Translog Flexible Functional Forms and Associated Demand Systems
Laurits Christensen, Dale Jorgenson, and Lawrence Lau (hereafter C-J-L) have introduced translog direct and indirect preferences and the associated systems of demand functions (see also -Jorgenson and Lau). These preferences are of interest for their own sake but are especially significant because of their properties as a flexible functional form. It is argued that they can represent arbitrary wellbehaved preferences in the neighborhood of a given point with an accuracy of the second order. This suggests, as Lau has claimed in his 1974 paper, that concern directed towards precise functional specification may be misplaced since a flexible functional form can always be used. Moreover C-J-L proposed a new methodology for testing the implications of demand theory. They calculate the restrictions on the approximating translog function corresponding to the restrictions that demand theory imposes on unknown true preferences at any given point of approximation. They then proceeded to test these restrictions on the approximating translog demand functions. The purpose of this paper is to examine this proposed methodology and the properties of the indirect translog system. The main results are: (a) With a utility approximation it is not theoretically possible to discriminate between the hypothesis that translog preferences hold globally and the hypothesis that the true (but unspecified) preferences satisfy integrability conditions at the base point of approximation. (b) It is possible to define equally accurate approximations at the level of the demand equations or at the level of the marginal rates of substitution which do permit this distinction and which involve different parameter restrictions within the same estimating form. It is thus not possible to test the restrictions of demand theory on true preferences at a given point independently of the method of approximation selected. (c) These alternative approximations also have the advantage of allowing distinct tests of homogeneity and symmetry. (d) Empirically, homogeneity of degree zero of the budget shares is a more questionable hypothesis than integrability of either the true demand system or the approximate demand system. (e) The proposed methodology has important econometric implications.
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