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Linear-quadratic approximation, external habit and targeting rules

  • Levine, Paul
  • Pearlman, Joseph G.
  • 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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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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  1. Benigno, Gianluca & Benigno, Pierpaolo, 2003. "Designing targeting rules for international monetary policy cooperation," Working Paper Series 0279, European Central Bank.
  2. Aubhik Khan & Robert G. King & Alexander L. Wolman, 2002. "Optimal Monetary Policy," NBER Working Papers 9402, National Bureau of Economic Research, Inc.
  3. 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.
  4. 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.
  5. Pierpaolo Benigno & Michael Woodford, 2003. "Optimal Monetary and Fiscal Policy: A Linear Quadratic Approach," NBER Working Papers 9905, National Bureau of Economic Research, Inc.
  6. Pierpaolo Benigno & Michael Woodford, 2004. "Inflation Stabilization and Welfare: The Case of a Distorted Steady State," NBER Working Papers 10838, National Bureau of Economic Research, Inc.
  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. repec:cup:cbooks:9780521441964 is not listed on IDEAS
  9. Evi Pappa, 2004. "Do the ECB and the Fed really need to cooperate? Optimal monetary policy in a two-country world," LSE Research Online Documents on Economics 512, London School of Economics and Political Science, LSE Library.
  10. Clarida, R. & Gali, J. & Gertler, M., 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and some Theory," Working Papers 98-01, C.V. Starr Center for Applied Economics, New York University.
  11. Svensson, Lars E O, 2005. "Monetary Policy with Judgement: Forecast Targeting," CEPR Discussion Papers 5072, C.E.P.R. Discussion Papers.
  12. 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.
  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. 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.
  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. 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.).
  18. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  19. 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.
  20. Choudhary, M. Ali & Levine, Paul, 2006. "Idle worship," Economics Letters, Elsevier, vol. 90(1), pages 77-83, January.
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