Krugman’s paying attention to global polarization again. His It theory is a sort of zero-one law of modernization:

One thing is clear: at any given time, not all countries have that mysterious “it” that lets them make effective use of the backlog of advanced technology developed since the Industrial Revolution. … Once a country acquires It, growth can be rapid, precisely because best practice is so far ahead of where the country starts. And because the frontier keeps moving out, countries that get It keep growing faster. … The It theory also, I’d argue, explains the U-shaped relationship Subramanian et al find between GDP per capita and growth, in which middle-income countries grow faster than either poor or rich countries. Countries that are still very poor are countries that haven’t got It; countries that are already rich are already at the technological frontier, limiting the space for rapid growth. In between are countries that acquired It not too long ago, which has vaulted them into middle-income status, but are able to grow very fast by moving toward the frontier.… and rising inequality within Western countries means that if you look at the global distribution of household incomes, you get Branko’s elephant chart.

The It theory implies that the rate of growth of per capita income is a quadratic function of per capita income since middle income countries who have It ought to grow faster than low income nations who don’t have It, as well as high income nations who, although they do have It, are too close to the technological frontier to grow rapidly. This has a certain plausibility since middle income countries seem to be the fastest growers while advanced economies and the least developed nations tend to grow slowly. Let’s test it to see if it accords with empirical reality.

If the It theory holds then the coefficients in the linear regression of growth rates as a quadratic function of log per capita income should be significant and bear the right signs. More precisely, the quadratic function has to be concave down (a hump shape), so that the linear coefficient ought to be positive and the coefficient of the quadratic term ought to be negative. Is it true?

We test this prediction against the Maddison dataset. We begin by running rolling regressions of the 5-year moving average of the rate of growth of per capita income as a quadratic function of log per capita income. Figure 1 displays the t-Stats (the ratio of the coefficient and its standard error) over time. Interestingly, Krugman’s It theory seems to hold for two periods, 1973-1986 and 2003-2012. But it seems to reverse in the 1990s. Is this because of the Soviet collapse?

To check this, we exclude the countries of the former Soviet Union and rerun our regressions. Figure 2 displays the estimates. That attenuates the problem. The nineties reversal is no longer statistically significant. Yet the overall pattern is unchanged. Why were middle income countries growing significantly faster than low and high income nations in these two periods but not otherwise?

The next figure displays the R^2 of the regressions. We see that the relationship really breaks down in 1986-2002. Why? We must dig deeper.

In order to get to the bottom of this we fit a linear mixed effects model. We restrict the sample to the past 50 years and fit the model,

,

where we allow for random effects for country () and year (). The results are pretty robust. With t-stats close to 10, both fixed-effect coefficients are extremely significant and bear the right sign.

Do the results continue to hold if we introduce fixed-effects for income group (“class”), ie dummies for low, middle, and high income groups? For if the coefficients remain significant and continue bearing the right sign despite the inclusion of dummies for income group, that would imply that the pattern extends within income groups.

The results are very interesting. Instead of attenuating, the quadratic coefficients increase slightly in magnitude. But the fixed-effect coefficients for low income group (“class_3”) and especially, middle income group (“class_2”) bear the wrong sign. This could be because we are controlling for income (and squared income). But that is not the case. Even dropping the income variables, and with and without random effects, the coefficients of the low and middle income group dummies remain resolutely negative and significant. Indeed, high income nations averaged a growth rate of 2.15% over the past fifty years, compared to 1.71% for the middle income group and only 0.72% for the low income group. So it seems that our intuition was wrong.

Krugman appears to be right on average if we stick to the past half century. There is indeed a statistically significant cross-sectional relationship between income and growth whereby growth rates are a quadratic (and concave upwards) function of per capita income. But the reality is far more complex than that simple picture would suggest. The next graph shows the time-variation in the quadratic relationship since 1800. There is substantial systematic time-variation in the relationship since it emerged. Moreover, we can see how truly novel this catch-up business is. The series looks stationary around zero all the way until the 1970s. In English, there was hardly any catch-up—more precisely, excess middle income growth—before the last quarter of the twentieth century. Even the two brief periods of relative convergence bookend a decade of major divergence. The graph thus testifies to both the late arrival of convergence and the failure of the mid-century dream of Modernization.

The big question thrown up by the present investigation is the dramatic pattern of convergence, divergence, and convergence over the past two generations. What explains this pattern? Could it have something to do with the global financial cycle? The next figure displays the global financial cycle from Farooqui (2016). It is also double-humped like the graphs above (also reproduced below), but the two seem to be out of sync with each other. While the financial boom of the late-1980s was gathering pace, the middle income premium in growth was collapsing. The second cycle is more congruent. So the evidence for a connection to the global financial cycle is mixed.

This requires more work. But we have the basic picture for now.

*Postscript*. I like scatterplots. It lets you quickly examine the strength of any hypothesized relationship. So I looked at actual average growth rates in the modern period versus that predicted by the fitted model. The fitted model is,

.

We do a sleight of hand and compare the predicted growth rate not with the actual growth rates by country-year. Instead we look at average growth rates in the modern era. The evidence that emerges is very strong. The quadratic model does a good job of predicting average rates of growth. Here we compare the predictions with the average rates of growth achieved since 1960. The estimated correlation coefficient is very significant (r=0.308, p<0.001). The picture is similar if we start the clock in 1950, 1970, 1980, 1990, or 2000. Krugman is really onto something.

*Post-postscript*. Actually, it is not so simple. The even simpler Biblical model does even better. [Matthew 13:12. *For whosoever hath, to him shall be given, and he shall have more abundance: but whosoever hath not, from him shall be taken away even that he hath.*]