  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.
