Bruce E. Hansen

Regression Kink with an Unknown Threshold

Journal of Business and Economic Statistics, 2017


This paper explores estimation and inference in a regression kink model with an unknown threshold. A regression kink model (or continuous threshold model) is a threshold regression constrained to be everywhere continuous with a kink at an unknown threshold. We present methods for estimation, to test for the presence of the threshold, for inference on the regression parameters, and for inference on the regression function. A novel finding is that inference on the regression function is non-standard since the regression function is a non-differentiable function of the parameters. We apply recently developed methods for inference on non-differentiable functions. The theory is illustrated by an application to the growth & debt problem introduced by Reinhart and Rogoff (2010), using their long-span time-series for the United States.

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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.