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Inference in Unbalanced Panel Data Models with Interactive Fixed Effects

Daniel Czarnowske, Amrei Stammann

Abstract

We derive the asymptotic theory of Bai (2009)'s interactive fixed effects estimator for unbalanced panels in which the source of attrition is conditionally random. For inference, we propose a method of alternating projections algorithm based on straightforward scalar expressions to compute the residualized variables required for bias correction and covariance matrix estimation. Simulation experiments confirm that our asymptotic results provide reliable finite-sample approximations. We also reassess Acemoglu et al. (2019). Allowing for a more general form of unobserved heterogeneity, we confirm significant effects of democratization on economic growth.

Inference in Unbalanced Panel Data Models with Interactive Fixed Effects

Abstract

We derive the asymptotic theory of Bai (2009)'s interactive fixed effects estimator for unbalanced panels in which the source of attrition is conditionally random. For inference, we propose a method of alternating projections algorithm based on straightforward scalar expressions to compute the residualized variables required for bias correction and covariance matrix estimation. Simulation experiments confirm that our asymptotic results provide reliable finite-sample approximations. We also reassess Acemoglu et al. (2019). Allowing for a more general form of unobserved heterogeneity, we confirm significant effects of democratization on economic growth.

Paper Structure

This paper contains 17 sections, 70 equations, 6 figures, 11 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Estimation and Inference
  3. Model, Estimator, and Asymptotic Distribution
  4. Estimation Algorithm
  5. Bias Correction
  6. Estimating the Number of Factors
  7. Simulation Experiments
  8. Empirical Example
  9. Other Related Estimators
  10. Concluding Remarks
  11. Appendix
  12. Derivation of Asymptotic Distribution
  13. Numerical Comparison of Matrix Completion Algorithms
  14. Empirical Example -- Sensitivity Checks
  15. Online Supplement (Not for Publication)
  16. ...and 2 more sections

Figures (6)

  • Figure 1: Missing Data Pattern for Different $\psi$ -- $\overline{N} = 100$ and $\overline{T} = 20$
  • Figure 2: GDP per capita before and after Democratization
  • Figure 3: Largest Singular Values in Descending Order
  • Figure 4: Sensitivity to Different Bandwidth Choices
  • Figure 5: Sensitivity to Number of Factors
  • ...and 1 more figures

Theorems & Definitions (4)

  • Remark 1: Additional Assumptions
  • Remark 2: Strict exogeneity
  • Remark 3: Selection of the tuning parameter
  • Remark 4: Alternative estimation procedures