We study the impact of selection bias on the gender pay gap, focusing on post 1981 period. Previous work on this question has found divergent results. Using Michigan Panel Study of Income Dynamics data and several identification strategies, we find that, after adjusting for selection, there were large declines in the raw and the unexplained gender wage gaps over the 1981-2015 period. Under our preferred method of accounting for selection, the raw median wage gap fell by 0.378 log points, and the median unexplained gap fell by 0.204 log points. These declines are larger than estimates that do not account for selection. Our results suggest that women's relative wage offers have increased over this period. However, substantial gender wage gaps remain. In 2015, at the median, the selectivity-corrected gaps were 0.242 log points (raw gap) and 0.206 log points (unexplained gap).