We propose a job search model with minimum wage regulations and imperfect compliance to explain the doubling of the mean and variance of hourly earnings of white males during the first 18 years of labor market experience. The model encompasses job mobility and on-the-job wage growth as sources of wage dynamics, and is estimated by simulated generalized method of moments using data from the National Longitudinal Survey of Youths 1979. Our estimates provide a good fit for the observed levels and trends of the main job and wage mobility data, and for the increase in the mean and variance of wages over the life cycle, as well as for the fall in the fraction of workers paid below the minimum wage. Job mobility explains 40–50% of the observed wage growth. Increases in the minimum wage and/or compliance deliver small effects on the wage distribution and the nonemployment rate. Copyright © 2010 John Wiley & Sons, Ltd.