George Evans at the University of Oregon did a fantastic video on the dynamics of a sub-optimal equilibrium (steady-state) if nominal interest rates were raised from the zero lower bound in order to push the economy out of a downward spiral for inflation and consumption, which is something we are seeing now. He points out that we want to escape the deflation trap region, and raising interest rates early would make it more likely that the economy would fall into the deflation trap region.

I want to present a model to show that the optimal steady-state has itself moved and that the Fed rate should be pushed up accordingly. I want to show that the "monetary zone" within which the Fed rate moves has shifted. I want to imply that the equilibrium points that George Evans uses have shifted to the left. As such, monetary policy is working in a new equilibrium, a new monetary zone, which is sub-optimal with a higher natural rate of unemployment. But this new monetary zone is calling for monetary policy to adjust by raising interest rates, acknowledging that employment and consumption will stay weaker even if the Fed rate stays at 0% for years.

First I need to set the foundation for understanding the z coefficient. I wrote about the z-coefficient in the equation to determine the interest rate for a central bank. The z coefficient determines an equilibrium point for an economy. So... how can we determine the z coefficient?

We first need an equation that translates just the TFUR and effective labor share into a value comparable to a central bank interest rate. Sounds easy... but it has consumed me for almost a week. I call it the Reflective Fed rate curve...

Reflective Fed rate curve = els*(els-TFUR)/(1+TFUR)

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)...

OK... so what is the point of this equation? Let's graph it considering an effective labor share of 80%. TFUR is along the x-axis and the interest rate along the y-axis.

Ok... simple enough. We can see it crosses the x-axis at 80% and rises as the TFUR decreases. The curve is not a straight line. It is actually a convex curve. Now we add in the curves to determine the path of the central bank interest rate (blue) and the effective demand limit (yellow) using a z coefficient of 58.2%. (see previous post for explanation of these equations)

ED prescribed Fed rate path = z*(TFUR^{2} + els^{2}) - (1 - z)*(TFUR + els) - inflation target

ED limit = 2*z* TFUR^{2} - 2*(1 - z)*TFUR - inflation target

(Note: These curves are plotted below with an inflation target of 0% in order to show the basic symmetry better.)

The blue line is the path to determine the central bank interest rate. The yellow line is the effective demand limit. The crossing point of the blue line and the yellow line is the LRAS curve, which is an important point to know.)

The fun thing about this reflective Fed rate curve (red) is that it crosses the Fed rate path (blue line) where the effective demand limit (yellow line) crosses the x-axis. This is marked by a vertical line around a TFUR of 72% . The other fun thing about this reflective Fed rate curve is that it itself crosses the x-axis where the blue and yellow lines cross. This is marked by the vertical line at a TFUR of 80%.

You can see the reason why I call this curve the "Reflective" Fed rate curve. It reflects important crossing points for the Fed rate curve. As long as the inflation target is 0%, these crossing points hold their symmetry with any change in the effective labor share or z coefficient. If you have an inflation target other than zero, the vertical line where the effective demand limit (yellow line) crosses the x-axis slopes a little. The vertical line for the LRAS curve (above at 80%) does not change.

Now the reflective Fed rate curve can be graphed with actual data. We don't need to know what the inflation target was in the past. We don't have to have a z coefficient. We just grab capacity utilization, unemployment and the effective labor share numbers and plot. Here is the historical plot for the reflective Fed rate curve since 1967...

We can see that the Reflective Fed rate curve moved within a fairly tight monetary zone from at least 1967 to the early 2000's (shown by red oval). The red oval shows the equilibrium zone of the economy. This equilibrium zone is comparable to what George Evans calls the locally stable steady-state. Monetary policy existed within this monetary zone from at least 1967 to the early 2000's. Because this zone is stable over many business cycles, we can use it to determine the z coefficient.

How do we determine the z coefficient? We take the effective demand limit curve and make it go right through the center of the zone. There is a mid-point in the business cycle of the TFUR that determines the z coefficient. We now add the effective demand limit curve.

The effective demand limit curve will actually be symmetrical to the regression line for the equilibrium zone, but I am not going to show that much detail. The effective demand limit curve is made to go through the center of zone by adjusting the z coefficient. The z coefficient since 1967 has been approximately 58.2%. (Note: the zone is a little longer than it would have been normally due to the unnatural Volcker recession.)

The fun thing about the effective demand limit curve is that it stays stable over time because it is determined by the z coefficient (stable), the inflation target (kept constant), and the TFUR (the variable that changes along x-axis). We have had the same effective demand limit curve since at least 1967! The only variable that may have changed through the years was the inflation target.

It is profound to think that in the realm of monetary policy, we have had the same effective demand limit curve since at least 1967. This fact reflects the locally stable steady-state.

But then look again at the graph. It seems as though the reflective Fed rate curve has moved to a new equilibrium zone (to the left). Or as George Evans would say, a new locally stable steady-state. And the zone is just starting to establish itself. This would be a big problem, because the consequence would be a lower zone for the TFUR, which translates into a higher natural rate of unemployment for both labor and capital.

Let's adjust the z coefficient to the new monetary equilibrium zone...

We can see that by raising the z coefficient to 60.3%, monetary policy would shift to the new monetary zone and we would again have a viable monetary policy. Eventually the Federal Reserve is going to have to raise nominal interests rates in this new zone just to have traction. And this takes me back to the video by George Evans.

So George Evans did research that raising the Fed rate during the liquidity trap would throw us into a sub-optimal deflation region with falling consumption. But I am seeing that the steady-state points of his graph have shifted to the left. As such, monetary policy should already be responding by raising the Fed funds rate. The implication is... if monetary policy continues to function with respect to the previous equilibrium monetary zone, it will be permanently ineffective. If it begins to function in the new equilibrium zone, it will become effective again.

We are in denial. We have to accept that we are in a sub-optimal optimal equilibrium zone. We have to accept the fact that the economy is broken and that unemployment will stay high as long as labor share of income stays low. We have to deal with the embarrassment of having produced an economy more like the sub-optimal economies of Latin America. And we need to start working on getting back to the previous more optimal steady-state by raising labor share.

The shift in the monetary zone is not dependent on a liquidity trap situation. It's not like the liquidity trap caused the shift in the monetary zone. In fact, my model here shows that the monetary zone was showing a tendency to shift 10 or so years ago after the 2001 recession, much before the crisis.

What should the Fed rate be in this new equilibrium monetary zone? Well, we can figure that out just by putting the inflation target of 2% and the current effective labor share of 74% into the fed rate path equation with a z coefficient of 60.3%. The result is...

ED prescribed Fed rate path = z*(TFUR^{2} + els^{2}) - (1 - z)*(TFUR + els) - inflation target

ED prescribed Fed rate = 0.603*(0.72^{2}+0.74^{2})-(1-0.603)*(0.72+0.74)-0.02 = 4.32%

(Note: effective demand limit curve dropped when a 2% inflation target was put into its equation.)

My treatment plan for monetary policy is to raise the fed funds rate to over 4%, acknowledging the new monetary zone, and then work on getting effective labor share back over 80%, which would eventually shift the economy back to the previous more optimal equilibrium.

(Caveat: Of course, one has to realize that a 4% Fed rate is a preliminary approximation, but the model shows a shift in the monetary zone. And the Fed rate should be higher than it is now according to this new monetary zone.)

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