Robust inference for threshold regression models

Abstract

This paper is concerned with 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. We nest previous works that assume either continuity or discontinuity at the threshold point and develop robust inference methods on the parameters of the model, which are valid under both specifications. In particular, we found that the parameter values under the kink restriction are irregular points of the Hessian matrix of the expected Gaussian quasi-likelihood. This irregularity destroys the asymptotic normality and induces the nonstandard cube root convergence rate for the threshold estimate. However, it also enables us to obtain the same asymptotic distribution as in Hansen (2000) for the quasi-likelihood ratio statistic for the unknown threshold up to an unknown scale parameter. We show that this scale parameter can be consistently estimated by a kernel method as long as no higher order kernel is used. Furthermore, we propose to construct confidence intervals for the unknown threshold by bootstrap test inversion, also known as grid bootstrap. Finite sample performances of the grid bootstrap confidence intervals are examined through Monte Carlo simulations. We also implement our procedure to an economic empirical application. JEL Classification: C12, C13, C24.

Estimation of dynamic panel threshold model using Stata

“…Even when the true model is a kink model, it is shown that the asymptotic distribution of the GMM estimator in the preceding section is valid. This contrasts with the least-squares estimator for the linear regression, for which Hidalgo, Lee, and Seo (2019) have shown that the cube root phenomenon appears.…”

Jump or kink: on super-efficiency in segmented linear regression breakpoint estimation

“…The estimator's convergence rate was further improved to within a logarithmic factor of O p (n −1/2 ) in Baranowski et al (2019) under more restrictive assumptions. See also Hansen (2017) for inference in the presence of a kink, Hidalgo et al (2019) for a test of continuity at the breakpoint, and an as yet unpublished 2017 paper by Y. Dong from the University of California Irvine for a related problem on treatment effect evaluation. There has also been work on kink location estimation in various univariate nonparametric regression settings.…”

Is there a nonlinear relationship between nonperforming loans and bank profitability? Evidence from dynamic panel threshold

“…Lastly, the study examines the presence of kinks in the models. The paper discovers that asides from the thresholds, there are kinks in the models (Hansen, 2017; Hidalgo, Lee, & Seo, 2019).…”