essays in the economics of education

Essays in the Economics of Education by Jesse Morris Rothstein A.B. (Harvard University) 1995 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Economics in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in charge: Professor David Card, Chair Professor John M. Quigley Professor Steven Raphael Spring 2003 UMI Number: 3183857 3183857 2005 Copyright 2003 by Rothstein, Jesse Morris UMI Microform Copyright All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 All rights reserved. by ProQuest Information and Learning Company. Essays in the Economics of Education Copyright 2003 by Jesse Morris Rothstein 1 Abstract Essays in the Economics of Education by Jesse Morris Rothstein Doctor of Philosophy in Economics University of California, Berkeley Professor David Card, Chair Three essays consider implications of the strong association between student background characteristics and academic performance. Chapter One considers the incentives that school choice policies might create for the efficient management of schools. These incentives would be diluted if parents prefer schools with desirable peer groups to those with inferior peers but better policies and instruction. I model a “Tiebout choice” housing market in which schools differ in both peer group and effectiveness. If parental preferences depend primarily on school effectiveness, we should expect both that wealthy parents purchase houses near effective schools and that decentralization of educational governance facilitates this residential sorting. On the other hand, if the peer group dominates effectiveness in parental preferences, wealthy families will still cluster together in equilibrium but not necessarily at effective schools. I use a large sample of SAT-takers to examine the distribution of student outcomes across schools within metropolitan areas that differ in the structure of educational governance, and find little evidence that parents choose schools for characteristics other than peer groups. 2 This result suggests that competition may not induce improvements in educational productivity, and indeed I do not obtain Hoxby’s (2000a) claimed relationship between school decentralization and student performance. I address this discrepancy in Chapter Two. Using Hoxby’s own data and specification, as described in her published paper, I am unable to replicate her positive estimate, and I find several reasons for concern about the validity of her conclusions. Chapter Three considers the role of admissions tests in predictions of student collegiate performance. Traditional predictive validity studies suffer from two important shortcomings. First, they do not adequately account for issues of sample selection. Second, they ignore a wide class of student background variables that covary with both test scores and collegiate success. I propose an omitted variables estimator that is consistent under restrictive but sometimes plausible sample selection assumptions. Using this estimator and data from the University of California, I find that school-level demographic characteristics account for a large portion of the SAT’s apparent predictive power. This result casts doubt on the meritocratic foundations of exam-based admissions rules. i To Joanie, for everything. ii Contents List of Figures iv List of Tables v Preface vi Acknowledgements x 1. Good Principals or Good Peers? Parental Valuation of School Characteristics, Tiebout Equilibrium, and the Incentive Effects of Competition among Jurisdictions 1 1.1. Introduction 1 1.2. Tiebout Sorting and the Role of Peer Groups: Intuition 10 1.3. A Model of Tiebout Sorting on Exogenous Community Attributes 15 1.3.1. Graphical illustration of market equilibrium 21 1.3.2. Simulation of expanding choice 24 1.3.3. Allocative implications and endogenous school effectiveness 27 1.4. Data 28 1.4.1. Measuring market concentration 28 1.4.2. Does district structure matter to school-level choice? 30 1.4.3. SAT data 34 1.5. Empirical Results: Choice and Effectiveness Sorting 37 1.5.1. Nonparametric estimates 38 1.5.2. Regression estimates of linear models 39 1.6. Empirical Results: Choice and Average SAT Scores 49 1.7. Conclusion 51 Tables and Figures for Chapter 1 55 2. Does Competition Among Public Schools Really Benefit Students? A Reappraisal of Hoxby (2000) 69 2.1. Introduction 69 2.2. Data and Methods 72 2.2.1. Econometric framework 76 2.3. Replication 78 2.4. Sensitivity to Geographic Match 80 2.5. Are Estimates From the Public Sector Biased? 82 2.6. Improved Estimation of Appropriate Standard Errors 85 2.7. Conclusion 88 Tables and Figures for Chapter 2 90 iii 3. College Performance Predictions and the SAT 97 3.1. Introduction 97 3.2. The Validity Model 100 3.2.1. Restriction of range corrections 101 3.2.2. The logical inconsistency of range corrections 102 3.3. Data 104 3.3.1. UC admissions processes and eligible subsample construction 106 3.4. Validity Estimates: Sparse Model 107 3.5. Possible Endogeneity of Matriculation, Campus, and Major 110 3.6. Decomposing the SAT’s Predictive Power 114 3.7. Discussion 119 Tables and Figures for Chapter 3 122 References 128 Appendices 135 Appendix A. Choice and School-Level Stratification 135 Appendix B. Potential Endogeneity of Market Structure 137 Appendix C. Selection into SAT-Taking 141 Appendix D. Proofs of Results in Chapter 1, Section 3 144 Tables and Figures for Appendices 153 iv List of Figures 1.1 Schematic: Illustrative allocations of effective schools in Tiebout equilibrium, by size of peer effect and number of districts 62 1.2 Simulations: Average effectiveness of equilibrium schools in 3- and 10-district markets, by income and importance of peer group 63 1.3 Simulations: Slope of effectiveness with respect to average income in Tiebout equilibrium, by market structure and importance of peer group 64 1.4 Distribution of district-level choice indices across 318 U.S. metropolitan areas 65 1.5 Student characteristics and average SAT scores, school level 66 1.6 Nonparametric estimates of the school-level SAT score-peer group relationship, by choice quartile 67 1.7 “Upper limit” effect of fully decentralizing Miami’s school governance on the across-school distribution of SAT scores 68 3.1 Conditional expectation of SAT given HSGPA, three samples 127 B1 Number of school districts over time 160 C1 SAT-taking rates and average SAT scores across MSAs 161 D1 Illustration of single-crossing: Indifference curves in q-h space 161 v List of Tables 1.1 Summary statistics for U.S. MSAs 55 1.2 Effect of district-level choice index on income and racial stratification 56 1.3 Summary statistics for SAT sample 57 1.4 Effect of Tiebout choice on the school-level SAT score-peer group gradient 58 1.5 Effect of Tiebout choice on the school-level SAT score-peer group gradient: Alternative specifications 59 1.6 Effect of Tiebout choice on the school-level SAT score-peer group gradient: Evidence from the NELS and the CCD 60 1.7 Effect of Tiebout choice on average SAT scores across MSAs 61 2.1 First-stage models for the district-level choice index 90 2.2 Basic models for NELS 8 th grade reading score, Hoxby (2000b) and replication 91 2.3 Effect of varying the sample definition on the estimated choice effect 92 2.4 Models that control for the MSA private enrollment share 93 2.5 Estimated choice effect when sample includes private schools 94 2.6 Alternative estimators of the choice effect sampling error, base replication sample 95 2.7 Estimates of Hoxby’s specification on SAT data 96 3.1 Summary statistics for UC matriculant and SAT-taker samples 122 3.2 Basic validity models, traditional and proposed models 123 3.3 Specification checks 124 3.4 Individual and school characteristics as determinants of SAT scores and GPAs 125 3.5 Accounting for individual and school characteristics in FGPA prediction 126 A1 Evidence on choice-stratification relationship: Additional measures 153 A2 Alternative measures of Tiebout choice: Effects on segregation and stratification 154 A3 Effect of district-level choice on tract-level income and racial stratification 155 B1 First-stage models for MSA choice index 156 B2 2SLS estimates of effect of Tiebout choice 157 C1 Sensitivity of individual and school average SAT variation to assumed selection parameter 158 C2 Stability of school mean SAT score and peer group background characteristics over time 158 C3 Effect of Tiebout choice on the school-level SAT score-peer group gradient: Estimates from class rank-reweighted sample 159 [...]... sorting; otherwise, it may understate the importance of effectiveness in output and in parental choices 8 nonlinearity in the causal effects of the peer group as well as to several specifications of the educational production function Moreover, although there is no other suitable data set with nearly the coverage of the SAT sample, the basic conclusions are supported by models estimated both on administrative... administrators, their choice of curricula, or their effectiveness in resisting the demands of bureaucrats and teacher’s 13 The distinction between direct and indirect effects of school composition is not always clear in discussions of peer effects Studies that use transitory within-school variation in the composition of the peer group (Hoxby, 2000b; Angrist and Lang, 2002; Hanushek, Kain, and Rivkin,... impacts of school choice programs, and the design of college admissions rules In each case, when I incorporate into the standard analysis the key fact that student composition may function as a signal of student performance (and vice versa), I obtain new vi insights into the underlying processes and new ways of thinking about the available policy options The first two chapters consider parents’ choice of. .. hypotheses for the degree of stratification of student test scores across schools, and I look for evidence of these implications in data on the joint distribution of student characteristics and SAT scores I find strong evidence that schools are an important component of the residential choice and that housing markets create sorting by family income across schools Tests of the hypothesis that this sorting... chairs” game, and the upper constraint serves to tie prices down, while the lower constraint avoids the need to define the peer group offered by a community with no residents 24 Of course, the income distribution cannot be continuous for finite N Relaxing the treatment to allow a discrete distribution would add notational complexity and introduce some indeterminacy in equilibrium housing prices, but... for Studies in Higher Education David Card and Alan Krueger provided the SAT data used throughout Cecilia Rouse provided the hard-to-obtain School District Data Book used in Chapters 1 and 2 Saul Geiser and Roger Studley of the University of California Office of the President provided the student records that permitted the research in Chapter 3 The usual disclaimer applies: Any opinions, findings, conclusions... is common in studies of consumer demand, and in particular underlies both the multicommunity and hedonic literatures If it is violated, of course, the motivating question of whether parents prefer good principals or good peers is not well posed 10 In view of the vast literature documenting the important role of family background characteristics—e.g ethnicity, parental income and education in student... higherincome families do as well; if any family prefers a district to another offering higher quality education, all lower-income families do also (This is proved in Appendix D.) As in other multicommunity models, the single crossing assumption drives the stratification results outlined below Market equilibrium is defined as a set of housing prices and a rule assigning families to districts on the basis... necessarily reflect the views of the National Science Foundation, the Fisher Center, the Center for Studies in Higher Education, the College Board, the UC Office of the President, or any of my advisors Last, but not least, there is a sense in which Larry Mishel deserves substantial credit for my Ph.D., as without his determined efforts at persuasion, I would never have pursued it in the first place xi... would de-link school quality from residential location Although some authors (i.e Epple and Zelenitz, 1981) include a supply side of the housing market, I assume that communities are endowed with perfectly inelastic stocks of identical houses 20 Communities differ in three dimensions: The average income of their residents and the rental price of housing, both endogenous, and the effectiveness of the local . Information and Learning Company. Essays in the Economics of Education Copyright 2003 by Jesse Morris Rothstein 1 Abstract Essays in the Economics of Education. Studley of the University of California Office of the President provided the student records that permitted the research in Chapter 3. The usual disclaimer applies: Any opinions, findings, conclusions. necessarily reflect the views of the National Science Foundation, the Fisher Center, the Center for Studies in Higher Education, the College Board, the UC Office of the President, or any of my advisors.