Some Unpleasant Properties of Log-Linearized Solutions When the Nominal Rate Is Zero

R. Anton Braun, Lena Mareen Körber, and Yuichiro Waki
Working Paper 2012-5a
Revised September 2012

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Does fiscal policy have qualitatively different effects on the economy in a liquidity trap? We analyze a nonlinear stochastic New Keynesian model and compare the true and loglinearized equilibria. Using the loglinearized equilibrium conditions, the answer to the above question is yes. However, for the true nonlinear model, the answer is no. For a broad range of empirically relevant parameterizations, labor falls in response to a tax cut in the loglinearized economy but rises in the true economy. While the government purchase multiplier is above two in the loglinearized economy it is about one in the true economy.

JEL classification: H30, E12, E62, E50

Key words: monetary policy, fiscal policy, zero bound

The authors thank participants from seminars at Australian National University, the Bank of Japan, the Bank of Portugal, the 7th Dynare Conference, the European Central Bank, the Federal Reserve Bank of Atlanta, Tokyo University, the University of Groningen, Vanderbilt University, and the Verein for Sozial Politik for their helpful comments. The authors also thank Larry Christiano, Isabel Correira, and Pedro Teles for their helpful comments. Lena Körber gratefully acknowledges financial support from Cusanuswerk, the ESRC, and the Heinz-Nixdorf Foundation. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to R. Anton Braun, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309, 404-498-8708,; Lena Mareen Körber, Department of Economics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, United Kingdom,; or Yuichiro Waki, School of Economics, the University of Queensland, 613 Colin Clark Building (39), QLD 4072, Australia, 61 7 336 56574,

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