Threshold Regression in Heterogeneous Panel Data with Interactive Fixed Effects

TL;DR

This paper develops a new threshold regression model for heterogeneous panel data with interactive fixed effects, providing estimation methods, tests, and applications to economic puzzles.

Contribution

It introduces a novel semi-homogeneous model with heterogeneous slopes and a common threshold, along with new convergence rates and testing procedures.

Findings

Threshold nonlinearity observed only in a small subset of countries.

The proposed methods perform well in small samples.

New asymptotic theory for models with heterogeneous thresholds and slopes.

Abstract

This paper introduces unit-specific heterogeneity in panel data threshold regression. We develop the asymptotic theory for models with heterogeneous thresholds, heterogeneous slope coefficients, and interactive fixed effects. The estimation methodology employs the Common Correlated Effects approach, which is able to handle heterogeneous parameters 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, as well as a modified information criterion which can select between the fully heterogeneous and semi-homogeneous models. Monte Carlo simulations demonstrate the good performance of the new methods in small samples. The new theory is used to examine the Feldstein-Horioka puzzle, showing that threshold nonlinearity with respect to trade openness occurs only in a small subset of countries.