The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound?

This 2012 Review of Economic Studies paper by Olivier Coibion, Yuriy Gorodnichenko, and Johannes Wieland asks what rate of steady-state (trend) inflation maximizes welfare in a New Keynesian DSGE model once the zero lower bound (ZLB) on nominal rates is explicitly modeled, rather than assumed away. The authors build a medium-scale NK model with Calvo staggered price-setting, habit formation in consumption, and a Taylor rule truncated at the ZLB, solving for ZLB episodes’ endogenous duration using the Bodenstein-Erceg-Guerrieri (2009) nonlinear algorithm; they calibrate the model to standard U.S. moments and to the historical post-WWII frequency of ZLB episodes, and evaluate welfare via a second-order approximation to utility that decomposes into a steady-state term (from Calvo price dispersion) and variance terms in the output gap, inflation, and consumption. In the baseline calibration the optimal trend inflation rate is 1.5% per year – “close to the bottom end” of the 1-3% target ranges central banks commonly use – because, although each ZLB episode is individually costly (an 8-quarter ZLB spell costs the equivalent of a 6.2% permanent consumption loss at 2% trend inflation), such episodes are calibrated to occur only about once every 20 years at 2% inflation, so the unconditional expected cost of the ZLB is small (0.08% of permanent consumption) relative to the perpetual costs of higher trend inflation (steady-state price dispersion, and a previously unidentified channel by which higher trend inflation makes inflation volatility itself more costly). The optimal rate proves robust to a wide range of alternative calibrations and extensions – remaining under about 3% even when the output-gap loss weight is scaled up 100-fold, capital is added (2.1%), parameter uncertainty is incorporated (1.9%, 90% CI [0.3%, 2.9%]), or the historical ZLB frequency is tripled – with the risk-premium shock’s persistence being the single most sensitive parameter (raising optimal inflation from 1.5% to 3% when its autocorrelation rises from 0.947 to 0.96). The rate is highly sensitive to the assumed monetary and fiscal policy regime, however: optimal inflation falls to about 0.2% under commitment to a stabilization policy, rises to 2.7% under discretion, and falls to well under 0.3% under even a modest price-level-targeting response, and it falls further still, to 0.3%, if downward nominal wage rigidity is added to the model. The authors caveat that their cashless-economy setup ignores the Friedman optimal-deflation motive and seigniorage, and that omitting endogenous countercyclical fiscal policy during ZLB episodes likely overstates both the cost of the ZLB and the resulting optimal inflation rate.

Johannes Wieland | Macro Paper Warehouse

The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound?