Re-visiting R*: Close to the end of the hiking cycle for the Fed

Last week I wrote a blog post in which I updated my outlook for US inflation based on the so-called P-star model.

In that blog post, I argued that my forecast in April 2021 for much higher US inflation essentially had been spot on, but also that inflation now is set to start to inch down relatively fast in the US.

The P-star model basically is a monetarist model that states that inflation is a result of money supply growth being faster than money demand growth.

However, the Federal Reserve normally does not communicate about monetary policy in terms of money supply growth but rather in terms of setting its policy rate.

I am as a (market) monetarist very skeptical about thinking about monetary conditions in terms of interest rates. Instead, I believe that central banks cannot in the longer run control interest rates. Rather, interest rates are determined by structural factors – essentially to clear the market for savings and investment.

What central banks can do is to set a policy rate that is comparable with what the Swedish economist Knut Wicksell called a natural interest rate, R*.

However, to set a policy rate below R* then the central bank will have to increase the amount of money in circulation in the economy. This will, however, cause an acceleration in inflation, which sooner or later will cause the central bank to revise its policy.

When central banks communicate in terms of their policy rate rather than in terms of for example money supply growth (or growth in nominal demand) then it becomes key to understanding the level of R*.

In that sense, we can understand the state of monetary policy by looking at the key policy rate relative to R*.

The problem of course is that we cannot observe R* directly, but we can try to estimate R* from the historical relationship between macroeconomic variables and the policy rate.

Back in February 2021, I presented such a model in a blog post “R* strikes back: The Fed will hike sooner rather than later”.

I have now updated that model and will use the updated model to evaluate US monetary policy over the past two years and to look ahead.

The R* model

This is how I described the variables in my R* model for the US back in February 2021:

“First of all, I look at potential nominal GDP growth (relative to population) growth.

This of course partly reflects the Fed’s inflation target and that we know from the so-called Fisher Equation that high inflation should cause higher nominal interest rates. Furthermore, this also captures the fact that higher productivity growth should be expected to lead to higher interest rates – as we for example recognize it from the so-called Solow growth model.

Second, I use population growth to capture both growth trends as well as for example the impact of changes in savings and risk appetite as a consequence of changes in demographic trends.

Third, even though the Fed’s task is to ensure ‘price stability’ it has not always succeeded in that. The opposite of price stability is price volatility and we, therefore, use a 10-year moving average of yearly changes in inflation to capture the degree of price (in)stability.

Finally, we also want to capture changes in investors’ and consumers’ optimism and pessimism and the general ‘business cycle’, and the general level of economic activity. I could have used unemployment or the output gap, but I also wanted to capture structural-demographic trends so I have used the so-called employment-population ratio as an explanatory variable.”

Furthermore, I took into account in the model that there apparently since 2008 has been a structural shift down in interest rates and yields globally – likely reflecting to a large extent banking regulation.

The graph below shows the effective Fed Funds rate since 1960 and until today and my estimate for R*. The model has been estimated until 2019 so as not to be influenced by lockdowns etc. from 2020.

We see that the model overall fits the development in the Fed funds rate quite well for more than six decades.

Below I will zoom in on the development in the Fed funds rate over the past five years and compare that with R*.

The Fed got it right in 2020, but failed massively in 2021

The US and the global economy and markets were hit by an unprecedented shock in early 2020 when the Covid pandemic spread around the world and governments – also in the US – moved to contain the virus by lockdown the economies and introducing draconian restrictions on civil and economic life.

In the initial phase, the reaction in the financial markets was very close to what we saw in the Autumn of 2008 and all indications were that the US economy would fall into a deep and potentially deflationary recession.

If we look at the model’s prediction of R* then we see that R* dropped sharply in the US in early 2020. In fact, the drop in R* was as sharp and as deep as in 2008 and as in 2008 R* turned negative. In fact R* became even more negative than in 2008.

Contrary to 2008 the Federal Reserve reacted swiftly to the drop in R* and cut the Fed Funds rate to zero and introduced massive quantitative easing. Hence, the Fed surely had learned the lesson from 2008 – when R* drops below zero it is not enough to cut the policy rate to zero – quantitative easing (money printing) is also needed.

The swift policy reaction from the Fed certainly worked – the US economy rebounded strongly as did financial markets.

The recovery was so impressive that I in May 2020 in a blog post argued that US unemployment would drop to 6% by November 2020. When I made that forecast US unemployment was at 15%. My forecast turned out to be nearly right – we got to 6.7% in November 2020.

The swift recovery let me to start thinking that the Fed would soon have to revise it policy stance and start hiking interest rates and undoing quantitative easing and that was very much driven by what I observed in terms of the development in R* relative to Fed’s actual policy.

This was also very visible in the graph above. We see that R* bottomed out around April 2020 close to -4%, but in months following that we saw R* increasing quite fast and by the end of 2020 R* was back to zero.

This would imply that the Fed would have ended its quantitative easing by the end of 2020 and have started interest rate hikes already in early 2021. And this is in fact what I thought the Fed would do – or at least start a process of “normalization”.

As I wrote back in my original R* blog post in February 2021:

“This means that we in 2021 are likely to see the Fed being forced to change its message quite a bit. I am tempted to say that this smells of the stop-go policies of the 1970s and even though the outcome is likely to be less catastrophic than during the 1970s we could very likely see an increase in financial market volatility as a result of this.”

But the Fed did not change its message. Hence, in early 2021 Fed chairman Jerome Powell, again and again, stated the pickup in inflation was temporary and in July 2021 Powell now famously stated the Fed did not even think about thinking about hiking interest rates.

If we compare this to our model for R* we see that by the summer of 2021 R* had increased to 4% – indicating that by the summer of 2021 US monetary policy had become extremely easing.

In fact, if we look at the difference between the actual Fed funds rate and R* – what we could call the R-gap – then this is the easiest US monetary policy has been since 1974. It therefore hardly should have been a surprise to anybody that we would see a sharp spike in inflation in 2021-22.

Hence, the R-gap is telling us the exact the same story as the P-star model – US monetary policy became excessively in 2021 and this is the main reason why we saw a sharp pickup in inflation in 2021-22.

Said in another way we got into 2022 the Fed was way behind the curve and there was a very urgent need to initiate monetary tightening. The Fed started signaling this in October-November 2021 and then initiated the rate-hiking cycle in 2022.

As we see from the graph above R* basically levelled off around 5% in mid-2020 and since then the gap between the actual Fed funds rate and R* has been closing as the Fed has continued to hike rates.

And with the expected rate hike this week from the Fed we are now very close to having closed the gap between the Fed funds rate and R* and it is safe to say that based on the R-gap US monetary policy is now close to being neutral.  

Next: Fed will start cutting rates as inflation comes down

The Fed got way behind the curve in 2021, but during 2022 the Fed has been fast catching up and based on our analysis above is clear that the Fed likely will end its interest rate hiking cycle in the near future.

The next question becomes when the Fed will start cutting interest rates and here we can also get a bit of guidance from our R* model.

What we essentially need to do is to make a forecast for R*, which to an extent gets us into endogenous problems – hence if the Fed keeps Fed funds too high for too long then inflation will drop faster and economic activity slow, which both will push R* down. On the other hand, if the Fed cuts rates too fast then it will cause inflation to come down at a slower pace and economic activity will be higher, which will push up R*.

This, of course, illustrates on of the problems with a policy of interest rate targeting – it is to a large extent a process of trail-and-error and given how much out of whack US monetary policy has been it is easy for the Fed to err in this process.

But on the other hand it is probably reasonable to assume that the Fed eventually will get it right – and bring inflation down towards 2%, while keeping unemployment close to its structural level (NAIRU). If we use this as input in out R* we can simulate a scenario for the Fed funds rate in the coming years.

This is what I have done below. In terms of inflation, I have used our P-star model from my previous blog post to make some assumptions for the development in inflation in the coming years. My base scenario for inflation is a simple average for the two inflation scenarios (“hawkish” and “dovish”) in my previous post.

The graph below shows the simulated Fed Funds rate, which we assume follows R*, based on our assumed scenario for US inflation going forward.

This is no doubt a very benign scenario where inflation comes down back to the Fed’s 2% inflation target gradually over the next couple of years and the Fed funds rate is cut gradually to reflect the drop in inflation.

There is of course a lot of room for mistakes and as such, it is very hard to make anything else than a conditional forecast for the Fed funds rate going forward. That being said given that I expect inflation to start declining rather significantly in the coming six months it is also clear that we are very close to the end of the hiking cycle and eventually the Fed will start cutting rates.

The Fed most definitely will not get it perfectly right, but I am actually somewhat more optimistic that the Fed will manage the next ‘stage’ of this episode better than what it did in 2021 so my ‘best estimate’ is that by 2025-6 we would probably see the Fed funds rate around 1.5% – more or less at the level we hade during the period 2015-2019.

Finally compared to market pricing the scenario above is not significantly different from market pricing. Hence, the market expectation is also for the Fed to initiate rate cuts during 2024, and even though my simulations are actually indicating that we could get rate cuts already in the second half of 2023 given the rather large uncertainties this is not a major difference. Note here that this is not because I assume the US economy will fall into recession – in fact, I have assumed it will not.

The overall conclusion is that while the Fed clearly erred on the overly easing side in 2021 and did right in tightening monetary policy during 2022 we are now entering a period where we have risks on both sides and the Fed can and likely will err in both directions in the coming 1-2 years.


US inflation set to fall sharply in the coming quarters

Back in April 2021, I wrote a blog post with the title “Heading for double-digit US inflation” in which I warned that we were likely to see a sharp increase in US inflation.

We didn’t quite get to 10% but it was close and US inflation certainly turned into the main US policy issue in 2021-22.

My forecast was based on two simple facts.

First, of all the fact that we in 2020-21 saw the largest expansion in the US money supply (I used M2 to illustrate that) ever in peacetime.

This is essentially a monetarist story – if you expand the money supply faster than the growth of money demand then nominal income growth will accelerate and sooner or later you will as Milton Friedman taught us have inflation.

The second point was that in early 2021 the Federal Reserve was eager to tell us that the increase in inflation was ‘transitory’. Or said in another way the Fed essentially refused to take responsibility for controlling over the development in nominal income and hence in inflation.

This is point is market monetarist in the spirit of Robert Hetzel – if the Fed refuses to do its job then it will cause an expectational shift that will accelerate the increase in inflation.

So to me, it was fairly straightforward to forecast higher inflation in the US at that time.

I fully admit that other factors played a role as well such as the much talked about “supply chain” problems as a result of Chinese Covid policies and higher energy prices, but I generally think the importance of these issues have been significantly overestimated.

The core reason US inflation rose sharply in 2021 was excessively easy monetary policy and the Fed’s refusal to take responsibility for price stability.

Furthermore, it should be noted that US inflation, in fact, rose well ahead of Putin’s invasion of Ukraine and inflation actually started to decline in 2022 – after the Fed demonstrated that it would again start to take responsibility for ensuring price stability.

In fact, US inflation was lower by the end of 2022 than at the beginning, which fits badly into a story that this was caused by Putin’s war.

However, the moderation in US inflation during 2022 fits well into the monetarist story I told in 2021. I will return to that below.

The graph below shows the simulation of a so-called P-star model – which is based on the monetarist quantity theory of money – I used to forecast inflation back in April 2021 and the actual development in US inflation since then.

My simulation from 2021 certainly didn’t get it perfectly right, but it is notable that we did indeed see a sharp spike in US inflation as forecasted, but it is equally notable that in the simulation from April 2021, we also saw that inflation wouldn’t just continue to accelerate.

In fact, the simulation indicated inflation would moderate – from a very high level – during 2022. This is in fact also what we have seen.

So our model both got the spike in inflation right in 2021 and the moderation in inflation in 2022 right. The difference, however, was that inflation didn’t quite increase as much (and as fast) as the initial simulation had indicated it would.

To understand that we need to go back to our original model – The P-star model – and what assumptions regarding monetary policy (and the monetary transmission mechanism) I made then.

The P-star model

In my blog post in April 2021, I based my forecast or simulation of future inflation on the so-called P-star model.

The P-star model is based on the equation of exchange:

(1) M•V=P•Y

Where M is the money supply (I used M2 for the US), V is the velocity of money, P is the price level and Y is the real GDP/Production.

If we assume that V over time follows a trend that is determined by structural factors such as financial regulation and demographic and similarly we assume that over time there is a potential level of Y that is determined by structural factors such as technology, taxes, the size of government, demographics, etc. then we can re-write (1):

(2) P* =M•V*/Y*

Where P* (or P-star) is the level of prices in the economy we should expect in the long run given the actual level of the money supply and the structural levels of V (V*) and Y (Y*).

The graph below shows my calculation of P* back in April 2021.

We see at that time due to the sharp increase in the money supply in 2020-21 P-star was significantly above the actual price level and that is basically why I made the call that inflation would increase sharply.

And as discussed above inflation did indeed rise very sharply as forecasted. However, we didn’t quite get to double-digit inflation as the simulation had indicated would have happened.

The Fed turned more hawkish than assumed

When I made the simulations back in April 2021 the Fed was still talking about inflation as something the Fed could not control and as ‘transitory’.

Hence, in March 2021 Fed chairman Jerome Powell said “However, these one-time increases in prices are likely to have only transient effects on inflation”.

Said in another way the Fed had no plans to tighten monetary policy.

So when I made the simulation in 2021 I had to assume that at least for some time the Fed would not tighten monetary policy but also that the Fed would not forever ignore the likely increase in inflation that I was forecasting.

So in my simulation in April 2021 I assumed that starting from May 2021 US money supply would gradually start to slow and from early 2022 it would follow the trend in money supply growth, which ensured around 2% inflation from 2010-19.

However, if we compare this with the actual development in money supply growth we can see that the Fed has turned decisively more hawkish than I had assumed it would.

The graph below shows the level of the US money supply (M2) that I assumed it would follow and how it actually developed.

We see that the development actually followed my assumption fairly closely through most of 2021 but from around November 2021 the growth of the money supply slowed dramatically and during 2022 the US money supply actually declined.

Interestingly enough the rather abrupt slowdown in money supply coincided with the reappoint of Fed chairman Jerome Powell and also with a maked shift in the communication from the Fed. Hence in late November 2021 Powell said “We tend to use [the word transitory] to mean that it won’t leave a permanent mark in the form of higher inflation.”…”I think it’s probably a good time to retire that word and try to explain more clearly what we mean.”

The gap between the ‘forecasted’ and the actual M2 level, however, particularly started opening up from April-May 2022, which marks an ‘acceleration’ of monetary tightening.

Consequently, we should expect inflation to continue to come down faster than forecasted in April 2021.

Re-doing the April 2021 simulation

When I did the simulation in April I used the P-star model to calculate the gap between the actual US price level and P-star – the P-gap.  

To do that I also needed to make assumptions about how fast the P-gap would close – or rather how sticky the inflation rate would be.

Given inflation didn’t increase as much as the simulation had indicated then is an indication that inflation was more sticky than I had assumed.

This is important when we need to forecast inflation going forward. We need to take into account this stickiness in inflation.

In the graph below I have essentially redone the simulation from April 2021, but done it will the actual development in the money supply and adjusted what we could call the ‘stickiness parameter’. We see that this simulation fits the actual inflation development remarkably well.  

I think it is important to note that price stickiness not only reflects that certain prices are fixed by contracts but also to a very large extent is determined by expectations. Hence, if economic agents expect the Fed always to conduct monetary policy in such a way that inflation will alway will be close to 2 percent then even a significant increase in the money supply will not cause a major increase in inflation.

But overall to the extent the original simulation from April 2022 was wrong, it was not primarily due to a wrong assumptions about money supply growth (in it was more or less correct for at least the first 8-12 months). The primary mistake in the simulation hence was the assumption about the degree of price stickiness.

So we certainly should not abandon the P-star model. Rather the model correctly forecasted the sharp rise in inflation and also that inflation would eventually come down again as the slowdown in money supply growth sat in. It is therefore also worthwhile updating the forecast from the model.

This is what I have done below.

Inflation seems set to drop significantly

In many ways, the forecast/simulation from April 2021 was a ‘control experiment’ as the US economy had been in a lockdown and the money so to speak had been printed. We can compare this to a situation where we drink a bottle of whiskey and now forecast that we will get a hangover. It is nearly given by nature that this will happen.

When I forecasted inflation to rise strongly in April 2022 the money had already been printed. There was at that time little to do about it – the hangover would arrive soon in the form of a sharp increase in inflation. The only question was how fast it would take the Fed to ‘stop drinking’ and slow money supply growth.  

The situation now is very different in the sense that it is much less clear what the Fed will do from here. The clear geopolitical risks, the upcoming US presidential elections in 2024 and a potential US recession all could trigger both changes in inflation expectations and also changes in the Fed’s policy reaction function.

So it is certainly not as straightforward to forecast inflation now as it was in April 2021. However, that is no reason for not trying.

But instead of making one forecast, I have instead made two different scenarios for US inflation based on two different assumptions for US money supply growth going forward.

The first scenario is what we could call the ‘hawkish’ scenario. In this scenario, I have essentially assumed that all of the excessive money supply growth during 2020-22 will be undone so the level of the US money supply will return to the ‘old’ 2010-19 trend in the coming year. This basically implies that the slowdown (relative to the pre-2020 trend) in M2 growth continues basically until we are back at the old trend in level terms.

In the second scenario – the ‘dovish’ scenario – I have assumed that from now on – Q1 2023 – US money supply growth will return immediately to the same growth rate as we saw pre-2020 but starting from higher a high level. This is what we normally would term letting bygones-be-bygones.

In both scenarios, the M2 will eventually grow at the same pace but the level of M2 will be different.

In the graph below I have simulated two different scenarios for US inflation based on the two different assumptions for M2 growth going forward and I have used a ‘stickiness parameter’ that ensure the best fit for inflation in the 2021-22 period.

A number of factors should be noted regarding these simulations. First of all, it should be noted that even though US money supply growth has slowed rather dramatically for more than a year there still is a considerable ‘monetary overhang’ – what I above called the P-gap is still positive (around 6-7% versus around 15% at the peak in early 2021). This means that even though money supply growth remains subdued there still are considerable ‘pent-up’ inflationary pressures.

On the hand as Milton Friedman often noted – monetary policy works with long and variable lags. In the simulations above I have assumed (based on the historical relationship) that there is a six-month lag between an increase in the P-gap and higher inflation. This also means that it will take time to bring inflation down, but also once money supply growth has slowed the impact will continue to feed through to inflation over a longer period.

These factors are clearly visible in both scenarios. First of all, we see that in the first half of 2023, inflation drops basically equally fast in both scenarios and the reason for that is that since we have assumed a six-month lag between changes in money supply growth (and therefore in the P-gap) it will take six months before any change in monetary policy is visible in inflation.

Therefore, in the model set-up any slowdown in inflation in the coming six months will be due to the slowdown in money supply growth we saw during 2022.

What is notable is that in the ‘hawkish’ scenario US inflation will continue to decline until the Autumn of 2025 and drop well below Fed’s 2% inflation target.

On the other hand in the ‘dovish’ scenario inflation will come down toward 2% gradually over the next 3-5 years.

The most likely scenario probably is a combination of the two scenarios where the Fed is likely to follow a stop-go or go-stop policy. Hence, with inflation likely to drop significantly in the next 3-4 months the Fed is also likely in that period to end it hiking cycle and therefore also to gradually start to re-accelerating money supply growth.

But the Fed also is likely to struggle with the famous long and variable lags – either by waiting too long to end monetary tightening or by initaiting easing monetary policy too early.

I think that there should be relatively little doubt that inflation will come down toward 4-5% over the next 6 months in the US. However, the tricky part will be for the Fed to get inflation back towards 2% and the policy discussion is likely to intensify in the second half of the year.

Even though the Fed is far from being able to declare victory on inflation we are nonetheless likely to see inflation worries subside considerably (unless a new major supply shock hits) in the coming 6 months.



Lars Christensen,

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