Does Duality Theory Hold in Practice? A Monte Carlo Analysis for U.S. Agriculture

The Neoclassical theory of production establishes a dual relationship between the profit value function of a competitive firm and its underlying production technology. This relationship, usually referred to as the duality theory, has been widely used in empirical work to estimate production parameters without the requirement of explicitly specifying the technology. We analyze the ability of this approach to recover the underlying production parameters and its effects on estimated elasticities and scale economies measurements, when data available for estimation features typical realistic problems. We design alternative scenarios and compute the data generating process by Monte Carlo simulations, so as to know the true technology parameters as well as to calibrate the dataset to yield realistic magnitudes of noise. This noise introduced in the estimation by construction prevents duality theory from holding exactly. Hence, the true production parameters may not be recovered with enough precision, and the estimated elasticities or scale economies measurements may be more inaccurate than expected. We compare the estimated production parameters with the true (and known) parameters by means of the identities between the Hessians of the production and profit functions.