The stylized facts suggest a negative relationship between tax progressivity and the skill premium from the early 1960s until the early 1990s, and a positive one thereafter. They also generally imply rising tax progressivity, except for the 1980s. In this paper, we ask whether optimal tax policy is consistent with these observations, taking into account the demographic and technological factors that have also affected the skill premium. To this end, we construct a dynamic general equilibrium model in which the skill premium and the progressivity of the tax system are endogenously determined, with the latter being optimally chosen by a benevolent government. We find that optimal policy delivers both a progressive tax system and model predictions which are generally consistent, except for the 1980s, with the stylized facts relating to the skill premium and progressivity. To capture the patterns in the data over the 1980s requires that we adopt a government policy which is biased towards the interests of skilled agents. Thus, in addition to demographic and technological factors, changes in the preferences of policy-makers appear to be a potentially important factor in determining the evolution of the observed skill premium.