COMPETITION IN PUBLIC SCHOOL DISTRICTS: CHARTER SCHOOL ENTRY, STUDENT SORTING, AND SCHOOL INPUT DETERMINATION

AuthorNirav Mehta
DOIhttp://doi.org/10.1111/iere.12246
Date01 November 2017
Published date01 November 2017
INTERNATIONAL ECONOMIC REVIEW
Vol. 58, No. 4, November 2017
COMPETITION IN PUBLIC SCHOOL DISTRICTS: CHARTER SCHOOL ENTRY,
STUDENT SORTING, AND SCHOOL INPUT DETERMINATION
BYNIRAV MEHTA1
University of Western Ontario, Canada
This article develops and estimates an equilibrium model of charter school entry, school input choices, and
student school choices. The structural model renders a comprehensive and internally consistent picture of
treatment effects when there may be general equilibrium effects of school competition. Simulations indicate that
the mean effect of charter schools on attendant students is positive and varies widely across locations. The mean
spillover effect on public school students is small but positive. Lifting caps on charter schools would more than
double entry but reduce gains for attendant students.
1. INTRODUCTION
The provision of school choice is often proposed as a way to improve educational outcomes
for students in poorly performing public schools. Charter schools are at the center of the recent
debate concerning education policy reforms, such as President Obama’s Race to the Top, which
rewards states that lift legislative caps on the number of charter schools; such caps are present in
most states with charter schools (White, 2009).2Policymakers would like to know how student
achievement has been affected by existing charter schools and how it would be affected if they
expanded the role of charter schools in public education. Advocates argue that charter schools
improve the performance of students attending charters (“direct effect”) and students attending
competing public schools (“spillover effect”). Critics of charter schools argue that they “cream-
skim”—that is, the better outcomes at charter schools represent student selection, not test score
gains—and that charter schools negatively affect students attending competing public schools.
The need to understand how charter schools affect student achievement has motivated a
large body of empirical work. Some of this work uses lottery designs, which estimate direct
treatment effects using oversubscribed schools (Hoxby and Rockoff, 2005; Angrist et al., 2012);
other work estimates value-added models of test score growth using panel data on students who
switch between public and charter schools (Bettinger, 2005; Bifulco and Ladd, 2006; Sass, 2006;
Hanushek et al., 2007). Bifulco and Ladd (2006), Sass (2006), Chakrabarti (2008), and Imberman
Manuscript received May 2014; revised July 2016.
1The data were provided by North Carolina Education Research Data Center. I thank Kenneth Wolpin, Hanming
Fang, and Elena Krasnokutskaya for their guidance, and the editor for many useful suggestions. I have greatly benefited
from discussions with Andrew Clausen, Tim Conley, Chao Fu, Eleanor Harvill, Lance Lochner, Rachel Margolis,
Salvador Navarro, Seth Richards-Shubik, Shalini Roy, David Russo, Panos Stavrinides, Todd Stinebrickner, Petra
Todd, and the participants in the Penn Empirical Micro lunch group and seminar. This research was supported by the
Institute of Education Sciences, U.S. Department of Education, through Grant R305C050041-05 to the University of
Pennsylvania and the SSHRC Insight Development Grant Program. The opinions expressed are those of the author
and do not represent views of the U.S. Department of Education or SSHRC. Please address correspondence to:
Nirav Mehta, Department of Economics, University of Western Ontario, London, ON N6A 3K7, Canada. E-mail:
nirav.mehta@uwo.ca.
2Though charter schools are publicly funded, and, therefore, technically a type of public school, for brevity, I typically
refer to them as “charter schools” and to traditional public schools as “public schools.” Like public schools, charter
schools cannot selectively admit students. They typically have considerably more autonomy than public schools regard-
ing personnel decisions, curricula, school hours, and pedagogical methods and often have lower per-pupil resources
due to a lack of separate capital funding streams. All students have access to a public school but not all students have
access to a charter school because charter schools enter certain areas and not others.
1089
C
(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social
and Economic Research Association
1090 MEHTA
(2011) use a variety of methods to estimate spillover effects of school choice. Estimates of direct
and spillover effects are widely mixed across studies, which is consistent with Gleason et al.
(2010), who find substantial heterogeneity in charter school impacts on attendant students.
Prior research highlights the heterogeneity of charter school effects on student achievement
but cannot provide a comprehensive evaluation of how charter school policy affects student
achievement for several reasons. First, policymakers interested in the effect of lifting caps on
the number of charter schools need a way to extrapolate findings from studies of existing charter
schools to new charter schools serving different populations of students. Second, prior studies
do not model why charter schools open in certain places but not in others (Hanushek et al.,
2007). Understanding where new charter schools would open and their effects in these areas is
crucial to the debate about lifting charter school caps. Third, increasingly popular lottery-based
designs cannot quantify the effect of all existing charter schools on student achievement because
they do not provide a way to extrapolate results from oversubscribed charter schools to those
that are not oversubscribed. The potential for bias could be large if oversubscribed charter
schools are also those that households believe will deliver stronger benefits. Fourth, although
several authors have quantified spillover effects, none have provided a coherent framework
that uses estimates of bias from spillovers to adjust estimated direct effects of school choice
(e.g., Cullen et al., 2006). This could be important if a charter school improved outcomes for all
students but students remaining at the public school benefited more than did those attending
the charter, in which case a lottery-based design would find a negative direct effect.
This article develops and estimates an equilibrium model of competition between charter
and public schools to confront these issues. It does so by modeling three key components
of the school choice debate: student school choices, charter and public school inputs, and
charter school entry decisions. The model incorporates selection on student ability in two
ways: Charter school entry decisions take into account market-level ability distributions and,
within markets, student sorting is a function of heterogeneous student ability and inputs at both
charter and public schools. Modeling student school choices as a function of both student and
school characteristics allows for generalization of estimates based on existing charter schools
to charter schools that might enter in new markets were caps lifted, even in the presence of
student sorting on unobserved ability. The model of school input choices allows charter schools
to have heterogeneous treatment effects across markets through variation in input provision
and also predicts what inputs for public schools would have been in the absence of charters,
which is necessary to properly quantify spillover effects. The equilibrium framework provides
an internally consistent method to quantify both spillover effects and the bias introduced when
one ignores equilibrium responses by public schools, unifying the two strands of the literature
where authors either estimate the direct effect of charter schools or use different students and
schools to estimate spillover effects on public school students. By modeling charter school
entry, it is possible to quantify how many more charter schools would open and in which
markets they would open were caps lifted, which is important if the effects of charter schools
are heterogeneous across markets. This article also estimates the extent to which peer ability
affects student achievement at public and charter schools, meaning that the model allows for
spillovers through changes in both student ability and public school input choices.
The model is estimated using maximum likelihood on administrative data from the North
Carolina public school system. The data contain the universe of schools and students in the
North Carolina public school system from 1998 to 2001 and include variables that enable
estimation of the model’s demand and supply sides, such as public and charter school locations,
charter school entry decisions, and detailed per-pupil school resources, which enter the model
as a per-pupil capital index. The school attended typical weekly hours of homework reported
done and standardized test scores are recorded for each student in each year. The data also
contain student locations, which enter the model through a distance cost of attending a school,
shifting the probability a student will attend a charter school. Student-level distance data are
aggregated into market-level distance distributions, which affect ability sorting and provide
variation to identify peer effects.

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