Effective Demand Research

New Capacity Utilization data

The 3rd quarter capacity utilization data came out... 78.0% for the 3rd quarter.

No surprises. The TFUR rose just a little to 72.3%. Still below the effective labor share of 73.1%.

Over the last 3 quarters, capacity utilization has been 78%, 77.9% and 78%. It is very stable.

No surprises.

 

A "weird" case for higher interest rates

Is there a case for raising interest rates by the Fed? Even a weird one?

In the previous post, I explained the reasoning behind the current lower level of real GDP. The explanation is that real GDP declines to an equilibrium with the low interest rate in the money market for labor income.

So if a lower interest rate lowers equilibrium real GDP, then would a rise in the interest rate raise real GDP?

First I want to show a graph posted by Nick Rowe back in August of 2011.

This graph shows a "weird" up-sloping IS curve as Mr. Rowe puts it. Yet, even though it is weird, I agree with the graph. The graph basically points to "where we are" and "where we want to be", and then draws a line between those points.

"Where we want to be" is a natural rate of interest that is positive. I have written before that the natural rate of interest is positive, but many economists say that the natural rate of interest is negative.

Mr. Rowe gives 2 definitions of the natural rate of interesting the comments section of the post where the graph comes from.

"1. What would equilibrate desired saving and investment given the actual level of income and actual expectations for future income.

2. What would equilibrate desired saving and investment if income were at the natural rate (LRAS) and were expected to remain so.

You are using it in sense 1; I am using it in sense 2."

I agree with Mr. Rowe that #2 is the better definition to use. When real income (real GDP) reaches its natural rate at the LRAS curve (effective demand limit), there is a natural rate of interest that will keep real GDP stable.

So how does he explain the up-sloping IS curve?

"3. Why does my IS curve slope up? It is not because I think that a higher interest rate would increase demand for newly-produced goods. Rather, it is because I think that a sustained increase in demand for goods would have such a strong self-reinforcing effect on desired investment and consumption that interest rates would need to rise to keep output demanded equal to output. The marginal propensity to invest plus the marginal propensity to consume exceeds one, in other words. Take a normal Old Keynesian IS curve, and assume mpc+mpi>1, and it will slope up.  I explain this more in an earlier post."

He is describing a mechanism by which a sustained increase in demand for goods would be accompanied by a rise in interest rates. The result would be that output demanded would equal output.

I don't want to get into the LM curve in this post, but my view is that the LM curve is flat now. But when the natural rate of real income is reached, it may continue horizontal or go vertical or anywhere in between depending on what the central bank decides. Mr. Rowe says as much for the vertical LM curve.

As Mr. Rowe says...

"The LM curve does not have a fixed slope. The slope of the LM curve is whatever the central bank wants to make it."

The LM curve comes from the equilibrium states in the model for the money market.

In the previous post, I divided the money market into two markets, one for labor income and one for capital income. These two markets behave differently, so we need to understand the money market for labor income because it is a powerful force to determine the purchasing power for goods.

Here is a video using this model of the money market for labor income to show how an increase in interest rates would coax a rise in real GDP a la Nick Rowe's "weird" IS curve. (previous video that set up this model.)

Just as Mr. Rowe's up-sloping IS curve was weird, the idea that business will invest more at a higher interest rate is weird. Yet the money market shows that possibility too. The idea is that the money market searches for its equilibrium. And if the only way to find that equilibrium is by shifting the demand curve, it will have to happen that way.

Also, Mr. Rowe saw in the IS curve that a higher demand for goods would result in a higher demand for investment. He also saw that the interest rate would respond by rising too. And I show that in the money market for labor income, a higher interest rate would coax demand for goods to a higher equilibrium, which would also create a self-enforcing effect on desired investment.

The demand curve in the money market can shift from a rise in prices or a rise in real GDP. The bet is that with a carefully increasing interest rate, real GDP would rise more than prices.

So according to these weird points of view, a higher interest rate would correspond to a higher real GDP and higher investment... bringing an end to the depressed 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 labor share of income dropped 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.

Future path of the utilization of labor and capital

So the cobra equation has made me re-evaluate many things about the Effective demand research.

The main cause was that the graph of the Cobra equation was showing that capital utilization would increase from this point on. I was assuming that as employment increased, that the utilization of capital would also increase. That is a mistake. The graph shows that capital will be less utilized as labor is more utilized at this point.

So here is the revised graph...

The blue dots show the economy moving from 2009 until 2nd quarter 2013. The blue oval shows the projected range of the equilibrium point where profit maximization crosses the effective demand limit.

I was projecting a lower limit of 7% for unemployment, but that was based on capital utilization rising. Now I have to reconfigure how low unemployment might go.

The 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. This post shows that the equilibrium point between the maximization of profits in the aggregate and the effective demand limit upon real GDP implies a natural rate of unemployment.

The simplified Cobra equation is now...

Measure of profitability = (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 equation is in 3 dimensions, but I have made a 2 dimensional graph of it with an Excel spreadsheet.

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

The equation for the orange line is...

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. In the graph 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 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 few times in the video.)

The Cobra equation and the 2001 recession

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.

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 dot.com 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.

This is 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...

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. (previous post, part 1)

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).

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

Notes to video: x*y ≤ effective labor share whatever it is. I say 74% in the video, but it can change. Also, the numbers in the Excel spreadsheet include the MFP, marginal factor productivity of $50, in the equation.

The video explains how the economy is moving within the constraint of the effective demand limit as firms reach for profits. The capacity utilization rate will stay steady or even decrease as the economy moves forward. It has already stayed constant for almost 2 years.

The video explains the process of the business cycle moving in a circular motion on the plot.

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.

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.

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. And the difference between them is described in how the data move before a recession.

A drawing of a cobra...

New equation is developing further in 3 dimensions

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.

Exploring New equation for Effective Demand

I am exploring a new equation to describe Effective Demand. The equation is not perfect... yet, but it is showing some things to look at.

Here is the equation...

measure of profitability = l * (c + e) - (c^2 + e^2 - c * e)

l = effective labor share

c = capacity utilization

e = employment rate (94% for example which means 6% unemployment)

The equation has two parts, a demand part and a production part.

The demand part...

l * (c + e) ... This part says that for the utilization rate of labor and capital, there is a portion determined by effective labor share that is paid out for demand of production.

The production part...

(c^2 + e^2 - c * e) ... This part is subtracted from the demand part. It is an expression to give a measure of the combined utilization of labor and capital. It is different than just a straight average.

The equation seeks to give a measure of the potential profitability for business in the aggregate.

Here is a little video showing what the equation looks like graphed out. (web site source for #D graph)

The graph shows that capacity utilization and employment will reach their maximums at 100%, where the effective labor share constraint is.

As the effective labor share declines, the maximum point of the graph moves with it.

When I apply this equation to actual data since the crisis. I get some graphs.

Graph #1

This graph shows contour lines from the 3d graph as the economy recovers from the crisis. The red dots show where the economy was at periods of 6 months. The first dot up to the left was low on the contour and showed there were returns to production available. Over time, the red dots are closer to the maximums of the contours meaning less profit potential available.

The measure of profitability has been dropping since the crisis by this is not normal. Usually the economy just moves up the contour but this time is different because labor share has been dropping, which shifts the lines down. Here is what the graph would look like if labor share had not fallen since the crisis.

Graph #2

As you can see, the measure of profitability would have continued upward on a normal path. Yet, the fall in labor share has hurt aggregate demand and thus profitability, thus many people are complaining about a sub-par economy. Graph #1 would say that the problem has to do with falling labor share of income.

Graph #2 is saying that if we factor out the effects of labor share, the utilization of capital has been recovering on a normal course.

In graph #1, as the utlization rate of capital increases, the profitability of the economy rises. So a business has an incentive to use capital for production. However, business must hire labor to run much of the capital, not always. Yet, there is a disencentive to hire labor as seen in the next graph.

Graph #3

The curve is sloping downward here, because on the surface of the 3D graph, the economy would be on the downsloping part over the topside. So increases in utilization of capital rise on the surface, whereas increases in employment slide down the surface. Be that as it may, I will flow with the logic of the moment and see where it leads.

As unemployment falls, the measure of profitability falls too according to the downward sloping curve. So as the economy recovers, it is profitable to put capital back to work. But it is not profitable to put labor back to work. However, if labor is not put back to work, and the labor share falls, the contours lines will fall even faster, thus lowering the measure of profitability even more.

Here is what graph #3 would look like if labor share hadn't fallen.

Graph #4

You may wonder why these lines shifted upward, but stayed steady in the graph for capacity utilization. The reason is that capital was employed much faster than labor in the early stages of the recovery. Whereas capital was re-employed at a normal rate, employment lagged behind. The result would have been an increase in potential profitability even for employment. The contours of employment would have reached a point of equilibrium with capacity utilization, as seen by the lines staying steady at a higher level of potential profitability.

So, even though profitability declines with employment, the general tendency if labor share stays constant is for the contour lines of employment to shift upwards as the economy recovers. Thus there are exogenous factors that make employment profitable. But the fall in labor share negated those factors.

Nevertheless, graph #3 shows that labor share fell after the crisis bringing down profitability.

We may wonder why profits are so high while these graphs are showing that profitability has declined. It is no wonder. The drop in labor share has pushed profits up at the expense of employment. It is like the mystery of a monopoly. How can a monopoly make more profits by producing less? It's a similar situation here.

OK... just wanted to show this equation as I am working on it.

Some Basic Principles of Effective Demand

I have created a synopsis page at the top of the right bar. Here is the beginning part.

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 restricted by the limit of effective demand.

Here are some basic principles of effective demand?

1. 100% utilization of available labor and capital requires 100% of total income paid out to labor as the consumer.

2. A business could use 100% of its available labor and capital to maximize production. But if labor is paid on 80% of total income received by the buiness, there won't be enough aggregate demand to sustain that level of production.

Therefore, there must be a lower limit for utilizing the factors of production that matches the rate paid paid to labor in to have demand.

The research of effective demand says that the lower limit on the utilization of the factors of production is the rate of total income paid to labor.

3.The utilization rates of labor and capital are limited by the % of income paid to labor, as the consumer.

4. When a business starts utilizing more of what it has than what it pays out, it will be beyond making a growing profit.

5. If businesses pay out 3/4 of its 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.