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.
There are lots of conclusions that could be drawn from this exercise, but I think the most important one concerns international capital mobility. Whenever capital is free to move from rich to poor countries, poor countries catch up.