Using Michigan Panel Study of Income Dynamics data, we study selection bias and the gender wage gap. Employing several methods, we find large declines in the total and unexplained gender gaps in wage offers between 1981 and 2015. Under our preferred selection correction method, the median total and unexplained gaps fell by 0.378 and 0.204 log points, respectively. These are larger declines than if we had not corrected for selection and simply measured convergence in observed wage gaps. However, substantial selectivity-corrected median gender wage gaps remain in 2015: 0.242 log points (total gap) and 0.206 log points (unexplained gap).