Summary of Effective Demand Monetary Rule

I want to post a summary of some of the ideas behind the Effective Demand Rule for determining the base nominal rate set by a central bank. It works like the Taylor rule but is not prone to the errors of trying to measure potential. 

 

First, here is a graph of my equation compared to the Fed funds rate over time...

You will see that my equation follows the Fed rate very close many times, and many times it is tracking parallel at a different rate. The 1970's were a time when the Fed rate was too low. My equation shows it should have been higher to control inflation. The 1980's were a time of an artificially high Fed rate to combat inflation, and my equation shows that a lower Fed rate would have led to fuller employment. But I agree with what Volcker did. The low rates of the 1970's needed to be corrected by higher rates later.

Then through the 1990's, my equation tracked very well. Around the turn of the century, my equation goes lower because it is based on a 3% natural real rate. The Fed may have been seeing a higher natural real rate around 4.5% of more considering the technology boom and GDP growth. If I change my estimation of the natural real rate from 3% to over 4%, then the lines come together more.

But I see the discrepancy around the turn of the century mostly due to the CBO estimating a positive output gap that was just too high. Greenspan had to see an immiment danger of pushing the inflationary gap too much.

After the 2001 recession, I lowered the natural real rate to 2.5%, and my equation was spot on. Since the crisis, my equation in the graph is assuming a 1.8% natural real rate. It is recommending that the balanced nominal base rate ought to be over 3% now. The ZLB is too low for where we are in the business cycle.

 

Now here is my equation...

Effective Demand Monetary Rule = z*(TFUR² + ELS²) – (1 – z)*(TFUR + ELS) + inflation target + 1.5*(current inflation – inflation target)

z = (2*ELS + NR)/(2*(ELS² + ELS))

TFUR = Total Factor Utilization Rate, (capacity utilization * (1 – unemployment rate)).
ELS = Effective Labor Share is Non-farm Labor Share: Business sector * 0.765. This value of labor share is the only value that makes the equation work. It is the basic factor to determine effective demand. ELS is determined by labor share's cyclical relationship with capacity utilization. ELS represents the central tendency in the cyclical movement of capacity utilization.
NR = Natural real rate of interest.
Inflation target = 2.0% (assumed to be 3% before 1980 in the graph above.)
Current inflation = The monthly value of CPI (less food & energy) is used in the graph.
1.5 coefficient = To give the Fed rate leverage when inflation gets off target. Fed rate would change 1.5x more than inflation is off target.

(NGDP targeting) Effective Demand Monetary Rule = z*(TFUR² + ELS²) – (1 – z)*(TFUR + ELS) + (1+a)*current core inflation + a*core inflation average - 2a*core inflation target

"a" is a weighting coefficient.

Some thoughts on this Effective Demand equation...

• A weakness of the Taylor rule is having to determine potential GDP or even potential unemployment. We see this is a problem now for the CBO as they continually downgrade potential. If one sees potential higher than it really is, they will say that the Fed rate should be lower. My equation does not have to calculate potential. Potential output is implicitly incorporated in the equation through effective labor share which determines the effective demand limit upon output. In effect, potential is automatically recalibrated through effective labor share. My equation was able to work so well in the past because it understands the effective demand limit upon output.
• The Taylor rule follows the Fed rate well because it is prone to the same errors of estimating potential. Thus errors of potential will not be revealed by the Taylor rule, because it uses the same estimation of potential that led to the Fed rate. The Effective Demand walks its own path and will reveal errors of estimating potential.
• My research uses the effective labor share value to determine the effective demand limit upon the utilization of labor and capital, and thus output. The ELS value makes the equation work. And I do not need any derived statistical coefficients to make it work. Just the plain ELS value does the trick.
• The equation is rooted in the geometry of my model. The equation is not made up on the fly. The equation represents the relationships in the model graphed below.

• The upsloping dotted line represents how the real interest rate should rise through the business cycle. The equation for this line simply drops the inflation targeting portion at the end of the ED rule... z*(TFUR² + ELS²) – (1 – z)*(TFUR + ELS). The upsloping dotted real rate line will cross the vertical red LRAS curve at the natural real rate (2.0% at 80% in the model).

• The upsloping solid line is the nominal rate path. The equation for this line is the full ED rule.

• The vertical red line is the ELS limit to the TFUR on the x-axis. It represents the LRAS curve (natural limit of GDP). The upsloping solid line of the nominal Fed rate will cross this line at (natural real interest rate + current inflation). The red line of ELS has been the top limit of all business cycles since the 1960's.

• The vertical green line is the current value of the TFUR, composite utilization of labor and capital. The point where this line crosses the upsloping nominal path prescribes the base nominal rate that the Fed would set (blue dot). The point where this line crosses the upsloping dotted line of the real rate shows the real rate that would balance growth through the business cycle (red dot).

• As the TFUR reaches the ELS limit (LRAS curve) the correct crossing points come into focus that represent the natural real rate and the nominal Fed target at the natural limit of the business cycle.

• The horizontal brown dotted line shows the current real rate (Fed rate - current inflation). When this line crosses where the vertical green line and upsloping dotted line cross (red dot), the Fed rate is set "perfectly" according to the ED rule.

• Economic slack is determined from the model. It is determined by the distance between the current TFUR and the vertical red line of the ELS. The economy has always respected this limit for all business cycles since I have data for capacity utilization starting in 1967.

• The z coefficient in the equation is based on ELS and the natural real rate. If you raise the ELS, the z coefficient decreases, and the upsloping lines shift right perfectly to maintain the crossing points. If you raise the NR, the z coefficient rises, and the upsloping lines shift left perfectly to maintain the crossing points in the model.

• The slope of the upsloping lines is seen in past movements of the Fed rate. 

Final thoughts...

The equation is accurate and uses straight-forward variables. Here is how to use the equation for data of July 2014.

We first determine the z coefficient...

z = (2 * 74.8% + 1.8%)/(2*(74.8%² + 74.8%)) = 57.91%

Then we determine the TFUR for July 2014...

TFUR = capacity utilization * (1 - unemployment rate)

TFUR = 79.2% * (1 - 6.2%) = 74.3%

 

Now we use the Effective Demand rule to determine the base nominal rate...

57.91%*(74.3%² + 74.8%²) - (1 - 57.91%)*(74.3% + 74.8%) + 2.0% + 1.5*(1.855% - 2.0%) = 3.4%

• There are no magical statistical coefficients that make it work. There are no error-prone estimations of potential.
• The nominal base rate that the equation is now prescribing of 3.4% is close to the rate projected at the natural limit of the business cycle of 3.8% (1.8% natural real rate + 2.0% inflation target). Thus, we are close to the end of the business cycle. Not too much of a surprise with the stock markets continually setting records. Does the Fed really think the stock market can continue setting records for 3 more years? 
• The equation worked automatically for past data using effective labor share. I would then assume that it will work again this business cycle. The ED rule is prescribing a base nominal rate now over 3%. The implication is that the business cycle is closer to the end than the Fed thinks... So the Fed would be quite a bit behind the curve at this point. Basically the Fed is still making an error in their determination of true slack. My ED rule uses the principles of effective demand to determine the demand-constrained limit upon productive potential. That is why my equation worked in the past, and why it would work again this time.