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Linear-quadratic approximation, external habit and targeting rules

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  • Levine, Paul
  • Pearlman, Joseph G.
  • Pierse, Richard

Abstract

We examine the linear-quadratic (LQ) approximation of non-linear stochastic dynamic optimization problems in macroeconomics, in particular for monetary policy. We make four main contributions: first, we draw attention to a general Hamiltonian framework for LQ approximation due to Magill (1977). We show that the procedure for the 'large distortions' case of Benigno and Woodford (2003, 2005) is equivalent to the Hamiltonian approach, but the latter is far easier to implement. Second, we apply the Hamiltonian approach to a Dynamic Stochastic General Equilibrium model with external habit in consumption. Third, we introduce the concept of target-implementability which fits in with the general notion of targeting rules proposed by Svensson (2003, 2005). We derive sufficient conditions for the LQ approximation to have this property in the vicinity of a zero-inflation steady state. Finally, we extend the Hamiltonian approach to a non-cooperative equilibrium in a two-country model. JEL Classification: E52, E37, E58

Suggested Citation

  • Levine, Paul & Pearlman, Joseph G. & Pierse, Richard, 2007. "Linear-quadratic approximation, external habit and targeting rules," Working Paper Series 759, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:2007759
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    References listed on IDEAS

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    5. 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.
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    11. Jinill Kim & Andrew T. Levin & Tack Yun, 2008. "Relative Price Distortion and Optimal Monetary Policy in Open Economies," Korean Economic Review, Korean Economic Association, vol. 24, pages 5-31.
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    Cited by:

    1. Campbell Leith & Ioana Moldovan & Raffaele Rossi, 2012. "Optimal Monetary Policy in a New Keynesian Model with Habits in Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 416-435, July.
    2. Tatiana Damjanovic & Vladislav Damjanovic & Charles Nolan, 2015. "Ordering Policy Rules with an Unconditional Welfare Measure," International Journal of Central Banking, International Journal of Central Banking, vol. 11(1), pages 103-149, January.
    3. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    4. Andrew Levin & David López-Salido & Edward Nelson & Yack Yun, 2010. "Limitations on the Effectiveness of Forward Guidance at the Zero Lower Bound," International Journal of Central Banking, International Journal of Central Banking, vol. 6(1), pages 143-189, March.
    5. Leith, Campbell & Moldovan, Ioana & Rossi, Raffaele, 2015. "Monetary and fiscal policy under deep habits," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 55-74.
    6. repec:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0061-2 is not listed on IDEAS
    7. Damjanovic, Tatiana & Girdėnas, Šarūnas, 2014. "Quantitative easing and the loan to collateral value ratio," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 146-164.
    8. Fujiwara, Ippei & Kam, Timothy & Sunakawa, Takeki, 2015. "Sustainable international monetary policy cooperation," Globalization and Monetary Policy Institute Working Paper 234, Federal Reserve Bank of Dallas.
    9. Dario Caldara & Jesus Fernandez-Villaverde & Juan Rubio-Ramirez & Wen Yao, 2012. "Computing DSGE Models with Recursive Preferences and Stochastic Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 188-206, April.
    10. Dario Caldara & Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Wen Yao, 2009. "Computing DSGE Models with Recursive Preferences," NBER Working Papers 15026, National Bureau of Economic Research, Inc.
    11. Holden, Thomas, 2016. "Existence and uniqueness of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 130142, ZBW - German National Library of Economics.
    12. Vestin, David & Lombardo, Giovanni, 2007. "Welfare implications of Calvo vs. Rotemberg pricing assumptions," Working Paper Series 770, European Central Bank.
    13. Ralph S.J. Koijen & Jules H. van Binsbergen & Juan F. Rubio-Ramírez & Jesus Fernandez-Villaverde, 2008. "Likelihood Estimation of DSGE Models with Epstein-Zin Preferences," 2008 Meeting Papers 1099, Society for Economic Dynamics.
    14. Holden, Tom D., 2016. "Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 127430, ZBW - German National Library of Economics.
    15. Günter Coenen & Giovanni Lombardo & Frank Smets & Roland Straub, 2007. "International Transmission and Monetary Policy Cooperation," NBER Chapters,in: International Dimensions of Monetary Policy, pages 157-192 National Bureau of Economic Research, Inc.
    16. van Binsbergen, Jules H. & Fernández-Villaverde, Jesús & Koijen, Ralph S.J. & Rubio-Ramírez, Juan, 2012. "The term structure of interest rates in a DSGE model with recursive preferences," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 634-648.
    17. Jinill Kim & Andrew T. Levin & Tack Yun, 2007. "Diagnosing and treating bifurcations in perturbation analysis of dynamic macro models," Finance and Economics Discussion Series 2007-14, Board of Governors of the Federal Reserve System (U.S.).
    18. Bodenstein, Martin & Guerrieri, Luca & LaBriola, Joe, 2014. "Macroeconomic Policy Games," Finance and Economics Discussion Series 2014-87, Board of Governors of the Federal Reserve System (U.S.).
    19. Hyuk Rhee & Nurlan Turdaliev, 2015. "Central bank policy instrument forecasts," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 221-245, October.
    20. Jinill Kim & Andrew Levin & Tack Yun, 2011. "Bifurcation in Perturbation Analysis:Calvo Pricing Examples," Computational Economics, Springer;Society for Computational Economics, vol. 37(3), pages 221-236, March.
    21. Campbell Leith & Ioana Moldovan & Raffaele Rossi, 2012. "Optimal Monetary Policy in a New Keynesian Model with Habits in Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 416-435, July.
    22. Thomas von Brasch & Johan Byström & Lars Petter Lystad, 2012. "Optimal control and the Fibonacci sequence," Discussion Papers 674, Statistics Norway, Research Department.

    More about this item

    Keywords

    dynamic stochastic general equilibrium models; Linear-quadratic approximation; 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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