Econometrica, 2019, Vol. 87, No. 5, pp. 1589-1631
MARCET, Albert, MARIMON, Ramon, Recursive contracts, Econometrica, 2019, Vol. 87, No. 5, pp. 1589-1631 - https://hdl.handle.net/1814/66074
Retrieved from Cadmus, EUI Research Repository
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 mu(t) summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with mu(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.
First published: 30 September 2019
Cadmus permanent link: https://hdl.handle.net/1814/66074
Full-text via DOI: 10.3982/ECTA9902
ISSN: 0012-9682; 1468-0262
Keyword(s): Recursive methods dynamic optimization Ramsey equilibrium time inconsistency limited commitment limited enforcement saddle-points Lagrangian multipliers Bellman equations
Sponsorship and Funder information:MCyT-MEyC of SpainGeneralitat de CatalunyaGeneralitat de CatalunyaAxa Research FundEuropean Research Council under the EU 7th Framework Programme (FP/2007-2013) Grant [324048-APMPAL]Programa de Excelencia del Banco de EspanaSevero Ochoa Programme for Centres of Excellence in RD [SEV-2015-0563]CIRIT
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