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.

*References*

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**

Thorstein Veblen“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.”

That’s it? only 15% of the time? Really?

“raising the target rate from 1.2% to 4% per year is equivalent to permanently reducing consumption by nearly 2%.”

Really? Given that if we had a 4% inflation target to begin with, we would likely have GDP that is more than 2% higher than it is currently, this is also tough to swallow. Can the shoe-leather costs be that high? And how solid is the data backing this up? Why do I suspect it’s largely been made up?

Also, if the Fed projects 1% inflation, and does nothing to get to the target of 2%, then it seems like, for all intents-and-purposed, we’ve got a 1% target. Secondly, I suspect the real reason the lower bound matters is because Ben Bernanke is reluctant to do QE unless the bottom is falling out of the market. If Bernanke weren’t so passive w/ QE, then the lower bound would matter much less than it seems to now…

2slugbaits“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”Is this reliance on historical experience appropriate given that over the last 60 years the Fed has operated under various kinds of monetary regimes? By using historical experience isn’t there an implicit assumption that the regime changes at the Fed don’t matter? For example, at one point the Fed focused on monetary aggregates rather than interest rates. Is it appropriate to build a model around interest rates when the Fed wasn’t always targeting interest rates?

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.This seems a little unconvincing. If the paper had been written 18 months ago would that 4 percent figure still hold? And if we’re stuck at the zero bound for another two years what would that do to the model’s prediction?

And is a New Keynesian model even appropriate here? It seems to hinge a lot on price stickiness, which is no doubt true a lot of the time, but does anyone seriously believe that the problem today is producer price stickiness and reluctance to change menu prices? Price stickiness was always something of a kluge that got hung on New Keynesian models in order to try and account for the fact that there is some stuff that a rational expectations/RBC type model just prefers to ignore. No doubt that there is price stickiness, but New Keynesian models are prone to giving it a leading actor role rather than a supporting actor.

But very interesting. Thanks. And when I get to the office tomorrow I’ll download it from NBER.

DanAnd this is relevant how?

Current crisis in this model is just a large shock? And the crisis goes away once the shock wears down, right?

And any ‘optimal policy’ in a NK model is a pointless exercise anyway. Only reasonable thing is to compare how this optimal policy or “welfare” change with different assumption, but even that is somewhat pointless.

Higher inflation is needed right now not only because it will make monetary policy more effective, but also because it will help households de-leverage and also bring real government debt burden down. Nothing about that in the model.

jonathanDid I read this sentence correctly: “Were the U.S. economy to have an average inflation rate of 0% per year, …” Doesn’t that imply deflation to account for any above 0% inflation at any time? How would that work in a model like this?

More importantly and though this is an excerpt, how many times other than this once have we actually been at the lower bound?

You say, “therefore the frequency of being at the zero lower bound on interest rates,” but in my lifetime, which goes back into the 1950′s, this has happened once in the US, meaning now. The only other occasion I’m aware of may be Japan, but that’s a very different place. My real question relates to how one can accept or deal with a model that discusses changes in the frequency of things that don’t seem to happen. In my line of work, I can model all sorts of things that don’t happen and even assign them a probability – of 0 – but I don’t trust the implications of the changes to a model that reduces the chances of what doesn’t happen. It kind of says, “Huh?” to me.

burkoI think the key message from the paper is that central bankers should not raise inflation targets and that the target should be a pretty low inflation rate (nowhere near 3 or 4 percent per year). To the extent the frequency of hitting zero lower bound is less then “estimated” in this work, the optimal rate of inflation should be lower than reported in the paper.

ppcmIt seems Central banks have done that already and even hitting an upper range.

see the CPI real versus actual

http://www.shadowstats.com/alternate_data/inflation-charts

Andy HarlessAs other commenters have noted, the estimated costs of inflation seem implausibly large. In addition, I think the methodology greatly understates the cost of recessions. From a brief look at the paper, I don’t see a way in which it models the cost of unemployment (as opposed to the cost of the aggregate lost consumption that results from unemployment). In practice, we dislike recessions not so much because they reduce average consumption possibilities a little bit as because they reduce consumption possibilities a lot for a few people. (Thus, for example, when we have 9.5% unemployment, I’m not tremendously comforted by the rapid growth in productivity.)

To put this another way, in the real world, the costs of cross-sectional dispersion are much higher during a recession than during a boom. In practice, we are not very concerned with the fact that people in some industries sometimes have to do more work than what would be optimal. We are, on the other hand, very concerned with the fact that some people sometimes can’t find work at all.

Steven KopitsInteresting article, acute comments.

The paper seems to have a ‘peacetime’ feel to it, when economics was about econ wonks tuning day-to-day policy. We seem to be in a far more war-like situation today, where we’re speculating rather desperately on whether cutting $5,000 checks for each household would save the economy.

Steven KopitsSlight OT:

There’s a very interesting article out from McKinsey on the forecasting bias of equity analysts. The title is “Equity Analysts: Still too Bullish”.

https://www.mckinseyquarterly.com/Corporate_Finance/Performance/Equity_analysts_Still_too_bullish_2565

LordWhile inflation has costs, deflation has far greater costs. How are these accounted for? The price level targeting result is interesting.

Ed DolanI agree with other comments–very interesting, but intuitively hard to believe. It is not easy to reconcile the authors’ estimate of the costs of inflation, or the idea of an optimal inflation rate in the neighborhood of 1%, with cross-sectional data on inflation and growth rates. For example, an IMF paper by Atish Gosh and Stephen Pillips (http://www.imf.org/external/pubs/cat/longres.cfm?sk=2590.0), which uses a very large sample, suggests that growth rates peak around 5-7% inflation, and that the peak is not very sharp, so that costs of inflation don’t really start to bite at the low rates discussed in this post. In short, I’ll file this away, but I need more convincing that the target should really be so low.

Get Rid of the Fed“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.”

What if the “downward-adjustment” for real wages all the way into negative terrority actually caused the “negative” shock in the first place?

Get Rid of the FedHere is a good post about the origins of the crisis in Australia:

http://bilbo.economicoutlook.net/blog/?p=277

I think the same logic applies to the USA and probably most high wage countries.

Get Rid of the Fed“One of the defining features of the current economic crisis has been the zero bound on nominal interest rates.”

I don’t think there are hardly any economists who understand what the zero bound can mean. What if it means supply and demand are in balance and therefore price inflation should be zero percent? If that is true, how is an economy going to price inflate?

Get Rid of the FedDan said: “Higher (MY ADD: price) inflation is needed right now not only because it will make monetary policy more effective, but also because it will help households de-leverage and also bring real government debt burden down. Nothing about that in the model.

If prices rise but wages don’t, how is that going to help most households delever (other than debt default)?

MikeRIs the zero rate lower bound on interest rates real?

Mike LairdThe unstated assumption here is that central banks can influence deflation. In the 1870s, we got into a deflationary period and back out of it without a central bank. Some think the 1930s deflation was caused more by the Smoot-Hawley tariff and the ramifications of collapsing world trade, than by Fed actions. The current deflationalry trend can be explained by the debt bubble, ala Fischer, a lot better than by looking at Fed actions, which have been stimulative and stronger (by trillions of dollars) than ever done before.

So until we have strong agreement on causality, this paper is stroking an imaginary cat, and hoping it purrs.

ppcmBut now I have an issue,as I found Pr Aruba “Informal sector,Government policy and Institutions” model and conclusion quiet convincing (see Econbrowser Inflation, taxation, and the underground economy)

Should the real CPI in USA be of the magnitude recorded by J WIlliams,shall we conclude as well of a larger share of unrecorded underground economy in the USA?

http://www.shadowstats.com/alternate_data/inflation-charts

LordI am not surprised by the results as the NK models have a blind spot towards deflation. They account for the cost of ‘flee money, seek goods’ but not ‘flee goods, seek money’. Under them the economy adjusts to deflation without much problem despite all evidence to the contrary. It’s a model problem.

don“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.”

I don’t understand this. For example, if prices are ‘sticky downward,’ wouldn’t a higher level of overall inflation to increase, rather than reduce, the ability of relative prices to adjust? And if average inflation is higher, aren’t more (not fewer) companies obliged to change prices each period?

Is the word ‘inflation’ in the first sentence a misprint? Should it be ‘deflation’?

GKYES, they should target higher inflation.

Liquidity is being mopped up by a new force that most economists don’t understand.

Read ‘The Technosponge’.

Technology is massively deflationary (but in a good way, as productivity also surges through the same force).

acerimusduxThe problem with this model is that it assesses only the potential costs of inflation, but considers none of the most significant potential benefits of a slightly higher target.

1. With an average historical inflation rate of 3.5%, inflation expectations will tend to be influenced by this long range evidence, and setting a much lower target will lead to pricing inefficiencies (including for long term assets).

2. Inflation is essentially a tax on wealth. Because maximum potential output depends on the allocation of resources, some level of regular redistribution is required in most economies. This is accomplished in most modern economies primarily through direct taxation, but inflation clearly still plays some role.

But while direct taxation overall is preferable to utilizing only inflation, what needs to be assessed here are the marginal costs of an additional small increase in inflation measured against the corresponding marginal increase in direct taxes which would be required to have the same impact.

It makes no sense to consider here only the welfare costs of higher inflation without comparing against the welfare costs of the higher marginal direct taxation which will be required to obtain the same result.

2slugbaitsThe authors of the paper rely heavily upon log-linearizations, which at least partly explains why they always assume some positive steady state level of inflation as well as a positive net interest rate. But aren’t the concerns about the zero lower bound precisely what happens when you have deflation and a negative real interest rate? In other words, I’m concerned that some of the artifcacts of the model itself have excluded from consideration the very facts we’re most concerned about when the Fed hits the zero bound. And the consumer welfare function that they use assumes that consumers are certain they will have funds (i.e., a job) across time periods and the central welfare question is about changes in total output across the economy. But a representative consumer has to take account of the fact that they may not have a job next year, so that will affect consumption this period. I don’t see that in their model and I would think that it’s kind of important because it gets right to the old paradox of thrift problem. I also don’t see how they can apply a Calvo menu pricing approach when there is a very real possibility of not just disinflation, but deflation. If there is deflation, then not changing prices can actually increase income relative to competitors who do change prices. In other words, doesn’t deflation turn Calvo pricing on its head? My last point is that their argument relies upon a zero lower bound happening endogenously. As a contribution to theory I’m sure that’s an important breakthrough, but I’m not sure that it really covers everything we want to know about the probability of hitting the zero lower bound in the real world. The real world does have exogenous shocks driving nominal interest rates to a zero lower bound, and these aren’t really addressed in the paper…or if they were, then I missed it. But it’s an interesting paper.

donStill waiting for an answert to above. The new macro models simply can’t be that counterintuitive.