Following on my train of thought in the previous post on nominal interest rates for Production vs. Labor income, I want to turn to the real rates.
First, a recap of the equations to determine the nominal interest rates on production and labor income. These rates signify the nominal cost if you wanted to invest in production or in labor income.
Base nominal interest rate of capital = N + p + a * (p - p*) + b * (c - c*)
N= natural rate of output growth
p= price inflation
p*= inflation target
c= capacity utilization
c*= target capacity utilization
a= coefficient, 0.5
b= coefficient, 0.5
Second, labor output...
Base nominal interest rate of labor = L + w + a * (w - w*) + b * (u - u*)
L= natural rate of growth in total labor hours
w= wage inflation
w*= target wage inflation
u= unemployment rate
u*= target unemployment rate (natural rate of unemployment)
In the first equation, the inflation and growth of production are considered.
In the second equation, the inflation and growth of labor income are considered.
To get the real rates of interest for production and labor income...
Real rate for capital = Fed rate - price inflation
Real rate for labor income = Base nominal interest rate of labor income - wage inflation
Here is the graph comparing these two real rates since 1967... (data for this graph comes from FRED). This graph assumes a wage inflation target of 2% to match a 2% price inflation target.)
The real rates followed each other pretty well since the 1980's. When the lines are close, the cost of production is similar to the cost of labor income. So if you were an investor, the cost of investing in capital output or labor income would have been a close.
We see a divergence in the late 1970's when the real rate of labor soared above that of production. The cause was that total labor hours was rising fast at over 5% annual basis and there was high wage inflation. So it was normal for the real rate of labor income to be high, but the capital production rate was low because the Fed rate was lower than the what would have been prescribed. The Fed rate should have been 6% higher. The difference exacerbated inflation as firms were given incentive to keep expanding with the price inflation. The Fed put a stop to that with the Volcker recession. Then we see the real rate of production stay high and bounce around as it beat down inflation and wage inflation.
Since the Volcker recession up until the crisis, the real rate of labor income never much surpassed the real rate of production. The reason is that labor income was falling short of production in real terms. A lower real rate of labor income for so long reflects a suppression of labor income, which also helped to keep price inflation in check.
If you look close at the point of time before a recession, the real rate of production will spike up over the real rate of labor income. The result is a contraction in production.
You will also notice that the real rate of capital does not go much below 0%. That is because of the zero lower bound on the Fed rate. Yet, the real rate of labor income will drop well below 0% during a recession, as labor hours get cut.
Currently, the real rate of labor income is higher than the real rate of production. The effect should be a rise in price inflation from a rise in wage inflation. But we are not seeing that rise in price inflation. We are actually seeing a suppression of price inflation, which makes the capital rate line move toward the labor income line.
There is a balancing effect that would want to keep these lines moving together. Low inflation seems to be raising the real rate of production toward the labor income line. The two lines started to move together at the end of 2010 when inflation dropped below 1%, and that would have been the moment for the Fed to start raising the Fed rate, but they kept the Fed rate at the ZLB and the two lines separated.
The real rate of labor income has recovered, but the real rate of capital production is being artificially supported by easy monetary policy. The effect strange enough is suppressing the growth of labor income. Why? It is more costly to invest in labor income as opposed to capital production. In other words, it is relatively less costly to invest in capital assets and capital production.
Could this be part of the reason why labor income and labor hours are lagging so much? ...why unemployment is staying high? ...why labor share has fallen?