Assessing the migration potential and predicting future migration streams are among the most relevant, yet least well understood topics of migration research. The usual approach taken to address aggregate-level prediction problems is to fit ad hoc specifications to historical data, and to extrapolate from these estimates on the basis of conditioning information that is assumed to be known with certainty. In this context, this strategy faces formidable problems that exceed the usual difficulties arising for the prediction of economic variables. This paper addresses this extrapolation problem formally, with an application to the case of EU-enlargement and the ensuing migration streams to be expected from Eastern Europe.