The effectiveness of migration policies has been widely contested, yet evidence has remained inconclusive due to conceptual and methodological limitations. Moreover, a general ‘receiving country bias’ in migration research, causes prior studies to focus on the effects of policies on inflows and fail to assess the simultaneous effect of policies on outflows. From a theoretical viewpoint, immigration restrictions reduce both inflows and outflows and, hence, overall circulation, which renders their effect on net migration theoretically ambiguous. To test this hypothesis, and using unique migration and visa datasets compiled by the DEMIG project (covering 38 countries over the 1973–2012 period), this paper assesses the short and long-term effects of travel visa policies on bilateral (country-to-country) inflow and outflow dynamics. The results suggest that travel visa policies significantly decrease inflows, but that this effect is to a large extent undermined by decreasing outflows of the same migrant groups. This seems to confirm that migration restrictions decrease circulation and tend to encourage long-term settlement, and thereby significantly reduce the responsiveness of migration to economic fluctuations in destination and origin societies.