Quasi-maximum likelihood estimation of short panel data models with time-varying individual effects

Since the commonly available time series on micro units are typically quite short, this paper considers a different estimation of linear panel data models where the unobserved individual effects are permitted to have time-varying effects on the response variable. We allow flexible possible correlations between included regressors and unobserved individual effects, and the model can accommodate both time varying and time invariant covariates. The quasi-maximum likelihood method is then proposed to obtain the estimates, which are easily executed by a simple iterative method. Two types of approaches to estimate the covariance matrix are introduced. The large sample properties are established when n→∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\rightarrow \infty $$\end{document} and T is fixed. The estimates are efficient when both the individual effects and random errors follow normal distributions. Simulation studies show that our estimates perform well even when the correlations between the regressors and unobserved individual effects are misspecified. The proposed method is further illustrated by applications to a real data.