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Threshold Regression in Heterogeneous Panel Data with Interactive Fixed Effects

Marco Barassi, Yiannis Karavias, Chongxian Zhu

TL;DR

This paper advances panel threshold regression by allowing unit-specific heterogeneity in both thresholds and slopes within a framework that includes interactive fixed effects (IFE). It develops a comprehensive asymptotic theory using a Common Correlated Effects (CCE) estimator to consistently estimate heterogeneous parameters, and introduces a semi-homogeneous variant with a common threshold to exploit pooling gains. The authors establish consistency and nonstandard convergence rates for the threshold estimators, derive their asymptotic distributions, and propose robust inference tools including a bootstrap-based likelihood ratio test and sup Wald tests for nonlinearity. An empirical application to the Feldstein-Horioka puzzle shows pervasive cross-country heterogeneity, with threshold effects present only for a subset of countries, underscoring the importance of accounting for both heterogeneity and nonlinearity in macro-panel analyses.

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.

Threshold Regression in Heterogeneous Panel Data with Interactive Fixed Effects

TL;DR

This paper advances panel threshold regression by allowing unit-specific heterogeneity in both thresholds and slopes within a framework that includes interactive fixed effects (IFE). It develops a comprehensive asymptotic theory using a Common Correlated Effects (CCE) estimator to consistently estimate heterogeneous parameters, and introduces a semi-homogeneous variant with a common threshold to exploit pooling gains. The authors establish consistency and nonstandard convergence rates for the threshold estimators, derive their asymptotic distributions, and propose robust inference tools including a bootstrap-based likelihood ratio test and sup Wald tests for nonlinearity. An empirical application to the Feldstein-Horioka puzzle shows pervasive cross-country heterogeneity, with threshold effects present only for a subset of countries, underscoring the importance of accounting for both heterogeneity and nonlinearity in macro-panel analyses.

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.
Paper Structure (8 sections, 10 theorems, 22 equations, 1 table)

This paper contains 8 sections, 10 theorems, 22 equations, 1 table.

Table of Contents

  1. Introduction
  2. Fully Heterogeneous Model Estimation
  3. Fully Heterogeneous Model Assumptions
  4. Asymptotic Theory
  5. A Semi-Homogeneous Threshold Regression Model
  6. Testing the Null Hypothesis of No Threshold Regression
  7. Empirical Application
  8. Conclusion

Key Result

Theorem 1

Under Assumptions ass:commonfactors-ass:uniboundmom, and as $(N,T) \rightarrow \infty,$$\hat{\gamma_i} \stackrel{p}{\rightarrow} \gamma_i^0.$

Theorems & Definitions (10)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Theorem 8
  • Theorem 9
  • Theorem 10