# The Optimal Inflation Target and the Natural Rate of Interest

In an environment where the natural real rate of interest is lower, raising the inflation target can mitigate the risk that the nominal interest rate will hit its zero lower bound (ZLB) more frequently, which would hamper the ability of monetary policy to stabilize the economy; however, the authors of this paper point out, there is not an obvious answer to the practical question of how high to raise the target. They argue that determining the optimal inflation target requires an assessment of how the tradeoff between the incidence of ZLB and the welfare cost induced by steady-state inflation is modified when the natural rate of interest decreases.

In addition to examining the extent to which a lower steady-state real interest rate calls for a higher optimal inflation target, this paper looks at whether the source of decline in the interest rate matters, how the parameter uncertainty affects the interest rate-inflation target curve, and the extent to which the strategy and rules followed by the central bank alter the relation between the steady-state real interest rate and the target inflation. The authors focus on the US economy, but their findings apply to other advanced economies, particularly the euro area.

This study employs a New Keynesian DSGE model estimated for the United States over a Great Moderation sample. The framework features price stickiness and partial indexation of prices to trend inflation, wage stickiness and partial indexation of wages to both inflation and productivity, and a ZLB constraint on the nominal interest rate. The first two features imply the presence of potentially substantial costs associated with non-zero steady-state inflation. The third feature warrants a strictly positive inflation rate in order to mitigate the incidence and adverse effects of the ZLB. To the authors’ knowledge, these three features have not been jointly taken into account in previous analyses of optimal inflation.

#### Key Findings

- According to this study’s simulations, the optimal inflation target obtained when policymakers are assumed to know the economy’s parameters with certainty is about 2 percent. This result is obtained in an environment with a relatively low, 6 percent probability of hitting the ZLB when the target for the inflation rate is set at the historical mean of inflation, and given the size of the shocks estimated in this paper’s Great Moderation sample.
- The simulations also show that a 1 percentage point decline in the natural rate of interest from its estimated 2.5 percent pre-crisis level will almost double the probability of hitting the ZLB if the central bank does not change its inflation target.
- The optimal reaction of the central bank is to increase the inflation target 0.9 to 1.0 percentage point, which will limit the increase in the probability of hitting the ZLB to just half of a percentage point.
- Across the different concepts of optimal inflation considered in this paper, the level of optimal inflation varies. However, the slope of the relationship between the steady-state real interest rate and optimal inflation target is close to –1 when the interest rate is near its pre-crisis level of 2.5 percent.

#### Implications

This paper’s analysis considers adjusting the inflation target as one of policymakers’ options for countering a lower real interest rate. They can also resort to other options, such as more frequent recourse to non-conventional monetary policies. However, as the authors point out, by implying a “low for long” interest rate at the end of a liquidity trap, the monetary policy rule that they consider in their simulations accounts, at least partially, for the effect of unconventional policies that were implemented in the aftermath of the Great Recession—forward guidance on interest rates and large-scale asset purchases, for example. More aggressive unconventional measures also could be considered as alternative strategies when the ZLB is reached, and fiscal policies could play a significant role as well. Therefore, the ZLB might be a less stringent constraint in a practical policy context than it is in this paper’s analysis. However, the authors say, analysis of these fiscal policies and unconventional monetary policies should consider their efficacy and costs.

Policymakers could also adopt variants of the price-level targeting strategy. The paper’s exercises emphasize that when the central bank follows such a strategy of “making-up” for past inflation deviations from its target, the case for increasing the inflation target can be greatly reduced. But these results are obtained under the assumption that private agents believe and understand the commitment of the central bank to deviating from its inflation target in order to compensate for previous deviations. This is a debatable assumption, because, for example, lower-for-longer guidance on future interest rates could be interpreted as good news of a commitment to future accommodation, or as bad news that the period of low inflation will last longer. And if the bad signals prevail, such a policy could be detrimental.

The authors argue that though, in the current low-inflation environment, increasing the inflation target in response to a drop in the real interest rate might raise credibility issues, a move toward make-up strategies could be similarly questioned, as such strategies imply an inconsistent commitment to deviate from the inflation target once it has been reached. Lastly, the authors note that the real interest rate certainly was among the key factors considered when an inflation target of 2 percent was selected, and therefore, as the Federal Reserve and other central banks reassess the real interest rate, it seems only appropriate to simultaneously reassessment the optimal inflation target.

#### Abstract

We study how changes in the steady-state real interest rate affect the optimal inflation target in a New Keynesian DSGE model with trend inflation and a lower bound on the nominal interest rate. In this setup, a lower steady-state real interest rate increases the probability of hitting the lower bound. That effect can be counteracted by an increase in the inflation target, but the resulting higher steady-state inflation has a welfare cost in and of itself. We use an estimated DSGE model to quantify that tradeoff and determine the implied optimal inflation target, conditional on the monetary policy rule in place before the financial crisis. The relation between the steady-state real interest rate and the optimal inflation target is downward sloping. While the increase in the optimal inflation rate is in general smaller than the decline in the steady-state real interest rate, in the currently empirically relevant region the slope of the relation is found to be close to –1. That slope is robust to allowing for parameter uncertainty. Under “make-up” strategies such as price level targeting, the required increase in the optimal inflation target under a lower steady-state real interest rate is, however, much smaller.