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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.

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?

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.

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\$

????

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.

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.)

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

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.

"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.

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

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.

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.

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.

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!

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

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.

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