On Approximating the Statistical Properties of Elasticities

Abstract

Empirical studies of consumer demand or of factor demand have now moved far beyond the Cobb-Douglas functional form and elasticities of interest are no longer estimated as parameters of the system. Instead, such elasticities are typically non-linear functions of the parameters that have been estimated and it is natural to want to be able to say something about the statistical properties of such elasticities. One way of dealing with this is to linearly approximate the elasticity formulas (in terms of the estimated parameters) and use classical statistical procedures to get approximations to the underlying variances. If y-f(x) and x has a variance covariance matrix V, the linear approximation is given by: Var(y) (8f/8x)V(8f/8x). The data needed for such an approximation are estimates of the parameters and of the associated variance-covariance matrix. Some of the earliest references that we have found to uses of this approximation technique in the elasticity context are to Griffin and Gregory (1976), Griffin (1977), and Fuss (1977), while the earliest references to