I have been working on understanding potential GDP better. I have been saying in the past that potential GDP is affected by demand and is not just by employing available labor and capital at "natural" rates". So now I have the model to show it.

I first start with this graph (data from 1967), which plots the differences between Effective demand, real GDP and potential GDP.

There are 3 variables to relate in this model, effective demand, real GDP and potential GDP. Real GDP is real current output. Potential is the center of the business cycle around which real GDP moves. Effective demand is the upper limit upon the cycle of real GDP.

The difference between effective demand and real GDP is on the x-axis. Then the blue line is the difference between effective demand and potential GDP through the business cycles. The orange line is the difference between real GDP and potential GDP. The black line is just effective demand - real GDP plotted to itself and has a slope of 1.

You can visualize the x-axis as potential GDP. The y-axis is the LRAS curve at the top of the business cycle. The blue line is effective demand over potential GDP in the business cycle. The orange line is how real GDP moves up and down around potential GDP in the business cycle. When the orange line is negative to the right, there is a recessionary gap... positive to the left is an inflationary gap.

Now these 3 variables do not move linearly in real time. Yet this model puts their relative movements in linear form.

Here is the recent data since 2010.

The trend line for the difference between effective demand and potential GDP has a slope of 0.83 and a y-intercept of 267. The trend line for the difference between real GDP and potential GDP has a slope of -0.17 and a y-intercept of 267. If you subtract the orange line from the blue line, you get the yellow line of effective demand - real GDP.

(ED - PGDP) - (rGDP - pGDP) = ED - rGDP

(0.83 * ED-rGDP + 267) - (-0.17 * ED-rGDP + 267) = ED - rGDP

There are more dynamics in the model that I will not mention in this post. I want to get to the equation for potential GDP.

I take both the equations for the orange and blue lines...

rGDP - pGDP = -0.17*(ED - rGDP) + 267

ED - pGDP = 0.83*(ED - rGDP) + 267

Both equations solve for the same potential GDP...

pGDP = 0.83*rGDP + 0.17*ED - 267

What does this equation say?... The movement of potential GDP (pGDP) is determined 83% by rGDP and 17% by effective demand. Most of potential GDP is determined by the productivity of the labor and capital utilized. Yet, a portion is determined by the effective demand limit which looms overhead. If real GDP stays steady, but effective demand falls, potential GDP will fall too... by 17% of the fall in effective demand.

PGDP will be below rGDP and ED when rGDP and ED are equal at the effective demand limit... in the currect case by $267 billion (2009 $$). Potential GDP is below because it represents the center of the business cycle which lies below the top end of the business cycle.

Potential GDP can also be put in terms of labor share, capacity utilization and unemployment... (els = effective labor share (labor share index: Business sector * 0.762 ... TFUR = capacity utilization * (1 - unemployment rate)

pGDP = 0.83*rGDP + 0.17*rGDP*els/TFUR - 267

PGDP = rGDP*(0.83 + 0.17*els/TFUR) - 267

As labor share rises, potential GDP rises in relation to real GDP. As labor and capital utilization rise, pGDP will fall in relation to real GDP.

The graphs above show us that we can predict the movement of real GDP relative to potential and effective demand very early in the recovery stage of a recession. And the first graph shows that the pattern is very reliable to know when a business cycle will end.

I posted months ago about how the first graph can be used to determine how low unemployment can go in a business cycle. The negative $267 billion y-intercept implies a higher natural rate of unemployment this business cycle.

Another way to view this equation for potential GDP is by dividing it by productive capacity.

pGDP/PC = (0.83 * rGDP + 0.17 * ED - 267)/PC

pGDP% of PC = 0.83*rGDP/PC + 0.17*ED/PC - 267/PC

pGDP% of PC = 0.83*TFUR + 0.17*els - 267/PC

TFUR = labor utilization * capital utilization... els = effective labor share (labor share index business sector, * 0.762)

So in addition, potential GDP is determined 83% by how productive labor and capital are... and 17% by the demand power of labor's income.

The ratio of 83% to 17% is the current business cycle. In all other cycles since 1967, rGDP affected pGDP by less than 83% as seen in the first graph. Likewise, effective demand (Ed) affected pGDP by more than 17%.

Summarizing thoughts...

Potential GDP as the center of the business cycle is based on output from labor and capital AND the demand constraint upon the production of labor and capital.

Potential GDP is the center tendency of the business cycle of real GDP.

Potential GDP is a stabilizing point between production and demand mostly determined by production, yet affected by movement toward the constraint of effective demand.

Potential GDP holds onto real GDP with an elastic rope. It will move with real GDP if demand does not constrain, but it will pull down on real GDP if demand falls.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.