Empirical factor demands : specification, estimation and inference

Abstract

The empirical analysis of factor demands and input substitution possibilities is a typical example of the strong links between theoretical microeconomics and applied econometrics [see Bemdt (1991, chap. 9) for details]. The pioneering study by Cobb and Douglas (1928) was aimed at testing empirically the marginal productivity theory and assumed that production was related to capital and labour inputs under constant returns to scale. Economists who were interested in estimating the elasticity of substitution between two inputs extended the Cobb-Douglas production function in order to allow for an estimation of the degree of substitution between two inputs: the Constant Elasticity of Substitution production function [Arrow, Chenery, Minhas and Solow (1961)] was bom, which did not constrain this elasticity to equal unity. An approach which is alternative to the estimation of the production function uses duality theory to specify a cost function that, under some testable regularity conditions, completely summarizes the relevant features of the underlying technology [Diewert (1974)]. The dual cost function represents the solution of the optimization problem facing the firm when it has to choose inputs so that costs of production are minimized, given the level of output, input prices and the form of the production function. Moreover, the production function parameters can be recovered from direct estimation of the demand equations derived from the dual cost function. The cost function approach is based on the maintained, rather than tested, assumption that production costs and input quantities are endogenous variables, while factor prices and level of output are exogenous.