# A look at Real Rates… Actual & Natural

The normal Taylor rule takes into account the difference between inflation and a target inflation, and output and a targeted potential output. I will take a modified version of the Taylor rule and apply it to both capital output and labor output.

First, capital output…

Simulated nominal interest rate of capital = N + p + a * (p – p*) + b * (c – c*)

N= natural rate of real GDP output growth, weighted moving average using past 8 quarters. (more weight put on recent quarters.)
p= price inflation, CPI without food and energy
p*= inflation target, 2.0%
c= capacity utilization
c*= target capacity utilization, determined by projected effective demand limit
a= coefficient, 0.5
b= coefficient, 0.5

Second, labor income…

Simulated nominal interest rate of labor income = L + w + a * (w – w*) + b * ((1 – u) – (1 – u*))

L= natural rate of growth in total labor hours, weighted moving average using past 8 quarters. (more weight put on recent quarters.)
w= wage inflation
w*= target wage inflation, 2.0%
u= unemployment rate
u*= target unemployment rate (natural rate of unemployment), determined by projected effective demand limit
a= 0.5
b= 0.5

How do these equations look over the years? Let’s graph them next to the effective Fed funds rate… (data for this graph comes from FRED). This graph assumes a wage inflation target of 2% to match a 2% price inflation target.) Both equations echo the general path of the Fed rate which should be no surprise since they measure correlated factors.

In the last two recoveries, the interest rate of capital (orange) rises above the rate for labor income (light blue). Utilization of capital is developed faster than labor income. Then labor income overtakes capital production before the next recession. We now see that labor income is overtaking capital which is a sign of the current business cycle coming to an end.

Now I turn to real rates of interest. To get the real rates of interest for production and labor income…

Actual real rate for capital = Fed rate – price inflation

Real rate for capital production = Simulated nominal interest rate of capital – price inflation

Real rate for labor income = Simulated nominal interest rate of labor income – wage inflation

Here is the graph comparing these two real rates since 1967… The real rates for capital and labor income are natural real rates. The real rates followed each other pretty well since the 1980’s. When the lines are close, the cost of investing in either capital output or labor income would have been a close.

We see a divergence in the late 1970’s when the natural real rates of labor income and capital soared above the actual real rate. As wage inflation, labor hours and price inflation rose fast, the actual real rate given from the Fed rate was low in comparison. The Fed rate should have been around 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 actual real rate stayed high in the early 80’s and bounced around as it beat down price inflation and wage inflation.

Interesting to note that from the Volcker recession up until the crisis, the real rate of labor income never much surpassed the real rate of production (light blue line stayed below orange line). 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 in favor of capital investment, which had the effect to keep price inflation in check.

The actual real rate does not go much below 0%, because of the zero lower bound on the Fed rate. Yet, the real rates of labor income and production will drop well below 0% during a recession, as labor hours and capacity utilization get cut.

If you look close at the point of time before most recessions, the actual real rate from the Fed rate (dark blue line) will spike over both the real rates of labor income and production. The result is a contraction in the whole economy. Yet, a contraction can happen with low actual real rates, as in 1970 and 1980.

Currently, the real rates of labor income and production are higher than the actual real rate. Does that mean a recession will never be triggered, because at this pace the actual real rate will never go over the other two rates?

Anyway, the effect of such a low actual real rate should be a rise in price inflation and wage inflation as happened back in the late 1970’s. But we are actually seeing a suppression of price inflation.

The actual rate started to move with the natural real rates 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 actual real rate disconnected from the natural real rates.

The real rate of labor income has recovered, but the real rate of capital production (orange line) is being artificially supported by easy monetary policy (low dark blue line). The effect strange enough is that labor income is a more costly investment, which suppresses the growth of labor income. In other words, it is relatively less costly to invest in capital assets and capital production. Labor is not seen as a valuable factor for producing profits relative to the low cost of capital.

What is the difference between the late 1970’s and now? Both times show very low actual real rates compared to the natural rates. Back in the late 1970’s, inflation was being supported by wage inflation, which grew between 6% and 9%. Wage inflation now is just beginning to grow faster than 2%. The mechanism to transfer money to labor was very strong back in the 1970’s. Now the mechanism is very weak. Money stays in circles of capital and price inflation stays low.

I am left thinking one thought… How much would the actual real rate have to rise in order to trigger a contraction now?