Residential Choice and the Demand for Public Education: Estimation Using Survey Data

Residential Choice and the Demand for Public Education: Estimation Using Survey Data

Description

The demand for publicly supported primary and secondary education has received the attention of economists for a long period of time. Yet only recently in the work of Gramlich and Rubinfeld (1982) and Bergstrom, Rubinfeld and Shapiro (1982) have individual survey responses (for a sample of Michigan citizens) been used to expand the scope of that study. This paper provides an overview of the econometric issues involved in the survey approach, and an expanded discussion of the relationship between community choice and the demand for local publicly supported education. Most studies of the demand for public goods use aggregated data (school district, community, etc.) and rely heavily on the assumptions of the median voter model. Following the example set by Bergstrom and Goodman (1973) and Borcherding and Deacon (1972), the analyses presume that community public expenditures are at the level demanded by the median voter, usually the “individual” with median income living in a median-valued house. If a restrictive set of distributional conditions are met, a regression of actual expenditure levels on income, tax price and other sociodemographic variables generates estimates of the parameters of the demand function. Highlighted by a recent paper by Goldstein and Pauly (1981), the median voter papers have come under attack. Goldstein and Pauly have shown that the median voter model will yield biased parameter estimates if individuals sort themselves into communities in part on the basis of their public goods preferences. Although the strength of the influence of public services on migration decisions is unknown, environmental factors are thought to play some part in residential choice. The survey approach offers an alternative which avoids the median voter assumption and which can account econometrically for the sorting of individuals into communities. The approach requires household interview data such as those obtained from the 1978 survey of Michigan residents and used in the papers by Gramlich, Rubinfeld and Bergstrom, Rubinfeld and Shapiro. The survey provides two distinct types of information, each of which can improve the prospects for estimating demand parameters. The first type is the detailed description of the individual, which in the survey approach can be distinguished from the average characteristics of the community or school district in which the individual resides. The second type is the individual's attitude towards public spending, which allows individual demands to be distinguished form average community demands. Each type of information can be used to generate alternative estimates of the demand for publicly supported education. The first alternative analyses the demand for publicly supported education as one would a private market good, but uses the detailed survey-based information describing individual characteristics. The survey tells each respondent's school district, from which the level of per-pupil expenditure on public education can be obtained. A regression of per-pupil public expenditures on personal and community characteristics yields an estimated demand function. In this paper, the results obtained from such a regression are reported solely for comparison purposes since the parameter estimates are subject to two sources of bias. The first arises because individuals may not consume the level of public spending on education that exactly equals their quantity demanded. The second difficulty arises because the actual public expenditure on education and the tax-price that individuals pay for publicly supported education may be jointly determined random variables. Failure to account for this joint determination will lead to simultaneous equations bias. The second alternative approach to demand estimation takes advantage of opinions that were obtained during the survey. Respondents were asked whether they wanted more, the same or less spending on publicly supported education after being made aware of the tax consequences of their actions. A model can then be developed in which the responses depended on the underlying personal demand (a latent variable). Probit and/or logit estimation can be used to estimate this model as reported in Bergstrom, Rubinfeld and Shapiro (1982), hereafter BRS. Since the publication of that paper we have become convinced that the probit estimators may be subject to a set of problems similar to the regression approach. Elsewhere we have shown that if preferences for education play a part in community choice, the discrete variable estimation of BRS can yield inconsistent parameter estimates. This “selectivity” bias has been studied extensively by Heckman (1979), Amemiya (1978), and others. Heckman's technique for correcting for selectivity involves the calculation of a “Mills ratio” reflecting an expected probability of selection from a probit estimation of discrete selection alternatives. This ratio is then used as an added explanatory variable in a regression with a continuous dependent variable. For example, a wage rate regression might be adjusted for selection bias relating to the choice of whether to work or not. Our approach, and also described independently by Rivers and Voung (1985), reverses the Heckman procedure. First, the residual from a regression using the continuous dependent variable (in our case actual public expenditure) and a number of explanatory variables is calculated. The residual is then used in a probit estimation of the probability of the more, same, less responses to obtain information about the latent desired demand variable. The resulting estimators are consistent and efficient under the null hypothesis of no bias. It is therefore possible to use asymptotic t-tests and likelihood ratio values to test tor selectivity effects. This paper describes one aspect of the [Rubinfeld, Shapiro and Roberts] approach which allows for both selectivity and simultaneous equation bias. The residuals from a reduced form simultaneous equation model of expenditure and tax price are included as variables in a probit equation of the more, less, same response probabilities. The resulting estimators are consistent and efficient under the null hypothesis of no selectivity or simultaneity effects. For reasonable specifications the resulting hypothesis tests reject the null hypothesis. The estimates of the selectivity and simultaneity parameters allow us to calculate the bias associated with the simple regression estimators of demand. When the regression parameters are corrected for bias, the corrected values are remarkably similar to the corrected probit values.

Source Publication

Behavioural Modelling in Geography and Planning

Source Editors/Authors

Reginald G. Golledge, Harry Timmermans

Publication Date

1988

Residential Choice and the Demand for Public Education: Estimation Using Survey Data

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