Global Regularity and Flexibility of Demand Systems in the Presence of Non-negativity Constraints: a Theoretical and Empirical Analysis

A vexing challenge when using the utility-maximization framework to estimate consumers’ decisions on which set of goods to purchase and how much quantity to buy, is obtaining a functional form of the utility that satisfies three criteria: tractability, flexibility and global-regularity. Flexibility refers to the ability of utility function to impose minimal prior restrictions on demand elasticities. Global regularity refers to the ability of utility function to satisfy regularity properties required by economic theory in the entire feasible space of variables. The tractable utility functions used in prior literature are either inflexible which could yield inaccurate estimates of underlying demand elasticities and thereby inaccurate results in policy simulations, or do not satisfy global regularity which can result in invalid expressions of likelihood and invalid policy simulations. The candidates that can potentially satisfy all three criteria are flexible functional forms of indirect utilities. The issue with flexible functional forms is that prior restrictions need to be imposed on their parameters so that they satisfy global-regularity. To have minimal impact on their flexibility, these restrictions should be necessary and sufficient conditions (i.e., the least restrictive conditions on the parameter space) that ensure global-regularity. However, only sufficient conditions have been proposed till date, which destroy their flexibility. We tackle this problem by deriving necessary and sufficient conditions for global-regularity of Basic Translog utility, a widely used flexible functional form. We show that as compared to alternatives used in the literature, our proposed demand system (a) imposes much fewer restrictions on demand elasticities (in terms of allowing for inferior/normal goods and complementarity/substitutability), and (b) yields better model fit, more accurately captures the true demand elasticities i and yields substantially different results in policy simulations.