Testing for Serial Correlation in Fixed-Effects Panel Data Models

TL;DR: In this paper, the authors proposed various tests for serial correlation in fixed-eects panel data regression models with a small number of time periods, including a simplified version of the test suggested by Wooldridge (2002), Drukker (2003), and a modification of the Durbin-Watson statistic.

Abstract: In this paper, we propose various tests for serial correlation in fixed-eects panel data regression models with a small number of time periods. First, a simplified version of the test suggested by Wooldridge (2002) and Drukker (2003) is considered. The second test is based on the Lagrange Multiplier (LM) statistic suggested by Baltagi and Li (1995), and the third test is a modification of the classical Durbin-Watson statistic. Under the null hypothesis of no serial correlation, all tests possess a standard normal limiting distribution as N!1 and T is fixed. Analyzing the local power of the tests, we find that the LM statistic has superior power properties. Furthermore, a generalization to test for autocorrelation up to some given lag order and a test statistic that is robust against time dependent heteroskedasticity are proposed.