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Linear-Quadratic Approximation, Efficiency and Target-Implementability

Author

Listed:
  • Paul Levine

    (University of Surrey)

  • Joseph Pearlman

    (London Metropolitan University)

  • Richard Pierse

    (University of Surrey)

Abstract

We examine linear-quadratic (LQ) approximation of stochastic dynamic optimization problems in macroeconomics (and elsewhere), in particular in policy analysis using Dynamic Stochastic General Equilibrium (DSGE) models. We first define the problem that is solved by a social planner, given that the objective of the latter is to maximize average welfare; this yields the efficient solution. We then comment on the LQ approximation when a tax or subsidy can be imposed such that the zero-inflation competitive steady state output level is equal to the efficient level. We then examine the correct procedure for replacing a stochastic non-linear dynamic optimization problem with a linear-quadratic approximation. We show that a procedure proposed by Benigno and Woodford (2004) for large underlying distortions in the economy can be more easily implemented through a second-order approximation of the Hamiltonian used to compute the ex ante optimal policy with commitment (the Ramsey problem). We then define the notion of Target-Implementability, which is also a sufficient condition for a particular steady-state maximum of the Ramsey problem, and explain the usefulness of this in the context of stabilization policy

Suggested Citation

  • 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.
  • Handle: RePEc:sce:scecfa:441
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    File URL: http://repec.org/sce2006/up.25695.1141160133.pdf
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    References listed on IDEAS

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    1. Batini, Nicoletta & Justiniano, Alejandro & Levine, Paul & Pearlman, Joseph, 2006. "Robust inflation-forecast-based rules to shield against indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1491-1526.
    2. 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.
    3. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
    4. Smets, Frank & Wouters, Raf, 2002. "An estimated stochastic dynamic general equilibrium model of the euro area," Working Paper Series 0171, European Central Bank.
    5. Currie,David & Levine,Paul, 2009. "Rules, Reputation and Macroeconomic Policy Coordination," Cambridge Books, Cambridge University Press, number 9780521104609, April.
    6. 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.
    7. Clarida, Richard & Gali, Jordi & Gertler, Mark, 2002. "A simple framework for international monetary policy analysis," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 879-904, July.
    8. Lars E O Svensson, 2005. "Monetary Policy with Judgment: Forecast Targeting," International Journal of Central Banking, International Journal of Central Banking, vol. 1(1), May.
    9. Faust, Jon & Svensson, Lars E O, 2001. "Transparency and Credibility: Monetary Policy with Unobservable Goals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 369-397, May.
    10. 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.
    11. Pierpaolo Benigno & Michael Woodford, 2004. "Optimal Monetary and Fiscal Policy: A Linear-Quadratic Approach," NBER Chapters,in: NBER Macroeconomics Annual 2003, Volume 18, pages 271-364 National Bureau of Economic Research, Inc.
    12. Svensson, Lars E. O., 2005. "Monetary policy with judgment: forecast targeting," Working Paper Series 476, European Central Bank.
    13. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January.
    14. Pierpaolo Benigno & Michael Woodford, 2005. "Inflation Stabilization And Welfare: The Case Of A Distorted Steady State," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1185-1236, December.
    15. Woodford Michael, 2002. "Inflation Stabilization and Welfare," The B.E. Journal of Macroeconomics, De Gruyter, vol. 2(1), pages 1-53, February.
    16. Petra M. Geraats, 2002. "Central Bank Transparency," Economic Journal, Royal Economic Society, vol. 112(483), pages 532-565, November.
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    Cited by:

    1. 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.
    2. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    3. Levine, Paul & McAdam, Peter & Pearlman, Joseph, 2012. "Probability models and robust policy rules," European Economic Review, Elsevier, vol. 56(2), pages 246-262.
    4. 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.
    5. Batini, Nicoletta & Levine, Paul & Lotti, Emanuela & Yang, Bo, 2011. "Monetary and Fiscal Policy in the Presence of Informal Labour Markets," Working Papers 11/97, National Institute of Public Finance and Policy.
    6. Nicoletta Batini & Paul Levine & Emanuela Lotti & Bo Yang, 2011. "Informality, Frictions and Monetary Policy," School of Economics Discussion Papers 0711, School of Economics, University of Surrey.
    7. Cantore, Cristiano & Levine, Paul & Melina, Giovanni & Yang, Bo, 2012. "A fiscal stimulus with deep habits and optimal monetary policy," Economics Letters, Elsevier, vol. 117(1), pages 348-353.
    8. Paul Levine & Joseph Pearlman & Richard Pierse, 2007. "Monetary Policy Coordination Revisited in a Two-Bloc DSGE Model," School of Economics Discussion Papers 0907, School of Economics, University of Surrey.
    9. 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.
    10. Nicoletta Batini & Paul Levine & Joseph Pearlman, 2007. "Monetary Rules in Emerging Economies with Financial Market Imperfections," NBER Chapters,in: International Dimensions of Monetary Policy, pages 251-311 National Bureau of Economic Research, Inc.
    11. 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: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 19, pages 441-463 Edward Elgar Publishing.
    12. 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.
    13. 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.

    More about this item

    Keywords

    Linear-quadratic approximation; dynamic stochastic general equilibrium models; utility-based loss function;

    JEL classification:

    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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