Efficient Estimates of a 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 duality theory, 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 argue 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 our general specification. The theory of the price-taking cost-minimizing, risk-neutral firm is based upon the expectation of prices and quantities as the relevant information used by the entrepreneur in making her decisions. The econometrician intervenes later on and collects information about those quantities and prices. In so doing, measurement errors creep into the econometric specification. A two-phase procedure is suggested to implement the primal-dual approach. A Monte Carlo analysis indicates that our primal-dual approach produces estimates that exhibit a smaller variance of the estimates than those obtained from either the traditional primal or the dual specification separately implemented. A bootstrapping approach is used to compute the standard errors of the model’s estimates.