Testing For Serial Correlation In Three Dimensional Panel Data Models

Panel data refers to the pooling of observations on several individuals at several time periods. And it is an important data type in the field of econometrics, statistics, biometrics and so on. In recent decades, panel data model has drawn more and more attention by researchers. Three dimensional panel data is frequently encountered in studying economic and financial phenomena. Compared with the commonly-used two-dimensional panel data, the three-dimensional panel data has three subscripts on their variables such as yijt, and it may be more useful in the study of empirical economic in practice.There are three main steps for modeling, i.e. modeling, parameter estimation and modeling checking. However, most of the literatures on three-dimensional panel data model are focus on the first two steps. The third step has not received the attention it deserves. This paper studies serial correlation testing for a general three-dimensional panel data model. We often assume that the idiosyncratic errors are mutually independent and identically distributed. If it holds that Cov(εijt,εijs)≠0,t≠s, then we may consider that the model exists serial correlation. Ignoring serial correlation can result in consistent but inefficient estimators of the regression coefficients and biased standard errors when it does exist, such that the conventional t test and F test may be invalidated. Hence, it is an important problem to test serial correlation for three-dimensional panel data models.The main result of this paper is that we develop the most robust testing methods for serial correlation in two-dimensional panels to the three-dimensional panels. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to asymptotically consistent and normal under some mild conditions. A residual-based statistic is then constructed to test for serial correlation in the idiosyncratic errors, which is based on the parameter estimates for an artificial auto-regression modeled by centering and differencing residuals. The test can be shown to asymptotically chi-square distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The test method needs no distribution assumptions of the error components, and is robust to the misspecification of various specific effects and specific forms of serial correlation. Monte Carlo simulations are carried out for illustration.