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Linear-quadratic approximation of optimal policy problems

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Author Info
Pierpaolo Benigno () (New York University - Department of Economics)
Michael Woodford () (Columbia University - Department of Economics)

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Abstract

We consider a general class of nonlinear optimal policy problems involving forward-looking constraints (such as the Euler equations that are typically present as structural equations in DSGE models), and show that it is possible, under regularity conditions that are straightforward to check, to derive a problem with linear constraints and a quadratic objective that approximates the exact problem. The LQ approximate problem is computationally simple to solve, even in the case of moderately large state spaces and flexibly parameterized disturbance processes, and its solution represents a local linear approximation to the optimal policy for the exact model in the case that stochastic disturbances are small enough. We derive the second-order conditions that must be satisfied in order for the LQ problem to have a solution, and show that these are stronger, in general, than those required for LQ problems without forward-looking constraints. We also show how the same linear approximations to the model structural equations and quadratic approximation to the exact welfare measure can be used to correctly rank alternative simple policy rules, again in the case of small enough shocks.

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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0607-02.

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Length: 65 pages
Date of creation: 2006
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Handle: RePEc:clu:wpaper:0607-02

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Frank Smets & Matthieu Darracq Pariès & Stéphane Adjemian, 2008. "A quantitative perspective on optimal monetary policy cooperation between the US and the euro area," Working Paper Series 884, European Central Bank. [Downloadable!]
  2. Michal Horvath, 2008. " Does Government Spending Optimally Crowd in Private Consumption?," CDMA Working Paper Series 0805, Centre for Dynamic Macroeconomic Analysis. [Downloadable!]
  3. Günter Coenen & Giovanni Lombardo & Frank Smets & Roland Straub, 2008. "International transmission and monetary policy cooperation," Working Paper Series 858, European Central Bank. [Downloadable!]
  4. Robert J. Tetlow & Brian Ironside, 2006. "Real-time model uncertainty in the United States - the Fed from 1996-2003," Working Paper Series 610, European Central Bank. [Downloadable!]
    Other versions:
  5. Marcus Hagedorn, 2008. "Nominal and real interest rates during an optimal disinflation in New Keynesian models," Working Paper Series 878, European Central Bank. [Downloadable!]
  6. Davide Debortoli & Ricardo Nunes, 2007. "Loose commitment," International Finance Discussion Papers 916, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  7. Matthieu Darracq Pariès & Stéphane Adjemian & Stéphane Moyen, 2007. "Optimal monetary policy in an estimated DSGE for the euro area," Working Paper Series 803, European Central Bank. [Downloadable!]
  8. Jung, Philip, 2007. "Optimal Taxation and (Female)-Labor Force Participation over the Cycle," MPRA Paper 8744, University Library of Munich, Germany, revised 13 May 2008. [Downloadable!]
  9. Alexander Kriwoluzky & Christian Stoltenberg, 2007. "Optimal Policy Under Model Uncertainty: A Structural-Bayesian Estimation Approach," SFB 649 Discussion Papers SFB649DP2007-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  10. Marcus Hagedorn, 2007. "Nominal and Real Interest Rates during an Optimal Disinflation in New Keynesian Models," IEW - Working Papers iewwp352, Institute for Empirical Research in Economics - IEW. [Downloadable!]
  11. Pierpaolo Benigno & Michael Woodford, 2005. "Optimal Taxation in an RBC Model: A Linear-Quadratic Approach," NBER Working Papers 11029, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  12. Michel Juillard & Florian Pelgrin, 2007. "Computing Optimal Policy in a Timeless-Perspective: An Application to a Small-Open Economy," Working Papers 07-32, Bank of Canada. [Downloadable!]
  13. Matthieu Darracq Pariès, 2007. "International frictions and optimal monetary policy cooperation - analytical solutions," Working Paper Series 834, European Central Bank. [Downloadable!]
  14. Lawrence Christiano & Roberto Motto & Massimo Rostagno, 2007. "Two Reasons Why Money and Credit May be Useful in Monetary Policy," NBER Working Papers 13502, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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