Recursive contracts
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0012-9682; 1468-0262
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Econometrica, 2019, Vol. 87, No. 5, pp. 1589-1631
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MARCET, Albert, MARIMON, Ramon, Recursive contracts, Econometrica, 2019, Vol. 87, No. 5, pp. 1589-1631 - https://hdl.handle.net/1814/66074
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 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.
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First published: 30 September 2019
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MCyT-MEyC of Spain
Generalitat de CatalunyaGeneralitat de Catalunya
Axa Research Fund
European Research Council under the EU 7th Framework Programme (FP/2007-2013) Grant [324048-APMPAL]
Programa de Excelencia del Banco de Espana
Severo Ochoa Programme for Centres of Excellence in RD [SEV-2015-0563]
CIRIT
Generalitat de CatalunyaGeneralitat de Catalunya
Axa Research Fund
European Research Council under the EU 7th Framework Programme (FP/2007-2013) Grant [324048-APMPAL]
Programa de Excelencia del Banco de Espana
Severo Ochoa Programme for Centres of Excellence in RD [SEV-2015-0563]
CIRIT