We evaluate the distributional effects of a minimum wage introduction based on a data set with a moderate sample size but a large number of potential covariates. Therefore, the selection of relevant control variables at each distributional threshold is crucial to test hypotheses about the impact of the treatment. To this end, we use the post-double selection logistic distribution regression approach proposed by Belloni et al. (2018a), which allows for uniformly valid inference about the target coefficients of our low-dimensional treatment variables across the entire outcome distribution. Our empirical results show that the minimum wage crowded out hourly wages below the minimum threshold, benefitted monthly wages in the lower middle but not the lowest part of the distribution, and did not significantly affect the distribution of hours worked.