Which median voter?

• Author: Turnbull, Geoffrey K.
• Position: On the appropriate definition of 'median income'

1. Introduction

   Under the median voter model the demand for local government spending is a function of the median voter income and median tax price of spending in the jurisdiction. The theory provides a convenient framework for analytically aggregating the individuals' public spending demands into a community public demand function.(1) It does not, however, provide guidance when selecting the proper definition of "median" income and tax share variables in empirical models. Data availability often dictates the selection of empirical proxies in applications, but the question nonetheless remains: is the appropriate empirical proxy median family income, median household income, or some other median income measure? This paper addresses this and related questions concerning the specification of empirical expenditure functions for local governments.

   The median voter model has proved to be an enduring device in public economics. But even while it continues to be widely used in both theoretical and empirical studies of local government spending behavior, the median voter model itself has become the focus of study. Although various specifications and modifications have been examined and compared in the literature, the question of the appropriate median definition in empirical models has been overlooked thus far.

   The usual methods of testing competing specifications in the local public spending literature is to evaluate prediction errors or the sign of key parameters in an estimated expenditure function [4; 6; 9; 11; 14; 19]. The nature of our question, however, requires a different type of test, one capable of evaluating competing hypotheses that entail mutually exclusive functional forms or sets of regressors. The Cox test represents an appropriate procedure for evaluating the competing median definitions and related functional form questions in this paper.

   This test, based on theoretical results by Cox [2; 3], has several advantages in our application. First, the test is tractable and the statistics have well-defined properties; the asymptotic distribution of the calculated statistics are known, thereby avoiding the use of bootstrap or other simulation methods in our evaluation. Second, the test allows for bilateral rejection, so that we can reject both median definitions if their performance is equally poor relative to an unspecified alternative definition. The possibility of bilateral rejection is an important characteristic which allows us to test each median definition against a broader class of alternatives than the specific definitions used in this paper. Third, the test criteria is very strict in practice, so that we may have confidence in hypotheses that do stand up to the alternatives [17, 692].

   In this paper we estimate reduced form expenditure functions and apply the Cox test using county expenditure data from five Midwestern states. We find that the median family and median household income definitions are statistically distinguishable in the most popular form of the model. Further, the importance of the test results is illustrated by observed parameter estimate sensitivity to median voter definition. The Cox test also demonstrates that, for county spending in this sample, the empirical models which impose income-aids symmetry dominate those which do not for both median definitions. Finally, our conclusions are robust for total spending as well as individual spending categories.

   The paper is organized as follows. Section II presents the empirical models, data, and expenditure function estimates under the alternative median voter definitions. Section III explains the testing procedure and performs the tests to evaluate the competing model specifications. The sensitivity of the results to expenditure aggregation is examined in Section IV. Section V presents the conclusion.

2. Empirical Expenditure Models

   We use the simplest median voter hypothesis as a starting point. Community fiscal behavior is fully represented as if it reflects the choices of the median voter, identified as that with the median income and facing the median tax price. The model implies that public expenditure, G, is a function of the median tax share, [t.sub.m], median income, I, intergovernmental aid receipts, A, jurisdiction population, N, and population density, D. Using the popular logarithmic specification [12], the estimable expenditure function is:

   ln [G.sub.i] = [[Alpha].sub.0] + [[Alpha].sub.1] ln [t.sub.mi] + [[Alpha].sub.2] ln([I.sub.i] + [t.sub.mi][A.sub.i]) + [[Alpha].sub.3] ln [N.sub.i] + [[Alpha].sub.4] ln [D.sub.i] + [[Epsilon].sub.i] (1)

   where [[Epsilon].sub.i] is a stochastic error term. Income and aid are aggregated as I +...