Panel threshold regression with unobserved individual-specific threshold effects

This paper provides a new approach to estimation and inference in multiple regime panel threshold regression with unobserved individual-specific threshold effects. Such effects are practically relevant and have features that distinguish them from traditional linear panel data models. It is shown that within-regime demeaning in the static model or within-regime first-differencing in the dynamic model both fail to deliver consistent threshold estimators. Instead, correlated random effects models are suggested to address endogeneity in such panel threshold systems. The paper develops a unified framework of estimation and inference for both static and dynamic models that applies irrespective of whether the unobserved individual-specific threshold effects exist or whether the number of regimes is correctly specified. The approach involves model selection based on sequential testing which allows for underestimation of the number of regimes, develops asymptotic theory for least squares estimation that is robust to such model misspecification, and proposes new inferential methods for the model parameters which have improved asymptotic and empirical properties over existing methods. Simulations combined with an empirical application illustrate the practical utility of the new methodology.