Threshold Regression in Heterogeneous Panel Data with Interactive Fixed Effects

Abstract: This paper introduces unit-specific heterogeneity in panel data threshold regression. We develop a comprehensive asymptotic theory for models with heterogeneous thresholds, heterogeneous slope coefficients, and interactive fixed effects. Our estimation methodology employs the Common Correlated Effects approach, which is able to handle heterogeneous coefficients while maintaining computational simplicity. We also propose a semi-homogeneous model with heterogeneous slopes but a common threshold, revealing novel mean group estimator convergence rates due to the interaction of heterogeneity with the shrinking threshold assumption. Tests for linearity are provided, and also a modified information criterion which can choose between the fully heterogeneous and the semi-homogeneous models. Monte Carlo simulations demonstrate the good performance of the new methods in small samples. The new theory is applied to examine the Feldstein-Horioka puzzle and it is found that threshold nonlinearity with respect to trade openness exists only in a small subset of countries.