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

The paper asks whether the zero lower bound (ZLB) on nominal interest rates justifies raising inflation targets above the near-zero rates that standard New Keynesian welfare analysis (ignoring the ZLB) recommends. Prior welfare treatments of steady-state inflation in NK models typically found optimal inflation near zero, driven by the costs of Calvo price dispersion; those analyses did not incorporate the possibility that a low trend inflation rate leaves little room for the central bank to cut nominal rates before hitting the ZLB during a large enough contractionary shock. The authors explicitly build the ZLB into the policy rule and solve for its consequences to see whether this “insurance” motive is large enough to push the optimal target meaningfully higher, as many post-crisis commentators had argued it should.

The authors use a medium-scale New Keynesian DSGE model with internal habit formation in consumption, Calvo (1983) staggered price-setting with a resetting probability of 1 minus λ each period, and a Taylor rule responding to inflation, the output gap, and output growth, truncated at the ZLB (r̂_t = max{r̂_t, −r̄}).* ZLB episodes’ duration is solved endogenously (not assumed fixed) using the nonlinear algorithm of Bodenstein, Erceg, and Guerrieri (2009). Welfare is evaluated via a second-order approximation to expected per-period utility (their Proposition 1) that decomposes into a steady-state term Θ_0 (capturing price-dispersion-driven resource misallocation, increasing in trend inflation π̄), and variance terms in the output gap, inflation, and consumption, whose weights Θ_1, Θ_2, Θ_3 are themselves functions of π̄ and the structural parameters.

Parameters are calibrated to standard values and to historical U.S. business-cycle moments rather than estimated on a single dataset: the Frisch elasticity is set to 1.00, the discount factor β = 0.998 (matching a 2.3% real rate), habit h = 0.70, the Calvo reset probability λ = 0.55 (midpoint of Bils-Klenow 2004 and Nakamura-Steinsson 2008 estimates), price indexation ω = 0 (per Cogley-Sbordone 2008), and Taylor-rule coefficients from Coibion and Gorodnichenko (2011). The risk-premium shock’s persistence (ρ_q = 0.947) is calibrated specifically to match the historical frequency of ZLB episodes at a 3.5% trend-inflation benchmark. At these values the model matches the standard deviations of HP-filtered U.S. consumption, output, inflation, and interest rates reasonably well (e.g., inflation volatility of 0.0067 in the model versus 0.0065 in the data, 1947Q1-2011Q1).

The baseline calibration implies an optimal trend inflation rate of 1.5% per year, which the authors describe as “close to the bottom end of the target range which are commonly between 1% and 3%.” Zero inflation is not optimal once the ZLB is modeled, but the ZLB motive pushes the optimal rate only modestly above zero, not toward the 4% or higher targets that some post-2008 policy proposals floated. A 5% inflation rate, by contrast, would lower welfare by an amount “equivalent to a permanent 1% decrease in the level of consumption” relative to the optimum – illustrating that the model’s welfare costs of inflation above the optimum are far from trivial.

The key intuition is a rare-events argument: an individual 8-quarter ZLB episode is costly (equivalent to a 6.2% permanent consumption loss at 2% trend inflation), but such episodes are calibrated to occur only about once every 20 years at that inflation rate, so the unconditional expected cost of the ZLB is small – just 0.08% of permanent consumption. As the authors put it, “the unconditional cost of the ZLB is small even though each individual ZLB event is quite costly.” Because higher trend inflation only reduces the frequency of these rare episodes while imposing costs (price dispersion, greater inflation-volatility costs) every period, the perpetual costs dominate the ZLB-insurance benefit at any inflation rate much above the 1.5% baseline optimum.

Three channels operate through the welfare function: (i) steady-state price dispersion from Calvo pricing, which misallocates labor across sectors and is increasing in trend inflation; (ii) an increasing cost of inflation volatility as trend inflation rises, because existing price dispersion means an inflation shock generates further relative-price distortions that must be compensated – a channel the authors describe as “previously unidentified” in the NK welfare literature; and (iii) a dynamic forward-looking effect, whereby higher trend inflation makes sticky-price firms more forward-looking and thus amplifies and prolongs their response to shocks, making inflation itself more volatile. Against these three costs stands the single ZLB-insurance benefit: higher trend inflation raises the steady-state nominal rate (via the Fisher relation), giving the central bank more room to cut before hitting the ZLB.

The result is described as “robust to a wide range of plausible calibrations,” with one notable exception. Varying the pricing parameters (θ, λ, ω) or the discount factor moves the optimal rate only slightly (e.g., even β = 0.9999, implying a 1.54% real rate, raises optimal π̄ by only 0.6 percentage points from the 3.5%-real-rate baseline); tripling the historical ZLB frequency to 15% (at 3% trend inflation) raises the optimum only to 3%; and even scaling the output-gap loss weight up 100-fold raises it only to 2.4%. The risk-premium persistence parameter ρ_q is the most sensitive input: raising it from the calibrated 0.947 to 0.96 pushes the optimal rate from 1.5% to 3%. Among structural extensions, adding capital raises the optimum modestly to 2.1%; incorporating model/parameter uncertainty by drawing from a parameter distribution gives an optimum of 1.9% (90% interval [0.3%, 2.9%]); Taylor-style time-dependent pricing gives 1.8-2.2% depending on contract length; and endogenous, state-dependent price stickiness lowers both the optimal rate and the associated welfare costs slightly. The one extension that moves the estimate sharply in the opposite direction is downward nominal wage rigidity (Section 5.3): adding it lowers the optimal rate to just 0.3%, because the “greasing the wheels” mechanism (Tobin 1972) reduces marginal-cost volatility and the frequency of ZLB episodes, a result the authors call “striking.”

The optimal rate is highly sensitive to whether the central bank can commit to a stabilization policy. Under commitment, optimal trend inflation falls to about 0.2%, because commitment to keep rates low after a ZLB episode “dramatically reduces” its welfare costs; under discretion, the inability to commit raises the ZLB’s welfare costs substantially, and the optimal rate rises to 2.7%. Introducing even a modest price-level-targeting (PLT) response (a coefficient of 0.25) lowers the optimal rate to under 0.3% per year – “virtually impl[ying] price-level stability” – because PLT limits deflationary spirals and, at a 0.3 PLT coefficient and 3.5% trend inflation, keeps the ZLB from binding more than 1.4% of the time; the welfare gain from moving the PLT coefficient from 0 to 0.25 is equivalent to a permanent 0.5% consumption increase.

The authors note several abstractions that bias the results in a particular, acknowledged direction, along with parameter uncertainty. The model is cashless (ignoring the Friedman 1969 optimal-deflation motive and seigniorage), excludes fixed nominal tax brackets (so the Feldstein 1997 cost of inflation is absent), and – most consequentially – omits endogenous countercyclical fiscal policy during ZLB episodes, which the authors state “likely overstates ZLB costs and therefore overstates the optimal π̄.” The welfare measure, a second-order approximation around the flexible-price steady state, does not capture distributional effects across low-income or low-wealth agents, involuntary unemployment, or income disparities that might raise the true welfare cost of output fluctuations. The risk-premium persistence parameter, identified as the most influential for the ZLB-hitting frequency, is itself uncertain, and the authors note that evidence on whether central banks actually practice price-level targeting “remains scarce.” They also flag that the optimal rate likely varies across countries, with smaller open economies facing more volatile terms-of-trade shocks potentially warranting higher targets than the U.S.-calibrated baseline.