Conditional factor demands

Abstract: This paper presents an econometric analysis of factor demands in the Norwegian primary aluminium industry using annual plant-level panel data. The translog cost function approach is applied, and a multivariate error-correction model of the cost shares of labour, raw materials and electricity is estimated. Capital is assumed tobe quasi-fixed. The hypothesis of fixed input coefficients is rejected for this industry, but the estimated own-price and cross-price elasticities suggest that relative price variations have limited effect on conditional factor demands.

Abstract: The purpose of this note is to provide an exhaustive reference for those interested in learning more about the Constant Elasticity of Substitution (CES) function and its use in the representation of producer behavior in the GTAP model. Particular attention is paid to the role of technical change variables and their effect on cost minimizing demands and input shares. This note is divided into three sections. In the first section, the basic cost minimization problem is laid out and conditional factor demands, as well as the unit cost function, are derived. In section two, this system of equations is expressed in terms of proportional changes, as currently specified in GTAP. This greatly facilitates decomposition of predicted changes in demands and costs between three effects, namely expansion, substitution, and technical change effects. Section two also shows the relationship between changes in cost shares and changes in prices and factor-biased technical change variables. Finally, section three relates these derivations to the notation employed in GTAP.

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.

Abstract: This paper examines a generalization of cost-production duality for regulated firms. It derives an equivalency between the production function and conditional factor demands for the case where the firm's optimization problem is subject to a set of additional (regulatory) constraints. This procedure is extended to an optimization problem within a dynamic framework which leads to the recovery of the firm's technology.