The Federal Reserve’s mandate is clear – ensuring the maximum level of employment while at the same time ensuring price stability.

Over time the Fed’s interpretation of this mandate has changed, but we can maybe get a bit closer by saying that the Fed has an ordering of the dual mandate.

First the Fed wants to insure that inflation (inflation expectations) over time is close to 2%.

Second, once this is the case the Fed will try to “push” economic activity in the “right” direction – meaning that the Fed will ease (tighten) monetary conditions if US unemployment is above (below) the structural level of unemployment (NAIRU).

This of course also is what is reflected in for example the traditional Taylor rule, where the Fed ‘sets’ its policy rate – the Fed Funds rate – to reflect both inflation relative to the inflation target and the output gap.

However, what is not often discussed is that the Fed does not actually ‘set’ interest rates. Or rather the Fed cannot just set a level of interest rates, which it likes.

Rather the Fed will have to set the interest rate relative to the structural level of interest rates – or what the Swedish economist Knut Wicksell termed the natural interest rate – or which is often today referred to as r*.

Hence, the task of the Fed is to set monetary conditions so to ensure that actual short-term interest rates are close to r*.

If the Fed tries to push interest rates significantly below r* for a sustained perioded by injecting large of amounts of liquidity into the economy then sooner or later we will get a spike in inflation.

Therefore, the Fed really isn’t in control of interest rates – or at least the fed cannot independent of its inflation target set interest rates.

All the Fed can do is to shadow r* and thereby ensuring than inflation will be close to its inflation target.

The challenge for the Fed is that r* isn’t constant over time.

Hence, we know both theoretically and empirically that the real interest rate has been moving up and down and is different from country to country.

Hence, r* reflects structural factors – such as demographics and productivity.

In this blog post the purpose is to try to help understand the development in r* over time and to assess what implications this has for present day monetary policy in the US.

To shed light on this matter I have estimated a rather simple, but nonetheless robust model for the development in the actual Fed Funds rate since the early 1960s. This is part of a bigger research project I am doing at Copenhagen Business School.

Normally models for the Fed funds rate is seen as ‘policy rules’.

The purpose here is not to estimate a ‘policy rule’ but rather to think about the Fed’s challenge to shadow r* by estimating a model for what the Fed historically has done with interest rates.

Estimating Fed’s r*

Basically the starting point for the analysis is that the Fed is both ‘targeting’ real and nominal economic activity, which is that the dual mandate is about. Real economic activity in terms of the ‘output gap’ and nominal activity in terms of inflation.

However, we also know that this has been changing over time and the Fed’s 2% inflation target is a fairly “new” target.

Furthermore, we also know that r* is not constant over time so even when inflation is at the inflation target and the output is closed (zero) then the Fed might have to change its policy rate to reflect changes in r* that are a result of for example higher saving in the US economy (for example due to consolidation of public finances) or to reflect higher or lower productivity growth.

To reflects these factors I have estimated a model for the Fed funds rate since 1962.

To explain the development in the Fed funds rate I use the following variables:

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 succeed 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.

Estimation results

I don’t want to bother the readers too much with the specific statistical tests, but what I have done is simply to run a simple linear regression explaining the (nominal) fed funds rate with the four variables discussed above. The estimation period is from 1962 and until today. I use quarterly data.   

The graph below shows the actual Fed Funds rate and the predicted Fed Funds rate and we see the fit over nearly six decades is quite good (R2=0.8).

Furthermore, all four explanatory variables are strongly statistically significant and the sign on all four variables are as expected positive – meaning growth nominal GDP and population growth push up the Fed Funds rate as do higher inflation volatility and a high employment-population ratio.

Furthermore, it is notable that the model well captures the major trends in interest rates over the past six decades – higher interest rates in the 1970s and the decline in rates from the mid-80s and the ‘flat lining’ of rates over the 12-15 years.

I will not go in to too much detail in terms of the decomposition of what drives interest rates during the different periods and I will return to that in later work, but it is sufficient to say that the very low level of interest rates we have seen in the US since 2008 is more or less fully explained by the four explanatory factors – lower potential NGDP/capita growth, low population growth, low inflation volatility and a moderately low level of employment-population ratio.

Hence, the Fed funds rate is not low because the Fed’s has “manipulated” interest rates and is not low because monetary policy is has been overly easy (if anything it has been too tight – at least until recently).

Rather, low interest rates in the past decade reflect economic conditions and mostly structural economic conditions – for example weak population growth and a declining labour force due to the aging of the US population (the baby boomers have been leaving the labour market).

Looking ahead – Fed will need to hike sooner rather than later

In response to the ‘lockdown’ crisis of 2020 the Fed has cut the Fed funds rate (and implemented quantitative easing). This is completely in line with what the prediction of the model have been.

In fact the model predicted that the Fed funds rate should have been cut to -3% (!) in the second quarter of 2020.

This of course didn’t happen due to Zero Lower Bound on interest rates, but the Fed instead has opted to undertake significant quantitative easing of monetary policy. Hence, the money base has been expanded significantly. This in mind my undoubtably has been the right policy – at least in terms of the magnitude of monetary easing.

The predicted decline in the Fed funds rate primarily reflected a sharp drop in the employment-population ratio.

However, both of these variables are now clearly improving, but despite of that the Fed has so far insisted that we are far away from any rate hikes.

However, this week we have nonetheless seen quite a bit of a repricing of the markets’ expectations for rate hikes.

To answer the question about the outlook for rates we can try to make a simulation based on the model we have estimated above.

What we will try to estimate is where the Fed Funds rate should be in ‘steady state’ – hence, once the US economy has moved out of the crisis and returned to the underlining trends that we saw prior to the ‘lockdown shock’ hit in 2020.

Lets have a look at the four explanatory variables.

First we see that potential nominal GDP growth (per capita) as calculated by the Congressional Budget Office (CBO) over the past decade has been stable around 3.0%  – considerably lower than earlier decades. Hence, we use 3.0% as our measure of the long-term growth rate of potential NGDP growth (per capita).

Second, in terms of population growth we use a forecast of 0.7% annual population growth in the US – reflecting more or less most forecasts for US population growth over the coming decade.

Third, we assume that inflation volatility will remain low around the same level as we have seen over the past decade (0.25).

Finally, we assume the decline in the employment-population ratio will continue to reverse – reflecting the closing of the output gap.

Judging from recent economic data this recovery will be quite fast. For simplicity we assume that the employment-population ratio will return 60% by mid-2022. This is not necessarily a forecast of what will happen, but rather an assumption we use when making a simulation for the Fed Funds rate for the medium-term.

Fed Funds rate is heading back to 1.5% sooner than you think

If we assume that these for variables over the coming 4-6 quarters return to their steady-state levels then we can simulate what we should expect to see in terms of the Fed Funds rate.

The graph below illustrates that.

According to the simulation the Fed Funds rate should return to positive territory in the middle of this year. This can be interpreted as the Fed will end QE and change its forward guidance in a more hawkish direction and in the second half of the year we should actually see the Fed start hiking the Fed Funds rate.

During 2022 the Fed Funds rate should approach 1.5%.

This is of course a much more aggressive rate hike path than presently signalled by the Fed and expected by the market (around 100bp above market pricing in by the end of 2022).

However, it does not reflect an extreme assumption regarding the economy.

Rather the only thing we here assume is a return to ‘normal’ over the next 6-8 quarters and given what we are seeing in terms of the macro data at the moment and the planned major fiscal easing this certainly does not seem to be an overly optimistic take on the economic outlook. In fact it might be too pessimistic.

Furthermore, this does not reflect the change in the Fed’s inflation target from a pure 2% inflation target to an average inflation target and it does not reflect any change in the risk premium on US debt despite a very significant expansion of US public debt.

So if anything there might be reason to speculate that the Fed could be forced to hike even faster than this simulation indicates.

What if the Fed fails to hike?

Fed officials continue to argue that there is no reason to hike rates any time soon. In fact Fed chairman Jerome Powell has argued that the Fed is not even thinking about thinking about hiking rates.

But what happens if the simulated path for the Fed Funds rate is right and the Fed despite of that sticks to the promise of not hiking rates?

Then the Fed effectively will be in a situation where it will try to keep r (significantly) below r*.

The Fed has tried such policies before in the later part of 1960s and going into the 1970s and the result was rather catastrophic – inflation rose sharply. As did economic volatility.  

I certainly don’t think that the Fed will repeat the mistakes of the 1970s – at least not to the same extent – but while the Fed mostly have erred on the downside (too tight monetary policy) over the past 12 years the opposite now seems to be the case.

Hence, during the next 2-3 quarters we will likely have a test of the Fed’s commitment to it’s 2% (average) inflation target. Will the Fed for example allow inflation expectation to increase above 3%?

Or – more likely – will the Fed reverse course once it realizes that the output gap will be closed already during 2021 and inflation risks will increase further if it refuse to hike rates.

Unfortunately, the Fed has continued the mistakes of the past and communicated its monetary policy stance in terms of its policy instruments rather than in terms of communicating in terms of its policy goals.

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.

PS there are also some elements of what we saw during 2006-7 in what is happening in financial markets, but I do not expect the same outcome as in 2008-9, but I might return to that in a later post.

PPS I have done similar modelling on the US 10 year Treasury bond yield. See here.