RECENT years have seen considerable progress toward an integration of the theory of consumer's choice with empirical demand analysis. Theory has been extended so as to bring dynamic adjustment and the effects of past expenditure decisions (primarily through the introduction of certain state variables) into its purview,1 while on the empirical side there now exist a number of studies whose demand functions respect to a letter the restrictions imposed by classical theory.2 Unlike the demand theorist, content to assume the existence of continuous partial derivatives through the second order and to specify the signs of first derivatives, the applied analyst must go considerably further and specify the actual analytical form of the utility function. Herein, however, lies one of the major obstacles to the continued progress in applied demand analysis, for the list of functions which are rich enough to incorporate the restrictions imposed by theory, but yet sufficiently simple to be estimated with the data and techniques at hand is not lengthy. Included in this list are: (1). The additive quadratic utility function used by Houthakker and Taylor (1970) and also by Phlips (1971); (2). The linear-expenditure system based on the Geary-Samuelson utility function employed by Stone and his associates (1954, 1965) and most recently by Phlips (1972); and (3). The Rotterdam system of demand functions developed by Barten and Theil.3 The present work was motivated initially by a desire to devise a better method of estimating the additive quadratic model (AQM) than that used by Houthakker and Taylor. In particular, H and T observed a tendency for the estimated marginal utility of income to decrease sharply at the very end of the sample period, and averred that this probably reflected a defect in the method of estimation (p. 230). However, once we began exploring this, it became clear that the defect was in the quadratic utility function itself. Accordingly, we then undertook a critical look at the appropriateness of the AQM as a tool for empirical research, and in so doing decided to do the same with the linear expenditure system (LES).

The economic effects of advertising have been a much studied and hotly debated topic for a number of years. By now, there is fairly general agreement that, inter alia, advertising is important as a barrierto-entry (see Joe Bain, William Comanor and Thomas A. Wilson, Leonard Weiss) and that advertising does succeed in shifting demand for individual products (see Neil Borden, Nicholas Kaldor, Robert Dorfman and Peter Steiner, Lester Telser (1962), Kristian Palda), but there is little agreement as to the effect of advertising on aggregate consumption. John Kenneth Galbraith would have us believe that much of consumers' spending is managed from Madison Avenue,' but such a view has still to find universal acceptance.2 What is surprising, however, is that no one who has been party to the rather spirited debate generated by the Tall Gentleman's thesis has seen fit to examine by econometric methods the proposition that advertising has an impact on the aggregate consumption function. To undertake this is the purpose of this paper. In a modest, yet not insignificant, way, we feel that we have made some progress. Based on an analysis of advertising expenditures in the aggregate, our results suggest that advertising does in fact tend to increase consumption at the expense of saving. But as to what the causal mechanism underlying this is, we unfortunately cannot say. It may be that advertising actually succeeds in altering tastes a la Galbraith, but then again it may be that advertising is simply serving to bring new goods and services to the attention of consumers. As already noted, our analysis concentrates on the effects of advertising in the aggregate, and is conducted in the framework of the state-adjustment model of Hendrik Houthakker and Lester Taylor, as applied to aggregate consumption. Following Houthakker and Taylor, two variants of the model have been employed; the first focuses on consumption, and the second on personal saving. Section I presents a brief description of the Houthakker-Taylor (H-T) model and discusses the ways that it can be extended to accommodate advertising. This section also provides a short description of the data and methods of estimation. Sections II and III are empirical, Section II being devoted to a presentation of results and Section III to their critical evaluation. The paper is then concluded with some final observations in Section IV.

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.