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## The stochastic specification of demand share equations: restricting predicted budget shares to the unit simplex

thesis

posted on 30.11.2017 by Jane M. Stagoll#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

In the context of estimating systems of demand share equations, the argument that "the component (shares) predicted or implied by the model should be non-negative and sum to (unity)" (Bewley (1980), p.2) is not new. As a result, the aggregation restrictions should play a central role in the analysis of demand· share equations.The traditional approach to estimating such systems of demand share equations is to append a multivariate normal stochastic component and carry out the estimation. However, such a specification does not exploit the aggregation restriction to its full extent. That is, although we may specify a deterministic component that is restricted to the (0,1) interval, the use of an additive multivariate normal error term means that there is, at least in theory, a non-zero probability that the shares implied or predicted by the model will be outside the(0,1) interval. [...]