Estimation of Panel Data Models with Parameter Heterogeneity when Group Membership is Unknown

Abstract This paper proposes two methods for estimating panel data models with group specific parameters when group membership is not known. The first method uses the individual level time series estimates of the parameters to form threshold variables. The problem of parameter heterogeneity is turned into estimation of a panel threshold model with an unknown threshold value. The second method modifies the K-means algorithm to perform conditional clustering. Units are clustered based on the deviations between the individual and the group conditional means. The two approaches are used to analyze growth across countries and housing market dynamics across the states in the U.S.