Aggregation and Arbitrage in Joint Production

Abstract

Two common problems in econometric models of production are aggregation and unobservable variables. Many production processes are subject to production shocks, hence both expected and realized output is unknown when inputs are committed. Expectations processes are notoriously difficult to model, especially when working with aggregated data or risk-averse decision makers. Duality methods for the incomplete systems of consumer demand equations are adapted to the dual structure of variable cost function in joint production. This allows the identification of necessary and sufficient restrictions on technology and cost so that the conditional factor demands can be written as functions of input prices, fixed inputs, and cost. These are observable when the variable inputs are chosen and committed to production, hence the identified restrictions allow ex ante conditional demands to be studied using only observable data. This class of production technologies is consistent with all von Neumann-Morgenstern utility functions when ex post production is uncertain. We then derive the complete class of input demand systems that are exactly aggregable, can be specified and estimated with observable data, and are consistent with economic theory for all von Neumann/Morgenstern risk preferences. We extend this to a general and flexible class of input demand systems that can be used to nest and test for aggregation, global economic regularity, functional form, and flexibility. The theory is applied to U.S. agricultural production and crop acreage allocation decisions by state for the years 1960–1999. Ongoing work includes applying this model to a recently updated data set created by the USDA/ERS through 2004 and estimating the intensive and extensive margin effects for state-level crop production with a stochastic dynamic programming model of risk aversion, asset management, and adjustment costs.

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