How Reliable is Duality Theory in Empirical Work?

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, such as elasticities and returns to scale, without the requirement of explicitly specifying the parametric form of the production function. We generate a pseudo-dataset by Monte Carlo simulations, which starting from known production parameters, yield a dataset with the main characteristics of U.S. agriculture in terms of unobserved firm heterogeneity, decisions under uncertainty, unexpected production and price shocks, endogenous prices, output and input aggregation, measurement error in variables, and omitted variables. Production parameters are not precisely recovered when performing econometric estimation based on the duality approach, and the elasticity estimates are inaccurate. Deviations of own- and cross-price elasticities from initial median values, given our parameter calibration, range between 6% and 229%, with an average of 71%. Also, own-price elasticities are as imprecisely recovered as cross- price elasticities. Sensitivity analysis shows that results still hold for different sources and levels of noise, as well as sample size used in estimation.