Duality theory econometrics: How reliable is it with real-world data?

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, commonly referred to as 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. We compute the data generating process by Monte Carlo simulations such that the true technology parameters are known. Employing widely used datasets, we calibrate the data generating process to yield a dataset featuring important characteristics of U.S. agriculture. 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. We conclude that, when the dataset bears minimum sources of noise, duality theory is able to recover the true parameters with reasonable accuracy. Also, that when it is employed in time series coming from an aggregation of technologically heterogeneous firms, the parameters recovered are close to the firm at the median of the distribution. The proposed calibration sets the basis for analyzing the performance of duality theory approaches when datasets used by practitioners are subject to other observed and unobserved sources of noise.