The small sample bias of Durbin's tests for serial correlation When one of the regressors is the lagged dependent variable and the null hypothesis is true

Durbin (1970) has recently proposed two asymptotically equivalent statistics which can be used to test for the presence of serial correlation when some of the regressors are lagged dependent variables. This study reports on simulation experiments designed to compare the two statistics, in use with small samples, in terms of their tendencies to detect serial correlation when none exists. Of the two test statistics, it is found that the one based on estimated residuals detects the absence of serial correlation in the expected proportion of trials; the other statistic (Durbin's h), which involves the application of a correction factor to the Durbin-Watson statistic, gives evidence of serious small sample bias which varies with both the sample size and the assumed size of the coefficient attaching to the lagged dependent variable.