What Hump-Shaped Relationship?

American Economic Review is arguably the most prestigious economics journal in the world. So it was especially worrying to see them publish Ashraf and Galor’s thesis claiming a hump-shaped relationship between genetic diversity and economic development. The claim has a certain plausibility to it. Very high diversity can be expected to generate ethnic fragmentation, presumably a catalyst for politico-economic dysfunction. Societies with extremely low diversity, assuming straightforward biological reductionism, can be expected to generate fewer innovations than Goldilocks societies with near-optimal levels of genetic diversity. Ashraf and Galor have shown that the hump-shaped relationship is detectable even after controlling for a number of biogeographic conditioners. Yet, the thesis remains unconvincing on both theoretical and empirical grounds.

The fundamental problem is threefold. First, it is not clear that genetic diversity is capturing anything other than the arrested development of shatter-belts and marginal zones. As James Scott and other have argued, projects of state formation repeatedly drove oppressed populations into marginal regions, particularly in uplands; so that over centuries these counter-zones became permanently organized so as to resist the domination of the paddy states. The Balkans and mainland Southeast Asia are classic shatterbelts. But it may help to think of the entire globe as a vast shatter-belt shaped above all by massive expansions of farmers, pastoralists, and grain states.

Second, A&G’s empirical strategy is to estimate genetic diversity as a function of migratory distance from Ethiopia along the Out-of-Africa route. They show that this holds for the 21 observations they do have, as the next figure shows. So what A&G are really saying is that there is a quadratic relationship between the migratory distance from Ethiopia and per capita income. And we can make sense of this by positing that the reduction in genetic diversity due to founder effects had causal consequences for economic development. The fact that A&G estimate genetic diversity severely weakens their case. The data for genetic diversity is now available at fine-scale. Their case would be more compelling had they used measured genetic diversity. Indeed, what would be really compelling would be to see genetic diversity predict variation after conditioning on distance from Africa. For that would then rule out all other factors captured by distance from Africa.

OfA_genetic_diversity.png

Third, the empirical relationship they do establish is considerably weaker than the Heliocentric model. In their baseline specification, the quadratic relationship explains only 15 percent of the variation in log per capita income. In our baseline (Köppen), the linear relationship with absolute latitude explains 25 percent of the variation in log per capita income. Of course, we don’t expect AER to publish a result that’s been known for more than 150 years. But we do expect a serious engagement with the relative magnitude of the relationships.

Koppen_AG.png

As the regular reader might have noticed, we have discovered a fairly reasonable method to compare the fixed effects of various conditioners. The trick is to consider the product of the absolute values of the slope coefficients and the interquartile ranges of the covariates. This allows us to visualize the relative magnitudes of the fixed effects in any multi-factorial model. Here we compare the relative effects of these two conditioners.

We have seen that Neolithic time-depth is explained by distance from the Levant. And we noted that absolute latitude made such a minor contribution that we decided to drop it. Yet, in a specification with distance from Ethiopia (A&G’s proxy for genetic diversity) and absolute latitude, we find an insignificant and minor effect for the former and a large and significant effect for the latter. The error bars display 95 percent confidence intervals.

FE_AG_NTD

Things improve for A&G when we look at log per capita income in 2000. Although the A&G factors are still smaller and less significant (tStat=3.2, -2.3) than absolute latitude (tStat=7.7). Moreover, the contribution of the offending quadratic term is small. Put simply, thermal burdens trump whatever effect too much genetic diversity may have on the economic performance of nations.

FE_AG_gdppc.png

And whatever effect of the A&G factors that still survives in the 2-factor model vanishes once we control for the obvious biogeographic conditioners. Here we control for percentage of arable land, distance from waterway, elevation and roughness. Both the linear and the quadratic term for genetic diversity (proxied as above by distance from Ethiopia) fall into insignificance (the 95 confidence intervals straddle zero).

FE_AG_gdppc_full.png

What is amply clear from this international cross-sectional regression is that the strongest correlate of income is absolute latitude. This is easier to interpret if we take the dependent variable to be per capita income percentiles (instead of log per capita income). The fixed effect is so large that moving from the 25th to the 75th percentile in absolute latitude increases log per capita income by 30 percentiles, as the next figure shows.

meng.png

So, although plausible, the A&G thesis is easily debunked empirically. This is true of all neoracialist accounts we have so far on offer. Although such accounts are not usually accepted for publication in top journals.


Postscript. It is not every month that I challenge the results of a paper published in AER. But now that I am saying that the results claimed by Ashraf and Galor (2013) cannot be replicated, I feel obliged to carry out at least common robustness checks. The basic problem with cross-sectional OLS is heteroskedasticity, meaning that the errors usually have different variances. The error bars in the next figure are confidence intervals calculated using robust standard errors (Newey and West 1987).

RobustA&G.png

Table 1 lays out my fixed effect calculations. Ashraf and Galor’s result really cannot be replicated.

Table 1. Fixed effect calculations. 
slope se pval iqr fixed effect error
abs latitude 0.97 0.117 0.000 27.56 26.84 3.217
elevation -12.63 3.459 0.000 0.40 -5.09 1.393
dist fr waterway -11.20 2.611 0.000 0.37 -4.15 0.967
dist fr Ethiopia 3.41 1.745 0.053 2.88 9.80 5.016
dist fr Ethiopia sqrd -0.12 0.091 0.200 32.23 -3.79 2.940
Source: Ashraf and Galor (2013), author’s computations. We report Newey West standard errors. Fixed effect = |slope| times iqr. Error = se times iqr. The dependent variable is per capita income percentile. N=153, Fstat=29.4, R^2=0.50.

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