Testing Serial Correlation in Fixed Effects Regression Models: the Ljung-Box Test for Panel Data

Testing the presence of serial correlation in the error terms of a fixed effects regression model is important for many reasons. While there have been a number of testing procedures developed so far (see, e.g., Bhargava, Franzini and Narendranathan (1982), Baltagi and Li (1995), Baltagi and Wu (1999), Bera et al. (2001), Wooldridge (2002), Drukker (2003), Hong and Kao (2004) and Inoue and Solon (2006)), testing for serial correlation has not been a standard practice in applied research that uses panel data, as recognized by Kédzi (2004) and Bertrand et al. (2004). As conjectured by Inoue and Solon (2006), the reason for this might be that there had been no simple testing procedure until very recently. Moreover, many simple testing procedures, such as those suggested by Wooldridge (2002), look only at the first order autocorrelation and are not portmanteau tests. Although portmanteau tests do exist for panel data, such as those proposed by Hong and Kao (2004) and Inoue and Solon (2006), there has been no test for serial correlation in micro economic panel data that is both portmanteau test and is as straightforward as the Ljung–Box or Box–Pierce test. (Fu et al. (2002) extend the Box–Pierce test to panel data settings. However, they consider only time effects and do not consider the presence of individual effects. In most applied economics research using panel data, we need to consider individual effects and their test is not readily applicable.) This paper seeks to provide a simple and straightforward portmanteau test to fill this gap.