IDEAS home Printed from https://ideas.repec.org/p/cpm/dynare/010.html
   My bibliography  Save this paper

Computation of LQ Approximations to Optimal Policy Problems in Different Information Settings under Zero Lower Bound Constraints

Author

Listed:
  • Levine, Paul
  • Pearlman, Joseph

Abstract

This paper describes a series of algorithms that are used to compute optimal policy under full and imperfect information. Firstly we describe how to obtain linear quadratic (LQ) approximations to a nonlinear optimal policy problem. We develop novel algorithms that are required as a result of having agents with forward-looking expectations, that go beyond the scope of those that are used when all equations are backward-looking; these are utilised to generate impulse response functions and second moments for the case of imperfect information. We describe algorithms for reducing a system to minimal form that are based on conventional approaches, and that are necessary to ensure that a solution for fully optimal policy can be computed. Finally we outline a computational algorithm that is used to generate solutions when there is a zero lower bound constraint for the nominal interest rate.

Suggested Citation

  • Levine, Paul & Pearlman, Joseph, 2011. "Computation of LQ Approximations to Optimal Policy Problems in Different Information Settings under Zero Lower Bound Constraints," Dynare Working Papers 10, CEPREMAP.
  • Handle: RePEc:cpm:dynare:010
    as

    Download full text from publisher

    File URL: https://www.dynare.org/wp-repo/dynarewp010.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
    2. Currie,David & Levine,Paul, 2009. "Rules, Reputation and Macroeconomic Policy Coordination," Cambridge Books, Cambridge University Press, number 9780521104609.
    3. 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.
    4. Miller, Marcus & Salmon, Mark, 1985. "Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies," Economic Journal, Royal Economic Society, vol. 95(380a), pages 124-137, Supplemen.
    5. Levine, Paul & Currie, David, 1985. "Optimal feedback rules in an open economy macromodel with rational expectations," European Economic Review, Elsevier, vol. 27(2), pages 141-163, March.
    6. Blake, Andrew P. & Kirsanova, Tatiana, 2004. "A note on timeless perspective policy design," Economics Letters, Elsevier, vol. 85(1), pages 9-16, October.
    7. Bennett T. McCallum & Edward Nelson, 2004. "Timeless perspective vs. discretionary monetary policy in forward-looking models," Review, Federal Reserve Bank of St. Louis, vol. 86(Mar), pages 43-56.
    8. John B. Taylor, 1999. "A Historical Analysis of Monetary Policy Rules," NBER Chapters, in: Monetary Policy Rules, pages 319-348, National Bureau of Economic Research, Inc.
    9. Michael Woodford, 1999. "Commentary : how should monetary policy be conducted in an era of price stability?," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 277-316.
    10. Levine, Paul & McAdam, Peter & Pearlman, Joseph, 2008. "Quantifying and sustaining welfare gains from monetary commitment," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1253-1276, October.
    11. Ehrmann, Michael & Smets, Frank, 2003. "Uncertain potential output: implications for monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1611-1638, July.
    12. Levine, Paul & Currie, David, 1987. "The design of feedback rules in linear stochastic rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 11(1), pages 1-28, March.
    13. Coenen, Gunter & Wieland, Volker, 2003. "The zero-interest-rate bound and the role of the exchange rate for monetary policy in Japan," Journal of Monetary Economics, Elsevier, vol. 50(5), pages 1071-1101, July.
    14. Adam, Klaus & Billi, Roberto M., 2007. "Discretionary monetary policy and the zero lower bound on nominal interest rates," Journal of Monetary Economics, Elsevier, vol. 54(3), pages 728-752, April.
    15. Dennis, Richard & Soderstrom, Ulf, 2006. "How Important Is Precommitment for Monetary Policy?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(4), pages 847-872, June.
    16. Pearlman, Joseph & Currie, David & Levine, Paul, 1986. "Rational expectations models with partial information," Economic Modelling, Elsevier, vol. 3(2), pages 90-105, April.
    17. Ascari, Guido & Ropele, Tiziano, 2007. "Optimal monetary policy under low trend inflation," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2568-2583, November.
    18. Levine, Paul & Pearlman, Joseph & Pierse, Richard, 2008. "Linear-quadratic approximation, external habit and targeting rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3315-3349, October.
    19. Magill, Michael J. P., 1977. "Some new results on the local stability of the process of capital accumulation," Journal of Economic Theory, Elsevier, vol. 15(1), pages 174-210, June.
    20. Currie, David & Levine, Paul, 1985. "Simple Macropolicy Rules for the Open Economy," Economic Journal, Royal Economic Society, vol. 95(380a), pages 60-70, Supplemen.
    21. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
    22. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
    23. Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
    24. Coenen, Guenter & Wieland, Volker, 2003. "The Zero-Interest-Rate and the Role of the Exchange Rate for Monetary Policy in Japan," CFS Working Paper Series 2003/09, Center for Financial Studies (CFS).
    25. John B. Taylor, 1999. "Introduction to "Monetary Policy Rules"," NBER Chapters, in: Monetary Policy Rules, pages 1-14, National Bureau of Economic Research, Inc.
    26. Calvo, Guillermo A, 1978. "On the Time Consistency of Optimal Policy in a Monetary Economy," Econometrica, Econometric Society, vol. 46(6), pages 1411-1428, November.
    27. Gauti B. Eggertsson & Michael Woodford, 2003. "The Zero Bound on Interest Rates and Optimal Monetary Policy," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 34(1), pages 139-235.
    28. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    29. 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.
    30. Daniel Cohen & Philippe Michel, 1988. "How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(2), pages 263-274.
    31. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    32. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, March.
    33. Olivier Blanchard & Giovanni Dell'Ariccia & Paolo Mauro, 2010. "Rethinking Macroeconomic Policy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 199-215, September.
    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


    Cited by:

    1. Campbell Leith & Simon Wren-Lewis, 2013. "Fiscal Sustainability in a New Keynesian Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(8), pages 1477-1516, December.
    2. Rajendra Narayan Paramanik & Bandi Kamaiah, 2014. "A Structural Vector Autoregression Model for Monetary Policy Analysis in India," Margin: The Journal of Applied Economic Research, National Council of Applied Economic Research, vol. 8(4), pages 401-429, November.
    3. Paul Levine & Joseph Pearlman & Bo Yang, 2012. "Imperfect Information, Optimal Monetary Policy and Informational Consistency," School of Economics Discussion Papers 1012, School of Economics, University of Surrey.
    4. Cristiano Cantore & Vasco J. Gabriel & Paul Levine & Joseph Pearlman & Bo Yang, 2013. "The science and art of DSGE modelling: II – model comparisons, model validation, policy analysis and general discussion," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 19, pages 441-463, Edward Elgar Publishing.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cristiano Cantore & Vasco J. Gabriel & Paul Levine & Joseph Pearlman & Bo Yang, 2013. "The science and art of DSGE modelling: II – model comparisons, model validation, policy analysis and general discussion," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 19, pages 441-463, Edward Elgar Publishing.
    2. Levine, Paul & McAdam, Peter & Pearlman, Joseph, 2008. "Quantifying and sustaining welfare gains from monetary commitment," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1253-1276, October.
    3. Paul Levine & Joseph Pearlman & Bo Yang, 2012. "Imperfect Information, Optimal Monetary Policy and Informational Consistency," School of Economics Discussion Papers 1012, School of Economics, University of Surrey.
    4. Levine, Paul & Pearlman, Joseph, 2011. "Monetary and Fiscal Policy in a DSGE Model of India," Working Papers 11/96, National Institute of Public Finance and Policy.
    5. Dennis, Richard & Kirsanova, Tatiana, 2010. "Expectations Traps and Coordination Failures: Selecting among Multiple Discretionary Equilibria," MPRA Paper 24616, University Library of Munich, Germany.
    6. Nicoletta Batini & Paul Levine, 2008. "Monetary and Fiscal Rules in an Emerging Small Open Economy," CDMA Conference Paper Series 0810, Centre for Dynamic Macroeconomic Analysis.
    7. Pelin Ilbas, 2006. "Optimal Monetary Policy rules for the Euro area in a DSGE framework," Working Papers of Department of Economics, Leuven ces0613, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    8. Levine, Paul & Pearlman, Joseph & Pierse, Richard, 2008. "Linear-quadratic approximation, external habit and targeting rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3315-3349, October.
    9. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    10. Levine, Paul & Pearlman, Joseph, 2010. "Robust monetary rules under unstructured model uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 456-471, March.
    11. Loisel, Olivier, 2008. "Central bank reputation in a forward-looking model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3718-3742, November.
    12. Roberto M. Billi, 2011. "Optimal Inflation for the US Economy," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(3), pages 29-52, July.
    13. Dennis, Richard, 2004. "Solving for optimal simple rules in rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(8), pages 1635-1660, June.
    14. Batini, Nicoletta & Gabriel, Vasco & Levine, Paul, 2010. "A Floating versus managed exchange rate regime in a DSGE model of India," Working Papers 10/70, National Institute of Public Finance and Policy.
    15. Christopher J. Gust & Benjamin K. Johannsen & J. David López-Salido, 2015. "Monetary Policy, Incomplete Information, and the Zero Lower Bound," Finance and Economics Discussion Series 2015-99, Board of Governors of the Federal Reserve System (U.S.).
    16. Paul Levine & Joseph Pearlman & Bo Yang, 2008. "The Credibility Problem Revisited: Thirty Years on from Kydland and Prescott," Review of International Economics, Wiley Blackwell, vol. 16(4), pages 728-746, September.
    17. Donato Masciandaro, 2023. "How Elastic and Predictable Money Should Be: Flexible Monetary Policy Rules from the Great Moderation to the New Normal Times (1993-2023)," BAFFI CAREFIN Working Papers 23196, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    18. Dennis, Richard, 2010. "When is discretion superior to timeless perspective policymaking?," Journal of Monetary Economics, Elsevier, vol. 57(3), pages 266-277, April.
    19. Otmar Issing, 2010. "The development of monetary policy in the 20th century – some reflections," Working Paper Research 186, National Bank of Belgium.
    20. Michael Paetz, 2007. "Robust Control and Persistence in the New Keynesian Economy," Quantitative Macroeconomics Working Papers 20711, Hamburg University, Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cpm:dynare:010. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sébastien Villemot (email available below). General contact details of provider: https://edirc.repec.org/data/ceprefr.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.