# Podcast

### Important Information:

## Charting the Path of Interest Rates

### Important Information:

Thomas Lubik and Christian Matthes discuss how economists wrestle with measuring the natural rate of interest or r-star, why this measure is important for monetary policymakers, and how their model has evolved to better chart the path of interest rates. Lubik is a senior advisor at the Federal Reserve Bank of Richmond and Matthes is a professor of economics at Indiana University.

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## Transcript

**Tim Sablik**: Hello, I'm Tim Sablik, a senior economics writer at the Richmond Fed. My guests today are Thomas Lubik and Christian Matthes. Thomas is a senior advisor in the Research Department at the Richmond Fed. Christian is a professor of economics at Indiana University and was a senior economist at the Richmond Fed from 2013 to 2020.

Thomas and Christian, thanks for joining me.

**Thomas Lubik:** Thanks for having us, Tim. Glad to be here.

**Christian Matthes**: Thanks, Tim.

**Sablik**: As listeners probably know, the Fed embarked on a series of rapid interest rate increases starting in March 2022 in response to rising inflation. In mid-2023, the Fed slowed the pace of increases as inflation began to move back toward its long-run target of 2 percent. The discussion among Fed policymakers now has been looking at whether the Fed's monetary policy is sufficiently restrictive and when it might be time to shift into a more neutral policy stance.

When talking about neutral policy, Fed officials and economists sometimes refer to the natural rate of interest, denoted as r* in economic models. Christian, can you tell us what r* is?

**Matthes**: In order to do that, I think it's useful to first define an intermediate concept just to bring everybody on the same page, and that's the real rate of interest. We define that as a nominal interest rate — in our case, the policy rate set by the Federal Reserve — minus the expected rate of inflation. Once we've defined this real rate, we can think about the natural rate.

In the work that Thomas and I have been doing, we think of the natural rate as the equilibrium or long-run real rate of interest that will prevail in the absence of any shocks or unexpected changes to the economy. So, in that sense, the real interest rate will naturally gravitate towards this natural interest rate that we are trying to estimate. As such, r* is a benchmark of where the real interest rate should be in the long run. It is comparable to the natural rate of unemployment that policymakers have often discussed in the context of setting U.S. monetary policy.

A key issue is that all these natural rates — whether it's the r* that we are interested in or the natural rate of unemployment — are unobservable. We cannot directly read them off data, we have to estimate them. We have to somehow use statistical methods to infer them, and that's where our work comes in.

**Sablik**: Thinking about how all this relates to Fed policy, Fed Chair Jerome Powell was asked at the press conference following the November 2023 FOMC meeting how r* factors into the committee's discussion about the stance of monetary policy. He said, "It's a very important variable in the way we think about monetary policy, but you can't identify it with any precision in real time."

Thomas, can you give some insight into how r* is used in policy discussions at the Richmond Fed?

**Lubik:** Our main policy process is briefing our president, Tom Barkin, before he goes to the FOMC meetings. In our policy process, we use numerous inputs in developing our view and his view of the economy and the preferred monetary policy stance. We use internal and external forecasting models and a whole bunch of data. r* is just one of those inputs.

We use r* in two areas. r* can be regarded as a metric for assessing how restrictive or accommodative current monetary policy is. When an economy is in a long-run equilibrium, when there are no shocks to the economy, then the real rate of interest is equal to its natural rate or r*. When the real rate is above r*, we would consider policy to be restrictive — the real rates that companies have to pay for loans is higher than its long-run rate — and vice versa when the real rate is below r*. We can look at this so-called real rate gap as a metric for assessing the policy stance and this is part of the discussion that we have before the FOMC meeting.

The second part where we use r* is in the quarterly Summary of Economic Projections or SEP for short. Four times a year — every other FOMC meeting — every FOMC member produces a forecast for a few years out about key macroeconomic variables: GDP growth, inflation, the unemployment rate, and the path of the federal funds rate. But we also produce our long-run estimates of where the economy is heading towards. r* then serves as an input for this discussion on where the long-run federal funds rate should be under our idea of optimal policy.

I also want to emphasize that there is no direct, one-to-one mapping between Christian's and my estimate of r* and the long-run federal funds rate.

One value that we see in our contribution to the policy process is that we've done this for almost 10 years, so we have a long time series of r* estimates. This allows us to benchmark our current estimates against its historical behavior. This puts a useful perspective on how we should interpret the most recent numbers.

**Sablik**: As you both mentioned, r* isn't something that we can just directly observe. You have to estimate it. In 2015, you both created a model to try and do that, to try and estimate r*. That estimate is updated quarterly and it's available on our website, Richmondfed.org.

I'm curious what motivated you initially to create this measure, and can you give us some sense of the inputs your model uses to make that estimate of r*?

**Lubik:** Christian and I started working on this when Christian was still an economist here at the Richmond Fed, maybe late 2013, early 2014. At that time, the economy was still recovering from the Great Recession. Monetary policy was very accommodative. The federal funds rate was at its zero lower bound. But the policy discussion started shifting, exiting from the low interest rates policy to normalizing the monetary policy stance.

As Christian mentioned, r* can serve as a metric for the monetary policy stance. Thomas Laubach and John Williams, who were then at the Board of Governors and the San Francisco Fed, respectively, had already developed a natural rate model in the 2000s. I think the sense in the Research Department at the Richmond Fed at that time was whether we could contribute our own r* measure.

**Matthes**: Our thought process at the time was that, while Laubach-Williams was very useful and provided great insights to help policymakers, we wanted to have a very flexible framework. We thought that's something that we could contribute to the discussion at large. And so, we use these flexible statistical models that Thomas has already introduced. What's really useful about this class of models is that it can adjust to changes in economic relationships over time.

We estimate this model using three key macroeconomic variables, namely the growth rate of real GDP, the inflation rate — in particular, we use a PCE-based measure — and a measure of the real interest rate. Intentionally, we use the same measure of the real interest rate as Laubach-Williams uses.

Why do I talk about measures of the real interest rate here? As I mentioned earlier, the real interest rate depends on expected inflation, so you have to take a stance on how you measure expected inflation.

Given this statistical model, we can then predict what the real interest rate will be in the future. And as our benchmark, our natural rate estimate is the five-year forecast of the real interest rate coming out of our model.

**Sablik**: Thinking more about the other model of r* — the Laubach-Williams model, which was later updated with additional work from Kathryn Holston and is now hosted by the New York Fed — has drawn some attention recently. Over the last two years, that estimate and your estimate have actually diverged quite notably. Your estimate of r* has steadily risen, while the Holston-Laubach-Williams estimate has declined. Do you have any sense what's behind this divergence?

**Lubik:** Ultimately, the divergence comes from the different type of assumptions and the modeling specifications that go into each estimate. Our model is what economists like to call a theoretical model. That's a purely statistical model that attempts to extract long-run trends from the observed data without making too many or any additional assumptions. In contrast, Holston-Laubach-Williams is what economists like to call a structural model. In that sense, it imposes additional and quite a few restrictions on how the different variables in the model interact. This allows for less flexibility but can actually lead to better and sharper estimates.

Our model is much more flexible and adapts more quickly to changing circumstances. As an example, our model actually performed remarkably well for forecasting during the COVID-19 pandemic when the data flow was really quite wild.

But what we have learned over the years is that our model is somewhat sensitive to recent data. For instance, it takes a strong signal from the sharp rise in real rates. So, at first, real rates were going down because inflation was going up. Then the Fed raised interest rates and then real rates were going up now with eventually declining inflation. The model interpreted this as it's likely that the natural real rate r* is going up.

I don't want to necessarily speak for what's going on in the Holston-Laubach-Williams model. But what they do have is that there's a tight link between r* and trend GDP growth. And what we know is that trend GDP growth has been falling now for the last 30 to 40 years. This, in their model, puts downward pressure on their r* estimate.

**Sablik**: Yeah, when it comes to estimating something unobservable like r*, it really depends on the ingredients that go into the model that you're using. I get the sense that it's sort of a work in progress.

You and Christian recently made some modifications to your r* model, which you described in a recent Economic Brief that we posted on our website last fall. Can you talk a little bit about the changes you made and why you decided to make them?

**Matthes**: As we already mentioned, we estimate this r* time series using a complicated, nonlinear statistical model. As such, it's really important — both as researchers but also for policymakers — to monitor in real time what the effects of modeling choices are in such complicated frameworks. Empirical modeling in economics is really an iterative process where you look at your latest results and, in light of these results, you update your assumptions on what goes into a model. This is exactly what we've done.

To go into detail into what we did recently, our model allows these parameters, these economic relationships to change over time. Given the recent data, as Thomas already mentioned, we concluded that the model parameters were adjusting too much to recent data. Why could we be worried about that? Well, there might be short spikes in volatility or there might be measurement error issues that our model does not explicitly incorporate. As such, we've decided to modify our priors to allow for slightly less time variation.

**Sablik**: Because r* can't be directly observed, and these various attempts to estimate it don't always agree, that has led some commentators to conclude that maybe it's not a very useful guide for monetary policy. How would you respond to that?

**Lubik:** In general, I think this is a fair comment. I mean, there is uncertainty surrounding what the correct model specification is, what the correct model is. There is estimation uncertainty. But I would say that even if it's completely pitch black, you can still use a flashlight on your smartphone to try to illuminate what's around you.

What do I mean by that? One value I see in the r* estimates is that it helps organize our thought process and policymakers' thought process around a common reference point. [It is a] reference point that is well in line with modern macroeconomic thinking and, as Christian explained, goes back more than 100 years. So, it would not be clear to me if we didn't use r* as a concept for discussing our policy what the alternative should be. As economists like to say, it takes a model to beat a model.

I would also say that there's a lot of value in having several competing models and their estimates. The two leading r* models, Holston-Laubach-Williams and Lubik-Matthes — provide their own independent views on what r* is. In an environment with fundamental uncertainty, this helps bound the range of possible outcomes. In addition, there's a lot of research in the economics and statistics literature — including recent work by Christian and me together with my Richmond Fed colleague, Paul Ho — that shows that combining different models, or model averaging, can actually help improve forecasting performance.

So, the fact that there are so many r* estimates out there, that there's uncertainty about r* can actually help sharpen ones thinking about monetary policy. This is very much evident in the debate right now. When our estimates were very close to those of Holston-Laubach-Williams, there was much less discussion of the inherent uncertainty in r*. Now there is and I think this is good for monetary policy thinking going forward.

**Sablik**: As you mentioned, there's a big debate now among economists about where r* will land in the long run. Over the last decade, most of the estimates agreed that r* was quite low. And so, there's a question, will it continue to be low after we move away from the pandemic or have we shifted to a persistently higher level now? Do you think there's any evidence that points in one direction or the other, or is it still too early to call?

**Lubik:** Yeah, I feel like in economics, everything is always too early to tell. [Laughs]

**Matthes**: All joking aside, there are and have been for a while several trends in the world economy that have influenced r* and will continue to influence r*. One that comes immediately to mind is demographics. Across most of the developed world, an aging population first increases the savings rates but then dissaves — once they retire, they need to live off their savings. That explains the secular fall in real rates over the last 30 to 40 years. But now, it's also consistent with the rise in the real interest rates.

**Lubik:** The point that Christian mentions ties into this whole discussion about the global savings glut, which was actually identified and brought into the policy discussion by the former Fed Chair Ben Bernanke in the early 2000s. (Incidentally, that was in a speech that he gave in Richmond.), Bernanke identified the global savings glut as the key driving force for real rates. Globally, savings were at an excessive rate and this was explained by the opening of China, extremely high savings rates in East Asian economies, export surpluses by natural resource producers, and so on. So, there were just a lot of savings in the world economy, which could prompt downward pressure on the interest rates and real rates. There are now convincing signs that this process is now going into reverse.

An additional important point is that after the Great Recession, the global financial crisis, and then the pandemic and the response to the pandemic, government indebtedness shot up dramatically across the globe, notably in the U.S. but also in many European countries. This also tends to push up interest rates.

**Sablik:** Thomas and Christian, thanks so much for coming on the show today.

**Lubik:** Thanks so much, Tim.

**Matthes:** Thanks for having us.

**Sablik:** If you enjoyed this episode, please consider leaving us a rating and review on your favorite podcast app.