Recursive Contracts

• Authors: Ramon Marimon and Albert Marcet.
• BSE Working Paper: 110039 | September 15
• Keywords: Recursive methods , dynamic optimization , Ramsey equilibrium , time inconsistency , limited participation , contract default , saddle-points , Lagrangian multipliers
• JEL codes: C61, C63, D58, E27
• Recursive methods
• dynamic optimization
• Ramsey equilibrium
• time inconsistency
• limited participation
• contract default
• saddle-points
• Lagrangian multipliers

We obtain a recursive formulation for a general class of contracting problems involving incentive constraints. These constraints make the corresponding maximization sup problems non-recursive. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle-point (infsup) functional equation (analogous to a Bellman equation) that characterizes the recursive solution to the planner’s problem and forward-looking constraints. Our approach has been applied to a large class of dynamic contractual problems, such as contracts with limited enforcement, optimal policy design with implementability constraints, and dynamic political economy models.