y r U stars not aligning?
There’s an obsession out there with determining “r-star”, the “non-inflationary interest rate”. If central bank policy rates equal r-star, then inflation neither rises nor falls. But, if policy rates exceed r-star then policy is considered restrictive and inflation should fall. If below, then policy is accommodative and inflation should rise.
The only problem? No one knows r-star. It’s just a theoretical concept.
In recent weeks, not a day has gone by when r-star didn’t come up on Bloomberg when I listen to the morning financial news. It’s all over X, the platform formerly known as Twitter, and hotly debated among economics/finance types. Dallas Fed President Lorie Logan recently noted that the FOMC's projections for r-star are rising.
How do we estimate it? Did it rise? Did it fall? What does all this mean? And…ahhhhh… what does it mean for Fed rate hikes or cuts this year?!?!
The other stars of the economic show
It turns out that r-star (r*) isn’t the real problem. Actually, y-star (y*) and U-star (U*) are causing all the confusion. Let me explain them briefly.
Let’s start with y*. For macroeconomists, “y” stands for real GDP1 and “optimal” real GDP, y* is defined as the most real GDP an economy can sustainable and consistently produce given the current level of knowledge and essential resources like labor and capital. If actual real GDP is higher than y*, then we are driving the economy too hard and it will overheat, causing inflation. If real GDP is below y*, then the economy is going too slowly, unemployment will rise and inflation will slow. We don’t actually call it “optimal”, by the way. We call it “potential real GDP” or “the full employment level of real GDP”.
The last sentence already hints that this is related to “the natural rate of unemployment”, U*. When real GDP is at y*, we say unemployment is at its natural rate, U*, which is also the non-inflationary amount of unemployment. Naturally, when y > y* and the economy is overheating, we are overusing or over-employing all our resources, including labor, and hence unemployment is really low (i.e., U < U*). When y < y*, we are under-employing resources, including labor, and unemployment rises (i.e., U > U*).
So… all these things line up in simple, chalkboard level classroom theory. If y = y*, then that determines that U = U* (literally, “by definition”), and the interest rate must be at r-star, r = r*. And, that order is kind of how economists think about it.
Who cares?
Well, good question. The main people interested are financial market traders and investors. If they think r* is, say, 3% but current US policy rates are around 5%, then inflation should be falling, and we can expect the Fed to cut interest rates soon as it falls, and restrictive policy is no longer needed. And, we’ll know how many interest rate cuts to expect, because we’ll know the rate has to go from 5% to 3%. Knowing that makes Wall Street financial types money.
Misaligning stars
The problem starts with U*. I complained about the obsession with the natural rate of unemployment before. New monetary models use it in a Phillips Curve to actually determine inflation. You can read my griping about that in older articles (See my “Who’s Afraid of the 1970s”, for example).
The problem currently with U* is that US unemployment is low today. US U* is commonly believed to be around 4%. Current unemployment is less, around 3.8%. This goes hand in hand with stronger than expected GDP growth, suggesting y > y*, which further indicates an overheating economy and upward pressure on inflation.
That doesn’t seem all that problematic, and is wholly consistent with persistent US inflation. This week we even saw that inflation has risen again for the third month in a row.
It is a problem, however, if you’re a trader and have convinced yourself and your colleagues that current Fed policy rates around 5.3% are historically high and anomalous. Then you also think that rates are higher than r-star, r > r* and should be lowering inflation, and need to be cut soon. But that’s just wishful thinking.
The stars are aligned, just not the way you want
The stars are aligned. It looks like y > y* and U < U* suggesting the economy is running hot. Inflation, now around 3.5-3.8%, is therefore not surprisingly higher than the Fed’s 2% target. And THOSE THINGS TELL US that r < r* today.
That means, if you believe all the economic models running on Wall Street computers, then the Fed should RAISE interest rates. They are not high enough to temper demand and cool economic growth. Prof. Larry Summers of Harvard actually said the same on Bloomberg yesterday.
That’s just not what investors and market traders want to hear. They want interest rates low. They liked having cheap money sloshing around.
So, it’s not really a confusion about r*. It’s not a deep question about measuring it and what it’s telling us. Everything is telling us that r* is higher than where rates are today.
y*, r*, and U* are concepts
These things are concepts. They are theoretical constructs in mathematical models. They aren’t deep constants of the universe.
How do you know you are at y*, r*, and U*? When inflation is at it’s target rate, currently 2% in the United States.
We don’t get to nail down r* and then chase it so that when you catch it, inflation stops rising. It’s the opposite. When inflation stops rising, you know you are at r*. That’s it. Nothing more, nothing less.
Bob Hall and Marianna Kudlyak have a new paper out that I was fortunate enough to see presented in a Hoover Economic Policy Working Group meeting recently (see link). They were looking at U*. Many people have tried to estimate U* for the US economy, is it 4% or 3.5%, or higher? Has it slowly changed over the years, or has it remained relatively constant?
It’s true that we naturally think of it as constant. When we draw a graph on a board in class, it’s a constant number. It is the unemployment rate when the economy settles into steady state (“dynamic equilibrium”). But we all know that in reality the economy is never in steady state. It’s always moving and adjusting. Hall and Kudlyak took economic theory and models seriously, approaching the question of estimating U* by looking for periods in history when inflation was at target, neither rising nor falling. BY DEFINITION at those points, U = U*, y = y* and r = r*.
Here's Figure 2 from their paper (link to paper here). The red dots on the unemployment line are points when U = U* and the blue line below is inflation (measured by the Fed’s preferred measure of PCE inflation). We do know that since 2010 the Fed’s target inflation rate has been a constant 2%. So, whenever inflation equals 2% (or is near enough, within 1.5% and 2.5%), they record unemployment as U* at that time.
They can easily identify the natural rate. It just turns out that it moves all the time which, when you think about it, should be no surprise at all. The US economy was very different in 2010 versus 2015 versus 2020.
It looks like a quick and dirty estimate of the natural rate of unemployment would just be to run a trend line through the unemployment numbers over time and you’d be close. By the way, that’s essentially how we estimate y*; we run a trendline through actual real GDP over time.
Conclusion
All this is just to say that r* is the same as U* and y*. It’s not a universal constant. It is defined by when inflation is at target. That’s all.
It’s fine to wonder if we are above or below. It’s fine to wonder where r* will be in 6 months or a year. But traders have, once again, to contend with the fundamental fact that we simply cannot know the future today. We can guess, but we can’t know. No math model or fancy code will ever change that.
The inflation numbers in the US this week answered the question. The answer is that interest rates are below r*. r* today must therefore be higher than 5.3%. Full stop.
Everyone hoped it was lower than that and inflation would fall. I did too. But that’s not the case. The stock market has been adjusting to this new, upsetting news, and rates on bonds have risen reflecting the recognition that rates will remain higher for longer than originally expected.
Thank you for reading.
Real GDP is adjusted for inflation. So we think of it as the actual, or real, goods and services produced and sold in an economy. It’s sort of “all the real stuff” we actually care about.