Education vouchers, the peer group problem, and the question of dropouts.

• Author: Ferris, J. Stephen

1. Introduction

   Since 1990, there has appeared a burgeoning literature, both theoretical and empirical, on the effects of school vouchers (see Hoxhy 1996; Hoenack 1997; West 1997; Hoyt and Lee 1998; Rouse 1998b). Because the use of vouchers increases the size of the private school sector at the expense of the public and because of the public policy controversy that that result has created, considerable attention has been directed at measuring the efficiency of private schools relative to public (Evans and Schwab 1995; Sander and Krautman 1995). Here the early claim in the literature--that Catholic schools "do better" (Coleman, Hoffer, and Kilgore 1982)--has driven much of the subsequent analysis and has led critics to emphasize that early results that at first sight seem favorable to Catholic schools could result from student and/or parent selection bias (Murnane, Newstead, and Olsen 1985; Neal 1997). After controlling for various selection biases (Figlio and Stone 1999), researchers have accordingly tended to find that priv ate schools (as a group) do not perform any better than do their public counterparts (Neal 1998). (1)

   Two aspects of this debate have attracted our attention. First, most participants use "student achievement" (i.e., the ability to score well on tests in math, English, science, and so on) as the benchmark for measuring educational performance and hence the basis for assessing the impact of vouchers. Our paper is both an addition to and a departure from this approach. We focus on the role of vouchers in relation to school dropouts, a somewhat different and, we believe, as important a measure of school performance. (2) Second, we have noticed that much of the evaluation of the performance of private and public schools compares only alternative benefits without invoking the caveat that efficiency issues cannot be resolved without a similar analysis of cost. Thus, while our analysis follows in this tradition by comparing only the effect of vouchers on alternative measures of education benefits, we recognize that greater voucher use may well bring about efficiency changes on the cost side that would dominate these considerations. (3)

   These comments are not to detract from the rich variety of approaches to the question of how the mix of school types affects academic performance and how vouchers relate to that mix. The current literature analyzes many issues that complement those raised in this paper. They include the role of vouchers in relation to student mobility and geographic location (Neal 1997; Hoxby 2000; Nechyba 2000), the relative performance of religious versus nonreligious private schools on high school achievement and completion rates (Figlio and Stone 1999), and the relationship between school dropouts and both teenage pregnancy (Ribar 1994) and alcohol use/ abuse (Ribar 1999).

   Our contribution to the voucher debate begins from a recent series of papers by Manski (1992), Epple and Romano (1998a, b), and Nechyba (2000), who have emphasized the presence of one particular educational spillover in the use of school vouchers--the "peer group" problem. This is an external effect that vouchers may have on public schools by helping private schools diminish the pool of higher-ability students that remain in the public system. By allowing lower-income students of high aptitude and ability to leave the public school system, it is argued, a voucher system encourages private schools to "skim the cream off" the public school system and so depreciate the average quality of students that remain behind. (4) Because the quality of education received by students is, in part, a function of the quality of their classmates, the loss of higher-ability students reduces the quality of education received by those remaining in the public system. On the other hand, private schools receiving the incoming benefi t are led by competition to internalize the externality through a fee structure that discriminates by ability (e.g., high fees to high-income students with scholarships given to higher-ability, low-income students). In this way, a voucher system, it is argued, will promote inequity across students even as it lowers education costs and improves the overall efficiency of the educational system.

   Our analysis does not deny that voucher use may further this external effect on public schools. However, it is our concern that the current focus on the inequity of the peer group effect has distracted attention from what might be an even more pressing horizontal inequity. By this we mean the effects arising from the still lower level of education received by the roughly 12% of students who drop out of the education system by the end of high school. (5) Thus, even though a voucher program may produce a deterioration in the quality of the education received by those who do not leave the public school system, a voucher program may improve horizontal equity if it helps retain within the school system more of those students who would have dropped out entirely.

   One measure of the importance of the peer group problem can be seen from the findings of the much-quoted work of Summers and Wolfe (1977).6 Using the difference in composite achievement scores between grade 3 and grade 6 as a measure of value added, Summers and Wolfe (p. 643) find that an increase in the percentage of high achievers in a student's school has two offsetting effects on student scores: one that significantly improves all students' scores and a second that reduces individual scores by an amount that depends on student ability. On net, average students were found to be largely unaffected by a peer group effect. However, students with the lowest levels of ability experienced as much as a half a year improvement in overall grade performance by the end of the three-year period, while students with the highest levels of ability were held somewhat back. (7)

   Without minimizing the significance of Summers and Wolfe's findings for low achievers, one can appreciate that the size of the peer group loss experienced by such students could be small relative to the losses experienced by potential students who did not attend school at all. It is then possible that the loss in public school achievement due to the negative peer group effect could be dominated by an offsetting educational gain. This would require a voucher program to retain a sufficient number of those students who would otherwise

   have left the school system. It is our objective, then, to reexamine vouchers from the perspective of the dropout problem and to highlight the resulting equity trade-off. We do this by extending Epple and Romano's (1998a, b) externality argument. Thus, while their analysis makes us more aware of the needs of those students who remain in the public system, the extended analysis allows us to highlight the potential benefits that vouchers can create for school dropouts in need. Becaus e the net effect will matter for an overall evaluation of a voucher program, our work also suggests that future voucher experiments should be designed to measure the effect of vouchers on the dropout rate as well as its effect on any associated peer group effect.

   Our paper incorporates dropouts in two stages. In the first part of the paper, the model of Epple and Romano (1998a, b; henceforth ER) is adapted to provide an additional rationale for voucher use. In our model, vouchers allow low-income students to escape the frustration of having to conform to the educational uniformity of the public school system by attending a private school rather than dropping out of school entirely. The reasons why students choose to drop out of school will, of course, involve more factors than simply the level of their frustration, and these factors will be discussed at length later in the paper. However, the dimension of frustration allows us an immediate and straightforward way of modifying ER's model. This means that we need not rely on lower production costs to motivate the emergence of a private school system or a reason for voucher use. (8)

   After abstractly modeling vouchers as an instrument for alleviating the dropout problem in sections 2 to 4, we turn to consider in section 5 whether greater voucher use can reduce the dropout rate. This involves a search of the education literature to see whether the greater use of the private school system could be expected to lower the dropout rate. At present, the dropout rate in the Catholic school system is lower than that of the public school system. This may arise either because private schools better provide the set of school characteristics that have been found to be most useful in reducing student dropouts or, as the more recent literature suggests, because the students and parents exercising choice have common characteristics that better match the private system. Ultimately, the size of the dropout effect relative to the peer group effect will be an empirical question. However, to the extent that voucher use can reduce the student dropout rate, it is clearly the case that the presence of a peer gro up externality is not in itself sufficient to prevent a reconsideration of the benefits of a voucher system on equity as well as efficiency grounds.

2. The Model

   In this model, we wish to motivate the emergence of a private school system from the demand rather than the supply side and so assume that private schools have no technical cost advantage relative to public schools. Similarly, we do not assume, as have others, that competition among private schools results in superior academic achievement, for example, via smaller school/classroom sizes, more student-centered learning, greater competition among schools, and so on. Rather, we assume that the private school system differs from the public only in that each private school can offer a bundle of education services to students and their parents that differs in its dimensions from the single-output mix...