A flow model of labor market participation is used to describe how various exogenous variations jointly affect unemployment and participation and provides short-run identification restrictions of a structural VAR. In some countries, fast rising female participation may have had a moderate short- and medium-run impact on unemployment rates. A variance decomposition exercise indicates that, in Continental Europe, participation is driven in the short run by unemployment shocks, whereas in the USA, it is driven by participation shocks (demography, immigration). Unemployment in Europe is driven by participation shocks, whereas in the USA, it is driven by unemployment shocks.