Equation for center of business cycle… another economic mystery??
I was up late last night tinkering in the “equation workshop” to calculate the center of the business cycle (potential GDP). The equation is opening up my eyes to some new insights.
The center of the business cycle is an important concept. It is the core foundation of the real GDP business cycle. Ultimately the level of real GDP is determined by its center. So, what drives the center? How does it move? A model and an equation is needed to answer these questions.
The idea is to calculate the business cycle center as a % of productive capacity. (Productive capacity is the total output that can be generated with 100% utilization of labor and capital.) The economy does not reach full productive capacity because of production and demand constraints.
There is a brute way to calculate the center of the business cycle. First find the productive capacity of the economy. There are two equations for this.
Productive capacity = Real GDP/T
Productive capacity = Effective demand/effective labor share
T = TFUR, multiplying labor utilization by capital utilization
Then to figure the center of the business cycle, this equation…
Center of business cycle = Real GDP – Biz cycle amplitude constant * (c/e – 1)
c = capacity utilization… e = effective labor share… Biz cycle amplitude constant is given in 2009 $$ as $3.4 trillion.
Then to find the % of productive capacity for the center of the business cycle…
% of productive capacity = center of business cycle/productive capacity
This equation does not give insights into what drives the center of the business cycle. So I searched for a more elegant equation.
Here is what I found…
Center of business cycle as % of productive capacity =
T * (1 + g * (1 – c/e)) ….. or ….. T * (1 + g – g * c/e)
g is a variable between 0 and 1. It seems that g has changed over the years. I will explore g in the rest of the post because it is the mystery of the equation. Finding the equation for g itself would open new insights.
I present a video to explain the equation. The video proposes that the variable g has declined over the years. The result is that capital utilization is now the preferred way to raise real GDP, instead of raising labor share. (link to video if not seen well.) The orange line in the graph on right keeps the other variables constant while changing labor share. The blue line on the right changes capacity utilization while holding other variables constant.
The center of the business cycle has been declining over the years as a % of productive capacity. The cause of that decline is the steady drop in labor share (effective demand). However, business now sees the way to generate growth is through capital utilization, even though capital utilization is suppressed by lower demand.
It is unlikely under this proposed dynamic that labor share will be rising any time soon.
Here is a graph for 3rd quarter data… Lines change holding all other variables constant.
Lambert, Edward. Building a growth model with effective demand. 4/6/13
Lambert, Edward. When labor share does not rise in the growth model. 4/6/13
Lambert, Edward. Super macroeconomic potential real GDP. 4/7/13
Edward I have something between a question, a bleg, and a suggestion that fits fairly well into your overall project.
As you probably know Social Security produces three different economic and demographic projections to project future solvency numbers, one more pessimistic for every variable considered (where pessimistic is defined as negative for solvency, it might be good news for soceity), one that is more optimistic for every variable, and then one that purports to hit the median for each, which latter is called Intermediate Cost. But in all three models the assumption is that all well settle out at a set of more or less static ‘ultimate’ numbers after 10 years. And by static they really mean ‘potential’, that is the mean around which the economy would naturally vary under the three scenarios.
For example Intermediate Cost projects the following numbers for every year starting in 2020: Productivity 1.67%, GDP Price Index 2.4%, Real Wage 1.12 , Unemployment 5.5%, Real GDP 2.1%, Inflation Nominal 5.9%, Inflation Real 2.8%
Now most of us don’t have a rigorous way to challenge these numbers, we may think some are unrealistically low by historical standards, but absent some defensible methodology we are kind of stuck with them.
But it seems to me that you are making a very serious attempt to develop exactly such a rigorous and defensible methodology. And it would be fascinating to me to see your suggestion as to what the Ultimate numbers would be in your model assuming some mid line policy response. Or alternately what numbers would result from varying policy adoptions.
Because we could drop the whole ‘Northwest Plan’ vs ‘Scrap the Cap’ debate as to the right way to boost revenues via taxation in favor of letting the economy do the lifting with fairly modest changes in this data set. For example the 2013 Low Cost data set comes very close to funding SS as is, and in past Report years did it fully.
The relevant Tables are B1 and B2 starting with this link:
I know you are already burning the midnight oil, but even a glance at the data tables might give you some food for thought.
The numbers you give as constants will definitely go through cycles. The real question is about those cycles. Surely the cycles will move around and through the numbers you give, but are the numbers on average correct?
Unemployment will be higher than people think. Productivity will be lower than people think.
I would love to see that change, but my research shows that the dynamics of a sub-optimal economy are being re-enforced by other dynamics.
I think of China. They have to raise labor share in order to have stronger domestic consumption in the future, but when I was studying medicine, one of my teachers had worked in China trying to set up a blood bank system. he had worked in many countries, but he said that only the Chinese did not want to give their own blood to other citizens. He encountered terrible resistance.
With that in mind, do you really think the rich Chinese are going to share their wealth more and more in the future? Household consumption is just 35% of GDP. It is an impossible task culturally for them. Their heart is not in it.
Then I look at the US. The heart of this nation is not set for raising the purchasing power of the people. And the people have very limited power to ask for more.
At the moment, I feel I am watching the decay of a great nation. The dynamics of decay seem like a natural process. Yet, there has to be a re-birth at some point, right?
But let me be more specific. Will productivity be less than the SSA Office of the Chief Actuary thinks? Will it actually lag 1.67%?
Will unemployment be higher? Do you see 5.5% as too low a figure? If so where would you peg the long term number?
Because in my semi-informed opinion the OACT has begged those numbers more pessimistically “than people think”. They are certainly more pessimistic than I think. I see no reason why ultimate productivity couldn’t come in at 2% and unemployment at 5% and Real Wage at 1.5% given even minimal policy committment to that by Congress and the Fed. That is arguments against those numbers seem to be more political than economic.
And while I also tend to see the current state of the nation as ‘decay’ I have not yet given up hope of that ‘rebirth’. Or better simple partial restoration. Because 5% unemployment, 3% GDP and 1.5% Real Wage are not crazy pie in the sky numbers. Not historically. And for a lot of purposes that is all it would take.
I see the natural rate of unemployment above 6.5%. That means that I see normal average unemployment running about 7%. With or without higher labor force participation. 1.5% seems like a fair number for real wages. I hope it comes in higher than 2%.
Productivity is a critical issue. Lightening the load of foreign debt relies a bit on that. It has been running flat for 3 years now. The problem is that lower wages lowers productivity by favoring low productive firms and not creating productive work.
I do see productivity coming in lower than 1.67%.
Productivity = wages/unit labor costs
I see unit labor costs staying low, with low inflation and low labor share. so if wages can rise, productivity can rise. However, can wages rise faster than labor share? I do not think so much… It really comes down to making firms and work more productive. And higher wages create more productive work by increasing relative demand.
The low prospects for wages in the future puts a dim light on everything.
Okay good enough. I asked for an answer and got one.
“I see the natural rate of unemployment above 6.5%.”
It is not the answer I wanted, and in the end it isn’t the policy outcome we can accept. Because it implies that on a fundamental basis employment has no upside from where we are sitting today. That is under the constraints that Edward sees on labor share we would appear to be very close to ‘full employment’ or at least ‘full natural rate of unemployment’. Which may not actually be the same thing. But either way not something we can allow to have stand. So I oddly took comfort from this from Edward from his 5:38
“Then I look at the US. The heart of this nation is not set for raising the purchasing power of the people. And the people have very limited power to ask for more”
Because this particular dark cloud has a built in silver lining, though maybe one that is set to vanish as the storm rolls in. Because the U.S. is still formally a representative democracy and most of the limits on the power of “the people” are self-imposed or at least self-accepted, and that to use Edward’s image as a result the heart has been almost beaten out of us. But the keyword there is ‘almost’. As long as there is any heatbeat it would seem that the power of “the people” is not dead.
So what I am going to take away from Ed’s piece is not despair but instead an understanding that we can’t expect the economy to just heal itself naturally. Because we are not going to like or even be able to accept that natural state. Which means that if we are ever going to be able to restore the heart to the American people and their well-being we have to accept the necessity of driving a stake through the heart of laissez-faire. We can’t just allow quietism and “Let it Be” rule here.
So forgive me Ed is I just take your analysis as a diagnosis of what ails the patient and not a set in stone prognosis. Not given the right surgical team.
Your words are powerful and true. They fill me with emotion. I stand by words and your wisdom.