Linear-quadratic approximation of optimal policy problems

• 成果类型: Article
• 署名作者: Benigno, Pierpaolo; Woodford, Michael
• 署名单位: Columbia University; Luiss Guido Carli University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2011.10.012
• 发表日期: 2012
• 页码: 1-42
• 关键词: Perturbation methods; Timeless perspective; policy rules

摘要

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 Benign 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. (C) 2011 Elsevier Inc. All rights reserved.