Microdata estimation of school expenditure levels: An alternative to the median voter approach

The main purpose of this paper has been to present an alternative approach to estimating individual demand for a local public good; in this case, education. Most empirical studies of the private demand for public goods utilize the median voter framework for preference aggregation to justify the use of median values over geographical areas for the independent variables in the estimation. However, the median voter approach assumes that voter characteristics are well represented by population characteristics and that median or mean values on all independent variables can be used to describe accurately the fictional median voter. We cannot know whether the crucial voter has the median income level or other median characteristics. With the median framework we also have great difficulty in specification of a model containing household characteristics. As an alternative, this paper utilizes actual household observations from a large random sample data set for the independent variables in the estimation. While we have no way of ascertaining whether the observations in our sample are in equilibrium or are for the crucial voters in their jurisdictions, the same problems exist for the median voter representation. We can, however, know that the results are statistically reasonable and that specification and simultaneity problems are greatly reduced relative to the median voter approach. In comparing the results from the two samples, we found major differences in the coefficient estimates and in the degrees of significance of the individual ‘taste’ variables. In particular, income is insignificant in the disaggregate estimation while it is significant and positive in sign when median income is used as as the explanatory variable. Because so many studies have purported to estimate the income elasticity of public good demand, these findings, using an alternative approach, are quite important. Likewise, differences in the significance and direction of effect for number of children (particularly when the squared term is added to the specification) and age and schooling of the head of household appear between the alternative estimations. Many of the problems with the median approach are largely statistical, since the use of averages can result in aggregation bias, in the picking up of external influences unconnected to the hypothesized relationships, in simultaneous equation bias and in specification related problems. The specification problems are particularly troublesome because the high level of interrelation between the aggregate proxies makes the results extremely sensitive to model specification. Changes in the model specification lead to vastly different results in the Aggregate estimation, whereas the disaggregate results are more stable. The sensitivity of the aggregate estimates leads to problems in both the confidence in and correct interpretation of aggregate estimation results from the median voter model. These results are consistent with the premise that individuals make choices about levels of public good consumption, such as education, in a similar manner to that in which they choose their private good consumption. However, these results do not indicate who the pivotal voter is or whether that voter received his or her desired level of services. The use of disaggregate data obviates the need to assume a pivotal voter within a jurisdiction. The use of such data also allows for a less arbitrary and more precise specification of the theoretical median voter model and should be the preferred alternative when the characteristics of actual voters are unknown. Copyright Martinus Nijhoff Publishers 1982