An Illustrated Guide to Racial Anthropometry: Or, the Narcissism of Small Differences

Despite the long-standing scholarly consensus that race is a social construct — more precisely, that it is a real abstraction; a fiction with all-too-real social consequences — essentialism refuses to relinquish its hold on the popular imaginary. Everyday folk suspect that the scholarly consensus is an artifact of rampant political correctness in academia. The vast majority of Westerners, while somewhat unsympathetic to notions of an unchanging racial hierarchy rooted in biology, imagine that there are indeed biological differences between Whites, Blacks, and Asians; differences that are relevant to understanding the social order.

Samuel G. Morton (1799-1851) pioneered the techniques of craniology in 1839, thereby founding the American school of ethnology. Morton and his followers were the advance vanguard of scientific racialism. He was the first to make inferences about racial hierarchy on the basis of measured cranial capacity. Big brained Caucasians, he argued, were demonstrably superior to small-brained Negros. Whatever the validity of the brain size=intelligence equation, is there any empirical support for the differences in skull-size championed by Morton and his intellectual descendents all the way down to Rushton today?

Physical differences between say national populations are in fact not a function of biology. Rather, they reflect nutritional status and disease burdens. Indeed, anthropometric measures like (the population means of) stature and BMI capture everyday living standards much more reliably than per capita income. We’ve previously interrogated the time-variation and international cross-sectional variation in these indicators to get an handle on global polarization that is largely independent of, and complementary to, national economic statistics. Following in the footsteps of Fogel, Waaler, and Kim, our investigation yielded a measure of living standards that we called effective stature that combined height and BMI. But if we are wrong and physical differences are in fact a function of biology, then that confounds our interpretation of at least the cross-sectional variation in effective stature. So independent of testing the claims of high racialists, it is very important for us to get to the bottom of this. (We’ll revisit that issue in a future post.)

The top panel in Table 1 displays the racial averages of a number of anthropometric measures for men in the US military. BMI is the ratio of weight in kilograms to squared height in meters; cranial capacity (CC) is the volume of the interior of the braincase measured in cubic centimeters estimated via the Lee-Pearson-Rushton formula for men from head length (L) and head breadth (B) [CC=6.752(L-11)+11.421(B-11)-1434.06]; brain mass is then computed via the Ruff et al. (1997) formula [brain mass=1.147CC^0.976]; encephalization quotient (EQ) is calculated from Martin’s relationship in mammals [EQ=brain mass/(11.22 body weight^0.76)]; and the cephalic index equals 100 times the ratio of head breadth to head length. The last has a particularly sordid history in the annals of racial craniology. And as opposed to brain size, which is only problematic, the cephalic index as a measure of intelligence potential has been totally debunked. We only include it here for the sake of completeness.

Table 1. Anthropometric measures of American men by “race.”
“Race” Sample size Stature (cm) Weight (kg) BMI Cranial capacity (cc) Head Circumference (cm) Brain Mass (g) EQ CI
White 2,817 176.4 85.8 27.6 1,474.3 57.4 1,419.3 7.6 77.1
Black 642 176.2 87.5 28.2 1,489.3 57.8 1,433.4 7.5 76.9
Hispanic 440 171.8 83.7 28.3 1,465.3 57.2 1,410.9 7.7 78.7
Asian 117 169.9 74.8 25.9 1,470.6 56.5 1,415.9 8.4 82.4
Other 66 172.9 84.0 28.0 1,481.4 57.1 1,426.0 7.7 79.3
All 4,082 175.6 85.5 27.7 1,475.7 57.4 1,420.7 7.6 77.4
Z scores
“Race” Stature Weight BMI Cranial capacity Head Circumference Brain Mass EQ CI
White 0.11 0.02 -0.03 -0.02 0.00 -0.02 -0.04 -0.09
Black 0.08 0.14 0.12 0.16 0.23 0.16 -0.07 -0.14
Hispanic -0.56 -0.13 0.15 -0.12 -0.17 -0.12 0.07 0.36
Asian -0.83 -0.75 -0.45 -0.06 -0.59 -0.06 0.91 1.39
Other -0.40 -0.11 0.08 0.07 -0.19 0.07 0.18 0.53
Source: ANSUR II (2012), author’s computations.

The second panel in Table 1 displays the z scores that tell us how much the racial means differ from the overall population means. Z scores within (-1.96,+1.96) indicate insignificance at the standard 5 percent confidence level. All the entries in the second panel lie within this interval, so right off the bat we can tell that anatomical differences between the “races” are statistically insignificant. As for brain size, whatever trivial differences that exist are in favor of African-Americans.

We have seen the means, but what do the distributions look like? In order to visualize these distributions, we assume that all measures are normally distributed. We collect and display the graphs for the distribution of all these variables in the following slideshow.

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From Table 1 and the distributional graphs we can see that Asians are a bit shorter and skinnier than Whites and Blacks. But despite their smaller bodies, their brain size is comparable to Whites and Blacks (since their encephalization quotient is a bit higher). And their heads are a bit more globular (their cephalic index is also a bit higher). But again these are minor differences. Interracial variation is swamped by intraracial variation.

The most extreme differences we can detect are in the encephalization quotient and the cephalic index between Asians and non-Asians. The next figure displays the two indices for Asians and Blacks. (There are too many observations for Whites, which clutters the scatter plot.) We see that even here, the overlap is substantial. Moreover, there is no evidence whatsoever that either measure has anything to do with intelligence or anything else of relevance to the social order.


The same is true of head circumference and cranial capacity. See next figure. Yes, Asian heads a bit more globular. But the overlap is still substantial. Note also the minor differences in the intercepts (12cc) and slopes (0.6cc per cm).


From the distributions it is clear that the most extreme phenotypic differences (although still statistically insignificant) are between Asians and non-Asians. This doesn’t mean that Asians can be identified as a biological race (in the sense of subspecies). There is substantial variation in human populations. But race is a poor way to understand it. Human populations vary continuously. What we have is geographic clines (which look like differences between discrete races in settler countries where geographically distant populations live cheek by jowl). However, this is not so much due to climatic adaptations (as skin reflectance would suggest) as due to population bottlenecks and founder effects (along with genetic drift) in human dispersal from Africa. Basically our race left our African homeland in small bands that had by definition much less genomic variation than the population left behind. This is why Africa has more genomic variation than the rest of the world combined. And why the best handle we have on phenotypic variation is distance from Africa. But more on that another time.

The bottomline is that race gives us no handle whatsoever on variation in human bodies, and above all, claims of racial differences in brain size have no basis in empirical reality. 


Cranial Capacity of Real and Imagined Races of Man

The fine art of turn of the century physical anthropology involved measuring the size of the skull (and therefore the size of the brain) to determine the innate capacity of the different “races” for civilization. It was commonly held that such morphological investigations had yielded “scientific proof” of the biological superiority of some races over others. This business was closely tied to Polygenism which emerged in the 18th century. Leading scientists considered races to be species separately created by God. After the acceptance of Darwinian evolution in the late-nineteenth century, the polygenic outlook was modified. The “races of man” were now thought to have evolved, pace Wallace (1864), from different primates or early hominids in more or less absolute isolation from each other.

Perhaps the most influential high racialist, certainly from a historical perspective, was Ernst Haeckel (1834–1919). Whereas Social Darwinism was used to justify laissez-faire capitalism in the Anglo-Saxon world, Haeckel emphasized the struggle for survival between the races as the motor of history. Our man celebrated the vanishing of weaker races and the proliferation of the vigorous ones. The Nazis were big fans. Indeed, National Socialism was nothing but “applied anthropology.” Haeckel’s thought formed the central theorem of Nazism; it was “the only element of the Nazi era which was neither modified nor manipulated in response to strategic or tactical requirements” (Rich 1973).

After Auschwitz, overt racialism was abandoned by mainstream anthropology. But it continued to thrive on the margins. The last hurrah of anthropological racialism was probably Carleton S. Coon’s Origin of the Races (1962). Coon pushed the idea that human races were different subspecies that had evolved in parallel with little or no contact. Himself a one-time president of the American Anthropological Association, he was harshly condemned by the then president, Washburn, at the 1962 meeting. At the end of the speech, the audience stood up, cheering.

Besides the racialized trauma of the mid-century passage, there was mounting evidence that all extant humanity could trace their lineage to Africa in the not too distant past so that not enough time had elapsed for the emergence of subspecies in humans. Of course, there is substantial biological variation in humanity. But it was by then understood that racial taxonomy was a poor way to understand this variation. Human biological variation is largely within populations; and even between populations it varies continuously, not discretely (a necessary implication of racial taxonomy). The modern understanding was captured by Frank Livingstone in the same year as the last hurrah of racial anthropology: “There are no races; there are only clines.

The fine art of human craniology survived in paleontology departments. Dealing with fossils from millions of years ago (Ma), there was much less at stake in morphological taxonomy. Nor was it a secondary issue. Hominin are classified above all by cranial capacity. Indeed, the definition of the genus Homo boils down to hominins with a cranial capacity greater than 600 cubic centimeters (cc). Early hominins, although committed bipedals (including late pre-Homo tool-manufacturers) are placed in different genera above all because their brains are considered too small. Figure 1 displays the evolution of average hominin cranial capacity by taxon.


Figure 1. Average cranial capacity by hominin taxon.

Two observations. First, H. neanderthalensis had slightly bigger brains than H. sapiens. This calls into question either the equation of cranial volume with intelligence, or our name, Homo sapiens, ie “wise guy.” Second, the averages shown in Figure 1 conceal massive variation as well as the exponential growth in hominin cranial volume. Figure 2 is more revealing. Note the log scale of the time axis. What the figure shows in exponential growth in human cranial volume since we split from our common ancestor with the chimps 7 million years ago (Ma).


Figure 2. Hominin cranial volume. Source: Spocter (2007).

The mixing of genera in Figure 2 would perhaps scandalize a purist. Figure 3 zooms into the past two million years; the Age of Homo. Red represents Neanderthal crania; blue, H. sapiens; and black, other “species” in the genus Homo.


Figure 3. Cranial volume in the genus Homo. Source: Spocter (2007).

What of the races imagined by the pioneers of craniology? Given all the hullabaloo, surely there was some empirical basis for the alleged racial differences in cranial capacity? Indeed, as late 1994, Rushton, the high racialist out-of-time, argued in Race, Evolution, and Behavior that Black crania were 80 cc smaller than White crania, which in turn were 17 cc smaller than Asian crania (thereby reversing the classical ordering claimed by high racialists: White > Asian > Black).  I have found that it is always a good idea to check such claims. Table 1 shows the summary statistics for cranial volume by “race.” The data is taken from the US Army’s ANSUR II Male working database which contains a total sample of 4,082 subjects. In order to calculate cranial capacity we use the formula from Rushton (1993).

Table 1. Cranial volume by “race.”
Source: ANSUR 2 (2012), author’s computations.
“Race” Num Mean Std Min Max Range
White 2,817 1,474 84 1,198 1,818 620
Black 642 1,489 91 1,148 1,792 644
Hispanic 440 1,465 85 1,185 1,767 582
Asian 117 1,471 87 1,256 1,725 469
Other 66 1,481 88 1,308 1,655 347
All 4,082 1,476 85 1,148 1,818 670

Turns out, it is precisely the other way around. On average, Black men’s crania are 15 cc larger than White men, who in turn have crania that is on average 3 cc larger than Asians. Of course, these differences are utterly insignificant in light of the substantial variation. For instance, 15 cc is a trivial 0.18 standard deviations. Indeed, the most important numbers in Table 1 are in the last three columns. They emphasize the dramatic scale of the variation at the individual level. The range for both Blacks and Whites is well over 600 cc! The standard deviation of cranial capacity for the other “races” in America is comparable. The only reason the range is lower is because of smaller sample sizes. Figure 4 shows a boxplot of the same data. Racial taxonomy gives us no handle at all on the variation in human craniology.


Figure 4. Boxplot of cranial volume by “race.” Source: ANSUR 2 (2012), author’s computations.

If you want to try this at home, you don’t need to make complicated measurements of your head. Instead, you can proxy cranial capacity by head circumference. Figure 5 shows the tight linear relationship. It also displays the estimated regression line, which you can use to get a quick and dirty estimate of your cranial volume.


Figure 5. Head circumference and cranial volume. Source: ANSUR 2 (2012), author’s computations.

Caspari et al. (2017) made a compelling argument that human subspecies are not a logical impossibility. Many extinct hominins in the genus Homo weren’t other species. Rather, they were human races or subspecies. H. erectus may indeed have been a different species since it diverged from our lineage 2 Ma; perhaps enough time for speciation. (Biologists reckon that across the animal kingdom speciation takes about 1 Ma.) But our last common ancestor with Neanderthals, Denisovans, as well as the ghost populations whose signature is all over our genome but whose fossils have yet to be found, lived some 600 Ka (thousands of years ago). That’s enough time for raciation but not speciation. More importantly, we interbred with these humans; not now and then but continuously after our multiple dispersals from Africa between 130 Ka and 40 Ka. (As we surely did with other races in our African homeland early in our career.)

H. sapiens emerged 200 Ka in Southern Africa and spread to East Africa soon after. (The “purest” H. sapiens today are the Koisan, the Kalahari Bushmen.) Meanwhile, Eurasia was populated by a number of now-extinct human races. For some half a million years then, we were genetically isolated from the hominins who populated Eurasia. Moreover, even by the standards of the late Pleistocene, Neanderthal populations were very small and isolated. Population densities were extremely low. And in the face of the violent glacial-interglacial whipsaw of Pleistocene Europe, they found themselves periodically isolated in refugia below the Alps. Dating in the Neanderthal world must have been tough! The prolonged isolation and extremely low population densities well-approximate the extended isolation of the races of the high racialist imaginary.

But isolated or not, Neanderthal were definitely people. From Capari et al. (2017):

Neanderthals were capable of complex behaviors reflecting symbolic thought, including the use of pigments, jewelry, and feathers and raptor claws as ornaments. All of this is probably evidence of symbolic social signaling, complementing the evidence of complexity of thought demonstrated by the multi-stage production of Levallois tools. Neanderthals were human.

Moreover, the notion that our race had cognitive advantages over the other races has to be abandoned. The difference wasn’t brains. Perhaps it was grandparents. … I am only half-kidding. The decisive difference seems to have been different life histories. Our race lived dramatically longer. And it is that which admitted a quantum leap in dynamism via the intergenerational transmission of knowhow and knowwhere and so on. More on that another time.


Figure 6. H. sapiens (Libben) and H. neanderthalensis (Krapina lx) survivorship curves.


Someone Finally Gets the GFC Right: Crashed by Adam Tooze


Adam Tooze’s Crashed: How a decade of financial crises changed the world was released today in the UK and will be out in the US next week. Of course, no matter where you are on the planet you can get the Kindle version from the UK store right away. [Full disclosure: Adam is a personal friend and soon-to-be doctoral advisor. I also helped a little bit as he was working on the manuscript. So, caveat emptor.]

Dozens and dozens of books have appeared on the global financial crisis. Many are blow-by-blow accounts that capture the drama of the GFC. Some are memoirs by actors in the eye of the storm. Then there are those, mostly by economists, that try to diagnose the causes of the GFC. It is the last that have failed spectacularly to impress … until now.

The principal reasons for the failure have varied. Too many are irredeemably US-centric; as if the GFC was an exclusively American affair. This is especially true of books that appeared before the eurozone crisis. Most are politically-biased; either focused on the crimes of the bankers or the misdemeanors of monetary authorities, political authorities, and above all, the Federal mortgage agencies. Some see the financial crisis as nothing but the latest rendition of financial manias and panics driven by irrational exuberance that have plagued the history of capitalism. Think Tulip mania, the Mississippi bubble, the “dot com” bubble, and so on. Finally, and perhaps most importantly, too many economists’ accounts have been incorrigibly wedded to a defunct picture of the global economy based on national economic statistics. For them, the roots of the GFC lie in persistent current account imbalances.

The GFC was not just an American subprime crisis but a crisis of global banking. It was not caused by the monetary policy of the Federal Reserve, even though ultra-low rates played their part in fanning a boom in mortgage lending (as they do in every cycle). It was not driven by Fannie and Freddie. The bulk of subprime loans made during the boom in 2004-2006 were not held by the agencies. Indeed, had that been the case there would’ve been no financial crisis.

The proof is straightforward. Even at the peak of the crisis, the week following the Lehman bankruptcy, the core component of the wholesale funding flywheel collateralized by default-remote bonds, US Treasuries and agency-RMBS (residential mortgage-backed securities issued by agencies with implicit US government backing), continued to spin just as fast. Investment banks that were understood to be over water, such as Goldman and JP Morgan, were still borrowing hundreds of billions of dollars in the tri-party repo market against agency-RMBS the day after the Lehman bankruptcy. Indeed, it was the introduction of default risk into the rapidly-spinning flywheel of the secured lending markets that was the source of instability. The whole thing imploded when escalating defaults forced a revaluation of the risk posed by private label-RMBS. That was the proximate cause of the GFC.

The mortgage lending boom was the giant sucking sound of the wholesale funding market. That is, the introduction of private label-RMBS into the rehypothecation flywheel was demand-driven. As Zoltan Pozsar argued, it was the demand for safe assets emanating from massive cash pools on the one hand and the demand for risk assets by leveraged bond portfolios on the other that drove dealers to slice and dice pools of mortgages to manufacture said assets. The construction of this manufacturing capacity required a dramatic transformation of banking practice, what Gowan called the New Wall Street System and now goes under the rubric of Shadow Banking. Here’s a map of the market-based credit system created by economists at the NY Fed.

Even the amplitude of the mortgage lending boom is not enough to understand the virulence of the global financial crisis. The other critical component was the leverage cycle. In a series of path-breaking papers, Adrian and Shin showed that unlike households, nonfinancial firms and even commercial banks, the leverage of wholesale-funded investment banks (ie, broker-dealers) is procyclical. This is not simply an artifact of the securities trading business. Because net worth goes up faster than liabilities when asset prices rise, leverage falls. Leverage is thus naturally counter-cyclical. The fact that leverage is procyclical for dealers implies that they aggressively manage their balance sheets. More precisely, when asset prices rise, value-at-risk falls; dealers respond by leveraging up; that in turn pushes up asset prices further. Conversely, when asset prices fall, value-at-risk rises; dealers respond by reducing leverage; which in turn pushes asset prices even lower. This is the “leverage cycle.”

The leverage cycle is exacerbated by the wholesale funding model. Since the value of collateral goes up along with asset prices, dealers not only want to but can borrow more on the same collateral. And on the way down, the falling value of collateral reinforces the doom loop. It was these dynamics endogenous to the financial intermediary sector that drove both the extraordinary amplitude of the financial boom and the virulence of the financial crisis.

Our account so far is seemingly US-centric. But that is far from the truth. As Shin has shown, European banks played a decisive role during the financial boom. The “round-trip” transatlantic circuit accorded “a pivotal role for European banks in determining financial conditions in the United States.”


Source: Shin (2012).

Moreover, because “round-trip” flows get netted out, one gets the wrong picture from net capital flows (which correspond to current account imbalances). Instead, one must look at gross capital flows. As soon as we do that (next figure) we uncover the full scale of transatlantic finance. European capital flows into the United States utterly dwarfed the flows from Asia, even as the latter ran large current account surpluses.


Source: Shin (2012). Percentage of US GDP.

To cut a long story short, what this means is that all accounts that trace the roots of the GFC to global imbalances are flat-out wrong. It was not Bernanke’s ‘global savings glut’; it was Shin’s ‘global banking glut’. More generally, what was responsible for the GFC was the ‘excess elasticity’ of the financial intermediary sector. The origins of the catastrophe must be traced to dynamics endogenous to high neoliberal global financial intermediation.

Before Crashed, the only books on the market that did even a little bit of justice to all these findings were Mehrling’s New Lombard Street (2010) that documented the functioning of market-based finance and Rajan’s Fault Lines (2011) that focused on the fragility of the global financial system. Mehrling tells the story of how the Fed became ‘the dealer of last resort’. Rajan pays more attention to international macro-financial linkages and spillovers. Both are definitely worth reading. But neither gets close to the full picture. Enter Adam Tooze.

Crashed gets more than just the functioning of the high neoliberal global financial system and origins of the global financial crisis right. As becoming of one of the most celebrated historians alive, Adam presents a properly historicized account of the political economy of the catastrophe and its enduring aftermath. His account does not stop with the end of the crisis in the United States with the deployment of ‘financial Powell doctrine’ or even the end of the eurozone crisis that fine day when Draghi promised to do whatever it takes (the eurozone version of the financial Powell doctrine). He goes on to chart the full unraveling of the international order that ensued in the aftermath of the GFC. (I’ll write about the geopolitical and political economy aspects of the book soon.)

We are of course still living very much in the shadow of the catastrophe so the story as they say is only half finished. That’s the risk one runs in writing contemporary history.  Be that as it may, Crashed supersedes all book-length treatments so far on the origins of the catastophe.






Causal Channels in Global Polarization: The evidence from anthropometry

International differences in mean height and weight contain significant economic information about global polarization. This is true of height because the heritable component gets averaged away when we take national means. And BMI contains very significant information about nutritional standards.


The simplicity of Waaler surfaces allows us to capture all the evidence from anthropometry with a simple actuarially fair measure. We posit that anthropometric status is linear in height and quadratic in BMI. We use OLS to regress life expectancy on this specification and use the fitted values as our estimate of anthropometric status. In effect, we allow the Waaler surface to pick the weights we use to combine height and BMI. The weights can be read as reflecting the trade-off in mortality risk between height and BMI. We recenter and rescale the estimates to match the mean and variance of contemporary stature in centimeters. We call this representation Effective Stature.

Effective stature is roughly equivalent to Kim (1996)’s Waaler Index. The difference is that while the method proposed in Kim (1996) required survival tables by height and weight, we have developed a new method that allows us to estimate Waaler surfaces from panel data. The time-variation in the panel allows us to stochastically detrend national means of life expectancy, height and BMI, and thus more efficiently extract information from the cross-sectional variation. See explainer.


Explainer: Waaler Index and Effective Stature.

In what follows, “Disease” refers to natural log of Years Lost to Infectious Disease estimated by the World Health Organization; “Temperature” refers to mean winter highs; “Nutrition” refers to the linear combination of food balances in vegetal calories, animal calories, vegetal protein, and animal protein that best tracks life expectancy. We begin with the correlation structure.

Correlation Coefficients
Nutrition Disease Effective stature
Temperature -0.72 0.67 -0.75
Nutrition -0.55 0.86
Disease -0.49

The strongest raw correlate of effective stature is Nutrition. Temperature is also a very strong correlate of effective stature. Disease is somewhat less so. Note also that Temperature and nutrition are strongly correlated. So too are Disease and Nutrition although not as strongly. What explains this correlation structure?

The standardized slope coefficients naturally contain the same information. Although already some clarity begins to emerge. It seems plausible that there are causal pathways that run from Temperature to Nutrition and Disease, from Nutrition to Disease, and from one or all three to Effective Stature.

Standardized Slope Coefficients
Columns are dependent variables Nutrition Disease Effective Stature
Temperature -0.78 0.71 -0.76
Nutrition -0.49 0.79
Disease -0.43

Unpacking the causal structure underlying these correlations is the key to understanding global polarization. Causal inference from linear models requires an identification strategy. This is not always possible. But if one is interested in testing the Heliocentric theory, things become considerably easier because we know a priori that causal vectors point out from Temperature and not towards it. This dramatically reduces the number of possible path coefficients. Simply put, the plausible direct effects are Temperature on Nutrition, Disease, and Effective Stature; Nutrition on Disease and Effective Stature; Disease on Nutrition; and Nutrition and Disease on Effective Stature. We can test these from the following “wholesale” regression table.

Global Polarization in human stature, weight and mortality
Dependent variable is Effective Stature. Estimates significant at the 1 percent level are in bold. All variables have been standardized to have mean 0 and variance 1.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7
Constant -0.24 -0.04 -0.07 -0.18 -0.25 -0.04 -0.18
0.00 0.36 0.30 0.00 0.00 0.35 0.00
Temperature 0.76 -0.30 -0.79 -0.35
0.00 0.00 0.00 0.00
Nutrition 0.79 0.63 0.75 0.65
0.00 0.00 0.00 0.00
Disease -0.43 0.04 -0.10 0.09
0.00 0.58 0.09 0.17
R^2 0.50 0.63 0.19 0.77 0.50 0.65 0.78
adj-R^2 0.50 0.63 0.18 0.77 0.49 0.65 0.77
N 114 172 180 105 112 163 103
Source: NCD-RisC, WHO, FAO, author’s computations.

To begin with, since there are no causal channels from Nutrition, Disease and Effective Stature to Temperature, we can expect the total effect of Temperature on Effective Stature to be identified by Model 1. Our estimate is statistically significant. A one standard deviation difference in Temperature implies a –0.76 standard deviation change in Effective Stature. All on its own, Temperature explains half the cross-sectional variation in Effective Stature.

What portion of this total effect is mediated by Disease and Nutrition? And what if any is the direct effect of Temperature on Effective Stature? In order to identify that we have to first identify the path coefficients “downstream.” The direct effect of Nutrition on Effective Stature is identified once we control for Disease (Model 6). Our estimated path coefficient is a highly significant 0.75. This is nearly as large as the total effect 0.79 of Nutrition on Effective Stature (Model 2). The direct effect of Disease is also identified once we control for Nutrition (Model 6 again). To our considerable surprise, this path coefficient turns out to be entirely insignificant. We can thus rule out causal channels that run through Disease.

The direct effect of Temperature on Effective Stature can now be identified by controlling for Nutrition (Model 4). Our estimate for the path coefficient is a statistically significant -0.30. That is an extremely large effect after controlling for Nutrition. Note also that if we control for both Nutrition and Disease the estimated path coefficient becomes slightly larger (Model 7). The indirect effect of Temperature on Effective Stature  mediated by Nutrition corresponds to the product of the path coefficients, 0.59 (-0.78*0.75). The total effect of Temperature on Effective Stature implied by the path coefficients is thus -0.89 (-0.3-0.59). This is significantly larger than the univariate estimate of -0.76 (Model 1). Is this because the two models are estimated from different samples? We refit all models with the same (slightly smaller) sample.

Restricted Sample Estimates
Dependent variable is Effective Stature. Estimates significant at the 1 percent level are in bold. All variables have been standardized to have mean 0 and variance 1.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7
Constant 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00
Temperature -0.75 -0.28 -0.76 -0.33
0.00 0.00 0.00 0.00
Nutrition 0.86 0.66 0.84 0.67
0.00 0.00 0.00 0.00
Disease -0.49 0.01 -0.04 0.09
0.00 0.88 0.54 0.17
R^2 0.56 0.73 0.24 0.77 0.56 0.74 0.78
adj-R^2 0.56 0.73 0.24 0.77 0.56 0.73 0.77
N 103 103 103 103 103 103 103


We see that coefficient estimates are very stable. No coefficients change sign or significance. The total effect of Temperature on Effective Stature from Model 1 is -0.75, while the direct effect from Model 4 is -0.28. The direct effect of Temperature on Nutrition with this sample is -0.78 (Model not shown above) while the path coefficient of the direct effect on Nutrition on Effective Stature is 0.84, yielding an indirect effect of Temperature on Effective Temperature mediated through Nutrition of -0.66 (-0.78*0.84) and thus a total effect of -0.93 (-0.28-0.66).

Recall also that we have standardized all variables to have mean 0 and variance 1. So the fact that the intercept vanishes in the restricted sample suggests that the estimates in the last table are more reliable than the estimates in the penultimate table. Moreover, the model fit is much better with three-fourths of the variation in more than a hundred countries explained by Nutrition alone. We can thus be fairly confident that we have identification. We estimate that the total causal effect of Temperature on Effective Stature is between -0.75 and -0.93, of which less than –0.3 is the direct effect of Temperature on Effective Stature and the rest is mediated through Nutrition. We posit that since thermal burdens suppress productivity the direct effect of Temperature on Effective Stature is mediated through productivity and hence income. We’ll leave that question open for future study. What is clear is that the Heliocentric theory is very hard to reject.

Nutrition emerges from this analysis as both the principal mediator between Temperature and Effective Stature and the most important causal influence on Effective Stature in its own right. We estimate the direct effect of Nutrition on Effective Stature to be 0.84, close to the total effect implied by the univariate coefficient, 0.86. It is quite simply the single best predictor of living standards as captured by Effective Stature. The strength of the relationship between nutrition and our purely anthropocentric measure suggests that we were not remiss in thinking of effective stature as a good measure of underlying nutritional status.

The empirical evidence from anthropometry suggests that the main causal channel from latitude to global polarization in living standards runs through Nutrition.


Global Rankings by Net Nutritional Status

Global Ranking by Effective Stature
Ranking Country Effective stature (cm) Height (cm) BMI Life Expectancy (years) Population (million)
200 Ethiopia 157 166 20 63 64
199 Eritrea 158 168 20 63 4
198 Timor-Leste 159 160 21 67 1
197 Rwanda 160 163 21 NA 8
196 Bangladesh 160 164 21 71 137
195 Madagascar 161 162 22 64 16
194 DR Congo 161 167 21 59 52
193 Zambia 161 167 21 60 10
192 Uganda 161 166 22 59 24
191 Niger 161 168 21 59 11
190 Viet Nam 162 164 22 72 79
189 India 162 165 22 67 1,004
188 Cambodia 162 163 22 67 12
187 Burundi 162 167 22 58 7
186 Sierra Leone 162 164 22 49 5
185 Mozambique 163 165 22 57 18
184 Central African Republic 163 167 22 51 4
183 Myanmar 163 165 22 65 44
182 Nepal 164 162 23 69 25
181 Lao PDR 164 161 23 64 5
180 Malawi 164 162 23 60 12
179 Indonesia 164 164 23 68 NA
178 Tanzania 164 165 22 61 34
177 Chad 164 170 22 52 8
176 Senegal 164 173 22 65 11
175 Burkina Faso 164 169 22 59 12
174 Kenya 164 170 22 64 31
173 Equatorial Guinea 164 167 22 58 0
172 Angola 164 167 22 60 10
171 Congo 164 167 22 63 3
170 Sri Lanka 164 166 23 73 19
169 Zimbabwe 164 169 22 59 12
168 Afghanistan 164 165 23 62 24
167 Somalia 164 167 23 54 7
166 Guinea 164 168 22 58 8
165 Nigeria 165 166 23 54 123
164 Philippines 165 163 23 66 81
163 Lesotho 165 166 23 51 2
162 Benin 165 167 23 60 7
161 Togo 165 168 23 60 5
160 Ghana 165 169 23 62 20
159 Guinea Bissau 165 168 23 58 1
158 Botswana 166 172 23 62 2
157 Namibia 166 167 23 61 2
156 Liberia 166 164 23 58 3
155 Mauritania 166 163 23 63 3
154 Yemen 166 160 24 64 17
153 Mali 166 171 23 57 10
152 Sudan 166 167 23 63 NA
151 Comoros 166 166 23 62 1
150 Gambia 166 165 24 61 1
149 Pakistan 167 167 23 66 146
148 Bhutan 167 165 24 70 1
147 Cote d’Ivoire 167 167 23 53 17
146 Djibouti 167 167 24 62 0
145 Cameroon 167 168 24 56 15
144 Sao Tome and Principe 168 167 24 67 0
143 Japan 168 171 24 81 126
142 Thailand 168 169 24 72 62
141 Gabon 169 168 24 64 1
140 Cabo Verde 169 173 24 71 0
139 China 169 172 24 75 1,263
138 Swaziland 170 168 25 55 1
137 North Korea 170 172 24 68 21
136 Maldives 170 168 25 77 0
135 Singapore 170 173 24 81 4
134 Papua New Guinea 170 164 25 64 5
133 Mauritius 170 170 25 72 1
132 Algeria 170 170 25 76 30
131 Bahrain 170 168 25 78 1
130 South Africa 170 167 25 60 45
129 South Korea 170 175 24 79 47
128 China (Hong Kong SAR) 171 174 25 NA NA
127 Bolivia 171 167 25 69 8
126 Malaysia 171 168 25 73 22
125 Guyana 171 170 25 64 1
124 Guatemala 171 163 26 70 11
123 Solomon Islands 171 164 26 70 0
122 Taiwan 172 175 25 NA NA
121 Morocco 172 170 26 75 30
120 Cuba 172 172 25 77 11
119 Vanuatu 172 168 26 70 0
118 Honduras 172 166 26 73 6
117 Dominica 172 176 25 NA 0
116 Peru 172 165 26 74 26
115 Iran 172 174 25 75 63
114 Suriname 172 173 25 69 0
113 Mongolia 172 169 26 66 3
112 Colombia 172 169 26 72 40
111 Grenada 172 177 25 71 0
110 Armenia 172 172 26 71 3
109 Dominican Republic 173 173 26 71 8
108 Tajikistan 173 171 26 69 6
107 Antigua and Barbuda 173 173 26 73 0
106 Tunisia 173 174 26 74 10
105 Seychelles 173 174 26 69 0
104 Panama 173 168 26 75 3
103 Azerbaijan 173 170 26 70 8
102 Kyrgyzstan 173 171 26 67 5
101 Nicaragua 173 167 27 73 5
100 Uzbekistan 173 169 26 70 25
99 Ecuador 173 167 27 74 12
98 Jamaica 173 175 26 74 3
97 Oman 173 169 27 75 3
96 Brunei Darussalam 173 165 27 76 0
95 Kazakhstan 173 171 26 66 15
94 Saint Vincent and the Grenadines 174 173 26 70 0
93 Brazil 174 174 26 72 176
92 Costa Rica 174 169 27 77 4
91 Russian Federation 174 176 26 66 147
90 Greenland 174 175 26 NA NA
89 Portugal 174 173 26 79 10
88 Turkmenistan 174 172 27 64 4
87 Haiti 174 173 27 61 8
86 El Salvador 174 170 27 69 6
85 Paraguay 174 173 27 73 6
84 Venezuela 174 172 27 70 23
83 Trinidad and Tobago 174 174 27 69 1
82 Barbados 174 176 27 73 0
81 Fiji 174 174 27 67 1
80 Egypt 175 167 28 69 71
79 Belize 175 169 28 68 0
78 France 175 180 26 80 61
77 Mexico 175 169 28 74 100
76 Moldova 175 175 27 68 4
75 Libya 175 174 27 71 5
74 Albania 175 173 27 75 3
73 Syrian Arab Republic 175 170 28 55 16
72 Bahamas 175 173 27 73 0
71 Marshall Islands 175 163 29 NA NA
70 Saudi Arabia 175 168 28 74 23
69 Austria 175 177 27 80 8
68 Romania 175 175 27 72 22
67 Belarus 175 178 27 68 10
66 Turkey 175 174 27 73 67
65 Iraq 175 170 28 67 23
64 Italy 175 178 27 81 58
63 Netherlands 175 183 26 81 16
62 Uruguay 175 173 28 73 3
61 Denmark 175 181 26 79 5
60 Bosnia and Herzegovina 175 181 27 75 4
59 Micronesia (Federated States of) 175 169 28 69 0
58 Finland 175 180 27 79 5
57 Switzerland 175 178 27 82 7
56 Bermuda 175 173 28 NA NA
55 Slovenia 175 180 27 79 2
54 Saint Kitts and Nevis 176 170 28 NA 0
53 United Arab Emirates 176 170 28 77 3
52 Chile 176 172 28 77 15
51 Georgia 176 174 28 69 5
50 Spain 176 177 27 81 40
49 Serbia 176 181 27 74 10
48 Ukraine 176 178 27 66 49
47 Sweden 176 180 27 81 9
46 Montenegro 176 178 27 74 1
45 Occupied Palestinian Territory 176 172 28 NA NA
44 Bulgaria 176 178 27 72 8
43 Jordan 176 171 29 73 5
42 Luxembourg 176 178 27 81 0
41 Andorra 176 176 27 NA NA
40 Malta 176 173 28 80 0
39 Cyprus 176 175 28 79 1
38 Lithuania 176 179 27 69 4
37 Poland 176 177 28 74 39
36 Belgium 176 182 27 79 10
35 Argentina 176 175 28 74 37
34 Macedonia (TFYR) 176 178 27 74 2
33 Lebanon 176 174 28 75 4
32 Puerto Rico 176 172 28 NA NA
31 United Kingdom 176 177 27 80 60
30 Qatar 176 170 29 78 1
29 Kiribati 176 169 29 64 0
28 Palau 176 168 30 NA 0
27 Iceland 176 180 27 81 0
26 Canada 176 178 27 81 31
25 Israel 176 177 28 81 6
24 Estonia 176 182 27 73 1
23 Greece 176 177 28 79 11
22 Latvia 176 181 27 70 2
21 Slovakia 176 180 28 74 5
20 Norway 176 180 27 81 4
19 Germany 177 180 27 79 82
18 Nauru 177 168 32 NA NA
17 Kuwait 177 172 29 74 2
16 Australia 177 179 28 81 19
15 Tuvalu 177 170 30 NA NA
14 Saint Lucia 177 172 30 73 0
13 Hungary 177 177 28 73 10
12 New Zealand 177 178 28 81 4
11 Ireland 177 179 28 80 4
10 Czech Republic 177 180 28 76 10
9 Croatia 177 181 28 75 4
8 United States of America 178 177 29 77 282
7 Cook Islands 178 175 33 NA NA
6 American Samoa 178 176 33 NA NA
5 Samoa 178 174 31 72 0
4 Tokelau 178 175 32 NA NA
3 French Polynesia 178 177 30 NA NA
2 Niue 178 176 32 NA NA
1 Tonga 178 177 31 71 0

Notes. Effective stature is an actuarially fair measure of net nutritional status. It combines anthropometric and actuarial information and is meant to be interpreted as a general measure of living standards. Simply put, it is the combination of mean population height and mean population BMI (linear in the former and quadratic in the latter) that best tracks life expectancy. Effective stature contains roughly the same information as the Waaler Index. Our estimates are based on the Waaler surface we extracted from panel data. We have rescaled and recentered our estimates to match the mean and variance of average height across nations. One can thus think of it as effective or risk-adjusted stature.


An Ultra-Brief History of Living Standards, 10000BC-Present

Here’s what I see going on with polarization since the human career began. The orthodoxy has it that the Neolithic Revolution and the Industrial Revolution demarcate stadial social evolution. Both the Neolithic Revolution and the Industrial Revolution are either overrated or misdated. The former is dated to ten or twelve centuries before Christ and said to last until the birth of civilization; the latter to 1760-1830 Britain. If we buy the anthropometric evidence, the second is bunk. There is also good reason to believe that Andrew Sheratt is right on the money so that what really mattered in the former case was not the Neolithic Revolution but the Secondary Products Revolution which began at Uruk and spread out from there between 4000 and 3000 BCE.

What the anthropometric evidence points to is that the premodern pattern prevailed until the late-nineteenth century. Indeed, it was not until the mid-century passage, 1920-1960, that the hockey stick is hit in earnest. I want to argue that it was the Second Industrial Revolution, 1860-1960, that made the hockey stick in living standards possible in the temperate zone; that it was the Secondary Industrial Revolution that repealed the Malthusian law; just as Sheratt’s Secondary Products revolution made Uruk the first central (and then the only existing) power. The issue is that there were indeed two general revolutions in the material possibility frontier. These were the secondary revolutions that revolutionized the value of generalized domestications in the first case and in the second case, generalized industrial production with fossil fuel-powered machinery in agriculture, industry, and transport, thus revolutionizing the thermodynamic basis of civilization.

There is indeed some truth to the stadial frame. The secondary revolutions made possible hitherto unimaginable living standards. In the first case, this began at Uruk sometime during the Ubaid period. From there on Babylonia was a part of the Central Civilization—the longest continuously urbanized macro-region is the zone at the intersection of Europe, Africa, and Asia. This is of course no coincidence. What happened in Babylonia is that a major climate shock made the lower Euphrates extraordinarily fertile. At Uruk in the fourth millennium BCE, agricultural yields, pottery manufacturing, metallurgy took off; they invented writing, administration, the potter’s wheel, the plow and the wagon; domesticated oxen for traction, cattle for milk products, and the donkey for transport; and mastered micro-domestication (leavened bread, cheese, beer and wine). The ‘early high civilization’ is an extraordinary case of polarization. The Sumerians played an extraordinary role as the founders of the Central Civilization when they had the field to themselves in the fourth millenium BCE. It was the transmission of Babylonian wagon technology at the very edge of the Uruk world-system, the steppe (southern Russia) that triggered the very formation of the Yamanaya (Proto-Indo European speakers). The wagon allowed the Yamanaya to tame the steppe since they could exploit the otherwise meager open steppe by near constant movement, as David Antony has argued so forcefully. In the history of the peopling of the world by west eurasians, Uruk thus plays the dramatic role usually assigned to alien civilizations in fiction.

The Secondary Industrial Revolution identified by Gordon as the Second Industrial Revolution, 1870-1970, made both living standards and war potential higher than hitherto imagined. (See the evidence from stature.) More generally, the evidence from anthropometry cannot be reconciled with the orthodox narrative. Let’s not forget that the hockey stick adds a dynamic element to the global condition. Interestingly, latitude is not priced in c. 1880. Far from being a “constant,” latitude’s influence was weak in the premodern era when stature was a function of the local availability of protein. It is the hockey stick that radically polarizes the world in terms of living standards. Latitude itself has a history that has yet to be told. But then so do both the secondary revolutions.

Any credible deep history of human welfare must put the secondary revolutions at the center of the narrative frame.


The geometry of Waaler surfaces

Waaler (1984) wondered whether looking at both and weight would be more informative than a single measure of nutritional status such as stature or BMI (the ratio of weight in kilograms to squared height in meters). He suggested that one could plot mortality risk (or any other measure of mortality or morbidity risk) as a function of height and weight. This suggestion was realized by Kim (1996) in his doctoral dissertation who named the resulting graphical survival table representation a Waaler surface.


Figure 1. A Waaler surface.

The geometry of Waaler surfaces turns out to be particularly simple for stable populations. Kim (1996) observed that the mortality risk information encoded in isorisk curves tend to satisfy three empirical regularities. First, risk is monotonically decreasing in stature; taller populations have a higher nutritional status for the same BMI as shorter populations. Second, optimal BMI is a decreasing function of stature; taller populations need to have smaller BMIs to face the same mortality risk. Third, risk is quadratic in weight; at any given height, health status is a function of the squared distance from optimal BMI.

Kim (1996) defined the Waaler Index as the difference in overall risk between a comparison and a reference population attributable to differences in shifts along the Waaler surface; that is, the component explained by  differences in the frequency distributions of height and weight. Let A be the reference population and B the comparison population. Let f denote the joint density of height and weight and R the survival table arranged by height and weight. Then the Waaler Index is given by,


We can define an equivalent measure as follows. Notice that under the three regularity assumptions noted above, Waaler surfaces are effectively one-dimensional. Specifically, we can map all points on an isorisk curve to the point where the isorisk curve intersects the optimal weight line. In Figure 2, for instance, B is risk-equivalent to D. This means that the Waaler Index captures exactly the same information as what we will call effective stature: the mean stature of a population facing the same average risk as B but with optimal BMI. This single overall measure captures all the actuarially-relevant information contained in the Waaler surface.


Figure 2. Risk measures with Waaler surfaces.

Under the same regularity conditions as above, we obtain a separation of variables. Even though risk is a joint function of height and weight, we can decompose the effect of BMI and stature geometrically. In Figure 2, B and C have the same stature. The difference in their mortality risk is the BMI risk premium, the greater risk incurred due to a suboptimal BMI. The difference in risk between A and C is then due solely due to the lower stature of population C and not due to BMI. We call this the stature risk premium. We can measure both in either centimeters or survival probabilities. We shall use the former.

Note that BMI is a measure of short-term health status while stature is a long-term measure of health status. This difference is extremely important for it allows us to think of the stature risk premium (the difference in stature between the comparison population and the reference population) as reflecting steady-state differences between populations since stationary populations sit on the optimal weight curve by construction. In economic history applications then, it is this latter measure that has pride of place. For instance, the settler premium in the early modern era that we isolated should be thought of in terms of the stature risk premium. Similarly, one can think of the latitude premium that exists due to differential protein availability at different latitudes (say as captured by cattlehead per capita).


Figure 3. Settler premium and latitude premium.

So we obtain two different anthropometric measures of health status. Stature risk premium is suitable for questions of long-term socio-economic polarization. Effective stature is an actuarially fair measure of health status suitable for overall contemporaneous evaluations. The two charts after the references are from Kim (1996).

Waaler, Hans Th. “Height. Weight and mortality the Norwegian experience.” Acta medica scandinavica 215.S679 (1984): 1-56.
Kim, John M. Waaler surfaces: the economics of nutrition, body build, and health. Diss. PhD dissertation, University of Chicago, USA, 1996.