ADJUSTING SCHOOL AID FORMULAS FOR THE HIGHER COST OF EDUCATING DISADVANTAGED STUDENTS THOMAS A. DOWNES* & THOMAS F. POGUE** Abstract - In this paper, we consider the problem of determining the appropriate method for adjusting state aid to com- pensate for cost differentials across locali- ties. The feasibility of using cost and ex- penditure functions to estimate these adjustments is considered. Data from Ari- zona are used to determine adjustments for districts with at-risk students (students with limited English proficiency or eligible for subsidized lunch). We find districts with at-risk students face higher costs, and we show that failing to account for temporally stable effects of omitted vari- ables leads to inaccurate estimates of cost differentials. We also discuss advantages of using cost functions for determining aid. INTRODUCTION Intergovernmental aid accounts for more than one-third of the revenue of United States local governments and more than *Northwestern University, Evanston, IL 60208 **Un~vers~ty of Iowa, Iowa City, IA 52242. one-half of the revenue of school dis- tricts. One purpose of this aid is to com- pensate for differences across communi- ties (states and localities) in the cost of public services. These differences are of concern because they can lead to fiscal disparities, which arise when the taxes that individuals bear in order to have a given level of public services depend on the location of their economic activities. To be effective in reducing disparities, aid must be distributed by formulas that take account of differences in the cost of public services. That is, the granting government must have estimates of how public service cost functions differ across communities. We compare two methods for estimat- ing cost function parameters: direct esti- mation of a cost function and identifica- tion from an estimated expenditure function. This comparison is important because the two methods require differ- ent information and impose different de- grees of structure. Direct estimation of cost function parameters requires mea- sures of public sector outputs. Identifica- tion of these parameters from an esti- 89 National Tax Journal Vol. 47, no. 1, (March, 1994), pp. 89-110