Advanced Search
MyIDEAS: Login

Linear-quadratic approximation of optimal policy problems

Contents:

Author Info

  • Pierpaolo Benigno

    ()
    (New York University - Department of Economics)

  • Michael Woodford

    ()
    (Columbia University - Department of Economics)

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.econ.columbia.edu/RePEc/pdf/DP0607-02.pdf
Our checks indicate that this address may not be valid because: 404 Not Found (http://www.econ.columbia.edu/RePEc/pdf/DP0607-02.pdf [301 Moved Permanently]--> http://econ.columbia.edu/RePEc/pdf/DP0607-02.pdf). If this is indeed the case, please notify (Discussion Paper Coordinator)
Download Restriction: no

Bibliographic Info

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

as in new window
Length: 65 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:clu:wpaper:0607-02

Contact details of provider:
Postal: 1022 International Affairs Building, 420 West 118th Street, New York, NY 10027
Phone: (212) 854-3680
Fax: (212) 854-8059
Web page: http://www.econ.columbia.edu/
More information through EDIRC

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
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.:
as in new window
  1. Lars Peter Hansen & Thomas J. Sargent, 1990. "Recursive Linear Models of Dynamic Economies," NBER Working Papers 3479, National Bureau of Economic Research, Inc.
  2. Bianca De Paoli, 2004. "Monetary Policy and Welfare in a Small Open Economy," CEP Discussion Papers dp0639, Centre for Economic Performance, LSE.
  3. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2004. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Econometric Society 2004 North American Winter Meetings 411, Econometric Society.
  4. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2003. "Optimal Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 70(4), pages 825-860.
  5. Andrew Levin & Christopher J. Erceg & Dale W. Henderson, 1999. "Optimal Monetary Policy with Staggered Wage and Price Contracts," Computing in Economics and Finance 1999 1151, Society for Computational Economics.
  6. LeRoy, Stephen F & Waud, Roger N, 1977. "Applications of the Kalman Filter in Short-Run Monetary Control," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 195-207, February.
  7. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  8. Jinill Kim & Sunghyun Henry Kim, 2007. "Two pitfalls of linearization methods," Finance and Economics Discussion Series 2007-64, Board of Governors of the Federal Reserve System (U.S.).
  9. Benigno, Pierpaolo & Woodford, Michael, 2004. "Optimal Taxation in an RBC Model: A Linear-Quadratic Approach," CEPR Discussion Papers 4764, C.E.P.R. Discussion Papers.
  10. Pierpaolo Benigno & Michael Woodford, 2003. "Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach," NBER Working Papers 9905, National Bureau of Economic Research, Inc.
  11. Robert King & Alexander L. Wolman, 1999. "What Should the Monetary Authority Do When Prices Are Sticky?," NBER Chapters, in: Monetary Policy Rules, pages 349-404 National Bureau of Economic Research, Inc.
  12. Marc P. Giannoni & Michael Woodford, 2003. "Optimal Interest-Rate Rules: I. General Theory," Levine's Bibliography 506439000000000384, UCLA Department of Economics.
  13. Paul Levine & Joseph Pearlman & Richard Pierse, 2006. "Linear-Quadratic Approximation, Efficiency and Target-Implementability," Computing in Economics and Finance 2006 441, Society for Computational Economics.
  14. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
  15. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Optimal Fiscal and Monetary Policy Under Sticky Prices," CEPR Discussion Papers 2942, C.E.P.R. Discussion Papers.
  16. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and Using Second Order Accurate Solutions of Discrete Time," Levine's Bibliography 666156000000000284, UCLA Department of Economics.
  17. J.H. Kalchbrenner & P.A. Tinsley, 1976. "On the use of optimal control in the design of monetary policy," Special Studies Papers 76, Board of Governors of the Federal Reserve System (U.S.).
  18. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  19. Pierpaolo Benigno & Michael Woodford, 2004. "Inflation stabilization and welfare: The case of a distorted steady state," Discussion Papers 0405-04, Columbia University, Department of Economics.
  20. Jinill Kim & Sunghyun Henry Kim, 1999. "Spurious Welfare Reversals in International Business Cycle Models," Virginia Economics Online Papers 319, University of Virginia, Department of Economics.
  21. Pierpaolo Benigno & Michael Woodford, 2004. "Optimal Stabilization Policy When Wages and Prices are Sticky: The Case of a Distorted Steady State," NBER Working Papers 10839, National Bureau of Economic Research, Inc.
  22. Benigno, Gianluca & Benigno, Pierpaolo, 2006. "Designing targeting rules for international monetary policy cooperation," Journal of Monetary Economics, Elsevier, vol. 53(3), pages 473-506, April.
  23. Ferrero, Andrea, 2009. "Fiscal and monetary rules for a currency union," Journal of International Economics, Elsevier, vol. 77(1), pages 1-10, February.
  24. Barro, Robert J, 1979. "On the Determination of the Public Debt," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 940-71, October.
  25. Bianca De Paoli, 2004. "Monetary policy and welfare in a small open economy," LSE Research Online Documents on Economics 19950, London School of Economics and Political Science, LSE Library.
  26. Stephanie Schmitt-Grohé & Martín Uribe, 2007. "Optimal simple and implementable monetary and fiscal rules," Working Paper 2007-24, Federal Reserve Bank of Atlanta.
  27. Hans M. Amman & David A. Kendrick, 1996. "The DUALI/DUALPC Software for Optimal Control Models: Introduction," CARE Working Papers 9602, The University of Texas at Austin, Center for Applied Research in Economics.
  28. Sutherland, Alan, 2002. "A Simple Second-Order Solution Method For Dynamic General Equilibrium Models," CEPR Discussion Papers 3554, C.E.P.R. Discussion Papers.
  29. Backus, David & Driffill, John, 1986. "The Consistency of Optimal Policy in Stochastic Rational Expectations Models," CEPR Discussion Papers 124, C.E.P.R. Discussion Papers.
  30. Kendrick, David A., 2005. "Stochastic control for economic models: past, present and the paths ahead," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 3-30, January.
  31. Jensen, Christian & McCallum, Bennett T., 2002. "The non-optimality of proposed monetary policy rules under timeless perspective commitment," Economics Letters, Elsevier, vol. 77(2), pages 163-168, October.
  32. Söderlind, Paul, 1998. "Solution and Estimation of RE Macromodels with Optimal Policy," Working Paper Series in Economics and Finance 256, Stockholm School of Economics.
  33. Andrew P. Blake, 2001. "A `Timeless Perspective' on Optimality in Forward-Looking Rational Expectations Models," NIESR Discussion Papers 188, National Institute of Economic and Social Research.
  34. Woodford Michael, 2002. "Inflation Stabilization and Welfare," The B.E. Journal of Macroeconomics, De Gruyter, vol. 2(1), pages 1-53, February.
  35. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:clu:wpaper:0607-02. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Discussion Paper Coordinator).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.