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Log-linear Approximation versus an Exact Solution at the ZLB in the New Keynesian Model

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  • Gauti B. Eggertsson
  • Sanjay R. Singh

Abstract

How accurate is a log-linear approximation of the New Keynesian model when the nominal interest rate is bounded by zero? This paper compares the solution of the exact non-linear model to the log-linear approximation. It finds that the difference is modest. This applies even for extreme events in numerical experiments that replicate the U.S. Great Depression. The exact non-linear model makes the same predictions as the log-linear approximation for key policy questions such as the size and sign of government spending and tax multipliers. It also replicates well known paradoxes like the paradox of toil and the paradox of price flexibility. The paper also reconciles different findings reported in the literature using Calvo versus Rotemberg pricing.

Suggested Citation

  • Gauti B. Eggertsson & Sanjay R. Singh, 2016. "Log-linear Approximation versus an Exact Solution at the ZLB in the New Keynesian Model," NBER Working Papers 22784, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:22784 Note: ME
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    References listed on IDEAS

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    1. Fernández-Villaverde, Jesús & Gordon, Grey & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Nonlinear adventures at the zero lower bound," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 182-204.
    2. Mark Gertler & John Leahy, 2008. "A Phillips Curve with an Ss Foundation," Journal of Political Economy, University of Chicago Press, vol. 116(3), pages 533-572, June.
    3. Raphael Schoenle & Gauti Eggertsson & Saroj Bhattarai, 2012. "Is Increased Price Flexibility Stabilizing? Redux," 2012 Meeting Papers 487, Society for Economic Dynamics.
    4. S. Borağan Aruoba & Pablo Cuba-Borda & Frank Schorfheide, 2012. "Macroeconomic Dynamics Near the ZLB: A Tale of Two Countries," PIER Working Paper Archive 14-035, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 19 Jun 2014.
    5. Boneva, Lena Mareen & Braun, R. Anton & Waki, Yuichiro, 2016. "Some unpleasant properties of loglinearized solutions when the nominal rate is zero," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 216-232.
    6. Phuong Ngo & Jianjun Miao, 2015. "Does Calvo Meet Rotemberg at the Zero Lower Bound?," 2015 Meeting Papers 602, Society for Economic Dynamics.
    7. McCallum, Bennett T., 2007. "E-stability vis-a-vis determinacy results for a broad class of linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1376-1391, April.
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    Citations

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    Cited by:

    1. Gauti B. Eggertsson & Neil R. Mehrotra & Jacob A. Robbins, 2017. "A Model of Secular Stagnation: Theory and Quantitative Evaluation," NBER Working Papers 23093, National Bureau of Economic Research, Inc.
    2. Vadym Lepetyuk & Lilia Maliar & Serguei Maliar, 2017. "Should Central Banks Worry About Nonlinearities of their Large-Scale Macroeconomic Models?," Staff Working Papers 17-21, Bank of Canada.
    3. Volker Hahn, 2017. "Policy Effects in a Simple Fully Non-Linear New Keynesian Model of the Liquidity Trap," Working Paper Series of the Department of Economics, University of Konstanz 2017-05, Department of Economics, University of Konstanz.
    4. Adiya Belgibayeva & Michal Horvath, 2017. "Real Rigidities and Optimal Stabilization at the Zero Lower Bound in New Keynesian Economies," Discussion Papers 17/01, Department of Economics, University of York.
    5. Taisuke Nakata, . "Reputation and Liquidity Traps," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics.
    6. Taisuke Nakata, . "Reputation and Liquidity Traps," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics.
    7. Jesper Lindé & Mathias Trabandt, 2017. "Should We Use Linearised Models to Calculate Fiscal Multipliers?," European Economy - Discussion Papers 2015 - 064, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.

    More about this item

    JEL classification:

    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General
    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General

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