Persistent Private Information Revisited

Abstract

This paper revisits Williams' (2011) (henceforth PPI’s) continuous-time principal-agent model of optimal dynamic insurance with persistent private information. We identify three independent issues in PPI that implicate its characterizations of incentive compatible and optimal contracts: (i) the agent cannot over-report increments of his type, a constraint that does not follow from the common assumption that the agent cannot over-report his type; (ii) the agent’s feasible set of reporting strategies does not include standard "no Ponzi" constraints, without which PPI’s main analysis of infinite-horizon incentive compatibility is incomplete; and (iii) most importantly, in PPI’s main application, which concerns hidden endowments, the contract identified as optimal is generically strictly suboptimal. For this application, we address the three issues by analyzing a class of “self-insurance contracts” that can be implemented as consumption-saving problems for the agent, and which includes the contract derived in PPI as a particular case. We characterize the optimal self-insurance contract and show that, generically, it strictly dominates PPI’s. Our analysis does not support PPI’s main economic finding that immiseration generally fails or its attribution of this failure to continuous time and persistence.