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Linear-quadratic approximation, external habit and targeting rules

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

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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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 10 (October)
Pages: 3315-3349

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:10:p:3315-3349
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. 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.
  2. repec:cup:cbooks:9780521441964 is not listed on IDEAS
  3. 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.
  4. 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.
  5. Michael Woodford & Pierpaolo Benigno, 2004. "Inflation Stabilization and Welfare: The Case of a Distorted Steady State," 2004 Meeting Papers 481, Society for Economic Dynamics.
  6. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2002. "Optimal Monetary Policy," NBER Working Papers 9402, National Bureau of Economic Research, Inc.
  7. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  8. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," CEPR Discussion Papers 1908, C.E.P.R. Discussion Papers.
  9. 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.
  10. Benigno, Pierpaolo & Woodford, Michael, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," CEPR Discussion Papers 5964, C.E.P.R. Discussion Papers.
  11. Benigno, Gianluca & Benigno, Pierpaolo, 2003. "Designing targeting rules for international monetary policy cooperation," Working Paper Series 0279, European Central Bank.
  12. Lars E.O. Svensson, 2005. "Monetary Policy with Judgment: Forecast Targeting," NBER Working Papers 11167, National Bureau of Economic Research, Inc.
  13. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January.
  14. Richard Clarida & Jordi Gali & Mark Gertler, 2002. "A Simple Framework for International Monetary Policy Analysis," NBER Working Papers 8870, National Bureau of Economic Research, Inc.
  15. 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.
  16. 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, 06.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
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