Log-linear Approximation versus an Exact Solution at the ZLB in the New Keynesian Model
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.
First Version: June 2015. We are grateful to Violeta Gutkowski, Neil Mehrotra, Kevin Proulx and Matthew Rognlie for detailed comments. We also thank the seminar participants at the SED Meeting 2015 for many useful suggestions. Remaining errors are our own. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Gauti B. Eggertsson & Sanjay R. Singh, 2019. "Log-linear approximation versus an exact solution at the ZLB in the New Keynesian model," Journal of Economic Dynamics and Control, . citation courtesy of