| This dissertation studies the consumer demand system by focusing on its functional form. The theoretical part investigates the regularity property of the flexible consumer demand system characterized by its normalized quadratic functional form. The regularity conditions of monotonicity and curvature are two of the axioms of the consumer demand theory. While other axioms are maintained by construction, these two conditions are only attained in the limited price-income space. We display the regular regions of the model using estimated parameter values from true underlying preferences. The model is estimated using different methods of imposing curvature: global imposition, local imposition, and no imposition. We find that the model often violates the monotonicity condition regardless of the way the curvature is imposed. We find a case where local and global curvature impositions achieve a global regularity within a very large space without causing any biases in estimating the true preference when the unconstrained model produces a non-regular region reflected by the violation of curvature. We also find a case where the globally concave model makes substitute goods more substitute and complement goods more complement.;In the empirical part, functional forms of the consumer demand system which are flexible in the total expenditure are used to estimate the cost of a child using Japanese household expenditure data. The consumer demand system which can describe complicated shapes of Engel curves is necessary to model household behaviors which can vary substantially in expenditure level as well as in demographic characteristics. We estimate the equivalence scales for types of households which differ in the number of children. In doing so, we employ the identifiable expenditure-dependent equivalence scales rather than the constant-equivalence scales usually used in the household welfare literature. A large number of observations with zero expenditures on some goods are addressed by using the Amemiya-Tobit type estimation method to correct potential biases in parameter estimation. The results show that the Japanese household equivalence scales are decreasing in total expenditure as well as increasing in number of children. This suggests the intuitive policy design that the child-support benefits, if any, should depend on household income to preserve equality in welfare level. The results also suggest that the new child-support program proposed by the current Japanese government may need to be reevaluated since it does not consider limiting income level in distributing these benefits. |
