How Reliable is Duality Theory in Empirical Work?

24 Pages Posted: 21 Apr 2020

See all articles by Francisco Rosas

Francisco Rosas

affiliation not provided to SSRN

Sergio H. Lence

Iowa State University - Department of Economics

Date Written: April 2019


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. 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 690%, with an average of 90%. 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, and sample size used in estimation.

Keywords: Data aggregation, duality theory, endogeneity, firm heterogeneity, measurement error, Monte Carlo simulations, omitted variables, uncertainty

Suggested Citation

Rosas, Francisco and Lence, Sergio H., How Reliable is Duality Theory in Empirical Work? (April 2019). American Journal of Agricultural Economics, Vol. 101, Issue 3, pp. 825-848, 2019, Available at SSRN: or

Francisco Rosas (Contact Author)

affiliation not provided to SSRN

No Address Available

Sergio H. Lence

Iowa State University - Department of Economics ( email )

260 Heady Hall
Ames, IA 50011
United States

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