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Contributions to Consumer Demand and Econometrics: Essays in Honour of Henri Theil
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Economics Letters —42 Google Scholar. In this chapter we revisit the ques- tion of how to specify an internally consistent system of mixed demand equations. We review the theoretical framework and show that mixed demand functions can be 1 Mixed demands also turn up in environmental economics e. It is well known, of course, that Stone-Geary preferences are restrictive. The mixed demand system that we derive, however, presents several motives of interest. First, it offers a theory-consistent benchmark against which more flexible mixed demand specifications may be compared. The question essentially boils down to which specification is affected by an error-in- variables problem, a situation that can lead to serious inconsistency in estimated pa- rameters.
To study this question one needs to compare direct and mixed and inverse, if desirable demand systems, and for that comparison to be meaningful the alterna- tive specifications must all be traceable to the same underlying preference structure. Because, as we show, Stone-Geary preferences permit the explicit solution of both direct and mixed demand functions, the model that we present is rather useful for that purpose. We illustrate this with a simple Monte Carlo experiment that contrasts a six- good direct demand system with a comparable mixed demand system.
The LES model has been used in countless applications, and its simplicity, exact aggregation properties, and parametric parsimony continue to make it of interest to practitioners. Its restrictive features include that it rules out inferior goods, and that it constrains the substitution possibilities across goods all goods are net substitutes.
Whether the latter is a serious problem depends on the intended application in most cases, goods are in fact expected to be net substitutes. Another restrictive feature of the LES system is that it entails linear Engel curves the underlying utility function is a special case of quasi-homothetic preferences. This attribute is most damaging in the context of complete demand systems, where Engel curves are expected to display substantial nonlinearity Deaton and Muellbauer a. But in conditional demand systems that model only a weakly separable partition of the consumption bundle, such as the one we present in our application to vegetable demand in Italy, this restriction on the shape of Engel curves may be less important.