Following the seminal work of Mirrlees (REStud, 1971), there has been a large amount of work on how to design an optimal tax system when agents' skills are private information. This literature makes a strong assumption: it assumes that the data generation process for skills in the economy is common knowledge among the agents and designer. In this paper, we relax this common knowledge assumption. There are two ways to proceed in this regard. We could treat agents' beliefs about their future skills, and the joint distribution of others' skills, as part of their true type. Then, we could solve for the optimal incentive-compatible allocations given this definition of agent's type, and design a tax system that implements this optimal allocation. We take a different approach, which follows the recent work of Bergemann and Morris (Econometrica, 2005). We focus on what we term robust allocations. A robust allocation is one that is incentive-compatible regardless of the specification of agents' beliefs. We look for optimal robust allocations, and seek to design a tax system that implements an optimal robust allocation. We prove two main theorems so far. The first theorem provides a complete characterization of robust allocations. A robust allocation must satisfy two conflicting restrictions. First, the period t allocation must be measurable with respect to the current and past realizations of skills for all agents in the economy. Second, the period t allocation must be ex-post incentive compatible. This means that it must be incentive-compatible, given that agents know their own future sequence of skills, and the joint distribution of skill sequences in the economy. (Intuitively, we have to allow for the possibility that agents receive a highly informative signal at the beginning of time about future skills.) THe second theorem derives a version of the inverse Euler equation of Rogerson (Econometrica, 1985) and Golosov, Kocherlakota and Tsyvinski (REStud, 2003) to this setting. This means that it is possible to design an optimal tax system in which total wealth tax collections are zero in every date and state. However, it is not true that in this system expected wealth taxes are zero - this depends on the unspecified beliefs of agents in the economy. Finally, we have numerical examples about the nature of optimal consumption-labor wedges. We show that a optimal robust tax system may have much higher labor taxes than is the case when the processs for skills is common knowledge.
