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.
This chapter, which is the shared responsibility of all the authors, has been written by David Edgerton.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
As far as we know the first article to use this approximation is Goddard (1983).
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.
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).
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.
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).
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.
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.
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).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Edgerton, D.L., Assarsson, B., Hummelmose, A., Laurila, I.P., Rickertsen, K., Vale, P.H. (1996). The Specification and Estimation of Demand Systems. In: The Econometrics of Demand Systems. Advanced Studies in Theoretical and Applied Econometrics, vol 34. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1277-2_4
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1277-2_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8545-8
Online ISBN: 978-1-4613-1277-2
eBook Packages: Springer Book Archive