We consider the dynamic regression model with lagged endogenous variables and moving average disturbances, when some observations on the endogenous variable are missing. The available data are assumed to be sampled at regular intervals of length m and can be linear combinations of the realizations of the variable over a finite number of periods. We discuss the identification of the parameters in the model. For some selected models, we evaluate the large sample variances of the maximum likelihood (ML) estimates for the incomplete data and complete data respectively. In this way, we get an indication of the loss of information when the data are incomplete. Finally, we give some results for the effects on the properties of the OLS estimator, when the interpolated series are substituted for the missing observations and we briefly discuss ways to obtain ML estimates. Our general conclusion is that when the sample is incomplete it is very important to use all available reliable a priori information to analyze the model.