The effectiveness of migration policies has been widely contested. However, because of methodological and conceptual limitations, evidence has remained inconclusive. Moreover, prior studies focus on the effects of policies on inflows and fail to assess the simultaneous effect of policies on outflows. This is essential from a theoretical point of view as immigration restrictions may reduce both inflows and outflows and, hence, overall circulation. This renders the effect of immigration restrictions on net migration theoretically ambiguous. To fill this gap, and using unique migration and visa data from the Determinants of International Migration (DEMIG) project, this paper assesses the short‐ and long‐term effects of travel visa policy regimes on bilateral immigration and emigration dynamics. The results suggest that travel visa policies significantly decrease inflows, but this effect is undermined by decreasing outflows of the same migrant groups. This confirms that migration restrictions decrease circulation and tend to encourage long‐term settlement, and thereby sharply reduce the responsiveness of migration to economic fluctuations in destination and origin societies. We also identify asymmetric policy effects with migration flows declining only very gradually after a visa introduction but increasing almost immediately after visa removal.