[Paper Review] Inference in Unbalanced Panel Data Models with Interactive Fixed Effects

Daniel Czarnowske, Amrei Stammann|ArXiv.org|Apr 7, 2020

Spatial and Panel Data Analysis44 references4 citations

TL;DR

This paper investigates the finite-sample performance of the interactive fixed effects (IFE) estimator from [7] in unbalanced panel data with randomly missing observations. Using simulation experiments, it finds that the inferential theory from [b2009mw2017] remains a reasonable approximation under missing data, though the fraction and pattern of missingness affect estimator performance. The study confirms significant effects of democratization on growth when using a more general unobserved heterogeneity structure.

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.

Motivation & Objective

• To assess the finite-sample behavior of the IFE estimator from [7] under randomly missing data in unbalanced panels.
• To evaluate whether existing inferential theory from [b2009mw2017] remains valid when data are unbalanced and missing.
• To reassess the baseline analysis of [1] using the IFE estimator to account for more general unobserved heterogeneity.
• To investigate how the fraction and pattern of missing data influence estimator performance and inference.

Proposed method

• The study employs simulation experiments to evaluate the IFE estimator under various missing data mechanisms and patterns in unbalanced panels.
• It applies the EM algorithm-based data augmentation method from [7] and [9] to handle missing data in the principal components estimation of factor loadings and common factors.
• The inferential theory from [b2009mw2017] is used to approximate the sampling distribution of the IFE estimator in the unbalanced, missing-data setting.
• The IFE estimator is applied to re-estimate the effect of democratization on economic growth using the dataset from [1], allowing for interactive fixed effects to capture complex unobserved heterogeneity.
• The paper compares the performance of the IFE estimator under different missing data fractions and patterns, including random and non-ignorable missingness.
• It uses the minimum distance estimator and nuclear norm relaxation as extensions to validate robustness and explore alternative estimation strategies.

Experimental results

Research questions

• RQ1 Does the inferential theory for the IFE estimator derived under balanced panels remain valid when applied to unbalanced panels with randomly missing data?
• RQ2 How does the fraction and pattern of missing data affect the finite-sample performance of the IFE estimator?
• RQ3 Can the IFE estimator reliably detect significant effects of democratization on economic growth when unobserved heterogeneity is modeled as interactive fixed effects?
• RQ4 To what extent does data augmentation via the EM algorithm preserve estimator properties in the presence of missing data?
• RQ5 How do different missing data mechanisms (e.g., MCAR, MAR) influence the size and power of hypothesis tests based on the IFE estimator?

Key findings

• The inferential theory from [b2009mw2017] provides a reasonable approximation of the sampling distribution of the IFE estimator even in unbalanced panels with missing data.
• The finite-sample performance of the IFE estimator is sensitive to both the fraction and the pattern of missing data, with higher missingness levels and non-random patterns leading to increased bias and size distortions.
• The IFE estimator successfully captures the significant effect of democratization on economic growth when applied to the [1] dataset, confirming the baseline result under a more general unobserved heterogeneity structure.
• The EM-based data augmentation step in the IFE estimator maintains consistency under missing data, but additional uncertainty from imputation affects finite-sample inference.
• The nuclear norm relaxation estimator offers a consistent alternative with slower convergence, but iterative post-estimation restores the asymptotic properties of the original IFE estimator.
• The study highlights the need for a formal inferential theory that accounts for uncertainty introduced by data augmentation in missing-data settings.