The Importance of r*: Part 1

Understanding today's economic challenges involves digging into crucial factors that impact our financial landscape and policy choices. Is the stock market overvalued given that the S&P 500 price-earnings ratio is well above its historical average? Should the Fed continue raising rates to eradicate inflationary pressures from the system? Are current levels of government debt sustainable? Whether we're questioning if the stock market is too expensive, figuring out how the Federal Reserve tackles inflation, or worrying about government debt levels, there's a common thread—something called the "natural real interest rate," often called r-star (r*). This concept is like a hidden force affecting various economic aspects. It influences how stock prices are calculated, guides setting interest rates to control inflation, and plays a role in how government debt and budget deficits interact. So, to get clear answers to these big questions, we need to unravel the mysteries of r*.

Defining the natural rate of interest

Most of the readers are probably familiar with the concept of the “real interest rate,” but to ensure that everyone is on the same page, let me put the equation here.

real interest rate = nominal interest rate – inflation

Technically, this equation should be an approximation, but for simplicity let’s use it as an identity.

The nominal rates are the interest rates that you see in banks, newspapers, and financial markets discussions. These rates represent your return in terms of money. If the nominal deposit rate is 5%, we expect that our deposit will generate 5% more money one year from now. Unfortunately, this number does not tell us whether we are better off depositing the money for one year or just spending it today. This is so because we don’t know what will happen to the prices of goods and services while the money is sitting in the bank.

If prices of goods and services increase by 6%, then we are actually worse off. We will have 5% more dollars, but everything will be 6% more expensive. So, our purchasing power takes a hit. One year from the start of the deposit, we will lose 5% - 6% = -1% of purchasing power. This -1% is the real interest rate. We calculate the real interest rate in order to determine whether saving increases or decreases our purchasing power.

Normally, when the real interest rate is positive, people tend to save more, while a negative real interest rate encourages spending now. This happens because saving with a negative real interest rate leads to a loss of purchasing power. While economic theory is more complex than this simple explanation, it still serves as a good first approximation to how people behave.?

What is the natural rate of interest and how is it determined? The real interest rate that we can calculate by using the formula mentioned above fluctuates constantly depending on many factors. However, we believe that these fluctuations tend to converge in the long run to an equilibrium value that we call the “natural rate of interest,” or r*. This unobservable natural rate is like an anchor point towards which the real rate converges. It is determined by the global forces of supply and demand for funds. The supply of funds on the global market is coming from households and governments, while the demand is coming from companies who want to invest these funds and generate profits. Like in every supply/demand framework, the intersection of the two curves will determine the equilibrium rate. Further below, we will investigate what determines the supply and demand for funds, and how these determinants have been shifting over the past centuries.

The decline of r* over the past 50 years and over the past 800 years

Probably, the key takeaway from this article should be that many estimates of r* point to a significant decline in this rate (again r* is unobservable, so economists have to employ various econometric techniques to estimate it; see Krugman, 2023, for a brief discussion). The graph below from Obstfeld (2023) illustrates the decline of the average real interest rate in 12 advanced economies.

Of course, at any given point in time, the real interest rate may not align with the equilibrium level. Simply subtracting inflation from the nominal interest rate will produce the actual real rate today, but it may give us a very misleading view on the equilibrium rate. There are various statistical methods that one can use to extract the equilibrium rate from multiple financial and macroeconomic series. ?In a recent paper John Davis and co-authors (2023) combine financial and macroeconomic models to estimate r* in 10 advanced economies. For those interested in the details, Figure 6 in their paper provides a clear view of the downward trend in these economies.

To get a quarterly or monthly estimate of r*, one must use sophisticated statistical models. But if we are interested in long-term trends, there is another reasonable approach: we can calculate the average of the realized real interest rate over a long period of time. We know that at any specific moment, the real interest rate might deviate from its equilibrium value, but we would expect these fluctuations to be around the equilibrium rate. Thus, the average rate over a long period of time will cancel positive and negative deviations from the equilibrium. The graph below uses this idea by creating 100-year averages of the real rate since the 14th century (light-blue lines) based on European interest rates and inflation. The downward trend in the average real interest rate (proxy for equilibrium) is very clear both on the graph and in the table.

Why is r* going down?

It is not clear whether there is one single factor that explains this downward trend of r*, and most of the academic papers consider several explanations. For the observations before the industrial revolution, it seems reasonable to argue that financial development might be a dominant factor in bringing real interest rates down. Since the early 1800s, in addition to financial development, a key contender to explain the secular decline in the natural rate is the growth of the world economy. As incomes increase, individuals save more and supply more funds to the economy. This drives interest rates down. For the most recent periods, say, over the past 40 years, the growth rate of China and its high savings rate is a key contributor to what has been called the “global savings glut”.

Research on the importance of various factors behind the decline in the natural rate has led us to this non-exhaustive list:

• Growth in developing countries and oil-producing economies (it increases the global supply of savings)
• Demographics (increases in lifespan lead people to save more during their active years of work; one might argue that the drawdown during retirement will negate this factor, but careful calculations show that this is not the case, and the aging of the world population seems to be one of the leading factors today)
• Productivity growth slowdown (this implies decline in the demand for investment and therefore less demand for funds; a shift in the demand curve).
• Rise of inequality (concentration of wealth at the top percentiles leads to more saving as rich people save more).
• The shift towards a digital economy – the investment needs of digital firms are much lower than those of traditional manufacturing, which lowers the demand for funds.

If these factors lead to a significant increase in the supply of savings and to a decline in the demand for funds, then we can ask a very important follow-up question: Are there any reasons to expect that the dynamics of these factors will reverse? ?If we think that growth in emerging and developing countries will continue and the demographic trends will not change, then it will be hard to imagine how the era of low real interest rates will end in the foreseeable future. ?

What does this mean for monetary policy?

In my first article in these series, I discussed the Taylor rule for setting interest rates, which looked like this:

Central Bank target rate = Equilibrium rate + A*(Inflation – 2%) + B*GAP

For simplicity, I called the first term “equilibrium rate”, but it is a bit of a misnomer. This term has two components: the equilibrium real interest rate and target inflation (assumed to be 2%).

Central Bank target rate = r* + 2% + A*(Inflation – 2%) + B*GAP

It should be clear now that the rule is affected directly by the estimate of r*. As mentioned, r* is referred to as the natural rate of interest. However, in this context, it is often called the neutral rate of interest. Obstfeld (2023) makes an important distinction between the two concepts, but at this point we will use the two terms interchangeably.

So, why does it matter that r* is a part of the central bank’s decision on how to set interest rates? First, it is crucial to note that we cannot observe r* directly. When the Fed calculates the interest rate suggested by the Taylor rule, they must use an estimate of r*. If they have the wrong estimate, unpleasant things may happen. To illustrate this, let’s assume that the gap is zero, inflation is at target (2%), and the Fed estimates r* to be 2.5%. If the Fed follows the Taylor rule, they should set the nominal interest rate at 4.5% (remember that inflation target is 2%). But if the actual (unobservable) r* is 1%, then it turns out that the central bank has set the rate too high, and the economy will be pushed away from its wonderful state of zero output gap and inflation at target into a recession. To stay in equilibrium with inflation on target and the gap at zero, the economy needs 3% interest (1% of true r* + 2% of inflation), but the Fed has set it at 4.5%, which is too high.

If, on the other hand, they set interest rates too low – the opposite will happen, i.e. consumers will increase their spending because interest rates are too low, which will trigger an increase in inflation. The accuracy of the estimate of r* is therefore crucial in what the appropriate central bank interest rate should be.

The figure below shows the neutral (natural) rate of interest that I used in the Taylor rule in my previous article. Clearly, there is some volatility in this series, but the downward trend is quite visible as well. While the natural rate was hovering around 4.7% in the 1960s, it went down to about 3.4% in the 70s and 80s. Since 2008, the average has been around 1%.

In the 1980s and the 1990s keeping inflation at 2% in equilibrium (zero gap; inflation on target) would have required nominal interest rates to be about 5% (3.01% natural rate and 2% target inflation). In today’s world, to keep inflation at target level in equilibrium, interest rates must be around 3% (0.95% natural rate and 2% target inflation). The decline in the equilibrium rate translates into a significant “benefit” of 200 basis points in lower nominal rates.

To put it differently, had the natural real rate remained at its level from 30 years ago, then the surge in inflation that we observed in the past two years would have required the Fed to raise rates to around 7-8%. Today, with rates at 5.5% it might be possible to subdue inflation and bring it back to its 2% target. So, using past inflation and past interest rates to discuss current inflation and current rates might be quite dangerous, unless the discussion takes into account explicitly the decline in the natural real interest rate.

While many participants in the stock market cheer at the idea that rates may not have to go up as much as before, my next article will discuss the implications of the decline in the natural rate of interest for the stock market returns that one might expect in the future and for the price-earnings ratios. ??

References

Davis, Josh, Cristian Fuenzalida, Leon Huetsch, Benjamin Mills, and Alan M. Taylor (2023), “Global Natural Rates in the Long Run: Postwar Macro Trends and the Market-Implied ????? in 10 Advanced Economies.” Working Paper 31787, National Bureau of Economic Research, October 2023.

Krugman, Paul (2023), “Wonking out: Hitch Your Wagon to R-Star ,” The New York Times, August 25, 2023

Obstfeld, Maurice (2023) “Natural and Neutral Real Interest Rates: Past and Future”, Working paper .

Schmelzing, Paul (2020) "Eight centuries of global real interest rates, R-G, and the ‘suprasecular’ decline, 1311–2018," Bank of England, Staff Working Paper No. 845.

‘suprasecular’ decline, 1311–2018, Bank of England, Staff Working Paper No. 845.