I study trade-induced transitional dynamics by estimating a structural dynamic equilibrium model of the Brazilian labor market. The model features a multi-sector economy with overlapping generations, heterogeneous workers, endogenous accumulation of sector-specific experience and costly switching of sectors. The model's estimates yield median costs of mobility ranging from 1.4 to 2.7 times annual average wages, but a high dispersion across the population. In addition, sector-specific experience is imperfectly transferable across sectors, leading to additional barriers to mobility. Using the estimated model for counter-factual trade liberalization experiments, the main findings are: (1) there is a large labor market response following trade liberalization but the transition may take several years; (2) potential aggregate welfare gains are significantly mitigated due to the delayed adjustment; (3) trade-induced welfare effects depend on initial sector of employment and on worker demographics. The experiments also highlight the sensitivity of the transitional dynamics with respect to assumptions regarding the mobility of capital.