*Most FOMC participants, including Yellen, agree that a unique feature of the post-Great Recession period is headwinds weighing on economic activity. These headwinds call for a policy temporarily more accommodative than otherwise. That’s reflected in her view that the “current” r-star is lower than would it would be in normal times. Yellen’s estimate of the current r-star is based on research by Laubach and Williams and, in her words, is near zero and has been there for some time. Yellen and her colleagues expect that, as headwinds dissipate, the current r-star will rise over time and converge to its higher normal level. In 2012, FOMC participants began to report their projections of the longer-run r-star. At that time, the median estimate was 2¼% (in real terms). I call Yellen’s story the “convergence hypothesis”: convergence of the current r-star to its normal level over the longer run. But Laubach and Williams view their r-star as the “new normal.” They say that’s where it is today and that’s where it is expected to be in the longer run. I call this the “new normal hypothesis.” But the median participant projection of the longer-run r-star has declined from 2¼% to ¾% today. That’s the convergence of the longer-run r-star toward the new normal. I interpret this decline as participants learning about the new normal. Jonathan Wright, the senior adviser, provided helpful comments. *

Headwinds and Convergence to Normal

For some time, the staff and participants have made a distinction between the “current” r-star and the “normal” r-star. (See A Cautionary Tale of Two R-Stars) The longer-run r-star, often referred to by Yellen and participants as the “normal” r-star, is identified as participants’ median estimate of the ”funds rate in the longer run”. The current r-star is the real fund’s rate that would keep the economy growing at potential if there were no output gap, to begin with. It can also be interpreted as the level of the real fund’s rate that would be required today to move output to its potential level, and leave it there. In this story, the current r-star is assumed to be below its longer-run or normal level today as a result of unique, but temporary, forces—referred to as “headwinds”—that have been weighing on economic activity in this expansion. To offset these headwinds, the fund’s rate must be lower than in normal times; that is, the current r-star must be temporarily below its normal level. As the headwinds abate and disappear, and the real fund’s rate is expected to converge to its normal, or longer-run level. I call this the “convergence” hypothesis.

The Funds Rate in the Longer Run

In 2012, participants began to report their estimate of the “funds rate in the longer run”, generally referred to as the “longer-run” or “normal” r-star.1 They report it in nominal terms, but I convert it to real terms to make it comparable to the model-based estimates of r-star that I discuss. Participants’ median estimate of the long run, or normal, r-star has declined from 2¼% in 2012 to just ¾% today.

^{1 }Of course, as participants have steadily been revising their estimate of the longer-run r-star, what they see as normal in the long run has been changing.

Laubach-Williams: The “New Normal”

While at the Fed, I asked two senior staff economists, Thomas Laubach, now director of Monetary Affairs there, and John Williams, now President of the San Francisco Fed, to develop a model of a time-varying real neutral funds rate. They first circulated their research in 2001 and published it in 2003.2 Their estimate of the neutral rate at that time was about 2½% in real terms, the level that I and many on the staff had been using. Very reassuring. But, over time, their estimate of r-star has steadily fallen, reaching zero in 2010, and remained near zero for many years. They refer to their r-star as the “new normal.”

The Laubach-Williams (2003) Model

To understand the Laubach-Williams’ estimate and why they see it as the new normal, it helps to take a peek at what underlies their model and their estimation of r-star.

r-star in Laubach-Williams (2003)

The key to the Laubach-Williams model is the process that drives the time varying r-star, captured in equation (1):

*1. r*_{t}** = c g*_{t}** + z*_{t}* *

where *r* *is their time-varying estimate of the real neutral fund’s rate, g* is the effect of potential growth on r-star and z is a time-varying unobserved component of r* that captures the effect of other unspecified influences on the natural rate.

There are two key features of Laubach-Williams r-star. First, g* and z, and hence r-star, are modeled as “random walks.” That means that the expected value of r-star in the future is whatever it is today. The concept, then, is that the estimated r-star is the “current” r-star, but the “long-run” r-star is forced to be the same. In practice, people don’t take this model literally so the two can diverge.

^{2 }Thomas Laubach and John C. Williams, “Measuring the Natural Rate of Interest,” FEDS 2001-56, December 2001. Thomas Laubach and John C. Williams, “Measuring the Natural Rate of Interest,” Review of Economics and Statistics 85(4), 2003, 1063-1070.

Second, both *g* *and *z*, and hence r-star, can vary over time. The role of *g* *was already well appreciated. Potential growth is a fundamental determinant of r-star. The innovation is the z term, the collective effect of all the other factors that affect r-star.

Here a simple description of the Laubach-Williams model and how it allows *z *to be updated each quarter:

*[The] principle is that one should partially adjust one’s estimate of the unobserved variables—the natural rate of interest, the level of potential output, and its trend growth rate—-based on the difference between the model’s predictions for real GDP and inflation and the actual outcomes. Roughly speaking, for a given estimate of the output gap (or equivalently potential output), the model uses an estimated I-S curve relating the output gap to its own lags and the lagged “real rate gap”—the difference between the actual real rate and the natural rate—to form a prediction for the output gap in the next period. If the output gap turns out to be lower than expected, the model responds by reducing the natural rate by a small fraction. ^{3}*

(Updated) Holston-Laubach-Williams Estimate of r-star

In 2016, Laubach and Williams, in a paper co-authored with Kathryn Holston, made a few revisions to their original model and produced a new series for r-star.4 The resulting pattern of r-star is similar to the earlier one, but the Holston-Laubach-Williams (2015) estimate is currently higher than the Laubach-Williams (2003) one and has been so for some time. I show the paths of the two estimates of r-star in Figure 1.

~~ ~~ ^{3 }Thomas Laubach and John C. Williams, “Measuring The Natural Rate Of Interest Redux,” Brookings Working Paper #15 November 2, 2015. The Phillips curve and inflation also play an important role in the estimation of z and r*. In their words: “The output gap estimate, in turn, is informed by an estimated Phillips curve that relates core inflation to its own lags, the lagged output gap, and movements in the relative prices of oil and non-energy imports. In particular, if inflation turns out lower than predicted by the existing estimates for potential output, the level of potential output is being revised up (that is, for a given level of real GDP, the output gap is revised down), with most of this revision assigned to an innovation that affects only the level of potential GDP, and only a relatively small fraction assigned to the trend growth rate.”

^{4 }Holston, Kathryn, Thomas Laubach, John C. Williams. 2016. “Measuring the Natural Rate of Interest: International Trends and Determinants.” Federal Reserve Bank of San Francisco Working Paper 2016-11. http://www.frbsf.org/economic research/publications/workingpapers/wp2016-11.pdf

Below, I focus on the updated estimates by Holston-Laubach-Williams (2015). This is the paper most cited now by participants when they talk about the current r-star, including recent speeches by Yellen, and Williams himself.^{5}

Learning About the New Normal

Laubach and Williams have pushed back against Yellen’s convergence hypothesis. They call it “possible”, but note that “it has proven an unreliable guide during the past seven years.”^{6 }But the “new normal” hypothesis seems to be holding up well. In Figure 2, I show the paths of the Holston-Laubach-Williams estimate and participants’ median estimate of the longer-run r-star, both in real terms. The Holston-Laubach-Williams estimate has been near 50 basis points since 2012.7 Over the same period, participants’ median estimate of the longer-run r-star has declined from 2¼% to ¾%. The gap between our estimate of the median participant projection of the longer-run r-star and the Holston-Laubach-Williams estimate of r-star has, as a result, narrowed from 150 basis points in 2012 to about 25 basis points today. This is convergence toward the new normal, rather than convergence toward participants’ estimate of the longer-run r-star.

Updating the Narrative

Let’s face it. The headwinds story doesn’t fit with the facts, so to speak. A narrative, more in tune with the facts, is that FOMC participants were running a Laubach-Williams-like model in their heads, and very gradually adjusting their estimate of r-star in response to a weaker-than-expected economy. But they neglected to take

^{5 }Chair Janet L. Yellen, “The Economic Outlook and the Conduct of Monetary Policy,” At the Stanford Institute for Economic Policy Research, Stanford University, Stanford, California, January 19, 2017; John C. Williams, “Interest Rates and the ‘New Normal’,” Remarks to the Community Banking in the 21st Century Research and Policy Conference, St. Louis, Missouri, October 5, 2017. 6 Laubach, Thomas, John C. Williams. 2015. “Measuring the Natural Rate of Interest Redux.” Federal Reserve Bank of San Francisco Working Paper 2015-16. In that paper, they imposed on their model a consensus forecast for GDP growth and core inflation over the next two years and observed how the estimate of r-star responded. Their estimates “barely budge.” I updated that test using the Holston-Laubach-Williams (2015) model. In this case, I plugged in participants’ median forecasts through 2020 from the September SEP into that model and solved for the path of r-star. I got similar results to what Laubach and Williams found, a relatively stable r-star. 7 You can see in Figure 2 that the last two observations are below 50 basis points, 40 basis points, and 27 basis points. While the most recent reading is supposed to be the new normal—the expectation of r-star in the future— I am not prepared to say at this point that the new normal, after a long period of stability, has fallen. But I am watching!

into account that r-star is a random walk. Over time, they slowly came on board with the idea that r-star is permanently lower.

An alternative perspective on learning about the new normal is that, in the immediate aftermath of the 2007- 2009 recession, participants thought trend growth had not slowed so much. In that case, they may have believed there was a huge negative output gap. While they may have thought that the current and long-run r-star were still about 2%, they may have believed that the economy needed a real rate well below that to close the gap. Over time, they came to agree with the Laubach-Williams narrative that the real neutral fund’s rate had fallen to near zero and this was the new normal.

Implications for Monetary Policy

Does this conclusion have implications for the course of monetary policy? To a degree, but less and less! The lower the gap between the prevailing fund’s rate and r-star, the slower the pace of rate hikes that will be appropriate. This favors the more patient camp. But the difference between what the FOMC sees as the current and longer-term r-star has narrowed to the point where it is hardly worth mentioning. The Holston

Laubach-Williams estimate has been relatively stable at ½%, while participants’ estimate of the longer-run r star has fallen to ¾%. In nominal terms, Williams has recently said that his estimate of what participants call the long-run r-star (and he calls the new normal) is now 2½%, compared with the current median of participants estimate of the long-run r-star, 2¾%.8 Much ado about nothing (or very little)? Still, it may be time to change the narrative and focus on explaining how and why participants’ estimates of the longer-run r-star have fallen to what now appears to be the new normal.