Sunday, May 19, 2013

Why is there a discrepancy, and where did the money go?

Following McConnell mostly (though McConnell does not use inflation-adjusted values), Graph #1 shows Personal Consumption Expenditures versus Disposable Personal Income as a scatter plot. The blue dots represent Personal Consumption Expenditures. The block dots show where the blue dots would have been, if none of disposable personal income had been saved.

Graph #1
Here's the Google spreadsheet.

To me, this graph is not a good way to see whether the Marginal Propensity to Consume falls as income rises. It shows the average consumption of everybody, rich and poor alike. To see differences of income, it depends on the passage of time. But surely, conditions were much different in the 1960s than they were 40 years later!

To me, Graph #1 makes it difficult to see the relation between the two sets of numbers. If the black dots were not there, could you really tell that the blue dots are slightly below the 45-degree line? When I first did this graph I had the axes reversed, and no black dots. The blue dots were running above the 45-degree line, but I couldn't tell.

I prefer to look at the two sets of numbers as a ratio, like this:

Graph #2: Real Personal Consumption Expenditures relative to Real Disposable Personal Income
Click Graph for FRED Source Page
Here you can see an unusual down-loop created by World War Two spending in the 1940s. You can also see, pretty unusual too, personal consumption expenditures reaching 100% of disposable income just at the end of the Great Depression in the 1930s. (The end of the gray bar part of it, I should say.)

Other than that, there seems to be a pretty strong downtrend until the mid-1970s, and a pretty strong uptrend since the early 1980s. The downtrend of consumer spending (relative to income) implies an increase in saving in the early years. The uptrend of spending in the later years implies a decrease in saving. And sure enough:

Graph #3: Two Versions of the Saving Rate

The "saving rate" runs clearly up till the mid-1970s, and clearly down after the early 1980s. Until the crisis, anyway. Even the late-1970s hump on Graph #2 is matched by an inverted hump on Graph #3!

Does this have anything to do with the Marginal Propensity to Consume? Seems to me it has more to do with general economic conditions and economic policies.

Clearness of mind on this matter is best reached, perhaps, by thinking in terms of decisions to consume (or to refrain from consuming) rather than of decisions to save.

I thought this post was finished before the Keynes quote above. But during repeated proofreads, those last two graphs fascinated me repeatedly. See how the one line goes down gradually, then up fast? The other one goes up gradually and then down fast. Like mirror opposites. Intriguing.

True: When spending goes up as a share of income, saving must go down. And when spending goes down as a share, saving must go up. Nonetheless.

Consumption is a high percentage of income, up near 100%. And the saving rate is a low percentage of income, down near zero. Still, there is something about the changes that cries out to me.

I went back to FRED and put the line from Graph #2 and the red line from Graph #3 together on a new graph. Chopped off everything before 1947 to get rid of the World War Two woopsie there, and to have the two lines start and end pretty much together. And I used annual data for both, to eliminate a distraction.

So, I put 'em on a graph. At first glance, then, the consumption-relative-to-income line (from Graph #2) was up high on the new graph and the saving rate (from Graph #3) was down low, with a lot of air between the two. Plus, they went in opposite directions.

To make the saving rate go in the same direction as the consumption-to-income line, I decided to use the minus of the saving rate. And I wanted to add about 100 to this mirrored saving rate, to move it up and get it closer to the consumption/income line. So what I graphed for saving was: 100 minus the saving rate.

It came out close. But not close enough. I played with it a bit and subtracted some from the hundred I added. The two lines are now very close:

Graph #4: Comparison of Personal Consumption Expenditures relative to Disposable Personal Income (ratio in blue) and Personal Saving as a Percentage of Disposable Personal Income (red) with saving inverted and shifted up to get it close to the blue line.

Two observations, maybe three.

First: Yes, certainly we should expect to see this similarity. We are looking at what we spend and what we save, as percentages of the income that we choose either to spend or save. Of course. Still, actually seeing the similarity is way better than just expecting it to be there. (I'm not big on expectations.)

Second: Close as they are, the red line gains on the blue line for the whole period shown. Or for sixty years anyway, from 1947 to the crisis. The red line starts out below the blue line. It slowly closes the gap but remains below until about 1980. After 1980 the red line runs above the blue consistently, to the crisis. And the gap widens.

Yeah, the lines cross at 1980, but that's not because of anything Reagan. I could make the lines cross earlier or later by subtracting a little more or a little less than 3 (see the last term in the second formula line, in the blue border across the top of the graph).

Forget 1980. What this graph shows is that the red line gains on the blue line for the whole 60 years between the Second World War and the Global Financial Meltdown.

What does that mean? I dunno, but I'm thinkin about it. The red line is gaining on the blue: The saving rate is gaining on the consumption rate. Except that the saving rate here is inverted, because I minus'd it.

Odd, isn't it? Consumption and saving together add up to disposable income. Our only choices are to spend the income or not spend it, to consume or to refrain. You would think that if the one goes up by n% of income, then the other has to go down by the same n% of income.

If consumption goes up, saving should go down. If consumption goes down, saving should go up. Invert saving, and the two should move together. And, yes, they do move together. But the red line is gaining on the blue.


Here: Before 1980, consumption (blue line) decreased. The red line went down more slowly, so the gap between red and blue disappeared. But the red line is inverted saving. Before 1980 the red line went down slower than consumption; this means that saving went up slower than consumption went down.

Something similar happened after 1980. And all the while, the red line was gaining on the blue.

Okay, let's put numbers on it. From 1947 to 1981 the blue line fell from 92% of disposable personal income to 86%. That's a drop of 6% of income.

During those same years the red line fell from 90% of income to 86%, That's a drop of 4% of income and it means that saving increased by 4% of income.

Fine. But consumption (the blue line) fell by 6% of income while saving increased by only 4% of income. What happened to the other 2%?

More numbers: From 1981 to the 2001 recession the blue line went from 86% to 93%, an increase of 7% of income. During those same years the red line went from 86% to 94%. The red line went up one percent (of income) more than consumption went up. That means saving went down one percent (of income) more than consumption went up. We lost another one percent!

We lost two percent of disposable personal income in the years before 1981 and another 1% in the years after 1981. That's three percent of income, total, that's missing.

Pretty weird.

One thing that should be obvious in all this: There was no great change around 1980. Income disappeared in the years before 1980, and income continued to disappear in the years after 1980.

Okay. What Graph #4 shows is that the red line gains on the blue line for the whole 60 years. The red line is saving, inverted. It's an indicator of income not saved.

The blue line is income spent.

If the red line gains on the blue line for 60 years, it means that "income not saved" gained on "income spent" for 60 years.

Why is there a discrepancy, and where did the money go?

Wait a minute. One more graph. I took the saving rate and added it to consumption as a percent of income. The money we spend plus the money we don't spend, together. It should equal 100% of the income we started with. But it doesn't:

Graph #5: Personal Consumption Expenditures as a Percent of Disposable Personal Income, plus the Saving Rate, together add up to less than 100% of Disposable Personal Income, and fall from 99% to 96% between 1947 and 2007.
Click Graph for FRED Source Page
Why is this line less than 100%. And why is it falling?


jerry said...

i know what i think you think the answer is, but why didn't you say it???

The Arthurian said...

Hey Jerry. I thought I knew at the start. By the time I was done writing it, I was less sure. Really, it depends on the definitions of terms, and on how the counting is done I suppose.

At the start, I was thinking the difference was cost-of-credit. By the end, I was thinking maybe taxes. Not sure about that because "disposable income" is supposed to be after-tax income. But after what tax?

I didn't say what I thought it might be, because I was hoping somebody knows.

Anyway, I really got into writing this one, and I think I did a good job of putting the arithmetic of the discrepancy into words.