Utility Function and Optimum Consumption in the models with Habit Formation and Catching up with the Joneses

TL;DR

This paper examines utility functions in habit formation and catching up with the Joneses models, proposing new specifications that produce more realistic consumption behaviors and highlighting differences in utility functions used.

Contribution

It introduces theoretically justified utility functions for habit formation and CuJ models, improving the plausibility of optimal consumption time series.

Findings

Habit formation utility should use power CRRA, unlike exponential CARA for CuJ.

Many existing models produce unrealistic consumption patterns.

Proposed utility specifications lead to more reasonable consumption dynamics.

Abstract

This paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional average consumption level. Few of these models give reasonable optimum consumption time series. We introduce theoretically justified utility specifications leading to a plausible consumption behavior to show that habit formation preferences must be described by a power CRRA utility function different from the exponential CARA used for CuJ.