Testing serial correlation in fixed effects regression models based on asymptotically unbiased autocorrelation estimators

Testing the presence of serial correlation in the error terms in fixed effects regression models is important for many reasons. This paper proposes portmanteau tests based on the sum of the squares of autocorrelation estimators. This approach is a direct extension of the Box–Pierce or Ljung–Box test from single time series to panel data settings. In fixed effects regression analysis, we may estimate the autocorrelations using the within-group autocorrelations of the residuals. However, the within-group autocorrelations may be severely biased when the length of the time series is not very large compared with the cross-sectional sample size, as a result of the incidental parameters problem. We overcome this problem by using asymptotically unbiased autocorrelation estimators for long panel data recently proposed by the author. Monte Carlo simulations reveal that the proposed tests have good size properties and are powerful against a wide range of alternatives.