Theory and methods of panel data models with interactive effects

TL;DR

This paper develops maximum likelihood estimation methods for panel data models with interactive effects, addressing issues of inconsistency in traditional estimators and extending the model to include various regressors.

Contribution

It introduces a maximum likelihood estimator for models with interactive effects, providing theoretical properties and extensions to include time-invariant and common regressors.

Findings

Maximum likelihood estimator is consistent and efficient.

Monte Carlo simulations demonstrate the estimator's performance.

Extensions to models with time-invariant and common regressors.

Abstract

This paper considers the maximum likelihood estimation of panel data models with interactive effects. Motivated by applications in economics and other social sciences, a notable feature of the model is that the explanatory variables are correlated with the unobserved effects. The usual within-group estimator is inconsistent. Existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient. The maximum likelihood estimator has desirable properties and is easy to implement, as illustrated by the Monte Carlo simulations. This paper develops the inferential theory for the maximum likelihood estimator, including consistency, rate of convergence and the limiting distributions. We further extend the model to include time-invariant regressors and common regressors (cross-section invariant). The regression coefficients for the time-invariant regressors are time-varying, and the coefficients for the common regressors are cross-sectionally varying.