Functional Form Specification in the Quarterly Demand for Red Meats in Canada

Most demand studies, particularly those for food products, choose somewhat arbi-trarily either a linear or a log-linear functional form. Since choice of functional form has implications for elasticities and their properties over time, either form may be consid-ered restrictive. An empirical test of functional form in the short-run (quarterly) demand for four red meats is presented in this paper. For beef demand, neither a linear nor a log-linear form is appropriate. Similarly for pork and lamb demand, a linear functional form is not appropriate, but the log-linear one is. For veal demand, although data supported both functional forms, a linear form is preferred when seasonal influences are accounted for. Most studies of demand for food products have used two functional forms- a linear (additive) formulation, where product de-mand is hypothesized as a linear combination of specified independent variables; and, a log-linear form where the logarithm of quan-tity demanded is linearly related to the logarithms of specified independent var-iables. If one hypothesizes that the demand (QD) for a food product (k) is determined by its own price (Pk), by prices of close substi-tutes or complements (Pk') and by consumer disposable income (DI), then the determinis-tic relationships1 are written as: (1) QDkt = 3o + p1 Pkt + 32 Pk't + P3 DIt, and (2) QDkt = o3 (Pkt)1l (Pk't)12 (DIt)13 Based on economic theory, there is no a priori reason for selecting either form. Works by Eisner, Chow, and Zarembka point out Surendra N. Kulshreshtha is Professor of Agricultural Economics at the University of Saskatchewan. 'A deterministic relation refers to the deletion of the stochastic error term. such indecision between the two forms in studies of monetary theory. Choice of functional form in agricultural product de-mand studies analysis is a difficult area that has not received adequate attention in the past. 2 Either a linear specification or a log-linear specification have been commonly used. Studies 3 by Kulshreshtha and Wilson, Brandow, Kulshreshtha and Reimer, Hassa