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

Listed author(s):
  • Gauti B. Eggertsson
  • Sanjay R. Singh

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.

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File URL: http://www.nber.org/papers/w22784.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 22784.

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Date of creation: Oct 2016
Handle: RePEc:nbr:nberwo:22784
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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, 06.
  3. Raphael Schoenle & Gauti Eggertsson & Saroj Bhattarai, 2012. "Is Increased Price Flexibility Stabilizing? Redux," 2012 Meeting Papers 487, Society for Economic Dynamics.
  4. 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.
  5. Phuong Ngo & Jianjun Miao, 2015. "Does Calvo Meet Rotemberg at the Zero Lower Bound?," 2015 Meeting Papers 602, Society for Economic Dynamics.
  6. 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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