# Estimating the GFT Form

## Abstract

Empirical tests of the Slutsky property of demand functions tend to dis-confirm fixed preference utility theory. In particular we refer to the tests of the Slutsky property by Christensen, Jorgenson and Lau (1975); Barten and Geyskens (1975); Theil (1975); Berndt, Darrough and Diewert (1977a, 1977b, 1977c); Rosen (1978); Lau, Lin and Totopoulous (1978); Conrad and Jorgenson (1979a, 1979b) and Deaton and Muellbauer (1980b). By ‘fixed preference utility theory’ we mean theory based on the assumption that, apart from random disturbances, consumers’ preferences are constant and, in particular, they do not depend on prices *p* _{ j } paid for commodities or on total expenditure, *M*, (*i.e.* there is no preference-changing variable such that (1.4) is not equal to zero). Systems of demand functions derived from fixed preference utility theory always possess the *Slutsky property* as outlined in Chapter II and depend solely on current prices paid and total expenditure. If a system of demand functions contains a systematic variable other than prices and total expenditure, or if it does not possess the Slutsky property, then the underlying direct utility function cannot be a fixed preference utility function, *cf.* Basmann and Slottje (1985, 1987).

## Keywords

Utility Function Demand Function Total Expenditure Marginal Rate Conspicuous Consumption## Preview

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## References

- 1.The authors mentioned in this section used expenditure and price data from various countries and different commodity groups. Christensen, Jorgenson, and Lau (1975) used U.S. data as did Rosen (1978). Blanciforti and Green (1984) also worked with U.S. data. Deaton and Muellbauer(1980b) used British data in their study while Lau, Line, and Totopoulous (1978) did Barten and Geyskens (1975) in their study. Theil (1975) used Dutch data and Barten and Geyskens did part of their study with Dutch data too. Finally, Berndt, Darrough, and Diewert (1977) used Canadian data. Christensen, Jorgenson, and Lau (1975, p. 380) using the translog functional form, flatly reject homogeneity and symmetry. Berndt, Darrough, and Diewert (1977) examined three functional forms; the translog indirect utility function (TL), the generalized Leontief indirect utility functional form (GL), and the generalized Cobb-Douglas indirect utility functional form (GCD). They reject symmetry for (GCD) and (GL) [Berndt,
*et.al.*, 1977, p 663] and reject homogeneity for all three forms[Berndt,*et.al.*, p. 664]. Rosen (1978) used the Stone-Geary utility function and rejected symmetry [p. 5129]. Conrad and Jorgenson (1979) used the translog direct and indirect utility functions and they rejected homogeneity in the indirect form [Conrad et.al., p. 163]. They reject symmetry in the direct functional form [Conrad et.al., p. 164]. Lau, Lin and Totopoulous (1975) used a linear logarithmic expenditure system. They accepted symmetry and homogeneity [Lau, et.al., p. 865]. They also used a .05 level of significance [Lau, et.al., p. 855]. Barten and Geyskens as well as Theil, used a .05 level of significance [see Barten (1977), p.46] for these figures. The study by Barten and Geyskens passed symmetry, negativity, and homogeneity at 0.05 level, while Theil passed only symmetry at 0.05.Google Scholar - 2.Basmann (1977) has used Department of Commerce data like those in Appendix A to test fixed preferences against the following alternative specification of parameters
*θ**i*in the direct utility function where and*u*= (*u*_{i},...,*u*_{n}) is a random vector with zero mean vector and finite covariance matrix. Elasticities of marginal rates of substitution with respect to current and lagged total expenditure*M*and*M*_{t−1}are not constant under this specification. This specification of an elementary variable preference hypothesis fits the eleven commodity grouping of Department of Commerce data used in (1977) equally closely as the maintained hypothesis*H*_{m}described in sec. 3.2 below. In a later study we propose to examine them as competing hypotheses in the face of the eleven commodity grouping of Department of Commerce data provided by Blanciforti and Green (1981). In his doctoral dissertation, Edwin Stecher estimated the expenditure functions derived from (3.1) with the specifications above using the eighty commodity grouping of Department of Commerce data. (Stecher, 1978, pp. 62–63.)Google Scholar - 3.Basmann (1955, 1956) studied advertisement as a preference changing parameter in the demand for tobacco. We have done a preliminary study in which the eleven commodities (see Appendix A) have been aggregated into three: (1) durables, (2) nondurables, and (3) services. The advertising level was constructed by dividing the advertising expenditure on the
*i*th commodity by the overall price level. (Source: U.S. Department of Commerce) Hence, the maintained hypothesis (3.2) included total expenditure, the price for each one of the commodities, and*z*_{1}and*z*_{2}are the real expenditures on advertising by the sellers for durable and nondurable commodities respectively. Our preliminary results indicated that the null hypothesis, that*M*,*p*_{1}, and*p*_{3}have no effect on preferences, could be rejected at .001 level of significance.Google Scholar - 4.Veblen did not propose a mathematical form for a utility function. His remarks about utility as a property of the act of purchasing, owning, controlling, and consuming commodities are open to a variety of reasonable interpretations when it comes to describing substantive utility in the mathematical form of a utility function or index. Veblen’s concepts are transparently consistent with attribution of maximizing behavior to real consumers (Veblen, 1899, p. 158). Veblen was very critical of the classical school and the marginal-utility school — Jevons and the Austrians — for their uncritical acceptance of the hedonistic calculus. (Veblen, 1908, 1909, pp. 181–182; also Veblen, 1909, pp. 232–235)Google Scholar
- 5.see Kenkle (1974) for an excellent discussion on the conditions for stabilityGoogle Scholar
- 7.See Zellner (1962).Google Scholar
- 9.See Theorem 11 p. 200 Mood, Graybill, and Boes (1974).Google Scholar
- 10.This discussion parallels Judge
*et al.*(1985) and Kmenta (1986) but extends it to the multivariate caseGoogle Scholar - 14.This is reviewed in Basmann, Molina and Slottje (1988)Google Scholar