Dynamic mechanism design with hidden income and hidden actions

Abstract

We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. In our baseline model, the principal observes nothing other than transfers. Nevertheless, optimal incentive-constrained insurance can be attained. Starting from a general mechanism with arbitrary communication, randomization, full history dependence, and without restrictions on preferences or technology, we show that the optimal contract can be implemented as a recursive direct mechanism. The state variable for this mechanism is a vector of utility promises conditional on realized income. However, the standard recursive formulation suffers from a curse of dimensionality which arises from the interaction of hidden income and hidden actions. The curse can be overcome by introducing judiciously chosen utility bounds for deviation behavior off the equilibrium path. Our methods generalize to environments with multiple actions and additional states, some of which may be observable, and to non-separable preferences. The key to implementing these extensions is to introduce multiple layers of off-path utility bounds.

Market Power and Asset Contractibility in Dynamic Insurance Contracts

“…(ii) Assets eliminate the insurer's ability to smooth the agent's consumption beyond self-insurance (Allen, 1985, andCole andKocherlakota, 2001). Or (iii) the environment becomes highly intractable (Fernandes andPhelan, 2000, andDoepke andTownsend, 2006). In contrast, we show that Markov-perfect insurance contracts result in simple dynamic programs with a single scalar state variable and avoid the curse of dimensionality, including the case with noncontractible savings.…”

Optimal Ramsey taxation with hidden actions

“…Certainly, some existing literature studied optimal dynamic taxation in the framework with hidden types, i.e., either the economic agent or the government has private information, requiring that incentive-compatible constraint met based on the revelation principle (see, Doepke and Townsend, 2006). As a consequence, there the tax policies play the role of implementation schemes, that is, implementing efficient allocations as a competitive equilibrium with truth-telling.…”

Dynamic Financial Constraints: Distinguishing Mechanism Design From Exogenously Incomplete Regimes

“…A problem with that approach arises from possible non-convexities induced by the incentive or commitment constraints. 15 Here, by way of contrast we operate in extremely general environments, following Fernandes and Phelan (2000) and Doepke and Townsend (2006). Our linear programming approach can be applied for any preference and technology specifications since, by construction, it convexifies the problem by allowing any possible randomization (lotteries) over the solution variables.…”

“…Because of the dynamic adverse selection problem in k , following Fernandes and Phelan (2000) and Doepke and Townsend (2006), 1 the proper state variable in the recursive representation of this problem is not as scalar (as in the MH regime) but a promised utility schedule, w ≡ { w ( k 1 ), w ( k 2 ), …, w ( k # K )} belonging to some set of schedules W (to be determined) where k 1 , k 2 , etc. are the elements of the grid K .…”

“…The proofs that the optimal contracting problems can be written in recursive form and that the revelation principle applies follow from Phelan and Townsend (1991) and Doepke and Townsend (2006) and hence are omitted. …”