This is a quick post...

I have been in the workshop tinkering. The result is an equation to replace the effective labor share equation.

Effective labor share = LSI * 0.765

The last two variables added to the limit function are for government expenditures and investment. Here is the final equation.

Effective Demand limit function, L = 0.70*LS + 20*NX/rGDP + 20*G/rGDP + 20*I/rGDP - 110*CPIall + 78*(ED-FF) - 75*(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

The equation has variables for domestic consumption power (LS), foreign consumption power (NX/rGDP), government consumption (G/rGDP), private investment (I/rGDP), inflation (CPIall) and monetary policy (ED, FF & 10year treasury). All these variables impact demand.

I gave NX, G and I the same coefficient (20) for parity in the equation. The other coefficients were designed to give a consistent limit. I explain this below.

I have put all these variables into an equation for effective demand... NOT AGGREGATE DEMAND, which is always equal to real GDP. Effective demand is the limit upon the utilization of labor and capital for production... and is by definition only equal to real GDP near the natural limit of real GDP.

So here is the graph of the equation above. The orange line is the effective demand limit function that marks the peaks of the TFUR business cycle (blue line). (TFUR = (capacity utilization * (1 - unemployment rate)).

I have pointed to the peaks of the TFUR which the equation is limiting. When the TFUR peaks, it meets the effective demand limit function.

Here is the graph showing the difference between effective demand and the TFUR since 1967 in the above graph. (Effective Demand - TFUR)

The TFUR consistently goes beyond the effective demand limit by *almost exactly* -1.0%. Of the 13 peaks in this second graph, 9 of them fall very close to the -1.0% line. Two fall closer to -2.0%. One falls at -3.5%. One falls at just under 0% (1984). The coefficients of the equation are designed to give this consistency.

By lining up the peaks on the consistent line of -1.0%, the probability increases that the next business cycle will end near the same -1.0% line. The probability was 92% that the TFUR peaks fell between -0.2% and -2.2% since the 1960's. The probability was 69% that they fell almost exactly on the -1.0% line.

Of the three peaks that fell below -1.0%, two led to very deep recessions (1973 & 2007). The deep peak at 1997 was due to the 10-year treasury temporarily increasing in relation to the Fed rate (year-over-year change). If not for that 10-year treasury increase, the peak at 1997 would have stopped exactly at -1.0%.

So this model of effective demand gives a reliable and consistent limit.

In 2015, the TFUR will get closer and closer to the effective demand limit. The TFUR will rise by employing more labor and capital. On the other hand, effective demand can fall in many ways...

- Labor share drops further
- net exports fall
- government expenditures as a % of real GDP falls more
- private investment as a % of real GDP stops rising
- inflation rises
- the Effective Demand Monetary rule starts prescribing a lower rate
- the Fed rate rises
- the 10-year treasury rate rises more than the Fed rate over the past year.

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