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How Reliable is Duality Theory in Empirical Work?

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  • Rosas, Francisco
  • Lence, Sergio H.

Abstract

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.

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  • Rosas, Francisco & Lence, Sergio H., 2019. "How Reliable is Duality Theory in Empirical Work?," ISU General Staff Papers 201904010700001698, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genstf:201904010700001698
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    1. Francisco Rosas & Bruce Babcock & Dermot Hayes, 2015. "Nitrous oxide emission reductions from cutting excessive nitrogen fertilizer applications," Climatic Change, Springer, vol. 132(2), pages 353-367, September.
    2. Rosas, Juan Francisco & Lence, Sergio H., 2015. "Duality theory econometrics: How reliable is it with real-world data?," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205294, Agricultural and Applied Economics Association.
    3. Rulon D. Pope & Richard E. Just, 2002. "Random Profits and Duality," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(1), pages 1-7.
    4. Pope, Rulon D. & Just, Richard E., 1996. "Empirical implementation of ex ante cost functions," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 231-249.
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