Panel threshold model with covariate-dependent thresholds and unobserved individual-specific threshold effects

This article introduces a panel threshold model with covariate-dependent and time-varying thresholds and unobserved individual-specific threshold effects (PTCDI). We develop methods for estimation and inference for threshold parameters in the proposed PTCDI model by employing the correlated random effects (CRE) device. We also suggest test statistics for linearity, threshold constancy, unobserved individual-specific threshold effects, and for determining the number of thresholds. We derive the asymptotic properties of the proposed estimator in the small-threshold-effect framework and establish the limiting distributions of the suggested test statistics. We also investigate the extension to dynamic panels and show that both the static and dynamic models can be handled uniformly in the CRE framework. Monte Carlo simulation results indicate that the estimation, inference, and testing procedures have the desired performance in finite samples. The model is illustrated with two empirical applications to the relationship between cash flow and investment and the nexus between inflation and economic growth.