Approximation formulae are developed for the bias of ordinary andgeneralized Least Squares Dummy Variable (LSDV) estimators in dynamicpanel data models. Results from Kiviet (1995, 1999) are extended tohigher-order dynamic panel data models with general covariancestructure. The focus is on estimation of both short- and long-runcoefficients. The results show that proper modelling of thedisturbance covariance structure is indispensable. The biasapproximations are used to construct bias corrected estimators whichare then applied to quarterly data from 14 European Union countries.Money demand functions for M1, M2 and M3 are estimated for the EUarea as a whole for the period 1991:I-1995:IV. Significant spilloversbetween countries are found reflecting the dependence of domesticmoney demand on foreign developments. The empirical results show thatin general plausible long-run effects are obtained by the biascorrected estimators. Moreover, bias correction can be substantialunderlining the importance of more refined estimation techniques.Also the efficiency gains by exploiting the heteroscedasticity andcross-correlation patterns between countries are sometimesconsiderable.