Likelihood-Ratio-Based Confidence Intervals for Multiple Threshold Parameters

Abstract

Abstract This paper proposes the inversion of likelihood ratio tests for the construction of confidence intervals for multiple threshold parameters. Using Monte Carlo simulations, conservative likelihood-ratio-based confidence intervals are shown to exhibit empirical coverage rates at least as high as nominal levels for all threshold parameters, while still being informative in the sense of only including relatively few observations in each confidence interval. These findings are robust to the magnitude of the threshold effect, the sample size and the presence of serial correlation. Applications to existing models with multiple thresholds for U.S. real GDP growth and for the wage Phillips curve demonstrate how the proposed approach is empirically relevant to make inferences about the uncertainty of threshold estimates.