independent of the work time TMW ; thus daycare pricem is subtracted from household income I as a lump sum part. Contrary to these other models, mymodel has the ability to predict different responses for child and home production time, depending onthe signs of ρK and ρH ; observe that this is due to the link between the net wage and the substitutionparameters in the power in (2.5) and (2.6), and by making m part of the mother’s opportunity cost.122.2. Model2.2.3 Estimating Structural Parameters from the Model’s Optimal DemandsIn order to recover the structural parameters from the Marshallian demands (2.5) and (2.6), I need toimpose a functional relationship between the time efficiency parameter γ and schooling. For individuali and good j (j = K,H,L), I assume a multiplicative structure19, that is γji = Sδji εji. Then, (2.5)implies the following regression equation for j = K between a non-linear function of the Marshalliandemand, the logarithm of schooling Si, and the logarithm of the net wage wi −mi:log(βKθKT¯ (1 + c)T ∗Ki− 1)=ρK1− ρK log θK+ρKρK − 1δK logSi−ρKρK − 1 log[(wi −mi)(1 +m1ρX−1i)]+ρKρK − 1 log εKi,(2.7)where c = τFwFw−m is a constant, by the stricter assumption that θK is a constant. Then, by estimatingthe regression model in (2.7), the coefficient on the log function of the net wage can be estimated andρK recovered. From ρK and the coefficient on logSi, δK can be recovered. In (2.7) the log of netwage wi−mi is likely endogenous, but, as discussed in more detail in the identification section, can beinstrumented by an exogenous policy change. The corresponding regression equation for j = H is:log(βHθHT¯ (1 + c)T ∗Hi− 1)=ρH1− ρH log θH +ρHρH − 1δH logSi −ρHρH − 1 log (wi −mi) +ρHρH − 1 log εHi.2.2.4 Reduced Form Predictions of the ModelThis section aims to answer three questions that get at the heart of the parental time-education puz-zle. First, how do the optimal cross-sectional choices of market goods and time depend on schooling.Second, how do optimal choices change in response to a daycare price decrease. Third, how do theseresponses depend on schooling. The answers need to account for the following two channels operatingsimultaneously: first, holding the mother’s wage w constant, higher-educated parents’ time is allowedto be differentially efficient in child human capital production, home production and leisure production(“time efficiency channel”). Second, holding the time efficiency γj constant, higher-educated mothers’wage (thus, the opportunity cost of her home production, child and leisure time) is higher (“wagechannel”). For simplicity, m is assumed to be identical across schooling.The Dependence of Optimal Cross-sectional Choices on SchoolingTo see how optimal choices of market goods depend on schooling, I totally differentiate the optimalchoices X∗j with respect to schooling S, and decomposedX∗jdS into a time efficiency channel∂X∗j∂γjdγjdS and19As an alternative functional specification, I assume an additive structure on the time efficiency: γKi = δ0+δKSi+εKi;then, the three structural parameters δ0, δK and ρK can be estimated with instruments Si, policytp and Si × policytp,in a General Method of Moments (GMM) framework, where εKi can be expressed asεKi =(βKθKT¯T ∗Ki(1 + c)− 1) ρK−1ρK(wi −mi)(1 +m1ρX−1i)θK − δKSi.132.2. Modela wage channel∂X∗j∂wdwdS (for j = K,H,L, and similarly for T∗j ). The time efficiency channel showshow the optimal choices change after a marginal change in γ, holding the wage w constant. The wagechannel shows how the optimal choices change after a marginal change in w, holding time efficiencyγ constant. This total differentiation is helpful to think about the puzzle; the empirical estimatesindicate which of the channels needs to dominate, given the education gradient observed in the data.In Appendix A.1 I show that these derivatives can be decomposed into three terms: a base term,an assortative matching term, and a remainder term. In the main text, I focus on the sign of the baseterm, as the assortative matching term is always positive, and the remainder term is relatively small.Proposition 1: The base wage channel, unambiguously and independently of the signof the elasticity of substitution parameters, is positive for all goods.Proposition 2: The base wage channel is positive for child time if ρK < 0 (comple-mentarity), and negative for home production time if ρH > 0 (substitutability).The intuition is that, ceteris paribus, higher-wage parents are more able to buy home productiongoods, and if inputs are substitutable, they spend less time on home production than lower-wageparents do. At the same time, higher-wage parents are also more able to buy child goods, and ifinputs are complementary, they spend more time with their children than lower-wage parents do.Proposition 3: The base time efficiency channel for the child good is positive if ρK < 0and δK > 0; for the home production good it is negative if ρH > 0 and δH > 0.Proposition 4: The base time efficiency channel for child time is negative if ρK < 0and δK > 0; for home production time it is positive if ρH > 0 and δH > 0.The intuition behind these propositions lies in the production technologies: if there is complementaritybetween inputs in child human capital production, then if time efficiency increases, the same level ofchild human capital can be attained by slightly increasing the level of child goods and decreasingchild time more, thereby achieving cost-savings. Similarly, suppose there is substitutability in homeproduction; then, if time efficiency increases, the same level of home production can be attained byslightly increasing home production time and decreasing more the level of home production goods.The model’s explanation for the parental time-education puzzle is the wage channel dominatingthe time efficiency one: keeping time efficiency constant, higher-wage parents are more able to affordall goods, and if there is complementarity in child skill formation, they also spend more time withtheir children, despite their time efficiency advantage in child human capital production. Thus, thepuzzle can be explained without introducing heterogeneity in time efficiency across education groups.142.2. ModelResponse to a Daycare Price DecreaseHow do optimal choices respond to decreasing daycare prices? First, a daycare price decrease generatesa dominating income effect, so demand for all market good increases—these results do not hinge onthe sign of the substitution parameters. The effect of a marginal decrease in daycare price on timespent with the child or on home production almost exactly mirrors the effect of a marginal increasein wage; the two effects would be identical but for the fact that fathers’ income is not dependent onm and 1− α (α is a function of the relative price of daycare and other child goods). Therefore, whenremainder terms are sufficiently small, in response to falling daycare prices, home production timedecreases and parental time increases—note that these results do hinge on the signs of the ρ’s.Proposition 5: A decrease in the price of daycare induces parents to increase theirdemand for all (child, home production and leisure) goods.Proposition 6: If ρK < 0 (complementarity), parents increase their child time whendaycare price falls. If ρH > 0 (substitutability), parents decrease their home productiontime when daycare price falls.The Dependence of Optimal Responses on SchoolingHow do responses to a daycare price decrease depend on schooling? To answer, let us totally differ-entiate the good responses∂X∗j∂(−m) and time responses∂T ∗j∂(−m) with respect to schooling, and decomposethe change into a wage channel and a time efficiency channel.Proposition 7: Suppose that δK > 0, ρK < 0 (complementarity) and δH > 0, ρH > 0(substitutability). Then the time efficiency channel is positive for the child human capitalgood, and is negative for the home production good if ρH <12 .Proposition 8: If ρK < 0 and ρH > 0, the wage channel is negative for the childhuman capital good, and is positive for the home production good if ρH <12 .Proposition 9: Suppose that δK > 0, ρK < 0 (complementarity),γK < 1 and δH >0, ρH > 0 (substitutability) and we exclude extremely large values of γH . Then the timeefficiency channel is positive for child time, and is negative for home production time.Proposition 10: If ρK < 0 and ρH > 0, the wage channel is negative for child time,and is positive for home production time if ρH <12 .This model reveals and emphasizes the critical role played by complements and substitutes in householdchoices about children. Consider the case of complementarity between inputs in the production of K;then, for child good responses, the time efficiency channel is positive, while the wage channel isnegative. Similarly for child time responses, the time efficiency channel is positive: keeping wageconstant, parents with more efficient parental time will increase their child time more. At the sametime, the wage channel is negative: ceteris paribus, parents with higher wage increase their parental152.3. Institutional Background and Available Evidencetime less. Thus, higher-educated parents increase time spent with their children more if the formerchannel dominates, i.e. if their time efficiency advantage in child human capital production is largeenough to outweigh their higher opportunity cost of time in non-market activities.For home production goods, for analytical convenience consider the case when ρH <12 ; thenthe time efficiency channel is negative, while the wage channel is positive. Regarding time responses,the time efficiency channel is negative: keeping wage constant, parents with more productive homeproduction time will decrease their home production time more. On the other hand, ceteris paribus,parents with higher wages (thus higher opportunity cost of time) will decrease their home productiontime less. Higher-educated parents decrease more their home production time if their time efficiencyadvantage is large enough to outweigh their higher wage.2.3 Institutional Background and Available EvidenceIn this section I describe the policy change that provides identifying variation for my empirical strat-egy. I also review existing empirical evidence, emphasizing the gaps my work seeks to fill.2.3.1 The Quebec Daycare Policy Change (1997)To enhance mothers’ labor force participation, child development, and equality of opportunity, in 1997the government of Quebec granted children aged 0-4 universal access to centre-based or home-basedgovernment-provided, regulated, institutional daycare20 at an out-of-pocket price of $5 per day. Theaccess was universal, irrespective of the parents’ labor market status, and without entry requirementsor means-testing. The phase-in was gradual by age: in 1997 all 4-year olds were exposed to the policy,and in the three consecutive years exposure was extended to all 3-, 2-, and less than 2-year olds.There were quantity and quality changes, as well as operational reforms associated with thepolicy change. First, approximately 65,000 extra regulated daycare spaces were opened between 1998and 2001, then an additional 90,000 until 2007 (Lefebvre and Merrigan, 2008).21 Second, in 2000the educational requirements for the regulated daycare institutions’ staff were substantially increasedand their wages were scheduled to increase by 35-40 percent over a four-year period. Finally, themaximum facility size was increased by holding staff-to-child ratios fixed (with the exceptions of 4-5year old children) and parental involvement in the board of directors increased (Baker et al., 2008).The quality audit study by Japel et al. (2005) shows that more (less) centre-based and home-baseddaycare providers provided good-quality (inadequate-quality) services than did for-profit daycares andunregulated for-profit daycares, by primarily excelling in the quality of the interactions between staffand children, and less in the quality of the educational activities and the personal care routines.20Institutional care incorporates daycare centers, nursery school/preschool and before/after schools.21According to Baker et al. (2008), the transition to the new system around 1997 happened with frictions, and the localgovernment responded to the excess demand by creating new subsidized places; they refer to media mentions suggestinga queue of 35,000 children initially. However, there is limited information available on the characteristics of the queuing:in the NLSCY only in waves 7 and 8—thus only in the post-policy period—there is information on Quebec-residentsattending the subsidized daycare program, and the reasons for not attending, including not enough space.162.3. Institutional Background and Available EvidenceAs Baker et al. (2008) document, this policy changed the financial incentives primarily for richerfamilies, as direct daycare subsidies for poorer families and a refundable tax credit, depending onfamily income, were already available before the policy change. Parents who received a subsidizeddaycare spot were not eligible for any further direct subsidy and provincial tax credit for daycareexpenses, but remained eligible for a federal deduction. Prior 1997 low-income families were eligiblefor direct daycare subsidies, and single women typically qualified for substantial subsidies. In theirAppendix A, Baker et al. (2008) review the family tax credits in Quebec and Canada, including, forinstance, the two types of income-dependent refundable tax credits (the Canada Child Tax Benefituntil 1999, and the National Child Benefit Supplement, introduced in 1998), and the Quebec FamilyAllowance, that changed in 1997, moving from universal to income-tested and targeted allowances.They also graph the effective subsidy of daycare prices by province over the 1990s, separately forparents in two-parent families with at least one child below the age of 5, and for single mothers; theyshow that the impact of the policy is by 50% smaller for the latter. These two reasons–substantialsubsidies for singles prior, and contemporaneous policy changes of the Quebec Family Allowance–ledthem to exclude single parents from their analysis, and I follow their sample selection.At the same time, Lefebvre and Merrigan (2008) highlight that possibly liquidity-constrainedlow-income families, who might have had problems in accessing reliable daycare services before, mayhave made use of the new daycare regime. They also emphasize the features of the new institutionaldaycare places, which many parents might have preferred over the relative-provided, non-licenseddaycare, as being available for longer hours, being licensed and regulated. Japel et al. (2005) findthat in centre-based daycare children received services of similar average quality irrespective of familybackground, while in regulated and unregulated home-based daycare and for-profit daycares attendedby disadvantaged children were of lower quality.2.3.2 Available Evidence on the Quebec Daycare Policy Change (1997)The first set of empirical evidence is clear: the policy increased maternal labor supply and daycareuse.22 Baker et al. (2008) show for two-parent families that being eligible for this program increaseddaycare usage, primarily in institutional care and care in other’s home (provided by a licensed non-relative) and increased maternal labor supply, with the fraction of working mothers having their childin daycare increasing the most. Lefebvre and Merrigan (2008) use data from the Survey of Laborand Income Dynamics (SLID) for 1993-2002, and find that the policy had a positive effect on theshort-term labor supply of mothers (on both margins and earnings), who had at least one child aged1-5; the effects are significant for mothers with more than a high school diploma. Lefebvre et al. (2009)find that the policy had long-term labor supply effects for mothers, who benefited from the programwhen their child was less than 6 years old; the results are driven by less educated mothers.The second set of empirical findings is controversial: Baker et al. (2008) show for two-parentfamilies that, on average, program eligibility led to worse child outcomes and parenting practices,22Empirical evidence on maternal labor supply from other countries include, e.g., Blau and Tekin (2007) and Tekin(2007) for daycare subsidies on single mothers, Fitzpatrick (2010) and Havnes and Mogstad (2011) for universal childcare,and Bauernschuster and Schlotter (2015) for public child care. Baker (2011) and Cascio (2015) provide a summary onthe evidence base of universal childcare.172.3. Institutional Background and Available Evidenceincreased maternal depression and family dysfunctioning.23 Kottelenberg and Lehrer (2013) substan-tiate these results by including more treated cohorts receiving the treatment when daycare centerswere better established, and supply constraints were less binding. Baker et al. (2015) show that thesenon-cognitive deficits persisted to teen ages, and that cohorts with increased daycare access had highercrime rates, worse self-reported health, and lower life satisfaction. Kottelenberg and Lehrer (2016) findthat parents in two-parent households of 4-year-old children, who were induced to increase daycareuse by the policy change, increased their propensity of reading to the child daily, while parents of0-3-year old children decreased their daily reading propensity. Brodeur and Connolly (2013) find thatthe policy decreased the level of happiness of married women, with no impact on their life satisfaction.I show evidence on the impact of program eligibility in Quebec on a new set of parental timeallocation outcomes, such as total time spent with the child, home production time and leisure time. Inaddition, I complement the parental quality time outcomes used by Kottelenberg and Lehrer (2016); Iconfirm that that program eligibility decreased parents’ propensity to read their child daily, but showthat it increases reading time at the lower end of the reading distribution, by decreasing the propensityto never read to child, and increasing the propensity to read once or several times per week.Regarding empirical evidence in other policy contexts, my set of time use outcomes are mostcomparable with the outcomes studied by Cascio and Schanzenbach (2013). They find that high-qualityuniversal pre-school availability in Georgia and Oklahoma induced low-educated mothers (having atmost a high school degree) to decrease total time spent with their children present, and to increasetime spent caring for or helping to children, with no detectable impacts for high-educated mothers.However, they do not find robust labor supply impacts for low-educated mothers, and do not detectany impacts for higher-educated mothers; as shown in Section 2.6.2., the time responses I detectfor high-educated mothers are triggered by an increase in their labor supply. In order to look atthe impacts of increasing incentives to work, Gelber and Mitchell (2012) exploit income tax changesbetween 1975 and 2004 using data from from the Panel Study of Income Dynamics, the American TimeUse Survey and Consumers Expenditure Survey. They find that changes in the Average Net-of-TaxRate substantially increases single mothers’ hours worked, at the expense of their home productionand leisure time—the same substitution pattern I show in Section 6. However, contrary to my findings,they report an insignificant positive point estimates for child time (with a value of t-statistics 1.4).To the best of my knowledge, this is the first paper on the impact of universal daycare availabilityon household expenditures on child goods, food, and on goods that help parents substitute their timeout from home production, such as eating out or hiring domestic help. My results align with the resultsof Gelber and Mitchell (2012), who find that, in response to increasing returns to work, expenditureson food prepared away from home and at home significantly increase and decrease, respectively, withno significant impact on hiring domestic services (although their point estimate is positive).23Empirical evidence on child development include, for instance, Carneiro and Ginja (2014) from Head Start, Berlinskiand Galiani (2007) from Argentina, Havnes and Mogstad (2015) from Norway, Datta Gupta and Simonsen (2010) fromDenmark and Dustmann et al. (2013b) from Germany. Empirical evidence on maternal mental health and child-parentinteractions include Herbst and Tekin (2014).182.4. Empirical Approach2.4 Empirical ApproachIn this section I describe my empirical framework. To keep it as simple as possible, I start with astandard Difference-in-Differences (DiD) framework. I then present the estimation equations to re-cover structural parameters of the model. Next, I test the widening behavioral skill gap by age; tosee through which channel maternal education is most related to child development, I assess how theinclusion of parental investment measures explain the gap. Finally, I discuss identification issues.2.4.1 Differential Reduced-Form Impacts of the Quebec Daycare PolicyFirst, I assess the overall and the differential impacts of the “$5/day” Quebec daycare policy bya DiD identification strategy, where I estimate Intent-to-Treat (ITT) effects—the effects of programavailability—in a repeated cross-section structure.24 I test whether the policy impact differs for higher-educated families: I differentiate families where the mother obtained—in addition to a high-schooldegree—some post-secondary, college-level studies (either finished or unfinished), from families wherethe mother obtained a high-school degree but had not studied at the post-secondary level. Usingchildren aged 0-4 in two-parent families25 in the NLSCY, the Census and the LFS, and two-parentfamilies with at least one child aged 0-4 in the GSS and the SHS, I estimate the following two models:Yi = α0 + α1policytp + α2Ci + α3Ui + α′4t + α′5p + α′6a + α′7Xi + νi, (2.8)Yi = β0 + β1policytp + β2policytp × high-educi + β3Ui+β′4t + β′5p + β′6a + β′7te + β′8pe + β′9Xi + εi.(2.9)where i indexes household, t time, p province, and a indexes the child’s age; Y is either a daycare use,a parental labor supply, a parental time use, a household expenditure, a home-environment, a childdevelopmental or a parental health outcome; policytp is an interaction between the child being born inan exposed cohort (alternatively, the family observed in the post-policy period) and residing in Quebec;C indicates that the mother obtained a high school degree and had some post-secondary, college-levelstudies that is at lower level than a Bachelor’s degree (including CEGEP, community college andtrade/technical degrees); U indicates that the mother obtained at least a Bachelor’s degree. In whatfollows, I will refer to high-educated families (high-educ = 1), where either C = 1 or U = 1. α4tand β5t correspond to a full set of year (or wave) dummies, α5p and β6p correspond to a full setof province dummies, α6a and β7a correspond to a full set of age dummies, β8te corresponds to avector of education-specific dummies, indicating the post-policy period, β9pe corresponds to a vectorof education-specific indicator-variables, indicating residence in Quebec and X includes the age andgender composition of the children, household size, and the parents’ age. The household’s educationis determined solely by the mother’s education, and I do not control for the father’s education.2624The standard DiD specification I implement is the same as implemented by Baker et al. (2008), Kottelenberg andLehrer (2013) and Lefebvre and Merrigan (2008).25Based on the discussion in Section 2.3.1 and following Baker et al. (2008), I exclude single parents from the analysis.26Results are essentially unchanged when I do control for the father’s education, or when I determine the household’seducation based on the interaction between the mother’s and the father’s education.192.4. Empirical ApproachStandard errors are clustered at the (province×post)-level, to account for within-province corre-lation of errors over time both in the pre-policy and post-policy period, allowing for a structural breakin the temporal correlation at the time of policy implementation.27Since the available data structure is not panel, but repeated cross-section, I do not observe pre-policy work history of mothers. To see whether the responses differ based on the mother’s propensityto work in the absence of the policy, I estimate additionally the following model:Yi = γ0 + γ1policytp + γ2policytp × propensityi + γ3policytp × propensity2i+γ4propensityi + γ5propensity2i + γ6Ci + γ7Ui + γ′8t + γ′9p + γ′10Xi+γ11postt × propensityi + γ12Quep × propensityi + ηi,(2.10)where propensity denotes the propensity of the mother working in the absence of the policy; to obtainit, I estimate a probit model on the pre-policy sample using pre-determined variables, and I predictthe propensities for the whole sample. post equals 1 if the child was born in an exposed cohort (alter-natively, if the family is observed in the post-policy period), and Que equals 1 if the household residesin Quebec. γ1 shows the policy impact for mothers with zero predicted propensity. A significantlypositive estimate of γ2 indicates that the policy impact is increasing with the predicted propensity towork in the absence of the policy. The propensity score is predicted by pre-determined variables notaltered by the policy change, as by the interaction of parents’ education, a full set of province andchild age fixed effects, the parents’ age, household size, and a linear time trend.282.4.2 Recovering Structural ParametersIn Section 1.2.3 I showed that by assuming a multiplicative functional form on the good-specificproductivity errors, the Marshallian demands can be transformed into the regression equation (2.7),where the coefficient on the schooling and net wage variables are nonlinear functions of the structuralparameters ρj (the substitution parameter) and δj (the time efficiency parameter), for j = K,H,LI aim to recover. In order to recover ρK and δK , the specific model I estimate by Ordinary LeastSquares (OLS) and Two-Stage Least Squares (2SLS) methods is the following:log(βKθKT¯ (1 + c)T ∗Ki− 1)= λ0 + λ1 logSi + λ2 log[(wi −mi)(1 +m1ρX−1i)]+ λ′3t + λ′4p + λ′5Xi + ξi,(2.11)where λ1 =ρKρK−1δK , λ2 = −ρKρK−1 , and the error term is ξi =ρKρK−1 log εKi; S is 2 if the mother obtainedat least some post-secondary education and 1 otherwise, w is the hourly wage of the mother and m isthe hourly daycare expenditure29, λ3t corresponds to a full set of year dummies, λ4p corresponds to afull set of province dummies, and X includes the mother’s and father’s age, and full set of dummies27The confidence intervals for the main estimates in Appendix Tables A.20-A.23 show that the standard errors arerobust to the Wild-bootstrapping method of Cameron et al. (2008), accounting for small number of clusters.28The estimation details in the NLSCY, the Census and the GSS datasets can be seen in Appendix Table A.24.29Since the GSS does not contain information on wages or daycare expenditures, while the Census does not containinformation on daycare expenditures, these variables needed to be imputed; details are available in the Appendix.202.4. Empirical Approachcorresponding to the age and gender composition of the children. Similarly, in order to recover ρHand δH , the specific model I estimate by OLS and 2SLS methods is the following:log(βHθHT¯ (1 + c)T ∗Hi− 1)= λ0 + λ1 logSi + λ2 log (wi −mi) + λ′3t + λ′4p + λ′5Xi + ξi. (2.12)I do not estimate the parameters of βθ , ρX or c =τFwFw−m , but assume the value ofβKθK= 0.31 ,βHθH= 0.21 ,ρX = −1 and c = 0.6, and perform sensitivity analysis.30The excluded instrument is policytp, an interaction between the child being born in an exposedcohort—alternatively, if the family observed in the post-policy period—, and residing in Quebec. Thus,the corresponding first-stage in case of T ∗Ki islog[(wi −mi)(1 +m1ρX−1i)]= ς0 + ς1 logSi + ς2policytp + ς′3t + ς′4p + ς′5Xi + ιi. (2.13)2.4.3 The ‘Human Capital Gap-Regressions’I next examine the importance of parental investments in explaining human capital gaps in earlychildhood. To highlight the importance of the chosen age range and to justify the focus on parental(quality) time in this chapter, I assess the widening behavioral human capital gap by age and I will referto them as ‘gap-regressions’. Using children aged 0-11 in the NLSCY, I run the following regression:yi = τ0 + τ1high-educi + τ2high-educi × age(3− 5)i + τ3high-educi × age(6− 8)i+τ4high-educi × age(9− 11)i + τ5HSi + τ ′6t + τ ′7p + τ ′8a + τ ′9Xi + ιi,(2.14)where i indexes household, t indexes time, p indexes province, a indexes the child’s age, y is the averageage-standardized behavioral score (measured by hyperactivity), high-educ indicates high-educated,defined as the mother having either some college, or university education, age(3 − 5) indicates thechild being between 3 and 5 years old, and HS indicates the mother having at most a high schooldegree. τ6t corresponds to a full set of year (or wave) dummies, τ7p corresponds to a full set ofprovince dummies, τ8a corresponds to a full set of child’s age dummies, and X includes the genderof the child, number of older and younger siblings (capped at 3 and 2, respectively), the size of thehousehold, the mother’s and father’s age, and the father’s education. Standard errors are clustered atthe (province×post)-level.The coefficients of interest are τ1 − τ4, corresponding to the behavioral/developmental humancapital gap—also called the noncognitive gap—across age-categories. τ1 shows the gap for children30ρX is the substitution parameter between daycare time and other market goods in XK ; since empirically I find thatboth of them increase as daycare prices fall, I assume a negative value -1 for ρX . βK and βH are taken to be 0.3 and0.2, respectively, and since I use the mother’s time in the estimation, I consider θK = θH = 1. Assuming τF = 14, 0.6corresponds to average wages observed in the data. The sensitivity analysis with respect to alternative parameter valuesis in Appendix Tables A.25 and A.26.212.4. Empirical Approachaged 0-2, while τ1 + τ2 shows the gap for children aged 3-5; so, for instance, τ2 shows whether the gapsignificantly widens after the first 3 years of life. I present the estimation results of (2.14), and assesshow the inclusion of parental practices, maternal health, maternal employment, daycare attendanceand parents’ reading practices change the estimated coefficients τˆ1 − τˆ4.The aim of this solely descriptive exercise is to see through which channel maternal education ismost correlated with child development; if, for instance, the estimated coefficients shrink by includingparental reading practices, that is an indication of parental reading being an important transmissionmechanism between socio-economic background and child development. Recognizing these channelsnot only help us understand which parental investment measures are crucial in shaping the gap, butalso help us to see in which measures educational differences matter the most. This approach is similarto controlling for mother’s ability, family income, and family structure to see by how much the averageanti-social behavior score percentile by income quartile or race is reduced, chosen by Cunha et al.(2006); or, reporting the ‘conditional difference’ by Baker and Milligan (2016), by controlling for someobservable characteristics after reporting the means of test scores at ages 4-5 across gender.2.4.4 IdentificationThe main requirement for the DiD model to provide a consistent estimator of the policy impact isthat the counterfactual time trend in outcomes in Quebec is parallel to the observed time trend in therest of Canada (i.e. the trends in the absence of the policy would have been parallel in and outside ofQuebec). Figures 2.1 and 2.2 show the time trends in the mother’s employment rate, working hoursand regulated daycare use, respectively. The pre-trends for Quebec and the rest of Canada are eitherparallel or converging for labor supply, and slightly diverging for daycare use; however, once the policyis implemented the trends diverge sharply.Besides the aforementioned graphs suggesting that the parallel trend assumption is reasonable,Baker et al. (2008) provide evidence that there were no detectable differential trends for several im-portant demographic/control variables in Quebec, relative to the rest of Canada. Kottelenberg andLehrer (2013) document similar trends for maternal labor supply and daycare usage in Quebec, rel-ative to the rest of Canada, before the introduction of the policy. To address any Quebec-specificshocks coincident with the Quebec daycare policy, (i) I check and confirm that the estimates shownin Section 6 are robust to the inclusion of province-specific economic conditions, (ii) that there areno policy impacts on older children who were never exposed to the policy, and who do not have anyyounger siblings exposed, and (iii) there are no or substantially lower impacts on household food anddomestic expenditures for households without children.31When estimating the structural parameters, there is a concern in the models (2.11) and (2.12) thatthe variable on wage is potentially endogenous. It is plausible that innate parental ability, althoughorthogonal to education, is related to the wage through some general ability. The model also providesguidance on the sign of the OLS estimator’s asymptotic bias of λ2, and predicts an upward bias forchild time, based on the following reasoning. First, holding wage and education constant, parents31The robustness and placebo check results of (i) and (ii) are available on request.222.5. Data, Measurement and Sample Selectionwith better parental abilities are predicted to spend less time with their children; thus, ceteris paribus,there is a positive correlation between the error term and the outcome variable log( βKθKT¯ (1+c)T ∗Ki− 1),in which optimal parental time T ∗Ki is in the denominator. Second, there is a concern of a positivecorrelation between the function of the net wage and parental ability in the error term.However, this potentially endogenous variable can be instrumented with policytp, the policy vari-able, provided that Cov(log εKi, policytp)= 0, where policytp equals 1 if the household lives in aprovince with a daycare policy in effect, and 0 otherwise. The identification assumptions are that thepolicy change was orthogonal to parental ability, but related to net wage. Thus, the source of theidentifying variation is the same in the reduced-form, as in the parameter estimation. However, whilethe first set of estimation results suggest the signs of the structural parameters based on the model,the second set of results reveal their magnitude, to perform policy simulations on childhood skill gaps.2.5 Data, Measurement and Sample SelectionIn this section I provide basic information on the five Canadian datasets used in the main analysis inSection 6. I then describe the measurement of the outcome variables, as well as the eligibility variable.2.5.1 DatasetsTo measure the total effect of a daycare price change on parental and child outcomes, I use Canadiandata from five sources: the first seven waves of the NLSCY, the 1996/2001/2006 waves of the CanadianCensus, the 1994-2006 cycles of the Canadian LFS, the cycles from 1986/1992/1996-2009 of the publiclyavailable SHS (previously named as Survey of Family Expenditures or FAMEX), and the cycles from1998, 2005 and 2010 of the Time Use Diary of the GSS. 2-11 and 0-4 years old children in two-parentfamilies are selected from the NLSCY, the Census and the LFS, and two-parent households with havingat least one 0-4 year old child are selected from the GSS and the SHS.The NLSCY follows the development and well-being of Canadian children from birth to earlyadulthood and collects information about factors influencing a child’s social, behavioral and emotionaldevelopment. An initial sample of 0-11 years old children was sampled in the first wave in 1994 andfollowed for fourteen years until 2008; I do not use the panel structure. Starting at Cycle 2 a new cohortof 0-1 years old children was added in each cycle, following the expansion of the NLSCY emphasizingearly childhood development. Data in the first cycle are representative of children between 0-11 in1994, data in the second cycle are representative of children between 0-13 in 1996, and so on.The LFS provides detailed labor market data on the civilian population 15 years of age and over(excluding persons living on Aboriginal reserves, full-time members of the Canadian Forces and theinstitutionalized population). Basic demographic information, such as gender and exact date of birth,is available for all family members in the household. The LFS uses a rotating panel sample design:selected households remain in the sample for six consecutive months.32The two main objectives of the GSS are to collect data on social trends to monitor changes in32More information is available at http://www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey&SDDS=3701.232.5. Data, Measurement and Sample Selectionthe living circumstances of Canadians, and to collect responses on a rotating set of particular topics.33One of the rotating topics is time use, measured in 1998, 2005 and 2010. The target populationconsists of all non-institutionalized persons 15 or older, living in the Canadian provinces. Until 1998the target sample of respondents included around 10,000 individuals, before 1998 around 25,000.34Besides household expenditures, the SHS collects information on annual income of householdmembers from personal income tax data, demographic characteristics of the household, certain dwellingand household equipment characteristics. The SHS combines a questionnaire with recall periods basedon the type of expenditure and a daily expenditure diary. The target sample is similar to the LFS’.352.5.2 The Measurement of Outcome Variables and EligibilityThe age-standardized behavioral score for ages 2-11 is the age-standardized hyperactivity score fromthe NLSCY, where larger values indicate worse behavioral/developmental outcomes as more severehyperactivity. The daycare use measures—also from the NLSCY—are all binary variables and indicatewhether the child is in institutional care (daycare centers, nursery school/preschool and before/afterschools), daycare in own home (provided by a relative/non-relative), daycare in others’ home (providedby a relative/non-relative), or in any care from the aforementioned ones. The home-environmentmeasures from the NLSCY include age-standardized36 hostility/consistency/positive parenting scores37the age-standardized depression score of the mother (a high score indicating the presence of depressionsymptoms), and the age-standardized family functioning score38. The parental labor supply measures,stemming from the NLSCY, the Census, and for robustness checks from the LFS, include an indicatorvariable of being employed, an indicator variable of being employed part-time, and actual hours worked.The time outcomes include work-related time39, child time, home production time and leisure time;measured in fraction of all time (in percentages) in the GSS Time Use Diary, and in categories of hoursspent per week in the Census. The household expenditures (from the SHS) include the fraction of foodexpenditures (all/from store/from restaurant), of expenditures on domestic help, and on the child asdaycare expenditures and expenditures on toys and games, out of all expenditures (in percentage).Eligibility is defined as follows: in the NLSCY, no 0-4-years old child is eligible in waves 1 and2 (1994 and 1996); in wave 3 (1998) the 4-year old children were eligible, while in later waves (2000,33These include commuting to work, labor market outcomes and perceptions, society and community, time use andunpaid work, and are usually repeated every 5 years.34More information is available at http://www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey&SDDS=4503.Time devoted to the child includes putting children to bed, getting them ready for sleep, personal care, help-ing/teaching/reprimanding/reading to children, talking to them/having conversations with them, medical/emotionalcare. Work time includes work for pay at main job and other jobs, overtime work, looking for work, unpaid workin a family business, travel during work, waiting/delays at work, meals/snacks at work, idle time before/after work,coffee/other breaks at work, travel to/from paid work. Leisure time includes personal care, relaxation, entertainment,social/educational/civic/volunteering/communicational/sport activities, reading/watching television/listening to media.35More information is available at http://www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey&SDDS=3508.36Note that age-standardization is with respect to the child’s age.37This last measure captures the frequency of positive encounters with the child, as laughing with or praising her.38This scale is used to measure various aspects of family functioning, e.g., problem-solving, communications, roles,affective involvement, affective responsiveness and behaviour control by capturing how cooperatively and constructivelythe family solves problems, how close the relationship is between the parents, how much is alcoholism a problem in thefamily, etc.39Work-related time includes not only hours of actual work, but commuting and other work-related time.242.6. Results2002, 2004 and 2006) all children are eligible. In the LFS, no 0-4 year old child is eligible before 1997;4-year old children are eligible in 1997 and 1998, 2-4-year old children are eligible in 1999, and allchildren are eligible from 2000 on. In the GSS, pre-policy year is 1998, post-policy years are 2005and 2010. In the Census, pre-policy year is 1996, post-policy years are 2001 and 2006. In the SHS,pre-policy years are 1986-1997, post-policy years are 1998-2009.2.6 ResultsI first present the impact of decreasing daycare prices on maternal labor supply, daycare use, parentaltime use, and household expenditures, for all observations and also by education. Next, I show thepolicy impacts by the mother’s predicted propensity of working in the absence of the policy. Then, Iassess the widening skill gap across ages. Finally, I present the estimated structural parameters, alongwith counterfactuals on how the behavioral gap would evolve under targeted or universal daycareregimes, or if high-educated (low-educated) parents had no time efficiency advantage (disadvantage).2.6.1 Reduced Form Results: Policy Impacts for All and by EducationIn each table from 2.1 to 2.6, I show the basic DiD results for numerous outcomes. Table 2.1 confirmsexisting evidence on daycare use and maternal labor supply responses to decreasing daycare prices.Tables 2.2 to 2.6 show the empirical contributions of this chapter on the following responses: parentaltime use, the propensity to read to the child and household expenditures on food, domestic help,daycare and child toys. The first row of each table shows the outcome variables (in bold), Panel Ashows the coefficients and standard errors on the policy and education coefficients from estimating theDiD models (2.8) and (2.9), where, for each outcome variable, the first column corresponds to (2.8),and the second column corresponds to (2.9). The coefficients on the interaction variables show whetherthere is a differential policy impact by socio-economic status, measured by the mother’s education. Inparticular, they show whether the policy impact is significantly different for families where the motherhas some post-secondary education or a university degree from families where the mother has at mosta high school degree without any post-secondary studies. Panel B shows the weighted baseline meansand the estimated policy impacts, by education, to see the size of the policy impact; for each outcomevariable, the first column shows the weighted baseline mean in the estimation sample for observationswhere policytp = 0, while the second column shows the estimated policy impact. The p-values in PanelC show whether the policy significantly impacted high-educated families, in terms of the correspondingoutcome variable; i.e. it corresponds to the test: H0 : β1 + β2 = 0; H1 : β1 + β2 6= 0.40As a reminder, the model predicts the following after a decrease in the price of daycare: first,demand for home production goods, child human capital goods and leisure goods increases. If inputs inhome production are substitutable, while in child human capital production they are complementary,40To see the policy impact graphically, Figures A.1, A.2 and A.3 show the estimated difference between Quebec andthe Rest-of-Canada across years, with a 95% confidence band, stemming from a variant of model (2.8); in these models,instead of interacting the eligibility-by-cohort indicator variable with indicator variable for Quebec, year-indicators areinteracted with the variable indicating residence in Quebec.252.6. Resultsthen, as a response, home production time decreases, while parental time increases. This time reallo-cation is larger for high-educated parents, if their time efficiency advantage in non-market activities issufficiently large to outweigh their higher opportunity cost of time in non-market activities.Daycare useTable 2.1 shows that, consistent with previous evidence and the aim of the policy, the Quebec daycarepolicy significantly increased daycare utilization in regulated (institutional) daycare and in any careby 18 and 13 percentage points (200 and 29 percent of the baseline mean), respectively.41 The policyimpact on institutional daycare utilization is significantly larger for high-educated families in absoluteterms, but not relative to their baseline mean (it is 247 and 190 percent for low- and high-educatedfamilies, respectively). The policy impact on daycare in any care is again significantly larger for high-educated families, but relative to their baseline mean the impact is approximately 29 percent for bothgroups.42 Despite the larger change in the financial incentives for high-educated, the relative impacton any daycare use is the same for low- and high-educated groups; hence differential intent-to-treatresults can be attributed to differential impact, as opposed to differential uptake of the policy.Maternal Labor SupplyTable 2.1 (and the Appendix Tables A.4-A.5) show the policy impact on parents’ labor supply alongthe extensive margin using data from the NLSCY (and, for robustness check from the Census andLFS); a daycare price decrease significantly increased the mothers’ immediate propensity of beingemployed, by 3.4 to 7.6 percentage points (by 6-13 percents relative to the baseline mean).43 Theseeffects are driven by high-educated mothers both in absolute and relative terms; low-educated mothersare more likely to work by 1-4 percentage points (significant depending on sample size).44 The impacton the father’s labor supply is considerably lower (0.6-1.3 percentage points, on a base of 88 percent).Table 2.1 (and the Appendix Tables A.4 and A.6) show that a daycare price decrease significantlyincreased mothers’ working hours, by 1.2 hours on a base of 20 hours45; the increase is driven by high-41Appendix Table A.1 shows that the Quebec daycare policy significantly decreased daycare usage in own home andin other’s home by 3 and 2.4 percentage points (13 and 22 percent of the baseline mean).Using waves 1-2 and 4-5 of the NLSCY, Baker et al. (2008) find that, after the implementation of the policy, theproportion of 0-4 year olds in any daycare rose by 14 percentage points in Quebec relative to the rest-of-Canada, that isvery close to my point estimate of 0.131, using waves 1-7. Using waves 1-2 and 5-7, Kottelenberg and Lehrer (2013) find apoint estimate of 0.196; this considerably larger point can be understood in light of Figure 2.2, as regulated (institutional)daycare use—that the policy targeted—rose the most between waves 3 and 5, and then 6 and 7.42On the intensive margin, Appendix Table A.2 shows that the daycare price decrease induced on average a significant5.9 hours (a 49 percent) increase in time spent in daycare, while the fraction of children being in daycare for at least20 hours per week increased by 16 percentage points (by 59 percent). Similarly to the extensive margin, the policyimpact on daycare hours is larger for high-educated families in absolute terms, but is not substantially different relativeto the baseline mean (44 and 50 percent increase in hours for low-and high-educated families). Appendix Table A.3 alsoreveals that the bigger part (approximately 75 percent) of the increase in (any) daycare use comes from mothers workingsimultaneously, while primarily low-educated mothers increased their daycare use without working at the same time (by4.9 percentage points on a base of 4.4 percent). Similarly, the bigger part (approximately 75 percent as well) of thedecrease in no-daycare use comes from decreasing non-working.43Regarding mothers’ labor supply on the extensive margin, Baker et al. (2008), Kottelenberg and Lehrer (2013) andLefebvre and Merrigan (2008) find a point estimate of 0.077, 0.110 and 0.073, respectively.44Using the SLID for years 1993-2002, Lefebvre and Merrigan (2008) only find significantly positive impacts for motherswith more education than a high school diploma, with a point estimate of 0.065.45Respondents who do not work any hours are included, as well. According to Appendix Table A.4, that is based onCensus data, fathers’ hours supplied decreased slightly, only for partners of low-educated mothers. However, AppendixTable A.6, that is based on LFS data, shows no detectable impact on fathers’ labor supply on the intensive margin.262.6. Resultseducated mothers. By taking the lower bound of the estimated extensive margin impact (0.034) andusing the fact that, on average, 75% of the working women work full-time (Table A.5), this increaseon the intensive margin comes entirely from changes on the extensive margin.Parental Time UseThis section shows the most important empirical contribution of this chapter. I show that eligibleparents increased total time spent with their child, at the expense of their home production and—forhigh-educated parents—leisure time. I show complementary parental quality time outcomes to theones used by Kottelenberg and Lehrer (2016); I confirm that eligibility for universal daycare programin Quebec decreased parents’ propensity to read their child daily, but I show that it increased readingtime at the lower end of the reading distribution, by decreasing the propensity to never read to child,and increasing the propensity to read once or several times per week.Table 2.2 reveals that parents decreased their propensity of never reading to their children byalmost 3 percentage points, corresponding to a large 33 percent decrease. Parents also increased theirpropensity of reading once a week to their children by 2 percentage points (50 percent, relative to tothe baseline), while increased reading 2-3 times a week by 3.6 percentage points (18 percent), with theformer response coming entirely from high-educated families. Reading daily to the children decreasedby 2.6 percentage points (3.9 percent), with no detectable differences across education groups.Table 2.3 shows the policy impact on the parents’ child and home production time allocation,measured in the Census. In response to decreasing daycare prices mothers increased their averagetime spent with their children by 0.87 hours (on a base of 44.8 hours); the response is significantlylarger for high-educated mothers. The same pattern holds for fathers; the corresponding impact is0.72 hours (on a base of 24 hours), which doubles for partners of high-educated mothers.46 At thesame time, mothers decreased their home production time by 2 hours per week (on a base of 30 hours),while fathers decreased their home production time 1 hour per week (on a base of 14 hours).47 Notethat the increase in child time is almost 33% larger than the difference between the average child timespent by high- and low-educated families.Table 2.4 presents the policy impact on time use for mothers, estimated from the Time UseDiary48: the policy induced mothers to increase time spent with their children by 1.5 percentagepoints (significant at 1%, at a base of 13 percent) and decrease home production and leisure time by46Appendix Table A.7, where the outcome is dichotomous, reveals that mothers were significantly less likely to spendat most 15 hours, but more likely to spend at least 30 hours with their child, by approximately 2 percentage points.Fathers show a 2.7 percentage point decrease in spending at most 15 hours per week with their child, and a 1.1 (1.9)percentage points increase in spending 15-30 (31-60) hours per week with the child (see Appendix Table A.9).47Appendix Table A.8 shows that mothers increased spending at most 15 hours per week on home production by 5.3percentage points, and decreased spending 15-30 hours (31-60 hours) on home production by 0.9 (2.8) percentage points,respectively. The decrease in spending 15-30 hours on home production comes entirely from high-educated mothers,otherwise the differences across education are not statistically significant. Fathers’ home production time response canbe seen in Appendix Table A.10.48There is a decrease in work time for low-educated mothers (significant at 10% confidence level), while the increasein work time is not statistically different from zero, presumably due to small sample size. While this might seemto contradict the results on hours in Appendix Table 2.1, a reminder that in the GSS only, work time also includescommuting, and anything work-related; if only hours are considered in the GSS, the point estimate stays negative andcannot be statistically distinguished from zero. The results on the extensive margin (not shown for the GSS) are consistentacross the datasets. These results are available on request.272.6. Results0.65 and 0.9 percentage points, respectively.49 These responses come from high-educated mothers: low-educated mothers significantly decreased work-time in favor of their leisure time, while high-educatedmothers significantly decreased home production time and leisure time (by 1 and 2.2 percentage points)in favor of their child time (corresponding to a 2.28 percentage point or a 17 percent increase).50Household ExpendituresThe policy impact on the fraction of particular household expenditures (measured in percentage ofall expenditures) can be seen in Tables 2.5 and 2.6. For each outcome variable, the first columncorresponds to (2.8) including all years of 1986, 1992 and 1996-2009, the second column correspondsto (2.8) including only years when education was measured (years 1986, 1992, 1996, 2007-2009), andthe third column corresponds to (2.9) in the same smaller sample. As before, the coefficients ofthe interaction variables show whether there is a differential policy impact by the mother’s education.Panel B shows the weighted baseline means in the estimation sample and the estimated policy impacts,by education. The p-values in Panel C correspond to the test β1 + β2 = 0.51Table 2.5 shows that, as a response to decreasing daycare prices, two-parent families increasedall food expenditures significantly by 0.8-0.9 percentage points (by 7 percent, relative to the baselinemean); expenditures on food from stores increased by 0.55 percentage points (5 percent), while eating-out expenditures increased by 0.34 percentage points (14 percent). The increase is significantly larger(in absolute and in relative terms) for low-educated families. Table 2.6 reveals that for high-educatedfamilies—more likely to use regulated, more expensive daycare before—daycare expenditures decreased(by 28 percent), while for low-educated families—more likely to use informal, even free daycare ar-rangements before— they increased (by 26 percent). At the same time, the increase in expenditureson child games and toys (representing child market goods), and domestic help (representing homeproduction goods) is not significantly different across education groups.These results confirm the model’s first prediction: as a response to decreasing daycare price,demand for home production goods (as eating out and domestic help) and child goods (as child gamesand toys) increase. These, together with results on increasing child time and decreasing home produc-tion time suggest that parents substitute their time away from activities where time is substitutablewith market goods to activities where it is complementary to market goods. Higher-educated parents’larger child time (home production time) increase (decrease) suggests that their time efficiency advan-tage in child human capital and home production dominates their higher opportunity cost of time innon-market activities.49Although the latter impacts are imprecisely estimated, primarily due to the small sample size. The child timeincrease comes primarily from increasing time devoted to playing with the children, putting them to bed, and help-ing/teaching/reprimanding; for higher-educated mothers there is an increase in travel-time to the daycare facility, whilefor lower-educated mothers there is an increase in reading to the children. The decrease in leisure time comes primarilyfrom decreasing personal care, relaxation, sleep, civic and voluntary activities and sports; these results are not shown forthe sake of brevity, but are available upon request.50Appendix Table A.11 shows that although that fathers in high-educated families increased their child time, thishappened at the expense of home production time and work time.51In Appendix Figure A.3 the estimated difference between Quebec and Rest-of-Canada can be seen for householdswith and without children aged 0-4, for general household expenditures (food and domestic help) as a falsification test.282.6. Results2.6.2 Reduced Form Results: Policy Impacts by the Propensity of MotherWorking in the Absence of the PolicyThe results so far suggest that on average, as a response to decreasing daycare prices, mothers si-multaneously increased their labor supply, work time and child time at the expense of their homeproduction and leisure time. However, the question remains whether this time trade-off has actuallybeen made also by mothers who would not be working in the absence of the policy, but increase theirlabor supply due to the policy change. Mothers who would work full-time presumably do not adjusttheir labor supply, only make use of the positive income effect for market goods, affecting their intra-household time allocation. Then, since high-educated mothers are more likely to work and use publicdaycare in the absence of the policy, their observed larger child time increase might be solely due tocomposition. To investigate this, I now pursue an analysis in which I compare mothers who wouldbe more likely to work and use daycare in the absence of the policy, with mothers who would be lesslikely to do so. The data structure does not allow me to observe mothers’ working history, thereforeI use a propensity score-based approach. First, using a probit model, for each household I combine aset of predetermined variables—such as education, age, household structure, number of children andtheir age—into a single index, that is the estimated propensity of the mother working in the absenceof the policy. Then, I estimate policy impacts by this propensity, using model (2.10); by controllinglinearly for the predetermined variables in X that were used for the score estimation, the variation leftcomes from higher-order interactions and the non-linearity of the probit model. Finally, I graph thepolicy impacts, where the horizontal axis shows the predicted propensities and the vertical axis showsthe estimated policy impact; low propensities correspond to mothers unlikely to work in the absenceof the policy, for whom both income and substitution effects are present.Figures 2.3 and 2.4 graph the estimated policy impacts by predicted propensities for high- andlow-educated families, respectively, with a 95% confidence band, based on estimates from the linearmodel (2.10)52. The first two panels of Figure 2.3 (lines in blue) show that for high-educated mothersthe policy impact on working now is significantly decreasing with the propensity of working in theabsence of the policy, accompanied by the same pattern for using any daycare. Comparing a high-educated mother with a low predicted propensity, say 0.5, with a very similar high-educated motherwith high predicted propensity, say 0.85, the policy impacts are 9.15 versus 1.35 percentage points onworking, and 14.5 versus 9.66 percentage points on (any) daycare use. The corresponding impacts onworking time are 1.49 versus 0.15 hours per week.53The previous results suggest that high-educated mothers unlikely to work in the absence of thepolicy are drawn into the labor market. Strikingly, the increase in the propensity to read to the child52The underlying coefficients can be seen in Appendix Tables A.14-A.18. Appendix Figures A.4 and A.5 show it for thequadratic model. The distribution of the predicted propensity in the NLSCY, Census and GSS datasets, by education,can be seen in Figure A.6, where the 5 ticks in each graph correspond to the 10th, 25th, 50th, 75th and 90th percentileof the predicted propensity distribution, respectively.53The underlying coefficients are in Appendix Tables A.14 (mother working and daycare use) and A.13 (hours). Usingdata from the Census and the LFS, respectively, Appendix Tables A.12 and A.13 substantiate the previous result from theNLSCY that for high-educated mothers the policy impact on working now is significantly decreasing with the propensityof working in the absence of the policy (see the linear model).292.6. Resultsis larger for these mothers.54 Comparing a high-educated mother with a propensity of 0.5, with the‘average’ mother (with a predicted propensity of 0.72), the former is by 1.2 percentage points more,while the latter is by 1.2 percentage points less likely to read several times per week to the child.The positive policy impact on child time is decreasing (line in red), while the negative policy impactson home production and leisure time are increasing with the estimated propensity (lines in black,although for home production time the estimates are very imprecise).55 These results suggest thatamong high-educated mothers, the largest intra-household time reallocation was made by the onesdrawn back or drawn into the labor market by less expensive daycare.Regarding parenting and mental health investments, panels in the third row of Figure 2.3 revealthat the non-likely worker high-educated mothers’ parenting behavior (measured by positive parentingand negative hostility) and mental health (measured by negative depression score) deteriorated to asignificantly smaller extent after the policy was implemented (lines in green); for mothers with lowestpropensities these outcomes even improved.56 For instance, the policy impacts on negative hostilityscore for a high-educated mother with propensities of 0.4, 0.6 and 0.8 are 0.047, -0.07 and -0.19 standarddeviations, respectively; the same impact on positive parenting are -0.013, -0.115 and -0.22 standarddeviations. High-educated mothers drawn into the labor market even with a predicted propensityof 0.55 actually show better mental health, with a 2.7 percent of a standard deviation decrease indepression score; the corresponding policy impacts on negative depression score for a high-educatedmother with a predicted propensity of 0.4, 0.6 and 0.8 are 13.5, -1 and 15.4 percent, respectively.The previous results suggest that high-educated mothers drawn into the labor market are notonly the ones who invest more in reading, but relatively more into parenting and—if one’s depressionscore reflects one’s mental health investments,—also into mental health. Consistent with these largerinvestments, panels in the fourth row of Figure 2.3 show that the behavioral outcomes of these high-educated mothers’ children deteriorated to a significantly smaller extent after the daycare price fall,and in some cases even improved (brown lines).57 For instance, the policy impacts on the child’snegative hyperactivity score for a high-educated mother with a predicted propensity of 0.4, 0.6 and0.8 are 0.043, -0.058 and -0.16 standard deviations, respectively; the same impacts on (negative)anxiety score are 0.031, -0.08 and 0.19 standard deviations, and on (negative) aggression score theyare 0.044, -0.042 and 0.13, respectively.It is unclear whether the same pattern—less deteriorating parental and child outcomes for moreworking mothers—holds for low-educated mothers, according to Figure 2.4. First, the policy impacton working now and working hours is significantly increasing with the propensity of working in theabsence of the policy for them.58 Second, both home production and leisure time is estimated toincrease with predicted propensity for them (although the former is imprecisely estimated).59 Third,only their propensity to read often (in the quadratic model) increases with propensity, while parenting54The underlying coefficients can be seen in Appendix Table A.15.55The underlying coefficients can be seen in Appendix Table A.16.56The underlying coefficients can be seen in Appendix Table A.17.57The underlying coefficients can be seen in Appendix Table A.18.58The underlying coefficients are in Appendix Tables A.14 (mother working) and A.13 (mother working and hours).59The underlying coefficients are in Appendix Table A.16.302.6. Resultsand mental health outcomes do not.60 Finally, the interaction point estimates for negative hyperac-tivity and negative aggression scores are positive, but imprecisely estimated, and for negative anxietyscore are even negative.612.6.3 Behavioral Skill Gap RegressionsI now turn to the parental investments explaining the behavioral skill gap in early childhood. Thepurpose of the following descriptive ‘skill gap-regressions’ is to see (1) at which ages the gap significantlywidens, and (2) which parental investment measures explain the gap.The first column (the ‘base’ specification) in Table 2.9 shows the estimation result of model (2.14).There is a significant gap between high- and low-educated parents’ children already in their first threeyears of life (in the ‘critical period’): 6 percent of a standard deviation of the average age-standardizedhyperactivity score in favor of high-status children. It significantly widens to 12.6 percent once thechildren reached 5 years of age, and the further changes in the gap cannot be statistically differentiatedfrom zero; this means that the hypotheses α2 = α3 and α2 = α4 can not be not rejected.To see through which channel parental education and child development is most related, addi-tional columns show the estimation result for the same model by adding the corresponding variableof parenting practices, maternal health, maternal work, daycare use or parental reading. The initialgap at is essentially unaffected with the inclusion of maternal work or daycare use, suggesting thatthese are not important channels through which high-educated parents’ children develop better thanlow-educated parents’ children do. However, comparing two similar children receiving the same pos-itive parenting practices at home, the disadvantaged child has worse behavioral outcomes on averageby 4.8 percent of a standard deviation; thus, 15% of the baseline gap in the critical period is operatingthrough positive parenting practices, that are not impacting the gap at later ages. The early childhoodgap reduces to 3.6-3.9 percent and becomes significant only at 10 percent, once controlling for maternalmental health or family functioning, accounting for 13 of the variation in the hyperactivity score. Theearly childhood gap reduces to 4.3 once controlling for parental reading practices, accounting for 14 ofthe variation. Inclusion of any of the parenting, family functioning, maternal health, daycare use orlabor supply measures do not alter by how much the childhood gap widens at later ages.The previous results justify the chosen age-range and the focus on parental (quality) time in thischapter. In addition, they indicate that maternal health, parenting practices and reading to the childare the most important transmission mechanisms through which parental education and child devel-opment are related. Also, they suggest that high-educated mothers drawn (back) to the labor marketinvest more in parenting measures that matters most for the shape of the gap. This compensatoryparenting behavior of high-educated parents–compensating more work time with more positive parent-ing, more bedtime reading and better mental health–is one of the mechanisms behind the widening gap.60The underlying coefficients are in Appendix Tables A.15 (child time) and A.17 (parenting and mental health).61The underlying coefficients are in Appendix Tables A.18. Appendix Table A.19 reveals that the increase in householdexpenditures is not solely, and not even primarily, due to income effects: families where the mother is drawn into thelabor market are significantly more likely to increase food and daycare expenditures, than do families where the motheris already working (the coefficients’ signs for food expenditures are consistent, but the estimates are noisy).312.6. Results2.6.4 Structural Parameters and Policy SimulationThe reduced-form results so far are consistent with a scenario where time and market goods arecomplementary in child human capital production (ρK < 0), and substitutable in home production(1 > ρH > 0); they are also consistent with a scenario where high-educated parents’ time is moreefficient in child human capital and home production (δK > 0, δH > 0). Now I turn to the estimationof these structural parameters to see their magnitude and use them to perform counterfactual analysis.Tables 2.7 and 2.8 show the estimation result of the models (2.11) and (2.12) for child time andhome production time, respectively, using the GSS and Census datasets. The first-stage F-statisticsare 46 and 71 in the case of child time, and 3 and 23 in the case of home production time forthe GSS and Census datasets, respectively. Although time use is measured differently in the twodatasets, the point estimates are relatively similar for child time and imply a substitution parameterfor child human capital production of approximately -0.4 in the Census. This estimate suggests amodest complementarity between time and market goods in child human capital production. Forhome production time the point estimates are almost identical: ρˆH = 0.67 in the Census, implyingstrong substitutability between time and market goods in home production.62The estimated time efficiency parameters (δˆK > 0 and δˆH > 0) imply that higher-educatedmothers’ time is more productive in both child human capital and home production. Thus, a one unittime investment made by a higher-educated mother increases her child’s human capital level more thana one unit time investment made by a lower-educated mother. This by itself would imply a behavioralhuman capital gap in the cross-section; the further difference in the levels of child human capital stemsfrom different choices between higher- and lower-educated parents. The reduced-form estimates showthat both types of parents increase daycare and parental time inputs after the daycare price falls, andif child human capital has only these two as inputs, the level of child human capital is predicted toincrease for both higher- and lower-educated parents’ children. Even though higher-educated parentsare found to increase their inputs even more, the skill gap between 0-4 aged children might shrink orexpand, depending on the concavity of the human capital production function, and the degree of timeefficiency advantage of higher-educated parents.To see the life-cycle implications of these estimated parameters, Figure 2.5 shows the gap in childhuman capital before and after the subsidized daycare policy change.63 I assume the policy to takeplace at the age of 2.5, which age corresponds to the largest widening in the behavioral skill gap seenin Table 2.5. The first panel shows how the gap widens in the absence of the policy. For ages 0-2,the level of child human capital (K) for higher- and lower-educated parents’ children in the controlgroup are calculated with the observed average daycare hours (XK) and hours spent with the child62As a reminder, I do not estimate the parameters of βθ, ρX or c =τFwFw−m , but assume the value of0.31, -1 and 0.6,when estimating the models (2.11) and (2.12) by 2SLS. Appendix Tables A.25 and A.26 show the robustness check fordifferent values of ρX and β. The implied substitution parameter ρK decreases with βK and ρX , but it is always negative,and is at most -0.23. Similarly, that the implied time efficiency parameter δK decreases with βK and ρX , but it is alwayspositive, and at least 0.18. The implied substitution parameter ρH increases with βH up to βH = 0.25 and then staysaround 0.66. The implied time efficiency parameter δH decreases with βH up to βH = 0.25 and then stays around 0.32.The alternative additive specification for the good-specific error, mentioned in footnote 14, yields an estimate of around-2 for ρK and 25 for δK , and 0.98 for ρH and 13 for δH (slightly depending on starting values in the optimization).63The summary table of the policy simulation results can be found in Appendix Table A.29.322.6. Results(TK) as inputs observed in the NLSCY and Census datasets, in the CES production function (2.2),using the estimated parameters ρˆK = −0.4 and δˆK = 0.36.64 The prior level of K for ages 0-2 is 3.11for lower- (L), and 4.23 for higher-educated (H) parents’ children (KL012 = 3.11, KH012 = 4.23), forwhom no daycare policy is in effect. Thus, the prior gap for ages 0-2 (gap012) is 1.12. The secondline shows how the gap would have evolved in the absence of the policy change, using the observedaverage daycare hours and hours spent with the child as inputs for ages 3-4 in the control group withno policy in effect. The no-policy level of K (K˜) for ages 3-4 is 3.8 for lower-, and 5.01 for higher-educated parents’ children (K˜L34 = 3.8, K˜H34 = 5.01); thus the no-policy gap for ages 3-4 (g˜ap34) is1.21. Using only daycare and parental time as inputs and abstracting from self-productivity in childskill formation, the gap from ages 0-2 to 3-4 widens by 8 percent in the absence of the policy.At age 2.5 the subsidized daycare policy takes place: for ages 3-4, the level of K has beenrecalculated with the observed change in daycare hours (4XK) and the observed change in hoursspent with the child (4TK) as inputs, just for ages 3-4 in the CES production function (2.2), keepingρˆK = −0.4 and δˆK = 0.36.65 As shown in the second panel, the actual level of K for ages 3-4 is 4.33for lower-, and 5.88 for higher-educated parents’ children (KL34 = 4.33, KH34 = 5.88), resulting in theactual skill gap of 1.55 (gap34). After the policy change, from ages 0-2 to 3-4, the level of K actuallyincreases by 39 percent for both higher- and lower-educated parents’ children; the gap from ages 0-2to 3-4 widens also by 39 percent as a result of the policy.66 Compared to the no-policy level of childhuman capital K˜H34, K˜L34 for ages 3-4, the actual level of K is by 17 and 14 percent higher for higher-and lower-educated parents’ children as a result of the policy; the actual skill gap of 1.55 is by 29percent larger than the no-policy gap of 1.21.67 If the policy had not been universal but targeted onlyat low-educated families, 56 percent of the actual skill gap could be eliminated.68To quantify the importance of the time efficiency advantage of higher-educated parents, thethird panel shows the counterfactual level of KH34 if higher-educated parents had no time efficiencyadvantage—i.e. if δ = 0 or equivalently in this model, S = 1—, that is only 5.73 (KˇH134 = 5.32). Asa reminder, the difference between the actual and no-policy level of KH34 is 0.87; this suggests thatapproximately 36 percent of this difference stems from higher-educated parents’ increase in inputs,while 64 percent is due to their time efficiency advantage.69 If higher-educated parents had no timeefficiency advantage, the actual skill gap would shrink by 36 percent, from the level of 1.55 to 0.99.70Finally, the fourth panel suggests that the difference between the actual and no-policy level of KL34 forlower-educated parents’ children would be by 80 percent higher if their parents had no time efficiencydisadvantage, in the counterfactual case of having more schooling with S = 2.71 If lower-educated64The underlying conditional means for daycare hours and parental time, for ages 0-2 and 3-4, for children in thecontrol group with no policy in effect, can be seen in Appendix Table A.27.65The underlying estimates can be seen in Appendix Table A.28.66This is by comparing Ke012 with Ke34. for e = L,H, and gap012 with gap34.67This is by comparing K˜e34. with Ke34. for e = L,H, and g˜ap34 with gap34.68This is because removing the policy would decrease the skill level of high-educated parents’ children, by moving themfrom the solid black line (from KH34 =5.88) to the dashed black line (to K˜H34=5.01).69The difference between the actual KH34 = 5.88 and no-policy K˜H34 = 5.01 is 0.87; the difference between the counter-factual KˇH134 = 5.32 and no-policy K˜H34 = 5.01 is 0.31. Thus,0.310.87∼ 36% of the (actual-no policy) difference is stemmingfrom increased inputs and the rest is due to time efficiency advantage.70This is by 1− 1.55−0.991.55∼ 36%.71The difference between the actual KL34 = 4.33 and no-policy K˜L34 = 3.80 is 0.53; the difference between the counter-332.7. Discussion of Alternative Modelsparents had no time efficiency disadvantage, the actual skill gap would shrink by 27 percent.722.7 Discussion of Alternative ModelsAs shown in Section 2, time efficiency differences in non-market activities across education groupscan explain both parents’ cross-sectional choices, and their responses to a daycare price change. Asshown in Section 6, the reduced-form predictions of the model with time efficiency differences acrosseducation groups are supported by empirical evidence (I further refer to this as ’baseline model’). Thequestion arises, however, what alternative models would arrive at the same predictions on parents’cross-sectional choices; especially, on higher-educated parents spending more time with their children.Therefore, instead of differences between education groups in time-efficiency, I explore alternativesources of heterogeneity. In particular, I allow for (1) differences in preferences for child human capital,and (2) differences in the substitution parameter between time and market good in child human capitalproduction, both across education groups. In addition, I show that (3) a variant of the original modelincluding a large daycare quality decrease concurrent with the daycare price decrease gives predictionsinconsistent with the data. These alternative models can be rejected based on responses to a pricechange; they thus help rule out competing explanations to the cross-sectional observation on choices.73Regarding (1), suppose that instead of the time efficiency γ, heterogeneity is introduced into theutility parameter βK , that is assumed to depend positively on schooling S and a preference error/shockεKβ: βK = SδKβi εKβi. This model allows for the possibility that higher-educated parents value childhuman capital more. To reject this model, I make use of the functional form assumption of Cobb-Douglas preferences, in the following way. First, since the base child time response depends positivelyon βK and negatively on w − m, this (1) and the baseline model give the same prediction for howthe response of TK to decreasing m depends on schooling. However, their prediction differs regardinghow the response of log TK depends on schooling: since∂ log TKi∂(−m) is independent of βKi, it depends onschooling only through the wage, unambiguously negatively. This prediction can be tested by runninga DiD model on log TKi, time fixed effects and province fixed effects. The main insight here is thatif the policy had no impact on either schooling or parental preferences either in Quebec or in therest of Canada, then the preference channel can be differenced out, and the coefficient on the policyvariable will give exactly the DiD estimate for log TK . However, this estimate is constant–and doesnot decrease by schooling–, thus alternative model (1) is not supported by the data.At this point I would like to re-iterate that the rejection of (1) is based on the functional form as-sumption of Cobb-Douglas utility function (2.1), and thus the log-separability of the utility parameterβj in the Marshallian demands (2.5 and 2.6). Note that the Marshallian demands in this problem arealmost identical to the the standard Marshallian demands in case of Cobb-Douglas utility, except thatin this problem there is no direct price of the goods child human capital K, home production good Hand leisure good L, but an equilibrium price index is formed from the underlying input prices (w−mfactual KˇL234 = 4.75 and no-policy K˜L34 = 3.80 is 0.95. Thus, the (actual-no policy) difference would be by0.950.53− 1 ∼ 80%larger if low-educated parents had no time efficiency disadvantage.72This is by 1− 1.55−1.131.55∼ 27%.73The detailed explanations and derivations can be found in Appendix 4.342.8. Income and Substitution Effects: The German Experimenton the time input TK and 1 one the time market good XK). Other than this difference, the demandsare linear in the utility parameter βj and in income, and the demand for the j-th good only dependson the input prices for the j-th good. If, for instance, instead of a Cobb-Douglas utility function, aStone-Geary utility function was used, the Marshallian demands (i) would not be log-additive in theutility parameter anymore, but additive in the ”committed” amount on each good, and (ii) woulddepend on all prices. Thus, they would considerably lose from their tractability and simplicity, andthe alternative model (1) would no longer be rejectable based on the aforementioned argumentation.Consequently, my results may depend on the chosen functional form of Cobb-Douglas utility.Suppose that heterogeneity by education is introduced into the substitution parameter ρ, andρj-s are assumed to depend on years of schooling S (negatively) and a good-specific error εKρ: ρK =Υρ(S, εKρ). This model allows for the possibility that the time of higher-educated parents is lesssubstitutable with daycare time, or, the substitution of time and market goods in producing childhuman capital is perceived to be lower for higher-educated parents—for instance, if they think thatmarket-purchased daycare is a poor substitute for their own quality time in child human capitalproduction. As I show in Appendix A.4, both channels predict that higher-educated parents increasechild goods, and also daycare to a smaller extent, contradicting the estimates presented in Section 2.6.Regarding (3), suppose that the CES function of child market good XK takes the following form:XK =[BρXK + (QD)ρX] 1ρX , where ρX is the substitution parameter between daycare time D andother child goods B, while Q denotes daycare quality. Denote the fraction of other child goods α,then, in optimum, the optimal ratio of B relative to D depends on the relative prices and daycarequality, according to: 1−αα = m1ρX−1QρX1−ρX . As I show in Appendix A.4, if daycare quality dramaticallydecreases parallel to a daycare price decrease and if higher-educated parents care about daycare qualitymore, then they are predicted to increase daycare use considerably less than low-educated parentsincrease daycare use. Again, this is not consistent with estimates presented in Section 2.6.2.8 Income and Substitution Effects: The German ExperimentUsing the policy change in Quebec, the total effect of a daycare price change on parents’ time andresource allocation can be measured. To disentangle income and substitution effects, I make use of thedaycare policy change in 2006 in Thuringia; this latter policy environment enables me to estimate theimpact of a compensated daycare price change and a pure income shock on parents’ time allocation.Between 1st July 2006 and 2010, the government of Thuringia had a daycare policy in effect,corresponding to a compensated daycare price increase. Under this system parents of 2-year-oldchildren received a subsidy of EUR150 if their child does not attend a publicly subsidized daycare.If the eligible child attended full-time public daycare, the full amount went the daycare provider; ifpart-time, the parents and the provider shared the amount proportionally.The policy impacted families differently depending on whether they would use public daycare inthe absence of the policy. Those who would, the policy change represents a fully compensated daycareprice increase: public daycare becomes more expensive relative to other daycare modes, but it is fullycompensated by the government. Parents with an eligible 2-year-old child in full-time daycare wouldpay an additional EUR150 per month to the facility, relative to the the baseline of approximately352.8. Income and Substitution Effects: The German ExperimentEUR80. Parents who would stop to use public daycare could use the windfall income to pay for otherprivate childcare arrangements or staying at home. Parents who would not use public daycare in theabsence of the policy are expected to respond differently, depending on whether they would not wantto or would not get a spot. If they would not want to, they are predicted to continue not to use publicdaycare, due to a negative substitution effect and a pure income shock. If they would not get a spotin the absence of the policy, they might use the opportunity of new spots becoming available.To shed light on income and substitution effects, I measure the policy impact of compensatedprice increase by the predicted propensity of using public daycare in the absence of the policy. Icomplement the analysis of Gathmann and Sass (2012), who measure the average policy impact witha DiD strategy using data on East-German bundeslands between 2000 and 2009. They find thatparents decreased public daycare use and informal daycare use, and mothers decreased their laborsupply in response to the policy change, but have not analyzed parental time use in depth.The preceding policy was means-tested, conditional on income and independent of daycarechoices: parents received a monthly subsidy of EUR300 if at least one parent worked less than 30hours per week, and the monthly household income was below a threshold of EUR1,375 for two-parentfamilies and EUR1,125 for single parents. Gathmann and Sass (2012) provide evidence that the newpolicy had little effect on the supply side, in terms of daycare places supplied, opening hours, atten-dance rates of non-eligible one- and three-year old children, quality or daycare fees; and there were nofurther changes in the legislation or regulation of publicly subsidized daycare facilities in Thuringia.However, a major parental leave reform took place in 2007, and although parental leave legislation isfederal in Germany, four bundeslands (Thuringia, Saxony, Baden-Wurttemberg, Bavaria) have com-plementary policies.74 Thus, to mitigate concerns about contemporaneous bundesland-specific changesin daycare/parental leave legislation, I exclude Lower-Saxony, Bavaria and Baden-Wurttemberg.For this analysis, the waves between 2000 and 2010 in the German Socio-Economic Panel(GSOEP) are used.75 The GSOEP is the German household panel study similar to the Panel Study ofIncome Dynamics in the United States and the British Household Panel Study; it is a representativelongitudinal study of private households in Germany since 1984, initially containing only West-Germanhouseholds and expanding to include the states of the former German Democratic Republic (GDR)in June 1990. In this dataset all members of the first-wave survey households and all their offspringsare followed, and all household members 17 years and older are interviewed.Using data on families with at least one 2-year-old child between 2000 and 2010, and excludingdata on Lower-Saxony, Bavaria and Baden-Wurttemberg, I estimate the following model:Yi = δ0 + δ1policytp + δ2policytp × propensity-daycarei + δ3Ci + δ4Ui+δ′5t + δ′6p + δ′7Xi + δ8postt × propensity-daycarei+δ9Thurp × propensity-daycarei + δ10propensity-daycarei + ςi,(2.15)where i indexes household, t indexes time (year), p indexes bundesland (German state), propensity-daycare denotes the propensity score of using public daycare in the absence of the policy, post equals74For instance, they paid in addition a means tested parental benefit extended to the 3rd year of parental leave, or inThuringia before 2006, childcare allowance extended a federal policy for all parents with children under the age of two.75More information on the GSOEP can be found in Wagner et al. (2007).362.9. Conclusion1 if the family is observed after 2006 July, Thur indicates the family residing in Thuringia, andX includes the child’s gender, parents’ age, household structure and household size. A significantlynegative estimate of δ2 indicates that policy impact is larger for families less likely to use public daycarein the absence of the policy. The propensity score is predicted by the interaction of parental educationof the mother and the father, a full set of province and child age fixed effects, a linear time trend,mother’s age, father’s age and household size. Similarly to the propensity of the mother working inthe absence of the policy used in section 2.6.2, propensity-daycare is obtained by estimating a probitmodel on the pre-policy sample and predicting propensities for the whole sample.According to Table 2.10, the impacts of the Thuringian Daycare Policy differ substantiallywhether the family would be more or less likely to use public daycare in the absence of the policy. Forinstance, a very unlikely daycare-user family (with a predicted propensity of 0.043 that correspondsto the 10th percentile in the distribution of the predicted propensity) is 22 percentage points morelikely to use public daycare after the policy is implemented. On the other hand, a very likely daycareuser family (with a predicted propensity of 0.82, corresponding to the 95th percentile), for whom onlythe substitution effect is present, is 4 percentage points less likely to use public daycare after thecompensated price increase. The same impacts for the mother’s labor supply on the extensive marginare 46 and -1.5 percentage points, and on hours worked per week are 12 and -2.8. These results suggestthat families respond to compensated daycare price increases as predicted by the theory. In addition,they suggest that families less likely to use public daycare in the absence of the policy are now drawninto it, with the mother more likely to work, and supplying more market hours—presumably thesefamilies take advantage of the outflow of children from public daycare in a rationed daycare market.76At the same time, these mothers increase their child time at the expense of their home production andleisure time—the same substitution pattern seen in the Canadian experiment. The increase in childtime is 1 hour on a usual weekday (imprecisely estimated), and the significant decreases in time spenton housework, errands and hobbies are -1.4, -0.29 and -0.57 hours on a usual weekday, respectively.2.9 ConclusionThis chapter contributes to the theoretical literature on the “parental time-education gradient” puzzleby extending the classic Beckerian framework with time efficiency differences across education groupsin child skill formation. It presents a new set of results on parental time and household expenditureallocation using exogenous daycare price variation. It also presents estimates of the model’s struc-tural parameters on substitutability between time market goods for child human capital and homeproduction, and on the between-education-group heterogeneity in non-market time efficiency.This chapter provides the following explanation to the puzzle documented by Guryan et al. (2008):keeping efficiency of time investments into children’s human capital constant, higher-wage parents aremore able to afford child market goods (such as daycare); if there is complementarity between timeand market goods in child human capital production, they will also spend more time with their child,despite their time efficiency advantage. This framework also predicts that higher-educated parentsincrease their child time more after daycare prices fall, if their time efficiency advantage in non-market76Evidence on whether there have been daycare supply constraints and/or rationing in Thuringia is mixed; accordingto Wrohlich (2006) there have been, contradicting evidence presented by Gathmann and Sass (2012).372.9. Conclusionactivities is large enough to outweigh their larger opportunity cost of time in non-market activities.Using the Quebec daycare policy change as a negative exogenous shock to the price of daycare,I show substantial labor supply responses, driven primarily by higher-educated mothers not workingin the absence of the policy. When higher- and lower-educated mothers increase their work-time, theytend to increase their time spent with their children (including reading more to the children), at theexpense of their home production and leisure time. Consistent with the model’s predictions, familiesincrease household expenditures that proxy for home production goods. My findings underline thepivotal role of substitutability between time and market goods, implying complementarity in childhuman capital production and substitutability in home production. Higher-educated parents’ largertime reallocation suggests their time efficiency advantage in child human capital and home production.I document and formally test the widening noncognitive gap between high-status and low-statuschildren, between ages 0 and 11. I find the largest widening after the first three years of life, oftenlabeled as the ‘critical period’. I also find that parental reading to the child, together with mater-nal health, family functioning and positive parenting, are more important transmission mechanismsbetween family background and behavioral scores in early childhood, than are daycare attendance ormaternal work. I argue that a compensatory parenting behavior of high-status parents—compensatingmore work time with more parental time and possibly other parental inputs—is one of the mecha-nisms behind the widening gap. As a suggestive evidence of this, I show that high-educated Canadianmothers drawn into the labor market invest more in reading, parenting and mental health; consistentlywith these larger investments, the behavioral outcomes (anxiety, hyperactivity, aggression) of thesemothers’ children deteriorated to a significantly smaller extent, and in some cases even improved, afterthe introduction of the Quebec Daycare Policy.382.10. Tables2.10 TablesGeneral Notes for Tables 2.1-2.6: in each table, Panel A shows the result of estimating the Difference-in-Differences models(2.8) and (2.9), on the Intent-to-Treat effect of subsidized daycare provided by the Quebec “5$/day” policy (1997). The policyvariable is an interaction between residing in Quebec and being eligible to the policy by cohort; the high-educated dummy refersto the mother having at least some post-secondary studies; province and year fixed effects and standard set of X-s are controlledfor (as the mother’s education, gender and age of the child, age structure of the parents, number and age structure of siblings,number of other household members). In Panel B, for each outcome variable, the first column shows the weighted mean in theestimation sample in the control group (policy=0), while the second column shows the estimated policy impact, for all and bymother’s education. The p-values in Panel C correspond to the test β1 + β2 = 0. Standard errors are in parentheses and areclustered at the (province×post)-level. *** p<0.01, ** p<0.05, * p<0.1.Table 2.1: Effect of a Daycare Price Decrease on Daycare Use (Extensive Margin) and Maternal LaborSupply (Both Margins); Policy Impact for All and by Education1: in institutional care 1: in any care 1: mother working mother hoursPanel A: Regression Results(1) (2) (3) (4) (5) (6) (7) (8)β1 : policy 0.184*** 0.130*** 0.131*** 0.088*** 0.076*** 0.042** 1.081*** 0.414*(0.007) (0.015) (0.009) (0.019) (0.008) (0.016) (0.172) (0.221)β2 : policy 0.070*** 0.061*** 0.048** 0.756**×high-educ. (0.014) (0.020) (0.018) (0.361)β3 : college 0.048*** 0.035*** 0.153*** 0.166*** 0.174*** 0.176*** 5.160*** 4.857***(0.014) (0.012) (0.011) (0.017) (0.011) (0.015) (0.396) (0.357)β4 : university 0.076*** 0.062*** 0.195*** 0.209*** 0.191*** 0.194*** 6.506*** 6.208***(0.011) (0.010) (0.008) (0.013) (0.017) (0.017) (0.606) (0.471)R2 0.123 0.124 0.117 0.117 0.094 0.095 0.074 0.074N 61,962 61,962 61,962 61,962 61,496 61,496 186,941 186,941data NLSCY NLSCY NLSCY NLSCY NLSCY NLSCY LFS LFSPanel B: Means and Policy Impactsmean impact mean impact mean impact mean impactall 0.092 0.184 0.437 0.131 0.614 0.076 19.296 1.081low-educ. 0.053 0.131 0.312 0.088 0.481 0.042 15.097 0.414high-educ. 0.106 0.201 0.484 0.141 0.663 0.09 21.376 1.170Panel C: P-values of Testing Coefficientsβ1 + β2 = 0 0.000 0.000 0.000 0.000Source of data: NLSCY waves 1-7, LFS 1994-2006, 0-4 years old children in two-parent families, both parents at most 50 years old.Table 2.2: Effect of a Daycare Price Decrease on Reading to the Child; Policy Impact for All and byEducation1: never reading 1: reading weekly 1: reading often 1: reading dailyPanel A: Regression Results(1) (2) (3) (4) (5) (6) (7) (8)β1 : policy -0.032*** -0.029** 0.0194*** 0.003 0.036*** 0.042*** -0.026*** -0.022(0.0037) (0.0117) (0.0017) (0.0063) (0.0032) (0.0124) (0.0035) (0.0261)β2 : policy -0.003 0.022*** -0.011 -0.004×high-educ. (0.0142) (0.0076) (0.0200) (0.0366)β3 : college -0.047*** -0.042*** -0.019*** -0.019*** -0.032** -0.046** 0.099*** 0.108***(0.005) (0.010) (0.004) (0.005) (0.012) (0.018) (0.015) (0.030)β4 : university -0.070*** -0.066*** -0.031*** -0.032*** -0.072*** -0.086*** 0.174*** 0.184***(0.013) (0.014) (0.003) (0.006) (0.016) (0.022) (0.021) (0.037)R2 0.118 0.119 0.015 0.015 0.035 0.035 0.139 0.139N 60,858 60,858 60,858 60,858 60,858 60,858 60,858 60,858dataset NLSCY NLSCY NLSCY NLSCY NLSCY NLSCY NLSCY NLSCYPanel B: Means and Policy Impactsmean impact mean impact mean impact mean impactall 0.088 -0.032 0.037 0.019 0.202 0.036 0.672 -0.026low-educ. 0.129 -0.029 0.055 0.003 0.248 0.042 0.567 -0.022high-educ. 0.073 -0.032 0.030 0.025 0.184 0.031 0.712 -0.026Panel C: P-values of Testing Coefficientsβ1 + β2 = 0 0.000 0.000 0.002 0.0344Source of data: NLSCY waves 1-7, 0-4 years old children in two-parent families, both parents at most 50 years old.392.10. TablesTable 2.3: Effect of a Daycare Price Decrease on Mother’s and Father’s Child Time and Home Pro-duction Time Use; Policy Impact for All and by Educationmother mother father fatherchild time home production time child time home production timePanel A: Regression Results(1) (2) (3) (4) (5) (6) (7) (8)β1 : policy 0.870*** 0.591** -2.046*** -2.233*** 0.718*** 0.442* -1.084*** -1.215***(0.1052) (0.2385) (0.130) (0.271) (0.135) (0.220) (0.059) (0.188)β2 : policy 0.677** 0.528 0.484* 0.278×high-educ. (0.2766) (0.334) (0.241) (0.260)β3 : college 1.175*** 1.809*** -1.232*** -0.793*** 1.505*** 1.714*** 0.097 0.106(0.374) (0.143) (0.345) (0.262) (0.223) (0.136) (0.201) (0.115)β4 : university -0.313 0.315* -4.272*** -3.848*** 1.741*** 1.947*** -0.451** -0.456***(0.293) (0.164) (0.575) (0.347) (0.108) (0.248) (0.199) (0.119)R2 0.067 0.067 0.023 0.023 0.028 0.028 0.016 0.016N 698,490 698,490 698,490 698,490 698,490 698,490 698,490 698,490data Census Census Census Census Census Census Census CensusPanel B: Means and Policy Impactsmean impact mean impact mean impact mean impactall 44.824 0.870 30.523 -2.046 24.104 0.718 14.115 -1.084low-educ. 44.409 0.591 32.403 -2.233 23.203 0.442 14.169 -1.215high-educ. 45.020 1.268 29.637 -1.805 24.530 0.927 14.089 -0.935Panel C: P-values of Testing Coefficientsβ1 + β2 = 0 0.000 0.000 0.000 0.000Source of data: Census (1996,2001,2006), two-parent families with at least one 0-4 years old child, both parents at most 50 yearsold.Table 2.4: Effect of a Daycare Price Decrease on Mother’s Time Use; Policy Impact for All and byEducationwork time child time home production time leisure timePanel A: Regression Results(1) (2) (3) (4) (5) (6) (7) (8)β1 : policy 0.059 -2.480* 1.493*** -1.008 -0.649 0.339 -0.903 3.150**(0.8497) (1.2718) (0.4010) (1.1648) (0.4227) (0.9489) (0.6593) (1.1468)β2 : policy 3.361* 3.289* -1.292 -5.358***×high-educ. (1.8350) (1.6850) (1.1086) (1.6155)β3 : college 2.966*** 2.711* -0.707 -0.318 -1.872*** -2.204** -0.387 -0.189(0.527) (1.461) (0.707) (1.625) (0.485) (0.856) (0.830) (0.801)β4 : university 4.751*** 4.523*** -0.505 -0.035 -3.407*** -3.787*** -0.839 -0.701(0.743) (1.502) (1.126) (1.658) (0.427) (0.957) (1.493) (1.008)R2 0.083 0.082 0.163 0.164 0.033 0.032 0.024 0.025N 2,001 2,001 2,001 2,001 2,001 2,001 2,001 2,001dataset GSS GSS GSS GSS GSS GSS GSS GSSPanel B: Means and Policy Impactsmean impact mean impact mean impact mean impactall 10.993 0.059 13.122 1.493 16.792 -0.649 59.093 -0.903low-educ. 8.485 -2.480 13.121 -1.008 18.180 0.339 60.215 3.150high-educ. 12.050 0.881 13.123 2.281 16.207 -0.953 58.620 -2.208Panel C: P-values of Testing Coefficientsβ1 + β2 = 0 0.465 0.007 0.056 0.021Source of data: GSS (1998,2005,2010), two-parent families with at least one 0-4 years old child, both parents at most 50 years old.402.10. TablesTable 2.5: Effect of a Daycare Price Decrease on Food Expenditures (%); Policy Impact for All andby Educationfood(%) food - store(%) food - restaurant(%)Panel A: Regression Results(1) (2) (3) (4) (5) (6) (7) (8) (9)β1 : policy 0.817*** 0.939*** 2.108*** 0.436*** 0.558*** 1.403*** 0.322*** 0.343*** 0.623***(0.114) (0.144) (0.234) (0.117) (0.127) (0.182) (0.057) (0.098) (0.148)β2 : policy -1.097*** -0.637** -0.407***×high-educ. (0.282) (0.256) (0.097)β3 : college -0.922** -1.001*** -0.804*** -1.020*** -1.098*** -0.950*** 0.103 0.100 0.145*(0.319) (0.301) (0.207) (0.279) (0.260) (0.171) (0.069) (0.066) (0.074)β4 : university -1.562*** -1.689*** -1.508*** -1.666*** -1.782*** -1.658*** 0.101* 0.088 0.142*(0.291) (0.262) (0.198) (0.323) (0.297) (0.148) (0.050) (0.054) (0.069)R2 0.13 0.17 0.17 0.13 0.17 0.18 0.04 0.04 0.04N 22,725 7,228 7,228 22,725 7,228 7,228 22,725 7,228 7,228Panel B: Means and Policy Impactsmean impact mean impact mean impactall 13.095 0.939 10.603 0.558 2.457 0.343low-educ. 14.845 2.108 12.269 1.403 2.539 0.623high-educ. 12.047 1.011 9.608 0.766 2.406 0.216Panel C: P-values of Testing Coefficientsβ1 + β2 = 0 0.000 0.001 0.021Source of data: SHS (1986,1992,1996-2009), two-parent families with at least one 0-4 years old child, both parents at most 50years old.Table 2.6: Effect of a Daycare Price Decrease on Child Good and Home Production Good Expenditures(%); Policy Impact for All and by Educationdaycare(%) games-toys(%) domestic help(%)Panel A: Regression Results(1) (2) (3) (4) (5) (6) (7) (8) (9)β1 : policy -0.125** -0.374*** 0.428*** 0.089*** 0.155*** 0.086 0.023** 0.094*** 0.049**(0.047) (0.073) (0.136) (0.018) (0.017) (0.068) (0.008) (0.006) (0.018)β2 : policy -1.093*** 0.134 0.032×high-educ. (0.179) (0.090) (0.026)β3 : college 0.116 0.163* 0.109 0.028 0.015 0.143* 0.002 0.006 -0.002(0.088) (0.087) (0.134) (0.048) (0.049) (0.068) (0.019) (0.018) (0.024)β4 : university 0.512*** 0.603*** 0.542** 0.038 0.017 0.159** 0.161*** 0.172*** 0.165***(0.121) (0.127) (0.181) (0.057) (0.054) (0.062) (0.029) (0.031) (0.019)R2 0.04 0.05 0.05 0.05 0.04 0.05 0.03 0.06 0.06N 22,725 7,228 7,228 22,725 7,228 7,228 20,578 5,081 5,081Panel B: Means and Policy Impactsmean impact mean impact mean impactall 2.088 -0,374 0.851 0.155 0.119 0.094low-educ. 1.627 0.428 0.866 0.086 0.0402 0.049high-educ. 2.365 -0.665 0.842 0.220 0.158 0.081Panel C: P-values of Testing Coefficientsβ1 + β2 = 0 0.000 0.001 0.000Source of data: SHS (1986,1992,1996-2009), two-parent families with at least one 0-4 years old child, both parents at most 50years old.412.10. TablesTable 2.7: Estimation of Structural Parameters - Child Human Capital ProductionGSS Time Use Diary CensusOLS 2SLS OLS 2SLSlog (wi −mi) (1 +m1ρX−1i ) -0.1027 -0.3598 0.0652*** -0.2826***(0.0786) (0.2464) (0.0113) (0.0464)logSi 0.1330 0.2343 -0.1728*** 0.1045***(0.1353) (0.1678) (0.0495) (0.0108)R2 0.1819 0.1855 0.0225 0.0502N 1,809 1,809 680,420 696,290first-stage F-statistics 45.77 71.18implied ρ -0.5621 -0.3939***(0.601) (0.0902)implied δ 0.6510* 0.3697***(0.3486) (0.0395)Note: this table shows the estimation result of (2.11), with the corresponding first-stage equation of (2.13), to recover the structuralparameters ρK (the substitution parameter between time T and market good X in child human capital production) and δK (thatshows how time efficiency in child human capital production γK depends on schooling). The excluded instrument is the policyvariable (an interaction between residing in Quebec and being eligible to the policy by cohort). The standard errors on the impliedparameters ρ and δ are calculated by the delta method. Standard errors are in parentheses and are clustered at the (province×post)-level. The coefficient on logSi isρKρK−1 δK , while the coefficient on the function of wi −mi is −ρKρK−1 . *** p<0.01, ** p<0.05, *p<0.1. Source of data: GSS (1998,2005,2010), and Census (1996,2001,2006), mothers in two-parent families with at least one 0-4years old child, both parents at most 50 years old.Table 2.8: Estimation of Structural Parameters - Home ProductionGSS Time Use Diary CensusOLS 2SLS OLS 2SLSlog(wi −mi) 0.4240*** 2.2938 0.2271*** 2.0580***(0.1198) (2.0508) (0.0274) (0.4532)logSi 0.0239 -0.8242 -0.1679*** -0.7184**(0.1005) (0.9234) (0.0518) (0.2027)R2 0.0473 0.0501 0.0866 0.608N 1,866 1,866 668,070 668,070first-stage F-statistics 3.1258 23.31implied ρ 0.6964*** 0.6730***(0.1890) (0.0485)implied δ 0.3593*** 0.3491***(0.0889) (0.0310)Note: this table shows the estimation result of (2.12), to recover the structural parameters ρH (the substitution parameter betweentime T and market good X in home production) and δH (that shows how time efficiency in home production γH depends onschooling). The excluded instrument is the policy variable (an interaction between residing in Quebec and being eligible to thepolicy by cohort). The coefficient on logSi isρHρH−1 δH , while the coefficient on the function of wi − mi is −ρHρH−1 . Standarderrors are in parentheses and are clustered at the (province×post)-level. The standard errors on the implied parameters ρ andδ are calculated by the delta method. *** p<0.01, ** p<0.05, * p<0.1. Source of data: GSS (1998,2005,2010), and Census(1996,2001,2006), mothers in two-parent families with at least one 0-4 years old child, both parents at most 50 years old.422.10. TablesTable 2.9: Documenting the Behavioral Skill Gap between High-status and Low-status Children overAges 0-11controlling for: parenting practices maternal health maternal work and carebase positive family func. depression 1:excellent 1:work 1:in care 1:readingτ1 : high-educ. -0.0559*** -0.0477** -0.0390* -0.0364* -0.0395** -0.0553** -0.0558*** -0.0429***(0.0186) (0.0185) (0.0189) (0.0185) (0.0182) (0.0203) (0.0160) (0.0148)τ2 : high-educ. -0.1261*** -0.1290*** -0.1302*** -0.1274*** -0.1306*** -0.1297*** -0.1257*** -0.1297***×age(3-5) (0.0225) (0.0234) (0.0223) (0.0233) (0.0207) (0.0202) (0.0229) (0.0238)τ3 : high-educ. -0.1049** -0.1145*** -0.1202*** -0.1232*** -0.1030** -0.1059**×age(6-8) (0.0399) (0.0392) (0.0390) (0.0380) (0.0394) (0.0399)τ4 : high-educ. -0.1023** -0.1119** -0.1176** -0.1204** -0.1045** -0.1027**×age(9-11) (0.0479) (0.0467) (0.0472) (0.0462) (0.0481) (0.0486)R2 0.035 0.039 0.038 0.043 0.041 0.035 0.022 0.024N 104,370 104,370 104,370 104,370 103,232 103,449 71,749 71,749Note: this table shows the result of estimating the base model (2.14) on the average age-standardized behavioral score; controllingfor a full set of year (or wave), province, child age dummies, and standard set of X-s, such as the gender of the child, numberof older and younger siblings (capped at 3 and 2, respectively), the size of the household, the mother’s and father’s age, and thefather’s education. high-educ. indicates high-educated, defined as the mother having either some college, or university education,age(3 − 5) indicates the child being between 3 and 5 years old. The coefficients of interest are τ1 − τ4, corresponding to thebehavioral/developmental human capital gap—also called the noncognitive skill gap—across age-categories. τ1 shows the gap forchildren between 0 and 2 years old, while τ1 + τ2 shows the gap for children between 3 and 5 years old; so, for instance, τ2 showswhether the gap significantly widens after the first 3 years of life. In the first column I present the base estimation results of(2.14), and in further columns I assess how the inclusion of parental practices, maternal health, maternal employment, daycareattendance and parents’ reading practices (highlighted in bold in the headlines of each column) change the estimated coefficientsτˆ1− τˆ4. Standard errors are in parentheses and are clustered at the (province×post)-level. *** p<0.01, ** p<0.05, * p<0.1. Sourceof data: NLSCY waves 1-7 (1994-2006), 0-11 years old children in two-parent families, both parents at most 50 years old.Table 2.10: Effect of a Daycare Price Increase on Public Daycare Use, Mother’s Labor Supply, andMother’s Time Allocation on Work, Children, Home Production and Hobbies; Policy Impact by thePropensity of Using Public Daycare in the Absence of the Policypublic daycare mother working work child housework errand hobbyPanel A: Regression Results(1) (2) (3) (4) (5) (6) (7)δ1 : policy 0.238*** 0.485*** 12.650*** 1.073 -1.505*** -0.276** -0.598***(0.055) (0.023) (0.939) (0.841) (0.140) (0.102) (0.175)δ2 : policy -0.340*** -0.610*** -18.885*** -1.714 2.087*** -0.259 0.720**×propensity-daycare (0.100) (0.053) (2.908) (1.752) (0.240) (0.257) (0.309)δ3 : college 0.028 0.025 2.545*** 0.873* -0.127 0.001 -0.345*(0.026) (0.019) (0.908) (0.446) (0.170) (0.080) (0.196)δ4 : university 0.068 0.012 2.609** -0.363 -0.611*** -0.184** -0.136(0.042) (0.026) (1.155) (0.448) (0.182) (0.089) (0.168)R2 0.31 0.09 0.15 0.08 0.17 0.06 0.07N 2,915 2,915 2,871 2,908 2,904 2,896 2,859Panel B: Means0.318 0.1086 10.005 10.018 3.157 1.469 1.381Note: Panel A shows the result of estimating the Difference-in-Differences model (2.15), on the Intent-to-Treat effect of a compen-sated daycare price increase, provided by the Thuringian daycare policy (2006). Standard errors are in parentheses and are clusteredat the (bundesland×post)-level. *** p<0.01, ** p<0.05, * p<0.1. Source of data: GSOEP (2000-2010), families with at least one2 years old child, both parents at most 50 years old, excluding bundeslands Lower-Saxony, Bavaria and Baden-Wurttemberg. Theoutcomes are in bold in the headline of each column. The first two outcome variables are binary, work hours are measured perweek, while the remaining activities (child, home production and leisure activities) are measured in hours per usual weekday. PanelB shows the mean for each outcome in the estimation sample. propensity-daycare denotes the predicted propensity of using publicdaycare in the absence of the policy.432.11. Figures2.11 FiguresFigure 2.1: Trends in Quebec and the Rest-of-Canada in Maternal Employment (Both Margins)Note: these graphs show the weighted mean of women’s employment rate and hours worked (below the age of 50, living in two-parenthouseholds), for Quebec and the rest of Canada between 1994 and 2006. Source of data: LFS (1994-2006), mothers with 0-4 yearsold children in two-parent families, both parents at most 50 years old. In 1997 the Quebec “5$/day” subsidized universal daycarepolicy was phased-in gradually for children aged 0-4 until 2000.Figure 2.2: Trends in Quebec and the Rest-of-Canada in Regulated (Institutional Daycare Use)Note: this graph shows the weighted mean of regulated (institutional) daycare use, for Quebec and the rest of Canada between1994 and 2006. Source of data: NLSCY waves 1-7 (1994-2006), 0-4 years old children in two-parent families, both parents at most50 years old. In 1997 the Quebec “5$/day” subsidized universal daycare policy was phased-in gradually for children aged 0-4 until2000.442.11. FiguresFigure 2.3: Estimated Policy Impacts by Propensity of the Mother Working in the Absence of thePolicy, with a 95% Confidence Band, for High-Educated Mothers (Linear Model)Note: these figures show the estimated policy impacts for high-educated families by the predicted propensities of the mother workingin the absence of the policy, with a 95% confidence band; based on estimates from the linear model (2.10), where the underlyingcoefficients can be seen in Appendix Tables A.14-A.18. Source of data: NLSCY waves 1-7 (1994-2006) and GSS (1998,2005,2010),0-4 years old children in two-parent families, both parents at most 50 years old. Propensities 55, 64, 72, 82 and 88 correspond tothe 10th, 25th, 50th, 75th, 90th percentile of the predicted propensity distribution for high-educated mothers in the NLSCY.452.11. FiguresFigure 2.4: Estimated Policy Impacts by Propensity of the Mother Working in the Absence of thePolicy, with a 95% Confidence Band, for Low-Educated Mothers (Linear Model)Note: these figures show the estimated policy impacts for low-educated families by the predicted propensities of the mother workingin the absence of the policy, with a 95% confidence band; based on estimates from the linear model (2.10), where the underlyingcoefficients can be seen in Appendix Tables A.14-A.18. Source of data: NLSCY waves 1-7 (1994-2006) and GSS (1998,2005,2010),0-4 years old children in two-parent families, both parents at most 50 years old. Propensities 33, 42, 52, 62 and 69 correspond tothe 10th, 25th, 50th, 75th, 90th percentile of the predicted propensity distribution for low-educated mothers in the NLSCY.462.11. FiguresFigure 2.5: Counterfactuals on the Child Human Capital Gap When Policy Implemented at Age 2.5Note: these figures show the gap in child human capital before and after the policy change.Panel1 (up-left): in the first panel for ages 0-2, the level of child human capital (K) for higher- and lower-educated parents’children in the control group are calculated with the observed average daycare hours (XK) and hours spent with the child (TK) asinputs in the CES production function (2.2) from Table A.27, using the estimated parameters ρˆK = −0.4 and δˆK = 0.36.For instance, KL012=3.1153=[(10.36 × 40.515)(−0.4) + 9.448(−0.4)]( 1−0.4) .The second vertical line shows how the gap would have evolved in the absence of the policy change, using the observed averagedaycare hours and hours spent with the child for ages 3-4 for the control group as inputs from Table A.27, using the estimatedparameters ρˆK = −0.4 and δˆK = 0.36.Panel2 (up-right): the second panel shows how the gap evolves under the policy change, using the observed average daycare hoursand hours spent with the child for ages 3-4 for the treated group as inputs from Table A.28, using the estimated parametersρˆK = −0.4 and δˆK = 0.36.For instance, K34L =4.3264=[(10.36 × (47.322 + 0.632))(−0.4) + (11.818 + 2.595)(−0.4)]( 1−0.4);or KH34=5.8811=[(10.36 × (47.322 + 0.632 + 0.228))(−0.4) + (11.818 + 2.595 + 5.840)(−0.4)]( 1−0.4) .Panel3 (down-left): the second vertical line in the third panel shows the counterfactual level of K if high-educated parents had notime efficiency advantage; i.e. if δ = 0 or equivalently in this model, S = 1.Panel4 (down-right): the second vertical line in the fourth panel shows the counterfactual level of K if low-educated parents hadno time efficiency disadvantage, in the counterfactual case of S = 2.47Chapter 3Returns to Starting School Later:Academic Redshirting vs. Lucky Dateof Birth3.1 Introduction“When the Harvard sociologist Hilary Levey Friedman was expecting her first child, one thing worriedher: her due date, January 3rd. It was uncomfortably close to January 1st, an often-used age cutofffor enrollment in academics and sports. “I was determined to keep him in until after January 1st,”she said. And if the baby came early? “I actively thought about redshirting,” she said.”77There is a non-trivial and potentially increasing fraction of parents postponing the entrance of theirage-eligible child into kindergarten, a practice known as ‘academic redshirting’.78 For instance, whilein 1968 96 percent of 6 years old children were enrolled in kindergarten in the United States, in 2005only 84 percent.79 The exact fraction of redshirted children in the United States is debated, but is ina range of 5 to 10 percent of kindergartners (Bassok and Reardon (2013), Stipek (2002), Aud et al.(2013)). Parents might have several reasons for justifying redshirting: the child might not be school-ready, or even if school-ready, they excessively value pre-school services. Alternatively, they may notwant their child to start primary school as one of the youngest children, but hope that an extra yearwould allow her/him to excel relative to younger peers in the classroom.Academic redshirting is essentially a voluntarily delayed school entry80, differing from the in-voluntarily delayed school entry prescribed for children born after the school enrollment cutoff date.Children born after and complying with the school enrollment date enter kindergarten a year older,usually at the age of 6. Redshirted children enter kindergarten a year older than prescribed, usuallyat the age of 6 instead of 5. If not school-ready, an extra year can help the child to make up forany learning or developmental/behavioral deficits and enter school not only a year older, but alsowith boosted human capital. However, redshirting can be a beneficial compensating alternative even77The New Yorker, September 19, 2013: http://www.newyorker.com/online/blogs/elements/2013/09/youngest-kid-smartest-kid.html.78Redshirting is “named for the red jersey worn in intra-team scrimmages by college athletes kept out of competitionfor a year.” The New Yorker, September 19, 2013.79According to Deming and Dynarski (2008), the school attendance rate of six-year-olds has not decreased, but theyare more likely to be enrolled in kindergarten rather than first grade. In addition, they show that only 25 percent ofthe aforementioned change can be explained by changes in school entry laws that increased kindergarten entrance ages.Since 1965, there is a trend of moving school enrollment cutoff dates from September-February to June-September in theUS states; see Figure on page 2 in Cannon and Lipscomb (2008). Note that several states do not have a uniform cutoffdate for all school districts (but delegate it to the discretion of Local Education Agencies) and some states do not havea legislation regarding kindergarten entry age.80In what follows, ‘being redshirted’, ‘withheld from primary school’ or ‘voluntarily delayed primary school entry’ foran additional year are synonyms.483.2. Institutional Backgroundfor a school-ready child: s/he could experience the gains of entering school a year older—gains aninvoluntarily delayed child has just from being luckily born after the school enrollment cutoff date.This chapter is, to the best of my knowledge, the first attempt to measure the causal impactof academic redshirting on child outcomes, using a natural experimental design. I exploit an ad-ministrative barrier to academic redshirting in the Hungarian educational system: a school-readinessevaluation, compulsory for potentially redshirted children born before January 1st. By the researchdesign, I measure the Local Average Treatment Effect (LATE) for children who would have not beenredshirted if born before January 1st, but are redshirted if born after; the compliers are children whoare or are not school-ready, and for whom the administrative barrier has a deterring impact. ThisLATE is then compared to the effect of involuntary delay of primary school entry by making use ofthe school enrollment cutoff date of June 1st; here the compliers are school-ready children assigned toenter primary school a year older. I utilize Hungarian administrative testscore, secondary school trackchoice and mental health survey data for years 2008-2014.The rest of the chapter is organized as follows. Section 3.2 presents the details of the relevantinstitutional features of the Hungarian educational system that is necessary to understand the identifi-cation strategy in section 3.3. Section 3.4 discussed data and measurement issues, section 3.5 presentsthe results, while section 3.6 concludes.3.2 Institutional BackgroundIn this part of the chapter I present the details of the relevant institutional features of the Hungarianeducational system, with a focus on transition from child care into primary school. I discuss the flexibleregulation of both child care and primary school entry, and the possibility of academic redshirting.Most importantly, I describe the three regimes of primary school start based on month of birth thatjustify the importance of the two cutoff dates in the identification strategy, January 1st and June 1st.Compared to North American educational systems, Hungary has a universal child care system81more integrated into the public education system, with 90 percent of the children spending at least 3years in child care before entering primary school. The last child care year is the school-preparationyear, approximately equivalent to the North-American kindergarten year, nevertheless still part ofthe child care system.82 Redshirting a child means making her repeat this school-preparation year inkindergarten and postponing primary school entry.Table 3.1 shows the most important institutional features of school entry in the Hungarianeducational system, by month of birth.83 Regime1 pertains to children born in the months September81Hungary has a universal child care system, with a minimal (less than 4 percent) fraction of private institutions. Publicchild care institutions in general provide an 8-hour long educational service per day free of charge, except for meal fees.According to the Act No. LXXIX of 1993 on Public Education (Public Education Act), 24(1), child care institutionseducate children from the age of 3 until the start of compulsory school attendance. According to the enactment ofthe Ministry of Education, 137/1996. (VIII. 28.), the child care institutions’ board of teachers is required to satisfy thephysical and mental needs of child care-relevant aged children: to assure a healthy lifestyle, to provide emotional security,socialization, and to help mental skill enhancement.82The minimum compulsory child care attendance time amount is 4 hours per day starting from 1st September for allchildren turning 5 in that particular calendar year (Public Education Act, 24(3)).83Besides the date of birth affecting primary school entry age, it also influences, although to a lesser extent, child care493.2. Institutional Backgroundto December: these children are prescribed to enter primary school at the age of 6, and for them theadministrative barrier to academic redshirting is present. Regime2 pertains to children born in themonths January to May: these children are prescribed to enter primary school at the age of 6, and forthem there is no administrative barrier to academic redshirting. Regime3 pertains to children born inthe summer: these children delayed involuntarily, are prescribed to enter primary school at the age of7 and for them academic redshirting is not allowed.The end of child care attendance is bound together with the start of compulsory school atten-dance. All children turning 6 before June 1st in any calendar year are required to start primary schoolon 1st September of that particular calendar year (Public Education Act 6(1)). Thus, the schoolenrollment cutoff date is June 1st in Hungary. As a consequence, if complying with the prescribedprimary school starting age, children born in the months January to May start primary school at theaverage age of 6 years 7.5 months to 6 years 3.5 months, children born in the months June to Auguststart primary school at the average age of 7 years 2.5 months to 7 years 0.5 months and children bornin the months September to December start primary school at the average age of 6 years 8.5 monthsmonths to 6 years 11.5 months. The regulation results in children born in May generally being theyoungest and children born in June generally being the oldest in the classroom.Nevertheless, with some restrictions and depending on month of birth, there is the possibility ofacademic redshirting, i.e. repeating the school-preparation year. As opposed to the United States,where redshirting is decided by the parents, together with significant input from child care providers,in Hungary redshirting is decided primarily by the parents, together with the evaluation of the childcare institution’s board of teachers and, depending on month of birth, possibly the local Develop-mental Advisory Board (DAB). While both the child care institution and the local DAB are part ofthe public education system, the latter is an independent pedagogic institution maintained by thelocal governments. According to the Public Education Act, 35(4), it is obliged to evaluate children’slearning, social/integrational and behavioral skills until reaching adulthood, to propose and conductskill enhancing activities involving the parents and child care teachers and, most importantly for thepurpose of this chapter, evaluate school-readiness if asked by the child care institution and/or theparents.In Regime1, children born in the months September to December are allowed to start their lastentry age. September-to-December-born children are more likely to enter child care at the age of 2, since these childrenare preferred by the child care institutions if there is a queue for entering child care at the age of 2. In particular, thechild care institution can admit 2 years old children, provided that all the 3 years old and older applicants living in theparticular municipality or capital district are admitted (Public Education Act 24(1)). However, children who are turning3 within 6 months of acceptance are preferred. Acceptance usually happens at the beginning of June and start of childcare happens only at the beginning of September (with very few exceptions). January-to-May-born children are mostlikely to enter at the age of 3, while summer-born children are most likely to enter at the age of 4. Table B.2 showsthe distribution of children by month of birth and age at child care entry, together with the fraction of children enteringschool at the age of 7 and average years spent in child care in each cell. The first observation is that keeping monthof birth fixed, the fraction of delayed children is monotonically increasing by child care entry age, and correspondingly,the average years spent in child care is monotonically decreasing by child care entry age. The second observation is thatchild care entry age is closely related to quarter of birth. September-to-December-born children are more likely to enterchild care at the age of 2 and and less likely to enter at ages 3,4,5 than what their overall fraction would indicate. Thereason behind is that these children are turning 3 within 6 months of acceptance, thus, they are preferred to enter at theage of 2 if local supply constraints permit it. January-to-May born children are more likely to enter child care at the ageof 3, while summer-born children are more likely to enter at the age of 4.503.2. Institutional Backgroundyear in child care on 1st September in the calendar year when they are turning 7, provided that theparents ask for the child’s additional year in child care and both the child care institution’s board ofteachers and the local DAB supports this decision (Public Education Act, 24(5)). As a consequence,these children start primary school at an age between 7 years 8.5 months and almost 8 years, ifredshirted.In Regime2, children born in the months January to May are allowed to start their last yearin child care on the 1st September of the calendar year when they are turning 6, provided that theparents ask for this and the child care institution’s board of teachers supports this decision84; i.e. thereis no need for the local DAB’s evaluation or support in this case. As a consequence, these childrenstart primary school at an age between 7 years 3.5 months and 7 years 7.5 months, if redshirted.In Regime3, children born in the summer months are assigned to start primary school at thedefault age of 7 and are not allowed to be redshirted; they are the involuntarily delayed children.The school-readiness examination conducted by the local DABs is free of charge and standard-ized. First, the developmental experts examine how the child behaves in social situations with otherchildren. Usually during drawing exercises they investigate how the child is able to work while beingdistracted, how much she is influenced, able to adapt and handle new situations. Then, in a one-on-one situation the developmental experts investigate how much the child knows about her environment,how developed her thinking and remembering abilities are, and how easily she becomes tired. Finally,the results are shared and discussed with the parents and under most circumstances, with the childcare teachers as well, in order to achieve a consensus that best meets the child’s interests.According to the interviews I conducted with the experts of 4 local DABs in Budapest85, Hungaryin June 2013, the major costs of a school-readiness examination are the following. First, in most casesthe accompanying parent needs to miss work for the time of the examination. Additionally, there aretraveling costs for parents living in municipalities where there is no DAB located (on average thereare 4-5 DABs per county and Hungary has 20 counties). Second, parents might be afraid of the result,and of their child’s potentially negative result being listed later, that might have—as they presume—harmful consequences on her educational career. Third, parents might be reluctant to go in front of anunknown formal committee; especially if the default option is to discuss their child’s development andschool entry with the child care teachers, with whom the parents are already familiar. Higher-educatedparents have presumably lower costs of taking this examination, as for them traveling costs might be alower share of the household budget, they might work more flexible hours, and might be less influencedby their child’s potentially negative result being listed later, or going in front of an unknown formalcommittee. This impacts that the results as far as which parents are systematically more likely toshow up for examination, and who are the compliers, for whom costs might have a deterring impact.84According to the enactment of the Ministry of Education, 11/1994. (VI. 8.), 15(5), part “b”, the child care in-stitution’s board of teachers is obliged to suggest an additional year in child care for every child who is assigned tostart primary school on 1st September in that particular calendar year, but who does not meet the requirements ofschool-readiness according to the opinion of the board of child care teachers.85The developmental experts emphasized during the interviews that their evaluation is suggestive, rather than decisive.The locally available child care services (number of child care places or teachers) are generally not taken into account bythe local DABs; only developmental aspects.513.3. Identification3.3 IdentificationIn this section I discuss identification issues; first, identification of individual returns to starting schoola year older, second, on how to disentangle absolute age effects from within-class relative age effects.3.3.1 Identification of Individual ReturnsPrimary school entry age is not only determined by an exogenous rule based on date of birth, butdepends additionally on the child’s abilities at her entry-relevant age or the parents’ preferences; bothunobserved. As a consequence, Ordinary Least Squares (OLS) estimates of the effect of school entryage on school achievement and other related outcomes are biased.Unobserved abilities bias the estimates downward. On one hand, unobserved child abilitiesaround the age of 6 are negatively correlated with school entry delay. On the other hand, keepingeverything else fixed, a child with worse abilities is expected to have worse student outcomes. Irre-spective of the ultimate sign of the bias, it is expected to be smaller around the cutoff date of June1st. The reason is that summer-born children are not allowed to be redshirted (at most “broughtforward”) and for them entering primary school at the age of 7 is prescribed by the regulation. At thesame time, for non-summer born children, redshirting is a possible practice.Unobserved parental valuation of child care leads to a bias with ambiguous sign. Parents withhigher valuation of child care services are more likely to delay their child’s primary school entry. Theseparents may be those who try to compensate for insufficient skill-enhancing resources at home, andwhose children presumably score lower on achievement tests, ceteris paribus. In this case unobservedparental valuation of child care leads to a downward bias. Alternatively, these parents may be thosewho, besides other early childhood education institutions and resources, view child care as equallyimportant and would want to provide it in the largest possible amount. The children of these parentspresumably score higher on achievement tests, ceteris paribus.From the previous description of the institutional background it follows that there are two maindiscountinuity points in the months of birth that greatly influence children’s educational paths andopportunities. First, a child born on June 1st vs. 31st May is prescribed to enter primary schoolat the age of 7 vs. 6. Second, there is no need for the local DAB’s evaluation or support for beingredshirted for a child born on January 1st; an administrative barrier that is present for a child born on31st December. To further support the importance of these discontinuity points, child care entry ageis increasing when moving from children born in September to children born in August, and higherchild care entry age is also associated with higher propensity of being delayed.This chapter uses the Wald estimand for fuzzy Regression Discontinuity design (RDD) that,under conditions discussed below, captures the causal effect on compliers. Compliers are definedas children whose school starting age (∼treatment status) changes as moving from the left of theparticular discontinuity point to the right. Since, as discussed soon, there is no information availableabout the exact birth date in the data set, each bin contains children born in the same month. A3-months window, leading to 3-3 bins, is used on the two sides of the discontinuity points. Month ofbirth is controlled for linearly and the linear trend in month of birth is allowed to have different slopes523.3. Identificationon the two sides of the discontinuity points.86The first-stage relationship isDi = β0 + β11 {Xi ≥ xd}+ β2Xi + β31 {Xi ≥ xd} ×Xi + β4Ci +T−1∑t=1µ1tFt + ηi, (3.1)and the second-stage relationship isYi = γ0 + γ1Di + γ2Xi + γ31 {Xi ≥ xd} ×Xi + γ4Ci +T−1∑t=1µ1tFt + υi, (3.2)where Yi is the outcome variable from the set of {testscore, grade repetition, secondary school trackchoice, mental health}, Di is a binary variable denoting age at primary school entry of child i (1: childentered primary school at the age of 7, 0: child entered primary school at the age of 6), Xi is monthof birth (=linear trend, recentered at xd), the discontinuity point xd is either January 1st or June 1stfor voluntary and involuntary delay, respectively, 1 {X ≥ xd} is the discontinuity dummy, Ci denotesthe vector of control variables and Ft variables denote year dummies corresponding to the year whenchild i was born (year is defined to start in September and end in August). Only 1 {Xi ≥ xd} is usedas an instrument and is excluded from the second-stage. The coefficients of interests are β1 and γ1.It is implausible that the potential outcomes and thus the effect of school starting age is homo-geneous in the population. Therefore, following Angrist and Pischke (2008, pp.111), the requirementsfor the aforementioned instruments to be valid in a heterogeneous framework are that (i) (relevanceor the existence of the first-stage relationship) the instrument is related to the endogenous variable;(ii) (independence) the instrument is as good as randomly assigned: it is independent of the vectorof potential outcomes and potential treatment assignments; (iii) (excludability) the instrument has nodirect relationship to student achievement, only an indirect relationship through the decision madeabout primary school entry age. In the following I discuss each of these requirements in detail.The existence of the first-stage relationship requires that month of birth should be systematicallyrelated to school starting age. More specifically, children who were born on/after January 1st and June1st should have significantly higher probability of starting primary school at the age of 7 than childrenborn before it, ceteris paribus.87An assumption, needed for the independence requirement to hold, is that month of birth aroundthe two cutoff points is effectively random. This requirement could fail in the following two cases.First, if children born on one side of the discontinuity points would have better-than-average innateabilities than children born on the other side. Or, to phrase it differently, if innate ability wouldnot be uniformly distributed across month of birth near the cutoff points. Second, it fails if parentswith particular preferences for early childhood investments plan conception systematically differentlyon the two sides of the discontinuity points. For instance, if they delay the birth of the child from86The results continue to hold if using a 2-months window or a quadratic trend; these robustness checks are notincluded in this chapter for the sake of brevity.87Table B.2 suggests the strength of the first-stage relationship in advance: there is a 17 and a 28 percentage pointsjump in the fraction of delayed children between children born in December and January and May and June, respectively.533.3. IdentificationMay to June so that the child likely would be among the older students in the classroom, and at thesame time they can provide the essential early childhood resources in their first years of lives. Table3.2, discussed later in detail, provides evidence that neither the fraction of boys, nor the fraction ofchildren with different parental education is changing discontinuously at the cutoff dates.Bound and Jaeger (2001, pp.96-99) review the potential factors associated with month of birth, ashealth or personality traits. For instance schizophrenia, mental retardation, autism, multiple sclerosisor manic depression has been found to vary across quarter of birth, while an association has beenfound between shyness and month of birth. The evidence on the association between IQ and month ofbirth is inconclusive. Buckles and Hungerman (2013) show large differences in maternal characteristicsfor births throughout the year. They document that women giving birth in the winter months areyounger, less educated, and less likely to be married than other women. They present evidence infavor of the relationship between month of birth and later outcomes being driven by differences infertility patterns across socioeconomic groups, rather than by natural phenomena or schooling laws.I compare children born at most in two consecutive quarters, with one of the discontinuity pointsbeing in the middle of the winter, the other being at the beginning of the summer season, thereforedifferences between summer and winter born children documented in the literature are less relevant.Dickert-Conlin and Elder (2010) test whether parents systematically plan childbirth to capturethe option value of sending their child to school at a younger age and thus avoiding an additional year ofchild care costs. They find no evidence of the option value influencing time of birth. Using exact birthdates, McEwan and Shapiro (2008) and, although in a somewhat different context, McCrary and Royer(2011), do not find that either birth frequencies or students’ observed socio-economic characteristicswould vary sharply around enrollment cutoff dates, suggesting that unobserved characteristics wouldalso vary smoothly around these dates.The excludability requirement fails if children born after the appropriate cutoff points are affectedin some way other than through an increased likelihood of delaying school entry. Clear potential threatsare absolute or relative age effects: comparing two, otherwise identical children with the same schoolstarting age, older students score higher.88 As a consequence, month of birth after the appropriatecutoff date is correlated with testscore for at least two reasons: an increased likelihood of spendingan extra in child care and a disadvantage stemming from being younger at the time test is taken.Even if month of birth were randomly assigned among children indicating that parents do not planconception systematically differently, and even if innate abilities were evenly distributed across months,the channel of the effects of the instruments would still not be unique. This concern can be eliminatedby comparing two children born just before or just after the cutoff date by narrowing down the windowaround the discontinuity point as much as possible. This approach is possible when exact birth date is88For instance, consider first the cutoff date of January 1st and consider two otherwise identical children: the firstborn in October, the second born in February in the next year. Suppose that both children are redshirted. Even thoughthe second child had a higher likelihood of being redshirted, the first one is still 4.5 months older than the second at thetime the test is taken. Next, consider the June 1st cutoff and consider otherwise two identical children, the first born inMarch, the second born in July in the same year. Suppose that the first child is redshirted and the second complied tothe prescribed school starting age of 7. Even though the second child had a higher likelihood of starting school at theage of 7, spending an additional, 4th year in child care, the first one is still 4.5 months older than the second at the timethe test is taken.543.3. Identificationknown89, unfortunately not available in the data set used in this chapter. However, a trend in monthof birth can be controlled for and thus the age-at-the-test concern can be lessened. More importantly,month of birth needs to be controlled for to account for the steadily increasing fraction of delayedchildren born in September to August, seen in Figure 3.190, and in order to identify off exclusively ofthe jump in the fraction of redshirted children at the cutoff dates.Figure 3.1 shows the identification strategy in a nutshell. The first-stage relationship betweenmonth of birth and the fraction of delayed children is marked with the dotted line. The reduced formrelationship between month of birth and student achievement is marked with the dashed line. Finally,the discontinuity cutoffs of January 1st and June 1st are marked with solid reference lines.The fraction of delayed children born in the months September to August is steadily increasing.However, there are clear jumps at the discontinuity points and exactly these jumps at January 1stand June 1st are used as instruments for voluntary and involuntary delay, respectively. The reduced-form relationship reveals that the average testscore by month of birth is steadily decreasing fromJune to December, then, the slope of the testscore sharply changes. Specifically, the average testscoreis decreasing for children born between December and September, then jumps by 0.023 standarddeviation between children born in December and January. Note that without the possibility ofredshirting and with 1st of June as the school enrollment cutoff date, the average testscore by monthof birth would presumably be steadily decreasing from June to May, from the oldest to youngest.From the subgroup analysis by child care entry age it can be seen that the jump at January 1stis less present for children who started child care at the age of 2 (approx. 17 percentage of all children,28 percentage of December-born children and 9.5 percentage of January-born children). From thesubgroup analysis it can also be seen that the initial decrease in testscores for children born betweenSeptember and December is driven by children who started child care at the age of 2; for children whostarted at the age of 3, this fraction is steadily increasing for children born between September andAugust. Despite these striking differences across children with different child care entry age, I do notcontrol for child care entry age as that would induce endogenous selection based on parents’ choice.This chapter’s identification strategy is most similar to the strategy used by Puhani and Weber(2007) and Kollo and Hamori (2011). To overcome the endogeneity of primary school starting age, theyapply an Instrumental Variable (IV) identification strategy using month of birth as the instrument.Their instrument, theoretical or predicted school entry age has the following form:I(bi, si) ={(72+si)−bi12 if 1 ≤ bi ≤ c(84+si)−bi12 if c < bi ≤ 12},where bi is child i’s month of birth, si is the month of primary school start and c is the enrollment cutoffmonth. Note that Puhani and Weber (2007)’s instrument is exactly of the same form as this chapter’sinstrument around the cutoff date of June 1st. However, despite the fact that their instrument isa function of month of birth, they do not control for a linear trend in month of birth, which might89Although Puhani and Weber (2007, pp.371) use this approach even in the absence of information about exact birthdate. They use students born in the 2-months adjacent to the respective school entry cut-off point in their IV regressionsto eliminate any direct seasonal effects and any bias from parental timing of birth.90See also Table B.2.553.3. Identificationquestion the validity of I(bi, si). On page 367 they mention that if bi and si are exogenous, thetheoretical school entry age is exogenous and can be used as an instrument for the actual age ofschool entry. They discuss factors that would invalidate their instrument, such as parental planning ofconception, or that month of birth “might exert some direct effect on physical and psychological health”(Puhani and Weber, 2007, pp.371). However, as discussed previously, exogeneity is not enough foridentification: even if month of birth was randomly assigned among children indicating that parentsdo not plan conception systematically differently, and even if innate abilities were evenly distributedacross months, the channel of the causal effects of the instruments would not be unique if absolute orrelative age effects are present. Also, trends around the cutoff date might be present.In order for the IV estimator to provide the Local Average Treatment Effect (LATE), the mono-tonicity requirement has to be satisfied. Monotonicity requires that while the instrument may notinfluence school starting age for some children, all of those who are influenced are done in the samedirection. Around the discontinuity point of January 1st monotonicity requires for all children to betrue that if she is redshirted when being born before January 1st (in the presence of the administrativebarrier to redshirting), then she would be definitely redshirted when being born on/after January 1st(in the absence of this barrier). Around the discontinuity point of June 1st monotonicity requires forall children to be true that if she starts school at the age of 7 when being born before June 1st (that isequivalent to being redshirted), then she would be definitely starting school at the age of 7 when beingborn on/after June 1st (as prescribed).91 I believe the assumption for both cutoffs is an innocuousone, and is very likely to hold.Given relevance, independence, excludability and monotonicity, the Wald estimand for fuzzyRDD has the interpretation of the local average effect of starting school at the age of 7, relativeto 6, on complier children, whose treatment status is influenced by the change in the instrumentaround the discontinuities. Perhaps my main insight is that the impact of redshirting incorporates notonly the age-impact (being older at the time of the test), but potentially also the impact of boostedhuman capital in that extra year before school for non-school-ready children. By comparing childrenborn around January 1st, I measure the combined impact of age and boosted human capital dueto redshirting, for complier children who might or might not have struggled with school-readinessproblems. By comparing children born around the June 1st school enrollment cutoff date, I measurethe sole age impact of starting school a year older for the complier children who, by definition, didnot struggle with any school-readiness problems—they start late if born after, but would have startedearly if born before the enrollment cutoff date. My results suggest this distinction is important, despitethat the school starting age literature concentrated almost exclusively on the sole age impact so far.Around the discontinuity point of June 1st the compliers are school-ready children who enterprimary school as prescribed by the regulation: 3 years if born before, but 4 years if born on/after June1st. Perhaps it is easier to capture who are the non-compliers in this case. Either the particularly weakor immature students who are redshirted if born before June 1st, or the particularly strong studentswho are brought forward if born on/after June 1st. Alternatively, non-complier parents have a veryclear opinion when their child should enter primary school and whose behavior is not influenced by91Or, equivalently, it cannot happen that a child’s school entry is delayed from age 6 to 7 when being born before June1st, but is brought forward from 7 to 6 when being born on/after June 1st.563.3. Identificationany enrollment cutoff date.Around January 1st, the first group of complier children are those who are not school-ready, andwould be redshirted if the parent only would have to discuss that issue with the child care teachers,but are not redshirted if the local DAB’s approval is needed in addition. For these parents it is toocostly to look for, visit, and let the child take the school-readiness examination; either because theywork, or traveling costs are too high, or they are less informed, and/or distrustful with the system.The second group of complier children are school-ready and whose parents could achieve theirredshirting in the child care institution if only the child care teachers’ approval is needed. However,these parents could be convinced by the developmental experts in the local DAB to let their school-ready child into primary school on time. These parents are either the ones who possess weaker lobbyingpower, or the ones who are more sophisticated/less concerned, so that they can be convinced.Although it is impossible to identify the compliers in the data set, it is possible to assess theiraverage characteristics ex post. Following Almond and Doyle (2011, pp.12-13), first let us define two,independent binary variables, the instrument Zj and the endogenous variable Dj as follows:Zj ={1 if born on/after the cutoff day0 if born before the cutoff day}; Dj ={1 if starting school at the age of 70 if starting school at the age of 6};with j=1,2 corresponding to the January 1st and June 1st cutoffs, respectively. In addition, letus denote DjZj as the value Dj would take if Zj were either 1 or 0. Then compliers are those withDj1 = 1 and Dj0 = 0. Let us denote their fraction piCj . Then, the observable characteristics of thecompliers can be written asE(X|Dj1 = 1, Dj0 = 0)=piCj + piAjpiCj[E(X|Dj = 1, Zj = 1)− piAjpiCj + piAjE(Dj = 1, Zj = 0)], (3.3)where piAj is the fraction of always-takers (for whom Dj1 = 1 and Dj0 = 1) and piCj = 1−piAj−piNj ,where piNj is the fraction of never-takers (for whom Dj1 = 0 and Dj0 = 0). Defiers (for whom Dj1 = 0and Dj0 = 1) are assumed away by the monotonicity assumption. Using the independence between Zjand Dj , piAj = Prob(Dj0 = 1) and piNj = Prob(Dj1 = 0).Note that this chapter does not attempt to disentangle the composite effect of being one yearolder in class (and, at the time of the test) from having spent one additional year in pre-school forthe following reasons. First, disentangling the composite effect in the Hungarian child care systemwould require fixing either the endogenous child care entry margin or the endogenous child care exitmargin, leading to non-random sorting on the two sides of the cutoffs in birth date.92 Second, thereare institutional setups in other countries that provide the suitable natural experiment to comparechildren in the same grade having the same age-at-the-test, but having spent different amount of timein pre-school; see, for instance, Dustmann et al. (2013a) for evidence in the United Kingdom.93 The92For instance, by fixing the time spent in child care at 3 years the effect of starting school at the age of 7 could beestimated, if time spent in child care would be exogenous.93Dustmann et al. (2013a) exploit variation in age-at-school-entry and effective length of first year in school. The effectof longer exposure to kindergarten, without controlling for age-at-the-test, is measured by DeCicca and Smith (2013)who exploit the introduction of the “dual entry” scheme into kindergarten mandated in 1990/1991 in British Columbia,573.3. Identificationsetup in Carlsson et al. (2015) is perhaps the closest to the ideal natural experiment to disentangle age-at-the-test impacts from impacts of time spent in school: they exploit conditionally random variationin the assigned test date for intelligence tests for 18 year-old Swedish males in preparation for militaryservice. In their setup, both age at test date and number of days spent in school vary randomly afterholding date of birth, parish, and expected graduation date fixed.Also, this chapter can not disentangle the effect of school starting age from the effect of age-at-the-test, since all children are tested at the same date. Using Norwegian data, Black et al. (2011) areable to disentangle the aforementioned effects by using scores from IQ tests taken outside of schooland exploiting the variation in the mapping between birth date and the year the test is taken.Finally, it is not possible to compare a delayed child’s student achievement with a non-delayedchild of the same age. First, among non-grade-repeaters, there is no variation in school starting ageby age-at-the-test, so additional information about students in a grade lower (5th/7th/9th) or a gradehigher (7th/9th/11th) would be needed to do this exercise. Second, although there is some variationin school entry starting age by age-at-the-test, this variation comes solely from grade-repeaters.3.3.2 Disentangling Absolute and Relative Age EffectsIn contrast to the reviewed literature’s data, the Hungarian administrative data used in this chapterhas information about all students’ month of birth and school starting age in a given class94, thus thechild’s relative age rank in class is known. To separate the effect of being one year older from therelative age rank in class, I augment (3.2) and include the child’s relative age rank in her class:Yi = pi0 + pi1Di + pi2RRi + pi3Xi + pi41 {Xi ≥ xd} ×Xi + pi5Ci +T−1∑t=1τ1tFt + ςi, (3.4)where Di is a binary variable denoting age at primary school entry of child i (1: child entered primaryschool at the age of 7, 0: child entered primary school at the age of 6), RRi is the child’s relative agerank in her class (in percentage terms), Xi is month of birth (=linear trend, recentered at xd), thediscontinuity point xd is June 1st, 1 {X ≥ xd} denotes the discontinuity dummy, Ci denotes the vectorof control variables, Ft denotes year dummies corresponding to the year when child i was born (yearis defined to start in September and end in August) and Yi denotes the outcome variable (testscore).As an alternative to RRi, I use a binary variable Qi that equals 1 if the child is in the highest quartilein the age distribution in her class and 0 otherwise.The coefficients of interests are pi1 and pi2. pi1 corresponds to the absolute age effect and showsthe impact of entering school a year older, by comparing two very similar children who also have thesame position in the age distribution in their class. pi2 corresponds to the relative age effect and showsCanada. This provisional policy experiment unintentionally decreased time in kindergarten to 6 months for childrenborn between November and December, 1985, while increased time in kindergarten to 16 months for those born betweenJanuary and April, 1986.94The class identifiers do not have any meaning across years, therefore they cannot be used for estimating class fixedeffects.583.3. Identificationthe impact of moving up in the relative age rank by 1 percentage point, by comparing two very similarchildren from the same cohort who started school at the same age (both 6 or both 7).Both Di and RRi/Qi are endogenous. Besides 1 {Xi ≥ xd}, the two additional instrumentalvariables are the fraction of summer-born children in the class and its interaction with 1 {Xi ≥ xd} .The intuition for these instruments is the following: summer-born children enter primary school at theage of 7 by law, thus, in the presence of not many redshirted peers, they are the oldest in the class.A larger fraction of summer-born children decreases the relative rank of any individual summer-bornchild in the class, ceteris paribus. Note that this decrease is smaller for June-born children than forAugust-born ones. The impact of this fraction for children born before the school enrollment cutoffdate depends on whether they are redshirted or not: for redshirted children the impact is positive, foron-time children the impact is negative. Since nearly 60 percent of March-to-May-born children areredshirted, the net impact is expected to be positive.The fraction of summer-born children is a valid instrument if it is related to testscore onlythrough the endogenous variables, Di and RRi/Qi. As opposed to the child’s relative age rank, thepropensity of starting school at the age of 7 is less likely to be related to the fraction of summer-bornchildren. However, this fraction violates the excludability assumption if children non-randomly sortinto classrooms within a school, based on student achievement. Since summer-born children generallyhave higher testscores, classes concentrating high-achievement students would very likely have summer-born children overrepresented in them. It is essential to see whether results on separating absoluteand relative age effects are robust to restricting the sample to children who study in schools that donot sort children systematically into classes within the school.To separate non-sorting schools from sorting schools, I follow a slightly modified method of Hor-vath (2015): for each school I test whether classroom assignment is significantly related to (i) studentachievement (mathematics testscore) or (ii) being born in the summer months. Technically, I run an F-test on the joint significance of classroom effects within school on outcomes (i) and (ii) (with year fixedeffects). The nullhypothesis corresponds to no sorting, while the alternative hypothesis corresponds tosorting. These tests relates within-class sum-of-squares of testsores/fractions to between-class sum-of-squares and a large enough within-variation is indicative of heterogeneous classes within, but roughlysimilar between, therefore sorting can be not be accepted. As a last step I identify “sorting” schoolsas those with p-values of the F-test less than 0.05. As a consequence I end up with a sub-sample ofschools that do not sort children into classes based on prior student achievement (called non-sortingschools “A”) and a sub-sample of schools that do not sort children into classes based on being bornin the summer (called non-sorting schools “B”).9595To illustrate sorting further, for each school I decompose the Total Sum-of-Squares of mathematics testscore,∑nsi=1(Yi − Y¯s)2into Between Sum-of-Squares,∑nsi=1(Y¯cs − Y¯s)2and Within Sum-of-Squares∑nsi=1(Yi − Y¯cs)2, whereY¯s is the average mathematics testscore in school s, ns is the number of students in school s and Y¯cs is the averagemathematics testscore in class c in school s. Finally, I present the average fraction of Within Sum-of-Squares for allschools and non-sorting schools.593.4. Data and Measurement3.4 Data and MeasurementThis chapter uses primarily data from two sources, one administrative and one survey dataset. First,data for 2008-2014 for 6th-, 8th- and 10th-graders on testscore in mathematics and reading, graderepetition and secondary school track choice, birth date and child care attendance is used, along withbackground characteristics from the Hungarian National Assessment of Basic Competences (HNABC).The time period 2008-2014 refers to the (uniform) date at which the test was taken in May. Second,data on mental health outcomes is used from the Hungarian Life Course Survey (HLCS).The HNABC does not measure the students’ knowledge regarding the compulsory curriculum;rather it measures how students are able to apply acquired skills in realistic situations, and to whatextent they possess the necessary competences for further development. The tests are low-stake, thecompletion of the mathematics and reading test sheets was mandatory for all children, and the resultof almost all students was centrally processed, counting towards the school’s average achievement.96Data on background variables, age-at-the-test, (imputed) school starting age and child care at-tendance is obtained from the student background survey of HNABC. The data set from this surveycontains detailed information about the students’ demographical and family background, but com-pletion of the survey was non-compulsory. Unfortunately, mainly due to voluntary completion of thebackground survey, information cannot be used about all students at grades 6, 8 and 10 in years2008-2014. The analysis is restricted to children for whom information about their time spent in childcare, gender, year and month of birth is available, who have valid testscore either in reading or inmathematics and whose parents’ highest educational attainment can be observed. The final samplecontains 76.5-81 percent of the original sample.97The excluded observations are very likely to be non-random. The missing response analysisof the HNABC 2006 and 2007 made at the Hungarian Academy of Sciences, Institute of Economics,Economics of Education Research Unit98 reveals that among students who did not have valid testscores,those with lower parental education are overrepresented. Additionally, students with valid testscoresobtained systematically higher grade from mathematics the year before. There was a significantnegative relationship between testscores and non-response behavior in the background survey. As aconsequence, excluded students with non-privileged family background and worse student achievementare presumed to be overrepresented. Since the returns of later school entry is expected to be largerfor the excluded students, the estimates shown in this chapter are presumably a lower bound.The HLCS is an individual panel survey conducted annually. The original sample (10,022 respon-dents, every 10th child from the population) was chosen in 2006 from the population of 8th-graderswith valid testscores from the HNABC. Students were followed throughout their school career and thequestionnaire contained detailed questions on ethnicity, schools, family background including poverty96Exceptions were made for students with special educational needs, e.g. corporeally/sensually/mentally disabled orautistic students. Students who suffered from physic developmental deficits (e.g. suffered from behavioural problems ordyslexia/dysgraphia/dyscalculia) were required to complete the test sheet, but their results were not taken into accountin the calculation of the school’s achievement. Children who suffered from a temporary injury that made them physicallyunable to do this were not required to complete the test sheet, neither those who missed the class on the testing day.97Table B.1 shows the details of sample selection.98The missing response analyses are available at http://www.econ.core.hu/kutatas/edu/produktumok/kostb.html.603.4. Data and Measurementand home environment, etc. Each wave had a special block as early childhood environment, secondaryschool application, ethnicity, alcohol and drug usage, social network, and prejudices.The outcomes are measured according to the following. Student achievement is measured bystandardized testscore, where standardization was made for the Final Sample by all interactions ofgrade (6/8/10), year (2008-2014) and subject of the test (mathematics and reading). Grade repetitionis measured by a binary variable indicating whether the child repeated at least one grade by grade6, 8 and 10. Secondary school track choice is measured by a binary variable indicating whether thechild attends the j-th track at grade 10. Track #1 is the lowest secondary school track, grantinga vocational, but no high school degree upon completion. Track #2 is the middle secondary schooltrack, granting both a vocational and a high school degree upon completion. Track #3 is the high-est (academic) secondary school track, granting a high school degree upon completion. Track #1does not allow continuation on tertiary level. Mental health outcomes are captured by an indicatorvariable denoting that child i has the j-th mental health condition, where j = 1 refers to havingheadache/stomachache/backpain every day, j = 2 refers to being afraid or being anxious or havingsleeping problems every day or several days per week, and j = 3 refers to feeling dizzy or exhaustedor nausea every day or several days per week.The background survey of the HNABC does not contain information on whether the child wasevaluated by the school-readiness committee, or whether there were concerns about school-readinessaround the age of 6. The exact day of birth is unfortunately not available either. Although thebackground survey of the HNABC asks directly primary school starting age, the information of schoolstarting age together with grade repetition show data inconsistencies in several cases.99 Therefore,school starting age from birth date information (year of birth and month of birth) and grade repetitionare imputed as follows. First, in the absence of exact birth date, assuming that all children were bornon 15th of the appropriate month and that the achievement test was taken on 15th of May in all years2008-2014, the age-at-the-test measured in months is computed according to the following formula:months-at-the-test = (year-of-the-test− year-of-birth− 1)× 12 + (12.5−month-of-birth) + 4.5.Second, assuming that school started on 1st of September in all years between 2008 and 2014,all children who have not repeated any grades lived 68.5 months since their primary school entry.Similarly, all children who repeated 1, 2 and 3 grades lived 80.5, 92.5 and 104.5 months since theirprimary school entry, respectively. Subtracting the appropriate months since school entry from age-at-the-test leads to the imputed primary school starting age.Information about years spent in child care results in the imputed child care starting age. Incases where imputed child care starting age is smaller than 2 or larger than 5, it has been replaced by2 and 5, respectively, and the number of years spent in child care has been modified accordingly.99In these cases, if one believes the provided school starting age and grade repetition, it is impossible for the child tobe in the 6th grade in the particular year, when testscore information is available for her. Moreover, families presumablyanswered these type of age-related questions differently based on whether the child already turned to the age of 6 whenstarting school, or she was in her 7th year of age. These differences can be especially striking between families where thechild was born in September (thus almost e.g. 7, but technically 6 when starting school) or in May (thus unambiguously6 when starting school).613.4. Data and MeasurementThe child background control variables are the followings: gender, highest parental educationalattainment (at most primary education, vocational education, secondary education and tertiary edu-cation), indicators about the family’s wealth situation (whether the child is considered to be disadvan-taged or excessively disadvantaged100, whether the child considers her family poor, whether the childis eligible for free meals and/or free books at school, whether the child has an own desk at home), thecomposition of the household (the number of the members of the household, whether the child livestogether with biological father and mother vs. stepfather and stepmother), the nature and qualityof interactions in the family (whether the parents regularly help in the homework, whether the childregularly discusses with the parents what happened at school or what she is currently reading), theamount and quality of cultural goods at home (access to internet, number of books at home, numberof books the child has on its own), indicators about parental interest (how often the parents visit theschool in order to discuss the child’s development and other school issues with the teachers) and themunicipality characteristics the family lives at (region and type of settlement).Additionally, I control for the local child care situation101 at the relevant age of school entry (atthe age of 6 or 7) and at the age of 2 for the following reasons. First, if there is a scarcity of locallyavailable child care services, then it may be the case that a child prescribed to enter primary schoolis not allowed to be delayed by the director of child care institutions and/or the child care teachers.Second, local child care circumstances likely influence child care entry age. Child care control variablesstem from 3 data sources: KIR-Stat102, the municipality-level demographical data set by cohorts of theHungarian Statistical Authority (received from Gabor Kertesi) and the Local Government TreasuryDataset. If applicable, I aggregated institution-level data to municipality-level and then I matchedto each observation the variables in the municipality she lived at her age of predicted primary schoolentry; i.e. at her age of 6 or 7, depending on month of birth. The following child care variables are usedas controls: average child care class size, number of child care teachers and child care places relative tochild care-relevant aged (3-6 years old) population, the ratio of 3, 4, 5, 6 years old children attendingchild care, a binary variable indicating if there exists no child care institution in the municipalitythe child lived at her age of predicted primary school entry, number of child care expenditures percapita, child care expenditures per available child care places and child care non-salary and salaryexpenditures relative to all local government expenditures.100According to Act No. LXXIX of 1993 on Public Education (121(1)) a child is disadvantaged if her family is eligiblefor child protection support based on her social circumstances; a child is excessively disadvantaged if, in addition, one ofher parents’ highest educational attainment is primary school.101Note that the decision of delaying childcare entry could be influenced by the primary school quality the parentsintend to take their child into first grade. For instance, if there is a waiting list in the local good quality school, butexcess supply of spots in the local worse quality school, parents would have an increased incentive to hold their child backin child care. Therefore, a school-specific primary school quality measure is estimated from an individual-level regressionwhere standardized testscore is regressed on year fixed effects, gender, highest parental educational attainment, familybackground variables, childcare control variables and missing response characteristics controls; the school residuals areestimated out for each child. All the results shown in this chapter are robust whether the aforementioned measure, orits average version (within municipality), or school fixed effects or school-year fixed effects are included as controls.102KIR-Stat provides the most comprehensive data about the Hungarian educational system. Every educational insti-tution every year is required to fill out a data form according to the enactment of the Ministry of Education 229/2006.(XI. 20.).623.5. Results3.5 ResultsIn this section I present the main results of the chapter. First, I show the results on individual returnsto starting school a year older on several student and mental health outcomes. Second, I present theresults on whether absolute age effects or within-class relative age effects dominate in the impact ofstarting school older due to the school enrollment cutoff date.3.5.1 Results on Individual ReturnsAfter showing some descriptive statistics of delayed children, in this part I present the fuzzy RDD/IVresults for all (based on (3.2)) and by gender and parental education (based on (3.5)) for standardizedtestscores at grades 6, 8 and 10; grade repetition by grade 6 and 10; secondary school track choice aftergrade 8 and mental stability measures, as anxiety and exhaustion, at grade 8.103 The second-stagerelationship, where the treatment dummy Di is interacted by gender and parental education isYi = γ0 + γ1Di + γ2boyi ×Di + γ3lowpi ×Di + γ4boyi × lowpi ×Di+γ5boyi + γ6lowpi + γ7boyi × lowpi + γ8Xi + γ91 {Xi ≥ xd} ×Xi+γ10Ci +∑T−1t=1 ξ1tFt + ϑi,(3.5)where Di is a binary variable denoting age at primary school entry of child i (1: child entered primaryschool at the age of 7, 0: child entered primary school at the age of 6), Xi is month of birth (=lineartrend, recentered at xd), the discontinuity point xd is either January 1st or June 1st, 1 {X ≥ xd}denotes the discontinuity dummy, boyi denotes the child’s gender, lowpi denotes that the child haslow-educated parents (the child’s parents have at most vocational, but no high school degree), Cidenotes the vector of control variables, Ft denotes year dummies corresponding to the year when thechild was born (year is defined to start in September and end in August), and Yi denotes the outcomevariable. In what follows, child i is considered and called low-status or disadvantaged if lowpi = 1.The first-stage relationship for all groups is in (3.1), where only 1 {Xi ≥ xd} is used as an instru-ment and is excluded from the second-stage relationship. When assessing the first-stage relationshipby gender and parental education, 1 {Xi ≥ xd} and its interactions with gender and parental educationare used as an instrument and are excluded. In the latter case there are four first-stage equations,corresponding to the endogenous variables Di, boyi × Di, lowpi × Di, and boyi × lowpi × Di. Thefirst-stage results for Di will be presented separately:Di = β0 + β11 {Xi ≥ xd}+ β2boyi × 1 {Xi ≥ xd}+ β3lowpi × 1 {Xi ≥ xd}+β4boyi × lowpi × 1 {Xi ≥ xd}+ β5boyi + β6lowpi + β7boyi × lowpi+β8Xi + β91 {Xi ≥ xd} ×Xi + β10Ci +∑T−1t=1 µ1tFt + ηi.(3.6)103The other outcomes that I considered but found no effect is high school completion, the first labor market outcomesand prosocial measures (alcohol, drug usage, smoking, teenage pregnancy and committing various crime types).633.5. ResultsDescriptive Statistics of Delayed ChildrenTable 3.2 shows the fraction of boys and children with different parental education by quarter of birthand school starting age around the January 1st and June 1st cutoff dates.104 Most importantly, thereis no indication of any discontinuity of the fraction of boys or children with various family backgroundsaround the cutoff dates. On both sides the fraction of boys is 49 percent, while the fraction of childrenwith parents at most 8 years of schooling, vocational training, high school degree or tertiary degree is11, 29, 31, 29 percent, respectively. The fraction of boys is approximately 14 percentage points higheramong delayed children, while children with low-educated (high-educated) parents are overrepresented(underrepresented) among them.The fraction of children with different developmental obstacles among redshirted and non-redshirtedchildren can be seen in Table 3.3. Children are significantly more likely to be redshirted if they expe-rienced a family shock (e.g. they were separated from their mothers/fathers before the age of 5 or thefamily had a negative income shock before then), a shock at birth (e.g. low birth weight, too early orbirth with complications), chronic illnesses (ear or nerve system disease at ages 0-5) or developmentalproblems (attention disorder, cognition disorder, hyperactivity at ages 5-6).First-stage Results and Complier AnalysisTable 3.4 shows the first-stage results on voluntary and involuntary school entry delay, using theadministrative data.105 In Table 3.4, PanelA shows the estimation result - coefficients, standard errors- for all groups (based on (3.1)), while PanelB1 shows the estimation result, based on (3.6). PanelB2shows the estimated effects of Zi = 1 {Xi ≥ xd} by subgroups, and their significance level. PanelB3shows whether the effects of Zi significantly differs across various subgroups. The values of the jointF-statistics, each of them above 300, suggest a very strong first-stage and no concerns passing tests ofweak instruments (Stock et al. (2002) and, in the presence of clustering, Olea and Pflueger (2013)).Children born after the January 1st and June 1st cutoff dates are by 11-13 and 18-25 percentagepoints (by 50 and 25 percent) more likely to be delayed than children born before. Boys are significantlymore likely to be redshirted than girls, if born on or after January 1st than if born just before; thisholds irrespective of their grade, family background and, in the case of high-status boys, their higherbaseline propensity of being redshirted. For instance, a 6th-grader boy with high-educated parents hasapproximately 19 percentage points higher likelihood of being redshirted if born on or after January1st than if born just before, while a very similar girl has only approximately 9 percentage points higherlikelihood of being redshirted. The same effects for low-status boys and girls are 14.5 and 9 percentagepoints, respectively. Thus, being born on or after January 1st induces high-status boys (girls) beingredshirted to a significantly larger (smaller) extent than very similar low-status boys (girls). The effectof quarter of birth is largest for high-educated parents’ sons also when comparing it to their baselinefraction of redshirted students: in 6th grade, for instance, their estimated coefficient is 2/3 of theirbaseline fraction. The same fraction for high-educated and low-educated parents’ daughters is 1/2,104The table contains data from the administrative data, grade 6; the fractions are very similar in grade 8 and 10,therefore I omit those grades for the sake of brevity.105Table B.3 shows the first-stage coefficients on all the endogenous variables.643.5. Resultswhile for low-educated parents’ sons it is around 40 percent.Girls are significantly more likely to be (involuntarily) delayed than boys, if born on or afterJune 1st than if born just before; a possible reason behind this is the girls’ lower propensity of beingredshirted if born in March to May. The effect of quarter of birth is highest for low-educated parents’daughters: they are approx. 35 percentage points more likely to start school at the age of 7 if born inthe summer months, than if born before June 1st (the estimated effect is around 48 percent of theirbaseline propensity). The same effect for high-status girls, high-status boys and low-status boys is 28,16 and 16 percentage points, respectively (40, 20 and 24 percent of their baseline propensity). Forboth genders, high-educated families are significantly more responsive to quarter of birth, althoughfor boys the difference is significant only in grade 10.Table 3.5 shows the first-stage results on voluntary and involuntary school entry delay, using thesurvey data.106 Although, mainly due to the smaller sample size, the value of the joint F-statisticsdecreased, each of them is still above 20. Children born after the January 1st and June 1st cutoffdates are by 15 and 30 percentage points more likely to be delayed than children born before.Similarly to the results using the administrative data, boys are significantly more likely to beredshirted than girls, if born on or after the corresponding cutoff date of January 1st; irrespectiveof their family background. The estimated coefficient for high-educated parents’ sons is 4/5 of theirbaseline fraction of redshirted children, while for low-educated parents’ sons it is 2/3. The samefraction for girls is around 55 percent. There are no significant differences by parental background forredshirting, presumably partly due to small sample size.As in the case of the administrative data, girls and high-educated parents’ children are signifi-cantly more likely to be induced to enter school at the age of 7 than boys and low-educated parents’children, if born in the summer than if born before. The effect of quarter of birth, in terms of theirbaseline fraction, is 68 and 57 percent for high-status and low-status girls, while it is around 33 percentfor high-status and low-status boys.The average characteristics of the compliers can be seen in Table 3.6, and can not be distin-guished from the average characteristics of all the students. This result is reassuring in the sense thatthe results presumably do not correspond to a very specific sub-population.Results on TestscoreTable 3.7 reveals that redshirted children achieved significantly, on average 0.24 of a standard deviation,higher score in mathematics on the 6th-grade and 8th-grade testings than on-time children, and theeffects, though drop to 0.16, persist in secondary school. The effect of involuntary delay is very similarin grade 6, but drop more, to 0.1 standard deviation in grades 8 and 10. This suggests that boostinghuman capital of non-school-ready children have a longer-lasting impact on mathematics score, thanbeing solely a year older at the time of the test. Table 3.8 shows that this is not the case for reading:the impact of school entry delay on 6th-, 8th-, and 10th-grade reading score is 0.23, 0.2 and 0.17standard deviations, irrespective of whether it is voluntary or involuntary.Redshirted disadvantaged boys score significantly higher on the 6th-grade mathematics test, than106Table B.4 shows the first-stage coefficients on all the endogenous variables.653.5. Resultshigh-status boys, ceteris paribus; otherwise no significant differences in the impact of redshirting acrossgender or parental education can be detected. In the case of voluntary delay, disadvantaged boys bene-fit significantly more from being one year older at the time of the 6th-grade and 8th-grade mathematicsand reading tests, than their otherwise very similar male high-status peers. Disadvantaged boys alsobenefit significantly more at the time of the 6th-grade and 8th-grade test, than disadvantaged girls;while high-status boys benefit more than high-status girls in grade 10.Results on Grade RepetitionAccording to Table 3.9, redshirted high-status children have 3.6 percentage points smaller likelihoodof grade repetition by grade 6 than on-time children, and these effects are very large compared to thebaseline propensity of grade repetition of these groups. There are no detectable effects by grade 10for them. Redshirted low-status girls have 5 percentage points smaller likelihood of repeating a gradeby 6th grade than on-time low-status girls and this effect is 66 percent of their baseline propensity.Low-status boys realize a significantly larger advantage from redshirting: their point estimate is -7.5percentage points (70 percent of their baseline propensity). Moreover, this effect persists through 10thgrade. Since grade repetition is by far the biggest problem for low-status boys at grade 10, leading inseveral cases to dropping out from secondary school, this persistent effect is important.The effect of starting school a year older due to the school enrollment cutoff date is more persistentfor groups other than disadvantaged boys (for whom it is equally persistent). For instance, while theeffects for high-status children at grade 6 are small and occasionally insignificant, high-status childrenwho started school at the age of 7 if born in the summer (but would have started at the age of 6if born before) have 2.5-3 percentage points smaller probability of repeating a grade at grade 10.For low-status children there are large impacts already at grade 6: their point estimate is approx.-3.5 percentage points, which is approx. 40 percentage of the baseline propensity of girls and boys,respectively. The point estimates increase further at grade 10 to -4.39 and -6.44 percentage points (32and 37 percent of the baseline). The point estimates are significantly higher for disadvantaged boysand girls; although, their baseline propensity of grade repetition is also higher.Despite the more persistent impacts of involuntary school entry delay to secondary school, theimpacts of redshirting are larger in grades 6 and 8: redshirted children are by 4.5 percentage pointsless likely to repeat a grade in primary school, than on-time children, while for involuntary delay theimpact is 2.5 percentage points. This suggests that boosting human capital of non-school-ready chil-dren have a larger impact on grade repetition in primary school, than solely entering school a year older.Results on Secondary School Track ChoiceThe effects of voluntary and involuntary delay on secondary school track choice are in Table 3.10.Secondary school track choice is measured by a binary variable indicating whether the child attendsthe j-th track at grade 10. Track #1 is the lowest secondary school track, granting a vocational, butno high school degree upon completion. Track #2 is the middle track, granting both a vocationaland a high school degree upon completion. Track #3 is the highest (academic) track, granting a highschool degree upon completion. Track #1 does not allow continuation on tertiary level.663.5. ResultsRedshirting significantly decreases the propensity of going to the vocational track by 9.25 per-centage points (50 percent), and significantly increases the propensity of going to the academic track by6.6 percentage points (16.5 percent), although the impact is significant only for boys and low-educatedgirls. For low-educated boys, the latter impact is almost half of the baseline propensity. The impactof involuntary delay is similar, although a bit smaller (larger) for the vocational (academic) track.Redshirted high-status girls have significantly, 10 percentage points lower probability of attendingthe lowest track; this effect is remarkable, given the very low baseline propensity of them attending thenon-academic tracks (approximately 40 percent). The impact is -8 and -7 percentage points for high-status boys and low-status girls, 70 and 25 percent of their baseline propensity, respectively. Redshirtedlow-status boys, overrepresented in the vocational track, have 12 percentage points (27 percent) lowerlikelihood of attending it, than on-time low-status boys, holding everything else constant.High-status girls who were induced to start primary school at the age of 7 by the school enrollmentcutoff date have significantly, 2.2 (6.06) percentage points lower probability of attending the vocational(middle) track at grade 10. The effect of involuntary school entry delay is -4 and -6 percentage pointsfor high-status boys and low-status girls, 40 and 22 percent of their baseline propensity, respectively.Low-status boys have 8 percentage points lower likelihood of attending it if induced to start school atthe age of 7 by the school enrollment cutoff date (20 percent of their baseline propensity).The point estimates of the effect on lowest track attendance is significantly larger for boys, irre-spective of family background; also, it is significantly larger for low-status than for high-status boys.The effect of involuntary delay on choosing the highest, academic track is between 7 and 8.4 percent-age points for the various groups; in terms of their baseline propensity, the effect is the highest forlow-status boys (50 percent), then for low-status girls (32 percent), high-status boys (19 percent) andhigh-status girls (13 percent). However, the differences in the point estimates are not significantlydifferent from zero, either by gender or by parental background.Results on Mental HealthThe aforementioned results indicate that disadvantaged boys are the primary winners of delayed schoolentry, irrespective whether it was voluntary or involuntary. In addition, redshirting has a longer-lastingand larger impact than involuntary delay exactly on outcomes where disadvantaged boys enjoy thelargest gains, as mathematics testscore, grade repetition in primary school and attending the vocationalsecondary school track. The following results suggest that mental health can be one of the mechanisms;i.e. boosted human capital in the extra year in child care leads to better mental health, associatedwith better student achievement.Mental health outcomes are captured by an indicator variable denoting that child i has the j-thmental health condition, where j = 1 refers to having headache/stomachache/backpain every day,j = 2 refers to being afraid or being anxious or having sleeping problems every day or several daysper week, and j = 3 refers to feeling dizzy or exhausted or nausea every day or several days per week.The aforementioned mental conditions likely prevent children from succeeding at school.107107I have not found evidence so far for gender differences in the aforementioned mental conditions; Duckworth andSeligman (2008) and Duckworth et al. (2012) argue that girls outperform boys on report card results and grades due totheir higher self-discipline.673.5. ResultsAccording to Table 3.11, the effect of redshirting is significant only for low-educated parents’sons. For instance, a low-status boy who was redshirted in the absence of the administrative barrierbut would not have been redshirted in the presence of it, is significantly less likely to suffer fromeveryday-pains, anxiety, sleeping problems and exhaustion than a very similar non-redshirted peer.The corresponding point estimates are -15,-29 and -21 percentage points, and are very large given thebaseline propensity of low-status boys having these mental conditions. The effect of involuntary schoolentry delay is significant only in one case: on severe exhaustion for high-educated parents’ sons.3.5.2 Results on Absolute vs. Relative Age EffectsFigure 3.2 shows the distributions of class size, the relative age rank in class (RR, in percentiles), andthe fraction of summer-born children in class, using all 6th-graders in 2008-2014 in the Hungarianadministrative data, separately for all schools and for non-sorting schools.108Table 3.12 contains the result of the first-stage regressions on the endogenous Di and RRi/Qivariables, separately for all schools and for non-sorting schools (based on non-sorting by prior testscores(“A”) or month of birth (“B”). Being born in the summer months, as opposed to being born betweenMarch and May, significantly increases both the likelihood of starting school at the age of 7 and thechild’s relative age rank in the class, either measured in continuous (RRi) or binary form (Qi). Thefraction of summer-born peers in the class is, as expected, not related to school starting age Di. Onthe contrary, it is significantly related to the relative age rank in class: for summer-born children a 1percentage point increase in the fraction of summer-born classmates leads to 0.11 percentage pointsdecrease in their relative age rank (measured in percentiles) or a 0.1 percent decrease in the probabilityof ending up in the highest quartile of the age distribution in their class, ceteris paribus. For childrenborn between March and May a 1 percentage point increase in the fraction of summer-born classmatesleads to 0.1 percentage points increase in their relative rank (measured in percentiles) or a 0.3 percentincrease in the probability of ending up in the highest quartile of the age distribution in class. Theseresults are robust to sub-samples of only non-sorting schools.Regarding the strength of the instruments, the joint F-statistic in the first-stage of the aforemen-tioned endogenous variables is all above 100, when all schools are considered. Due to the reductionof the sample size, the aforementioned value considerably drops when only non-sorting schools areconsidered, nevertheless still above 40 in each case. In addition, each of the Cragg-Donald Wald F-statistics are above 70 and each of the Kleibergen-Papp F-statistics are above 40. Therefore, weakidentification can be excluded. Regarding the validity of the instruments, each of the p-values of theHansen J-statistic are above 0.2, therefore the nullhypothesis of valid (excludable) instruments cannotbe rejected at the usual significance levels.Table 3.13 shows the OLS and IV results for the effect of Di and RRi/Qi on 6th-grade standard-ized mathematics testscore, separately for all schools and for non-sorting schools (based on non-sortingby prior testscores (“A”) or month of birth (“B”)). Columns (1) to (3) show the OLS results if absolute108See Table B.5 for further descriptive statistics. Table B.6 shows the fraction of Within Sum-of-Squares of mathematicstestscore for school-year pairs with at least 2 classes in grade 6.683.6. Conclusionand relative age effects are entered separately. It can be seen that both starting primary school at theage of 7 and the relative age rank in class are either negatively associated with student achievement,or not significantly related to it. Once absolute and relative age effects are entered together (columns(4) and (5)), the association between school starting age and testscore switches sign and becomessignificantly positive. On the other hand, there is a negative association between relative age rankand student achievement, holding school starting age fixed.Looking at the IV results, both higher school starting age and the relative age rank positivelyaffect student achievement if entered separately. For instance, according to columns (6), enteringprimary school a year older leads to a 0.22-0.27 standard deviation increase in mathematics testscorein grade 6 (depending on the subset of schools considered), ceteris paribus. In contrary, moving up onthe relative age distribution in the class by 1 percentage point leads to a 0.37-0.48 percentage pointsincrease in the score, ceteris paribus. However, column (8) and (9) reveal that once starting primaryschool at the age of 7, the relative rank has no additional causal effect on testscores. According tocolumn (8), a child who entered primary school at the age of 7 is predicted to have 0.2-0.35 standarddeviations higher student achievement than the one who entered primary school at the age of 6, andhas the same position in the relative age distribution in her class. These results indicate that absoluteage effects dominate relative age effects.3.6 ConclusionIn this chapter I measure the causal effect of academic redshirting using Hungarian administrativetestscore data and survey data on mental health for years 2008-2014. The main institutional featureexploited is a school-readiness evaluation, compulsory for potentially redshirted children born beforeJanuary 1st. By comparing children born around January 1st, I measure the combined impact of ageand boosted human capital due to academic redshirting, for the complier children who might or mightnot have struggled with school-readiness problems, and for whom this administrative barrier had adeterring impact. By comparing children born around the June 1st school enrollment cutoff date, Imeasure the sole age impact of starting school a year older due to involuntary school entry delay, forthe complier children, who by definition do not struggle with any school-readiness problems: theystart late if born after school enrollment cutoff date, but would have started early if born before.I find four striking results. First, although there are large gains for all children, disadvantagedboys benefit the most from school entry delay. Second, redshirting has a longer-lasting or largerimpact than involuntary delay exactly on outcomes where disadvantaged boys enjoy the largest gains;namely grade repetition (especially in primary school), mathematics testscore and avoiding the lowest,vocational secondary school track. Third, redshirting impacts mental health, measured by anxiety andexhaustion, positively only for disadvantaged boys. Finally, exploiting natural variation in the fractionof summer-born children in class, I find the positive effects of higher school entry age to be driven byabsolute, rather than within-class relative age effects.693.7. Tables3.7 TablesTable 3.1: Predicted Path into Primary School in Hungary, by Month of BirthMonth of Birth Predicted Age Possibilityat School Entry for Redshirting? RegimeJune 7 years 2.5 months no 3July 7 years 1.5 months no 3August 7 years 0.5 months no 3September 6 years 11.5 months yes, with administrative barrier 1October 6 years 10.5 months yes, with administrative barrier 1November 6 years 9.5 months yes, with administrative barrier 1December 6 years 8.5 months yes, with administrative barrier 1January 6 years 7.5 months yes, no administrative barrier 2February 6 years 6.5 months yes, no administrative barrier 2March 6 years 5.5 months yes, no administrative barrier 2April 6 years 4.5 months yes, no administrative barrier 2May 6 years 3.5 months yes, no administrative barrier 2Table 3.2: The Fraction of Boys and Children with Different Parental Education, by Month of Birthand School Starting Age, Administrative Data Grade 6month of birth: October-December January-Marchxd : January 1st non-delayed delayed non-delayed delayedfraction of boys 47.474% 61.714% 44.072% 58.222%(mean) 49.433% 49.252%fraction of parental education: at most 8 years in school 9.259% 24.216% 8.782% 15.271%(mean) 11.584% 11.310%fraction of parental education: at most vocational training 28.652% 35.080% 28.146% 31.446%(mean) 29.437% 29.439%fraction of parental education: at most high school degree 32.437% 23.467% 32.755% 28.776%(mean) 31.043% 31.196%fraction of parental education: tertiary degree 29.652% 17.236% 30.317% 24.507%(mean) 27.936% 28.056%month of birth: March-May June-Augustxd : June 1st non-delayed delayed non-delayed delayedfraction of boys 41.182% 55.743% 35.408% 49.664%(mean) 49.615% 49.471%fraction of parental education: at most 8 years in school 9.083% 12.303% 9.803% 10.915%(mean) 11.428% 11.648%fraction of parental education: at most vocational training 28.924% 28.888% 23.754% 29.666%(mean) 28.982% 29.627%fraction of parental education: at most high school degree 32.438% 30.320% 27.720% 31.542%(mean) 30.937% 30.976%fraction of parental education: tertiary degree 29.555% 28.488% 38.723% 27.877%(mean) 28.653% 27.749%Note: source of data: HNABC (grade 6) 2008-2014.703.7. TablesTable 3.3: The Fraction of Children with Different Developmental Obstacles born between Septemberand May by School Starting Age, Survey Datafraction of children who: among redshirted among on-time p-value of diff.were separated from mother before age 5 3.68% 2.28% 0.002were separated from father before age 5 16.56% 13.40% 0.001were born before week 36 12.01% 6.94% 0.000were born with complications 16.01% 13.97% 0.038were born with low birth weight 14.35% 8.36% 0.000were born with very low birth weight 3.39% 1.59% 0.000said first words 1 year or older 36.98% 30.73% 0.000had problems with speaking at age 5 25.24% 17.56% 0.000had chronic ear disease at ages 0-3 14.21% 10.30% 0.000had ever problems with nerve system 1.33% 0.70% 0.012were diagnosed with dislexia/disgrafia/discalculia at ages 6-7 19.42% 12.02% 0.000had cognition disorder at ages 5-6 3.73% 1.48% 0.017had attention disorder at ages 5-6 5.80% 2.74% 0.000diagnosed with hyperactivity at ages 5-6 2.84% 1.94% 0.029had negative income shock in family before age 6 10.35% 7.95% 0.000Note: source of data: HCLS. The last column tests whether the difference in the fraction between redshirted and non-redshirtedchildren in significantly different from 0. *** p<0.01, ** p<0.05, * p<0.1.713.7. TablesTable 3.4: The Effect of Quarter of Birth - First-stage Results on School Entry Delay, with full set ofinteractions by Gender and Parental Education, Administrative Data, Grades 6/8/10Di = 1 {school entry at age 7} Academic Redshirting Involuntary Delayxd : January 1st xd : June 1stgrades 6 8 10 6 8 10Panel A: effects for all groupsZi = 1 {Xi ≥ xd} 0.1312*** 0.1139*** 0.1149*** 0.1819*** 0.2174*** 0.2525***[0.004] [0.003] [0.003] [0.005] [0.005] [0.005]N 223,924 206,499 219,901 227,185 219,173 214,092R2 0.177 0.181 0.127 0.276 0.302 0.333mean of dependent variable: 0.263 0.200 0.197 0.768 0.746 0.712Panel B: effects for subgroupsPanel B1: coefficients and standard errorsZi = 1 {Xi ≥ xd} 0.0884*** 0.0703*** 0.0730*** 0.2553*** 0.2896*** 0.3086***[0.005] [0.004] [0.004] [0.006] [0.006] [0.006]boyi × Zi 0.0987*** 0.0850*** 0.0860*** -0.1326*** -0.1327*** -0.1186***[0.004] [0.004] [0.004] [0.004] [0.004] [0.004]lowpi × Zi 0.0122** 0.0230*** 0.0122** -0.0304*** -0.0352*** -0.0088*[0.005] [0.005] [0.005] [0.005] [0.005] [0.005]lowpi × boyi × Zi -0.0540*** -0.0335*** -0.0231*** 0.0241*** 0.0372*** 0.0286***[0.007] [0.007] [0.007] [0.006] [0.006] [0.007]N 223,924 206,499 219,901 227,185 219,173 214,092R2 0.179 0.183 0.13 0.281 0.307 0.337joint F − statistic 395.49 356.4 360.93 689.48 815.57 1939.44Panel B2: estimated effects of Zigirl, high parental educ. 0.088*** 0.070*** 0.073*** 0.255*** 0.290*** 0.309***mean of dependent variable: 0.177 0.134 0.148 0.716 0.694 0.666boy, high parental educ. 0.187*** 0.155*** 0.159*** 0.123*** 0.157*** 0.190***mean of dependent variable: 0.283 0.217 0.221 0.807 0.786 0.755girl, low parental educ. 0.134*** 0.085*** 0.100*** 0.332*** 0.375*** 0.373***mean of dependent variable: 0.265 0.203 0.191 0.748 0.729 0.688boy, low parental educ. 0.145*** 0.145*** 0.148*** 0.116*** 0.159*** 0.210***mean of dependent variable: 0.358 0.281 0.257 0.811 0.789 0.749Panel B3: p-values of testing differences of effects of Zigirl, high-low parental educ. 0.022 0.000 0.013 0.000 0.000 0.091boy, high-low parental educ. 0.000 0.067 0.059 0.216 0.691 0.000high parental educ., boy-girl 0.000 0.000 0.000 0.000 0.000 0.000low parental educ., boy-girl 0.000 0.000 0.000 0.000 0.000 0.000Note: this table shows the result of estimating a LPM of Di on Zi, boyi ×Zi, lowpi ×Zi, boyi × lowpi ×Zi and control variables.Di is a binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: childentered primary school at the age of 6). Zi is a binary variable denoting quarter of birth of child i (1: child was born on/afterJanuary 1st or June 1st, 0: child was born before January 1st or June 1st). Control variables include: linear trend in month ofbirth and its interaction with a binary variable denoting quarter of birth, cohort fixed effects, family background and child carevariables listed in Part 4, and missing response characteristics controls. Estimation restricted to children who were born in thethree-months window around the cutoff dates of January 1st and June 1st. Standard errors clustered at the school level. ***p<0.01, ** p<0.05, * p<0.1. Source of data: HNABC (grades 6,8,10) 2008-2014, KIR-Stat/DEM 1998-2006, LGT 1998-2005. Thecorresponding equation is (3.1).723.7. TablesTable 3.5: The Effect of Quarter of Birth - First-stage Results on School Entry Delay, with full set ofinteractions by Gender and Parental Education, Survey DataDi = 1 {school entry at age 7} Academic Redshirting Involuntary Delayxd : January 1st xd : June 1stPanel A: effects for all groupsZi = 1 {Xi ≥ xd} 0.1533*** 0.3022***[0.019] [0.024]N 6,899 6,116R2 0.210 0.329mean of dependent variable: 0.2377 58.92Panel B: effects for subgroupsPanel B1: coefficients and standard errorsZi = 1 {Xi ≥ xd} 0.0990*** 0.3583***[0.023] [0.030]boyi × Zi 0.0868*** -0.0555**[0.023] [0.028]lowpi × Zi 0.0338 -0.0647**[0.029] [0.033]lowpi × boyi × Zi -0.0171 -0.0152[0.040] [0.044]N 6,899 6,116R2 0.213 0.331joint F − statistic 20.85 42.85Panel B2: estimated effects of Zigirl, high parental educ. 0.0990*** 0.3583***mean of dependent variable: 0.176 0.522boy, high parental educ. 0.1858*** 0.3028***mean of dependent variable: 0.238 0.614girl, low parental educ. 0.1328*** 0.2936***mean of dependent variable: 0.245 0.579boy, low parental educ. 0.2025*** 0.2229***mean of dependent variable: 0.318 0.659Panel B3: p-values of testing differences of effects of Zigirl, high-low parental educ. 0.238 0.050boy, high-low parental educ. 0.561 0.008high parental educ., boy-girl 0.000 0.047low parental educ., boy-girl 0.035 0.043Note: this table shows the result of estimating a LPM of Di on Zi, boyi ×Zi, lowpi ×Zi, boyi × lowpi ×Zi and control variables.Di is a binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: childentered primary school at the age of 6). Zi is a binary variable denoting quarter of birth of child i (1: child was born on/afterJanuary 1st or June 1st, 0: child was born before January 1st or June 1st). Control variables include: linear trend in month of birthand its interaction with a binary variable denoting quarter of birth, cohort fixed effects, family background and child care variableslisted in Part 4, and missing response characteristics controls. Estimation restricted to children who were born in the three-monthswindow around the cutoff dates of January 1st and June 1st. Standard errors clustered at the school level. *** p<0.01, ** p<0.05,* p<0.1. Source of data: HLCS, KIR-Stat/DEM 1998-2006, LGT 1998-2005. The corresponding equation is (3.1).733.7. TablesTable 3.6: Academic Redshirting and Involuntary Delay, Average Characteristics of Compliers, Ad-ministrative DataJanuary 1st cutoff June 1st cutoffcharacteristics complier sample complier samplefemale 0.4476 0.5101 0.5105 0.5080highest parental education: primary 0.1061 0.1107 0.1057 0.1085highest parental education: vocational 0.2915 0.3023 0.3042 0.2984highest parental education: secondary 0.3209 0.3196 0.3197 0.3175highest parental education: tertiary 0.2815 0.2675 0.2703 0.2756disadvantaged 0.2940 0.2929 0.3042 0.3013excessively disadvantaged 0.1028 0.1026 0.1020 0.1028discount on meal at school 0.2712 0.2774 0.2673 0.2725free meal at school 0.2525 0.2030 0.2522 0.2380free books at school 0.4881 0.4881 0.4947 0.4939# of books at home : 0-50 0.1534 0.1522 0.1515 0.1523internet at home 0.8176 0.7612 0.8084 0.7939own books at home 0.9535 0.9541 0.9555 0.9544own desk at home 0.9164 0.9185 0.9220 0.9207considers own family to be poor 0.1961 0.1836 0.1884 0.1867biological mother in household 0.9532 0.9625 0.9612 0.9610biological father in household 0.7271 0.7610 0.7475 0.7507stepmother in household 0.0206 0.0157 0.0156 0.0159stepfather in household 0.1003 0.0948 0.0981 0.0968# of individuals in household 4.4411 4.4672 4.4509 4.4682parents, siblings help in homework 0.2985 0.2916 0.2915 0.2941school issues discussed at home 0.7638 0.7633 0.7698 0.7682child’s current readings discussed at home 0.1795 0.1680 0.1712 0.1705parents regularly visit school meetings 0.8442 0.8526 0.8617 0.8573type of settlement: county centre 0.2140 0.1610 0.1574 0.1586type of settlement: other city 0.3493 0.3526 0.3523 0.3501type of settlement: village 0.2968 0.3739 0.3765 0.3765region: Central Trans-Danubia 0.1109 0.1124 0.1110 0.1107region: Western Trans-Danubia 0.0906 0.0971 0.0996 0.0987region: Southern Trans-Danubia 0.0968 0.0961 0.0954 0.0942region: Northern Hungary 0.1210 0.1339 0.1325 0.1330region: Northern Great Plain 0.1810 0.1841 0.1836 0.1840region: Southern Great Plain 0.1264 0.1366 0.1377 0.1363child care expenditures per capita in municipality (Fts in 2005) 318.1707 314.4123 314.3697 314.9296child care teachers per 3-6 old children in municipality 0.0830 0.0812 0.0814 0.0814child care places per 3-6 old children in municipality 3.8154 3.2885 3.3191 3.3327fraction of 6-year olds in child care in municipality 0.2305 0.2231 0.2267 0.2251no child care in municipality 0.0233 0.0304 0.0302 0.0307Note: source of data: HNABC (grade 6) 2008-2014, KIR-Stat/DEM 1998-2006, LGT 1998-2005. Relevant sample includeschildren who were born in the months October to March or March to August. The corresponding equation is (3.3).743.7. TablesTable 3.7: The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Resultson 6th/8th/10th-grade Mathematics testscore, with full set of interactions by Gender and ParentalEducation, Administrative Data, Grades 6/8/10Yi: mathematics testscore Academic Redshirting Involuntary Delayxd : January 1st xd : June 1stgrades 6 8 10 6 8 10Panel A: effects for all groupsDi 0.2402*** 0.2493*** 0.1620** 0.2146*** 0.1181*** 0.0998***[0.061] [0.077] [0.071] [0.046] [0.038] [0.033]N 223,851 206,415 219,782 227,127 219,081 213,983R2 0.195 0.193 0.223 0.209 0.216 0.236Panel B: effects for subgroupsPanel B1: coefficients and standard errorsDi 0.2181*** 0.2593*** 0.1529* 0.1955*** 0.0930*** 0.0755**[0.075] [0.097] [0.090] [0.041] [0.035] [0.031]boyi ×Di 0.005 0.0044 0.0221 0.001 -0.0006 0.0407*[0.041] [0.051] [0.049] [0.029] [0.027] [0.022]lowpi ×Di 0.0333 -0.0289 0.0206 0.0227 0.0486** 0.0289[0.044] [0.054] [0.054] [0.023] [0.023] [0.020]lowpi × boyi ×Di 0.0269 -0.0054 -0.0543 0.0477 0.0204 -0.0232[0.058] [0.069] [0.067] [0.040] [0.036] [0.032]N 223,851 206,415 219,782 227,127 219,081 213,983R2 0.195 0.193 0.223 0.21 0.217 0.236Panel B2: estimated effects of Digirl, high parental educ. 0.2181*** 0.2593*** 0.1529* 0.1955*** 0.093*** 0.0755**boy, high parental educ. 0.2231*** 0.2637*** 0.175*** 0.1965*** 0.0924* 0.1162***girl, low parental educ. 0.2514*** 0.2304** 0.1735* 0.2182*** 0.1416*** 0.1044***boy, low parental educ. 0.2833*** 0.2294*** 0.1413* 0.2669*** 0.1614*** 0.1219***Panel B3: p-values of testing differences of effects of Digirl, high-low parental educ. 0.446 0.595 0.701 0.327 0.031 0.149boy, high-low parental educ. 0.095 0.431 0.454 0.029 0.018 0.843high parental educ., boy-girl 0.902 0.931 0.653 0.972 0.981 0.068low parental educ., boy-girl 0.477 0.985 0.582 0.161 0.513 0.492Note: this table shows the second-stage result of Yi on Di, boyi ×Di, lowpi ×Di, boyi × lowpi ×Di and control variables. Di isa binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: child enteredprimary school at the age of 6). Zi is a binary variable denoting quarter of birth of child i (1: child was born on/after January 1stor June 1st, 0: child was born before January 1st or June 1st). Control variables include: linear trend in month of birth and itsinteraction with a binary variable denoting quarter of birth, cohort fixed effects, family background and child care variables listedin Part 4, and missing response characteristics controls. Testscores have been standardized to have mean 0 and standard deviationof 1 in each year and grade. Estimation restricted to children who were born in the three-months window around the cutoff dates ofJanuary 1st and June 1st. Standard errors clustered at the school level. *** p<0.01, ** p<0.05, * p<0.1. Source of data: HNABC(grades 6,8,10) 2008-2014, KIR-Stat/DEM 1998-2006, LGT 1998-2005. The corresponding equation is (3.2).753.7. TablesTable 3.8: The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Results on6th/8th/10th-grade Reading testscore, with full set of interactions by Gender and Parental Education,Administrative Data, Grades 6/8/10Yi: reading testscore Academic Redshirting Involuntary Delayxd : January 1st xd : June 1stgrades 6 8 10 6 8 10Panel A: effects for all groupsDi 0.2307*** 0.1975*** 0.1736** 0.2456*** 0.2119*** 0.1649***[0.060] [0.073] [0.069] [0.042] [0.037] [0.032]N 223,879 206,433 219,802 227,153 219,125 214,018R2 0.261 0.268 0.257 0.272 0.274 0.264Panel B: effects for subgroupsPanel B1: coefficients and standard errorsDi 0.1873** 0.1742* 0.1757** 0.2218*** 0.1816*** 0.1334***[0.073] [0.092] [0.088] [0.037] [0.033] [0.030]boyi ×Di 0.0402 0.0704 -0.0016 0.0013 0.0201 0.0524**[0.038] [0.048] [0.049] [0.028] [0.026] [0.021]lowpi ×Di 0.0641 -0.0262 0.0084 0.0196 0.0261 0.0262[0.040] [0.050] [0.054] [0.022] [0.021] [0.019]lowpi × boyi ×Di -0.0254 -0.0263 -0.0217 0.0835** 0.0639* 0.0003[0.054] [0.065] [0.068] [0.040] [0.036] [0.032]N 223,879 206,433 219,802 227,153 219,125 214,018R2 0.261 0.269 0.257 0.272 0.274 0.264Panel B2: estimated effects of Digirl, high parental educ. 0.1873** 0.1742* 0.1757** 0.2218*** 0.1816*** 0.1334***boy, high parental educ. 0.2275*** 0.2446*** 0.1741*** 0.2231*** 0.2017*** 0.1858***girl, low parental educ. 0.2514*** 0.148* 0.1841** 0.2414*** 0.2077*** 0.1596***boy, low parental educ. 0.2662*** 0.1921*** 0.1608** 0.3262*** 0.2917*** 0.2123***Panel B3: p-values of testing differences of effects of Digirl, high-low parental educ. 0.107 0.600 0.877 0.383 0.221 0.164boy, high-low parental educ. 0.268 0.218 0.769 0.001 0.002 0.337high parental educ., boy-girl 0.293 0.143 0.973 0.962 0.438 0.013low parental educ., boy-girl 0.727 0.397 0.695 0.011 0.004 0.038Note: this table shows the second-stage result of Yi on Di, boyi ×Di, lowpi ×Di, boyi × lowpi ×Di and control variables. Di isa binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: child enteredprimary school at the age of 6). Zi is a binary variable denoting quarter of birth of child i (1: child was born on/after January 1stor June 1st, 0: child was born before January 1st or June 1st). Control variables include: linear trend in month of birth and itsinteraction with a binary variable denoting quarter of birth, cohort fixed effects, family background and child care variables listedin Part 4, and missing response characteristics controls. Testscores have been standardized to have mean 0 and standard deviationof 1 in each year and grade. Estimation restricted to children who were born in the three-months window around the cutoff dates ofJanuary 1st and June 1st. Standard errors clustered at the school level. *** p<0.01, ** p<0.05, * p<0.1. Source of data: HNABC(grades 6,8,10) 2008-2014, KIR-Stat/DEM 1998-2006, LGT 1998-2005. The corresponding equation is (3.2).763.7. TablesTable 3.9: The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Results onthe Probability of Repeating a Grade by 6th/10th-grade, with full set of interactions by Gender andParental Education, Administrative Data, Grades 6/8/10Yi = 1 {having repeated a grade} Academic Redshirting Involuntary Delayxd : January 1st xd : June 1stgrades 6 8 10 6 8 10Panel A: effects for all groupsDi -0.0472*** -0.0407** -0.0256 -0.0253** -0.0239*** -0.0375***[0.014] [0.017] [0.026] [0.010] [0.009] [0.011]N 223,924 206,499 219,901 227,185 219,173 214,092R2 0.089 0.084 0.074 0.099 0.088 0.077mean of dependent variable: .0478 .0463 .1088 .0451 .0469 .0954Panel B: effects for subgroupsPanel B1: coefficients and standard errorsDi -0.0361** -0.0355* -0.02 -0.0172** -0.0136* -0.0257***[0.016] [0.020] [0.031] [0.008] [0.007] [0.010]boyi ×Di -0.0005 -0.0089 -0.0103 0.0002 0.0002 -0.0033[0.007] [0.009] [0.016] [0.005] [0.005] [0.006]lowpi ×Di -0.0131 0.0087 0.0275 -0.0153*** -0.0207*** -0.0182***[0.010] [0.012] [0.019] [0.006] [0.006] [0.007]lowpi × boyi ×Di -0.0259* -0.0175 -0.0514** -0.0059 -0.0064 -0.0172[0.015] [0.018] [0.026] [0.011] [0.010] [0.012]N 223,924 206,499 219,901 227,185 219,173 214,092R2 0.087 0.084 0.074 0.099 0.088 0.077Panel B2: estimated effects of Digirl, high parental educ. -0.0361** -0.0355* -0.0200 -0.0172** -0.0136* -0.0257***mean of dependent variable: .0135 .0143 .0585 .0123 .0137 .0499boy, high parental educ. -0.0366*** -0.0444*** -0.0303 -0.0170 -0.0134 -0.0290**mean of dependent variable: .0217 .0248 .0893 .0191 .0246 .0771girl, low parental educ. -0.0492*** -0.0268 0.0075 -0.0325*** -0.0343*** -0.0439***mean of dependent variable: .0758 .0704 .1537 .0744 .0735 .139boy, low parental educ. -0.0756*** -0.0532*** -0.0542*** -0.0382** -0.0405*** -0.0644***mean of dependent variable: .1103 .1086 .1910 .1058 .1090 .1719Panel B3: p-values of testing differences of effects of Digirl, high-low parental educ. 0.207 0.468 0.152 0.006 0.000 0.009boy, high-low parental educ. 0.000 0.476 0.151 0.020 0.001 0.000high parental educ., boy-girl 0.935 0.309 0.518 0.967 0.963 0.604low parental educ., boy-girl 0.059 0.109 0.007 0.600 0.529 0.054Note: this table shows the second-stage result of Yi on Di, boyi ×Di, lowpi ×Di, boyi × lowpi ×Di and control variables. Di isa binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: child enteredprimary school at the age of 6). Zi is a binary variable denoting quarter of birth of child i (1: child was born on/after January 1stor June 1st, 0: child was born before January 1st or June 1st). Control variables include: linear trend in month of birth and itsinteraction with a binary variable denoting quarter of birth, cohort fixed effects, family background and child care variables listed inPart 4, and missing response characteristics controls. Estimation restricted to children who were born in the three-months windowaround the cutoff dates of January 1st and June 1st. Standard errors clustered at the school level. *** p<0.01, ** p<0.05, * p<0.1.Source of data: HNABC (grades 6,8,10) 2008-2014, KIR-Stat/DEM 1998-2006, LGT 1998-2005. The corresponding equation is(3.2).773.7. TablesTable 3.10: The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Resultson 10th-grade Secondary School Track Choice, with full set of interactions by Gender and ParentalEducation, Administrative Data, Grade 10Yi = 1 {being in track j} Academic Redshirting Involuntary Delay(j = low,middle, high) January 1st cutoff June 1st cutofftracks low middle high low middle highPanel A: effects for all groupsDi -0.0925*** 0.0263 0.0662* -0.0456*** -0.0357* 0.0812***[0.029] [0.040] [0.036] [0.012] [0.019] [0.017]N 219,901 219,901 219,901 214,092 214,092 214,092R2 0.223 0.039 0.199 0.235 0.044 0.203mean of dependent variable: .184 0.416 0.40 .171 .4096 .4193Panel B: effects for subgroupsPanel B1: coefficients and standard errorsDi -0.1001*** 0.0394 0.0607 -0.0218** -0.0606*** 0.0824***[0.035] [0.052] [0.049] [0.011] [0.018] [0.016]boyi ×Di 0.0173 -0.0226 0.0052 -0.0206*** 0.0185 0.0021[0.016] [0.030] [0.029] [0.007] [0.013] [0.012]lowpi ×Di 0.0279 -0.0508 0.0229 -0.0370*** 0.0358*** 0.0011[0.022] [0.032] [0.030] [0.008] [0.012] [0.011]lowpi × boyi ×Di -0.0627** 0.0930** -0.0302 -0.0007 0.0159 -0.0152[0.030] [0.039] [0.035] [0.014] [0.019] [0.016]N 219,901 219,901 219,901 214,092 214,092 214,092R2 0.223 0.039 0.199 0.234 0.043 0.203Panel B2: estimated effects of Digirl, high parental educ. -0.1001*** 0.0394 0.0607 -0.0218** -0.0606*** 0.0824*mean of dependent variable: .052 .346 .606 .047 .332 .621boy, high parental educ. -0.0828*** 0.0168 0.0659** -0.0424*** -0.0421* 0.0845*mean of dependent variable: .117 .454 .429 .106 .446 .448girl, low parental educ. -0.0722* -0.0114 0.0836* -0.0588*** -0.0248 0.0835*mean of dependent variable: .295 .460 .245 .283 .459 .258boy, low parental educ. -0.1176*** 0.059 0.0586* -0.0801*** 0.0096 0.0704*mean of dependent variable: .444 .428 .128 .426 .433 .141Panel B3: p-values of testing differences of effects of Digirl, high-low parental educ. 0.207 0.112 0.447 0.000 0.002 0.917boy, high-low parental educ. 0.098 0.077 0.700 0.002 0.001 0.247high parental educ., boy-girl 0.291 0.450 0.856 0.003 0.140 0.865low parental educ., boy-girl 0.123 0.030 0.351 0.116 0.031 0.283Note: this table shows the second-stage result of Yi on Di, boyi × Di, lowpi × Di, boyi × lowpi × Di and control variables. Diis a binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: childentered primary school at the age of 6). Zi is a binary variable denoting quarter of birth of child i (1: child was born on/afterJanuary 1st or June 1st, 0: child was born before January 1st or June 1st). Secondary school track choice is measured by a binaryvariable indicating whether the child attends the j-th track at grade 10. Track #1 is the lowest secondary school track, granting avocational, but no high school degree upon completion. Track #2 is the middle secondary school track, granting both a vocationaland a high school degree upon completion. Track #3 is the highest secondary school track, granting a high school degree uponcompletion. Control variables include: linear trend in month of birth and its interaction with a binary variable denoting quarter ofbirth, cohort fixed effects, family background and child care variables listed in Part 4, and missing response characteristics controls.Estimation restricted to children who were born in the three-months window around the cutoff dates of January 1st and June 1st.Standard errors clustered at the school level. *** p<0.01, ** p<0.05, * p<0.1. Source of data: HNABC (grade 10) 2008-2014,KIR-Stat/DEM 1998-2006, LGT 1998-2005. The corresponding equation is (3.2).783.7. TablesTable 3.11: The Effect of Academic Redshirting and Involuntary School Entry Delay - IV Results onMental Health Outcomes at grade 8, with full set of interactions by Gender and Parental Education,Survey DataYi = 1 {having mental condition j} Academic Redshirting Involuntary Delay(j = pain, anxiety, exhaustion) January 1st cutoff June 1st cutoffpain anxiety exhaustion pain anxiety exhaustionPanel A: effects for all groupsDi -0.1443* -0.2716* -0.1904 -0.0342 0.0305 -0.0986[0.082] [0.155] [0.149] [0.041] [0.070] [0.078]N 6,899 6,899 6,899 6,116 6,116 6,116R2 0.016 0.030 0.015mean of dependent variable: 0.0524 0.1827 0.1941 0.0519 0.1808 0.1932Panel B: effects for subgroupsPanel B1: coefficients and standard errorsDi -0.1469 -0.3295 -0.1779 -0.0342 0.0979 -0.0883[0.113] [0.205] [0.196] [0.043] [0.074] [0.080]boyi ×Di 0.0192 0.1055 0.0432 0.0072 -0.1216** -0.0485[0.057] [0.104] [0.102] [0.030] [0.051] [0.054]lowpi ×Di -0.0049 0.0775 -0.0483 -0.0033 -0.0685 0.0041[0.076] [0.118] [0.114] [0.045] [0.065] [0.066]lowpi × boyi ×Di -0.0167 -0.1476 -0.0264 -0.0109 0.1004 0.0595[0.083] [0.141] [0.137] [0.056] [0.088] [0.094]N 6,899 6,899 6,899 6,116 6,116 6,116R2 0.015 0.029 0.014Panel B2: estimated effects of Digirl, high parental educ. -0.1469 -0.3295 -0.1779 -0.0342 0.0979 -0.0883mean of dependent variable: 0.0642 0.1832 0.2059 0.0675 0.1980 0.2160boy, high parental educ. -0.1277 -0.224 -0.1347 -0.027 -0.0237 -0.1368mean of dependent variable: 0.0213 0.1456 0.1910 0.0848 0.2378 0.2125girl, low parental educ. -0.1518 -0.252 -0.2262 -0.0375 0.0294 -0.0842mean of dependent variable: 0.0855 0.2328 0.2108 0.02501 0.1383 0.1915boy, low parental educ. -0.1493* -0.2941** -0.2094** -0.0412 0.0082 -0.0732mean of dependent variable: 0.0394 0.1660 0.1671 0.0345 0.1501 0.1658Panel B3: p-values of testing differences of effects of Digirl, high-low parental educ. 0.948 0.513 0.672 0.941 0.293 0.951boy, high-low parental educ. 0.592 0.382 0.358 0.672 0.591 0.353high parental educ., boy-girl 0.736 0.310 0.672 0.811 0.018 0.373low parental educ., boy-girl 0.970 0.707 0.874 0.938 0.767 0.887Note: this table shows the second-stage result of Yi on Di, boyi ×Di, lowpi ×Di, boyi × lowpi ×Di and control variables. Di isa binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: child enteredprimary school at the age of 6). Zi is a binary variable denoting quarter of birth of child i (1: child was born on/after January1st or June 1st, 0: child was born before January 1st or June 1st). Control variables include: linear trend in month of birth andits interaction with a binary variable denoting quarter of birth, cohort fixed effects, family background and child care variableslisted in Part 4, and missing response characteristics controls. Estimation restricted to children who were born in the three-monthswindow around the cutoff dates of January 1st and June 1st. Standard errors clustered at the school level. *** p<0.01, ** p<0.05,* p<0.1. Source of data: HLCS, KIR-Stat/DEM 1998-2006, LGT 1998-2005. The corresponding equation is (3.2).793.7. TablesTable 3.12: First-stage Results on School Entry Delay (Starting School at 7) and the Change inRelative Rank in Class, Administrative Data, Grades 6with sorting schoolsDi RRi(%) Qi1 {Xi ≥ xd} 0.185*** 16.22*** 0.0681***(0.00711) (0.536) (0.0103)peers summeri 0.000258 0.107*** 0.00302***(0.000173) (0.0113) (0.000181)1 {Xi ≥ xd} × peers summeri -0.000143 -0.211*** -0.00199***(0.000181) (0.0146) (0.000281)N 223,422 223,422 223,422R2 0.276 0.080 0.078joint F-statistic 476.73 356.83 111.03Hansen J-statistic p-value 0.2327 0.3677Cragg-Donald Wald F-statistic: 409.19 194.49Kleibergen-Paap rk Wald F-statistic: 242.93 110.61without sorting schools A without sorting schools BDi RRi(%) Qi Di RRi(%) Qi1 {Xi ≥ xd} 0.175*** 15.97*** 0.0603*** 0.182*** 15.93*** 0.0582***(0.0122) (0.923) (0.0185) (0.00792) (0.599) (0.0115)peers summeri 0.000277 0.108*** 0.00320*** 0.000298 0.111*** 0.00313***(0.000291) (0.0192) (0.000303) (0.000195) (0.0128) (0.000204)1 {Xi ≥ xd} × peers summeri -0.000122 -0.219*** -0.00208*** -0.000196 -0.211*** -0.00188***(0.000303) (0.0245) (0.000508) (0.000203) (0.0164) (0.000315)N 78,810 78,810 78,810 188,116 188,116 188,116R2 0.268 0.078 0.091 0.268 0.076 0.082joint F-statistic 164.07 118.42 44.64 375.53 278.23 96.24Hansen J-statistic p-value 0.8328 0.5693 0.4837 0.2000Cragg-Donald Wald F-statistic: 163.65 73.01 325.04 171.30Kleibergen-Paap Wald F-statistic: 93.70 42.27 192.81 95.36Note: this table shows the first-stage results of Di and RRi/Qi, where Di is a binary variable denoting age at primary school entryof child i (1: child entered primary school at the age of 7, 0: child entered primary school at the age of 6). RRi is the continuousmeasure of the child’s relative age rank in the class, measured in percentiles, so 100 means the child is the oldest in class. Qi isthe binary measure of the child’s relative age rank in the class (1: child is in the highest quartile of the age distribution in class).1 {Xi ≥ xd} is a binary variable denoting quarter of birth of child i (1: child was born on/after 1st June 1st, 0: child was bornbefore June 1st). peers summeri denotes the fraction of summer-born children in child i’s class. Control variables include: lineartrend in month of birth and its interaction with a binary variable denoting quarter of birth, cohort fixed effects, family backgroundand child care variables listed in Part 4, and missing response characteristics controls. Estimation restricted to children who wereborn in the three-months window around the cutoff date June 1st. Standard errors clustered at the school level. *** p<0.01, **p<0.05, * p<0.1. Source of data: HNABC (grade 6) 2008-2014, KIR-Stat/DEM 1998-2006, LGT 1998-2005. The corresponding2nd-stage equation is (3.4). Non-sorting schools “A” are the ones that do not sort children systematically into classes based onprior student achievement, while non-sorting schools “B” are the ones that do not sort children systematically into classes basedon month of birth.803.7. TablesTable 3.13: OLS and IV Estimates of the Effect of Involuntary School Entry Delay (Starting Schoolat 7) and the Relative Rank in Class on Mathematics Score, Administrative Data Grade 6Panel A: including sorting schoolsOLS OLS OLS OLS OLS IV IV IV IV(1) (2) (3) (4) (5) (6) (7) (8) (9)Di -0.0462*** 0.0710*** -0.0248*** 0.2150*** 0.2700** 0.2071***[0.005] [0.011] [0.006] [0.046] [0.121] [0.047]RRi -0.0013*** -0.0022*** 0.0038*** -0.0009[0.000] [0.000] [0.001] [0.002]Qi -0.0576*** -0.0496*** 0.1312[0.005] [0.005] [0.120]N 223,364 223,364 223,364 223,364 223,364 223,364 223,364 223,364 223,364R2 0.226 0.227 0.226 0.227 0.226 0.214 0.207 0.215 0.203Panel B: without sorting schools AOLS OLS OLS OLS OLS IV IV IV IV(1) (2) (3) (4) (5) (6) (7) (8) (9)Di -0.0564*** 0.1140*** -0.0249*** 0.2730*** 0.1771 0.2725***[0.008] [0.018] [0.009] [0.078] [0.185] [0.078]RRi -0.0017*** -0.0031*** 0.0048*** 0.0017[0.000] [0.000] [0.001] [0.003]Qi -0.0802*** -0.0722*** -0.0143[0.007] [0.008] [0.180]N 78,797 78,797 78,797 78,797 78,797 78,797 78,797 78,797 78,797R2 0.240 0.241 0.241 0.242 0.241 0.222 0.208 0.218 0.223Panel C: without sorting schools BOLS OLS OLS OLS OLS IV IV IV IV(1) (2) (3) (4) (5) (6) (7) (8) (9)Di -0.0497*** 0.0647*** -0.0297*** 0.2053*** 0.3506*** 0.2036***[0.006] [0.012] [0.006] [0.052] [0.133] [0.052]RRi -0.0013*** -0.0021*** 0.0037*** -0.0025[0.000] [0.000] [0.001] [0.002]Qi -0.0561*** -0.0468*** 0.0541[0.005] [0.006] [0.126]N 188,076 188,076 188,076 188,076 188,076 188,076 188,076 188,076 188,076R2 0.229 0.230 0.229 0.230 0.229 0.218 0.211 0.220 0.214Note: this table shows the estimated OLS and IV effects of Di and RRi on standardized mathematics testscore in grade 6, whereDi is a binary variable denoting age at primary school entry of child i (1: child entered primary school at the age of 7, 0: childentered primary school at the age of 6). RRi is the continuous measure of the child’s relative age rank in the class, measured inpercentiles, so 100 means the child is the oldest in class. Qi is the binary measure of the child’s relative age rank in the class (1:child is in the highest quartile of the age distribution in class). The first-stage results corresponding to the IV strategy can be seenin Table3.12. Control variables include: linear trend in month of birth and its interaction with a binary variable denoting quarter ofbirth, cohort fixed effects, family background and child care variables listed in Part 4, and missing response characteristics controls.Estimation restricted to children who were born in the three-months window around the cutoff date June 1st. Standard errorsclustered at the school level. *** p<0.01, ** p<0.05, * p<0.1. Source of data: HNABC (grade 6) 2008-2014, KIR-Stat/DEM1998-2006, LGT 1998-2005. The corresponding 2nd-stage equation is (3.4). Non-sorting schools “A” are the ones that do not sortchildren systematically into classes based on prior student achievement, while non-sorting schools “B” are the ones that do not sortchildren systematically into classes based on month of birth.813.8. Figures3.8 FiguresFigure 3.1: Fraction of Children who Started School at the Age of 7 and Average MathematicsTestscores, by Month of Birth and child care Starting AgeNote: source of data: HNABC (grade 6) 2008-2014. See Chapter 4 Data and Measurement for details. Average testscores, shownon the right y-axis, standardized to have 0 mean and 1 standard deviation.823.8. FiguresFigure 3.2: Histogram of Number of Peers in Class, of Relative Age Rank (%) in Class, and of Fractionof Summer-born Peers in Class; Administrative Data Grade 6Note: source of data: HNABC (grade 6) 2008-2014. Non-sorting schools “A” are the ones that do not sort children systematicallyinto classes based on prior student achievement, while non-sorting schools “B” are the ones that do not sort childrensystematically into classes based on month of birth.83Chapter 4Do Health Insurers Innovate? Evidencefrom the Anatomy of PhysicianPayments4.1 IntroductionHealth insurers have a powerful ability to shape the efficiency of health care delivery. Insurers straddlethe relationship between patients and medical providers, and enter into contracts with both sides of themarket. Consumers or employers purchase insurance plans whose copayments and deductibles influencesubsequent demand for care. However, contracts with physicians and hospitals govern how providerswill be compensated for treating insured patients, and hence the caregivers’ financial incentives.The literature on optimal consumer cost-sharing is long and well-developed (Feldstein, 1973;Besley, 1988). Only recently, however, has an empirical literature begun to explore how privateinsurers set copayments in practice. Einav et al. (2016) show that private insurers provide more risk-protection for drugs subject to less moral hazard. They contrast this with public insurance plans,which offer relatively uniform coverage with regards to cost-sharing. Starc and Town (2015) showthat insurers responsible for patients’ non-pharmaceutical spending provide more generous coveragefor drugs that can keep people out of the hospital.We investigate whether insurers apply a similar logic to the payments they negotiate withproviders. To what extent do private insurance carriers adopt Medicare’s cost-based approach tophysician payment? Looking at the flip side of this question, we analyze how much private insurerscustomize their physician reimbursements relative to Medicare’s industry standard.Despite recent high-level changes in the U.S. health insurance market, the incentive structurethrough which physicians are paid remains predominantly “fee for service.”109 A physician’s incomedepends on the quantity and intensity of the treatment she provides—even when part of a largermanaged care plan or “accountable care organization” (Zuvekas and Cohen, 2016).110 A growingbody of evidence finds that these high-powered incentives help drive the level and composition ofmedical spending (McClellan, 2011).The structure of physician payments is a potentially powerful tool for insurers to encouragemore efficient care. Relatively little is known, however, regarding the extent to which private insurerscustomize their fee-for-service payments for this purpose. Clemens and Gottlieb (2017) find that109Data from the 2004-2005 Community Tracking Study (CSHSC 2006, 46) show that 52 percent of physicians earnzero revenue from capitated contracts, and 79 percent earn less than a quarter of their revenue from such contracts.110Among those same physicians referenced in footnote 109, who earn little from capitated contracts, 65 percent earnmore than one quarter of their revenue from managed care (CSHSC 2006, 47). CSHSC (1999) reports similar estimatesfrom 1996-1997.844.1. Introductionprivate payments rise and decline quite strongly with Medicare’s payments, which raises the questionof whether private insurers’ payments are meaningfully different from Medicare’s rate schedule. Inthis chapter, we shed light on this question using detailed data on physician payments.Medicare compensates physicians and outpatient providers through a detailed fee-for-servicepricing system. Physicians submit bills for each instance in which they provide any of 13,000 recognizedservices. The system assigns each service a certain number of Relative Value Units, determiningpayment. These relative values aim to measure average cost but not medical value. This procurementmodel thus has little capacity to steer treatment towards effective—let alone cost-effective—care. Ithas particular difficulty managing the use of capital-intensive diagnostic imaging services, for whichaverage cost payments exceed providers’ marginal costs—as they must in order to facilitate entry.Private reimbursement arrangements are less transparent than Medicare’s. To peer into theblack box of these business-to-business contracts, we begin by developing a cross-sectional methodfor systematically assessing whether payments are benchmarked to Medicare’s rate structure. Ourfirst approach involves a classification algorithm motivated by the bunching literature.111 Using theoutpatient claims data of Blue Cross Blue Shield of Texas (BCBS-TX), we begin by computing theratio of each private payment to the applicable Medicare payment. Among the payments to individualphysician groups, the distribution of these ratios reveals spikes that are indicative of exceptionallycommon markups. We use these exceptionally common mark-ups to identify which payments arelikely benchmarked to Medicare’s relative rate structure.We complement our cross-sectional method with an analysis of updates to Medicare’s structureof relative payments. If the Medicare links we identify are accurate, then payments for Medicare-benchmarked services should update mechanically when Medicare’s schedule of “relative value units”is revised. We are able to assess this mechanical pass through at a high frequency by applyinginstitutional knowledge of the exact dates on which BCBS-TX implements Medicare’s updates to therelative value scale.112 We find that the payments associated with 55 percent of in-network, outpatientspending (and around three quarters of services) are linked to Medicare. These estimates are quitesimilar to the estimates we obtain using our cross-sectional bunching approach.We continue our analysis with an effort to understand the circumstances under which paymentsare more and less likely to be benchmarked to Medicare’s relative rate structure. Deviations frombenchmarking exhibit several distinctive patterns. Looking across physician groups, payments torelatively large firms are less tightly benchmarked to Medicare than payments to small firms. Paymentsfor only ten percent of services provided by the smallest firms, representing 20 percent of their spending,deviate from Medicare’s relative values. The same is true of 40 percent of services—and two-thirds ofspending—from firms with total billing exceeding $1 million per year.Looking across service categories, payments are more likely to deviate from Medicare’s rela-tive values for capital-intensive services, like diagnostic imaging, than for labor-intensive services likestandard office visits. Payments for roughly 45 percent of imaging services, but only 15 percent of111Our setting differs from standard bunching applications in that the bunching we observe is not driven by kinks ornotches in budget sets (Kleven, 2016). Instead, it results from clustering around reference points.112The relatively high frequency at which we can conduct our analysis allows us to limit if not eliminate the rele-vance of potential confounders including active contract renegotiations and payment changes connected to substantivetechnological advances.854.2. Medical Pricing Institutionsevaluation and management services, deviate from Medicare’s menu. Within imaging, Medicare dis-tinguishes between two types of services: a capital-intensive component for taking the image and alabor-intensive component for interpreting the image. Medicare explicitly amortizes the fixed cost ofthe imaging equipment into the former. We find that private insurers’ payments for interpretation arefar less likely to deviate from Medicare rates than are its payments for taking the image itself. Thedirections of these deviations reveal that the adjustments narrow likely gaps between marginal costsand Medicare’s average-cost payments. We find that payments for labor-intensive services tend to beadjusted up while payments for capital-intensive services are adjusted down.We continue in section 4.2 by presenting institutional background on price setting in U.S. physi-cian markets and potential explanations for the phenomenon we examine. Section 4.3 introduces ourclaims data. In section 4.4 we present the empirical approaches that estimate the share of paymentsbenchmarked to Medicare using updates to Medicare’s relative prices. Our main empirical results arein section 4.5. In section 4.6 we show that the deviations from these Medicare-linked rates narrowgaps between prices and marginal costs. Section 4.7 concludes.4.2 Medical Pricing InstitutionsPublic and private payments for health care services are set through very different mechanisms. Medi-care reimbursements are set based on administrative estimates of the resource costs of providing care,which we describe in section 4.2.1. For patients with private health insurance, providers’ reimburse-ments are determined through negotiations between the insurers and providers, which we describe insection 4.2.2. Section 4.2.3 offers economic rationales for a potential link between reimbursement ratesacross these two segments of the market.4.2.1 Medicare Price Determination113In 1992, Congress established a system of centrally administered prices to reimburse physicians andother outpatient providers. This Resource-Based Relative Value Scale (RBRVS) is a national feeschedule that assigns a fixed number of Relative Value Units (RVUs) to each of 13,000 distinct healthcare services. Legislation specifies that the RVUs for service j are supposed to measure the resourcesrequired to provide that service. Since the costs of intermediate inputs differ across the country,RBRVS incorporates local price adjustments, called the Geographic Adjustment Factor (GAF), tocompensate providers for these differences. The payment for service j to a provider in geographicregion i is approximately:Reimbursement ratei,j,t = Conversion Factort ×Geographic Adjustment Factori,t× Relative Value Unitsj,t. (4.1)113This section draws from Clemens and Gottlieb (2014).864.2. Medical Pricing InstitutionsThe “reimbursement rate,” a term we use interchangeably with “price,” is the amount Medicare paysfor this service. The Conversion Factor (CF) is a national scaling factor, usually updated annually.The variation in payments is mainly driven by the number of RVUs assigned to a service. Thisassignment is constant across areas while varying across services. Medicare regularly updates the RVUsassigned to each service, primarily based on input from the American Medical Association, using theformal federal rule-making process. These updates are intended to account for technological andregulatory changes that alter a service’s resource intensity. We exploit these changes in the empiricalstrategy we introduce in section 4.4.4.2.2 Private Sector Price SettingU.S. private sector health care prices are set through negotiations between providers and private insur-ers.114 The details of these negotiations are not transparent, and our limited knowledge about privatesector prices comes from claims data that reveal the reimbursements paid once care is provided.115A common feature of physician contracts, central to both our theoretical and empirical analyses, is aform of benchmarking to Medicare.Practitioners emphasize that Medicare’s administrative pricing menu features prominently inprivate insurers’ contracts. Newsletters that insurers distribute to participating providers frequentlydraw explicit links between Medicare’s maximum allowable charges and the insurer’s fee schedule. Forexample, reimbursement rates might be linked to Medicare by default unless the contract specifiesotherwise. But the relative value scale does not determine an absolute price level. As in Medicare,computing private reimbursements requires multiplying RVUs by a dollar scaling factor. Providers andinsurers can simplify contracting by negotiating over these constant markups, but sometimes haggleover reimbursements for specific services or bundles (Gesme and Wiseman, 2010; Mertz, 2004).Our empirical work will examine specifically when and why this benchmarking occurs in practice.We measure how often exceptions apply, and whether they systematically arise in cases when we wouldexpect the cost of Medicare’s inefficiencies to be particularly large.4.2.3 Potential RationalesWhy might contracts between physicians and private insurers use Medicare’s relative rate structure asa benchmark? We consider several, broadly complementary explanations. A first explanation is thatbenchmarking against Medicare’s relative rate structure enables insurers and physicians to greatlysimplifying their contracts. A uniformly benchmarked contract requires negotiating over a singleparameter, namely the mark-up; alternative contract structures could require negotiating paymentsfor hundreds if not thousands of distinct billing codes. Medicare’s payment model may serve this114In rare exceptions, such as in Maryland, the state government determines all hospital payment rates.115A growing literature finds that physician concentration significantly affects this bargaining process. Payments arehigher in markets where physicians are more concentrated (Dunn and Shapiro, 2014; Baker et al., 2014; Kleiner et al.,2015; Clemens and Gottlieb, 2017).874.3. Medical Pricing Datapurpose because it is an “industry standard” with which all parties are familiar. In Appendix C.1, wepresent a formal model of this idea, which generates several empirical predictions that are consistentwith what we find in our empirical analysis.A second, strongly complementary explanation speaks to the Medicare menu’s information con-tent. By design, Medicare’s payment model contains substantial information regarding the relativecosts of providing physicians’ services. If average cost reimbursement is, more or less, what insur-ers desire to implement, Medicare’s payment model provides a natural “information standard” forprivate insurers to adopt. That is, Medicare’s relative cost estimates can be interpreted as a publicgood. Although they may fail to reflect variations in local cost structures, the expense to insurers ofindependently calculating these costs may be quite high.A third possibility is that providing care for Medicare beneficiaries represents physicians’ primaryoutside option when they negotiate with private insurers (Clemens and Gottlieb, 2017). Because Medi-care accounts for a large share of the market, its payments inevitably loom large in insurer-physiciannegotiations. Benchmarking private payments to Medicare’s payments may be a straightforward wayfor contracts to acknowledge and mechanically adjust in response to that option.A fourth possibility emphasizes insurance regulations. Regulations require insurers to ensureaccess to “medically necessary” services. Benchmarking payments to Medicare’s rate structure may bethe easiest approach to satisfying this requirement. Private payments are almost universally “marked-up” rather than “marked-down” relative to Medicare’s rates. Consequently, this payment structureensures that private insurers are paying sufficiently high rates to generate at least as much care accessas Medicare beneficiaries enjoy.4.3 Medical Pricing DataOur main analysis considers firm-to-firm pricing in the context of medical claims processed by one largeinsurer, Blue Cross Blue Shield of Texas (BCBS). Our main database covers the universe of BCBS’spayments for outpatient care in 2010; we expand our sample to cover 2008–2011 for one analysis.116 Foreach claim, the database provides information on the service provided, location, physician, physiciangroup, and BCBS’s payment to that group. We restrict this universe along several dimensions. Thefull 2010 dataset contains 57,613,494 claim lines and $4.29 billion in spending, which we restrict alongseveral dimensions. We clean the data as described in Appendix C.2.1, which initially leaves us with44,055,829 service lines and $2.63 billion of spending. This initial cut eliminates payments made toout-of-network physicians, who have not reached a negotiated agreement with BCBS on reimbursementrates. We will subsequently examine this segment of the data separately.In order for private insurers to benchmark prices to Medicare, at a minimum they would need touse Medicare’s billing codes. We thus merge the remaining claims with Medicare billing codes, whichprovides an upper bound on the potential benchmarking. This merge only loses notable portions of one116Our empirical results for other years are very similar to those for 2010; we focus on this one year for brevity andshow other years’ results in the appendix.884.4. Empirical Approachbroad spending category, namely laboratory tests, for which both Medicare and BCBS frequently basepayments on non-standard codes. We retain over 97 percent of claims for evaluation and management,diagnostic imaging, and surgical services. The final analysis sample includes 3,681 unique HCPCScodes, which comprise 23,933,577 service lines and $2.05 billion of spending.117The claims data further allow us to describe the provider groups serving BCBS beneficiaries,at least in terms of the care they provide to that sample. To enable our subsequent investigation ofheterogeneity in Medicare benchmarking, we measure the total value of the care each group providesto BCBS patients in a given year. Our final dataset includes care provided by over 80,000 physiciangroups, identified by their billing identification number.118 15,000 of these groups bill more than$10,000 annually, and account for 97 percent of BCBS spending. Table 4.1 presents summary statisticson the physician groups in our final sample.4.4 Empirical ApproachOur first empirical goal is to estimate how often private reimbursement rates rely directly on Medi-care’s. We begin by presenting visually striking evidence of bunching in the ratios of physician groups’payments relative to Medicare’s payments. We formalize this visual evidence and then present anempirical approach for exploiting policy-driven changes to Medicare’s Relative Value Units (RVUs).Finally, we discuss the complementarity of these approaches.4.4.1 Measuring Medicare Benchmarking with BunchingTo measure the relationship between private and Medicare pricing in the cross-section, we exploit astraightforward insight. For each claim, we divide the private payment by the corresponding Medicareprice, yielding the private markup applying to that payment. When the markups for many paymentsto a given physician group exhibit bunching at a common level, we infer that these payments reflecta contractual link to Medicare’s relative rates.We begin by simply dividing BCBS’s payment to group g for service j at time t (Pg,j,t) byMedicare’s allocation of RVUs. This defines an “Implied Conversion Factor” (ICF) as:ICFg,j,t =Pg,j,tRV Uj,t. (4.2)An ICF is defined for every claim. But simply computing an ICF does not tell us whether anygiven claim was actually priced according to Medicare’s RVUs. To gauge the relevance of such pricingschemes, we ask how often a particular group’s payments reflect the same ICF. Figure 4.1 providesconcrete illustrations. Panel A shows payment rates for the services provided regularly by a single117Appendix Table C.1 shows the exact data loss resulting from each step of cleaning. The key conclusion from thistable is that, once we restrict ourselves to the relevant universe of data, additional losses from merging in Medicare codesand eliminating infrequent codes are not substantial.118This is analogous to the commonly used tax ID number in Medicare claims data, but our version is anonymized.894.4. Empirical Approachphysician group in the 2010 BCBS claims data.119 Each circle on the graph is a unique paymentamount for a unique service code. That is, if the group received two unique payment values for astandard office visit (HCPCS code 99213), say $45 and $51, those two amounts would show up asseparate circles. The Blue Cross payment amount is on the y-axis and the Medicare payment for theservice is on the x-axis, both shown on log scales. Taking logs of equation (4.2) reveals that Medicare-linked pricing implies a 1 for 1 relationship between the log Medicare payment and the log privatereimbursement.120 So we draw a solid line in Panel A with a slope of 1, coinciding with the group’smost common ICF.121Panel A shows the data from a mid-sized group (billing BCBS between $200,000 and $1 millionin 2010) for which a single ICF dominates the payment picture. The most natural interpretation ofthis graph is that those services on the solid line are priced according to Medicare’s fee schedule witha common ICF, while the remaining services are priced separately. Several of the circles below thesolid line plausibly involve instances of a less common, but still contractually specified, ICF for thisgroup. A conservative estimate would view these and other circles off the solid line as deviations fromMedicare-linked pricing.Panel B shows the full distribution of this group’s markups over Medicare rates. To calculatethese markups, we simply divide the y-value of each dot in Panel A by its x-value.122 Panel B showsa clear spike in the distribution of these ratios at around 1.4, indicating that most claims were paidbased on a 40 percent markup over Medicare. This spike includes all of the services along the red linein Panel A. Other scattered values reflect the deviations away from that line.Panels C through F show graphs constructed analogously, but for two larger groups that providemore unique services at more distinct prices. The group shown in Panels C and D exhibits two clearspikes in the ICF frequency distribution, with a smattering of other values. The one shown in PanelsE and F has a range of ICFs, none of which visually dominates the payment picture. These plotsindicate a remarkably complicated contract with BCBS.Estimating the pervasiveness of “common” ICFs requires a definition of “common.” The esti-mates presented in section 4.6 thus explore sensitivity to the threshold we impose for the regularitywith which an ICF must appear in a group’s payments. This further requires an assumption on ourrounding of the ratio of private to public payments. We explore sensitivity to the choice of roundingas well.After defining and computing the ICFs, we run descriptive regressions to understand how they119The figures exclude any code-by-payment combination that appears ten times or fewer in the data for the relevantphysician group. The more systematic analysis presented below has no such exclusion. Throughout this analysis, werestrict to data from the period before BCBS implemented the RVU updates (January 1—June 30, 2010). This way ourcalculations are not confounded by RVU changes.120Rearranging (4.2) and then taking logs yields:ln(Pg,j,t) = ln(ICFg,j,t) + ln(RV Uj,t), (4.3)which has an implied coefficient of 1 on ln(RV Uj,t).121As equation (4.3) shows, the y-intercept (in logs) is the log of the ICF.122This distribution has the same sample restrictions as in Panel A; see footnote 119 for details. Note that eachobservation from Panel A has equal weight in the distribution in Panel B, so the distributions in Panels B, D, and Fare not weighted to reflect the frequency with which we observe each markup. A weighted version would increase therelative heights of the highest bars, since the common ICFs are, by definition, more common than other markups.904.4. Empirical Approachvary. We estimate models of the formln(ICFg,j) = Xg,jγ + eg,j (4.4)where Xg,j contains characteristics of the physician group or local market, such as firm size or concen-tration. We measure firm size as log total billings to the insurer. We compute firm market share withina local health care market (hospital service area) and specific service, and we measure the degree ofconcentration across all physician practices within that market (using the HHI at the service-by-arealevel).4.4.2 Framework for Analyzing Benchmarking Using RVU UpdatesWe next develop an estimation framework based on changes in Medicare’s relative value scale. Acommittee of the American Medical Association, composed of representatives of various physicianspecialties, recommends RVU updates to Medicare (Government Accountability Office, 2015). Theseupdates come in two main forms: reassessments of the resources required to provide a single service,and revisions to part of the underlying methodology. For example, a revision to the method forcomputing physician effort can change the weights assigned to many service codes. At least one broadupdate of this sort appears to occur annually over the period we study, as do hundreds of largerservice-specific reassessments.The vast majority of updates to Medicare payments go into effect on January 1 each year. Buteven when relying on these rates, private insurers have a choice about whether and when to shift fromone year’s relative value scale to the next year’s (Borges, 2003). BCBS informs its providers of thedate on which such updates go into effect through its provider newsletter, the Blue Review. Duringour sample, the newsletter announced updates taking place on July 1, 2008, on August 15, 2009, onJuly 1, 2010, and on September 1, 2011 (BCBS 2008; 2009; 2010; 2011). In all four years, the standarddeviations of RVU changes are around 7 percent, generating substantial pricing variation for us toexploit.Figure 4.2 Panel A shows one example of how these changes impact physician payments in ourBCBS data. This graph shows average log payments by day for the most commonly billed servicecode, a standard office visit with an established patient (code 99213). The average log payment jumpsdistinctively on July 1, 2010, the day on which BCBS implemented the 2010 relative values. Medicare’slog RVUs for this service rose by 0.068 between the 2009 and 2010 fee schedules. BCBS’s average logpayment rose by just under 0.05. Appendix Figure C.1 shows further examples. To study examplesof this sort systematically, we next develop a method for using high frequency RVU changes to inferthe share of private reimbursements linked to Medicare.Our empirical method exploits the institutional details we documented in section 4.2 about howMedicare benchmarking works in practice. When a payment Pg,j,t is linked to Medicare’s relative914.4. Empirical Approachvalues, we can writePg,j,t = ϕg,t ·RV Uj,tor, in logs, ln(Pg,j,t) = ln(ϕg,t) + 1 · ln(RV Uj,t), (4.5)where ϕg,t is the Implied Conversion Factor (ICF) from section 4.1. Equation (4.5) describes a linearrelationship between log private insurance payments and log RVUs for a service. It predicts thatempirical estimates of this relationship would find a coefficient of 1 on log RVUs. If the markup ϕ isa constant, it will be reflected in the constant term. If it varies across physician groups, then groupfixed effects capture ln(ϕg). If it changes over groups and across time, then group-by-time fixed effectsserve the same role.The institutional details, plus the occasional deviations observed in Figure 4.1, suggest thatpayments may alternatively be negotiated without reference to RVUs. In this case, we denote thepayment byPg,j,t = ρg,j,t =⇒ ln(Pg,j,t) = ln(ρg,j,t), (4.6)with no role for ϕg,t or RV Uj,t.When RVUs change, equations (4.5) and (4.6) show how private reimbursements will adjust.Consider two time periods, across which Medicare shifts payments by ∆ ln(RV Uj,t). Let εg,j,t =∆ ln(ρg,j,t) be any change in the alternative non-benchmarked payment. We can now write both typesof prices in terms of service fixed effects and changes as follows. For Medicare-linked services, we have:ln(Pg,j,t) = φj1j + φg1g + φg,j1g · 1j + ∆ ln(RV Uj,t) · 1{t=post}. (4.7)For services not linked to Medicare, we have:ln(Pg,j,t) = φj1j + φg1g + φg,j1g · 1j + εg,j,t · 1{t=post}. (4.8)In these equations, 1{t=post} is an indicator for the second time period. In both types of price setting,the fixed effects capture baseline payments to group g for service j in the first period, while theinteraction with 1{t=post} captures the change between the two periods.The linearity of equations (4.7) and (4.8) implies a simple way to measure how many services arelinked to Medicare. Equation (4.7) says that a linear regression of log private payments on changesin log Medicare RVUs, for services with prices linked to Medicare, should yield a coefficient of 1 aftercontrolling for appropriate fixed effects. Equation (4.8) shows that the same regression should yielda coefficient of 0 for services not priced based on Medicare, as long as the non-Medicare paymentchanges (εg,j,t) are uncorrelated with RVU updates.More generally, suppose that both types of payments exist, and specifically that a constant shareσ of payments are benchmarked to Medicare prices, while 1 − σ are set independently. (We willsubsequently allow for heterogeneity.) The average of log reimbursements is then given by a weighted924.4. Empirical Approachaverage of equations (4.7) and (4.8), and the coefficient on log RVU updates can reveal the linkedshare σ:ln(Pg,j,t) = φj1j + φg1g + φg,j1g · 1j + σ ·∆ ln(RV Uj,t) · 1{t=post} + ηg,j,t, (4.9)where we define ηg,j,t = (1 − σ) · εg,j,t · 1{t=post}. Equation (4.9) suggests that, in a linear regressionwith appropriate fixed effects, we can infer the Medicare-linked share from the coefficient on log RVUchanges. This motivates our baseline specification for estimating σ. We use data at the level ofindividual claims, indexed by c, to estimate:ln(Pc,g,j,t) = β∆ ln(RV Uj) · 1{t=post} + φt1{t=post} + φj1j + φg1g + φg,j1g · 1j + ηc,g,j,t. (4.10)This is just a claims-level version of equation (4.9) where βˆ estimates the share of payments based onMedicare rates. It adds a time period fixed effect 1{t=post} in case private payments shift broadly acrossthe two time periods. This parametric difference-in-differences specification also incorporates full setsof group (1g), service (1j), and group-by-service (1g ·1j) effects to account for all time-invariant group-and service-specific terms. Thus our estimate of βˆ is identified only using changes in RVUs acrossthe two time periods. The time effect further limits the identifying variation exclusively to relativechanges in RVUs across services.To obtain the share of spending linked to Medicare, we will primarily estimate equation (4.10)weighted by the average pre-update price of each service.123 For the estimate of βˆ in specification(4.10) to equal the true Medicare-linked share σ, we must make several assumptions about activerenegotiations of reimbursement rates. Since group and group-by-service fixed effects are intendedto capture the level of markup ϕ, any changes in this markup over time may show up in the errorterm. In Appendix C.3.2, we discuss the situations in which this challenges our ability to identifythe parameter σ. Thanks to the context and data, which allow us to estimate responses at a highfrequency, our assumptions are quite plausible.To describe the timing with which BCBS incorporates Medicare updates into its reimbursements,we also present dynamic estimates from the following parametric event study:ln(Pc,g,j,t) =∑t6=0βt∆ ln(RV Uj) · 1t + φt1t + φj1j + φg1g + φg,j1g · 1j + ηc,g,j,t. (4.11)When estimating equation (4.11), we normalize t such that t = 1 is the month in which BCBShas announced that it will implement Medicare’s fee updates. We thus expect to see βˆt = 0 forperiods preceding the updates’ incorporation, t < 0, while the βˆt for t > 0 are our estimates of howoften Medicare updates are incorporated into private payments. A flat profile of the post-updateβˆt estimates would suggest that all price changes correlated with Medicare changes are implementedinstantaneously. An upward trend in these coefficients might suggest that our baseline estimates areaffected by ongoing renegotiations between BCBS and firms whose bargaining positions are affected123Since the unweighted regression treats each claim equally, it effectively weights service codes by the frequency withwhich they are used.934.5. Baseline Benchmarking Resultsby Medicare updates. We discuss this concern in detail in Appendix C.3.4.4.3 Relating Our ApproachesThe analyses we implement have complementary strengths and weaknesses. A shortcoming of thecross-sectional analysis of “bunching” is that it requires us to observe a constant markup across manyservices. So it may fail to detect genuine Medicare linkages involving markups that are common acrossrelatively small numbers of services. But these linkages would be detected by the analysis of Medicarepayment updates. Regardless of how common the markup is, the associated payments will changewhen the underlying relative values change.A shortcoming of the latter approach, on the other hand, is that it could be biased if Medicareupdates occur contemporaneously with changes driven by new contract negotiations. Our robustnessanalysis and our investigation of the precise timing of Medicare-linked changes provide evidence thatnew contract negotiations are unlikely to underlie our results. Nonetheless, these analyses cannot ruleout active contract renegotiations altogether.The “bunching” and “changes” approaches are thus complementary in that the bunching ap-proach is prone to underestimating the extent of benchmarking while the changes approach is proneto overestimating the extent of benchmarking. We connect these approaches, and demonstrate consis-tency across the two analyses, by showing that the service-firm pairs we identify as benchmarked arestrongly correlated across our approaches. We do this by dividing the data into subsamples accordingto the benchmarking results we obtain in our bunching analysis. We then estimate equation (4.10)separately on these subsamples.4.5 Baseline Benchmarking Results4.5.1 Bunching EstimatesTable 4.2 presents estimates of the share of services linked to Medicare in each year according to themethod from section 4.4.1. The estimates explore our approach’s sensitivity to two key assumptions.First, we round the value of each ICFc,g,j,t to the nearest 20 cents, 10 cents, or 2 cents to exploresensitivity to rounding error. Second, we define “common ICFs” as those that rationalize a sufficientlylarge share of the insurer’s payments to a single physician group. In Figure 4.1, for example, the redline in Panel A should undoubtedly qualify as common. Other values may also qualify depending onthe strictness of the threshold we apply. We consider thresholds ranging from 5 to 20 percent of agroup’s claims, then calculate the share of the insurer’s payments associated with any of a group’scommon ICFs.The Medicare-benchmarked shares range from 65 to 90 percent depending on the rounding andfrequency thresholds; they decrease substantially with the stringency of the definition for a common944.5. Baseline Benchmarking ResultsICF, but are not sensitive to the choice of rounding threshold. Appendix Table C.2 shows thatalternative measures generate qualitatively similar results.124Going forward, we require as our baseline that common ICFs account for 10 percent of a group’sclaims, when rounded to the nearest $0.02. The motivation for adopting a stringent rounding thresholdis to be conservative in the extent to which our method detects false positives. At the same time, the10 percent threshold ensures that multiple ICFs can be readily detected. Using this definition, overhalf of firms have just one common ICF. Fewer than 5 percent have more than 2 common ICFs.Having identified these ICFs, we use them to describe how the generosity of BCBS reimburse-ments relates to firm and market characteristics. Table 4.3 presents estimates of equation (4.4), whichregresses the ICF values themselves (in logs) against physician group and market characteristics.125Columns 1 through 3 reveal that each of firm size, market share, and market concentration is, byitself, positively correlated with the generosity of the firms’ payments. Consistent with other work onhealth care pricing (Dunn and Shapiro, 2014; Baker et al., 2014; Kleiner et al., 2015; Cooper et al.,2015; Clemens and Gottlieb, 2017), payments to large firms in markets with high levels of concen-tration are more generous than payments to small firms in markets with low levels of concentration.Columns 4 and 5 include all three characteristics together, with column 5 also adding fixed effects forservice codes and geographic areas. Firm size remains a strong predictor of the average generosity ofa firm’s payments, as does overall market concentration. Market share switches signs, likely becauseof collinearity with log firm size.4.5.2 Results from Medicare Fee Change AnalysisWe next move on from estimating ICFs to exploiting Medicare’s RVU changes. Using the methodfrom section 4.4.2, Panel B of Figure 4.2 presents event study estimates of the link between Medicare’srelative value scale and BCBS reimbursements. It shows estimates of equation (4.11) for the Medicarepayment changes implemented in 2010. BCBS’s provider newsletters say that updates to Medicare’spayments took effect that year on July 1, 2010.The estimates reveal substantial—but not universal—links between Medicare updates and thepayments providers receive from BCBS. The coefficients imply that σˆ = 55 percent of spending islinked to Medicare’s relative values. The dramatic dynamics in the figure suggest that this reflectsa contractual link between Medicare’s relative values and BCBS payments. As in the raw data forstandard office visits presented in Panel A, we see that payment changes occur when we expect.Importantly, the estimates of σ are both economically and statistically larger than 0 and smaller than1, implying that payments for a substantial share of services deviate from strict benchmarking toMedicare’s relative values. Sections 4.5.3 and 4.6.1 will investigate these deviations in detail.124If we only count the single most common ICF for each group, the estimates are very similar to those reported inTable 4.2 when imposing a 20 percent threshold. Unfortunately, theory does not provide guidance as to which thresholdis most appropriate, and the choice of threshold substantially affects our estimate of the linked share. Our changes-basedestimation strategy is not sensitive to choices of this sort.125Appendix Table C.3 also shows how these same characteristics relate to the frequency of deviations from Medicarebenchmarking, and the value of the deviations when they occur.954.5. Baseline Benchmarking ResultsColumn 1 of Table 4.4 presents our baseline estimates of equation (4.10), which summarizesthis result in a single coefficient. The estimate in column 1 of Panel A confirms that roughly 55percent of BCBS’s spending is linked to Medicare’s relative values. In Panel B, we weight servicecodes equally rather than according to baseline payments. The unweighted estimate implies that,on average, roughly three quarters of BCBS’s physician claims are paid based on Medicare’s relativevalue scale. The difference in coefficients between Panels A and B implies that payments for relativelyexpensive services are less likely to be benchmarked to Medicare than are payments for low-costservices.1264.5.3 Robustness and Cross-Validation of the Two ApproachesTable 4.4 probes the robustness of our changes-based estimates to a variety of specification checks.Column 1 reports our baseline specification, which includes a full set of group-by-HCPCS code fixedeffects and controls for time effects with a simple post-update indicator. Column 2 drops the group-by-HCPCS code fixed effects in favor of a more parsimonious set of HCPCS code fixed effects. Column3 augments the baseline specification by controlling for a cubic trend in the day of the year, which weinteract with the size of each service’s Medicare fee change. Column 4 allows the cubic trend in day todiffer between the periods preceding and following the fee schedule update, as in a standard regressiondiscontinuity design. The table shows that these specification changes have essentially no effect on theestimated coefficient βˆ. This reinforces the interpretation that, among services billed using standardHCPCS codes, roughly 55 percent of BCBS’s spending is linked to Medicare’s relative value scale.The estimates presented in Figure 4.2 and Table 4.4 may differ from the true Medicare bench-marking parameter σ if changes in other terms of providers’ contracts covary with the Medicarechanges. Indeed, payment changes that significantly alter physician groups’ average Medicare pay-ment can move private payments in subsequent years, due in part to the resulting changes to theirbargaining positions (Clemens and Gottlieb, 2017). In Appendix C.3.2, we thus draw on institutionaldetail and theoretically motivated specification checks to explore how much our estimates might devi-ate from the true share of payments benchmarked to Medicare’s relative values. We find no evidencethat renegotiations confound the relationship between BCBS’s and Medicare’s payments over the timehorizons we analyze. Appendix C.3.2 thus bolsters the case for interpreting our estimates of βˆ asmeasuring the fraction of services tied directly to Medicare.To validate that our classification algorithm correctly captures services whose prices are actuallylinked to Medicare rates, we estimate our baseline changes-based regression separately for the servicespriced by common ICFs and those that are not. We classify each group-service pair (g, j) as Medicare-linked if all of group g’s claims for service j in the pre-update period appear to be linked to Medicarerates, and as non-linked otherwise. We estimate equation (4.10) separately for these two samples.Panel D of Figure 4.2 shows two binned scatterplots analogous to Panel C, relating log BCBSprice changes to log Medicare fee changes separately for the two samples. The linked sample, shownwith red triangles, has a slope of 0.9, indicating that BCBS prices for 90 percent of linked services126Appendix Tables C.5 and C.6 replicate Panels A and B, respectively, in other years’ data.964.6. How Do Private Payments Deviate from Medicare?update in response to Medicare changes. The non-linked sample, shown with blue circles, has a muchsmaller slope of 0.3. Although smaller, this slope is significantly positive, indicating that around one-third of the services not priced according to common ICFs nevertheless react to Medicare changes.1274.6 How Do Private Payments Deviate from Medicare?In order to illuminate the economic determinants of benchmarking, we next consider variation in thestrength of the link between private payments and Medicare’s relative values. We consider the twodimensions that enter into reimbursement contracts: differences across physician groups and types ofcare.4.6.1 Deviations from Benchmarking across Physician GroupsOne key difference across groups, motivated by theory, is the scale of their business with BCBS. Wemeasure the quantity of care each group provides in our data. To estimate heterogeneity along thisdimension, we simply add interactions with practice size to our baseline changes regression, equation(4.10).Table 4.5 shows the results. The first column reports the baseline, equally weighted regressionfrom Table 4.4. The second column introduces interactions between the Medicare updates and in-dicators for the size of the physician group providing the care. We define mid-sized firms as thosewith $200,000 to $1,000,000 in annual billing with BCBS, and large firms as those with more than$1,000,000 in annual billing. Each of these categories comprises one-quarter of the sample, with theremaining half of claims coming from smaller firms. The estimates imply that nearly 90 percent ofservices provided by firms billing less than $200,000 are benchmarked to Medicare, while roughly 60percent of services provided by firms billing more than $1,000,000 are benchmarked. Columns 3 and4 present similar, but dollar-weighted, estimates. The results in column 4 suggest that 77 percent ofpayments to firms billing less than $200,000 are benchmarked to Medicare, while one-third of paymentsto firms billing more than $1,000,000 are benchmarked.128Figure 4.4 shows that we find a similar relationship between the share linked to Medicare andphysician group size using our cross-sectional bunching approach. The series in the figure reveal thatthis is true in both the equally weighted and payment weighted series. It is also true whether or notwe adjust for the underlying composition of each group’s services, to which we now turn.129127One way to interpret this one-third of services is that they still use Medicare’s RVUs as a unit of measurement, butthen use independent conversion factors. In this sense the RVUs are analogous to a currency; even though these one-thirdof prices are negotiated separately, they denominated in the “currency” of RVUs. But this appears not to be the casefor most of the non-linked services.128Appendix Table C.9 shows similar results in data from other years.129To check whether the relationship between benchmarking and group size is affected by the composition of large andsmall groups’ services, we run a regression that allows group size and service composition to enter simultaneously. Wedefine fixed effects 1b(j) at the level of the same 1-digit “Betos” classification we used in section 4.6. To measure therelationship between group size and the Medicare-linked share, we categorize physician groups g according to vigintilesof their aggregate private billing in a year, using 1s(g) to denote vigintile fixed effects. We then estimate the following974.6. How Do Private Payments Deviate from Medicare?4.6.2 Which Services Deviate from the Medicare Benchmark?The value of improving on Medicare’s menu depends on the severity of that menu’s inefficiencies. Be-cause it is difficult to systematically quantify Medicare’s inefficiencies across a large range of individualservices, we focus on one of the Medicare fee schedule’s most salient problems. Medicare rates are com-puted based on average-cost reimbursement, so its reimbursements will hew closer to marginal costs forlabor-intensive services than for capital-intensive services. Standard optimal payment models suggestthat the latter would be more appropriately reimbursed through combinations of up-front financingof fixed costs and incremental reimbursements closer to marginal cost (Ellis and McGuire, 1986). Wecan proxy for services’ capital and labor intensity by comparing the frequency of benchmarking acrosscategories of care produced with different inputs, such as labor-intensive Evaluation & Managementservices versus capital-intensive Imaging.130Table 4.6 estimates equation (4.10)—the relationship between private prices and changes inMedicare’s relative values—separately across broad categories of services. The estimates imply thatnearly 30 percent more of the payments for Evaluation & Management services are linked directly toMedicare’s relative values than for Imaging services.131Second, we divide Imaging codes into subcomponents with high capital and high labor content.Providers often bill separately for taking an image (the capital-intensive part, since it requires animaging machine) and interpreting it (the labor-intensive part). When the same group supplies bothcomponents, it submits the bill as a “Global” service. The results in columns 5 through 7 show thatpayments for the labor-intensive Professional Component are more tightly linked to Medicare’s relativevalues than are the payments for the capital-intensive Technical Component. These patterns supportthe hypothesis that physicians and insurers are more likely to contract away from Medicare’s menufor capital-intensive services than for labor-intensive ones.Table 4.7 shows that we find a similar relationship between the share linked to Medicare andservice categories using our cross-sectional approach. Using our cross-sectional approach, we find thatbenchmarking is 30–50 percent less frequent for Imaging, Procedures, and Tests than for Evaluation &Management services. The results across columns reveal that we find similarly substantial differentialswhether or not we control for firm size and whether services are weighted according to the spendingthey represent.These results suggest that private contracts deviate when Medicare’s rates are most problematicfrom an efficiency perspective. One way to interpret this is in light of negotiation and adjustmentcosts. Private bargaining can overcome these frictions more easily when Medicare’s rates are fartherregression at the group-code level:Medicare-Linked Sharej,g = νb1b(j) + ζs1s(g) + υj,g. (4.12)The orange diamonds in Figure 4.4 show the estimates of ζˆs. These illustrate the relationship between Medicare linksand group size, adjusted for service composition. The composition-adjusted relationship remains strongly negative. Theremaining measures in Figure 4.4 show similar results in terms of dollars spent, rather than number of services.130We split all of the medical services in our data into the “Betos” categories defined by Berenson and Holahan (1990).This hierarchical classification system goes from the broad categories we use here (such as Evaluation & Management andImaging) to 2-digit (e.g. Advanced Imaging [MRIs and CAT scans]) and 3-digit classifications (e.g. CAT Scan: Head).131Appendix Table C.8 replicates this analysis in other years’ data.984.6. How Do Private Payments Deviate from Medicare?from the efficient or equilibrium level that would obtain under unconstrained negotiations.4.6.3 How Do Deviations Change Incentives Relative to Medicare?What are physicians and insurers aiming to achieve when they negotiate reimbursements that deviatefrom Medicare’s relative prices? In this section, we present evidence on the direction of deviationsfrom strictly Medicare-benchmarked rates to investigate what services BCBS rewards through upwardadjustments and discourages through downward adjustments. We do so by describing residuals fromthe following regression:ln(Pg,j) = ψ ln(RV Uj) + µg + eg,j . (4.13)In a world of perfect benchmarking, we would find ψˆ = 1 and eg,j uniformly equal to 0. So the em-pirical prediction errors eˆg,j contain information about the direction of deviations from strict Medicarebenchmarking. We examine heterogeneity in this prediction error across categories of services.132Table 4.8 presents means of eˆg,j from equation (4.13) across Betos categories.133 The table showsthat payments for Evaluation & Management and Testing services generally have positive residualswhile payments for services in Imaging and Procedures have negative residuals. Figure 4.5 Panel Aplots the distributions of these residuals by service category. The distribution for Imaging shows farmore density of negative residuals than those for other services. Testing has more positive residuals,although that is largely driven by one outlier code.134 Compared to the relative payments impliedby Medicare’s relative values, BCBS systematically adjusts its contracts to discourage imaging ser-vices. This coincides with the conventional wisdom that Medicare’s relative values underpay forlabor-intensive services relative to other services, and suggests that BCBS aims to partly rectify thatmispricing.Differences in BCBS’s adjustments for labor- and capital-intensive services are particularly sharpacross the subcategories of diagnostic imaging. Payment adjustments for the labor-intensive Profes-sional Component of these services are substantially positive, at around 0.07 in logs (approximately7 percent). Payment adjustments for the capital-intensive Technical Component of these services aresubstantially negative, averaging −0.12 in logs. Figure 4.5 Panel B shows that this pattern holdsthroughout the distribution. While it is clear that BCBS reimbursements lean heavily on Medicare’srelative values for their basic payment structure, these results suggest that BCBS adjusts its con-132A subtle but important point is that this approach captures deviations from Medicare’s relative prices that comethrough the introduction of multiple Medicare-benchmarked conversion factors. If an insurer thinks the Medicare menu’sprimary inefficiency is that it uniformly overpays for diagnostic imaging services relative to other services, for example,its preferred contract may simply set a low conversion factor for imaging services and a high conversion factor for otherservices. Our previous analyses would describe such a contract as being fully linked to Medicare. The analysis in thecurrent section will capture the fact that this is structured to discourage the use of imaging services relative to otherservices.133To be precise, these means are eˆg,j =1Nb∑j∈b eˆg,j , where each Betos group b comprises Nb claims for all servicesj ∈ b in that group.134In the Testing category the vast majority of residuals are negative, with the exception of one of the more commontests, which has a large and positive average residual. Recall from section 4.3, however, that Testing is the one categorywith significant missing data problems.994.7. Conclusiontracts to increase the generosity of payments for labor-intensive services and decrease its payments forcapital-intensive services. This is consistent with deviating from Medicare with an eye towards moreclosely targeting either marginal costs, or medical value.4.7 ConclusionThis chapter uses physician payments from a large private insurer as a window into how privatefirms contract for services in complex environments. Using two empirical strategies, we show thatthey benchmark to Medicare’s schedule of relative prices to significantly simplify this problem, andestimate that roughly 75 percent of services and 55 percent of spending are directly linked to Medicare.We find evidence that the one quarter of services and nearly half of payments that deviate fromMedicare’s relative rate structure involve an effort to improve the payment structure. Insurers tendto deviate when the value of doing so appears to be highest. Deviations occur disproportionately incontracts with large physician groups, where significant mutual gains can be achieved. They signifi-cantly reduce payments for diagnostic imaging services, a category of care for which many academicsand policy makers believe marginal benefits are low relative to costs (Winter and Ray, 2008; MedPAC,2011). But they hew closely to Medicare in payments for services where average-cost reimbursementswill be most aligned with marginal costs, such as labor-intensive primary care services. When contractsdeviate from Medicare, the direction of payment adjustments would tend to encourage the provisionof primary care and discourage care for which over-utilization is a more widespread concern.1004.8. Tables4.8 TablesTable 4.1: Summary Statistics by Physician GroupPanel A: All Groups(N=80,675) Mean Median Std. Dev. Min. Max.Number of unique services 9.70 3 27.23 1 ∼1,700Number of patients 87.59 2 698.85 1 ∼61,930Number of doctors 1.73 1 7.93 1 ∼1,100Number of claims 201 3 1,763 1 ∼163,360Mean allowed amount 108.91 84.43 125.16 0.64 ∼7,680Total BCBS revenue 25,457 383 274700.3 0.64 ∼43,000,000Panel B: Groups with Billings > $10, 000(N=15,235) Mean Median Std. Dev. Min. Max.Number of unique services 35.99 24 53.12 1 ∼1,700Number of patients 424.35 151 1,523 1 ∼61,930Number of doctors 4.14 2 17.56 1 ∼1,100Number of claims 981.13 386 3860 1 ∼163,360Mean allowed amount 105.52 84.65 136.3 10.75 ∼7,680Total BCBS revenue 124,687 44392 606,644 10000 ∼43,000,000Note: this table shows summary statistics for data by physician group. Source: Authors’ calculations using claims data from BCBS.Table 4.2: Services Priced According to Common Implied Conversion FactorsPanel A: Dollar-WeightedFrequency Threshold:5% 10% 20%Rounding for ICFs:$0.02 83% 76% 66%$0.10 86% 80% 71%$0.20 87% 80% 71%Panel B: Service-WeightedFrequency Threshold:5% 10% 20%Rounding for ICFs:$0.02 87% 81% 70%$0.10 89% 84% 75%$0.20 89% 85% 75%Note: each cell shows the share of services for which payments are associated with a common Implied Conversion Factor (cICF),as defined in the main text. Data are from January 1—June 30, 2010, over which time BCBS used the 2009 version of Medicare’sResource Based Relative Value Scale. The cells within each panel show how the linked share varies as we apply different thresholdsfor the frequency required to quality as a cICF. The column labeled “Rounding” indicates the rounding applied to each estimatedICF. An ICF is defined as “common” for the payments to a physician group if it accounts for at least the fraction of servicesassociated with the specified Frequency Threshold. Source: Authors’ calculations using claims data from BCBS.1014.8. TablesTable 4.3: Firm Size and Implied Conversion Factors(1) (2) (3) (4) (5)Dependent variable: Log implied conversion factor (ICF)Firm Size (Log Spending) 0.058** 0.058** 0.040**(0.004) (0.005) (0.006)Firm Market Share 0.241** -0.158** -0.092**(0.015) (0.037) (0.029)Market Concentration 0.238** 0.318** 0.159**(0.020) (0.036) (0.028)N 20,736,449 20,736,449 20,736,449 20,736,449 20,736,449No. of Clusters 23,098 23,098 23,098 23,098 23,098Code Effects No No No No YesHSA Fixed Effects No No No No YesNote: **, *, and + indicate statistical significance at the 0.01, 0.05, and 0.10 levels respectively. This table shows estimates ofrelationship between features of physicians’ contracts and measures of firm size and/or market concentration. The construction ofall variables is discussed in the main text. Source: Authors’ calculations using claims data from BCBS.Table 4.4: Estimating Medicare Benchmarking Using RVU Changes(1) (2) (3) (4)Dependent variable: Log private reimbursement ratePanel A: Weighted by PriceLog RVU Change × Post 0.539** 0.544** 0.568** 0.538**(0.061) (0.061) (0.060) (0.061)N 23,933,577 23,933,577 23,933,577 23,933,577No. of Clusters 3,681 3,681 3,681 3,681Panel B: UnweightedLog RVU Change × Post 0.750** 0.748** 0.765** 0.749**(0.038) (0.038) (0.043) (0.038)N 23,933,577 23,933,577 23,933,577 23,933,577No. of Clusters 3,681 3,681 3,681 3,681Group-by-Code Effects Yes No Yes YesCode Effects No Yes No NoCubic Time × RVU Change No No Yes NoCubic Time × Post No No No YesNote: **, *, and + indicate statistical significance at the 0.01, 0.05, and 0.10 levels respectively. The table shows the resultsof OLS specifications of the form described in section 4.4.2. Each column in each panel reports an estimate of βˆ from equation(4.10). Observations are at the claim-line level and are equally weighted (Panel B), or weighted according to each service’s averagepayment during the baseline period (Panel A). Data are from 2010. Standard errors are calculated allowing for arbitrary correlationamong the errors associated with each HCPCS service code (including modifiers for the professional and technical componentsof diagnostic imaging services). Additional features of each specification are described within the table. The construction of allvariables is further described in the main text. Sources: Authors’ calculations using updates to Medicare’s RBRVS as reported inthe Federal Register and claims data from BCBS.1024.8. TablesTable 4.5: Medicare Benchmarking by Firm Size(1) (2) (3) (4)Dependent variable: Log private reimbursement rateLog RVU Change 0.750** 0.882** 0.539** 0.775**× Post-Update (0.038) (0.073) (0.061) (0.094)Log RVU Change -0.074 -0.140*× Post-Update × Midsize (0.098) (0.069)Log RVU Change -0.293* -0.448**× Post-Update × Large (0.117) (0.102)N 23,933,577 23,933,577 23,933,577 23,933,577Weighting: Service Service Dollar DollarNote: **, *, and + indicate statistical significance at the 0.01, 0.05, and 0.10 levels respectively. Columns 1 and 3 report thebaseline estimates from Table 4.4 Panels A and B respectively. In columns 2 and 4 we augment these specifications to includeinteractions between firm size indicator variables and both the “Post” indicator and the interaction between the “Log RVU Change”and “Post” indicator. The omitted category is small firms, defined as those with less than $200,000 in billings. Mid-sized firms arethose with billings between $200,000 and $1 million, and large firms are those with billings exceeding $1 million. Data are from2010. Standard errors are calculated allowing for arbitrary correlation among the errors associated with each HCPCS service code(including modifiers for the professional and technical components of diagnostic imaging services). Sources: Authors’ calculationsusing updates to Medicare’s RBRVS as reported in the Federal Register and claims data from BCBS.Table 4.6: Public-Private Payment Links Across Service Categories(1) (2) (3) (4) (5) (6) (7)Dependent variable: Log private reimbursement rateEvaluation Imaging Procedures Tests Imaging Sub-Categories:Global Technical ProfessionalLog RVU Change 0.841** 0.564** 0.720** 1.066** 0.545** 0.387* 0.982**× Post-Update (0.036) (0.084) (0.081) (0.066) (0.109) (0.152) (0.066)N 12,259,186 3,630,019 4,750,313 1,542,254 1,826,666 209,178 1,594,175No. of Clusters 221 1,085 1,936 408 408 244 433Note: **, *, and + indicate statistical significance at the 0.01, 0.05, and 0.10 levels respectively. The table shows the results ofOLS specifications of the form described in section 4.4.2. The cells in each panel report estimates of βˆ from equation (4.10), withsamples selected to contain the HCPCS codes falling into broad service categories. The name of the relevant service categoryaccompanies each point estimate. Data are from 2010. Standard errors are calculated allowing for arbitrary correlation among theerrors associated with each HCPCS service code (including modifiers for the professional and technical components of diagnosticimaging services). The construction of all variables is further described in the main text. Sources: Authors’ calculations usingupdates to Medicare’s RBRVS as reported in the Federal Register and claims data from BCBS.1034.8. TablesTable 4.7: Medicare Benchmarking by Betos Category(1) (2) (3) (4)Dependent variable: Payments with Common Conversion FactorsSpending Share Service ShareImaging -0.427** -0.471** -0.300** -0.355**(0.053) (0.047) (0.030) (0.024)Procedures -0.309** -0.352** -0.336** -0.388**(0.030) (0.028) (0.054) (0.052)Tests -0.383** -0.415** -0.258** -0.297**(0.051) (0.047) (0.055) (0.054)Constant 0.921** 0.828** 0.941** 0.829**(0.015) (0.015) (0.020) (0.017)N 542,207 542,207 542,207 542,207Omitted Category Evaluation & ManagementAdditional Controls Group Size None Group Size NoneNote: **, *, and + indicate statistical significance at the 0.01, 0.05, and 0.10 levels respectively. This table shows estimates ofthe ηb coefficients in equation (4.12), namely the relationship between Betos category and the Medicare-linked share of claim lines(columns 1 and 2) or spending (columns 3 and 4). Medicare links are measured using the common Implied Conversion Factors(cICFs) defined in section 4.4.1, using data from January 1 through June 30, 2010. We require that cICFs account for 10 percent ofa group’s claims, when rounded to the nearest $0.02. Columns 1 and 3 show estimates after controlling for vigintile of group size,as measured with BCBS spending, and columns 2 and 4 show estimates without group size controls. Standard errors are two-wayclustered (Cameron et al., 2011) by Betos category and physician group. Sources: Authors’ calculations using claims data fromBCBS.Table 4.8: In What Direction Does BCBS Adjust Its Payments for the Various Service Categories?(1) (2) (3) (4) (5) (6) (7)Distributions of Payment Residuals by Betos CategoriesEvaluation & Imaging Procedures Tests Imaging Sub-Categories:Management Global Technical ProfessionalResidual Mean 0.0112 -0.0624 0.0107 0.0301 -0.122 -0.124 0.0150Residaul SD (0.169) (0.246) (0.279) (0.319) (0.272) (0.281) (0.177)N 6,010,826 1,743,011 2,312,734 751,726 883,419 102,465 757,127Note: this table presents means and standard deviations of residuals from estimates of equation (4.13) in data from 2010. Thatis, we regress the log of BCBS’s payments on a set of physician-group fixed effects and the log of each HCPCS code’s number ofRelative Value Units. This table describes the residuals from that regression. We restrict the sample to the pre-update period(January 1 through June 30, 2010) so that the relative value units are constant for each service throughout the sample. Source:Authors’ calculations using claims data from BCBS.1044.9. Figures4.9 FiguresFigure 4.1: Raw Payments For Illustrative Physician Groups110100100010000BCBS Payment (Dollars on log scale)1 10 100 1000 10000Medicare Payment (Dollars on log scale)Panel A: Early 2010 Payment Data for a Mid-Size Group0306090Frequency0 .5 1 1.5 2 2.5Markup Relative To MedicarePanel B: Distribution of Markups for a Mid-Size Group110100100010000BCBS Payment (Dollars on log scale)1 10 100 1000 10000Medicare Payment (Dollars on log scale)Panel C: Early 2010 Payment Data for a Large Group04080120Frequency0 .5 1 1.5 2 2.5Mark-up Relative To MedicarePanel D: Distribution of Markups for a Large Group110100100010000BCBS Payment (Dollars on log scale)1 10 100 1000 10000Medicare Payment (Dollars on log scale)Panel E: Early 2010 Payment Data for a Large Group0102030Frequency0 .5 1 1.5 2 2.5Markup Relative To MedicarePanel F: Distribution of Markups for a Large GroupNote: Panels A through F present the raw data on BCBS reimbursement rates, and associated Medicare reimbursement, for 3different physician groups in 2010. In Panels A, C, and E, each observation is a unique reimbursement paid for a particular serviceto the group. The lines have a slope of 1 (in logs) and represent the groups’ most common Implied Conversion Factors. PanelsB, D and F plot the distribution of markups relative to the Medicare rates for all payments each group received. They show clearspikes at the values that we identify as common Implied Conversion Factors in Panels A, C, and E. To comply with confidentialityrules, we omit from these graphs a small share of each group’s claims. The share of claims whose observations are suppressed is14.2% in Panels A and B, 1.94% in Panels C and D, and 2.95% in Panels E and F. Source: Authors’ calculations using RVUs fromthe Federal Register and claims data from BCBS.1054.9. FiguresFigure 4.2: Benchmarking Estimates Based on Price ChangesPanel A Panel B44.14.24.34.4Ln(Allowed Charge)01jan2010 01apr2010 01jul2010 01oct2010 01jan2011Date Charge IncurredOne Service Example: Office Visit 99213-0.2500.250.50.751Share Linked to RVUs0 3 6 9 12MonthLink to RVU Update95% CI Lower Bound/95% CI Upper BoundStrength of Public-Private Relationship: 2010 RVU UpdatesEstimates by MonthPanel C Panel D-.1-.050.05.1Change in Log BCBS Payment for Service-.2 -.1 0 .1Change in Log Medicare RVUs for ServiceMedicare and Private Changes: 2010-.1-.050.05.1Change in Log BCBS Payment for Service-.15 -.1 -.05 0 .05 .1Change in Log Medicare RVUs for Service Non-Linked  LinkedCross-Validation of Two Methods: 2010Note: all panels use data from calendar year 2010. BCBS implemented its update from the 2009 to 2010 relative value scales onJuly 1, 2010, as indicated by the vertical dashed line in Panels A and B. Panel A presents daily averages of BCBS’s log paymentfor a standard office visit. Panel B reports estimates of the βp from estimates of equation (4.11). Panel C presents a binnedscatterplot of the relationship between Medicare payment updates (sorted into 20 vigintiles) and changes in private payments. InPanel C, private price changes are computed as the difference between service-level average payments after and before July 1, 2010.Panel D is similar, but with separate data and estimation for services that we identify as being linked to Medicare on the basis oftheir implicit conversion factors and those we identify as being non-linked. For presentation in the binned scatterplot, observationswithin each class of services (i.e.,linked or non-linked) are grouped into twenty vigintiles on the basis of the log change in the servicecode’s Medicare RVU allocation. The regression lines shown in Panels C and D are estimated at the underlying service-code level.Sources: Authors’ calculations using RBRVS updates from the Federal Register and claims data from BCBS.1064.9. FiguresFigure 4.3: Estimating Multiple Years’ RVU Updates Simultaneously-0.2500.250.50.751Share Linked To RVUs2008q1 2009q1 2010q1 2011q1Quarter2008 2009 2010Year of RVU changes:Note: the figure reports estimates of β08t , β09t and β10t from the following modification of equation (4.11):ln(Pc,g,j,t) =∑t6=0β08t ∆ ln(RV Uj,08) · 1t +∑t6=0β09t ∆ ln(RV Uj,09) · 110t +∑t6=0βt∆ ln(RV Uj,10) · 1t + φt1t + φj1j + φg1g + φg,j1g · 1j + ηc,g,j,t.(4.14)In this specification, ∆ ln(RV Uj,T ) refers to the log of Medicare’s RVU updates from calendar year T − 1 to calendar year T .The corresponding coefficients βTt indicate what share of the year-T RVU updates were incorporated into BCBS payments duringcalendar quarter t. BCBS implemented its RVU updates on July 1, 2008, August 15, 2009, and July 1, 2010. The omitted interaction(t = 0) is 2008Q2 for all of the RVU update variables. The regression line is estimated at the underlying service-code level and isdollar-weighted. Sources: Authors’ calculations using claims data from BCBS.Figure 4.4: Frequency of Benchmarking and Physician Group Size.2.4.6.81Share linked to Medicare ICFs0 5 10 15 20Vigintiles of group-level spending (smallest to largest)Share of spend based on Medicare-linked ICFs (adj. for service comp.)Share of services based on Medicare-linked ICFs (adj. for service comp.)Share of spend based on Medicare-linked ICFs (weighted)Share of services based on Medicare-linked ICFs (weighted)Note: this figure shows the relationship between a group’s Medicare-linked service share and group size. Specifically, it plotsvariation in the share of services priced according to common Implied Conversion Factors (cICFs), as defined in section 4.4.1,according to physician group size. We measure group size by forming 20 vigintiles based on the group’s BCBS billing. We requirethat cICFs account for 10 percent of a group’s claims, when rounded to the nearest $0.02. The green dots and orange diamondsshow estimates of ζb from equation (4.12), which adjust for the composition of each group’s services. The blue ×’s and red squaresare unadjusted, but weighted to measure the Medicare-linked share of spending in dollar terms as opposed to the share of services.All data are from 2010. Sources: Authors’ calculations using claims data from BCBS.1074.9. FiguresFigure 4.5: Deviations from Medicare Benchmark by Service CategoryPanel A0.2.4.6.81Distribution-.4 -.2 0 .2 .4Log ResidualEvaluation ImagingProcedures TestingBetos Categories: 2010Panel B0.2.4.6.81Distribution-.4 -.2 0 .2Log ResidualGlobal TechnicalProfessionalImaging Sub-Categories: 2010Note: the figure presents residuals g,j from estimates of equation (4.13). The distribution of residuals is shown within either broadBetos categories (Panel A), or within the subcategories of Imaging (Panel B). The distributions are smoothed using a local linearregression, with an Epanechnikov kernel and a bandwidth of 0.01. Source: Authors’ calculations using claims data from BCBS.108Chapter 5ConclusionThis thesis consists of three chapters in family economics, early childhood development, economicsof education and health economics. In all chapters I examine how a unique institutional feature ofa major economic sector—a universal daycare price change, the opportunity of academic redshirtingand Medicare price change—shapes families’ and firms’ incentives and impacts their behavior.First I study parents’ quality time allocation to their children, and show that universal daycareprice can be an effective policy instrument to influence parental quality time. I focus on differencesacross education groups, where the motivation stems from the parental time-education puzzle. Toresolve it, I examine parents’ responses to a shock to the opportunity costs of their time. For identifi-cation, I exploit a drastic decrease in universal daycare prices in Quebec in 1997, leading mothers towork more and households to consume more of typical home production and child market goods. Strik-ingly, I find that higher-educated parents do not only they spend more time with their children in thecross-section, but they increase child time even more, after daycare price falls. The child time increaseand home production time decrease is driven by higher-educated mothers drawn (back) into the labormarket—for whom mental health and parenting practices improved, impacting positively their child’shyperactivity/aggression/anxiety scores. The mechanism I confirm is that higher-educated parents’time has a larger marginal return in non-market activities, outweighing their higher wage. My find-ings uncover the pivotal role of substitutability between time and market goods, and suggest: parentssubstitute their time from activities where time is substitutable with market goods (home production)to activities where time is complementary to market goods (child human capital production).One immediate policy implication of my findings is that since both higher- and lower-educatedparents increase parental time and daycare time after daycare price falls, the level of child humancapital–if produced solely from these two inputs–is expected to increase for both; whether the childhoodskill gap shrinks or expands depends on the concavity of the human capital production function, andthe degree of time efficiency advantage of higher-educated parents. Compared to the counterfactualscenario of no policy for ages 3-4, the subsidized daycare policy actually increases the level of childhuman capital by 17 and 14 percentages for higher- and lower-educated parents’ children, respectively;resulting in a 30 percent larger skill gap. If the policy had not been universal but targeted only atlow-educated families, approximately half of this (increased) gap could be eliminated. Thus, there isa trade-off between increasing the level of child human capital versus decreasing inequality, and thesecompeting policy objectives need to be weighed when designing a universal or a targeted daycare policy.By quantifying the importance of the time efficiency mechanism I find that (1) roughly 36 percentof the actual increase in the level of child human capital comes from high-educated parents’ largerincrease in inputs, while the rest is due to their time efficiency advantage, and (2) if lower-educatedparents had no time efficiency disadvantage, the actual skill gap could be closed by 27 percent.109Chapter 5. ConclusionIn the second chapter I present the causal impact of academic redshirting–the practice of postpon-ing school entry of an age-eligible child. I show that redshirting can be a beneficial flexible opportunitywithin the educational system primarily for disadvantaged boys; this is an important policy-implicationfrom the aspect of equality of opportunity, since disadvantaged boys are the most likely to suffer fromschool-readiness problems, such as hyperactivity or attention disorders. My results suggest that mentalhealth is one of the mechanisms behind disadvantaged boys benefiting the most from delayed school en-try: boosted human capital in the extra year before school leads to better mental health–such as loweranxiety–, associated with better student achievement. This presumed mechanism based on humancapital is also consistent with the finding that entering primary school a year later matters because itmakes the child older in absolute terms, rather than making him/her older relative to classmates.In the third chapter with co-authors Jeffrey Clemens and Joshua Gottlieb we investigate how fre-quently privately negotiated physician payments deviate from the public sector (Medicare) benchmark,and find that prices for 25 percent of physician services, representing 45 percent of spending, do devi-ate. We use administrative outpatient claims data from a large private insurer Blue Cross Blue Shieldof Texas (BCBS), and exploit the institutional detail of the exact day on which BCBS implemented theannual Medicare payment updates (e.g. July 1st in 2010). We show that the Medicare-benchmarkedshare is high for services provided by small physician groups and low for capital-intensive services,for which Medicare’s average-cost reimbursement schedule deviates most from the marginal cost. Ourresults suggest that providers and private insurers coordinate around Medicare’s menu of relativepayments for simplicity but—when the value at stake is sufficient—do indeed innovate.A number of different factors could contribute to this behavior, and we hope that future researchwill disentangle them. Benchmarking could be the market’s way of simplifying a complex contractingproblem, analogous to bounded rationality for individuals. Relatedly, it could reflect insurers’ desireto free-ride off of Medicare since computing optimal prices for every service may be excessively costly.Alternatively, it could purely reflect a bargaining outcome in which Medicare is the outside optionfor many, but not all, services. 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