PRESENCE OF STOCHASTIC ERRORS IN THE INPUT DEMANDS: ARE DUAL AND PRIMAL ESTIMATIONS EQUIVALENT?

Abstract

Duality is a very useful approach in production theory because it represents a direct and natural way to elaborate and analyze an economic problem. But the dual representation does not exist independently of the primal formulation. Although the primal approach has the advantage of an immediate and intuitive interpretation, duality can be analytically more convenient in some complex problems. But the debate about which approach best serves economists is still alive. Duality held great promise when it was popularized over 30 years ago. According to Just (2000), to capture the empirical benefits of duality both primal and dual implications of their estimates must be compared to other empirical studies, regardless of whether the estimated relationships have been derived by primal or dual approaches. This study is an attempt to illustrate the possibility that both dual and primal formulations produce good results when some empirical complications are added to the model. A data set based on some representative agent behavior is created through Monte Carlo simulation and used to estimate econometrically the primal and dual functions associated to the technology chosen. The objectives of this investigation are: first, the empirical verification of the properties of the OLS estimator for primal and dual formulations under a Hicks-Neutral technical change when there are stochastic errors in the output and input demands. Second, the policy implications when the presence of such errors is not taken into account by the policy makers.