Testing For Individual Effects In The Error Component Model With Incomplete Panels

In recent years, panel data models have been widely used in the fields of economy, finance, biomedicine and so on. In practice, one often find that some data are incomplete or unbalanced, which means not all individuals are observed for the whole time periods. Incomplete panel data models are more likely to be the norm in typical empirical settings.As an important step of modeling, diagnostic checking has drawn much attention by researchers. In aspects of diagnostic checking for panel data models, testing for the random effect seems very important. Misspecification of random effects in the error component will lead to seriously biased standard errors and inefficient statistical inference. It is therefore important to test for the existence of random effects in the error component with incomplete panels.The main result of this paper is that we develop a new method to test for the individual effects in the error component with incomplete panels, which can be regarded as the extension of the moment-based test methods of Wu and Li (2014) to the case with incomplete panels. Specifically, on the base of the difference of variance estimators of the idiosyncratic errors at different levels, we construct a statistic to test for the existence of individual effects, which can be shown to asymptotically normally distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis and has a larger asymptotic power than the corresponding ANOVA F test when the individual heterogeneity effects are correlated with covariates. We also conduct several small Monte Carlo simulation experiments to evaluate the performance of our testing method and several other commonly-used testing methods. A real data example is analyzed for illustration.