Aggregation and Closed-Form Results for Nonhomothetic CES Preferences

TL;DR

This paper derives new closed-form expressions for nonhomothetic CES preferences, characterizes aggregate demand with heterogeneous households, and links expenditure shares to a discrete-choice model, advancing understanding of nonhomothetic utility.

Contribution

It introduces four novel theoretical results, including closed-form expenditure and demand functions, for nonhomothetic CES preferences, enhancing analytical tractability and empirical relevance.

Findings

Closed-form expenditure function for nonhomothetic CES.

Aggregate demand characterization with heterogeneous households.

Expenditure shares as solutions to a discrete-choice logit problem.

Abstract

We provide four novel results for nonhomothetic Constant Elasticity of Substitution preferences (Hanoch, 1975). First, we derive a closed-form representation of the expenditure function of nonhomothetic CES under relatively flexible distributional assumptions of demand and price distribution parameters. Second, we characterize aggregate demand from heterogeneous households in closed-form, assuming that household total expenditures follow an empirically plausible distribution. Third, we leverage these results to study the Euler equation arising from standard intertemporal consumption-saving problems featuring within-period nonhomothetic CES preferences. Finally, we show that nonhomothetic CES expenditure shares arise as the solution of a discrete-choice logit problem.