I have written about the death of the Fed funds rate. Now I will do an autopsy to show how it died.

The Effective demand rule used to determine the prescribed Fed Funds rate has special and specific dynamics. These dynamics explain the death of the Fed rate.

We first start with the equation for the Effective demand rule. (Note: Effective demand rule has been updated and revised since this post. Complete version of equation)

ED rule = 0.61 * (TFUR^{2} + els^{2}) - 0.438 * (TFUR + els) - inflation target

TFUR is total factor utilization rate (product of the utilization rates of labor and capital)... els is effective labor share (labor share: Business sector (2005=100) * 0.78)... the inflation target is expressed as a percentage, such as 2.0%.

The Fed funds rate has bounds within which it moves. These bounds are constraints. The Fed rate has a lower bound of 0%, below which it cannot go. Yet, there are other lower bounds beyond which the Fed rate will not naturally go.

### The Lower Bounds of the Effective demand rule

I will start by just showing the graph of the Effective demand rule with the lower bounds.

The graph puts the prescribed Fed funds rate on the y-axis and the TFUR on the x-axis. The TFUR represents utilized capacity of labor and capital. The curved lines represent the Effective demand rule at various rates of effective labor share. Currently the effective labor share is around 74% (the yellow curve is identified).

In a recession the TFUR falls. In an expansion the TFUR rises. We can see that as the economy expands, the Fed rate should rise along one of the curves depending on the rate of effective labor share.

The 0% lower bound of the Fed rate is drawn. The other lower bounds are shown by a black line. One lower bound which must be an internal boundary at the Federal Reserve is calculated with the equation... =0.61*TFUR - 0.438. It is from this equation that the ED rule gets its coefficients. Another lower bound is marked by green dots. Each green dot shows the Effective demand limit where the TFUR will not go beyond. For example, on the blue line of the 82% effective labor share, a rising TFUR will not go beyond 82%. It is a basic principle of Effective demand that the TFUR is constrained by the effective labor share.

The red area below these lower bounds marks the area where the Fed funds rate will not naturally go.

### How does this graph show the death of the Fed rate?

The primary goal should be to always have a Fed rate above the lower bounds. Sounds obvious since the Fed rate cannot go below a lower bound. Yet, look at the current effective labor share (els) curve. The whole curve is in the red area. This means that the Fed rate will always be stuck on a lower bound never able to reach the 74% els curve. In effect, with an effective labor share of 74%, the Fed rate will never have any traction (traction refers to the ability of the Fed rate to effect monetary changes in the economy). It is rendered powerless, unable to fulfill its full duty. It is unable to breathe. The Fed rate drowns.

In effect, the Fed rate has drowned below the waters of the lower bounds, unable to breathe.

If we were to have an effective labor share of 82%, the difference is great. The Fed rate would have traction from a TFUR of 65% to 82%. We had an effective labor share of 82% in the late 80's and before the 2001 recession. And the Fed rate was able to move around and along the 80% to 82% effective labor share curves fulfilling its function. The Fed rate never lost traction.

When the effective labor share fell below 76%, the Fed rate started drowning. The 78% els curve in the graph is above the lower bounds. The 74% is below. A curve for an els of 76% just starts submerging completely below the lower bounds. 76% is the critical level for the Fed rate. Effective labor share should never go below 76% or the Fed rate will die.

Normally it is thought that when capacity utilization reaches around 80% that inflation will start to appear. If the Fed is waiting for this to happen, they will ultimately be disappointed. With the current Effective demand limit, capacity utilization will not surpass 80%. This is due to low effective labor share and high unemployment, capacity utilization itself is hitting its upper limit.

If labor share of income does not rise, the Fed rate will stay dead no matter what they try to do. If the effective labor share rises above 76%, the Fed rate will begin to resuscitate.

The Effective demand rule is an equation with extraordinary precision to determine the point of death for the Fed rate. Just to show that the Fed rate obeys these lower bounds. Here is a graph of actual data for the Fed rate and the various lower bounds.

The blue line shows the movement of the Fed funds rate since 1988. There is one blue dot that crossed a lower bound. That happened in the 4th quarter of 1997, a time of "irrational exuberance". The Fed rate quickly jumped straight back from the other side of the lower bound. We can see along the 0% lower bound that the Fed rate is hitting the "0.61*TFUR - 0.438" lower bound. I expect to see changes in the utilization of labor and capital to keep the TFUR on the left side of this lower bound.

There we have it. The cause of death for the Fed funds rate is drowning from low labor share of income.

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