In the model for monetary policy based on the principles of Effective demand, it has been easy to determine an equation for the z coefficient. What is the z coefficient? It's a variable in the equation to determine the interest rate from a central bank. Here is the equation...

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

Here is the model for the Effective demand monetary policy with the violet line being the path of the central bank interest rate...

The effective range of the Fed rate should be positioned over the cyclical movement of the TFUR. The range is only effective when the violet line is positive and to the left of the LRAS curve.

The z coefficient moves the Fed rate path up and down. As the Fed rate path moves up, the effective range gets wider. As the Fed rate moves down, the effective range gets more narrow. So how does one determine the correct value for z in the above equation? We first look to see what ranges have occurred in the past...

Since 1967, the TFUR falls and rises through the business cycles. The range has been from 7% to 17%. One could say that an average range would be 13% from peak to trough. So we would like an equation that determines the z coefficient based on the width of the range that we want.

Here is the equation...

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

e = effective labor share anchor... t = inflation target, such as 0.02... w = the width of the range that we desire, such as 0.13.

Let's just take the current effective labor share anchor of 73.8% and the current inflation target of 2.0%. Then we want a width of 0.13 (or 13%). We feed those variables into the equation and we get a z coefficient of 60.43%. Here is the graph...

We now have our monetary framework in place ready for the current business cycle. If you want to give a little breathing room for the range and have a little more protection against a liquidity trap, the range could be widened to 15%. The equation says that the z coefficient would rise to 60.73%.

Of course, this is just a basic theoretical model and far from ever being used by the Fed, but you never know. As time goes by and the Fed gets more and more frustrated, especially through a series of recessions with completely ineffective monetary policy, they would eventually look for other models to resuscitate the Fed rate. This should be one to consider.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.