Estimating Substitution and Expansion Effects: Reply

Abstract

Hertel's major point is that some of my estimates (Lopez) would violate predicted outcomes based on economic theory. These outcomes correspond to the so-called normal case as discussed by Hicks and others. Two types of normal outcomes are violated by my results, namely the gross input complementarity condition and the requirement that gross or Marshallian own-price elasticities need to be larger (in absolute values) than compensated or Hicksian elasticities. The gross complementarity condition does not follow from the theory of the profit-maximizing firm. It rather arises from assumptions regarding second derivatives of the production or transformation functions (i.e., cross-second derivatives among inputs are positive). The second set of conditions does follow from the theory of the firm, and its violation may suggest inconsistency between the estimated results and the underlying model. Therefore, these two sets of conditions are based on fundamentally different sources: the former depends on superimposed assumptions about the production technology on the profit maximization model, while the latter is inherent to the model. Hence, the evaluation of estimated elasticities using the first set of conditions is a dubious procedure since there is no a priori reason to assume that the technological assumptions underlying these conditions are of general validity, particularly in the multi-input, multi-output context.' Rather, the more reasonable approach would be to use empirical estimates to verify the degree of generality of such assumptions. With respect to the second set of conditions, I believe that they constitute sensible criteria for the evaluation of empirical estimates that are based on the profit-maximizing model. Their violation may reflect that the profit-maximizing model is inadequate, data problems, aggregation problems, etc. In my estimates this condition is not satisfied by the land and structures input when its own-price elasticities are evaluated at mean values of the variables. As discussed in the 1984 article (p. 364) the land and structures input is likely to suffer from measurement problems. It appears that the adjustments for land and structure quality were insufficient mainly due to the lack of data on qualitative aspects of structures. It is also interesting to indicate, however, that this condition is not violated at all sample points. In fact, when the elasticities are evaluated at about 25% of the sample points, the own gross-price elasticities of land and structures are greater in absolute value than the compensated elasticities, as the profit-maximization hypothesis implies.