The Effective demand rule to determine the Fed funds rate is developing rapidly. Last night I began to look back at Fed rate data from the 1960's. And I began to think about other countries where the utilization of labor and capital and the labor share rates are much lower than the US.

I wondered why those poor countries don't have a 0% central bank interest rate all the time. Why do they have positive rates? Aren't their economies so depressed, more so than the US economy right now? and Yet, those poorer developed countries still have a positive central bank interest rate. How would my equation determine the central bank rate to apply in those countries?

Well, to make a lot of thought into a short story, I had to understand my equation better. Here is the equation I had yesterday...

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%.

I came to realize that the coefficients of 0.61 and 0.438 must be similar to ones used by the Federal Reserve for internal calculations of the Fed rate. It is like they determine a lower bound within the Federal Reserve, but have no model that I can see. So I had to scrap those coefficients and look deeper.

I was looking at those other countries trying to figure out how the equation could change so that their low TFUR rates and labor share rates would calculate regular central bank type interest rates. And I realized that the proportion between the coefficients had to change.

I noticed that they almost added up to 1. (0.61 + 0.438 = 1.048) So I simply concluded that they are portions of 1%. In this way, there is only one coefficient. The other coefficient is simply (1 - the coefficient).

So then I re-wrote the equation...

ED rule = z * (TFUR^{2} + els^{2}) - (1 - z) * (TFUR + els) - inflation target

z = the coefficient of the equation.

I then put the z coefficient into the equation for the effective demand limit used in this monetary policy model. The equation yesterday was...

ED limit = 2 * 0.61 * TFUR^{2} - 2 * 0.438 * TFUR - inflation target

The equation is now...

ED limit = 2 * z * TFUR^{2} - 2 * (1 - z) * TFUR - inflation target

I use the letter z for the coefficient because it seems the ultimate variable to determine the internal power of an economy. Everything comes down to this coefficient. If the z coefficient is low, an economy can achieve higher utilization rates of labor and capital. This is good for more people in society. If the z coefficient is high, an economy will have large portions of unemployed and marginalized workers. There will be a greater difference between the poor and the rich. Basically the z coefficient determines at what level a central bank will have a viable monetary policy... or not.

Only the two equations above are needed to determine the interest rate for a central bank's monetary policy. The only variables needed are the unemployment rate, capital utilization rate, the effective labor share (unit labor costs & price level), the z coefficient and the inflation target. Let's start by looking at a graph with an economy with a z coefficient of 61%.

In this graph, there are 4 paths for a central bank's interest rate. Each path is based on a different level effective labor share (from 50% to 80%). A path based on 50% would correspond to an underdeveloped country, for example like one that focuses on exporting natural resources while the population is poor and unemployed. A path of 80% would correspond to a developed country where labor income is a higher percentage of national income and almost everyone has a job.

The black line is the effective demand limit determined when the TFUR equals the effective labor share. I have written many times about how the TFUR does not like to go above the effective labor share rate (els). The black line determines the limit of the interest rate path for a central bank. If the path is negative until it reaches the effective demand limit (green dot), the economy will always be in a liquidity trap situation with the central bank interest rate at 0%. When the path goes positive before it reaches the effective demand limit (green dot), the central bank will be able to set a viable interest rate to regulate the economy.

In the above graph, the red dot shows the dividing point. Paths above the red dot have viable monetary policies. Paths below don't. We can determine that an effective labor share above 66% would allow a viable monetary policy with a z coefficient of 61%.

Let's look at the United States now. The United States has a z coefficient of 58.2%. This value comes from the lower bound seen in past Fed rates. (0.61/1.048)... A coefficient of 58.2 allows the effective demand limit to cross the x-axis at around 74%, which fits past data.

We can see that in the United States, an effective labor share of 70% would not allow a viable monetary policy, whereas an effective labor share of 80% would. We can also see that the United States' economy functions with a TFUR in the range of 65% to 80%.

How about an economy that functions with a TFUR from 40% to 50%? What would the graph look like for this economy?

First, we can see that the z coefficient has risen to 70%, which raised the paths of the interest rate and shifted them left. Now an economy with a low effective labor share can have a viable monetary policy. The cost is large numbers of unemployed workers, but at least the central bank can work with a viable monetary policy.

We should ask the question... What would happen if this country started raising their labor share of national income? If their coefficient did not change, the central bank would have to start raising its interest rate, basically due to stronger liquidity increasing aggregate demand.

How can a country change its coefficient? And how can we determine the z coefficient? Good questions to be answered at another time.

I want to finish by showing two graphs of the United States. Here is the present situation of the United States.

The current effective labor share gives a negative path all the way to the effective demand limit. At this rate, the Federal Reserve will never have a viable monetary policy before the next economic contraction. We can also see the point at which inflation will turn into hyper inflation. And it would happen fairly quicky because there is little run up of the Fed rate to the LRAS curve. (LRAS curve sits where effective demand crosses the path of the Fed funds rate.)

Now we look at a hypothetical case for if the United States had an effective labor share of 80%.

The United States would have a viable monetary policy with the current TFUR of 72% (green dot). If you follow the red arrows, this would have been the path of the Fed funds rate if we had been able to maintain an effective labor share of 80%. The TFUR would have been able to reach as high as 78%, which translates to a capacity utilization of 82% and an unemployment rate of 5%. (0.82 * (1 - 0.05) = 78%)

Don't we wish we were there now? Well, the people who own capital are making record profits so there is mixed incentive to raise labor share of income. But if the Federal Reserve wants to save itself, it would fight for a higher labor share of income. The corresponding dynamics of liquidity would allow the Federal Reserve to have a viable monetary policy.

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