Statistical uncertainty and coarse contracts

This paper studies a robust contracting problem with a standard principal and a strictly risk-averse agent who is (i) uncertain about the production technology and (ii) ambiguity-averse in the sense of the Bewley (1986) incomplete preferences criterion. When the agent's uncertainty is sufficiently limited, the optimal contract is fully contingent on the state of the world, as in the classical problem. Conversely, when that uncertainty is sufficiently extensive, the optimal contract is (generically) a binary contract with only two distinct payment levels. In intermediate cases, the optimal contract becomes progressively more detailed as the agent becomes increasingly certain about the technology. We provide a statistical interpretation of our model under which the principal's beliefs and the agent's belief sets are as if they were derived from the public observation of i.i.d. output data.