By Olivier Coibion, Yuriy Gorodnichenko, and Johannes Wieland
Today, we’re fortunate to have Oli Coibion, and Yuriy Gorodnichenko, Professors of Economics at William and Mary and at UC Berkeley, respectively, and Johannes Wieland, Ph.D. candidate at UC Berkeley, as a Guest Contributors.
“The crisis has shown that interest rates can actually hit the zero level, and when this happens it is a severe constraint on monetary policy that ties your hands during times of trouble. As a matter of logic, higher average inflation and thus higher average nominal interest rates before the crisis would have given more room for monetary policy to be eased during the crisis and would have resulted in less deterioration of fiscal positions. What we need to think about now is whether this could justify setting a higher inflation target in the future.”
— Olivier Blanchard, February 12, 2010
One of the defining features of the current economic crisis has been the zero bound on nominal interest rates. With standard monetary policy running out of ammunition in the midst of one of the sharpest downturns in post-World War II economic history, some have suggested that central banks should consider allowing for higher target inflation rates than might have been considered reasonable just a few years ago (see among others Daniel Leigh, Paul Krugman, Ken Rogoff, and Greg Mankiw), while others, including most notably Ben Bernanke and Jean-Claude Trichet, categorically reject this suggestion. Higher inflation rates would imply higher nominal interest rates and therefore more scope for countercyclical monetary policy in the face of large negative shocks to the economy such as those experienced in 2007 and 2008 as the housing bubble deflated and the financial crisis amplified the contraction in the real economy. Despite the importance of central banks’ inflation targets, modern monetary models have been strikingly ill-suited to address this question because of their pervasive reliance on the assumption of an average inflation rate of zero percent (see e.g. Woodford 2003). In a recent paper, we extend the baseline New Keynesian model to allow for positive steady-state inflation, derive the associated welfare function, and allow for the zero-lower bound (ZLB) on interest rates to assess the implications for the optimal inflation rate.
1. Optimal inflation rates in a simple New Keynesian model
The primary cost of inflation in the basic New Keynesian model comes from the infrequent adjustment of prices: when firms fail to adjust their prices every period, relative prices across goods do not properly reflect their relative costs, leading to an inefficient allocation of production. This reduces consumption and welfare and requires variation in the amount of labor supplied across industries which is undesirable from workers’ point of view. Higher average inflation leads to a greater misallocation of resources, and hence is costly.
On the other hand, the ZLB on interest rates means that, in the face of large negative shocks to the economy, monetary policy-makers’ ability to stabilize the economy through interest rate adjustments is severely constrained. This leads to episodes, like the current recession, when production falls by large amounts and monetary policy-makers are unable to respond via standard policy tools. Higher inflation targets, by leading to higher nominal interest rates, are a way to insure against these disproportionately bad outcomes by leaving policy-makers more room to adjust interest rates during dire economic times.
By calibrating the parameters of the model and using historical estimates of the volatility and persistence of the different shocks hitting the U.S. economy, we can quantify the effect of the average inflation rate on the frequency at which the ZLB would be binding. This is illustrated in Figure 1 below.
Figure 1: The effect of inflation rates on the ZLB for the U.S.
At an average inflation rate of 3.5% per year (approximately the average rate for the U.S. since the 1950s), the model predicts that the economy should be at the ZLB approximately 4 percent of the time, which corresponds closely to the historical frequency for the U.S. The benefit of higher inflation rates is clear in the figure: these lead to higher average interest rates and therefore to a lower frequency of being at the ZLB. Were the U.S. economy to have an average inflation rate of 0% per year, the model predicts that the ZLB would be binding over 15% of the time.
In the paper, we show how to approximate the welfare of consumers when steady-state inflation rates are non-zero. This allows us to quantify the costs and benefits associated with different inflation rates as illustrated in Figure 2 below.
Figure 2: Utility at different levels of steady-state inflation
The optimal inflation rate implied by the model is 1.2% per year which is within, but near the bottom, of the range of implicit inflation targets used by central banks in industrialized countries of 1-3% per year. In addition, the welfare loss from higher inflation rates is non-trivial: raising the target rate from 1.2% to 4% per year is equivalent to permanently reducing consumption by nearly 2%. In short, using a calibrated model of the U.S. economy which balances the costs of inflation arising from infrequent adjustment of prices against the benefit of reducing the frequency of hitting the ZLB yields an optimal inflation target which is certainly no higher than what is currently in use by central banks.
2. What could raise the optimal inflation rate?
The basic New Keynesian model abstracts from several features which could tend to push the optimal rate of inflation higher. In this section, we briefly discuss and quantify the implications of these mechanisms.
- a. Endogenous price stickiness: Our baseline model assumes that the rate at which firms change prices is invariant to the average inflation rate, so we also consider a variant of the model in which firms change prices more frequently when the average inflation rate is higher, calibrated to match the evidence in Nakamura and Steinsson (2008). We find that allowing for this mechanism does not affect the optimal inflation rate but reduces the welfare costs of higher inflation. This is because the increased frequency of price adjustment associated with higher inflation reduces the misallocation of resources across industries. Similarly, using Taylor-pricing instead of Calvo-pricing (as in our baseline) has little effect on the optimal inflation rate but lowers the implied costs of higher inflation rates because of the reduced price dispersion associated with these alternative pricing models. In short, our results on the optimal inflation rate do not critically hinge on how we model the infrequent adjustment of prices.
- b. Model-Uncertainty: If policy-makers are uncertain about the exact volatility of shocks or other parameters of the model, they might optimally choose a higher target rate of inflation to ensure against the possibility of more frequent large negative shocks. Given the sampling uncertainty associated with our baseline parameter values, we find that the optimal inflation rate increases only mildly, to 1.4% per year with the 90% confidence interval of optimal inflation rates ranging from 0.4% per year to 2.1% per year.
- c. Capital-Formation: Our baseline model follows much of the New-Keynesian literature and assumes that the only input into production is labor. We extend our model and results on welfare approximations to a setting in which capital is also utilized in the production process. The optimal inflation rate again is hardly affected, rising to 1.4% per year.
- d. Downward-Wage Rigidity: A common motivation for positive inflation targets for central banks is the “greasing the wheels” effect suggested by Tobin (1972): if it is difficult to lower nominal wages, as commonly observed, then positive inflation will facilitate the downward-adjustment of real wages required to adjust to negative shocks. Strikingly, the addition of downward nominal wage rigidity to the model lowers the optimal inflation rate to well under 1% per year. The reason is that, with nominal wage rigidity, marginal costs, and in turn inflation, become less volatile leading to the ZLB binding less frequently.
3. Policy prescriptions and concluding remarks
One of the most significant advantages of working with a micro-founded model and its implied welfare function is the ability to engage in normative analysis. In addition to studying the optimal inflation rate in the model, we are also able to study the welfare effects of the systematic response of policy-makers to endogenous fluctuations (i.e. the coefficients of the Taylor rule) in conjunction with the optimal steady-state rate of inflation. The most striking finding from this analysis is that even modest price-level targeting could raise welfare by approximately 1% of steady-state consumption for any target inflation rate. In addition, by reducing the volatility of inflation and output, and therefore the frequency of being at the zero lower bound on interest rates, price-level targeting can lead to much lower optimal rates of inflation than in our baseline findings. In fact, the optimal policy rule for the model can be closely characterized by the name of “price stability” as typically stated in the legal mandates of most central banks.
In summary, using a New-Keynesian model properly adjusted to fully incorporate the effects of positive average inflation rates, we find that the zero-lower bound on interest rates is insufficient to push the optimal inflation rate for the U.S. above the implicit inflation targets of modern central banks. In addition, our model abstracts from several costs of inflation which would tend to push the optimal inflation rate even lower. For example, our approach assumes that monetary policy-makers have no tools other than interest-rate adjustments in the face of the ZLB (i.e. we ignore the possible positive effects of quantitative easing) and similarly abstracts from the possibility that fiscal authorities might respond with expansionary policies during these episodes. Finally, we abstract from the long literature on the costs associated with holding money, which push toward the well-known Friedman rule of optimal deflation. Thus, one could reasonably interpret our results as placing an upper bound on the optimal inflation rate for a country like the U.S.
Coibion, Olivier, Yuriy Gorodnichenko and Johannes Wieland, 2010. “The Optimal Inflation Rate in New Keynesian Models,” NBER Working Paper 16093. [pdf]
Nakamura, Emi, and Jon Steinsson, 2008. “Five Facts About Prices: A Reevaluation of Menu Cost Models,” Quarterly Journal of Economics 123(4), 1415-1464. [pdf]
Tobin, James, 1972. “Inflation and Unemployment,” American Economic Review 62(1), 1-18.
Woodford, Michael, 2003. Interest and Prices. Princeton University Press.
This post written by Olivier Coibion, Yuriy Gorodnichenko, and Johannes Wieland