Economies of Scale in Public Education: An Econometric Analysis
Chakraborty, Kalyan, Biswas, Basudeb, Lewis, W. Cris, Contemporary Economic Policy
W. CRIS LEWIS [*]
This article investigates the sources of scale economies in the production of public education. The relationship between the average cost of producing educational output and school characteristics including school and district size is estimated using a neoclassical cost function. The empirical analysis uses panel data from Utah school districts and estimates the function using the covariance and error component models after making necessary corrections for heteroskedasticity and autocorrelation. The uncorrected fixed effects model generates a significant negative coefficient on district size in both the cost and expenditure functions; the coefficient on number of students has the hypothesized sign but is not significant in either equation. After making various corrections for autocorrelation and heteroskedasticity, the coefficients have the correct signs and are significant in all equations. Thus, it is concluded that scale economies arise from both sources but that the evidence is stronger for district size . (JEL I21, D24, C23)
I. INTRODUCTION AND BACKGROUND
The rationale for the consolidation of schools and school districts  in the United States largely has been based on the expectation that it would result in a reduction in the average cost of the educational services being provided; equivalently, it was thought that there are significant economies of scale operating in the public education production function. In general, this hypothesis has been confirmed by a large body of research. For example, Riew (1966, 1986) found scale economies in the operation of high schools up to a size of 1,675 students and evidence of scale economies in elementary school operation. Cohn's (1968) study of Iowa high schools reported similar results, as did Butler and Monk (1985) in their study of school districts in New York State. Outside the United States, Bee and Dolton (1985) found that average cost declines with increasing school size in England, and Kumar's (1983) study of Canadian schools also concluded that economies of scale existed.
While most published research has confirmed the scale economies hypothesis, the work of Callan and Santerre (1990), Tholkes (1991), and Monk (1990) is less confident that additional consolidation would lead to unit cost reduction. In particular, Monk argues that further cost reduction could be achieved by schools and districts sharing regional facilities and administrative services without actual consolidation.
In this article, the existence of economies of scale at both the school and district levels is tested by estimating both a cost and an expenditure function using panel data for Utah school districts for academic years (1982-83, 1987-88, and 1992-93). Both the fixed-effects and random-effects models were considered, but the Housman test suggests that the fixed effects model is the more appropriate. The robustness of the estimation is verified by controlling for autocorrelation and heteroskedasticity.
The empirical results of the estimation procedure are generally consistent with the hypothesis that there are significant economies of scale at both the district and individual school levels, although the evidence is weaker for school size. That is, after controlling for other influences, and correcting for timewise autocorrelation and cross-sectional heteroskedasticity, the data indicate that the effect of increased size of school and district is to reduce per unit cost.
This article is organized as follows. First, the theory underlying the development of the cost and expenditure functions is outlined. Next, the data set is described and a summary of descriptive statistics presented. Then the parameter estimation procedures are reviewed and the empirical results presented. The final section includes summary comments.
II. DEVELOPING THE COST FUNCTION
The model described below was specified by Downes and Pogue (1994) in their estimation of cost functions for Arizona's elementary and secondary education system. The authors started with the standard cost function or the dual of the neoclassical production function. The conventional specification is the log-linear relation between total cost as the dependent variable and the quantity of output, input prices, and measures of attributes of the school district as explanatory variables with a stochastic disturbance term added to the equation. The problem arises when public sector output cannot be measured satisfactorily. Since output is not observable, Chambers (1978), Bradbury et al. (1984), Ladd and Yinger (1989), and Ratcliffe, Riddle, and Yinger (1990) suggest a method of estimating output as a function of some exogenous variables, one of which is the median income of families. The expenditure function is derived by substituting these variables for output in the cost function. The basic underlying assumption is that there is no lag in the adjustment between a community's actual and preferred output. Consistent estimates of the parameters in both the cost and expenditure functions are dependent on the correct measure of output and correct specification of the expenditure function.
In this study, the cost function parameters are estimated both directly and indirectly (by using the expenditure function) and compared. The comparison is important because the two methods require different information and impose different degrees of structure. Direct estimation of the cost function requires measurement of public sector outputs, while identification of these parameters from an estimated expenditure function does not require that output be measured. However, identification does require specific assumptions about how spending in the community is determined.
Each school district  can be thought of as producing a vector of outputs, Q, using a vector of inputs, X. Hence, the underlying cost function in this production relationship for community j at time t is
(1) C([cdotp]) = pX
= c(Q,p,S), such that f(x) = Q,
where C is total cost, p …
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Publication information: Article title: Economies of Scale in Public Education: An Econometric Analysis. Contributors: Chakraborty, Kalyan - Author, Biswas, Basudeb - Author, Lewis, W. Cris - Author. Journal title: Contemporary Economic Policy. Volume: 18. Issue: 2 Publication date: April 2000. Page number: 238. © 2003 Western Economic Association International. COPYRIGHT 2000 Gale Group.
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