固定效应的分位数回归估计--经典

Private school vouchers and student achievement:A

fixed effects quantile regression evaluation ☆

Carlos Lamarche ⁎

Department of Economics,University of Oklahoma,321Hester Hall,729Elm Avenue,Norman,

OK 73019,United States

Available online 3May 2008

Abstract

Fundamental to the recent debate over school choice is the issue of whether voucher programs actually improve students'academic ing newly developed quantile regression approaches,this paper investigates the distribution of achievement gains in the first school voucher program implemented in the US.We find that while high-performing students selected for the Milwaukee Parental Choice program had a positive,convexly increasing gain in mathematics,low-performing students had a nearly linear loss.However,the program seems to prevent low-performing students from having an even bigger loss experienced by students in the public schools.

©2008Elsevier B.V .All rights reserved.

JEL classification:I21;I28

Keywords:School choice;V ouchers;Milwaukee;Fixed effects;Quantile regression

“While we celebrate those [students]doing well,we can't turn a blind eye to those who are not ”Rod Paige,US secretary of Education,to the NY Times.

Available online at

Labour Economics 15(2008)575–

590

☆Version:March 31,2008.This paper is based on Chapter 2of my dissertation “Quantile Regression for Panel Data ”at the University of Illinois at Urbana-Champaign.I especially thank my advisor Roger Koenker for advice and detailed comments.I am grateful to Dan Bernhardt,Greg Burge,Todd Elder,Lynn Gottschalk,Kevin Hallock,Kangoh Lee,Darren Lubotsky,as well as labor lunch participants at the University of Illinois at Urbana-Champaign and seminar participants at Texas Tech and the 2007Annual Meetings of the European Association of Labour Economists.I thank Professor Cecilia Rouse for providing the Milwaukee Parental Choice program's data.I would like to thank the Guest Editor as well as two anonymous referees for their very helpful comments.⁎Tel.:+14053255857.

E-mail address:lamarche@

.

0927-5371/$-see front matter ©2008Elsevier B.V .All rights reserved.

doi:10.1016/beco.2008.04.007

576 marche/Labour Economics15(2008)575–590

1.Introduction

Fundamental to the recent debate over school choice is the issue of whether voucher programs actually improve students'academic achievement,while decreasing inequalities between the best and worst ton Friedman's proposal to use vouchers as a method of improving the quality of education is based on the idea that private schools are more productive than public schools,which is still a highly controversial issue.If private schools are in fact more efficient than public schools,governments can improve the quality of education by offering tuition vouchers to families that want to send their children to private schools.The Milwaukee Parental Choice program,the first program implemented in the US,has been providing vouchers to low-income students to attend private school since1990.

The simplicity of the program's idea contrasts sharply with the complexities that plague the program's evaluation.The voucher programs'effect,for example from time t to t',is the difference between what would have happened at time t'if the student was selected and remained in a choice school during the time interval,and what would have happened at time t'if the student was not selected,and remained in the Milwaukee public school.This counterfactual exercise is impossible to obtain using observational data(Rubin,1974).It may be possible,however,to construct groups using a randomized experiment(e.g.,children randomly assigned to attend choice schools and to attend public schools).At time t',the difference between students' academic performances could be attributed to the type of school since the initial assignment was random.However,the Milwaukee Parental Choice program was not implemented under idealized conditions(Witte,2000),and therefore the selection of the control group plays a major role.

Given the lack of a valid control group,it is not surprising that previous empirical studies have delivered mixed findings.Rouse's(1998)seminal study used a sample of students in the Milwaukee public schools as a comparison group and individual fixed effects to control for latent characteristics,such as more motivated parents or student abilities that may differ between treatment and comparison groups.The presented approach builds upon Rouse by employing a newly developed fixed effects form of quantile regression that not only controls for unobserved individual heterogeneity,but also allows an examination of the program effects at different points of the educational attainment distribution.

The empirical literature(e.g.,Witte,1997;Green et al.,1997;Rouse,1998)has focused upon estimating how the selection to attend the Milwaukee choice schools affects mean test scores. This approach to evaluation may be incomplete for policy analysis of programs serving heterogeneous students.To illustrate,if a stated policy goal is to raise students'achievement to a predetermined minimum standard,it may not be optimal to pursue a program that benefits strong students while causing weaker students to fall further behind.Because education is expected to play an important role in mitigating inequality,“the distribution of achievement gains... constitutes an appropriate criterion for evaluating a school choice intervention”(Howell and Peterson,2002).This paper focuses on the estimation of the selection to attend choice schools on the entire distribution of test scores,considering patterns of achievement in terms of quantiles.

There are important reasons why economists,educators,and policy makers are interested in how voucher programs affect students'achievement beyond the mean effect,which is typically estimated with Ordinary Least Squares(OLS)or Instrumental Variables(IV).First,the standard methodology may miss how a policy affects achievement differently at different points of the conditional test score distribution,as illustrated in Eide and Showalter(1998).Second,the possibility that vouchers may increase the differences between high-and low-performing students in the private schools,concern notably reflected in Ascher,Fruchter,and Berne(1996)question