This paper develops and estimates a joint hazard-longitudinal (JHL) model of the timing of migration and labor market assimilation - two processes that have been assumed to be independent in the existing literature. The JHL model accounts for the endogenous age of entry in estimating the returns to years since migration by allowing cross-equation correlations of random intercepts with individual rates of wage assimilation. Commonly ignored sample selection issues due to non-random survey attrition and missing wages are also addressed. Using German household panel surveys from 1984 to 2014 and home country-level data from 1961, we find large upward bias in the OLS-estimated average rate of wage assimilation. Our estimates suggest that immigrants with lower unobserved skills and with a higher unobserved propensity to migrate early have a faster assimilation rate.