# The Inflation Target and the Equilibrium Real Rate

Many economists have proposed raising the inflation target from 2 percent to 4 percent, claiming that doing so will raise nominal interest rates and thus reduce the probability of hitting the zero lower bound (ZLB). It is widely assumed that raising the inflation target will not affect the equilibrium real interest rate and therefore raising the inflation target by 2 percentage points will raise the equilibrium nominal rate by a corresponding 2 percentage points.

This paper presents a new channel by which raising the inflation target lowers the equilibrium real rate. The IMR channel has two stages. First, price rigidities imply that a rise in the inflation target lowers firms’ markup (the ratio of their price to their nominal marginal cost). Second, household heterogeneity (through overlapping generations or idiosyncratic risk) implies that a fall in the markup lowers the equilibrium real rate. The author therefore refers to the channel as the inflation markup real rate (IMR) channel.

More specifically, a fall in the markup lowers firms’ profits and reduces the value of shares and the value of overall savings. A fall in the value of savings, all else being equal, lowers the consumption of old people relative to that of young people, which means that the old have higher marginal utility from consuming compared with the young. Therefore, there is greater competition among young people to save for when they are old, and so the price of savings rises. As it rises, the return on savings (the equilibrium real rate) falls. If the equilibrium real rate drops, then the nominal rate will not rise as much as expected when inflation rises, and therefore, raising the inflation target will reduce the probability of hitting the ZLB by less than is commonly believed.

#### Key Findings

- In the author’s baseline model with life-cycle features, raising the inflation target from 2 percent to 4 percent lowers the equilibrium real rate 3 basis points. Allowing for a lower intertemporal elasticity (IES) of substitution of 0.1 instead of 0.5 boosts the effect to 8 basis points.
- With high firm discounting, raising the inflation target from 2 percent to 4 percent lowers the equilibrium real rate 11 basis points. With both high firm discounting and low IES, the equilibrium real rate falls 28 basis points.
- The IMR channel has little effect on how much it is optimal to raise inflation following exogenous declines in the real interest rate. This finding holds true even in a model where raising the inflation target substantially lowers the equilibrium real interest rate.

#### Implications

Particularly relevant to policymakers is the finding that a rise in the inflation target will lower the equilibrium real rate and therefore lead to an increase in average nominal interest rates that is smaller than generally believed. This implies that raising the inflation target is likely to be less effective than expected in reducing the probability of hitting the ZLB. Introducing the IMR channel into the analysis does not substantially affect how much of a rise in the inflation target is optimal. This is because, while the IMR channel implies that, relative to what is generally believed, real interest rates will be lower and the probability of hitting the ZLB will be higher when the inflation target is raised, it also indicates that the effectiveness of raising the inflation target is lower.

Furthermore, the findings in this paper imply that raising the inflation target can have long-run redistributional effects as well as short-run redistributional effects. A rise in inflation reduces profits and thus reduces the value of shares and total savings. This implies that older people, who rely on savings, will consume relatively less, and younger people will consume relatively more indefinitely as a result of a rise in the inflation target.

#### Abstract

Many economists have proposed raising the inflation target to reduce the probability of hitting the zero lower bound (ZLB). It is both a common assumption and a feature of standard models that raising the inflation target does not impact the equilibrium real rate. I demonstrate that in the New Keynesian model, once heterogeneity is introduced, raising the inflation target causes the equilibrium real rate to fall. This implies that raising the inflation target will increase the nominal interest rate by less than expected and thus will be less effective in reducing the probability of hitting the ZLB. The channel involves a rise in the inflation target lowering the average markup by price rigidities and a fall in the average markup lowering the equilibrium real rate by household heterogeneity, which could come from overlapping generations or idiosyncratic labor shocks. I find that raising the inflation target from 2 percent to 4 percent lowers the equilibrium real rate between 3 and 28 basis points. Since raising inflation lowers the equilibrium real rate, it might seem optimal to raise inflation by more in response to the ZLB. However, this channel also implies that the marginal benefit of raising inflation is lower because a given increase in inflation raises the nominal interest rate by less and thus is less effective at preventing the ZLB. In a welfare simulation, these two effects approximately cancel out each other. Therefore, even though this channel implies that raising the inflation target is less effective in preventing the ZLB, the inflation target should still be raised by a similar amount in response to the problem of the ZLB.