Threshold Regression in Heterogeneous Panel Data with Interactive Fixed Effects

Abstract

This paper introduces unit-specific heterogeneity in panel data threshold regression. Both slope coefficients and threshold parameters are allowed to vary by unit. The heterogeneous threshold parameters manifest via a unit-specific empirical quantile transformation of a common underlying threshold parameter which is estimated efficiently from the whole panel. In the errors, the unobserved heterogeneity of the panel takes the general form of interactive fixed effects. The newly introduced parameter heterogeneity has implications for model identification, estimation, interpretation, and asymptotic inference. The assumption of a shrinking threshold magnitude now implies shrinking heterogeneity and leads to faster estimator rates of convergence than previously encountered. The asymptotic theory for the proposed estimators is derived and Monte Carlo simulations demonstrate its usefulness in small samples. The new model is employed to examine the Feldstein-Horioka puzzle and it is found that the trade liberalization policies of the 80's significantly impacted cross-country capital mobility.