Testing for Threshold Effects in Regression Models

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LRtype test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function. The article provides an alternative, novel method that can be used to establish the asymptotic null distribution, even when the usual quadratic approximation is intractable. We illustrate the usefulness of our approach in the examples of the maximum score estimation, maximum likelihood estimation, quantile regression, and maximum rank correlation estimation. We establish consistency and local power properties of the test. We provide some simulation results and also an empirical application to tipping in racial segregation. This article has supplementary materials online. Terms of use: Documents in

Testing linearity against threshold effects: uniform inference in quantile regression

“…These tests are pointwise, i.e., they test linearity of the conditional quantile function at a given quantile, say median, and their formulations of the testing problems are different from ours. In an independent study, Lee et al (2011) considered a test of linearity against a threshold nonlinear alternative for a fixed quantile. This test is also pointwise, and they do not allow for dynamics in the model.…”

A contribution to the Reinhart and Rogoff debate: not 90 percent but maybe 30 percent

“…We use the updated Reinhart-Rogoff dataset (Reinhart and Rogoff (2013a)) and apply the test for threshold effect developed in Lee, Seo and Shin (2011). This method allows us to test for threshold effect in median regression when the threshold value is unknown.…”

“…We can simulate valid p-values of the quasi-likelihood ratio test, following Lee, Seo and Shin (2011). To implement the test, it is necessary to specify the range of the parameter space Γ of the threshold parameter γ.…”

Best subset binary prediction

“…This difficulty naturally arises, for example, in the context of resampling (Delgado, Rodrıguez-Poo, and Wolf, 2001;Abrevaya and Huang, 2005;Lee and Pun, 2006;Patra, Seijo, and Sen, 2015) and change-point problems (Lee and Seo, 2008;Lee, Seo, and Shin, 2011). It would be an interesting future research topic to investigate numerical performance of our method (e.g.…”