Not all unbalanced panels provoke a problem with PCSEs. From brief
experimentation it seems that strong collinearity among the
regressors is a contributory problem.
Which is what I have experienced: the very last time dummy in my model is dropped due to collinearity, which provokes two questions:
(1) how do I prevent that (T-2) dummies from being dropped? I don't necessarily want to drop any X variables from the model;
(2) as there is no LDV, how do I ensure that I select robust SEs that do not correct for autocorrelation?