In the previous post, I showed how a linear regression can be used to determine a natural rate of unemployment. That natural rate of unemployment can also be used to estimate the lower limit of unemployment in a business cycle expansion. The previous post estimated a lower limit of 7.3% for unemployment before the next contraction.

Here is another simulation to determine a lower limit for the unemployment rate.

This graph starts by putting the approximate numbers for 4Q-2012 on the far left with unemployment of 7.8% (quarterly number). Then the unemployment rate is allowed to fall. In the simulation capacity utilization also falls at a rate 2.4x the change in unemployment. Thus as you move right on the graph, factors of production (labor and capital) are being utilized more and output (real GDP) increases. As output increases through increased utilization of labor and capital, effective aggregate demand decreases. Where effective aggregate demand and aggregate supply intersect, we have *effective demand* as Keynes would define it.

We can also see the UT index falling as available factor capacity is used up. ("Available" simply means within the constraint of effective demand. Michael Kalecki wrote about "idle" capacity, but didn't seem to define it explicitly as within the constraints of effective demand.)

It is not likely that the UT index will reach absolute zero from looking at past data. Therefore, the lower limit of the unemployment rate will most likely be a little on the left of absolute zero. Ultimately this simulation based on approximated data shows a lower limit of around 7.0% for the unemployment rate. The Federal Reserve has a plan for when unemployment reaches 6.5%, but according to the equation of effective demand, unemployment will not reach 6.5%.

Also... Real GDP can increase while the UT index for available factor capacity stays unchanged. This is more likely to happen when the UT index is low and we may see some of that in the next year or two. However, if this situation occurs, the lower limit for the unemployment rate will only change if the ratio of effective labor share to capacity utilization changes. This is according to the equation...

unemployment rate = 1 - (effective labor share - UT index)/capacity utilization

At lower limit, UT is small, therefore equation emphasizes the ratio...

unemployment rate = 1 - effective labor share /capacity utilization

If effective labor share rises in relation to capacity utilization, the lower limit of unemployment will decrease. (Implied also is that the natural rate of unemployment will decrease too.) Thus, if labor share of income rises enough, unemployment could reach the 6.5% threshold of the Federal Reserve.

Example, at UT = 0%, unemployment lower limit = 1 - 74.3%/80% = 7.12%

Raise effective labor share, UT = 0%, unemployment lower limit = 1 - 76%/81% = 6.17%

Do you see how capacity utilization went up (80% to 81%), but the lower limit of unemployment still went down? Raising the labor share of income would be a good thing for the economy.