The Econometrics of Demand Systems pp 63-92 | Cite as

# The Specification and Estimation of Demand Systems

Chapter

## Abstract

In the previous chapter we discussed some of the principal notions behind the theory of consumer demand. In this chapter we consider how to make this theory operational.

### Keywords

Covariance Income Autocorrelation Prefix Estima## Preview

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### References

- 1.Various intuitively plausible criteria, such as
*regularity, domain of applicability, flexibility, etc.*, have been suggested to assist us with this choice, see Lau (1986) and Thompson (1988) for example.Google Scholar - 3.As far as we know the first article to use this approximation is Goddard (1983).Google Scholar
- 4.Other possibilities for AIDS models are to replace the lagged budget shares by lagged quantities (Ray(1984)), or to take account of demographic factors (Alessie and Kapteyn (1991)). For the translog model Manser (1976) has suggested using lagged total expenditure.Google Scholar
- 9.The true cost of living index is only exactly independent of
*u*if the group preferences are homothetic. Using the theorem of Wilks (1938) described earlier, we can expect the approximation we have described to be adequate as long as the number of elementary commodities is large, see also Edgerton (1993a).Google Scholar - 10.Many definitions of exogeneity exist, see for example Geweke (1984). Both
*strict exogeneity*and*weak exogeneity*are sufficient, but not necessary, conditions to allow consistent estimation when treating the “exogenous” variable as nonstochastic.Google Scholar - 11.The unconditional demand function is simply the function found by substituting (21a) into (21b) through (22), see LaFrance’s equation (19). The conditions needed for the consistency of least-squares methods are, for systems that are linear in expenditure, quite similar to those given by Deaton, and are related to Theil’s (1971) “rational random errors hypothesis”. For systems nonlinear in expenditure the situation is more complicated. See also Blackorby
*et al*(1978 p. 279).Google Scholar - 15.Bowden and Turkington (1981) call this method
*strict*2SLS/3SLS, but in their later book (Bowden and Turkington (1984)) define the method as an (unnamed) alternative to the method of*internal instruments*. Consistency has been established by Kelejian (1971) and Edgerton (1972), whilst Edgerton (1973) and Amemiya (1974) give the asymptotic standard errors. The latter is unfortunately misprinted in Bowden and Turkington’s book. It is the method of external instruments that is to be found in the TSP and SAS program packages.Google Scholar - 23.At the time of going to press it was brought to our attention that the omnibus test proposed by Mardia and Foster (1983) provides an appropriate small sample test of multivariate normality.Google Scholar
- 26.It is important to use the same metric (estimate of
*∑*) for both the restricted and unrestricted models when estimating with non-ML methods. The test statistics can otherwise become nonsensical in small samples, see Engle(1984).Google Scholar

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© Kluwer Academic Publishers 1996