Dynamic Optimal Taxation with Persistent Private Information

We study dynamic optimal taxation in a class of economies with private information over idiosyncratic skill shocks. We consider economies in which the skill distribution is first order Markov. We show that there exists a tax system that implements the constrained optimal allocation as competitive equilibrium in a market economy where agents can trade current consumption and risk-free claims to future consumption. Under this system, an agent's tax payments are conditioned only the following observable characteristics: her accumulated stock of claims, or wealth, her labour earnings in the current and past period, and her savings. The optimal tax function is not additively separable in these variables. We show that if the skill process is positively correlated, the marginal tax on savings is increasing in current labor earnings, implying a "savings subsidy" for low skill agents