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

Author

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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
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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. Bhattarai, Saroj & Eggertsson, Gauti B. & Schoenle, Raphael, 2018. "Is increased price flexibility stabilizing? Redux," Journal of Monetary Economics, Elsevier, vol. 100(C), pages 66-82.
    4. S Borağan Aruoba & Pablo Cuba-Borda & Frank Schorfheide, 2018. "Macroeconomic Dynamics Near the ZLB: A Tale of Two Countries," Review of Economic Studies, Oxford University Press, vol. 85(1), pages 87-118.
    5. Taisuke Nakata & Sebastian Schmidt, 2014. "Conservatism and Liquidity Traps," UTokyo Price Project Working Paper Series 059, University of Tokyo, Graduate School of Economics, revised Jul 2015.
    6. 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.
    7. Phuong Ngo & Jianjun Miao, 2015. "Does Calvo Meet Rotemberg at the Zero Lower Bound?," 2015 Meeting Papers 602, Society for Economic Dynamics.
    8. 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, 2019. "A Model of Secular Stagnation: Theory and Quantitative Evaluation," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(1), pages 1-48, January.
    2. Jesper Lindé & Mathias Trabandt, 2018. "Should we use linearized models to calculate fiscal multipliers?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 937-965, November.
    3. 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.
    4. 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.
    5. 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.
    6. Taisuke Nakata, 2018. "Reputation and Liquidity Traps," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 252-268, April.
    7. repec:wly:iecrev:v:59:y:2018:i:3:p:1403-1435 is not listed on IDEAS
    8. Taisuke Nakata, 2018. "Reputation and Liquidity Traps," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 252-268, April.
    9. Eric Sims & Jonathan Wolff, 2018. "The Output And Welfare Effects Of Government Spending Shocks Over The Business Cycle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(3), pages 1403-1435, August.
    10. Lansing, Kevin J., 2017. "Endogenous Regime Switching Near the Zero Lower Bound," Working Paper Series 2017-24, Federal Reserve Bank of San Francisco.
    11. repec:eee:inecon:v:115:y:2018:i:c:p:80-98 is not listed on IDEAS
    12. Hettig, Thomas & Müller, Gernot J., 2018. "Fiscal policy coordination in currency unions at the effective lower bound," Journal of International Economics, Elsevier, vol. 115(C), pages 80-98.

    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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