Vouchers in a community choice model with zoning. (includes appendix)

This paper investigates the impact of voucher plans for private schools on voter support for public schools when both school and community choice are allowed. Contrary to popular opinion, voucher plans can increase voter support for public school quality in a median voter sating. In cases where the voucher plain causes migration of households toward the poorer community, there is an increase in the quality of public education in both poor and rich communities. Thus, vouchers initiated in poorer communities may raise public school quality in the entire economy.

I. INTRODUCTION

People widely recognize that the choice of community is determined in a large part by school quality. Of those parents choosing public education, 52.7 percent indicate that the public school influenced their choice of residence (National Center for Education Statistics (NCES), p. 117). How does this fact affect the consequences of school voucher plans? This paper develops a framework for addressing some features of this question. In particular, it highlights how vouchers and community choice interact to determine voter support for public school quality in local communities.

The model follows in the spirit of Epple, Filimon, and Romer (1983, 1984), but while they focus on housing and abstract from the role of schools in community choice, we do just the opposite. Sonstelie (1982), Flowers (1988), and Rangazas (1994) focus on school choice and voting for public schools but abstract from the possible interactions with community choice that we attempt to highlight here. All these efforts can be viewed as preliminary steps toward a fully integrated analysis of community choice, housing, and schooling. However, as is clear from the difficulties that arise in the simpler models, a complete model will be hard to manage technically and hard to grasp intuitively. At this stage, building an understanding of the separate components of the problem in rather abstract settings is necessary before further progress can be made. Section II compares the model of this paper to previous community choice and voting models and to what one may consider to be a "complete" model that includes all the elements mentioned above.

Sections II-V motivate and set up the model, introduce the equilibrium concept, and discuss conditions leading to existence and uniqueness of equilibrium; considerations that have proved to be difficult in both community choice models without schooling and in schooling choice models within a fixed community. While no general existence proof is offered, the sufficient conditions identified are helpful in forming a numerical simulation of equilibrium. Households make three important decisions in the model: the location of residence, the choice of schooling (public or private), and the preferred quality of public education (voting behavior). For the purpose of analyzing voucher plans, an interesting equilibrium in this setting is what we call a complete stratification equilibrium. In this case communities are stratified by wealth. Furthermore, the less wealthy members of each community choose public schooling and the more wealthy members choose private education (a property consistent with the facts (NCES 1991, pp. 27, 117). The complete stratification equilibrium allows one to consider both marginal and discrete community-specific voucher plans in rich or poor communities, or an economy-wide voucher plan that is simultaneously implemented in all communities.

Section VI provides a numerical example of a complete stratification equilibrium in a no-voucher economy. This serves as the initial baseline for the voucher experiments of Section VII.(1) Vouchers have a theoretically ambiguous effect on the internal voting equilibrium of a community of fixed size. By reducing public school attendance, vouchers both lower the median voter in the wealth distribution, thereby reducing voter support for public schooling, and lower the marginal tax price of school quality per student, thereby raising voter support for public schooling.

The effects of vouchers working through migration are more complicated and depend on the details of the voucher plan. A voucher plan initiated in a relatively poor community will tend to attract relatively wealthier households. Migration of wealthier households planning to attend private schools will reinforce both of the internal effects on voting mentioned above, implying an ambiguous effect of migration on public school quality in poor communities. Migration of these relatively less wealthy households out of the rich community will raise the median voter in the wealth distribution of the rich community and lower the attendance in the public schools of the rich community. Thus, the wealth and tax-price effects work together to unambiguously increase the quality of public schooling in the rich community.

The migration effects of a voucher initiated in the rich community depends on how vouchers impact the internal voting equilibrium. If the tax-price effect dominates the wealth effect, causing the quality of public schooling to rise, then there will be migration into the richer community. This migration out of the poor community will again have ambiguous effects on the public school quality of the poor community, but will work against the internal voting effects in the rich community by lowering the quality of public schooling there.

To resolve some of the ambiguous predictions, we carry out simulations under a reasonable calibration of the model. While the simulations are only illustrative, they do highlight some interesting empirical possibilities. The results show a rather strong negative effect of vouchers on school attendance and a small positive effect on public school quality. The possibility of a positive effect on public school quality is contrary to much public opinion.(2) In addition, while the quality effect seems small, it is sufficient to lessen the inequality between those initially demanding public education and those initially demanding private education in our model. However, this finding is only true for fairly modest voucher proposals. Once the size of vouchers reaches approximately forty percent of the initial tax payer cost of public education, public school attendance drops below fifty percent and voter support for public education collapses.

In cases where the voucher causes migration of households to the poor community, there is an increase in the quality of public schools in both communities. In cases where the voucher plan causes migration toward the rich community, there is a decrease in the quality of education in the poor community, and in the rich community relative to what it would have been without migration effects. Thus, vouchers initiated in poorer communities may raise public school quality in the entire economy, as well as narrow the differences across communities. On the other hand, vouchers initiated in rich communities may not only widen the gap in quality across communities, but may also reduce school quality in an absolute sense in poorer communities.

II. MOTIVATING THE MODEL

To understand the particular approach taken in this paper, one must begin with the key relationship affecting the quality of public schools in a community. It will be assumed throughout that there is an insufficient number of community sites to satisfy all the tastes and wealth levels of households in the economy. With an incomplete market for communities, voting for local public goods and services becomes an important and complicated process to model. The usual assumption is that the level of publicly provided goods is determined by the median voter. In the present context this implies the quality of public education, as measured by the public school teacher-pupil ratio (pi), is determined by the median voter's demand for public education.(3) The median voter demand function for (pi) in community i can be written generally as:

[pi.sup.m.sub.i] = varPi([Z.sup.m.sub.i],[gamma.sub.i]w[h.sup.m]/[h.sup.a] (0)

where [Z.sup.m.sub.i] is the median voter's wealth and [gamma.sub.i]w[h.sup.m]/[h.sup.a] is the marginal tax price of [pi] for the median voter. The marginal tax price is a function of the percentage of households (taxpayers) who send their children to public schools (gamma.sub.i), the wage rate for the public school teachers (w), and the relative share of the housing tax base owned by the median voter ([h.sup.m]/[h.sup.a], where [h.sup.a] is the average quantity of housing in the community).

There are two theoretical frameworks in the literature that allow two special cases of Equation 0 to be analyzed. The simplest case assumes [gamma.sub.i] = 1 and [h.sup.m] = [h.sup.a], which is an application of the model developed by Westhoff (1977, 1979). Here the marginal tax price is just w, which is independent of [pi] under the assumption that the local economy is "small" relative to the national economy. With a community of fixed size, [Z.sup.m.sub.t] is median community wealth and is also independent of [pi] (at least in a static model). Thus, solving Equation 0 is very simple since the right-hand-side is independent of [pi]. However, with community choice, [Z.sup.m.sub.i] becomes a function of the quality of education offered in all communities. This dramatically complicates the proof of the existence of equilibrium and the solution to Equation 0. Westhoff (1977) was able to prove existence under fairly general conditions, but later questioned whether the equilibrium would be stable and warned against doing policy analysis in such a setting. The important message of Westhoff's work is that even in the simplest possible settings, far too simple to discuss many of the interesting policy questions of local communities, a general analysis will not be possible.

Epple et al. (1983, 1984) accepted the challenge of generalizing Westhoff by allowing for endogenous housing prices and quantities. Their model allows the special case of Equation 0 with [gamma.sub.i] = 1 and [h.sup.m] [no equal to] [h.sup.a] to be examined. …