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STRUCTURAL THRESHOLD REGRESSION

Published online by Cambridge University Press:  20 April 2015

Andros Kourtellos ,
Thanasis Stengos  and
Chih Ming Tan
Andros Kourtellos*
Affiliation:
University of Cyprus
Thanasis Stengos
Affiliation:
University of Guelph
Chih Ming Tan
Affiliation:
University of North Dakota
*
*Address correspondence to Andros Kourtellos, Department of Economics, University of Cyprus, P.O. Box 537, CY 1678 Nicosia, Cyprus; e-mail: andros@ucy.ac.cy.
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Abstract

This paper introduces the structural threshold regression (STR) model that allows for an endogenous threshold variable as well as for endogenous regressors. This model provides a parsimonious way of modeling nonlinearities and has many potential applications in economics and finance. Our framework can be viewed as a generalization of the simple threshold regression framework of Hansen (2000, Econometrica 68, 575–603) and Caner and Hansen (2004, Econometric Theory 20, 813–843) to allow for the endogeneity of the threshold variable and regime-specific heteroskedasticity. Our estimation of the threshold parameter is based on a two-stage concentrated least squares method that involves an inverse Mills ratio bias correction term in each regime. We derive its asymptotic distribution and propose a method to construct confidence intervals. We also provide inference for the slope parameters based on a generalized method of moments. Finally, we investigate the performance of the asymptotic approximations using a Monte Carlo simulation, which shows the applicability of the method in finite samples.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 4 , August 2016 , pp. 827 - 860
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

We thank the editor Peter C. B. Phillips, the co-editor Oliver Linton, and two anonymous referees whose comments greatly improved the paper. We also thank Bruce Hansen for helpful comments and seminar participants at the Athens University of Economics and Business, Hebrew University of Jerusalem, Ryerson University, Simon Fraser University, Universit libre de Bruxelles, University of Cambridge, University of Palermo, University of Waterloo, the University of Western Ontario, 10th World Congress of the Econometric Society in Shanghai, 27th Annual Meeting of the Canadian Econometrics Study Group in Vancouver, and 23rd (EC)2 conference. Kourtellos thanks the University of Cyprus for funding. Tan thanks the Greg and Cindy Page Faculty Distribution Fund for financial support.

References

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