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Econometrica
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Recursive Contracts

Recursive contracts
Authors: Albert Marcet; Ramon Marimon;
Abstract

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.

Countries
Italy, Spain, United Kingdom
Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
58
Top 10%
Top 10%
Top 1%
Green