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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

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Paper provided by European Central Bank in its series Working Paper Series with number 0759.

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Date of creation: Jun 2007
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Handle: RePEc:ecb:ecbwps:20070759

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

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  1. 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.
  2. 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.
  3. 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.
  4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  5. Pierpaolo Benigno & Michael Woodford, 2004. "Inflation stabilization and welfare: The case of a distorted steady state," Discussion Papers 0405-04, Columbia University, Department of Economics.
  6. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February.
  7. Svensson, Lars E. O., 2005. "Monetary policy with judgment: forecast targeting," Working Paper Series 0476, European Central Bank.
  8. 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.
  9. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2001. "Optimal monetary policy," Working Papers 01-5, Federal Reserve Bank of Philadelphia.
  10. Pierpaolo Benigno & Michael Woodford, 2003. "Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach," NBER Working Papers 9905, National Bureau of Economic Research, Inc.
  11. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," NBER Working Papers 12672, National Bureau of Economic Research, Inc.
  12. Jinill Kim & Sunghyun Henry Kim, 2007. "Two pitfalls of linearization methods," Finance and Economics Discussion Series 2007-64, Board of Governors of the Federal Reserve System (U.S.).
  13. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January.
  14. 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.
  15. 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.
  16. Currie,David & Levine,Paul, 2009. "Rules, Reputation and Macroeconomic Policy Coordination," Cambridge Books, Cambridge University Press, number 9780521104609, April.
  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 & Andrew Levin & Tack Yun, 2006. "Relative Price Distortion and Optimal Monetary Policy in Open Economies," Computing in Economics and Finance 2006 211, Society for Computational Economics.
  19. 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.
  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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