Working Paper: NBER ID: w17064
Authors: Harold L. Cole; Felix Kubler
Abstract: Marcet and Marimon (1994, revised 1998, revised 2011) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a flat region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through - one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal's choice set is not convex but where randomization is possible.
Keywords: Dynamic Contracting; Pareto Frontier; Randomization; Recursive Methods
JEL Codes: C61; D82
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| recursive saddle point method (C69) | handle weakly concave Pareto frontiers (D69) |
| end-of-period lottery (H27) | recursive multiplier captures implicit prior promises (D86) |
| public randomization (C90) | address incentive constraints (M52) |
| extension of recursive saddle point method (C69) | optimal policy functions (C61) |
| identification of extreme actions (P37) | feasible and optimal outcomes (C61) |