Most previously used measures of immigrant labor market assimilation will be biased if there is non-random emigration of immigrants. We use longitudinal data on immigration to Sweden 1970-1990 to examine the extent and pattern of immigrant emigration and its consequences for measures of assimilation. Large fractions of the immigrants leave the host country shortly after arrival; within five years, more than a quarter of the people studied emigrated. As expected, economic migrants are much more likely to emigrate than political ones. Further, within these two groups, it is the least economically successful who leave. This creates the impression that immigrants well-being relative to natives improves with time in Sweden. However, not adjusting for emigration leads to overestimating the rate of economic assimilation, for Nordic and OECD immigrants by about much as 75 percent.90 percent or more.