How does the limit function for Effective Demand work?

The limit function calculates the effective limit upon the utilization of labor and capital (TFUR, (capacity utilization * (1 - unemployment rate)). Here is the version of the limit function that I am using.

Limit function, L = 0.650*LSI+35*NX/rGDP+35*G/rGDP+35*I/rGDP-122*CPIall+80*(ED-FF)-80*(yoyC,10year-FF)

LS = labor share index (non-farm business sector), 2009 base year
NX = real net exports
rGDP = real GDP
G = real Government consumption expenditures and gross investment
I = real Gross private domestic investment
CPIall = year over year % change of CPI for all items.
ED = policy rate prescribed by Effective Demand Monetary rule after non-monetary variables have been set.
FF = Fed Funds rate
10year = 10-year Treasury Constant maturity rate
yoyC = year over year change for (10year-FF)

 Here is how I work this equation...

Step 1...

I calculate L for the current economic condition without the monetary response. To do that, I set the coefficients for (ED-FF) and (yoyC,10year-FF) equal to zero.

Limit function, L = 0.650*LSI+35*NX/rGDP+35*G/rGDP+35*I/rGDP-122*CPIall+0*(ED-FF)-0*(yoyC,10year-FF)

The graph looks like this...

Step 2...

Then I take the numbers for the limit function (L, orange line), and put them into the Effective Demand Monetary rule...

Effective Demand Monetary rule = z(TFUR² + L²) - ( 1 - z)*(TFUR + L) + inflation target + 1.5(inflation - inflation target)

z = (2*L + Natural real rate)/(2*(L² + L))

I get this graph... Dashed line is the Fed rate, which the limit function would prescribe for the economic conditions for effective demand.

Step 3...

Then I take the difference between what the ED monetary rule says the Fed rate should be and the actual Fed rate set by the Fed. The Fed rate is most of the times different. Sometimes lower, sometimes higher. Most of the time lower though.

I feed this difference back into the limit function and reactivate the coefficient on the (ED-FF) term.

Limit function, L = 0.650*LSI+35*NX/rGDP+35*G/rGDP+35*I/rGDP-122*CPIall+80*(ED-FF)-0*(yoyC,10year-FF)

Now the limit function shows how the Fed rate is influencing effective demand. The limit function graph now looks like this...

Step 4...

Then I reactivate the coefficient for the (yoyC,10year-FF) term...

Limit function, L = 0.650*LSI+35*NX/rGDP+35*G/rGDP+35*I/rGDP-122*CPIall+80*(ED-FF)-80*(yoyC,10year-FF)

Now the limit function will show the influence of changes of the 10 year long-term rate in relation to changes in the overnight Fed rate. The limit function is now complete and shows a more complete view of the influence of monetary policy on effective demand. The limit function looks like this...

Step 5...

Then I take the complete limit function and put it back into the Effective Demand Monetary rule to see the implied Fed rate for the economy. Now the view takes into account the changes in long-term rates. If the Fed rate is different from the implied rate, the Fed rate is off the balanced curve. (The line from step 2 above is faded in the background for comparison.)

The ED monetary rule rate has moved closer to the actual Fed rate because the limit function was adjusted for the effect of the Fed rate. The ED monetary rule rate and the Fed rate are not equal though. The ED monetary rule will still show when the Fed rate is tighter or looser than effective demand would prescribe.

The Fed rate is much lower than what the ED Monetary rule would prescribe now, but the Federal Reserve wants to extend the business cycle as much as possible. They are solely employing discretionary policy. They are not putting much weight on monetary rules. They can do that, but the economy is weakened.