Improving Likelihood-Ratio-Based Confidence Intervals for Threshold Parameters in Finite Samples
22 Pages Posted: 27 Mar 2014 Last revised: 13 Aug 2017
Date Written: August 10, 2017
Within the context of threshold regressions, we show that asymptotically-valid likelihood-ratio-based confidence intervals for threshold parameters perform poorly in finite samples when the threshold effect is large. A large threshold effect leads to a poor approximation of the profile likelihood in finite samples such that the conventional approach to constructing confidence intervals excludes the true threshold parameter value too often, resulting in low coverage rates.
We propose a conservative modification to the standard likelihood-ratio-based confidence interval that has coverage rates at least as high as the nominal level, while still being informative in the sense of including relatively few observations of the threshold variable. An application to thresholds for U.S. industrial production growth at a disaggregated level shows the empirical relevance of applying the proposed approach.
Keywords: Threshold regression; Inverted likelihood ratio; Confidence Interval; Finite-sample inference
JEL Classification: C13, C20
Suggested Citation: Suggested Citation