This paper analyzes intergenerational earnings mobility in a model where human capital is produced using schooling and parental time. In steady-states more mobile societies have less inequality, but in the short run higher mobility may result from an increase in inequalilty. Starting from the same inequality, mobility is higher under public than under private education. A rise in income shocks, for example due to increased returns to ability, or a switch from public to private schooling both increase inequality. However, increased shocks raise mobility in the short run and do not affect it in the long run, whereas an increased role for private schooling reduces mobility in both the short and long run. That these differences may help to identify the source of changes in inequality, and other real-world implications, are illustrated in a brief discussion of time trends and cross-country differences.