Optimal Community Educational Attainment: A Simultaneous Equation Approach

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T HIS research provides an estimate of the demand for educational attainment across states within a framework of optimal community choice. The communi,ty is envisioned as having the ability to choose a level of educational attainment for its students which will maximize its net benefits subject to the prevailing technical relationship. The technical relationship specified in this paper considers separately the impact of school inputs, pupil inputs, and social characteristics on educational attainment. Most previous studies of the educational industry have failed to specify a structural model of educational attainment which simultaneously accounts for supply and demand factors. Those which have attempted to measure the effects of inputs on educational attainment have failed to standardize for demand conditions. Expenditure studies have either ignored supply conditions or have resulted in reduced form equations in which the structural parameters cannot be identified. McMahon (1970) estimated the relationship between expenditures and inputs using state data. His conceptual framework did not, however, permit the estimation of the price and income elasticities of demand.' Estimates of income elasticities have been made by Hirsch (1960), Brazer (1959), and Pryor (1968). Their estimates utilized a single equation expenditure function approach which failed to take account of variations in price and the simultaneous aspects of the determination of price and quantity. With the exception of a recent paper by Barlow (1970) estimates of price elasticities have not been published in studies of educational expenditures.2 While Barlow's demand function is similar in form to our own, his single equation estimation procedure ignored the effects of supply changes and thereby introduced the possibility of simultaneous equation bias. The approach utilized in this research is to take account explicitly of the simultaneous nature of demand and supply. Our conceptual framework permits the identification of both price and income elasticities as well as output elasticities for the inputs. Our price and income elasticities are statistically significant and consistent with theoretical expectations. We find that school inputs, pupil inputs, and community characteristics all have important impacts on educational attainment.