A Flexible Yet Globally Regular Multigood Demand System

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 a utility function to impose minimal prior restrictions on demand elasticities. Global regularity refers to the ability of a utility function to satisfy regularity properties required by economic theory in the entire feasible space of variables. The tractable utility functions used so far are either inflexible, which could yield inaccurate estimates of underlying elasticities, or do not satisfy global regularity, which can result in invalid expressions of likelihood and invalid policy simulations. I tackle this problem by deriving necessary and sufficient conditions for global regularity of Basic Translog utility. Using simulated and scanner data, I show that the proposed demand system yields better model fit, more accurately captures underlying elasticities, and yields substantially different results in counterfactuals compared to alternatives used in prior literature. Specifically, unlike the alternatives used so far, the proposed demand system allows for complementarities between goods, and more accurately captures the extent of their inferiority, the extent of their substitutability, and asymmetries in cross price effects.