Panel Kink Regression Model with a Covariate-Dependent Threshold  


This paper extends the kink regression (KR) model with a constant threshold in Hansen (2017) to a panel data framework with a covariate-dependent
threshold, where the threshold is modeled as a function of informative covariates. We
suggest an estimator based on the within-group transformation, and propose test statistics for kink threshold effect and threshold constancy. We establish the asymptotic joint
normality of the slope and threshold estimators, and derive the limiting distributions
of the test statistics. Our asymptotical results show that the inclusion of a covariatedependent threshold does not affect the asymptotic joint normality of the slope and
threshold estimates in the kink regression model. Monte Carlo simulations show that
the finite sample proprieties of the proposed estimator and test statistics are generally
satisfactory. Applying the proposed model to investigate the threshold effect of public
debt on economic growth, we find strong statistical evidence supporting that there is
a debt threshold above which debt becomes a drag on economic growth; moreover, we
also find that the debt threshold is significantly negatively affected by inflation, which
tends to resist the urge to inflate public debt away in order to reduce the debt burden.