States and localities are increasingly experimenting with higher minimum wages in response to rising income inequality and stagnant economic mobility, but commonly used public datasets offer limited opportunities to evaluate the extent to which such changes affect earnings growth. We use administrative earnings data from the Social Security Administration linked to the Current Population Survey to overcome important limitations of public data and estimate effects of the minimum wage on growth incidence curves and income mobility profiles, providing insight into how cross-sectional effects of the minimum wage on earnings persist over time. Under both approaches, we find that raising the minimum wage increases earnings growth at the bottom of the distribution, and those effects persist and indeed grow in magnitude over several years. This finding is robust to a variety of specifications, including alternatives commonly used in the literature on employment effects of the minimum wage. Instrumental variables and subsample analyses indicate that geographic mobility likely contributes to the effects we identify. Extrapolating from our estimates suggests that a minimum wage increase comparable in magnitude to the increase experienced in Seattle between 2013 and 2016 would have blunted some, but not nearly all, of the worst income losses suffered at the bottom of the income distribution during the Great Recession.