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Linear-quadratic approximation of optimal policy problems

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  • Benigno, Pierpaolo
  • Woodford, Michael

Abstract

We consider a general class of nonlinear optimal policy problems with forward-looking constraints, and show how to derive a problem with linear constraints and a quadratic objective that approximates the exact problem. The solution to the LQ approximate problem represents a local linear approximation to optimal policy from the “timeless perspective” proposed in Benigno and Woodford (2004, 2005) [6,7], in the case of small enough stochastic disturbances. We also derive the second-order conditions for the LQ problem to have a solution, and show how to correctly rank alternative simple policy rules, again in the case of small enough shocks.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 1 ()
Pages: 1-42

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:1:p:1-42

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Perturbation methods; Timeless perspective; Policy rules;

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