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ROBUST ESTIMATION AND INFERENCE FOR THRESHOLD MODELS WITH INTEGRATED REGRESSORS

Published online by Cambridge University Press:  27 October 2014

Haiqiang Chen
Haiqiang Chen*
Affiliation:
Xiamen University
*
*Address correspondence to Haiqiang Chen, Xiamen University, Xiamen, Fujian 361005, China; e-mail: hc335@xmu.edu.cn.
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Abstract

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This paper studies the robust estimation and inference of threshold models with integrated regressors. We derive the asymptotic distribution of the profiled least squares (LS) estimator under the diminishing threshold effect assumption that the size of the threshold effect converges to zero. Depending on how rapidly this sequence converges, the model may be identified or only weakly identified and asymptotic theorems are developed for both cases. As the convergence rate is unknown in practice, a model-selection procedure is applied to determine the model identification strength and to construct robust confidence intervals, which have the correct asymptotic size irrespective of the magnitude of the threshold effect. The model is then generalized to incorporate endogeneity and serial correlation in error terms, under which, we design a Cochrane–Orcutt feasible generalized least squares (FGLS) estimator which enjoys efficiency gains and robustness against different error specifications, including both I(0) and I(1) errors. Based on this FGLS estimator, we further develop a sup-Wald statistic to test for the existence of the threshold effect. Monte Carlo simulations show that our estimators and test statistics perform well.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 4 , August 2015 , pp. 778 - 810
Copyright
Copyright © Cambridge University Press 2014 

Footnotes

I would like to thank Professor Peter C.B. Phillips and the referees for helpful comments. Special thanks also go to Zongwu Cai, Jiti Gao, Wolfgang Härdle, Yongmiao Hong, and seminar participants at Cornell University and the 3rd XMU-Humboldt Workshop. The research was supported in part by the National Nature Science Foundation of China grants #11201390, #71201137, #71131008, and #71271179 as well as Deutsche Forschungsgemeinschaft (DFG) through the SFB649 “Economic Risk”.

References

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