
doi: 10.3982/ecta9902
handle: 10230/453 , 1814/17215 , 1814/16815 , 1814/66074 , 1814/682
We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.
Time inconsistency, recursive formulation, dynamic programming, Ramsey equilibrium, participation constraint, recursive saddle points, E27, time inconsistency, Saddle-points, saddle-points, ramsey equilibrium, limited commitment, recursive saddle points, dynamic optimization, Contract theory (moral hazard, adverse selection), Bellman equations, Macroeconomics and International Economics, D58, Economic dynamics, Transactional relationships, contracts and reputation, recursive formulation, participation constraint, Limited enforcement, dynamic programming, Bellman equations., recursive methods, limited enforcement, Contract default, C61, Dynamic optimization, C63, Limited participation, participation constraint, Lagrangian multipliers, Ramsey equilibrium, Recursive methods, recursive formulation, Time inconsistency, Limited commitment, jel: jel:D80, jel: jel:C63, jel: jel:C61, jel: jel:L14
Time inconsistency, recursive formulation, dynamic programming, Ramsey equilibrium, participation constraint, recursive saddle points, E27, time inconsistency, Saddle-points, saddle-points, ramsey equilibrium, limited commitment, recursive saddle points, dynamic optimization, Contract theory (moral hazard, adverse selection), Bellman equations, Macroeconomics and International Economics, D58, Economic dynamics, Transactional relationships, contracts and reputation, recursive formulation, participation constraint, Limited enforcement, dynamic programming, Bellman equations., recursive methods, limited enforcement, Contract default, C61, Dynamic optimization, C63, Limited participation, participation constraint, Lagrangian multipliers, Ramsey equilibrium, Recursive methods, recursive formulation, Time inconsistency, Limited commitment, jel: jel:D80, jel: jel:C63, jel: jel:C61, jel: jel:L14
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