Threshold Regression in Heterogeneous Panel Data with Interactive Fixed Effects

2023-08-08

AI Summary

This paper addresses the inadequate modeling of unit heterogeneity in threshold regression for panel data. We propose a heterogeneous panel threshold regression model incorporating interactive fixed effects, allowing both threshold values and slope coefficients to vary across units. Innovatively, we employ unit-specific empirical quantile transformations to characterize threshold heterogeneity and, for the first time, jointly model threshold heterogeneity and interactive fixed effects. Under a shrinkage threshold assumption, we develop a simultaneous shrinkage identification mechanism that improves convergence rates. We establish consistency and asymptotic normality of the estimators under mild regularity conditions. Monte Carlo simulations confirm the estimator’s finite-sample performance. Empirically, applying the model to cross-country data, we find that trade liberalization in the 1980s significantly enhanced international capital mobility.

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.

Problem

• Handling heterogeneous thresholds in panel data
• Modeling interactive fixed effects with heterogeneity
• Testing threshold nonlinearity in economic relationships

Innovation

• Heterogeneous panel data threshold regression
• Common Correlated Effects estimation approach
• Semi-homogeneous model with novel convergence rates