Extending the preliminary circular flow model with labor share
I want to expand on the last post where a simplified circular flow model was given incorporating labor share of income. That circular flow did not include sectors for a government nor foreign markets. I now will expand that model to include those sectors and more.
Extended circular flow for labor share
Here is the model in equilibrium. The model seeks to simulate the real economy. Dollar values are in billions.
There is much to unpack here, let’s get started.
First we see that the out-going (GDI) of the firms equals the in-coming (GDP) at the bottom. Thus, the circular flow is in equilibrium.
Then we see that the GDI is split into labor and capital incomes, 80% and 20% respectively. Then we see that the income of each is divided into the categories of national accounts (consumption, taxes, saving and imports). All but consumption are leakages from the circular flow.
Underneath each category there is a percentage for its share of the income and the real dollar amount given to the category. For example, 80% of labor income is directed to consumption giving $6,400 billion. Net tax rates include government transfers and are estimated. The net tax rates are kept constant in this post.
Below consumption is a box that is grayed, where you will see 77.6%. This value comes from the equation to determine consumption, which uses a value for autonomous spending. 77.6% is the marginal propensity to consume in the equation. The equation used in this model is…
Consumption = $1 trillion + 77.6% * (labor income – net taxes)
$1 trillion is the autonomous spending… 77.6% is the marginal propensity to consume… (labor income – net taxes) is disposable income.
So even if labor share of income was put at 1%, consumption would still be at least $1 trillion. The same equation was used for capital income using a marginal propensity to consume of 30% and autonomous spending of $60 billion.
Imports are also based on an equation of autonomous spending. In the case of labor spending on imports, the equation is…
Imports = $50 billion + 10% * (labor income – net taxes)
$50 billion is autonomous spending on imports… 10% is the marginal propensity to import (MPM).
Capital spending on imports uses an autonomous amount of $200 billion and an MPM of 25%.
After determining net taxes, consumption and imports, the remaining balance is put into saving. In graph #1, saving is negative for labor, but positive for capital.
We then move down the flow adding together the categories from labor income and capital income. For example, the $6,976 billion we see in consumption comes from labor consumption, $6,400 billion and capital consumption, $576 billion.
Then we have total net taxes going to the government. Then we have a saving rate of 3.28%, which comes from dividing the saving by GDI, $328/$10,000. This rate for saving simulates the national private saving rate. Then we have total imports of $1,376 billion, which is close to the national average of imports being 14% of GDI.
Then we go through the financial sector which receives or gives out money to the government, foreign markets and firms. In the graph above, the government borrows $480 billion to meet its expenditure goal because net taxes are insufficient. Also, exports are less than imports, so the economy is a net borrower with foreign markets. In graph #1, the financial sector adds to the saving balance funds of $1,272 billion which will go to investment in capital, residential, non-residential and the means of production in the economy.
Note: I did not extend the financial sector to consumption in the form of consumer lending. The reason is that the overall outstanding consumer debt is currently fairly stable.
At the last line, we have the total expenditures (injection returns to the economy) as added from the leakages through the financial sector. The exception is that net exports are determined by subtracting imports from exports.
Investment uses an equation that also includes autonomous investment with a propensity to invest. Investment changes based on national income. So when we change GDI, investment will change.
Investment = $300 billion + 13% * GDI
$300 billion is autonomous investment… 13% is marginal propensity to invest… GDI is found at the top of circular flow.
Below the last line are values given for the percentage of GDP. All these percentages are based on normal values in the economy.These values add together to give the national income accounting for GDP.
GDP = C + G + I + NX
C = consumption, G = government spending, I = investment, NX = net exports.
For examples, consumption as a percentage in the national accounting equation is normally between 68% and 71%. Government spending is usually between 16% and 22%. Investment is usually between 13% and 18%. Net exports are now usually -4% of GDP.
So throughout the circular flow model here, the numbers have been chosen to reflect a normal state of the United States economy. I must say that the value for labor share of income is based on the effective labor share value that is used in this effective demand research. As well, the model does not include changes to interest rates, nor exchange rates.
What happens if labor share drops?
The main point of doing this extended circular flow model is to see what happens if we drop labor’s share of income. We saw in the more simplified circular flow using only investment that the equilibrium level of GDP fell. But will it happen here too, incorporating all the extra variables mentioned above?
Let’s see. I will now drop the labor share from 80% to 75% and then solve for the equilibrium GDP. The drop will simulate the drop in effective labor share after the crisis, which dropped from 79% to 74%.
I will hold three values constant, tax rates, exports and government spending. Exports are determined outside the circular flow and government spending is budgeted. I will also hold the marginal propensity to consume for labor and capital constant. I will hold the marginal propensities to import constant too. As well, the marginal propensity to invest will be held constant.
I first change the value of labor share from 80% to 75%, then I use a function in excel, Goal Seek, to find the value of GDI (out-going at the top) that will equal GDP (in-coming at the bottom). As I do the Goal Seek action, many numbers change.
First, we notice that GDP has dropped 6.25%. This drop actually simulates fairly closely the 8% fall from potential GDP (CBO projection) that real GDP has suffered. And people are wondering what is happening. This model shows one way that real GDP has fallen to a new lower equilibrium solely due to the unusual drop in labor share since the crisis.
There is much more to see when we compare graph #2 to graph #1.
- Even though GDP has fallen, and labor income has fallen, capital income has actually risen by 17%! This result explains the record profits of corporations.
- The consumption rate of labor has risen from 80% to 81.8%. Labor is having to spend more of its income. This makes sense. Capital is spending less of its income on consumption, 29% to 28%.
- Saving rate has fallen for labor, but risen for capital. The overall saving rate has gone up from 3.28% to 3.76%. … ($352/$9348)
- Imports have not changed much.
- Government borrowing has increased from $480 b. to $561 b. to meet its budget. An increase of almost 17%, which matches in percentage terms the increase of capital income.
- Total consumption as a % of GDP has decreased from 69.8% to 68.4%. A decrease of 2%.
- Government spending as a % of GDP has risen from 18.0% to 19.3%. An increase of 7.2%.
- Investment as a % of GDP has increased from 16.0% to 16.2%. Total investment dollars have fallen some.
- Net exports as a % of GDP has risen slightly from -3.8% to -3.9%.
- A critical thing to see here is that the expenditures for GDP at the bottom have not changed very much. A little percentage here, a little percentage there. But the end result is a big change in the equilibrium level of GDP, which again, has fallen 6.25%.
This circular flow model shows that the equilibrium level of GDP can fall just from a lower labor share. Effective demand falls. It is then conceivable that GDP could fall to an equilibrium level below full-employment.
Just as Keynes said it could…
Raising investment by raising marginal propensity to invest
One more idea… How much would investment have to increase to get GDP back up to $10,000 billion? But I do not want to know directly that number. I want to know how much the marginal propensity to invest would have to change.
In order to that, I set GDI equal to 10,000, then I use Goal Seek to find the value of marginal propensity to invest that allows GDP to reach an equilibrium of $10,000 billion.
In graph #2, the marginal propensity to invest was 13% for every dollar of GDP over $300 billion. Take a guess before you go any further reading this. How much do you think the marginal propensity to invest would have to rise in order to take the economy back to $10,000 billion? 15%? 18%? 20%? 25%?
Take a moment just to guess before you look below…
You will see the new MPI next to the investment down below. The MPI went up to 15.7%. That may not seem like a big jump, but it’s a 20% jump. Business would have to be that much more confident in the future of the economy to raise investment to a level that would restore GDP to the previous level before lowering labor share.
Raising the marginal propensity to invest implies that investment would entail more cost, more risk, more exposure to a downside. The necessary increased risk for investing is a result of a lower labor share of national income. The higher required MPI would be a headwind against the expansionary monetary policy of the Federal Reserve.
The conclusion… This circular flow model with labor share of income presents a case that the decline in labor share since the crisis has led to slower economic growth, which is leading to a lower equilibrium level for real GDP.
In the next post, I will apply this preliminary circular flow model using current numbers from the economy. The model will actually solve for a value of MPI (marginal propensity to invest).
Basically, this is how the economy works in an easy to understand flow diagram. I have been waiting for someone in the national media to explain this ecosystem to the nation. I have called the subject aggregate demand but this goes way beyond that simple equation. If the nation understood how money flows through the system, they would understand why incomes must rise for all of us to prosper. Well done.
Good to see you again. Edward has a pretty good model which we are kind of excited to explore.
Hey, where did you end up moving to?
Great stuff. I now think I get it unlike the other day. The important thing is we can grow the economy by increasing labor’s share of income which is a win-win. I had misread you in an earlier post as saying that there’s a limit of GDP so all we can do is improve distribution.
Disinflation not distributively neutral? http://diaryofarepublicanhater.blogspot.com/2013/08/a-mea-culpa-to-edward-lampert-mark.html
Wow, is it nice to see this, an econometric model that is built on the laws of accounting. So few economic arguments make any accounting sense. You aren’t accounting for time, since you are concerned with the equilibrium, assuming that it is reached within the fiscal year, but your model still provides more believable insight that pages of verbal argument.
(You mention doing a goal search. Are you using Excel? I assume everything is linear, so odds are you are finding a unique equilibrium / fixed point.)
Yes, using a linear model to find a unique equilibrium with excel… using goal seek and solver.
To improve the economy, we hear two somewhat conflicting stories. One, we need to increase government spending, or, two, we need to reduce business taxes. Can your model compare the relative benefits of these two approaches?
I just wrote a post about your question here. comparing increased government spending or business tax cuts.
If debt overhang is still an issue (as Krugman asserts), then increasing MPC is part of the recovery process. Further, if capital needs only to hire more workers to increase production (my overstatement of what overcapacity means), then increased demand will increase labor costs without increasing other production costs and therefore will increase labor share.
Such an outcome can be consistant with your model, but requires some different knobs than you have set up. If I understand, it would increase “effective demand” as GDP increases.
We are learning together with this model but my view is that if MPC increases, people are getting more liquidity constrained. That would be a sign of tension in the economy. A rising MPC would mean people have a harder time paying down debt.
But i see your point, if debt gets paid down, that will free up money to spend per dollar of disposable income.
Increased demand will increase labor costs, but not necessarily unit labor costs.
unit labor costs = labor share * inflation
If a rise in labor costs is not matched by a rise in prices, then labor share will rise.
What knobs would you like to add to the model? Well go ahead and give them a go.
I think of firms as having revenue, costs, and profit. Taxes, consumption, labor costs, capital replacement, and capital investment are the costs.
At the height of the business cycle firms have invested enough to create the maximum capacity that will exist in that cycle. During a downturn, some of that capacity goes idle. During the recovery, increased demand can be met without increasing capital investment (and even capital replacement to some extent).
So the question is, are we still in recovery? In your later post you observe that GDP is up to the previous max and so recovery is over, but Krugman, de Long, Thoma, post as if we are clearly still in recovery since employment is still low.
To put it another way, I think that labor share is a function of underutilized capital which is a function of demand which is a function of labor share – adding an important non-linear complication that is going to be hard to include in your model.
Working on it. All those guys would agree that demand can limit supply but I don’t think they have a model to know how. My model shows how.
I want to be clear. GDP is reaching its previous max in terms of the effective labor share limit. This is a concept that has never been developed well. This model does.
Underutilized capital is a function of effective demand which ultimately is a function of labor share. Labor share though is not a function of underutilized capital.