Application of flexible functional forms to substitutability among metals in U.S. industries

This report looks at the use of a new functional form - the Symmetric Generalized Mcfadden Cost Function (SGM) - to estimate substitutability among metals in five U.S. industries. The SGM specification has the advantage of imposing curvature conditions globally on the cost function, thus ensuring that the results satisfy basic, widely believed economic theory. For the first time, this study assumes separability in estimating an SGM system, and experiments with a"bootstrapping"technique to estimate the standard errors of parameters derived from flexible functional forms. The paper provides empirical evidence of structural change in U.S. industry. A jump in the own-price elasticities of energy during the sample period coincided with a sharp increase in oil prices. The SGM flexible functional form found aluminum and steel to be complementary in four out of five industries but suggests that they are substitutes in the technically compensated sense: when total metals use is constant, an increase in the price of one metal reduces consumption of that metal and increases consumption of the other. Use of the bootstrapping technique provided insights into the stability of the elasticity estimates. The results are promising at the aggregate level when the number of free parameters is not large compared to the sample size. Bootstrapping also clarifies the problem at the disaggregated level where most elasticities are not significantly different from zero.