Let's take a look at the Effective demand equation which determines the Fed funds rate. I want to point something out about the relationship between inflation and unit labor costs. Here is the Effective demand rule for the prescribed Fed rate...

ED rule for Fed rate = 0.61*(TFUR^{2} + els^{2}) - 0.438*(TFUR + els) - 2.0%

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)... 2.0% at the end of the equation is the inflation target.

You will notice that inflation is not in the equation. You might wonder... how can we determine the Fed rate without using the existing inflation rate? If the inflation rate rises, we need to be able to raise the Fed rate to slow it down. And it appears that this equation wouldn't respond correctly.

Well, this equation does include the inflation rate. We use use the equation for effective labor share...

Effective labor share (els) = ulc_{e}/(1+i)

ulc_{e} is the effective unit labor costs (unit labor costs: Business sector (2005=100) * 0.78)... i is the inflation rate.

We substitute in for els...

ED rule for Fed rate = 0.61*(TFUR^{2} +(ulc_{e}/(1+i))^{2}) - 0.438*(TFUR + ulc_{e}/(1+i)) - 2.0%

Now we can see that a change in the inflation rate will change the prescribed ED rule Fed rate. But there is a catch... if we change the inflation rate, we would also change effective labor share and/or unit labor costs. Let's look at the possibilities.

- If we raise inflation and unit labor costs hold steady, effective labor share will decrease and the Fed rate should then decrease. That's right. A higher inflation rate would warrant a lower Fed rate.
- If we raise inflation and effective labor share holds steady, that means unit labor costs have increased at the same rate as inflation and the prescribed Fed rate will not change.
- If inflation rises and unit labor costs decrease, effective labor share and the prescribed Fed rate also decrease.
- If we raise inflation and effective labor share declines and unit labor costs increase at a rate slower than inflation, the prescribed Fed rate should be lower.
- If inflation increases and effective labor share increases too, then unit labor costs have risen faster than inflation and the prescribed Fed rate will rise.

So, the prescribed Fed rate should only rise with an increase in inflation, where unit labor costs rise faster than inflation.

Only when unit labor costs rise faster than inflation is there a true threat of higher inflation. This equation responds appropriately.

Let's look at the relationships between unit labor costs, inflation and labor share since the crisis.

Since the crisis, unit labor costs have increased a bit, and labor share has decreased. This scenario corresponds to option #4 above where a lower Fed rate would be prescribed. Is it any wonder why the Fed rate is languishing on the zero lower bound?

In effect, we need option #5 for the Fed rate to pop out of its doldrums.. We need labor share of income to rise, and unit labor costs to rise faster than inflation.

(note: TFUR could also increase to warrant a higher Fed rate, but its increase is being constrained now low effective demand.)