In the previous post, I presented the model with equations for a universal monetary policy that can be applied to any economy. The model was based on two equations that interact to pinpoint the interest rate of a country's central bank. The Effective demand rule sets the path of a central bank's interest rate. The Effective demand limit shows the central bank where the LRAS curve is (long-run aggregate supply). With these two equations a central bank can have a stable monetary policy.

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

Effective demand limit = 2*z* TFUR^{2} - 2*(1 - z)*TFUR - 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)... inflation target is expressed as a percentage, such as 2.0%... the z coefficient is what I will talk about next.

What is the z coefficient?

The z coefficient establishes the stabilization zone within which an economy will move.

The z coefficient actually calculates the stabilization zone for the model for monetary policy. The equation for this is...

Equilibrium point = (1 - z)/z

Let me show you what this looks like.

On this graph there are four values for the z coefficient. (0.80, .070, 0.582 and 0.50). For each value of z, there is a pair of lines that cross on the x-axis perfectly at the point of (1-z)/z. These two lines are the equations given above for the Effective demand rule, which determines the path of the interest rate and the Effective demand limit.

The green lines cross at a TFUR of 72% with a z coefficient of 0.528. This is the stabilization zone of the United States at least since 1967. Now the TFUR has averaged 74.8% in the United States since 1967. So why the difference between 72% and 74.8%? The graph above uses an inflation target of 0% so that the lines will nicely cross on the x-axis. But if you factor in an inflation target of 2%, the lines will cross 2% below the x-axis. Thus with a 2% inflation target, the lines would cross closer to 74%.

The z coefficient itself will tell us where an economy is in terms of utilization rates of labor and capital and effective demand. If you walk into a country and calculate a z coefficient of 0.68, you would generally know how socially efficient the economy is in utilizing its capital and labor resources. The TFUR will average a little above (1-0.68)/0.68, say around 50%. In general terms it might be an economy with an average capacity utilization of 60% and an average unemployment rate of 20%. The economy could likely be in an early stage of developing its capital infrastructure.

If the country tells you that their unemployment rate is only 7%, you would have to doubt their measurement. Obviously they are not counting people who are plainly marginalized from the labor force. The effective demand isn't developed enough to have less unemployment. The estimate of the effective labor share of income would be about 5% to 10% more than the average TFUR, around 57%.

If you walk into a country and the z coefficient is 56%, you would know that this country is utilizing its labor and capital at a high rate in its production. And you would also know that the effective labor share is high in order for the production rates to be high. This is a mature economy, where labor receives a higher share of the national income because the capital infrastructure is well-developed and maintained.

The United States could have become an economy with a z coefficient of 56% if it had matured properly. I wrote about this process in an earlier post. But now the US is heading in the other direction. I predict the z coefficient for the US will rise during the next recession, to around 0.60. It is hard to estimate exactly because there will be slippage in the process.

A rise in the z coefficient won't be good and means that more people will be marginalized from the work force. But it will have to happen in order for the Federal Reserve to regain a viable monetary policy with an interest rate able to regulate the economy.

Some time back, there were economists calling for the Fed rate to rise. If the Fed had raised the Fed rate at that time, the z coefficient would officially have risen, and many people would have been marginalized outright from the work force. But the Federal Reserve is not giving in yet. They are holding out hope that the economy will recover. Well, at the present low rate of effective labor share, the Fed will eventually have to give in and just raise the Fed rate. When they do, we will have officially gone backwards in our economic growth.

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