Regularized Bayesian estimation in generalized threshold regression models

Estimation of threshold parameters in (generalized) threshold regression models is typically performed by maximizing the corresponding profile likelihood function. Also, certain Bayesian techniques based on non-informative priors are developed and widely used. This article draws attention to settings (not rare in practice) in which these standard estimators either perform poorly or even fail. In particular, if estimation of the regression coeffcients is associated with high uncertainty, the profile likelihood for the threshold parameters and thus the corresponding estimator can be highly affected. We suggest an alternative estimation method employing the empirical Bayes paradigm, which allows to circumvent deficiencies of standard estimators. The new estimator is completely data-driven and induces little additional numerical effort compared with the old one. Simulation results show that our estimator outperforms commonly used estimators and produces excellent results even if the latter show poor performance. The practical relevance of our approach is illustrated by a real-data example; we follow up the anlysis of cross-country growth behavior detailed in Hansen (2000).