We present new empirical evidence for the way inflation reduces the inequality of the income distribution in the U.S. economy. The main mechanism emphasized in this paper is the "bracket creep" effect according to which inflation pushes income into higher tax brackets. Governments adjust the nominal income tax brackets slowly due to the rise in prices, typically less often than once every other year in the U.S. postwar history. We also develop a theoretical general equilibrium monetary model with income heterogeneity. In line with our time series evidence, it is rather the frequency of income tax schedule adjustments than the overall level of inflation that has a perceptible impact on the distribution of income. We find that a longer duration between two successive adjustments of the schedule reduces employment, savings, and output significantly.