In order to set an appropriate Fed rate, it is important to know the natural rate of interest. The Fed rate is set in relation to the natural rate of interest. But the natural rate of interest has not been easy to calculate... until now.

The best source that I have found to explain the natural rate of interest is a Federal Reserve paper written by John Williams in 2003.

What is the natural rate of interest? Here is a definition from the mentioned paper...

"In this *Letter*, the natural rate
is defined to be the real fed funds rate consistent with real GDP equaling
its potential level (potential GDP) in the absence of transitory shocks
to demand. Potential GDP, in turn, is defined to be the level of output
consistent with stable price inflation, absent transitory shocks to supply."

Graph #1

The dark solid line is the calculated natural interest rate. Here is an explanation of the calculation.

"One way to allow for structural changes that may influence the natural rate of interest is to compute averages of past values of the real funds rate while putting less weight on older data."

The natural rate of interest was thought to hover around 3% or 5% historically speaking. But is it that easy to calculate the natural rate of interest?

The conclusion of the paper states...

"Economists have made progress in estimating the natural rate of interest in recent years. But they have not yet hit a "home run." For example, although the Kalman filter has proven its usefulness in this effort, it is important to note that the resulting estimates are not very precise; that is, from a statistical viewpoint, we cannot be confident that these estimates are correct."

The understanding is that when real GDP is above potential real GDP, the Fed rate should be above the natural rate of interest. When real GDP is below potential real GDP, the Fed rate should be below the natural rate of interest. The amount that the Fed rate is above or below the natural rate of interest depends on the output gap.

For me, it was a fairly simple task to formulate the natural rate of interest from the Effective demand monetary framework. I determined the effective labor share anchor since 1967. It has only shifted a few times. Then I set a standard width for the effective range for the Fed rate of 22.7% with an inflation target of 0%. Then I calculated the corresponding z coefficient. Then I determined the position of the potential real GDP as 22% of the width of 22.7% for the effective range of the Fed rate, which comes to 5.0% in terms of the TFUR (total factor utilization rate). Then using the quarterly changes in effective labor share, which move the fed path up and down, I calculated the natural rate of interest with the equation for the path of the Fed rate.

Path of Fed rate = z*(TFUR^{2}+els^{2}) - (1-z)*(TFUR+els) - inflation target

Natural interest rate = z*((0.22*width)^{2}+els^{2}) - (1-z)*((0.22*width)+els) - inflation target

TFUR (total factor utilization rate) = capacity utilization * (1 - unemployment rate)... els is the effective labor share (labor share: business sector, 2005=100) * 0.78... width is estimated range of business cycle in terms of TFUR.

z coefficient = (2e - w + t)/(2e(e-w+1) + w(w-1))

e = effective labor share anchor... t = inflation target, neutral inflation target of 0% was chosen... w = the width of the range that we desire, such as 0.22.

Here is a graph using the framework for monetary policy with the shifts in effective labor share since 1967. (These are rough preliminary calculations, but they use normal and standard numbers of the effective demand monetary model.)

The blue line is the quarterly natural rate of interest. The red line is 3-year moving average.

Now I compare to the actual Fed rate (gold line) and the Fed rate that the Effective demand equation would prescribe using an inflation target of 2%, a static business cycle of 22.7%.

Some general thoughts on this graph #3.

- I think the Fed rate has been too low ever since 2001 and has caused great damage. I compare the gold line to the purple line.
- The economy survived the high Fed rate from 1981 to 1991. There was growth and stability in spite of the high rate.
- In the 1990's, the Fed rate was well-balanced in my opinion.

Now, I want to show a graph as if the monetary framework hadn't shifted. The effective labor share anchor did shift after the 2001 recession and at the end of 2009, but I leave those shifts out of this graph #4. (If the Fed continues to calculate the natural rate of interest based on past values, their graph of the natural rate of interest could look similar to this...)

You can see a big difference since 2003. In this graph the natural rate of interest has continually fallen to below 1%. This is part of the reason why the Fed rate is held at the zero lower bound. The reasoning compounded by the belief that there is an enormous negative output gap between real GDP and potential real GDP. So the Fed sees a low natural rate of interest, and they see a large negative output gap. So they would like to push the Fed rate into negative territory.

However, in graph #2 above, I shifted the effective labor share anchor and as such shifted the monetary framework to correspond to the current business cycle. In doing so, the natural rate of interest stayed in the 3% to 4% range.

Once you have the natural rate of interest, then you have to decide where potential real GDP is. Then the current real GDP of $13.75 trillion will be measured against it. I say potential real GDP is currently around $13.6 trillion. The CBO says it is currently around $14.6 trillion. That is a huge difference. My determination of potential real GDP says that the Fed rate should be above the natural rate of interest. Using the CBO number, the Fed rate should be below the natural rate of interest.

If I am right, the Fed is making a big mistake by keeping the Fed rate so low for so long. They are expecting the economy to grow to the increasing trend of $14.6 trillion. However, I have calculated that the economy will run into the effective demand limit at $14.1 trillion. My view is that we will never see that delusional potential real GDP trend line become a reality without a bubble again. And there is no chance of getting a big bubble like that again.

There is still more to develop in this model in order that it can properly determine where the Fed rate should be. It will take a few posts to do that.

The most striking thing about graph #3 is the huge gold-purple divergence 78-85. Does this suggest that fed policy should have been much looser to be "balanced" as in the 90s? Conditional factors?

Posted by: Steve Roth | 06/09/2013 at 08:44 AM