Detecting multiple equilibria for continuous dependent variables

Abstract

This article considers structural equations where continuous dependent variables are related to independent variables and unobservables through a nonparametric function. Multiple equilibria may arise when the structural equations admit multiple solutions. This article proposes a detecting criterion for the existence of multiple equilibria. The main finding is that multiple equilibria would reveal itself in the form of jump(s) in the density function of the dependent variables. When there is a unique equilibrium, the density function of dependent variables will be continuous, whereas when there are multiple equilibria, the density will have jump(s) under reasonable conditions.