As WOOL:10;textualplm, Sec. 10.5.4 observes, under
the null of no serial correlation in the errors, the residuals of a
FE model must be negatively serially correlated, with
\(cor(\hat{u}_{it}, \hat{u}_{is})=-1/(T-1)\) for each
\(t,s\). He suggests basing a test for this null hypothesis on a
pooled regression of FE residuals on their first lag:
\(\hat{u}_{i,t} = \alpha + \delta \hat{u}_{i,t-1} +
\eta_{i,t}\). Rejecting the restriction \(\delta = -1/(T-1)\)
makes us conclude against the original null of no serial
correlation.
pwartest estimates the within model and retrieves residuals,
then estimates an AR(1) pooling model on them. The test statistic
is obtained by applying a F test to the latter model to test the
above restriction on \(\delta\), setting the covariance matrix to
vcovHC with the option method="arellano" to control for serial
correlation.
Unlike the pbgtest() and pdwtest(), this test does
not rely on large--T asymptotics and has therefore good properties in
``short'' panels. Furthermore, it is robust to general heteroskedasticity.