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.