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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
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    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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