Thursday, March 19, 2020

Arthurian Profit Study 2.0: The Mysteries of Science

Graph #1: Financial Business Share of Corporate Business Profits
When the value of a ratio wanders up and down, as in the graph above, all you know is that one component of the ratio is changing relative to the other. You don't know if one is increasing and the other is stable, or one is decreasing and the other is stable, or which one it might be. Maybe one is going up and the other is going down; you don't know. It's even possible that they're both going up -- or both going down.

From the ratio, you can't tell. So I want to look at the components of the ratio. For the above graph, that would be the profits of Corporate Business (CB), Nonfinancial Corporate Business (NCB), and the one minus the other, Financial Corporate Business (FCB).

For the record, FRED uses the abbreviation NCB for "Nonfinancial Corporate Business" in the series names, sometimes at the beginning of the name. For example:
And sometimes at the end of the name:
But sometimes they drop a stitch, as with these two:
And sometimes, they don't even try:
FRED uses NCB quite often as a memory-jogger for Nonfinancial Corporate Business. But I don't think they ever use FCB for Financial Corporate Business, and I don't remember ever seeing them use CB for Corporate Business -- except embedded in "NCB", of course.

But anyway, we wanted to look at the profits of CB, NCB, and FCB. Here ya go:

Graph #2: CB (blue), NCB (red), and FCB (green)
Bottom to top, we have the Financial business (green) portion, the Nonfinancial business (red) portion, and the total of the two: Corporate Business profits (blue). Just by eye, all three measures appear to have been increasing slowly until around 1970, then moderately fast until around 2000, and then extremely fast, though with significant declines as well.

Actually, it is hard to tell how fast they increased, because when the line goes up and off the chart, the whole plotted line has to shrink down to fit on the graph. When the plotted line shrinks, the low numbers get closer to zero and differences between the low numbers take fewer pixels of space. And the numbers that were in the middle move lower on the graph, so the next time the plotted line has to shrink, those numbers will get lower and closer to zero, with less pixels for differences. The higher numbers -- typically, recent ones -- always make older, lower numbers look small. This is what Graph #2 shows.

It shows the increase in profits. But it doesn't show the growth of profits. To see the growth we can take the "log" of the values. Doing that gives us this graph:

Graph #3
Graph #3 shows the same data as #2. But #3 shows it a different way. Shows it in a way that gives us a better look at the growth of profit.

Here: Increase versus Growth: "Increase" means to add more. As children, we learn to count, and we learn the word "more". As adults, when we  think more we think increase by one or more. When we put it into numbers, it looks like this:
1, 2, 3, 4, 5, 6...
It looks like counting.

But suppose you're counting your money. You start with one, and then you get one more, so you have two, and you say: "Wow, I doubled my money!"

But then you start with two, and you get one more, so you have three, and you say, "Wow, I only got half as much this time," and there is some disappointment in the "wow" this time.

And then you start with three, and you only get one more. You drop the "wow" and say "Things are getting bad!" And you start looking for for ways to increase your money faster.

You're thinking in terms of growth. If you start with a dollar and you double it, you want to double it again, and again, and double it every time. When we put that into numbers, it looks like this:
1, 2, 4, 8, 16, 32...
"1, 2, 3, 4..." is constant increase. "1, 2, 4, 8..." is constant growth.

On Graph #2 we could see that the increase of profits was slow early on, and a lot more rapid later, as with "1, 2, 4, 8". That pattern emerges because people try to grow their profits, not just increase them. But Graph #2 is designed to show increase rather than growth. So the growing profits appear to be increasing at an alarming rate.

Graph #3 is designed to show growth rather than increase. On #3, you could draw a straight line down the middle of one of the plotted lines, and it would fit quite nicely. On the graph of "logged" values, your straight line would show constant growth, or a constant growth rate, lets say. The plotted line would vary some from your straight line, but not very much.

What this means is that the growth rate of profits, though it did vary, was close to constant from the late 1940s to the most recent data.

You can see as you move from left to right on the graph, from the 1940s to 2000 or later, the green line was going up faster than the red and blue. The green line -- Financial corporate business profit -- was growing faster than the other measures of profit, reliably, for all that time.

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I used the FRED data from Graph #2 to make an Excel graph, and made the vertical scale a Log Scale to make a graph similar to Graph #3. Then I put exponential trend lines on each series. By some miracle of science, when you show an exponential curve on a Log Scale graph, the exponential curve comes out perfectly straight.

The graph below shows just one profit measure, Corporate Business (CB) profits (that is, Financial plus Nonfinancial business profits. The total of the two). The blue line from Graph #3 is repeated here on Graph #4, along with an exponential trend line in black. Note than on a Log Scale graph, exponential trend lines appear as straight lines:

Graph #4
I included the trend line equation so you know that this trend line is an exponential line calculated by Excel, not just a line that I added to the graph by eye. Just below the trend line equation, Excel gives an R-Squared value that, at 0.9786 is pretty darn close to a perfect match. (1.0 is perfect.) The 0.9786 is evidence of the "nice fit" I mentioned above.

As I said above, the blue line on Graph #4 is the same as the blue "CB" (Corporate Business) line you can see on Graph #3. And here's something interesting: For Graph #4, I used the original data values that I got from FRED, and made the vertical scale a Log Scale. But that method didn't work for Graph #3, the FRED graph. (The plotted green line uses calculated values; FRED's Log Scale option never works when I try to use it for calculated values). For #3 I used a different method: I plotted the Logs of the data values instead of the values themselves. Then, because the values were logged, #3 didn't need the vertical scale to be a Log Scale.

The plotted line comes out the same either way: The blue line on Graph #4 is identical to the blue line on #3. Far as I can tell, anyway.

But compare the numbers on the vertical scales for Graphs #3 and #4. On #3 (with Logged values) the vertical scale only goes from zero to 8. All of the plotted values are less than 8. By contrast, on Graph #4 (with the original data values) the lowest number is around 30 -- and the highest is in the neighborhood of 2000, the same as on Graph #2.

Graphs #2 and #4 use the same values, but the plotted lines are different. Graphs #3 and #4 use different values, but the plotted lines are the same. Ah, the mysteries of science.

Hey, if you make enough graphs, it all starts to make sense.

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So you've seen what Corporate Profit on a Log Scale looks like, paired with its exponential trend. I know, it is hard to believe that that straight line is an exponential curve. But you can prove it to yourself, if you want: Open up Excel, enter the numbers
1,2,4,8,16,32
in adjacent cells -- just the numbers, not the commas -- then select those cells, and insert a line graph. Then click your plotted line, click the Chart Tools "Layout" option on the menu, click "Trendline", and click "Exponential Trendline". You get a thin, black, curved line that runs so close to the plotted line that it's hard to see. A curved line. Now click the graph to select it, and from the Chart Tools "Layout" menu, under "Axes" click "Primary Vertical Axis" and click "Show Axis with Log Scale". Watch the graph as you make that last click: Both your plotted line and the curved, exponential trend line will change to straight lines because you're using a Log Scale! Seeing is believing.

Under "Primary Vertical Axis" you can click "Show Default Axis" to go back to the curved lines, and then "Show Axis with Log Scale" again and watch it change to the straight lines again.

This next graph shows all three profit data lines -- blue, red, and green -- as on Graph #3. It also shows exponential trend lines for each of the three, similar to the one on Graph #4. All told, six lines.

Graphs look messy to me when they show more than two lines. Oh, well:

Graph #5
The plotted lines are narrow ("thin") this time and the trend lines wide ("heavy"), to emphasize the trends. The uppermost pair, blue, is the same as shown on Graph #4, FRED's Corporate Business profits.

The three plotted lines (not the trend lines) are the same as shown on Graph #3: Blue is CB, red is NCB, and green is FCB profits. The heavy lines, the trend lines, are all Excel's exponential trend calculations, as on Graph #4. Here the trend lines are color-coded to match the plotted lines. The colors don't signify anything in particular, far as I know. By default, Excel makes the first line you put on a graph blue, the second one red, and the third one green.

(FRED uses the same sequence of colors: blue first, then red, and then green. Also, I never used it but I'm pretty sure that when you make a graph in "R" you get the same color sequence. I wonder who came up with that sequence -- and who decided to stick with it.)

Anyway, the trends. By eye, the plotted lines run pretty close to the trend lines. (Observing the high R-Squared value, we already confirmed that for the blue line. Here, for each of the three pairs, the plotted line never runs far from its exponential trend. The one exception is at the end of 2008 where the green line momentarily drops down and off the chart. Yeah, that one looks like the page view count in my blog stats when I write a long, involved post like this one...

Oh, by the way, that exception, the green line that drops way low, it bottoms out at the value 0.01. I made up that number. Just that one number. I made it up because the actual value was negative -- it was -67.947, actually. Excel wouldn't give me the trend line because, I dunno, exponential calculations don't work with negative numbers or something. It's that science thing again. Weird science.

I suppose my green trend line slopes up a little more than it would if the negative number worked. But not much higher.

My reason for showing you Graph #5 is so you can see that the green line slopes uphill quite a bit more than the red or blue. Because the vertical scale is a Log Scale, the slope of the line represents the growth rate. (Remember I said some graphs show increase and some show growth? I switched to the log scale to see the growth of profits rather than the increase. And now you know why: The slope of the line represents the growth rate.)

The green line goes uphill faster than the red or blue. So we know that Financial Corporate Business profits grew faster than Nonfinancial Corporate Business profits (red) as a rule, since the late 1940s. And we know that those Financial profits grew faster than total Corporate Business profits (blue). Financial profits grew the fastest. And remember: The financial (F) profit arising from the financial (F) assets of nonfinancial (N) corporate business is counted as part of the profits of nonfinancial (N) corporate business!

The financial (F) profit of  Nonfinancial (N) Corporate Business is counted as N profit, not F profit. It makes F profit look lower than it really is, and it makes N profit look higher than it really is.

It is true that some part of the fast growth the green trend line shows is due to the fact that I changed one value from -67 to 0.01 so that the Log thing would work. But that part of the fast growth of F is nothing compared to the accounting of F profit as N profit simply because it accrues to N. Look: The more economic policy favors F over N, the more F will grow and the less N will grow. And the more that happens, the more people will think that F is the better investment, so F will grow even more and N will grow even less as a result.

F is Financial and N is nonfinancial, but N is productive, and F is nonproductive!

And remember: Financial profits have grown faster than Nonfinancial for the last 70 years or more.

Now, I think, we are ready to begin.
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