01 October 2012

Is US Per Capita GDP Growth in Decline?

UPDATE 10/2: Mislabeled graph fixed at the bottom of this post. Thanks to Mark Bahner in the comments!

In my column last week at The Breakthrough Institute on Robert Gordon's analysis of US per capita economic growth, I identified what I believe to be an error in his calculation of post-1950 growth rates. Such an error matters because Gordon's recent discussion paper has been called “the summer’s most talked about working paper in economics” and argues a data-based case for US decline. My view is that such discussions should at least start with a solid empirical basis and re-checking assertions grounded in data claims is fair game (not all agree, however).

Gordon has written the following to explain his main graph, which appears just below:
"Each of the successive periods after 1950 exhibits a downward step in per-capita real GDP growth, with steps downward marked at 1964, 1972, and 1987."
I cannot reconcile Gordon's claim with the actual data on the US economy. The data on growth rates (from BEA and US Census, which Gordon has confirmed to me as the correct datasets to use) shows the following rates of change in per capita GDP growth at the break points identified by Gordon:
1928 to 1950 - 2.4%
1950 to 1964 - 2.1%
1964 to 1972 - 2.9%
1972 to 1987 - 2.1%
1987 to 2006 - 1.9%
These numbers do not show successive downward steps in US GDP per capita growth rates from 1950. In fact, the peak is right in the middle of the periods, and otherwise the growth rates are very similar through the period. The calculation of trends on the time series is very sensitive to the start and end point chosen for analysis -- which should raise a red flag for chartist-based arguments.

This discrepancy between our analyses of the data explains why the linear trend I calculate from 1950 to 2006 shows a tiny decrease, essentially no decline, contrary to his sharp decline graphed in red in the figure above. The graph at the top of this post shows data from FRED from 1960 (start of that dataset) on US per capita GDP (plotted on a log scale).  Similarly, it shows no evidence of any stair-step decline in growth rates, certainly not a decrease by half illustrated in Gordon's graph.

I have invited Gordon to address the discrepancy in our datasets and help me to identify where I have made a mistake or perhaps if his data is in error. Readers are welcomed to chime in.

UPDATE: In the original graph posted at The Breakthrough Institute I showed ten-year growth rates for the Maddison dataset rather than the annual values as stated in the graph title. The annual values are shown below. There are no implications for the analysis -- the data is the same. Sorry for the error.


Barba Rija said...

"most talked"?

Really? I thought that the most talked about thing in economics this summer was the "infinite QE" suggestion that the FED ended up taking.

However, this paper seems very familiar to me. I've seen a very similar graph in the Olduvai Theory.

Whenever I see a graph of this kind I just smile and file under "tin foil hat stuff"...

Michael said...

I can't for he life of tease out Gordon's graph from GDP data. Where is the Great Depression? I found this logarithmic graph of GDP in dollars over time to be consistent with a near linear trend in percent growth. High r-squared value: http://www.singularity.com/charts/page99.html

Joshua said...

If you want to understand the recent decline, you need to consider the widespread phenomenon of attempting to perpetuate the unsustainable (short-term) returns realized through financial engineering prior to 2007 - gains that CFOs realized through irresponsible leveraging and deliberate and systemic under-evaluation of risk.
Also consider that the short-term mentality of believing that profits earned by differentially relying on cheap overseas labor inevitably has run up against the reality that such a profit-model is not sustainable long term. It offers no competitive advantage. People can always copy making profits from cheap labor, and the profits based on such a business model dry up as the economies grow in those localities that supply the cheap labor.

I don't think those trends are fully explanatory - but I don't see how any analysis that doesn't take them into account can be considered comprehensive.

For years, the "best and brightest" in the private sector gravitated to the exponentially growing financial sector - uninterested in the more mundane private sector activity of building sustainable long-term business models by selling good products at a good price.

These are real changes. Projecting economic growth going forward fails to address these systemic changes in economic processes at a macro-level. I doubt that growth is dead. But while simply projecting from past trends may in the end prove to be correct, it is basically coincidence if you haven't accounted for why systemic changes may very well, indeed, diminish future economic growth.

Mark B. said...

"the reality that such a profit-model is not sustainable long term. "

Someone doesn't know - in the long term, we're all dead. Nothing is sustained long term - and nothing has to. We do not live in a static world.

n.n said...

How does debt accumulation (e.g. federal, bonds, etc.) affect analysis of GDP changes? Is it a positive, negative, or neutral component of GDP assessment?

n.n said...

How do we assess GDP changes which are the result of short-term incentives or favorable conditions? For example, we are beneficiaries of substandard civil, labor, and environmental conditions in China. However, there is evidence that discontent with the communist leadership is growing among the Chinese, along with traditional resistance to that form of governance.

Are we prepared to pursue domestic resource recovery and production when external resources become limited or unavailable? It seems that we are not. Many people do not realize that policies such as "green" or renewable energy do in fact have consequences for the environment and people. Most of the negative aspects are out-of-sight and out-of-mind, and the remainder do not encourage discussion in public forums.

It seems that climate change is the least of our concerns. The redistribution schemes, domestic and foreign, those motivated by the "global warming" campaign, etc., have shorter sustainable lifetimes, and the consequences of those games are now evident and undeniable. The result has been a progressive corruption of individuals, institutions, and culture.

Joshua said...

"Someone doesn't know - in the long term, we're all dead. Nothing is sustained long term - and nothing has to. We do not live in a static world."

Mark - For the sake of argument, let's just say that you agree with me: The economic growth we saw for the decade or two prior to 2007 - as reflected in the huge growth in the financial sector along with a significant decline (as a % of GDP) in the manufacturing sector - was largely based on an increased influence of a short term focus on returns on risky investments, massive leveraging of assets to invest, etc.

Is it really true that you would say that relying on growth from such practices would not be ill-advised?

Do you really think that that the crises (and lack of growth) from 2007 'till now is unrelated to the phenomena I am talking about?

Mark Bahner said...


Here are *world* per-capita GDP growth rates for 1900-2000, and then projected from 2000 to the year 2100 (by Arnold Kling, Jesse Ausubel, Wilfred Beckerman, and me).


Roddy said...

Roger, am I being banal or would a rolling chart of GDP per capita growth over prior period, say decade, not show trend fairly well?

I don't understand how you can pick periods of such different lengths, and look for steps and breaks, I could do that for the fortunes of Tottenham Hotspur? On which subject :) :) :)

MattL said...

-7- Joshua,

I agree that there are some unsavory things about the recent past. However, I think the problem wasn't so much the focus on financial means of profit itself, but the distortions (e.g., easy money, giving legal but ultimately illegitimate authority to ratings agencies, morally hazardous bail outs that often flouted the rule of law) created by governments that magnified and in some ways created the bubble.

Until you get rid of the people, I don't think you can get rid of the bubbles. But we can hope to stop enacting policies that exacerbate them.

Roger Pielke, Jr. said...


Thanks ... I agree, and here is that chart:


The "periods of different lengths" are straight out of Gordon's paper.

And yes, very nice work Spurs, 23 years is a long time and I'm happy for Dempsey;-)

Mark Bahner said...

Hi Roger,

I don't seem to get the same values for Maddison that you have on this chart:


...if I use the data from Googling: "Historical statistics of the World Economy 1-2008 AD"

Your graph for Maddison is much more flat around 2 percent than my graph of the data is. For example, I get growth rates for the 1960 to 1970 time period as shown below, where the first column is the year, the second column is GDP per capita (1990 International Geary-Khamis dollars), and the third column is the growth rate from the previous year:

1960 11,328 0.88
1961 11,402 0.65
1962 11,905 4.41
1963 12,242 2.83
1964 12,773 4.33
1965 13,419 5.06
1966 14,134 5.33
1967 14,330 1.39
1968 14,863 3.72
1969 15,179 2.13
1970 15,030 -0.99

I don't have time right now to check the values for the periods in the paper.

Best wishes,

Roger Pielke, Jr. said...

-12-Mark Bahner

Thanks ... I see that I was unclear in that graph. The Maddison data shows previous ten-year growth rates.

However, as Gordon has confirmed to me that his numbers are BEA NIPA 1.1.6 divided by population (US Census), the Maddison numbers are less relevant for this critique.


Roger Pielke, Jr. said...

-13-mark bahner

Updated graph above and here:


Mark Bahner said...


Hi Roger,

Ah, good. I figured there was some sort of smoothing going on.

I only commented because of my own work on the prospects for world economic growth, e.g.:


That work was based on an initial interesting exercise in which I sent an email to about 30 people, asking them to submit their predictions for economic growth in the 21st century. I don't recall exactly who the 30 were, but I'm pretty sure the list included Robert Solow, Robert Lucas Jr., and Herman Daly. (So it was a very broad sampling. ;-))

It was a bit disappointing to only get three responses, but interesting nonetheless:


...with Jesse Ausubel and Wilfred Beckerman basically predicting a growth rate essentially the same as the world growth rate from 1900 to 1950, and Arnold Kling predicting a huge jump in the 2020-2040 time frame. I was between those varying predictions.

My subsequent calculations of the number of "human brain equivalents (HBEs)" added each year by personal computers has led me to think that Arnold Kling's prediction is likely to turn out amazingly prophetic. The only criticism I would have at this point is that the knee in the growth rate curve is likely to be even sharper than he predicted. By my calculations, the number of HBEs added each year are:

1 million in 2015
1 billion in 2024
1 trillion in 2032

So I think that, somewhere between approximately 2020 and 2030, world per-capita GDP will begin increasing at over 10 percent per year. If it does, Arnold Kling should definitely get a Nobel Prize in Economics. (But he probably won't. Nobel politics! ;-))

It is astonishing to me how little the economics profession appears to understand the profound impact on economic growth that’s likely to occur as the result of inexpensive human-level artificial intelligence.

Best wishes,

Mark Bahner said...

Hi Roger,

You had the following breakdown for U.S. per-capita growth rate, based on BEA and U.S. Census:

1928 to 1950 - 2.4%
1950 to 1964 - 2.1%
1964 to 1972 - 2.9%
1972 to 1987 - 2.1%
1987 to 2006 - 1.9%

I've finally had the chance to get the following, based on Maddison's data (obtained by Googling: "Historical statistics of the World Economy 1-2008 AD"):

1928 to 1950 - 1.7%
1950 to 1964 - 2.1%
1964 to 1972 - 2.8%
1972 to 1987 - 2.1%
1987 to 2003 (data to 2006 not available) - 1.8%

As should be no surprise to anyone, the results are very similar using the Maddison data, because your re-graphed values (using annual Maddison data) are essentially identical to the BEA/US Census results for the 1950-2006 period.

One curious result is that the time period when the Maddison and BEA/US Census are most different is from 1928 to 1950. Maddison has a per-capita GDP value of $6569 for 1928 and $9561 for 1950, for an annual growth rate of 1.7%, by my ciphering.

So using Maddison's data produces results that are even *less* like Robert Gordon's graph. Robert Gordon is clearly wrong. So it's highly unfortunate that it's "the summer's most talked-about working paper in economics."

Perhaps more importantly, his projections for the future ("continuing" decline in per-capita growth rate for the U.S.) is probably very, very wrong.

Someone needs to point the economics profession to Julian Simon's observation that (free) human minds are what create wealth, and to Ray Kurzweil's observation that very shortly computers will approach (and then vastly exceed) human minds.

Best wishes,

Post a Comment

Note: Only a member of this blog may post a comment.