Regularized Bayesian Estimation of Generalized Threshold Regression Models

In this article we discuss estimation of generalized threshold regression models in settings when the threshold parameter lacks identifiability. In particular, if estimation of the regression coefficients is associated with high uncertainty and/or the difference between regimes is small, estimators of the threshold and, hence, of the whole model can be strongly affected. A new regularized Bayesian estimator for generalized threshold regression models is proposed. We derive conditions for superiority of the new estimator over the standard likelihood one in terms of mean squared error. Simulations confirm excellent finite sample properties of the suggested estimator, especially in the critical settings. The practical relevance of our approach is illustrated by two real-data examples already analyzed in the literature.