Economic growth and convergence

One of the main predictions of standard neoclassical growth models is convergence. If there are diminishing returns to capital, countries that have relatively higher levels of capital will have lower rates of return on investment than will countries in which capital is relatively scarce. Since poor countries offer higher rates of return on investment, they will accumulate capital at a faster rate - and will eventually catch up to rich-country levels of income.

Unfortunately for the model, empirical evidence in favour of the convergence hypothesis appears to be pretty weak. Here is what you get when you look at the relationship between income levels in 1950 and average growth rates over the period 1950-2001 for the 146 countries for which data are available (source is Angus Maddison's estimates):

If convergence was occurring between 1950 and 2001, the relationship between initial income and average growth rates should be negative: countries that were relatively poorer in 1950 should have had higher growth rates, so that they might catch up to richer countries. But the estimated relationship above is essentially zero.

Upon closer examination, things start to look a little odd. I've plotted an handful of countries whose importance - demographic, economic or (in the case of Canada) purely subjective - seemed to merit a second look. If you look at just those countries, the estimate seems somewhat surprising - a casual glance suggested that the negative relationship is in fact there.

One problem with the estimates in the above graph is that it treats each country as an equally-important observation. If we weigh the observations by population, we get this:

This isn't new; others have found the same thing. But I thought it would be interesting to look at how this relationship has evolved over time (John Maheu and I have a project on structural breaks, so this is a question I ask myself fairly frequently these days). So here are the population-weighted results for the sub-periods of 1820-1870, 1870-1913, 1913-1950, 1950-1975 and 1976-2001. I've kept the same scale for each graph.

In the early 19th century, the story was clearly not one of convergence: countries that had industrialised first had higher incomes than those that hadn't, and they extended their lead.

In the latter part of the century, the dominant trend is still the distinction between high-growth industrialised countries and the rest of the world. But within that group, the convergence story begins to apply: the US and Germany start to catch up with the UK over this period, and countries such as Canada and Argentina benefited from capital flows from richer countries. Note also that since high-income countries had been growing faster, the dispersion of incomes in 1870 is greater than it had been in 1820.

By 1913, the US had caught up to the UK, and since geography set it (and Canada) from the worst of the effects of the two world wars, it emerged as the leading economic power. 

This graph more or less corresponds to the Bretton Woods era. Although this period had the highest rates of growth in history, this growth was mainly concentrated in countries that were already relatively rich in 1950. If there's a convergence story to be told, it's in the performance of Japan and Germany - countries that had lost ground against the US during the first part of the century.   

It is only in the last 25 years or so where we finally see convergence. The most important data point is of course China, but even if China is excluded from the sample, the relationship between initial incomes and average growth rates is still negative.

[I'm taking a break from blogging over the holidays, and recycling some earlier posts. This one was first published on March 25, 2006.]

Comments

[Nick Rowe]

The way I think about the data is that there are two groups of countries:

1. Countries that have basically got their economic act together.
2. Economic basket cases.

Over time, countries switch from group 2 to group 1 (with occasional relapses).

Group 1 diverges from group 2. Within group 1 there is convergence. Within group 2 there is neither convergence or divergence.

In 1800 all countries were milling around at the Malthusian start line. Then England started running. Then with various lags, other countries started running. The late starters catch up with the early starters, as they copy their technology. But the runners diverge from those who haven't started yet. And just to complicate the picture, some countries who were running stop to take a breather.

I like looking at the data that way. But unfortunately, unless I have an independent proxy for whether a country belongs in group 1 or 2, this "theory" imposes no restrictions on the data.

[Nick Rowe]

Or does my "theory" impose some restrictions on the data?? It does seem to imply that the later a country joins the race, the faster it will run when it does join the race. Look at Japan, China and India?

[Stephen Gordon]

I think that's a useful dichotomy. As I noted here, Argentina and Canada followed very similar paths until the 1930, and the most plausible explanation for the divergence involves poor policy choices by successive Argentine governments.

[MattM]

Can somebody explain how the following can all be true:

1) China's GDP per capita in 1820 is given as ~640$
2) Its growth rate in per capita GDP over the next 50 years is slightly negative
3) Its GDP per capita in 1870 is given as ~1000$
4) Its growth rate in per capita GDP over the next 43 years is slightly positive
5) Its GDP per capita in 1913 is given as ~600$

????

[Phillip Huggan]

I'm sure the theory is fine but there are bigger forcings. Matt's right, why use USD in the 19th century? All that does is measure how much faster USA enacted ICEs (I'm saying I think they got inflows because they sold ICE factory goods; much stronger than the effect of capital to forge initial ICEs) than world and when they went to war with Canada, themselves, and Mexico. I bet if you correlate years of public education, harvests, penetration of ICE's, sanitation infrastructure, unions/minimum wages (19th cenutury Gini), you find effects that are stronger than capital inflow. If Cochise had a thousand infantry we'd have Ohio Indiana Michigan and Illinois; 34:40.

It's too bad Harper and L.Asper cut the possibly-best-Crown-on Earth (was best in Canada) Court Challenges programme because many developing nations are using our Charter it as a template for the above investments. Now they won't know how to improve their own indigenous Charters of Human Rights. Great to be an Albertan.

[himaginary]

MattM:"Can somebody explain how the following can all be true:"

I suppose "3) Its GDP per capita in 1870 is given as ~1000$" is false.
You can obtain GDP and Population data from the chart in OECD page which Stephen linked.
(Slide the tab below to select year, and move cursor over to the graph, then figures pop up)

Here is the data:
Year Gdp Pop Cap Grw
1820 228 381 598
1870 189 358 528 -0.25%
1914 248 443 560 0.13%
1950 240 546 440 -0.67%
1975 843 899 938 3.08%
2001 4409 1268 3477 5.17%

(Gdp in billions, Population in millions. Cap=Gdp/Pop*1000.
Grw=(Cap/Cap(-1))^(1/(year-year(-1)))-1.)

[Just visiting from macleans]

It would seem to me that in this type of analysis, there is merit in splitting China into two parts, the prosperous eastern provinces which have seen all of the recent investment and growth, and the impoverished western provinces:

Although China’s economic successes get much media attention, the images of rising skyscrapers can obscure the “other” China: the half of China’s 1.3 billion people still living in extreme poverty, earning less than $2 a day.
...
In recent years, China’s remarkable economic boom has become a mainstay of world headlines. Following market-based reforms of the 1980s, China has averaged nearly 10% annual GDP growth for over 25 years, rising to be the world’s 3rd largest economy in 2008.i Yet, in terms of income per capita, China’s economy ranks only #133 in the world.ii This spread reflects the scale of China’s development challenge, and gives a hint to the income gap between the 800 million rural villagers and the wealthy urbanites in coastal cities like Shanghai and Guangzhou.

http://www.chinafaqs.org/library/chinafaqs-two-chinas-shape-climate-views

[Luis Enrique]

you might be interested in this recent publications:

The Econometrics of Convergence
Durlauf, S. N., Johnson, P. A., and Temple, J. R. W. (2009). The Econometrics of Convergence. In Terence C. Mills and Kerry Patterson (eds.) Palgrave Handbook of Econometrics, Volume 2: Applied Econometrics. Palgrave Macmillan, June.

[westslope]

"Unfortunately for the model, empirical evidence in favour of the convergence hypothesis appears to be pretty weak. " -SG

That is not what I learned in graduate school. Professors and textbooks argued that conditional or beta convergence has empirical support.

[Stephen Gordon]

Sure. But the notion of conditional convergence was introduced to deal with the fact that we couldn't see unconditional convergence in the data.

[Victor Galis]

I remember running across a theory in economic geography that might explain the pattern above. (I think it came from the Krugman, Fujita, and Venables book whose name escapes me at the moment, but it might have come from a paper.)

It had a model, where the world had two regions with similar endowments of factors of production, with capital being mobile, non-trivial transport costs between the two regions, and increasing returns to scale in production (within specific goods).

The model was used to trace the state of the world as transport costs between the two regions went from infinity to zero. For a long time, the two regions looked identical as transport costs were too high to permit significant trade. Then as costs came down sufficiently to allow some trade, most of the capital flowed to one region, which became much richer and produced most of the goods (This is because of the increasing returns to scale; which region got richer was arbitrary). As costs came down further, it becomes cost effective to use components built in the other region or export the labor intensive step in production (at least with goods whose assembly can be divided that way). The poorer region industrializes rapidly, and the two converge again.

I'm almost certainly mis-representing some of the assumptions of the model because I don't remember it perfectly, but essentially it had three phases:

high transport costs - autarky, both regions doing equally well
medium transport costs - one region heavily industrialized and richer, the other poorer than before; large benefits to producing in the region that has a network of suppliers and customers for your products, exports consisting of only finished products
low transport costs - new convergence with both regions better off than autarky, importance of co-location with suppliers and customers declines, undermining the forces that concentrated capital in the richer region before

I'll see if I can figure out where I read this theory.

[Victor Galis]

Ok, so I had the authors right, but not the source:

Krugman, P. and A. J. Venables (1995). "Globalization and the Inequality of Nations." The Quarterly Journal of Economics 110(4): 857-880.

[Zoominfo]

There has been convergence among Canadian provinces (and US states). In a common legal and monetary environment, convergence is a robust fact.

I think there are some pretty charts illyustrating this in Barro's last intro textbook.

[Ronanlyons]

While it's certainly fun to knock neoclassical growth theory, the sport is not a new one and misses a few key points about the complexity of that theory. In particular:
(1) Predictions of convergence are stronger, the more basic the theory. Solow predicts convergence (and almost nothing else), whereas most of the theories to which growth economists appeal now are much more ambiguous in their predictions of convergence.
(2) Convergence is also a steady-state phenomenon. Even in Solow, putting in reasonable parameters leads to a convergence period of over 100 years, with absolutely nothing else happening. As we know, lots of other things are happening, each of which is shaking up the snow-globe of the world economy, preventing it from settling where theory might suggest.
(3) Parameters such as education rates, savings rates and so on do differ across countries (as well changing within countries across time), which may alter the conclusions.

Those points aside, though, an interesting article. Bourguignon/Morrisson and Milanovic have done similar work in this area and one of the main points seems to be, it's easy to be equal when no countries are particularly well-off and easy to be unequal when some countries are!

[Nick Rowe]

What does "conditional" convergence mean? (I think I used to know the answer to this question, but have forgotten). Conditional on what?

[Stephen Gordon]

As far as I can tell, it's conditional on the conditions that are necessary for the standard model to generate convergence. Functioning markets, properly-run public institutions, etc.