A note on regression kink model

Abstract

This note develops a score-like test for the existence of threshold effect in regression kink model. The test statistics is based on the CUSUM process of subgradients, and only requires fitting the model under null hypothesis. The critical values can be obtained by residual bootstrap. Four kinds of methods are also proposed for estimating the kink point and other model coefficients: grid-search, segmented, smoothed and Bayesian. The simulation results suggest that the proposed test is more computationally efficient and outperforms better than other existing test procedures. All the four estimating methods have good finite sample performance, but influenced by the location of threshold. Two empirical examples are presented to briefly manifest the charm of the regression kink model.

Keywords:

• Regression kink
• threshold effect
• CUSUM test
• parameters estimation

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (71774053) and the Hunan Provincial Natural Science Foundation of China (2019JJ40041).