A Nonlinear Generalized Additive Error Model of Production and Cost

In 1944, Marschak and Andrews published a seminal paper on how to obtain consistent estimates of a production technology. The original formulation of the econometric model regarded the joint estimation of the production function together with the first-order necessary conditions for profit-maximizing behavior. In the seventies, with the advent of econometric duality, the preference seemed to have shifted to a dual approach. Recently, however, Mundlak resurrected the primal-versus-dual debate with a provocative paper titled “Production Function Estimation: Reviving the Primal.” In that paper, the author asserts that the dual estimator, unlike the primal approach, is not efficient because it fails to utilize all the available information. In this paper we demonstrate that efficient estimates of the production technology can be obtained only by jointly estimating all the relevant primal and dual relations. Thus, the primal approach of Mundlak and the dual approach of McElroy become nested special cases of the general specification. In the process of putting to rest the primal-versus-dual debate, we solve also the nonlinear errors-in-variables problem when all the variables are measured with error.