ISSUES CONCERNING SYSTEMS OF DEMAND EQUATION (INTEGER, ORDERED, STOCHASTIC, HETEROSCEDASTICITY)
WALKER, MARY ELIZABETH
Doctor of Philosophy
This dissertation examines two separate issues concerning systems of demand equations. The first essay deals with the econometric implementation of demand systems and the second analyzes the demand for integer-ordered goods. In the first essay, we examine the consequences of adopting the random utility hypothesis as an approach for randomizing a system of demand equations. Random utility models are appealing since they allow the usual assumption of deterministic utility maximizing behavior by each consumer to co-exist with the apparent randomness across individuals which is exhibited by data. Our results show that the use of random utility models implies that the disturbances of the demand equations may not be homoscedastic but must be functions of prices and/or income. If the demand system is generated by random utility maximization, then empirical studies of demand which have assumed homoscedastic disturbances will suffer the usual inferential difficulties. A possible explanation for the prevalent finding of nonsymmetry, therefore, is provided by the fact that most previous demand studies have, in fact, assumed homoscedasticity. An appropriate structure for the disturbances is obtained for the specific case of the linear expenditure system. A system of demand equations for international travel is estimated and compared using both the typical homoscedastic disturbances and the alternative specification we derive. The second essay develops a model of consumer behavior when consumers are confronted with lumpy alternatives. Specifically, the case of a single discrete good which can be purchased only in integer quantities is modeled. The model uses a systems approach, incorporating demand for the discrete good with demand for continuous goods into a complete system of demand equations. After deriving a general form for the mixed integer/continuous model, a particular functional form for the model is derived by imposing linearity constraints on the demand equations. To obtain the stochastic specification, the framework of random utility maximization is adopted. Finally, the model is shown to be identified and an estimation procedure is developed using maximum likelihood methods.