Essays in the economics of education

Essays in the Economics of Education by Jesse Morris Rothstein A. (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 Copyright 2003 by Rothstein, Jesse Morris All rights reserved. UMI Microform 3183857 Copyright 2005 by ProQuest Information and Learning Company.

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. Box 1346 Ann Arbor, MI 48106-1346 Essays in the Economics of Education Copyright 2003 by Jesse Morris Rothstein 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. 1 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.

2 To Joanie, for everything. i 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. Tiebout Sorting and the Role of Peer Groups: Intuition.

A Model of Tiebout Sorting on Exogenous Community Attributes. Graphical illustration of market equilibrium 21 1. Simulation of expanding choice 24 1. Allocative implications and endogenous school effectiveness 27 1.

Measuring market concentration 28 1. Does district structure matter to school-level choice? 30 1. Empirical Results: Choice and Effectiveness Sorting. Regression estimates of linear models 39 1.

Empirical Results: Choice and Average SAT Scores .51 Tables and Figures for Chapter 1. Does Competition Among Public Schools Really Benefit Students? A Reappraisal of Hoxby (2000) 69 2. Data and Methods. Sensitivity to Geographic Match.

Are Estimates From the Public Sector Biased?. Improved Estimation of Appropriate Standard Errors.88 Tables and Figures for Chapter 2. College Performance Predictions and the SAT 97 3. The Validity Model.

Restriction of range corrections 101 3. The logical inconsistency of range corrections 102 3. UC admissions processes and eligible subsample construction 106 3. Validity Estimates: Sparse Model.

Possible Endogeneity of Matriculation, Campus, and Major. Decomposing the SAT’s Predictive Power .119 Tables and Figures for Chapter 3.122 References 128 Appendices 135 Appendix A. Choice and School-Level Stratification. Potential Endogeneity of Market Structure.

Selection into SAT-Taking. Proofs of Results in Chapter 1, Section 3.144 Tables and Figures for Appendices .153 iii List of Figures 1.1 Schematic: Illustrative allocations of effective schools in Tiebout equilibrium, by size of peer effect and number of districts .2 Simulations: Average effectiveness of equilibrium schools in 3- and 10-district markets, by income and importance of peer group.3 Simulations: Slope of effectiveness with respect to average income in Tiebout equilibrium, by market structure and importance of peer group.4 Distribution of district-level choice indices across 318 U.5 Student characteristics and average SAT scores, school level .6 Nonparametric estimates of the school-level SAT score-peer group relationship, by choice quartile.7 “Upper limit” effect of fully decentralizing Miami’s school governance on the across-school distribution of SAT scores .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 iv List of Tables 1.1 Summary statistics for U.2 Effect of district-level choice index on income and racial stratification.3 Summary statistics for SAT sample.4 Effect of Tiebout choice on the school-level SAT score-peer group gradient.5 Effect of Tiebout choice on the school-level SAT score-peer group gradient: Alternative specifications.6 Effect of Tiebout choice on the school-level SAT score-peer group gradient: Evidence from the NELS and the CCD.7 Effect of Tiebout choice on average SAT scores across MSAs.1 First-stage models for the district-level choice index .2 Basic models for NELS 8th grade reading score, Hoxby (2000b) and replication .3 Effect of varying the sample definition on the estimated choice effect .4 Models that control for the MSA private enrollment share.5 Estimated choice effect when sample includes private schools .6 Alternative estimators of the choice effect sampling error, base replication sample .7 Estimates of Hoxby’s specification on SAT data .1 Summary statistics for UC matriculant and SAT-taker samples .2 Basic validity models, traditional and proposed models.4 Individual and school characteristics as determinants of SAT scores and GPAs .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.education Preface It is a well-established fact that students’ socioeconomic background has substantial predictive power for their educational outcomes. Children whose parents are highly educated, whose households are stable, and whose families have high incomes substantially outperform their less advantaged peers on every measure of educational output. With nearly as long a pedigree is the idea that these family background effects may operate above the individual level.

The school-level association between average student background and average performance is typically much stronger than is the same association at the individual level. The interpretation of school-level correlations is nevertheless controversial: They may arise because academic outcome measures are noisy, implying that group means are more reliable than are individual scores; because students with unobservably attentive parents disproportionately attend schools that enroll observably advantaged students; because the system of education funding assigns greater resources to schools in wealthy neighborhoods; or because there really are peer effects in educational production. For many purposes, however, one need not know why it is that schools with advantaged students outscore those with disadvantaged students; the fact that they do is itself of substantial importance. This dissertation focuses on two such topics: The competitive 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 essays.education insights into the underlying processes and new ways of thinking about the available policy options. The first two chapters consider parents’ choice of schools for their children. The claim that parental choice can create incentives for schools to become more productive is a tenet of the neoclassical analysis of education. It relies crucially on the assumption that parents will choose effective, productive schools.

This is far from obvious—if peer effects are important, parents may be perfectly rational in preferring wealthy, ineffective schools to competitors that are less advantaged but more effective, and even if there are no peer effects, the strong association between school average test scores and student composition may make it difficult for parents to assess a school’s effectiveness. But if parents, in practice even if not by intent, choose schools primarily on the basis of their student composition rather than for their effectiveness, the incentives created for school administrators will be diluted. Chapter One develops this idea and implements tests of the hypothesis that school effectiveness is an important determinant of residential choices among local-monopoly school districts. I model a “Tiebout”-style housing market in which house prices ration access to desirable schools, which may be desirable either because they are particularly effective or because they enroll a desirable set of students.

I develop observable implications of these two 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 is driven by parental pursuit vii essays.education of effective schools, however, come up empty. This suggests that residential choice processes–and possibly, although the analogy is not particularly strong, non-residential choice programs like vouchers—are unlikely to create incentives for schools to become more effective.

This result conflicts with a well-known recent result from Hoxby (2000a), who argues that metropolitan areas with less centralized educational governance, and therefore more competition among local school districts, produce better student outcomes at lower cost. In Chapter Two, I attempt to get to the bottom of the discrepancy. I reanalyze a portion of Hoxby’s data, and find reason to suspect the validity of her conclusions. I am unable to reproduce her results, which appear to be quite sensitive to the exact sample and specification used.

I find suggestive evidence, however, that her estimates, from a sample of public school students, are upward biased by selection into private schools. Moreover, an investigation of the sampling variability of Hoxby’s estimates leads to the conclusion that her standard errors are understated, and that even her own point estimates of the competitive effect are not significantly different from zero. Chapter Three turns to a wholly different, but not unrelated, topic, the role of admissions exam scores in the identification of well-prepared students in the college admissions process. The case for using such exams is often made with “validity” studies, which estimate the correlation between test scores and eventual collegiate grades, both with and without controls for high school grade point average.

I argue that there are two fundamental problems with these studies as they are often carried out. First, they do not adequately account for the biases created by estimation from a selected sample of students whose collegiate grades are observable because they were granted admission. I propose and viii essays.