Until the 2008 crisis, observers often contrasted the ability of U.S. and European labour markets to rebound from cyclical shocks. The U.S. was generally viewed as more resilient, i.e., harder hit in the short term but returning more easily to its initial path. Between 1986 and 2007, the U.S. did display an output gap that was both subject to wider swings and quicker to return to equilibrium. But this evidence does not suffice to conclude that the U.S. was more resilient. The difference in response may also have been due to differences in the nature of the shocks to which the U.S. and Europe were exposed. To assess these two interpretations, we rely on a structural approach directly inspired by Kai Christoffel and Tobias Linzert. We use twin intertemporal dynamic general stochastic equilibrium (DSGE) models, calibrated separately for the U.S. and France, and incorporating a Diamond-Mortensen-Pissarides matching model. The latter attributes the existence of equilibrium unemployment to the presence of frictions in the encounter between the unemployed and business firms. The frictions are generated by the imperfection of information on potential matches. The match between an unemployed person and a firm is not automatic. At any given moment, job-seekers coexist with vacancies ready to be filled. Our approach shows that the resilience gaps are wide for labour-market shocks (here, the U.S. has the advantage) and narrower for productivity and monetary-policy shocks. We use the same models to estimate the historical shocks in each economy between 1986 and 2007 and to quantify the contributions of each type of shock to output-gap fluctuations. We find that the divergence in the two countries' paths is mainly due to different historical combinations of shocks, more than to unequal shock-absorbing capabilities.