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Linear-quadratic approximation, external habit and targeting rules

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  • Levine, Paul
  • Pearlman, Joseph
  • 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
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  • 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.
  • Handle: RePEc:eee:dyncon:v:32:y:2008:i:10:p:3315-3349
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    1. 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.
    2. 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.
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    6. 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.
    7. 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.
    8. Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Solving DSGE models with perturbation methods and a change of variables," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2509-2531, December.
    9. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    15. Pappa, Evi, 2004. "Do the ECB and the fed really need to cooperate? Optimal monetary policy in a two-country world," Journal of Monetary Economics, Elsevier, vol. 51(4), pages 753-779, May.
    16. 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.
    17. 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.
    18. Jinill Kim & Sunghyun Henry Kim, 2007. "Two Pitfalls of Linearization Methods," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 995-1001, June.
    19. Svensson, Lars E. O., 2005. "Monetary policy with judgment: forecast targeting," Working Paper Series 476, European Central Bank.
    20. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January.
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    Cited by:

    1. Vestin, David & Lombardo, Giovanni, 2007. "Welfare implications of Calvo vs. Rotemberg pricing assumptions," Working Paper Series 770, European Central Bank.
    2. 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.
    3. 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.
    4. 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.
    5. Holden, Thomas, 2016. "Existence and uniqueness of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 130142, ZBW - Leibniz Information Centre for Economics.
    6. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    7. 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.
    8. Holden, Tom D., 2016. "Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 127430, ZBW - Leibniz Information Centre for Economics.
    9. 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.
    10. Dario Caldara & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez & Wen Yao, 2009. "Computing DSGE Models with Recursive Preferences," PIER Working Paper Archive 09-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    11. 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.
    12. 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.
    13. Fujiwara, Ippei & Kam, Timothy & Sunakawa, Takeki, 2015. "Sustainable international monetary policy cooperation," Globalization Institute Working Papers 234, Federal Reserve Bank of Dallas.
    14. 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 (US).
    15. 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.
    16. repec:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0061-2 is not listed on IDEAS
    17. 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.
    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 (US).
    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

    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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