Stochastic Generalizations of Demand Systems with an Application to Telecommunications
Systems of demand equations are considered for at least two reasons. First, they offer a theoretical completeness, and second, they embody a number of restrictions which lead to a more parsimonious specification concerning the number of parameters. As it turns out, the quantity and quality of the data are often such that the demand systems considered are not restrictive enough in the sense that large numbers of parameters still remain which cannot be estimated with ‘great precision’. Paradoxically, the restrictions that are considered are often rejected by the data.
In this paper we propose a system of random coefficient telecommunications demand equations in a panel data framework. These equations correspond to alternative ways (which have different costs) of placing a call. The system is formulated in such a way that it incorporates the homogeneity condition, as well as stochastic versions of the symmetry and weak separability restrictions. The stochastic versions are given in terms of moments and so they do not have to hold in each individual case. Under certain conditions they reduce to their deterministic counterparts. Finally, we empirically implement the model and compare the results to what they would be in a corresponding deterministic framework.