No. 3/2025: A pitfall in models of external habit formation

Abstract

This paper points out a flaw in the solution method for dyanmic optimization with external habit formation, such as in Campbell and Cochrane (1999). Their method, which is common in the literature, is to impose the equality between the agent’s and peers’ decisions in the agent’s optimization problem upon deriving the first-order condi- tions. This paper demonstrates the fallacy of this shortcut. Based on the dual function approach, I show that the results are likely to be different qualitatively as well as quan- titatively if the above equality instead is imposed after optimization as the solution to a fixed-point problem in market equilibrium.