3rd thoughts on 21st century economic growth

Arnold Kling asks the question:

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

Geez, he's good! I hope the kids he teaches appreciate that! :-) That got me thinking (that's what good teachers will do for you), and led me to prepare the following:

1) A table of the annual per capita GDP growth for the period from 1600-1900 based on DeLong (1998):

Time period...Percent Annual Per Capita GDP Growth

1600-1650.......................0.12
1650-1700.......................0.18
1700-1750.......................0.16
1750-1800.......................0.18
1800-1850.......................0.87
1850-1900.......................1.65

2) Plot those six data points, with the end year on the x axis, and the percentage annual growth on the y axis.

3) Then, draw a straight line regression through the last three data points. The regression line gives an equation of y = 0.0146x - 26.195. If I plug in the year 1950, which is the middle of the 20th century, I get an annual per capita GDP growth rate of 2.28 percent.

So that's what my prediction of the average per capita growth rate for the 20th century would be, based on the data up to the year 1900.

So what was the actual annual per capita GDP growth rate for the 20th century? It was 2.29 percent! In other words, I would have been virtually dead-on...accurately predicting per capita growth in the 20th century, based on data up to 1900.  Smokin'!

4) What would that regression line do for predicting growth rate in the 21st century? To get that answer, we plug the year 2050 into the equation y = 0.0146x - 26.195. We get an average annual per capita world GDP growth for the 21st century of 3.74 percent.

5) That got me to thinking that I ought to add the data from the 20th century to the 6 data points I had previously. The data points for the 20th century are:

Time period...Percent Annual Per Capita GDP Growth

1900-1950.......................1.76
1950-2000.......................2.83

6) Now, determine a regression line for the five data points ending in years 1800, 1850, 1900, 1950, and 2000. The regression equation is y = 0.124x - 22.033. Plugging in the year 2050, we get a world average annual per capita GDP increase for the 21st century of 3.39 percent.

The whole mess looks like this:

.
.
.
.
.
.

.

7) But even in the face of this information, I'm going to rely on the analysis of Ray Kurzweil. I'm going to expect that computers will be comparable in ability to a human brain in the 2020-2030 time frame. So I'm going to boost my predictions of per capita (P/C) economic growth for the 21st century way beyond those I made in December 2003. My new predictions are:

Time..........Annual P/C GDP growth...Annual P/C GDP growth
Period..........Oct 2004 prediction......Dec. 2003 prediction

2000-2010................3.0...........................2.5
2010-2020................3.5...........................3.0
2020-2030................4.5...........................3.5
2030-2040................6.0...........................4.0
2040-2050................8.0...........................4.5
2050-2060...............11.0...........................6.0
2060-2100........the differences keep growing...!

8) When I plot my new (October 2004) predictions with my old (December 2003) predictions, as well as the extrapolation of the linear regression from the 1800-2000 data...and the predictions of Arnold Kling, Wilfred Beckerman, and Jesse Ausubel...I get this mess:

.
.
.
.
.
.
.
.
Or expressing it in per capita GDP, rather than per capita GDP growth rate, I get this:

.
.
.
.
.
.
.

Executive Summary

Economic growth in the 21st century will be spectacular. Growth will be way beyond anything in the "economic literature," as reported by the IPCC. By the end of the century, average world per-capita GDP will be well over $20,000,000 per year. In fact, world per-capita GDP will cross $100,000 sometime around 2050. This has huge implications for just about every aspect of thinking about the 21st century. More on the implications later. (I know I promised to discuss implications at the end of my "second thoughts"...but I really mean it this time.)

Comments

[John Baltutis]

Just a couple of questions.

You wrote: "…draw a straight line regression through the last three data points"; why not use all of them?

and "…what was the actual annual per capita GDP growth rate for the 20th century? It was 2.29 percent!"; based on what source? Adjusted for inflation?

[Mark Bahner]

Hi John,

You ask, "why not use all of them?" (i.e., including the data points for the periods ending in the year 1650, 1700, and 1750).

I didn't include the data points for the periods ending in 1650, 1700, and 1750 because they would not have fit well (using a linear regression line) with the three data points for the periods ending in 1800, 1850, and 1900.

If you look at the first figure in my post, the linear regression line for the the three data points for the periods ending in 1800, 1850, and 1900 has an "R squared" of 0.9985, which is an incredibly "tight" fit.

It also makes sense not to include the data points for the periods ending in 1650, 1700, and 1750 for another, historical reason: all those points are before the Industrial Revolution. It appears from plotting the data that the Industrial Revolution significantly increased the world per-capita GDP growth rate. That makes sense, since the Industrial Revolution freed people from subsistence farming, allowing them to do many new wealth-producing jobs (e.g., boilermaker, automobile assembler, textile factory worker).

You also ask what my source is for the calculated per capita GDP growth rate in the 20th century of 2.29 percent. That's from Brad DeLong's work:

http://www.j-bradford-delong.net/TCEH/1998_Draft/World_GDP/Estimating_World_GDP.html

And you ask if that figure includes an adjustment for inflation? Yes, it does. All Brad DeLong's numbers are adjusted for inflation to year 1990 dollars.

[bill yarberry]

Excellent blog. I was looking for statistics on the growth of factory worker output from 1900 until now but this is helpful too. I'm writing a book about Information Technology Governance.

I like Kurzwell's stuff. Even if robots never get generally smart like humans, they'll be able to do so much anyway that the effect on our standard of living will indeed make us wealthy, maybe even third world countries.

[Tim Curtin]

Mark, More exponential power to your elbow! You are just a bit conservative relative to Moore's Law. Yours is the best blog I know, and I love your postings on the dismal Tim Lambert's Deltoid.

[rawgreenpower]

Having once been involved in the development of fore casting models for Canada at a senior level a num,ber of false assumptions always led to very false predictions even as the model became more and more complex!

These miscalculations if you will are especially difficult to explain in terms for example of the diminishing of per capita income in the so called Third World whose per capita income is badly out of sync for example with Korea which has managed to raise its per capita income primarily to 20,000 in the last fifty decades.
But only at extraordinary socio cultural cost , and it would now appear to be in such a downturn that it will never get out of it.

In the mean time they have over exploited every conceivable form of resource including their human resource -- so that one after another indicator shows the highest stress levels in the world.

The difficulty when North KOrea implodes will compounf regional security thereby affecting all the so called growth states!

[GK]

I personally believe in the linear regression line. Why would it be anything other than that, particularly based on the history of the last 200+ years?

Does that line change much if you take the linear regression back 500 years, to 1500 AD?

All of Kurzweil's predicted innovations can be included in the linear regression line, and in fact are a necessary part of it. I think Arnold Kling's forecast is just too optimistic.

[Mark Bahner]

Hi GK,

You write, "I personally believe in the linear regression line. Why would it be anything other than that, particularly based on the history of the last 200+ years?"

The reason it would be different is that computer intelligence will very shortly (i.e., within the next 2-4 decades) equal and then exceed human hydrocarbon intelligence.

See my post here:

http://markbahner.typepad.com/random_thoughts/2005/11/why_economic_gr.html

From the graph in that post, I calculate that the total brainpower of all personal computers added in 1996 was only equal to ONE human brain. That's because even though 200 million personal computers were added, because they were dumber than cockroaches, they didn't add much to total world intelligence.

However, I calculate that by 2033, the total brainpower added by personal computers each year will be equal to ONE TRILLION human brains (i.e., more than 100 times greater than the entire population of the world).

It's this exponential astounding increase in computing power that will boost economic growth to much higher levels than mere extrapolation from the last 200 years.

"Does that line change much if you take the linear regression back 500 years, to 1500 AD?"

Yes, the line didn't start going up (i.e., an increase in the percentage growth) up until about 1800. See this graph:

http://markbahner.typepad.com/photos/uncategorized/per_capita_gdp_growth_1650_on_rev1_1.JPG

"All of Kurzweil's predicted innovations can be included in the linear regression line, and in fact are a necessary part of it."

No, I don't agree. The extrapolation of the linear regression line can't take the exponential growth of computer intelligence into account because the last data on the graph is for the 50 years ending in the year 2000. In that period, computers were simply too dumb to have any substantial effect on the economy.

That won't be the case in the coming decades. In the coming decades we'll see computers as:

1) drivers of cars and buses,
2) airplane pilots,
3) checkout attendants at grocery stores,
4) short order cooks and cashiers at fast food resturants,
5) construction workers and road builders,

... and eventually:

6) scientists,
7) engineers,
8) basically anything humans can be.

This will tremendously boost economic growth.

For example, suppose you have a house that's built by a crew of 6 people being paid $30,000, working for 1 month to build a house. That means it costs you $15,000 in labor to build that house.

Now suppose you have a house that's built by a crew of 6 robots, each costing $10,000 (and lasting 10 years), and costing $200 a month in energy and maintenance, working for the same month. Well, that brings the cost down to less than $1500 in labor to build the house. That's a huge improvement.

"I think Arnold Kling's forecast is just too optimistic."

Economist Robin Hanson thinks that Arnold Kling's forecast may not go up quickly enough. Robin Hanson thinks the curve will go up even more sharply (though he doesn't know when).

I think that if we see even a couple years of world per-capita GDP growth above 5 percent before the year 2020, I'll be even more convinced that Arnold Kling is right. And if in the 2020-2030 time frame, if we see a couple years abouve 6 percent per year, I'll be virtually certain he's correct.

Mark

[GK]

Mark,

That is not a compelling argument.

You yourself said that Arnold Kling stated that if you were in the year 1900, and took the data to predict where per-capita GDP would be in 2000, it could be predicted with a lot of precision.

The growth from 1900 to 2000 was predictable PRECISELY because the rate of technological change was predictable. All the inventions of the 20th century are what enabled STAYING at the trendline.

The same goes for Kurzweil's predictions. All those advances are part and parcel of keeping up with the linear regression line. If 1900 to 2000 did not deviate from the linear regression, it is naive (in a dot-com bubble sense) to assume that the 21st century will magically deviate from the linear regression.

You said :

"... and eventually:

6) scientists,
7) engineers,
8) basically anything humans can be."

Then why do they need us at all, much less maintain us and make us wealthy? I see them doing to us what humans have done to whales, elephants, and tigers - displacing us.

Even with the linear regression, the magical $100,000 line is still reached only 40 years later than Arnold Kling. 40 years is nothing amidst thousands of years of human civilization.

[Mark Bahner]

GK,

"You yourself said that Arnold Kling stated that if you were in the year 1900, and took the data to predict where per-capita GDP would be in 2000, it could be predicted with a lot of precision."

Ummm...no. That's not what I said at all.

Arnold Kling never "stated" anything at all. Arnold Kling asked a question, he didn't make a statement. Specifically, he asked, "If in 1900 you had used previous economic growth to predict growth in the twentieth century, how far wrong would you have been?"

I took that question and made what might have been a plausible prediction in 1900 for 2000. It HAPPENED to be pretty accurate.

But just because the trend from 1800 to 1900 continued from 1900 to 2000, doesn't mean that the trend is going to be the same from 2000 to 2100. It might continue at the same rate from 2000 to 2100, but there is no physical law or other reason that says it has to.

You comment about robotic artificial intelligence, "Then why do they need us at all, much less maintain us and make us wealthy? I see them doing to us what humans have done to whales, elephants, and tigers - displacing us."

Well, that's certainly a possibility. It's certainly possible that once artificial intelligence gets way advanced compared to human hydrocarbon brains, the artificial intelligence will simply decide to get rid of us. We'll definitely be in deep doo-doo if that happens, because presumably their brains and bodies would be so advanced that we would be essentially powerless to stop them.

"Even with the linear regression, the magical $100,000 line is still reached only 40 years later than Arnold Kling. 40 years is nothing amidst thousands of years of human civilization."

Yes, I certainly agree that considering the whole timescale of human civilization, the timescale is extremely short. But whether the growth is like Arnold Kling and I think, or whether it follows the more slowly rising linear regression makes a difference to the Baby Boomers and Generation X people. If the growth is as fast as Arnold Kling and I think, even the Baby Boomers and Generation X people should be OK in their retirements.