Arnold Kling  

Nonlinear Thinking

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Mark Bahner writes,


So we have "the economic literature" with a per-capita GDP mean value in 2100 of $22,900, versus Arnold Kling saying over--way over, in fact!--$20,000,000. What in the world is going on?! Is Arnold Kling a lunatic or completely ignorant, such that he's off by *more* than a factor of 1000?

I don't think so. I think he's right (plus or minus a factor of 10).


The standard literature sees annual economic growth rates of two percent or so. I am thinking that in the middle of this century the growth rate will hit ten percent. Of course, that cumulates to a big difference.

In looking at the future, I tend to agree with Ray Kurzweil, who these days is known for his goal of immortality.


At MIT last week, Kurzweil described a future in which he's convinced immortality--or a drastically longer life span--will be possible thanks to emerging technologies. His new book, which will hit stores in a few weeks, outlines a special "longevity program" of diet, exercise and nutritional supplements aimed at slowing the aging process.

See my essay on Nonlinear Thinking, chapter 16 in Learning Economics.

My thought process is actually quite simple: Economic growth has accelerated in each of the last three centuries. There is enough potential in biotech, nanotech, and computer tech to make it possible for growth to accelerate further.

UPDATES: For some historical perspective, Bruce Bartlett emails me this link to Angus Maddison's data.

For more nonlinear thinking, see Robin Hanson.


Economists’ best estimates of total world product (average wealth per person times the number of people) show it to have been growing exponentially over the last century, doubling about every fifteen years, or about sixty times faster than under farming. And a model of the whole time series as a transition from a farming exponential mode to an industry exponential mode suggests that the transition is not over yet - we are slowly approaching a real industry doubling time of about six years, or one hundred and fifty times the farming growth rate.

...It seems that each new growth mode starts when the previous mode reaches a certain enabling scale. That is, humans may not grow via culture until animal brains are large enough, farming may not be feasible until hunters are dense enough, and industry may not be possible until there are enough farmers.

...I cannot help but wonder: are we in the last mode, or will there be more?

If a new growth transition were to be similar to the last few, in terms of the number of doublings and the increase in the growth rate, then the remarkable consistency in the previous transitions allows a remarkably precise prediction. A new growth mode should arise sometime within about the next seven industry mode doublings (i.e., the next seventy years) and give a new wealth doubling time of between seven and sixteen days.


The link to Hanson was forwarded to me by Alex Tabarrok, under the heading, "Arnold Kling is a pessimist!!"

For Discussion. If in 1900 you had used previous economic growth to predict growth in the twentieth century, how far wrong would you have been?


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CATEGORIES: Growth: Consequences



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The author at Muck and Mystery in a related article titled Micro Macro writes:
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COMMENTS (18 to date)
Steve writes:

Real GDP 1800-1900: 3.97%
Real GDP 1901-2000: 3.34%

So you would be wrong by 63 BPS according to
http://www.eh.net/hmit/gdp/gdp_answer.php.

Even though 200 years is a long period, isn't this representative of a one-time shift, i.e. industrialization, modern healthcare IT etc.? Concievably there are future economic shifts of a similar magnitude in the future (for example one could imagine the results of a technology that gave energy the same sort of deflationary returns that the semiconductor industry provided from 1970-2000). However, 500 years of 3% real GDP growth would give a per capita GDP on par with Bill Gates today (around $60 billion). Is this realistic to assume? As an analogy one could reasonably argue that in many ways an individual making 22,900 today has a level of material wealth that surpasses any Roman Emperor (just go to the doctor or dentist to prove this). However this person certainly cannot afford a palace on the island of Capri or to personally outfit a couple of army divisions.

Mark Bahner writes:
If in 1900 you had used previous economic growth to predict growth in the twentieth century, how far wrong would you have been?

Hi,

I think we need to set this up a bit. Assuming I'd had a Brad-DeLong-type analysis in 1900, I'd know these world GDP per capita values (expressed in 1990 dollars), and these resultant percent annual per capita GDP increases (for the previous period):

Year....GDP/cap.......ann. chg., pct.

1600.....141.............

1650.....150.............0.12

1700.....164.............0.18

1750.....178.............0.16

1800.....195.............0.18

1850.....300.............0.87

1900.....679.............1.65

If I draw a straight line through the last 3 points, I get a line that crosses 3.2% per year at the year 2000. So the average percent annual growth for the the century from 1900 to 2000 would be (1.65 + 3.2)/2 = 2.43 percent per year. That produces a world GDP per capita of $12,200 in 2000.

But the average growth in the 20th century was more like 2.29% per year, producing a world GDP per capita in 2000 of only $6539.

D-oh! I blame the commies and Nazis. (And hippies. I hate hippies. ;-))

Actually, that's not bad at all for a prediction. The thing is, if I extend that straight line up to 2100, I get a percent per year increase in 2100 of 3.2 + 3.1 = 6.3% per year. So that makes the average per capita GDP growth in the 21st century "only" 4.75%...producing a per-capita GDP in 2100 of "only" $678,000.

Oh! Another thought...

If I plug in the actual values for 1950 and 2000, I get

Year.......GDP/cap......% ann growth

1900.........679

1950........1622...........1.76

2000........6539...........2.83

Now a straight line starting from 1800 only produced a predicted annual growth in 2100 of about 4%, with an average for the 21st century of 3.3%.

That produces a GDP per capita in 2100 of only $168,000.

Better quit before I depress myself too much. Or put myself to sleep...as I'm sure I have everyone else.

Mark (King of Geeks)

Robert Schwartz writes:

If I have to pick a model its not going to be a linear exponential model based on a simple compound interest formula.

I would pick a model that produces a yeast growth curve. i.e. an elongated S. There is some upper bound on production, it may be enviromental carrying capacity, it may be the availibility of labor (birth rates drop as GDP goes up) or it may be the limit on the time of consumers have to consume; But there is an upper bound and GDP growth will reach it.

Arnold KLing writes:

I don't think Steve's source is consistent with other data I've seen (not that it's easy to be definitive about historical GDP data, so that's understandable). But look at DeLong's data, which I copied here: http://arnoldkling.com/econ/book/growth/growthfacts.html

GDP per capita grew more quickly from 1900 to 2000 than from 1800 to 1900, as Mark Bahner calculated.

Mark, if someone in 1900 had decided to extrapolate a nonlinear trend, they would have had a high estimate. But with a linear trend, they would have under-estimated.

I think that the limits-to-growth argument does not hold, at least in the foreseeable future. Too many technological opportunities out there.

Mark Bahner writes:
I don't think Steve's source is consistent with other data I've seen (not that it's easy to be definitive about historical GDP data, so that's understandable).

Steve seems to be giving numbers for GDP, rather than GDP per capita. Plus, the site he references is for the United States, not the world.

If one uses the "real GDP/capita" box at that (neat!) site, one gets:

1800....$1420

1900....$4310

2000...$34758

That would be about 1.1% per year from 1800 to 1900, and almost exactly 2.2% per year for 1900 to 2000.

Mark, if someone in 1900 had decided to extrapolate a nonlinear trend, they would have had a high estimate. But with a linear trend, they would have under-estimated.

Actually, extending a linear trend based on data from 1800 to 1900 out to 2000 gives me 2.43% per year, which is almost exactly equal to the 2.29% per year that occurred during the 20th century.

NOTE: I goofed in my previous numbers (going quickly, not checking work). I wrote that 2.43% per year would increase the $679 in 1900 to $12,200 in year 2000. But it actually works out to $7500 in year 2000, which is very close to the $6539 that actually occurred.

So a linear extrapolation was a very good method to use to predict growth in the 20th century. And even using the most conservative (yielding lowest GDP) linear extrapolation to 2100 gives a world per capita GDP of $168,000 in 2100. I think that's going to be way, way lower than the actual value. And apparently, that's way *above* the value found by the IPCC in the "economic literature." So either the IPCC is looking in the wrong literature, or you (and Robin Hanson) are the only pros out there, Arnold. :-)

I would pick a model that produces a yeast growth curve. i.e. an elongated S. There is some upper bound on production, it may be enviromental carrying capacity, it may be the availibility of labor (birth rates drop as GDP goes up) or it may be the limit on the time of consumers have to consume; But there is an upper bound and GDP growth will reach it.

I definitely don't see any limit on carrying capacity...not on populations that we are likely to experience in the next 100 years.

I don't see birth rates dropping enough to crash the population in the next 100 years. I figure we'll stay between 6 and 12 billion the whole century.

Regarding the time of consumers to consume...unless we achieve Ray Kurzweil's immortality, there would be that limit. But consumers can consume an awful lot. For instance, I wouldn't mind trading in my perfectly acceptable $120,000 townhome for something costing 10 or 20 times as much...if I was making about 10 or 20 times what I'm making right now. And I wouldn't mind trading in my generally nice 13 year old Beemer for a brand new Lexus. (Plus a minivan for hauling stuff.) And then there is the possibility of vacations in Hawaii every year. Ooh...and LASIK surgery. So I can think of plenty to spend money on. :-) (Even though I've already got more junk than I really need.)

So I don't see what the production limit is. Especially as computers reach--and then shoot way past--the capacity of the human mind. That will make the "effective" human population approach infinity.

Mark Bahner writes:
Mark, if someone in 1900 had decided to extrapolate a nonlinear trend, they would have had a high estimate. But with a linear trend, they would have under-estimated.

Oh! I just realized what you meant by "linear." You meant, "GDP per capita goes from $300 in 1850 to $679 in 1900, so it will go up by another $379 by 1950, and another $379 to 2000."

Yeah, they'd definitely be way low doing that. Whada bunch of amachures!

:-)

Austin writes:

Over the past 5000 years, there was only one big change in the rate of productivity growth and that was in the mid 1800's.

If I imagine myself as an economist in the year 1504, I would be pretty excited. The printing press had been around for a while, and it is pretty revolutionary. Similar to the computer, it is a tool that completely changed communication and learning.

However, the printing press turned out to be just a really big step in a series of steps until the industrial revolution.

It seems like the computer is also a really big step in a series of steps until the next revolution.

Maybe the next economic revolution will be like Kurzweil's idea. Maybe the revolution will happen in the next 50 years. Neither will probably happen because predicting a economic revolution that far in the future is nearly impossible.

spencer writes:

I suspect there is a major flaw in the thinking behind this line of analysis. It is the problem
of the difficulty of being first. The bulk of the last 200 years of growth has been concentrated in N. America , Europe and Japan.
Now, other areas can learn and borrow from the early developers. China can grow much faster over the next 50 years than N. America ever did because they are second, consequently their growth does not depend on new technology developments. They can grow fast just by starting to use already existing technology. Thus, if you are looking at the world growth rate you should be able to project much faster growth over the next century than the past century even if growth in the developed world does not accelerate.

Mark Bahner writes:
Thus, if you are looking at the world growth rate you should be able to project much faster growth over the next century than the past century even if growth in the developed world does not accelerate.

Yes, this is an important concept, and can already be seen from the 20th century data. Germany and Japan grew tremendously after those countries were practically reduced to rubble/ashes at the end of WWII (e.g., Hiroshima, Nagasaki, Tokyo, Dresden, Berlin, etc.).

Similarly, now that mainland China and India have given up most of their failed socialist economic policies, they are growing remarkably fast.

In other words, in previous centuries, if a city or country was destroyed, it would could only prevailing, much lower, economic level. In the 1700's, for example, even the most advanced countries only had per capita annual GDPs of $1000 to $2000 (expressed in 1990$).

Now, the most advanced countries have per capita annual GDP's of $30,000 to $40,000. So coming from a per capita GDP of, say $300 per year, is now a factor of 100+...where in the 1700s it would only have been a factor of 3+.

Which brings me back to my original point, that the IPCC (Intergovernmental Panel on Climate Change), and the "economic literature" that they quote, spectacularly underestimate the likely economic growth in the 21st century:

Second thoughts on economic growth in the 21st century

Mark Bahner writes:
In other words, in previous centuries, if a city or country was destroyed, it would could only prevailing, much lower, economic level.

Oops. That should have read:

"In other words, in previous centuries, if a city or country was destroyed, it could only grow to the prevailing, much lower, economic level."

Eyvind Hillblom writes:

Robert Schwartz wrote:

If I have to pick a model its not going to be a linear exponential model based on a simple compound interest formula.

Exactly.

Even though GDP growth is normally presented as a percentage, we have to keep in mind that this is just an ad hoc measure. This way of tinking about growth gives rise to an implicit exponetial model.

Before making predictions, please motivate why GDP growth should be exponential.

I bet that you can't.

pragmatist writes:

The big invention of the 20th century was NOT the computer.

The big invention of the 20th was the
transistor.

This tiny device has been the driver of the
incredible economic growth we have since
in the second half of the 20th century.

Computers - and every other electronic device -
have become significantly more efficient because
of the transistor.

Mark Bahner writes:
Before making predictions, please motivate why GDP growth should be exponential. I bet that you can't.

As I pointed out in my comments, GDP per capita HAS been growing not merely exponentially, but what Ray Kurzweil would call "double exponentially" for more than 200 years.

That is, GDP/capita hasn't merely increased at the same percentage (which would be exponential growth) but the percentage increase has actually gotten larger over time.

Given that fact that this greater-than-exponential growth has been happening more or less steadily for the last 200+ years, I don't think the burden of proof is on those who say that the trend will continue...the burden of proof is on those who say it will stop.

But a reason GDP/capita might grow exponentially is because new knowledge is gained faster than old knowledge is forgotten. People each generation see farther than the generation before, because they stand on the shoulders of giants. For example, we don't have to have the brilliance of Einstein to come up with the implications of Special and General Relativity, because Einstein did that for us (thank goodness).

Eyvind Hillblom writes:

The burden of proof should be on the one who makes the prediction. I believe this "extrapolation game" to be entirely futile. It is also unscientific since it does not explain anything and is not falsifiable.

Of course, if the reason for the modelling is to point to the meninglessness of the predictions in "the economic literature" I see the point.

John Johnson writes:

I've been doing statistics for around 8 years, and, in that time, no model I have used has been correct. Does this mean that I have spent 8 "futile" years? Of course not, because those models have given me insight I didn't have before applying them.

By the same token, no one is pretending that this "extrapolation game" will produce correct results or perhaps anywhere near correct. However, I does make us stop to think about the history of economic growth and its relationship to technology, among other things. And that is valuable.

Dez Akin writes:

I'm afraid that those who dismiss the notion we are headed for a revolution in productivity are discounting the importance of AI on the labor pool. Some time over the next fifty years, we will develop artificial intelligence with the capacity of a human. Then the labor pool is only bounded by capital investment rather than any real physical constraint, which has never happened in history. Economic analysis of removing this constraint indicate annual growth rates of around 40%...

Whether this leads to a paradise of wealth on the backs of robot slaves or terminator bots exterminating useless humans is the topic of another discussion.

Mark Bahner writes:
The burden of proof should be on the one who makes the prediction.

*Everyone* is making predictions, Eyvind. I'm making predictions. Arnold Kling is making predictions. I'm making predictions. (My predictions are now so similar to Arnold’s predictions that it probably doesn't really matter, other than to note that my predictions have changed to more closely match his.)

The IPCC is making predictions. (Only they're faux scientists, and call them "projections"...so when their predictions don’t come true, they will claim it doesn't matter.) The "economic literature" is making predictions.

What are your predictions?

You seem to be predicting that GDP/capita will *not* grow exponentially in the 21st century. If not, what will happen to it? Will GDP/capita switch to arithmetic growth? Will it level off at some value? Will it fall?

I believe this 'extrapolation game' to be entirely futile.

Actually, the "extrapolation game" is merely the method I use to show why per-capita GDP growth in the 21st century will be higher than it was in the 20th century. The “extrapolation game” just points to an average annual per-capita GDP in the 21st century of about 3.3% (using a straight line extrapolation based on data from both the 19th and 20th century. I rely on Ray Kurzweil’s knowledge of the development of computers to project per-capita GDP growth to be 3% from 2000-2010, 5% from 2010-2020, 7% from 2020-2030, and 10%+ thereafter.

It is also unscientific since it does not explain anything...

Not all models are intended to yield a fundamental understanding of the system being modeled. The people who first used compasses almost certainly didn't know that the earth had an iron core. They just knew that a needle suspended with very little friction always points in one direction (north). That doesn't make the maps that they made any less "scientific." The important thing was that the compass gave accurate and repeatable readings.

...and is not falsifiable.

Au contraire! The predictions Arnold Kling and I have made are easily falsifiable. If per capita GDP growth doesn't average 3% per year from 2000-2010, and 5% from 2010-2020, and 7% from 2020-2030, and 10%+ thereafter, I'll readily admit my model was wrong. Conversely, if economic growth does behave that way, I'd say the "economic literature" will have been proven wrong. Spectacularly wrong, in fact.

Saxdrop writes:

Regarding Kurzweil:

"I don't want to achieve immortality through my work... I want to achieve it through not dying."
--Woody Allen

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