Estimating school district expenditure functions under conditions of closed-end matching aid

Several studies have used ordinary least squares (OLS) to estimate school district expenditure functions for states with closed-end matching aid. The present paper demonstrates that the estimates of these studies may be inconsistent. A two-stage technique which guarantees consistent estimates is described and is used to estimate the price elasticity of expenditure for Pennsylvania school districts. The two-stage estimates indicate expenditure to be substantially more price-elastic than do the OLS estimates. The two-stage technique is appropriate for estimating any input demand or expenditure function when closed-end matching aid is involved.