# Robust inference for threshold regression models

*Javier Hidalgo*,
*Jungyoon Lee* and
*Myung Hwan Seo*

*Journal of Econometrics*, 2019, vol. 210, issue 2, 291-309

**Abstract:**
This paper considers robust inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump, nesting previous works that assume either continuity or discontinuity at the threshold. We find that the parameter values under the kink restriction are irregular points of the Hessian matrix, destroying the asymptotic normality and inducing the cube-root convergence rate for the threshold estimate. However, we are able to obtain the same asymptotic distribution as Hansen (2000) for the quasi-likelihood ratio statistic for the unknown threshold. We propose to construct confidence intervals for the threshold by bootstrap test inversion. Finite sample performances of the proposed procedures are examined through Monte Carlo simulations and an economic empirical application is given.

**Keywords:** Change point; Kink; Grid bootstrap; Cube root (search for similar items in EconPapers)

**JEL-codes:** C12 C13 C24 (search for similar items in EconPapers)

**Date:** 2019

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:econom:v:210:y:2019:i:2:p:291-309

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