Elasticities of factor substitution in the production of education

Abstract

This paper uses data from the state of Michigan and a translog cost function to estimate and compare three measures of elasticities of factor substitution — Allen, Morishima and Shadow — in the production of education. We find that the magnitudes of the calculated values of each of the three elasticities are different from the others. While theoretically, the three measures of elasticities of substitution differ from each other, we find that all three calculated elasticities of factor substitution classify all inputs as substitutes. Differences among the different measures of elasticities of substitution are consistent with our finding that the education production function is not of the Cobb-Douglas functional form — a functional form that makes all three measures of elasticities of factor substitution equivalent.