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Recursive Contracts

Marcet, A; Marimon, R; (2019) Recursive Contracts. Econometrica , 87 (5) pp. 1589-1631. 10.3982/ECTA9902. Green open access

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Abstract

We obtain a recursive formulation for a general class of optimization problems with forwardlooking 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 µt summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with µt 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.

Type: Article
Title: Recursive Contracts
Open access status: An open access version is available from UCL Discovery
DOI: 10.3982/ECTA9902
Publisher version: https://doi.org/10.3982/ECTA9902
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Recursive methods, dynamic optimization, Ramsey equilibrium, time inconsistency, limited commitment, limited enforcement, saddle-points, Lagrangian multipliers, Bellman equations.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/10079283
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