Wednesday, February 15, 2023

Seeing growth slowing

At FRED, the annual version of Real GDP -- the one with inflation stripped out of the numbers so we can see a real (honest) measure of economic growth -- looks like this:

Graph #1: GDP with price changes removed, to show real growth

The blue line begins in 1929 and ends in 2022. It curves gradually upward over time, and growth appears to be good. But I think we know that growth is not good.

Graph #1 doesn't show the growth rate of GDP. It shows amounts of GDP. Bigger amounts are higher on the graph. But increasing amounts don't always mean better growth. It's like getting a 10-cent raise in your paycheck: It is an increase, yes, but you're not even keeping up with the cost of living.

There are two things: There's the data that you put on the graph, and there's the way the graph shows the data.

The GDP data we're using has inflation stripped away so that the numbers don't increase from prices going up. The numbers only increase from producing more stuff. You have to do that to see GDP growth. But to see or compare changes in growth, you have to do something else. This second thing is to tweak the graph to make the vertical scale a log scale.

Graph #1 shows GDP gradually curving up. The graph shows that we we are producing more and more. But we need to know more than that. We need to know if we're growing as much, now, as we did 10 years ago. Or 30 years ago, or 50. 

Are we growing faster than we did years ago, or slower, or about the same? You cannot tell by looking at the first graph. But you can tell by looking at this one:

Graph #2: GDP with price changes removed and the Vertical Axis showing a Log Scale

The second graph shows the same data as the first. I only checked a box to make the vertical axis show a Log Scale. Just the vertical axis is different. But the line now shows a downward curve rather than an upward curve. The downward curve on a log scale graph means growth is slowing.

On a graph with a log scale, a straight line indicates a roughly constant rate of growth. And the steeper the line, the faster the growth is.

To my eye, the blue line from 1950 to 1970 is pretty straight, and more steep than from 1966 to 2007. And then from 2010 to 2022 the line is even more straight, and even less steep. I added three trend lines by eye, based on these straights and dates:

Graph #3: Same as #2, with three trendlines added by eye

The early period (1950-1970) goes uphill faster than the midsection, and the midsection goes uphill faster than the period since 2010. Economic growth has been slowing. You can't see it on graph #1, but growth has been slowing. The log scale graph makes it easy to see.

You may notice that the middle period starts before the early period ends. Yeah. I look for straight-line trends from left to right, and I look again from right to left. Sometimes the right-to-left view suggests an earlier date, like the 1966 of the middle period. Also I think that when a trend changes, it often takes a few years for the change to be completed -- and 1966-1970 is one of those times.

I jotted down my dates for the three "straight" sections where the growth rate doesn't change much. Then I went back to the FRED data and figured the average growth rate for each of those three sections. There is more difference than I expected:

Graph #4: Average rates of Growth, where the plotted line is relatively straight

Just over 4% in the early period. Just over 3% in the middle years. And just over 2% in the most recent period. Growth slowed by about one percentage point after 1970 and again after 2007.

I know, one percent doesn't sound like much. But one percent every year from 1970 to 2007, compounded, does add up. In his 1995 book To Renew America, Newt Gingrich said that if we can get "a 1 percent increase in our economic growth rate" then "the Social Security Trust Fund never runs out of money". One percentage point more growth means a lot more GDP.

And yes, Gingrich was yearning for the good growth of the 1950-1970 period. As am I.


Trend lines by eye are nice, but trend lines by Excel are better. The next graph shows Real GDP (the same data as before) and a trend line based on the 1950-1970 data, using a log scale:

Graph #5: Real GDP and the 1950-1970 trend line

The trend line (red) is an exponential curve, the curve that curves uphill like crazy, like a covid graph. But an exponential curve shows a constant rate of growth, so on a Log Scale graph the exponential curve is a straight line. Yeah, I am still amazed by this -- and sometimes fooled by it.

Now, think of the red trendline as showing where Real GDP would be if growth kept to the 1950-1970 trend rate. And the Real GDP line, well, it's just sad and droopy. Real GDP is growing a lot slower now than it did 50 to 70 years ago:


10 comments:

Lorraine said...

Do we really need a positive second derivative at all times? How is that even remotely sustainable?

The Arthurian said...

Oh, the things I have to write to get your attention!

I object to economic decline created by the policies of policymakers who don't know what they are doing, or are doing it on purpose.

Long term economic decline makes civilization unsustainable.

Lorraine said...

If (1) economic growth is a prerequisite for civilization and (2) only accelerating growth counts as growth, then civilization is a pyramid scheme. But admittedly I haven't figured out how to walk the tightrope of getting degrowth (or even steady state) without regressing to primitivism or some other variant on the Deep Green cult. Perhaps some technology not yet in evidence, such as quantum computing or asteroid mining or nuclear fusion, will emerge as our get-out-of-jail-free card. But I don't like to count the chickens before they're hatched.

The Arthurian said...

Lorraine, would you point out specifically what I said that you take as meaning "only accelerating growth counts" or "counts as growth". I only want a good growth rate, but that should be adequate.

I have been out of school a long time and maybe I used the wrong terminology. That would be bad.

Economic growth has been slowing for 50 years; that is my complaint.

The Arthurian said...

By the way, these sentences are just wonderful:

"But admittedly I haven't figured out how to walk the tightrope of getting degrowth (or even steady state) without regressing to primitivism or some other variant on the Deep Green cult. Perhaps some technology not yet in evidence, such as quantum computing or asteroid mining or nuclear fusion, will emerge as our get-out-of-jail-free card. But I don't like to count the chickens before they're hatched."

"Regressing to primitivism" is a major problem, maybe THE major problem of (what I call) long-term decline. There is no guidance on how to regress while keeping the best. And there is a lot of I-hate-the-government and lets-toss-the-baby-with-the-bathwater thinking -- if you can call hate "thinking"

I had to look up "deep green". Your thoughts are full of things that I have to look up!
Your "technology" sentence does a superb job of putting that solution out of reach.
And you end with down-to-earth chickens.

I could read stuff like that 100 times.

Lorraine said...

In mechanics, velocity is the rate of change (derivative) of position with respect to time. Acceleration is the rate of change of velocity with respect to time, or the "rate of change in the rate of change (second derivative) of position with respect to time. Position is measured in meters, althought it's a vector quantity, so (say) x meters east, y meters north, and z meters above some reference point. Velocity is measured in meters per second. Acceleration is measured in meters per second per second (which can be called "meters per second squared"). 9.8 meters per second squared (or 32 feet per second squared) is the rate at which things accelerate as they fall, on this planet anyway. Of the above terminology, I'm quite certain. Economics terminology is your wheelhouse, not mine, so please correct me if any of the following is wrong.

Net worth is measured in units of currency. Income is measured in units of currency per unit of time (dollars per year, perhaps).

GDP of the US (as far as I know) is measured in US dollars, but with the understanding that it's annualized, so I'm gonna guess it's really in dollars per year, sort of like if you state your annual income in "dollars," the word "annual" implies "per year." I'm guessing the GDP is the the first derivative of some kind of estimate of "amount of wealth in existence."

If you're stating GDP growth as a percent, say i (what letter do economists use to denote this, btw? I majored in math, and the most "money-oriented" thing I ever studied is "theory of interest" which is all in terms of i), then you're stating that the rate of change of GDP with respect to time is (GDP+i)/GDP, but putting GDP on a logarithmic scale makes the vertical coordinate some constant multiple of i.

log(GDP) as a function of time is a straight line if i is constant. A decrease in the slope of log(GDP) does not imply a shrinking economy, although the slope going negative of course does.

On closer examination, I can see that your complaint isn't that the GDP growth rate isn't itself growing, but that it has been shrinking (although remaining positive at most times).

What I don't understand is, why does the prosperity of the people (let alone the fate of civilization) require not only constant growth, but, if not accelerating growth, at least unflagging growth? Unflagging real growth, so apparently not to "keep up with inflation."

Lorraine said...


Concerning how to regress without keeping the best, it never occurred to me to take a meritocratic approach. One source of guidance I would go to would be David Graeber. The best jobs, the ones (that might be) worth keeping, would be the non-bullshit jobs. "Everyone gets necessities before anyone gets luxuries" is a rule I can live with, but I don't know how to formulate (let alone enforce) such a principle as a policy decision. I do think "luxuries" and "necessities" can be defined with some objectivity, although I understand economic terminology prefers euphemisms such as "preferred goods" and "inferior goods." I also think that the existence of poverty is a policy decision if the GPP (is gross planetary product a thing?) per capita is above the "poverty line" by a comfortable enough margin. If growth in such an economy to even bigger than its (by definition) already adequate-to-the-task size is an absolutely necessary condition for increasing incomes at the zeroth percentile (i.e. "trickle down" is the only income stream which will be allowed to reach the bottom rungs of the ladder), then it would be perfectly reasonable to refer to the economy itself as a pyramid scheme. In a country where GDP per capita is below subsistence, I would say that rapid, ideally accelerating, GDP growth is a moral mandate. It would be economically unjust if poor economies were not growing faster than rich ones, and for that matter if poor people were not "taking the jobs" of the first world proletariat. In so-called first-world countries, I'm not so sure. Perhaps our duty is to lead the way in addressing planetary concerns, rather than putting more chickens in every pot and more SUVs in every driveway.

From the website of the Center for the Advancement of the Steady State Economy:

Economic growth is an increase in the production and consumption of goods and services. For distinct economic or political units, economic growth is generally indicated by increasing gross domestic product (GDP). Economic growth entails increasing population times per capita consumption, higher throughput of materials and energy, and a growing ecological footprint. Economic growth is distinguished from “economic development,” which refers to qualitative change independent of quantitative growth. For example, economic development may refer to the attainment of a more equitable distribution of wealth, or a sectoral readjustment reflecting the evolution of consumer preference or newer technology.

They give the following definition: "A steady state economy is an economy of stable or mildly fluctuating size." Mildly fluctuating, I would think, would imply occasional mild recessions. At any rate, I don't realistically expect the economy to stop being cyclical in nature. Non-cyclical systems are characterized by positive feedback, which is to say, runaway growth, or as the teachers of Diff. E. Q. say, "blowing up."

I'd like to think we could take Schumpeter's idea of "creative destruction," but have it in a way that enterprises and not human individuals are what is destroyed by (necessary?) periods of economic contraction, obsolescence, failure to second guess demand, etc. As an added bonus, it would be nice if the characteristics of surviving enterprises are having product offerings more relevant to real needs, being more more responsive to changes in those needs, and more responsible about social and planetery needs,

Maybe use Calvert-Henderson Quality of Life indicators instead of GDP as the metric?

The Arthurian said...

In calculus, (dx over dt) is one infinitely small value divided by another. In econ the smallest time quantity that I've seen used for a "derivative" is one quarter of a year. Maybe that's valid, maybe it's not. I wouldn't know. But I'm not comfortable using calculus terminology to describe the butchery that economists do.

LL: "Net worth is measured in units of currency. Income is measured in units of currency per unit of time (dollars per year, perhaps)."
Yeah. MMT people talk in terms of "stock" and "flow". For example, stock is the amount of water in the bathtub at some point in time. Flow is gallons-per-minute flowing into the tub or draining out of it.
A stock accumulates over time. flows in and out can be used to calculate changes in the stock. So I guess the federal deficit is a flow that adds N dollars to the stock of debt during a year.
I'm getting to the good part.
A stock accumulates as the years go by. For example, debt does not reset to zero every year; it accumulates.
A flow does not accumulate beyond its time period. At the end of a year the amount of the deficit is added to the debt, and the deficit resets to zero.
Like the deficit, GDP is a flow variable that resets to zero with each new year.
Here is the good part: The federal debt accumulates as the years go by. But GDP resets to zero at the start of every year. THAT IS WHY THE FEDERAL DEBT IS SO BIG, RELATIVE TO GDP!
It's a stupid math game that both sides play, and neither side admits the fact.
(That does *not* mean the debt isn't a problem. It is a problem. But the way the game is set up, it is almost impossible to avoid the endless increase of federal-debt-relative-to-GDP, especially in a monetary system where money is created by *lending* it into existence.)

LL: "I'm guessing the GDP is the the first derivative of some kind of estimate of 'amount of wealth in existence.'"
Not sure how formal my definition is, but I define wealth as something that produces income. The debt that I owe is wealth to my creditor. A business is wealth because its purpose is to make a profit. And the Goose that lays golden eggs is wealth because the eggs are ... income.
GDP is not wealth like that. Some of the stuff in GDP is bought by businesses and used for making money; that part is wealth, at least by my standard. GDP was defined for me in econ class as "final spending". If Ford buys tires from Goodyear and puts them on the car you buy, the price you pay includes the price of the tires (plus a markup). Since the car is counted in GDP, tires and all, the sale of the tires to Ford cannot be counted in GDP as that would be "double counting".

Another way to figure GDP is to add up all the income (using strict economic definitions that I don't know) produced in making and selling the stuff we produce in a year. Again it is necessary to avoid double-counting.

That's too much for one sitting.

LL: "I can see that your complaint isn't that the GDP growth rate isn't itself growing, but that it has been shrinking (although remaining positive at most times)."
YES!! Thank you!

The Arthurian said...

LL: "If you're stating GDP growth as a percent, say i (what letter do economists use to denote this, btw? ..."

Vollrath discussing the Piketty inequality "r > g" identified "g" as "the growth rate of aggregate GDP"

But I don't know if that is standard practice.

The Arthurian said...

RE: "Regressing to primitivism" as a major problem...
I was thinking of the rejection of the covid vaccine as a typical example. The whole plan for economic improvement, from the political right, is to go back in time to the "free banking" era, a period of two and a half decades just before the civil war. Sound like a good plan to you?

The whole plan for economic improvement from the political left is not much different: a return to the more recent past of Keynes and Kennedy's Camelot.

Both views are (to say the least) backward looking. But we cannot restore the economy to some preferred past state unless we manage to change *every* relevant variable. No chance in Hell.

By contrast -- and JUST for contrast, I'm not trying to sell anything here -- I see the economy as a system that changes, usually gradually but pretty much all the time. The "Stages of Capitalism" thing.

I do not like the idea of regressing to a former state because time does not move backwards. I like the idea of *carefully* and *accurately* figuring out what the economic problems are, and the causes of those problems. And then applying carefully considered solutions in the present, to move to a better future.

Politicians are probably not the best people to have in charge of such things.

I should say also that by "economic problems" I mean the problems that make the economy respond in ways people don't like. Most people seem to think the things they don't like *are* the problems -- unemployment, inequality, things like that. I say those are the *consequences* of the problems. If we want the economy to behave in a certain way, we have to create the conditions that make it move in that direction.

The purpose of examining the past is to understand how things have changed and what is different now; and to examine the differences, looking for those that may be creating what we see as problems. Basically it comes down to gathering data on monetary balances and imbalances, and seeing imbalances as potential trouble spots. But words like "unemployment" and "inequality" seldom or never arise in such a study. So it goes.

As far as which jobs are "the non-bullshit jobs" it seems to me that in a thriving economy people would be able to make those decisions for themselves. What the answers might be, I certainly couldn't say. I know only that I am not qualified to make decisions like that for everyone, and I would likely generalize from this view.

If this response is a jumble of incoherent thoughts, I suppose it is because I don't spend much time thinking about such things. I gave it some time, but it didn't help much.