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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. Copyright 2007 The Ohio State University.

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:mcb:jmoncb:v:39:y:2007:i:4:p:995-1001
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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. 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.
    4. 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.
    5. 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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    1. repec:csg:ajrcwp:06 is not listed on IDEAS
    2. 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.
    3. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Fujiwara, Ippei & Kam, Timothy & Sunakawa, Takeki, 2015. "Sustainable international monetary policy cooperation," Globalization and Monetary Policy Institute Working Paper 234, Federal Reserve Bank of Dallas.
    9. 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.
    10. Davide Debortoli & Jinill Kim & Jesper Lindé & Ricardo Nunes, 2017. "Designing a simple loss function for central banks: Does a dual mandate make sense?," Economics Working Papers 1560, Department of Economics and Business, Universitat Pompeu Fabra.
    11. Viktors Ajevskis, 2013. "Non-Local Solutions to Dynamic Equilibrium Models: the Approximate Stable Manifolds Approach," Working Papers 2013/03, Latvijas Banka.
    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. 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.
    14. 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.

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