Temporary migration, though empirically relevant, is often ignored in formal models. This paper proposes a migration model with heterogeneous agents and persistent cross country income differentials that features temporary migration. In equilibrium there exists a positive relation between the stock of migrants and the income differential, while the net migration flow becomes zero. Consequently, existing empirical migration models, estimating net migration flows, instead of stocks, may be misspecified. This suspicion appears to be confirmed by our investigation of the cointegration relationships of German migration stocks and flows since 1967. We find that (i) panel-unit root tests reject the hypothesis that migration flows and the explanatory variables are integrated of the same order, while migration stocks and the explanatory variables are all I(1) variables, and (ii) the hypothesis of cointegration cannot be rejected for the stock model.