Improved estimation in threshold regression with applications to price transmission modeling

Abstract

Estimation of threshold parameters in (generalized) threshold regression models is typically performed by maximizing the corresponding profile likelihood function. Certain Bayesian techniques based on non-informative priors have also been developed and are widely used. This thesis draws attention to finite-sample settings in which these standard estimators perform poorly. It develops an alternative regularized Bayesian estimator that circumvents the deficiencies of standard estimators in small samples. The new estimator can be obtained employing the empirical Bayes paradigm and, hence, requires little additional numerical effort compared with commonly used estimators. Simulations confirm excellent properties of the suggested estimator, especially in the critical settings. Real-data examples illustrate the practical relevance of the approach. The thesis further explores the properties of the new estimator for the threshold vector error correction model, which is a popular tool for the analysis of spatial price transmission and market integration. Problematic settings are likely to occur in empirical application in this context. Simulations show that the regularized Bayesian estimator also outperforms the profile likelihood estimator within this more complex modeling framework. Two empirical applications -- a reassessment of the seminal paper by Goodwin & Piggott (2001), and an analysis of price transmission between German and Spanish markets for pork -- demonstrate the value of the new method for spatial price transmission analysis.