International migration is characterized by two puzzling facts: First, only a small share of the population tends to migrate although substantial and persisting income differences across countries exist. Second, net migration rates tend to cease over time despite persisting income differences. This paper addresses these issues in a migration model with heterogeneous agents that features temporary migration. In equilibrium a positive relation exists 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 empirical 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.