Relevant and even prescient commentary on news, politics and the economy.

A tale of two incomes in the money market

Real GDP has dropped to a new level. Many economists think it will return to its previous trend before the crisis.

I made this video to explain how real GDP can drop to a new level as a result of labor share of income dropping after the crisis.


Capital income rose after the crisis, while labor income fell in relative terms. Thus the supply of money to capital rose, and the supply of money to labor fell. So, the interest rate had to fall in the capital income money market, and the interest rate had to rise in the labor income money market in order to reach equilibrium. (Remember that the money in the labor market used for real GDP is many times greater than the money in the capital market.)

However, capital income controls the bond market, so interest rates fell. The result was that either prices or real GDP had to fall in order for the labor income money market to be in equilibrium at the lower interest rate. Prices have fallen some but not nearly enough to reach equilibrium in the labor income money market.

Economists talk about a recession, because real GDP is low. And they talk about having to lower interest rates to stimulate the economy. Yet, the result of the Fed keeping interest rates low is that real GDP is forced down to keep the money market for labor income in equilibrium. Meanwhile, interest rates are low for capitalists, and we have actually seen investment much stronger than would normally be seen after a recession.

The interest rate was able to adjust in the capital income money market, which meant that real GDP had to adjust in the labor income money market.

So in a word, it is LUDICROUS that the Fed is keeping interest rates low in the face of lower labor share of income. The lower interest rate forces down real GDP and creates the appearance of a recession. The answer is to find a mechanism to transfer money into the money supply of the money market for labor income. Real GDP will then rise as a result. And eventually interest rates will be able to rise.

Without a rise in the supply of money to labor, the Fed is spinning its wheels against a real GDP that has fallen to a lower equilibrium.

The Fed’s worry is creating inflation. Once again, LUDICROUS.

Projecting the utilization of labor and capital

So the cobra equation has made me re-evaluate the dynamics of the effective demand limit. The main reason is that the graph of the Cobra equation shows that capital utilization decreases as employment increases at the effective demand limit. I was assuming that as employment increased, the utilization of capital would also increase. That was an error.

As businesses in the aggregate reach for profits, the path at the effective demand limit shows that capital will be less utilized as labor is more utilized.

I had been thinking that unemployment would bottom out at 6.7% to 7.0%. That was assuming that capital utilization would increase. But now I see that unemployment can go lower, because capital utilization will not increase.

Here is the path of the utilization of labor and capital (blue circles) since 2009 up to today’s data from unemployment. (3rd quarter unemployment is 7.3%, which is 92.7% in the graph.)

 cobra 2a

Equations for the two lines are given above the graph.

The blue oval shows the projected range of the equilibrium point where profit maximization crosses the effective demand limit. The economy gravitates toward that blue oval area. The utilization of labor and capital (blue circles) is moving along the effective demand limit following increasing profits toward the blue oval.

The Cobra equation is the equation that I have been searching for since last year. Now that I can see it, the dynamics of profit at the effective demand limit are coming clear. I still see the environment for a recession starting in one year, but the dynamics of that environment are clearer.

For reference… here is the Cobra equation to measure the profitability of utilizing labor and capital dependent upon labor share.

Measure of profitability in the aggregate = (x + y) – ax2y2

x = capital utilization rate
y = employment rate
a = coefficient for labor share to establish profit maximization.
Coefficient “a” = (els)2 – 2.474*(els) + 2.0 … (els = effective labor share, for example 80% as 0.80).

A natural rate of unemployment in the Cobra equation

This post continues the exploration into the Cobra equation, which measures the profitability of utilizing labor and capital as a function of labor share. Now it looks as though the Cobra equation is implying a natural rate of unemployment.

The simplified Cobra equation is now…

Measure of profitability in the aggregate = (x + y) – ax2y2

x = capital utilization rate
y = employment rate
a = coefficient for labor share to establish profit maximization.
Coefficient “a” = (els)2 – 2.474*(els) + 2.0 … (els = effective labor share, for example 80% as 0.80). (Note: I have stream-lined the equation for the coefficient “a”. No change from the previous version over the effective range of the economy.)

The Cobra equation is in 3 dimensions, but I have made a 2 dimensional graph of it with an Excel spreadsheet.

Cobra 1
The orange line marks the profit maximization for utilizing labor and capital in the aggregate.

The equation for profit maximization (orange line) is simply the derivative of the profitability measure above with respect to x then solved for y, employment…

Profit max = (1/(2*a*x))0.5

The blue line is the effective demand limit, which has the equation…

Effective demand limit = (els)/x
x = capital utilization
els = effective labor share (This is determined by multiplying Labor Share index for the business sector by 0.766… 2009 as base year.)

As the economy utilizes more labor and capital in the expansion phase of the business cycle, it eventually reaches one of the two lines and stops. Then the economy will either rise up the line employing more labor or it will contract into a recession.

It appears so far in the data that the economy gravitates to the crossing point of the orange and blue lines. The blue dots mark the crossing points as changes in labor share shift the lines. (Labor share is increasing from left to right.)

The blue dots imply a natural rate of unemployment, because the economy gravitates to there in equilibrium. The natural rate of unemployment implied in the graph stabilizes at higher rates of labor share (to the right). Then as labor share falls to 70%, the equilibrium crossing point drops implying a higher natural rate of unemployment. Then as labor share falls below 70%, the equilibrium point reverses direction and starts rising implying a lower natural rate of unemployment.

I have prepared a video about this. The video starts out with a recap of the equation. (Sorry that I mixed up employment and unemployment a couple of times in the video.)

Update to Cobra Equation… 2001 recession

In the morning I posted about the Cobra equation and included some graphs using past data. The graphs showed how capital utilization and employment of labor would increase up to the profit maximization line and then fall back into a recession. But I did not include a graph for the years before the 2001 recession, because it is a special case. So I present it now.

The red dots are from the 3rd quarter for each year, from 1992 to 2001. The recession started in 2001. The coefficient a is 0.6652. (see below for equation.) The effective labor share was 80%. The effective demand limit line shows (capital utilization * employment = 80%) The red line is the measure of profitability. (See equation below) As the numbers in the graph increase, profitability increases. The red line shows the maximum profitability for each employment rate.

3d 2001 rec

Link to graph.

This time period shows more clearly than other time periods how the economy moves up the lines of effective demand and profit maximization. The match is uncanny. The red dots move almost perfectly along the slopes of the two lines.

In other examples given in the morning’s post, the economy didn’t move much along the lines before a recession. But in this example, we see 7 years of data where the economy moved along the two lines. The graph seems to explain very well what is going on.

I would have expected more inflation as the economy moved up along the profit maximization line after 1997. There wasn’t much inflation. Yet, there was inflation in the bubble. The inflation apparently was transferred to that bubble.

Yet it is important to see how capital utilization decreased as employment increased through those years. One might expect capital to be utilized more as more people are employed. But this cobra equation shows that as more labor is employed on the profit maximization line, less capital will be utilized.  We have 7 years of data here showing this.

Is this a breakthrough in understanding?

Once again, here is the Cobra equation…

Measure of profitability = MFP * ((x + y) – a * (x^2 * y^2))

MFP = marginal factor productivity (assumed $50 in graph).
x = capital utilization rate
y = employment rate
a = coefficient for labor share to establish effective demand limit on capacity utilization.
Coefficient a = 0.88*s^2 – 2.31*s + 1.95 … (s = effective labor share, for example 80% as 0.80).
Keep in mind… the key to making this equation work is to have a factor that determines the coefficient a correctly. Labor share is the factor that shifts this equation appropriately with the data.

The Cobra Equation for the Effective Demand business cycle (part 2)

OK… so the exploration is continuing into the new equation which I am calling “The Cobra Equation” because the 3D curve looks like a cobra. This equation shows promise in its ability to explain the process of the business cycle and to ascertain the utilization of labor and capital near the end of the business cycle.

I have simplified the equation to this form…

Measure of profitability = MFP * ((x + y) – a * (x^2 * y^2))

MFP = marginal factor productivity (assumed $50 in video).
x = capital utilization rate
y = employment rate
a = coefficient of labor share to establish effective demand limit on capacity utilization. Coefficient a = 0.88*s^2 – 2.31*s + 1.95 … (s = effective labor share, for example 80% as 0.80).

I plotted the equation for the current effective labor share of 74%. And made a video. (source of 3D graphic in video.)

Link to video.

Notes to video: The constraint is x*y ≤ effective labor share. I say 74% in the video, but effective labor share can change. Also, the numbers in the Excel spreadsheet include the MFP, marginal factor productivity of $50, in the equation. The 3D graphic equation did not include the MFP.

The video explains how the economy is moving within the constraint of the effective demand limit as firms reach for profits along the profit maximization line. The capacity utilization rate will stay steady or decrease as the economy moves forward toward the end of a business cycle. For example, capacity utilization has already stayed constant for almost 2 years. We may be sliding backwards as far as capacity utilization. This equation is new so we have to watch it.

Even so, the video explains the process of the business cycle moving in a circular motion on the plot.

Other examples…

Here is a graph for the data before the 2008 crisis, when the effective labor share was 78%. The red dots start from 3Q-2003 and go to 3Q-2009. The red dots move to the profit maximization line and stayed there for a year or so and then fell back into the crisis going to the red dot for 2009. The coefficient a used for this plot is 0.6836, which corresponds to a 78% effective labor share. (Red dots are one year apart.) (Red dots are for quarterly data.)

3d crisis runup

Link to graph.

As you follow the red dots from 2003, they slightly swoop in and look like they will start heading up and to the right on the profit max line, but the recession started at the end of 2007.

Here is the plot running up to the 1980 recession when there was an 81% effective labor share. Coefficient a is 0.6563. (Red dots are 6 months apart.)

3d 1980 rec

Link to graph.

Data since 2009, the depth of the crisis. This data was shown in the video but not with the red dots. The coefficient a is 0.7225. (Red dots are 6 months apart.)

3d since crisis

Link to graph.

Note: The above graphs use MFP constant at $50, but even if MFP was to change, the Maximum profit line (red line) would not change position.

One thing I forgot to mention in the video, which is a very important point, is that Keynes stated that the effective demand limit was related to the maximization of profits. He stated that an entrepreneur’s expectation of profits would be maximized at the effective demand limit. When we look on the graph and see the two lines, one for effective demand limit and one for profit maximization, we see a close relationship between them. They are not the same, but they move close to one another even as labor share changes. We may find through further research that the economy tends to head toward their crossing point.


3 dimensional equation gives another view of the path to a recession

I am working on a new equation and want to pass it along for feedback. The equation is 3 dimensional and simulates the effective demand limit upon the utilization of labor and capital. Here is the equation…

Measure of profitability = MFP * ((x+y) – a * (x^2 * y^2) – b * (x^2 + y^2))

MFP = Marginal factor productivity
x = capital utilization rate
y = employment rate
a = coefficient of labor share to establish effective demand limit on capacity utilization. Note: If coefficient b is zero, then a can be used alone.  a = 0.88*s^2 – 2.31*s + 1.95 … (s = effective labor share, for example as 80%, 0.80).
b = coefficient as 1/6 to 1/10 of a. This coefficient may be zero thus taking out the last part of the equation, but it is added for exploration.

The equation gives a measure of profitability for utilizing more or less labor and capital. Basically the equation takes a measure of total utilization of labor and capital, (x+y), then subtracts out diminishing returns from production and demand based on labor share.

As I am just beginning to develop this equation, I present in the light of exploration. What is it saying? What does it show? What am I seeing so far? Yet, I want to present the equation because it is showing something interesting.

I have prepared a video explaining what is interesting.
The first graphic you will see in the video shows numbers representing the surface of a 3 dimensional curve. The numbers rise as profitability increases and vice versa.
What is interesting is that the plot in the graphic is showing a different path to a recession. The numbers show that as the economy recovers from a recession it will employ more capital and labor. Then, a limit is reached for capital utilization. But then the economy has a profit incentive to employ more labor, but as it does so, capital will be dis-employed. So as employment is pushed below a natural level as companies reach for profit, the decrease in capital utilization triggers a recession.

Here is the video to explain…

A recession may simply be a reach for more profits that causes a contraction in capital utilization. The mechanism would be something like… as capital utilization falls and employment rises, production is held in check and inflation begins to appear from increased money in the hands of labor. Then the Fed reacts to control inflation and then both capital and labor will start to contract in a cascading dynamic.

The economy recovers along the original path until capital utilization reaches its maximum. Then labor is employed in an effort to reach for more profits and a capital contraction is induced. Eventually the path to more profits ends in a contraction.

The contraction of capital and then labor is actually seen in historic data before a recession. This equation presents a path of profitability to explain how that might happen.

Labor market is improving, but hanging high

The Federal Reserve Bank of San Francisco published a letter about the labor market. The letter is titled, Gauging the Momentum of the Labor Recovery, and written by Mary C. Daly, Bart Hobijn, and Benjamin Bradshaw. They observe 6 indicators to judge how well the labor market is improving. The 6 indicators are the insured unemployment rate, initial claims for unemployment insurance, capacity utilization, the jobs gap, the Institute for Supply Management (ISM) manufacturing index, and private payroll employment growth.

They see that the labor market has improved over the past year. The labor market is important for Fed policy in regards to Quantitative Easing. They conclude their letter with  these words…

“All these indicators show that the recovery has more momentum now than a year ago. This is a strong signal that labor market improvement will continue at their current modest pace, and could even accelerate in the coming months. Of course, whether this increase in momentum amounts to a “substantial improvement” in the outlook for the labor market is a question for policymakers to decide.”

I am left with the thought that “substantial improvement” is in the eye of the beholder.

Yet there is another issue of how low unemployment can go. Will it go to the expected natural level between 5% and 6%? They write this in their letter.

“…while most of these indicators have not returned to normal levels, they are beginning to approach their historical averages, represented by the zero line.”

They very carefully give a warning here that the end of the business cycle is in sight. Here is the graph that they refer to in their letter.


Link to graph.

The indicators are returning to historic averages, but look closely. The bold black line of the unemployment rate itself trended below the other lines before the crisis. Now it is riding higher than the other lines as they return to their historic averages. The implication is that the unemployment rate has shifted higher. My view is that the natural rate of unemployment has shifted higher, and this graph supports the idea.

The key indicator to watch is the initial claims. When this indicator shows signs of bottoming out, the unemployment rate will slow its descent. According to the slope in the graph, initial claims would start bottoming out in about a year. John Williams of the same Federal Reserve Bank of San Francisco predicts that the unemployment rate will be around 6.5% at the beginning of 2015.

So if the indicators reach their historic low averages in a year, will the unemployment rate really get down to 6%?

Some basic principles of effective demand

Since I write about effective demand quite a bit here, I just want to post some of its basic principles.

What is Effective Demand?

Effective demand is a measure of the potential demand for the output of an economy. This potential establishes a limit upon output. In simple terms, the output of the economy will be constrained by the limit of effective demand, even below full-employment if such a situation was to arise.

Basic principles of effective demand

1. 100% utilization of available labor and capital would require paying out 100% of the total value-added income received to labor, namely the consumer.

2. Businesses in the aggregate could use 100% of the available labor and capital to maximize production. But if labor is paid less than 100% of total income received by businesses, 80% for example, there won’t be enough aggregate demand for businesses to sustain that level of production profitably. Therefore, there must be a lower limit for utilizing labor and capital that allow the rate paid to labor to create sufficient aggregate demand for profitable incentives.

3. The integrated utilization rates of the factors of production, labor and capital, are limited by the % of national income paid to labor, namely the consumer.

4. When businesses in the aggregate start utilizing more of their available resource factors, labor and capital, than what they pay out, profits will start to decrease.

5. If businesses pay out 3/4 of their income in the aggregate, they can only expect to use at most 3/4 of the aggregate productive capacity, as determined by multiplying together the utilization rates of labor and capital.

These principles are supported by the data so far.

Dynamic model of tax transfers may see effective demand as an attractor state

A comment by Arne in a previous post raised the idea that a tax transfer from capital to labor would raise the effective demand limit. So a video was made using the dynamic model for the circular flow to test his idea. As it turns out, the model shows that the natural real GDP equilibrium level would rise… holding other variables constant.

(Click on title of post to open up post and see videos.)

Janet Yellen serves all people, but trusts firms to set optimal wages

In her acceptance speech for Fed Chair, Janet Yellen said… (at the 1:30 point in this video from The Daily Conversation)

“The mandate of the Federal Reserve is to serve all of the American people”

And then it appears as though she almost choked on those words. She must sense the rage and power seething among people, especially the young and underpaid. or she senses the embarrassment of an economy gone elitist. It would be nice if the Federal Reserve could do more to help people, but what can the Fed do?

She says…

“The Federal Reserve can help, if it does its job effectively. We can help insure that everyone has the opportunity to work hard and build a better life.”

Many people already work hard and don’t get ahead in life.

The problem she faces is that there is no transmission mechanism to put money into the hands of people. Many people are simply marginalized from the economy. They can’t get loans. Wages are stuck. Social programs are in jeopardy. A lack of aggregate demand is keeping unemployment high. And labor has no bargaining power, not even with the government.

She wrote a paper on efficiency wages back in the 1980’s. The idea of efficiency wages justifies the going wage rate and does not address what a socially optimal wage would be.

She writes in her paper on efficiency wages…

“However, for a natural but subtle reason, the efficiency-wage model is consistent with nominal wage rigidity and cyclical unemployment.”

“In the Akerlof-Yellen model, firms are efficiency-wages setters and monopolistic competitors. In the long run, wages and prices are set by all firms in an optimal way. In the short run, in response to aggregate demand shocks, some firms keep nominal wages and prices constant, while other firms choose these variables optimally.”

What she wrote back in the 1980’s would lead me to think that she trusts firms to set appropriate wages. She would not question how or why firms set the wages that they do. And yet, she must know that firms have private interests as their priority, not social interests. Then how can she trust that wages will be optimal? Does she mean optimal for firms? But what about optimal for society?

She said nice words yesterday, but there is nothing that she can do short of stating a case for higher wages.

Ben Bernanke never gave much weight to the idea of raising wages. He felt that people needed to raise their skill level and education. But now we see many college graduates not finding appropriate jobs. Somewhere he got it wrong.

I have no hope that she will do anything to help labor directly.  All her actions will help firms directly, and labor indirectly, if labor is so lucky. But then again, she says that firms set wages in an optimal way. I doubt she understands that firms have been taking advantage of their power to suppress wages over the years in a sub-optimal way for the overall economy.

So… To expect that Janet Yellen will do anything directly to help labor would be expecting too much.