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Two Pitfalls of Linearization Methods

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  • JINILL KIM
  • SUNGHYUN HENRY KIM
Abstract
This paper illustrates two types of pitfalls when linearization methods are improperly applied. First, if we linearize the constraints before deriving the optimality conditions, the derived conditions are not correct up to first order. Second, even when we obtain the behavior of the economy that is correct to the first order, applying this behavior to welfare implications may lead to incorrect results. We also review different ways to avoid those pitfalls.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jmoncb:v:39:y:2007:i:4:p:995-1001
    DOI: 10.1111/j.1538-4616.2007.00055.x
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    References listed on IDEAS

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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. 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.
    3. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    4. McGrattan, Ellen R, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 41-44, January.
    5. Benigno, Pierpaolo & Woodford, Michael, 2006. "Optimal taxation in an RBC model: A linear-quadratic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1445-1489.
    6. Kim, Jinill & Henderson, Dale W., 2005. "Inflation targeting and nominal-income-growth targeting: When and why are they suboptimal?," Journal of Monetary Economics, Elsevier, vol. 52(8), pages 1463-1495, November.
    7. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
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    Cited by:

    1. 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.
    2. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    3. Garth Heutel, 2012. "How Should Environmental Policy Respond to Business Cycles? Optimal Policy under Persistent Productivity Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 244-264, April.
    4. Ippei Fujiwara & Yuki Teranishi, 2009. "Financial Stability in Open Economies," IMES Discussion Paper Series 09-E-09, Institute for Monetary and Economic Studies, Bank of Japan.
    5. 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.
    6. Davide Debortoli & Jinill Kim & Jesper Lindé & Ricardo Nunes, 2019. "Designing a Simple Loss Function for Central Banks: Does a Dual Mandate Make Sense?," The Economic Journal, Royal Economic Society, vol. 129(621), pages 2010-2038.
    7. Garth Heutel, 2012. "How Should Environmental Policy Respond to Business Cycles? Optimal Policy under Persistent Productivity Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 244-264, April.
    8. Ajevskis, Viktors, 2019. "Nonlocal Solutions To Dynamic Equilibrium Models: The Approximate Stable Manifolds Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2544-2571, September.
    9. Fujiwara, Ippei & Teranishi, Yuki, 2017. "Financial frictions and policy cooperation: A case with monopolistic banking and staggered loan contracts," Journal of International Economics, Elsevier, vol. 104(C), pages 19-43.
    10. Pablo Cuba‐Borda & Luca Guerrieri & Matteo Iacoviello & Molin Zhong, 2019. "Likelihood evaluation of models with occasionally binding constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1073-1085, November.
    11. Paul Levine & Joseph Pearlman & Bo Yang, 2008. "The Credibility Problem Revisited: Thirty Years on from Kydland and Prescott," Review of International Economics, Wiley Blackwell, vol. 16(4), pages 728-746, September.
    12. Levine, Paul & McAdam, Peter & Pearlman, Joseph, 2008. "Quantifying and sustaining welfare gains from monetary commitment," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1253-1276, October.
    13. Romain Duval & Lukas Vogel, 2012. "How Do Nominal and Real Rigidities Interact? A Tale of the Second Best," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(7), pages 1455-1474, October.
    14. Fujiwara, Ippei & Kam, Timothy & Sunakawa, Takeki, 2019. "Sustainable international monetary policy cooperation," Journal of Economic Dynamics and Control, Elsevier, vol. 106(C), pages 1-1.
    15. repec:csg:ajrcwp:06 is not listed on IDEAS
    16. Robert Kirkby, 2023. "Quantitative Macroeconomics: Lessons Learned from Fourteen Replications," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 875-896, February.

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