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
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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
vi
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
vii
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
viii
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
ix
implement an omitted variables estimator that is unbiased under restrictive, but sometimes
plausible, assumptions about the selection process.
A second shortcoming of the validity literature is more fundamental. In a world in

which student background characteristics are known to be correlated with academic success
(i.e. with both SAT scores and collegiate grades), it is quite difficult to interpret validity
estimates that fail to take account of these background characteristics. A study can identify a
test as predictively valid without being informative about whether the test provides an
independent measure of academic preparedness or simply proxies for the excluded
background characteristics.
In University of California data, I find evidence that observable background
characteristics—particularly those describing the composition of the school, rather than the
individual’s own background—are strong predictors of both SAT scores and collegiate
performance, and that much of the SAT’s apparent predictive power derives from its
association with these background characteristics. This suggests that the SAT may not be a
crucial part of the performance-maximizing admissions rule, as the background variables
themselves provide nearly all the information contained in SAT scores. It also suggests that
existing predictive validity evidence does not establish the frequent claim that the SAT is a
meritocratic admissions tool, unless demographic characteristics are seen as measures of
student merit.
x
Acknowledgements
I am very much indebted to David Card, for limitless advice and support throughout
my graduate school career. The research here has benefited in innumerable ways from his
many suggestions, as have I. It is hard to imagine a better advisor.
I am grateful to the members of my various committees—Alan Auerbach, John
Quigley, Steve Raphael, Emmanuel Saez, and Eugene Smolensky—for reading drafts that
were far too long and too unpolished, and for nevertheless finding many errors and
omissions.
I have benefited from discussions with David Autor, Jared Bernstein, Ken Chay,
Tom Davidoff, John DiNardo, Nada Eissa, Jonah Gelbach, Alan Krueger, David Lee,
Darren Lubotsky, Rob McMillan, Jack Porter, and Diane Whitmore, and from participants at
several seminars where I have presented versions of the work contained here. I also thank
my various officemates over the last five years, particularly Liz Cascio, Justin McCrary, Till

von Wachter, and Eric Verhoogen, for many helpful conversations. All of the research
contained here has been much improved by my interactions with those mentioned above,
and with others who I have surely neglected here.
One must live while conducting research. I thank my family and friends for putting
up with me these last five years and for helping me to stay sane throughout. I hope that I
have not been too unbearable.
Much of my graduate career was supported under a National Science Foundation
Graduate Research Fellowship. In addition, the research in Chapters 1 and 2 was partially
supported by the Fisher Center for Real Estate and Urban Economics at U.C. Berkeley and
xi
that in Chapter 3 by the Center 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 or recommendations expressed are my own and do not 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.
1
Chapter 1.
Good Principals or Good Peers? Parental
Valuation of School Characteristics, Tiebout
Equilibrium, and the Incentive Effects of
Competition among Jurisdictions

1.1. Introduction

Many analysts have identified principal-agent problems as a major source of
underperformance in public education. Public school administrators need not compete for
customers and are therefore free of the market discipline that aligns producer incentives with
consumer demand in private markets. Chubb and Moe, for example, argue that the interests
of parents and students “tend to be far outweighed by teachers’ unions, professional
organizations, and other entrenched interests that, in practice, have traditionally dominated
the politics of education,” (1990, p. 31).
1
One proposed solution—advocated by Friedman
(1962) and others—is to allow dissatisfied parents to choose another school, and to link
school administrators’ compensation to parents’ revealed demand. This would strengthen
parents relative to other actors, and might “encourage competition among schools, forcing
them into higher productivity,” (Hoxby, 1994, p. 1).

1
Chubb and Moe also identify the school characteristics that parents would presumably choose, given more
influence: “strong leadership, clear and ambitious goals, strong academic programs, teacher professionalism,
shared influence, and staff harmony,” (p. 187). See also Hanushek (1986) and Hanushek and Raymond
(2001).
2
The potential effects of school choice programs depend critically on what
characteristics parents value in schools. Hanushek, for example, notes that parents might
not choose effective schools over others that are less effective but offer “pleasant
surroundings, athletic facilities, [and] cultural advantages,” (1981, p. 34). To the extent that
parents choose productive schools, market discipline can induce greater productivity from
school administrators and teachers. If parents primarily value other features, however,
market discipline may be less successful. Hanushek cautions: “If the efficiency of our school
systems is due to poor incentives for teachers and administrators coupled with poor decision-
making by consumers, it would be unwise to expect much from programs that seek to
strengthen ‘market forces’ in the selection of schools,” (1981, p. 34-35; emphasis added).

Moreover, if students’ outcomes depend importantly on the characteristics of their
classmates (i.e. if so-called “peer effects” are important components of educational
production), even rational, fully informed, test-score-maximizing parents may prefer schools
with poor management but desirable peer groups to better managed competitors that enroll
less desirable students, and administrators may be more reliably rewarded for enrolling the
right peer group than for offering effective instruction.
The mechanisms typically proposed to increase parental choice—vouchers, charter
schools, etc.—are not at present sufficiently widespread to permit decisive empirical tests
either of parental revealed preferences or of their ultimate effects on school productivity.
2

Economists have long argued, however, that housing markets represent a long established,
potentially informative form of school choice (Tiebout, 1956; Brennan and Buchanan, 1980;

2
Hsieh and Urquiola (2002) study a large-scale voucher program in Chile, but argue that effects on school
productivity cannot be distinguished from the allocative efficiency effects of student stratification.
3
Oates, 1985; Hoxby, 2000a). Parents exert some control over their children’s school
assignment via their residential location decisions, and can exit undesirable schools by
moving to a neighborhood served by a different school district. As U.S. metropolitan areas
vary dramatically in the amount of control over children’s school assignment that the
residential decision affords to parents, one can hope to infer the effect of so-called Tiebout
choice by comparing student outcomes across metropolitan housing markets (Borland and
Howsen, 1992; Hoxby, 2000a).
3

In this chapter, I use data on school assignments and outcomes of students across
schools within different metropolitan housing markets to assess parents’ revealed
preferences. To preview the results, I find little evidence that parents use Tiebout choice to

select effective schools over those with desirable peers, or that schools are on average more
effective in markets that offer more choice.
In modeling the effects of parental preferences on equilibrium outcomes under
Tiebout choice, it is important to account for two key issues that do not arise under choice
programs like vouchers. The first is that residential choice rations access to highly-
demanded schools by willingness-to-pay for local housing.
4
As a result, both schools and
districts in high-choice markets (those with many competing school districts) are more
stratified than in low-choice markets. Increased stratification can have allocative efficiency
consequences that confound estimates of the effect of choice on productive efficiency.


3
Hoxby argues that this sort of analysis can “demonstrate general properties of school choice that are helpful
for thinking about reforms,” (2000a, p. 1209). Belfield and Levin (2001) review other, similar studies.
4
Small-scale voucher programs may not have to ration desired schools, or may be able to use lotteries for this
purpose. One imagines that broader programs will use some form of price system, perhaps by allowing
parents to “top up” their vouchers (Epple and Romano, 1998).
4
A second issue is that there is little or no threat of market entry when competition is
among geographically-based school districts. In the absence of entry, administrators of
undesirable districts are not likely to face substantial declines in enrollment. Indeed, a
reasonable first approximation is that total (public) school and district enrollments are
invariant to schools’ relative desirability.
5
Instead, Tiebout choice works by rewarding the
administrator of a preferred school with a better student body and with wealthier and more
motivated parents. There are obvious benefits for educational personnel in attracting an

advantaged population, and I assume throughout this chapter that the promise of such
rewards can create meaningful incentives for school administrators.
My analysis of parental choices focuses on the possibility that parents may choose
schools partly on the basis of the peer group offered. Although existing research does not
conclusively establish the causal contribution of peer group characteristics to student
outcomes (see, e.g., Coleman et al., 1966; Hanushek, Kain, and Rivkin, 2001; Katz, Kling,
and Liebman, 2001), anecdotal evidence suggests that parents may place substantial weight
on the peer group in their assessments of schools and neighborhoods. Realtor.com, a web
site for house hunters, offers reports on several neighborhood characteristics that parents
apparently value. These include a few variables that may be interpreted as measures of
school resources or effectiveness (e.g. class size and the number of computers); detailed
socioeconomic data (e.g. educational attainment and income); and the average SAT score at
the local high school. Given similar average scores, test-score maximizers should prefer

5
Poor school management can, of course, lead parents to choose private schools, lowering public enrollment.
Similarly, areas with bad schools may disproportionately attract childless families. These are likely second-
order effects. The private option, in any case, is not the mechanism by which residential choice works but an
alternative to it: Inter-jurisdictional competition has been found to lower private enrollment rates (Urquiola,
1999; Hoxby, 2000a).
5
demographically unfavorable schools, as these must add more value to attain the same
outcomes as their competitors with more advantaged students.
6
While it is possible that
parents use the demographic data in this way, it seems more likely that home buyers prefer
wealthier neighborhoods, even conditional on average student performance (Downes and
Zabel, 1997).
7

With several school characteristics over which parents may choose, understanding
which schools are chosen and which administrators are rewarded requires a model of
residential choice. I build on the framework of so-called multicommunity models in the
local public finance literature (Ross and Yinger, 1999), but I introduce a component of
school desirability that is exogenous to parental decisions, “effectiveness,” which is thought
of as the portion of schools’ effects on student performance that does not depend on the
characteristics of enrolled students. Parental preferences among districts depend on both
peer group and effectiveness, and I consider the implications of varying the relative weights
of these characteristics for the rewards that accrue in equilibrium to administrators of
effective schools.
Hoxby (1999b) also models Tiebout choice of schools, but she assumes a discrete
distribution of student types and allows parents to choose only among schools offering

6
This does not rely on assumptions about the peer effect: The effect of individual characteristics on own test
scores, distinct from any spillover effects, is not attributable to the school, and test-score-maximizing parents
should penalize the average test scores of schools with advantaged students to remove this effect (Kain,
Staiger, and Samms, 2002).
7
Postsecondary education offers additional evidence of strong preferences over the peer group: Colleges
frequently trumpet the SAT scores of their incoming students—the peer group—while data on graduates’
achievements relative to others with similar initial qualifications, which would arguably be more informative
about the college’s contribution, are essentially non-existent. Along these lines, Tracy and Waldfogel (1997)
find that popular press rankings of business schools reflect the quality of incoming students more than the
schools’ contributions to students’ eventual salaries (but see also Dale and Krueger, 1999, who obtain
somewhat conflicting results at the undergraduate level).
6
identical peer groups. I allow a continuous distribution of student characteristics, which
forces parents to trade off peer group against effectiveness in their school choices. This
seems a more accurate characterization of Tiebout markets, as the median U.S. metropolitan

area has fewer than a dozen school districts from which to choose. It leads to a substantially
different understanding of the market dynamics, as Hoxy’s assumption of competing schools
with identical peer groups eliminates the “stickiness” that concern for peer group can create
and that is the primary focus here.
As in other multicommunity models, equilibrium in my model exhibits complete
stratification: High-income families live in districts that are preferred to (and have higher
housing prices than) those where low-income families live. That this must hold regardless of
what parents value points to a fundamental identification problem in housing price-based
estimates of parental valuations:
8
Peer group and, by extension, average student
performance are endogenous to unobserved determinants of housing prices. One
estimation strategy that accommodates this endogeneity is that taken by Bayer, McMillan,
and Reuben (2002), who estimate a structural model for housing prices and community
composition in San Francisco.
I adopt a different strategy: I compare housing markets that differ in the strength of
the residential location-school assignment link, and I develop simple reduced-form
implications of parental valuations for the across-school distribution of student
characteristics and educational outcomes as a function of the strength of this link. This
across-market approach has the advantage that it does not rely on strong exclusion
restrictions or distributional assumptions. My primary assumptions are that the causal effect


8
Shepard (1999) reviews hedonic studies of housing markets
7
of individual and peer characteristics on student outcomes does not vary systematically with
the structure of educational governance; that the peer effect can be summarized with a small
number of moments of the within-school distribution of student characteristics; and that
school effectiveness acts to shift the average student outcome independent of the set of

students enrolled.
Like Baker, McMillan, and Reuben (2002), I identify parental valuations by the
location of clusters of high income families: If parental preferences over communities depend
exclusively on the effectiveness of the local schools, the most desirable—and therefore
wealthiest—communities are necessarily those with the most effective schools. If peer
group matters at all to parents, however, there can be “unsorted” equilibria in which
communities with ineffective schools have the wealthiest residents and are the most
preferred. These equilibria result from coordination failures: The wealthy families in
ineffective districts would collectively have the highest bids for houses assigned to more
effective schools, but no individual family is willing to move alone to a district with
undesirable peers.
The more importance that parents attach to school effectiveness, the more likely we
are to observe equilibria in which wealthy students attend more effective schools than do
lower-income students. Moreover, if parental concern for peer group is not too large, the
model predicts that this equilibrium effectiveness sorting will tend to be more complete in
high-choice markets, those with many small school districts, than in markets with more
centralized governance. This is because higher choice markets divide the income
distribution into smaller bins, which reduces the cost (in peer quality) that families pay for
8
moving to the next lower peer group district and thus reduces the probability that wealthy
families will be trapped in districts with ineffective schools.
Effectiveness sorting should be observable as a magnification of the causal peer
effect, as it creates a positive correlation between the peer group and an omitted variable—
school effectiveness—in regression models for student outcomes.
9
This provides my
identification: I look for evidence that the apparent peer effect, the reduced-form gradient
of school average test scores with respect to student characteristics, is larger in high-choice
than in low-choice markets. If parents select schools for effectiveness, wealthy parents
should be better able to obtain effective schools in markets where decentralized governance

facilitates the choice of schools through residential location, and student performance should
be more tightly associated with peer characteristics in these markets. If parents instead select
schools primarily for the peer group, there is no expectation that wealthy students will attend
effective schools in equilibrium, regardless of market structure, and the peer group-student
performance relationship should not vary systematically with Tiebout choice.
I use a unique data set consisting of observations on more than 300,000
metropolitan SAT takers from the 1994 cohort, matched to the high schools that students
attended. The size of this sample permits accurate estimation of both peer quality and
average performance for the great majority of high schools in each of 177 metropolitan
housing markets. I find no evidence that the association between peer group and student
performance is stronger in high-choice than in low-choice markets. This result is robust to

9
Willms and Echols (1992, 1993) are the first authors of whom I am aware to note the importance of the
distinction between preferences for peer group and for effective schools. They use hierarchical linear
modeling techniques (Raudenbush and Willms, 1995; Raudenbush and Bryk, 2002), and estimate school
effectiveness as the residual from a regression of total school effects on peer group. This is appropriate if
there is no effectiveness sorting; otherwise, it may understate the importance of effectiveness in output and in
parental choices.
9
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 data measuring high school completion rates and on the
National Education Longitudinal Study (NELS) sample.
This result calls the incentive effects of Tiebout choice into question, as it indicates
that administrators of effective schools are no more likely to be rewarded with high demand
for local housing in high-choice than in low-choice markets. To explore this further, I
estimate models for the effect of Tiebout choice on mean scores across metropolitan areas.
Consistent with the earlier results, I find no evidence that high-choice markets produce

higher average SAT scores. Together with the within-market estimates, this calls into
question Hoxby’s (1999a, 2000a) conclusion that Tiebout choice induces higher productivity
from school administrators.
10

There are three plausible explanations for the pattern of findings presented here.
First, it may be that school and district policies are not responsible for a large share of the
extant across-school variation in student performance. We would not then expect to
observe effectiveness sorting, regardless of its extent, in the distribution of student SAT
scores. Second, the number of school districts may not capture variation in parents’ ability
to exercise Tiebout choice. Results presented in Section 1.4.2 offer suggestive evidence
against this interpretation, but do not rule it out. A final explanation is that effectiveness


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Hoxby (2000a) argues that market structure is endogenous to school quality. Instrumenting for it and using
relatively sparse data from the NELS and the National Longitudinal Survey of Youth, she finds a positive
effect of choice on mean scores across markets. I discuss the endogeneity issue in Appendix B, and consider
several instrumentation strategies. As none indicate substantial bias in OLS results, the main discussion here
treats market structure as exogenous. Chapter 2 investigates Hoxby’s results in greater detail.