Evaluating the adequacy of parametric functional forms in estimating monotone and concave production functions

We consider situations where the a priori guidance provided by theoretical considerations indicates only that the function linking the endogenous and exogenous variables is monotone and concave (or convex). We present methods to evaluate the adequacy of a parametric functional form to represent the relationship given the minimal maintained assumption of monotonicity and concavity (or convexity). We evaluate the adequacy of an assumed parametric form by comparing the deviations of the fitted parametric form from the observed data with the corresponding deviations estimated under DEA. We illustrate the application of our proposed methods using data collected from school districts in Texas. Specifically, we examine whether the Cobb-Douglas and translog specifications commonly employed in studies of education production are appropriate characterizations. Our tests reject the hypotheses that either the Cobb-Douglas or the translog specification is an adequate approximation to the general monotone and concave production function for the Texas school districts.