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Flexible Functional Forms and Global Curvature Conditions

W. E. Diewert
T. J. Wales

Abstract

Empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions. Lau and Gallant and Golub have worked out methods for imposing the appropriate curvature conditions locally, but those local techniques frequently fail to yield satisfactory results. We develop two new methods for imposing curvature conditions globally in the context of cost function estimation. The first method adopts Lau's technique to a generalization of a functional form first proposed by McFadden. Using this generalized McFadden functional form, it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally. The second method adopts a technique used by Diewert, McFadden, and Barnett, who is based on the fact that a nonnegative sum of concave functions will be concave. Our various suggested techniques are illustrated using the U.S. manufacturing data utilized by Berndt and Khaled.