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.



Latitude and World Order: Evidence from the Cross-Section of Human Stature

Adam Tooze​ wrote recently about the challenge posed by economic statistics both to historical actors and to historians. The upshot is that all national economic statistics must be taken with a pinch of salt. This concern has prompted me to focus on human stature instead of per capita income and output per worker as the carrier of information on global polarization. What I have discovered has astonished me. The picture that emerges suggests that latitude was not in fact all that important until the passage to modernity. Indeed, the empirical evidence reveals that the world got polarized along latitude only in the twentieth century. It suggests that a satisfactory history of global polarization has yet to be written; one that ties the polarization of global living standards to the Second Industrial Revolution.


Figure 1. Transition to modernity in global stature. Our reported gradient is the product of (1) the slope coefficient in a simple linear regression with both variables standardized to have mean 0 and variance 1 (also called beta) and (2) 1-pValue of said slope coefficient. This means that insignificant coefficients are mechanically attenuated.

The basic outline of human statures over the past three hundred years is that until about the mid-nineteenth century the classic premodern pattern held—everywhere we had medium-term cycles characteristic of the Malthusian Trap and a significant settler colonial premium in stature. In 1860-1890, the settler colonial premium vanishes, but global polarization was still modest. It is not until 1920-1960 that we hit the hockey stick in earnest. In the century 1860-1960, Western heights grew 10cm on average; 7cm in 1920-1960 alone. Elsewhere heights grew much more modestly. By 1960, global statures stabilized in the modern pattern—highly polarized along latitude with the Dutch leading the way. Everyday living standards were revolutionized by the Second Industrial Revolution because it was broad-based enough to repeal the Malthusian Law. That’s why the settler premium vanished and we hit the hockey stick. Any explanation of global polarization must take latitude as the point of departure because thermal burdens dictate the work intensity that can be sustained on the factory floor and therefore the cross-section of output per worker.


Figure 2. Latitude and stature.

With this interpretation in mind (premodern 1700-1890, hockey stick 1920-1960, modern regime 1960-) the following estimates make for very interesting reading. Turns out, latitude was not the strongest correlate of stature in premodern 1880; it was cattlehead per capita. (As it presumably had been since the Secondary Products Revolution.) To be sure, latitude was definitely priced in as well. But latitude explained less than 10 percent of the variation. (The percentage of the variation in Y explained by X is just the square of the gradient once we standardize both X and Y to have mean 0 and variance 1.)  Meanwhile, cattle per head explained 37 percent of the cross-sectional variation in 1880. This is evidently the premodern pattern. Given the extraordinary cost of bulk transport, the governing variable for stature was the local availability of protein (meat and secondary). It is astonishing that this premodern pattern persists until as late as 1880. The exit from the Malthusian Trap was indeed very, very slow.


Figure 3. Transition to modernity. Latitude, cattlehead, and stature.

By 1920, the relative positions of latitude and cattlehead per capita had reversed. The latter fell into insignificance. But latitude explained no more than 18 percent of the cross-sectional variation so that everyday living standards were still only modestly polarized. It is only in 1960 (and thereafter) that the coefficient of latitude becomes 0.68, meaning that it singlehandedly explained 46 percent of the cross-sectional variation in stature. This corresponds to the considerably heightened polarization in everyday living standards in the modern era (1960-). Cattlehead meanwhile continues to be priced in (even after controlling for latitude) but explains only a modest 5 percent of the variation. See the estimates reported in Table 1-3 below and Figure 3 above.


Figure 4. Per capita income and stature.


Figure 5. Disease burden and stature.

Before the turn of the century, latitude was priced into the cross-section of stature but not after controlling for cattlehead per capita. Astonishingly, even per capita income is not a significant correlate of stature (in 1920 and 1960—we don’t have sufficient observations to test this in 1880) once we control for latitude or disease burdens (infant mortality). The evidence can be read off Table 1-3.

Table 1. Stature, 1880
Standard errors below estimates. Estimates in bold font are significant at 5 percent.
Latitude 0.32 0.25 0.32
0.14 0.13 0.25
Cattle 0.61 0.51
0.15 0.16
Infant mortality -0.29 -0.34
0.11 0.14
Income 0.54 0.43 -0.04
0.17 0.19 0.19
N 42 43 11 18 39 18 18
R^2 0.12 0.30 0.42 0.39 0.36 0.45 0.45
adj R^2 0.09 0.28 0.36 0.35 0.32 0.37 0.37
Table 2. Stature, 1920
Standard errors below estimates. Estimates in bold font are significant at 5 percent.
Latitude 0.43 0.39 0.54
0.12 0.13 0.22
Cattle 0.36 0.23
0.12 0.13
Infant mortality -0.36 -0.23
0.17 0.23
Income 0.85 0.53 -0.12
0.17 0.20 0.43
N 58 61 13 23 55 23 23
R^2 0.19 0.13 0.28 0.53 0.25 0.64 0.64
adj R^2 0.18 0.11 0.21 0.51 0.22 0.60 0.60
Table 3. Stature, 1960
Standard errors below estimates. Estimates in bold font are significant at 5 percent.
Latitude 0.68 0.67 0.58
0.10 0.10 0.20
Cattle 0.33 0.21
0.12 0.11
Infant mortality -0.72 -0.74
0.10 0.19
Income 0.66 0.18 -0.04
0.10 0.20 0.19
N 58 61 43 58 55 51 51
R^2 0.45 0.11 0.58 0.42 0.50 0.49 0.49
adj R^2 0.44 0.09 0.57 0.41 0.49 0.47 0.47

The empirical case for the Heliocentric model becomes even stronger once we observe that per capita income and disease burdens (and cattlehead until 1920) are themselves functions of latitude. See Table 4.

Table 5. Functions of latitude.
Standard errors below estimates. Estimates in bold font are significant at 5 percent.
Infant Income Cattle
1880 1920 1960 1880 1920 1960 1880 1920 1960
Latitude -0.19 -0.34 -0.84 0.48 0.70 0.84 0.41 0.34 0.25
0.64 0.45 0.09 0.27 0.18 0.09 0.13 0.13 0.13
N 11 13 39 20 23 52 55 56 56
R^2 0.01 0.05 0.71 0.15 0.42 0.65 0.16 0.11 0.06
adj R^2 -0.10 -0.04 0.71 0.10 0.39 0.65 0.14 0.09 0.05


Table 6. Gain in stature, 1920-1960
Standard errors below estimates. Estimates in bold font are significant at 5 percent.
Latitude 0.56
Cattlehead per capita (change) -0.08
Per capita income (change) 0.33
Infant mortality (change) -0.64
N 58 61 23 13
R^2 0.29 0.01 0.13 0.41
adj R^2 0.27 -0.01 0.08 0.36

What is especially striking is that gain in per capita income is a poor predictor of gain in stature. Change in per capita income in 1920-1960 does not explain gain in stature in the same period (although admittedly, the sample is small). What explains the cross-section of the gain in stature is again latitude. See Table 5. Also compare the bottom-right graphs in Figure 2, Figure 4, and Figure 5.

So the question is not whether but why global living standards are polarized along latitude. Moreover, the weight of the empirical evidence suggests a very late date for polarization in living standards. Before the onset of the global condition living standards were not radically different across the world. As late as 1920, the gradients were modest. Polarization in global stature really and truly obtains only during the mid-century passage, 1920-1960. This is consistent with the modern understanding of global living standards we find in the work of David Edgerton and Adam Tooze. Fascinating that one can read it off the cross-section of stature so clearly.


An Illustrated Guide to Western Stature, 1700-2000

It has recently been rediscovered that stature contains information about the populace’s health, well-being and standard of living. Now that we are all sick of national economic statistics, perhaps it is time to examine the evidence from human biology. It is known that mean national height is a strong correlate of per capita income, life expectancy, infant mortality, disease burdens, latitude and mean temperatures in the cross-section. We shall however concentrate on the dispersion and evolution of Western stature in this dispatch, for as we shall see, this variable contains very interesting information on historical polarization within the Western world.


Figure 1. Western stature, 1710-1990. Source: Clio Infra.

Figure 1 displays the mean heights in eight rich, Western nations. In the eighteenth century, the Americans towered over the Europeans. In 1710-1790, they were on average around 5cm taller than Britons, Swedes and Dutch, 6cm taller than the Italians, and 7cm taller than the French. In the nineteenth century, we see Americans and Canadians towering over the Europeans. This supremacy was not confined to North America. Figure 2 shows stature in Anglo-Saxon settler colonies and Britain. We see that there existed a significant setter colonial premium in stature that did not vanish until the end of the nineteenth century. Despite the British Industrial Revolution in 1780-1830, Britain did not close the gap with the Americans, Canadians, Australians, and the Kiwis until the turn of the century.


Figure 2. Anglo-Saxon stature. Source: Clio Infra.

We can calculate the settler colonial premium more broadly as the mean difference with American heights. Figure 3 displays this measure. We see that the premium broadly vanished over the course of the late-19th century. Note that the US-Canadian differential is bounded by (-2cm,+2cm), which we can think of as containing information on the underlying volatility of the error term. With this ballpark in mind, we can be confident that the ~6cm premium during the ancien régime, 1700-1860, is significant. Note that 6cm is the central tendency until the mid-nineteenth century. But the range is wide. Americans were more than 10cm taller than Germans in 1840, but only 4cm taller than Swedes. Britons came within reach of a 2cm premium in 1750 but diverged again, not to close the gap until the turn of the century. And it was really only in 1930 that Britons became taller than Americans for the first time.



Figure 3. Settler colonial premium in Western stature, 1710-1980. Source: Clio Infra.

More broadly, the settler colonial premium vanished over the course of the late-nineteenth century. But the transition to modern stature does not take place until the mid-20th century. Go back to Figure 1. As late as 1920, we had no observations over 174cm. By 1960, they are all above 174cm. So we have two different transformations. First, the settler colonial premium vanishes in 1860-1890. Then, after 1920 but continuing a movement that started decades earlier in many countries, mean heights increase rapidly until they stabilize by 1960.

In the modern regime, 1960-1980, the Dutch have enjoyed an extraordinary primacy. They are about 2-3cm taller than the Germans and the Swedes, 3-4cm taller than Americans and Canadians, 6cm taller than Britons and the French, and an extraordinary 8cm taller than the Italians. This polarization is suggestive. Might the naive Heliocentric theory explain it? It is indeed known that latitude is priced into the cross-section of stature. Since we don’t have a large enough sample we cannot try to replicate that result. Still, Figure 4 suggests a ballpark estimate of 20mm per degree so that a 20 degree difference in latitude predicts a 4cm difference in stature. That’s a very impressive gradient for what is dismissed as a “Tropical issue.” And the earlier estimates for the gradient are much larger. The truth is likely closer to the latter since even after the vanishing of the settler colonial premium, the United states is an outlier. The problem is of course that the US is so large that even though it has a mean latitude of 37º, much of the country lies in the temperate zone. So the true gradient is probably closer to 30-40mm per degree than 20mm, implying that a 20 degree increase in latitude would predict a 6-8cm gain in stature with all that implies about everyday living standards.


Figure 4. Latitude and stature in selected Western countries. Source: Clio Infra, author’s computations. Small sample estimates. Note that we drop the United States and Canada from our 1820 and 1860 samples to avoid the distortion induced by the setter premium.

How do we make sense of the panel evidence in Figure 1? We suggest the following periodization: premodern era 1700-1860, transition period 1860-1960, and modern era 1960-1980. A significant setter colonial premium of around 4-8cm was the invariant of the premodern era. European stature was always below 170cm, roughly around 167cm, while the Anglo-Saxon setters were all above 170cm, roughly around 172cm. National stature went up and down in medium-term cycles characteristic of the Malthusian trap. Multiple cycles can be discerned in Figure 2. As late as the mid-19th century Americans were getting shorter by the decade. Things got better for two or three generations, then they got worse for a while. Stature fell together with real wages and life expectancy. Repeat ad infinitum … or more precisely, until the exit from the Malthusian trap. That exit did not obtain until after 1900. See Figure 5.

Screen Shot 2018-07-05 at 2.27.18 AM

Figure 5. Decadal growth in stature in the US, Britain, and Canada. Source: Clio Infra.

In the modern era, 1960-1980, Western heights were distributed around 180cm, a full 10cm above the Malthusian boundary between the settler colonies and the continent. They are ordered roughly by latitude with the Dutch leading the way. Dutch primacy is an invariant of the modern regime. But the broader Heliocentric polarization is a much older story. It holds before and after the exit from the Malthusian trap.

During the transition era, we first see the collapse of the settler colonial premium in 1860-1990, and then the beginnings of a major upward movement in 1890-1920. But it is only in the course of the transformative mid-century passage, 1920-1960, that all previous records for mean stature are broken. As late as 1920, the Western average was still 171cm; high for a premodern European country but not for the settler colonies. But by 1960, the Western average jumps to 178cm. Over the whole century of the transition to modernity, 1860-1960, Western stature increased by 10cm; clocking an astonishing rate of increase of 1cm per decade.

The evidence from human stature suggests that the physical environment dictated everyday basic living standards in the ancien régime. This meant that there was a significant settler premium. Anglo-Saxon setters dwarfed Europeans. The vanishing of this setter premium in 1860-1890 suggests an earlier data for transition to modern living standards than the period of major growth in Western stature, 1930-1960. But these suggested dates are in fact consistent. What we have here is this: The Second Industrial Revolution, which unlike the more limited British revolution, 1760-1830, was broad-based enough to repeal the Malthusian Law. The vanishing of the setter colonial premium attests to this fundamental transformation in the nature of the game. It is only then, after the turn of the century, that everyday living standards are revolutionized. We emphasize that the revolution in Western living standards obtained very, very slowly. It is not until the mid-century passage that we hit the hockey stick in earnest.

The revolution in stature was in no way confined to the Western world. Figure 7 shows that the transition to the modern pattern was global in 1860-1960. The global median rose from 165cm in 1860 to 170cm in 1960, exactly where it is now. Although patchy coverage suggests caution, there seems to have been a decline in global stature in the neoliberal era. Median global height fell 2cm in 1980-1990, then recovered half the loss in 1990-2000.

Neoliberal collapse in global stature

Figure 7. Evolution of global stature. Source: Clio Infra.

The broad historical pattern of Western and global stature suggests that the transition to modernity took place in 1860-1960. This was accompanied by a Great Divergence in living standards. Western stature rose roughly 10cm from around 170cm to 180cm, while world-wide (Western and non-Western) median stature rose by only 5cm from 165cm to 170cm, implying that the rise in non-Western standards was much more modest.

Bonus chart.


Figure 8. Setter colonial premium in Anglo-Saxon stature. Source: Clio infra.


Isotherms and Regional Polarization: Evidence from Italy, US, Chile, China, and India

It was argued in the previous dispatch that the international cross-section of productivity and hence per capita income is explained by the distribution of heat on the surface of the planet. More precisely, productivity is a function of the intensity and tempo of work performed in a factory. And the intensity and tempo of factory work is a function of the thermal environment. That the human thermal balance is a binding constraint on work intensity in countries across the globe is clear from known facts about global temperatures (countries face wildly different thermal regimes) together with known facts about the human physiological response to heat (the human thermal balance equation).

Wet bulb temperature

Figure 1. Work performance and heat. Source: Wyndham (1969).

Figure 1 shows the fall-off in work performance in a South African mine where precise control of wind velocity and wet bulb temperature allowed Wyndham to carry out scientific controlled experiments. As a physiologist in Apartheid South Africa, Wyndham was able to test racial differences under controlled conditions. What he found was that the fall-off in productivity as a result of heat was more or less uniform across the races. The most important factor in work intensity was acclimatization. Between acclimatized Bantu and South African White men, the differences in heat tolerance and productivity were minor compared to the importance of wind velocity, which is already a second-order correction to the contribution of humidity-adjusted temperature (“wet bulb temperature”).

The Heliocentric model has a specific implication for the regional polarization of countries straddling isotherms. Namely, cooler regions should be richer than warmer regions. We can test this hypothesis by visual inspection of per capita income and temperatures. We begin with Italy.


Figure 2. Isotherms and per capita income distribution in Italy.

Figure 2 displays the mean temperatures and per capita incomes in Italy. This is the  pattern we expect to find if the Heliocentric Hypothesis is true. The cool, northern extremity had a mean per capita income above 30,000 euros in 2010; the hot, southern half of the Italian peninsula had a mean per capita income less than 18,000 euros. The former is close in per capita income to the countries of northwestern Europe; the latter to the Mediterranean region.

If the Heliocentric model is correct, mean temperatures should be “priced in” the cross-section of per capita income across regions. By that we mean that the gradient in a simple linear regression of per capita income onto mean temperatures should be economically and statistically significant. This is easy enough to check by hand.


Figure 3. The Italian cross-section.

Figure 3  displays the mean urban temperatures and per capita incomes of the Italian administrative regions. We obtain a statistically significant gradient of 1,683 euros per degree Celsius. That is, a six degree difference, such as that which exists between Sicily and Lombardy, translates into a difference of nearly 11,000 euros in per capita income. The scatter plot in fact suggests that there are two quite different clusters with their own gradients: Rich Italy, Poor Italy. Sardinia has the highest income of the latter but is still shy of 20,000 euros. Liguria has the lowest income of Rich Italy, 27,200 euros. There is a “gap” of 7000 euros where we have no observation.

Figure 4 displays Rich Italy and Poor Italy data two side-by-side. The gradient of mean temperature for rich Italy is a statistically significant 927 euros per degree Celsius; that of the poor Italy is not statistically significant but it has the right sign. The thermal variable explains 30 percent of the variation in the full sample, and 47 percent of the variation once we restrict the sample to the rich regions. That’s very high.



Figure 4. Rich Italy, Poor Italy.

Table 1 displays the mean temperature and per capita incomes of the 15 administrative regions of Italy.

Table 1. Regional polarization in Italy.
Region Per capita income Mean temperature (Celsius)
Sicily 16,600 18.4
Apulia 17,100 15.8
Campania 16,000 15.7
Lazio 29,900 15.7
Liguria 27,200 14.7
Emilia-Romagna 32,100 14.0
Tuscany 28,200 13.6
Sardinia 19,700 13.5
Piedmont 28,200 12.6
Calabria 16,400 12.4
Lombardy 33,900 11.9
Veneto 30,200 11.9
Basilicata 18,300 11.7
Trentino-Alto Adige 34,450 10.0
Aosta Valley 33,700 9.7

We move on to the United States. Figure 3 displays the cross-section of per capita income for US states. When we project per capita income onto mean temperatures we obtain a gradient of $740 per degree Celsius (statistically significant at 5 percent). That is, if the mean temperature of a state is just 5 degrees Celsius higher, we expect its per capita income to be $3,700 lower. To be sure, the temperature gradient only explains 12 percent of the interstate variation in per capita income, so this is obviously an inadequate theory of regional polarization in the United States. But the gradient is priced in. And that is really remarkable. The United States is the most powerful and capable state in the world. If even the US cannot counter the polarization induced by the heat, we ignore the thermal variable at our own peril.


Figure 3. Regional polarization in the United States.

A very interesting case is that of Chile. It extends more than 4000 kilometers on a roughly north-south axis but is nowhere more than 200 kilometers wide. It hugs the Andes for almost the entire length with the result that elevation plays a very significant role in governing the isotherms (lines of equal temperature). The northern bit is the Atacama desert; sparsely populated and with significant mining wealth. The southern bit is again sparsely populated forest merging into tundra as one goes further south. The central zone is the bread-basket where two-thirds of the population lives. We have to keep these observations in mind when we examine Chile’s regional polarization.


Figure 4. Chile, population density and per capita GDP.


Figure 5. Chile, rainfall, temperature, and per capita GDP.


Half the Chilean population lives in Santiago and Valparaíso where the per capita GDP is in the range $20,000-$25,000. The Köppen climate classification of these two regions is Cfc meaning that they have a temperate climate with a dry, cold summer. This is very attractive territory and the concentration of population here is no coincidence. By contrast, Maule, Bío Bío and Araucanía, where a quarter of the Chilean population lives, are classified as Csb, meaning that they have a temperate climate with a dry, warm summer. Their per capita income is in the range $11,000-$16,000. So the difference between a temperate climate with dry, cold summer and a temperate climate with dry, warm summer translates into a $9,000 advantage. That’s roughly the difference is per capita income between Wisconsin and Kentucky.

Though it has a low population density, O’Higgins is exceptional. Despite hot summers, the million odd people of O’Higgins have an average income of $21,500. (Geography is not destiny.) The high per capita incomes in some of the sparsely populated northern and southern regions is a function of mining activity that is quite pronounced particularly in the Atacama desert.

Table 2. Regional polarization in Chile.
Name Latitude rank Area Population Population density per capita income Climate
Arica and Parinacota 1 16,873 239,126 14 13,268 Cold arid desert
Tarapacá 2 42,226 336,769 8 27,100
Antofagasta 3 126,049 622,640 5 60,439
Atacama 4 75,176 312,486 4 29,278
Coquimbo 5 40,580 771,085 19 14,355
Valparaíso 6 16,396 1,825,757 111 20,223 Temperate, dry cold summer
Santiago 7 15,403 7,314,176 475 25,328
O’Higgins 8 16,387 918,751 56 21,501 Temperate, without dry season, hot summer
Maule 9 30,296 1,042,989 34 13,971 Temperate, dry warm summer
Bío Bío 10 37,069 2,114,286 57 15,633
Araucanía 11 31,842 989,798 31 11,574
Los Ríos 12 18,430 404,432 22 14,623 Temperate, without dry season, warm summer
Los Lagos 13 48,584 841,123 17 16,277
Aysén 14 108,494 108,328 1 26,949
Magallanes 15 132,291 164,661 1 27,968 Temperate, without dry season, cold summer

We turn now to Asia where the real action is. At least if the following “high-pass” population density map is interpreted strategically. Germany, the Gangetic plain and the region between the Yangtze and the Yellow Sea emerge as the core regions of the globe.


Figure 6. A “high-pass” world map of population density.


Figure 7. A “high-pass” map of population density in eastern Eurasia.

The “high pass” density map in Figure 7 shows a finer resolution of the core regions of eastern Eurasia. This is the key figure to keep in mind. On the subcontinent, population densities are very high along a vast belt stretching from Punjab to Bengal. This is good alluvial soil constantly replenished by the floodwaters of the Ganges. The same riverine detail is behind the Chinese distribution. (Note the shape of the high density zone in China.) Indeed, Asian population density maps onto the river systems originating in the Tibetan plateau. See Figure 8.


Figure 8. The Tibetan origins of the river systems of eastern Eurasia.

We have to keep these in mind as we look at India and China. The two have been dealt very unequal hands by the dealer. Recall the thermal map of the globe (Figure 9 below) that displays the number of days of the year with temperatures above 20 degrees Celsius. We see that India is hot, while China is cool. However, southern China is hotter than northern China. Might this explain the density map of China in Figure 7?

Days exceeding heat load

Figure 9. Number of days above 20 degrees Celsius.

Let’s take a closer look at China’s geography. Figure 10 displays density by administrative region. We see that the core region is a triangle with vertices in Beijing, Henan, and Zhejiang. The center of mass is Jiangsu, and of course, Shanghai. Call it “the Han triangle.” In southeastern China, only Guandong exceeds 400 persons per square kilometer.


Figure 10. Population densities in China.

Keeping that Han triangle in mind, observe the location of the high income provinces in Figure 11. The northern coastal provinces, Beijing, Tianjin, Jiangsu, Shanghai, and Zhejiang, are not only more populous but richer than the southern coastal Guangdong and Fujian. Even Shandong is more populous and as rich as Guangdong. Only Henan is more populous but poorer; but it is inland. Beyond river basins and coastlines, Can isotherms explain this over-weighting of wealth and population in Jiangsu and Shanghai?


Figure 11. China’s regional polarization.

Figure 12 suggests that isotherms may be a factor. The cool provinces lying across the Yellow Sea (Beijing, Tianjin, Jiangsu and Shanghai) are favored over the warm provinces lying across the East China Sea (Zhejiang), which are in turn favored over the still warmer provinces facing the Taiwan Strait (Fujian), and all of them are trailed by the hot provinces facing the South China Sea (Guangdong and Hainan). Before the Yangtze bends upwards towards Shanghai, the temperature gradient does not turn favorable until well beyond the northern shores of the Yangtze. Riches and people are overweight Jiangsu relative to Guangdong, despite the latter being the center of gravity of maritime trade, because the former is cooler. More generally, the northern bias of the coastal core of China has the definite imprint of the macroclimate.


Figure 12. Chinese isotherms.

We turn last to India before gathering our results. As we saw in Figure 7, the Indian population is packed into the Gangetic plain stretching from Punjab to Bengal. There is an independent high density zone in the extreme south.


Figure 13. Indian population density by state.

Figure 14 shows that mean average temperatures on the vast bulk of the subcontinent, including the Gangetic belt, range over 20-30 degrees Celsius. By comparison, the region with the highest mean annual temperature among Italian administrative regions is Sicily at 18 degrees Celsius. Lombardy and Veneto have a mean of 12 degrees. If the Heliocentric model is right, India is twice as disfavored as Sicily compared to Lombardy. Unfortunately, because it is so hot everywhere in India except the northern and northeastern extremities, we should not expect the thermal variable to be priced in the cross-section of state-level per capita income. The Heliocentric model’s main implication for the subcontinent would be higher expected incomes in the regions that are cooler—J&K, Himachal, Uttarakhand, Nepal, Sikkim, Bhutan, Meghalaya and Arunachal.


Figure 14. Indian isotherms.

The evidence from Figure 15 is not altogether unfavorable. Sikkim and Uttarakhand do have high incomes; Himachal and Arunachal also have modestly higher incomes than average. But Meghalaya and J&K do not; although that comes as no surprise since both are sites of violent insurgency and counter-insurgency. The odds of observing this configuration by chance are not terribly low, so we should take this evidence with a pinch of salt.


Figure 15. Per capita GDP, Indian states.

Time then to gather our results. We documented that the thermal variable is priced into the cross-section of per capita income across US states and Italian administrative regions. We documented evidence of climate-related polarization of the core regions of Chile and China. We also documented some evidence of an income advantage in exceptional Indian states with cooler climates. The weight of the qualitative and quantitative evidence marshaled so far is consistent with the hypothesis that the distribution of heat on the surface of the earth is an important cause of regional polarization. It would be ideal to test the Heliocentric model at a finer resolution, say county level, and for as many nations and macroregions straddling isotherms as possible. It would also be useful to flesh out the geoeconomic, geopolitical and grand-strategic implications of the Heliocentric model. We’ll leave these two tasks to future work.



What explains the Polarization of the Globe?

Why are some nations rich and others poor? Why are some powerful and other weak? What explains the roster of great powers? What explains the global distribution of wealth and power? What explains the cross-section of per capita income? Who put the responsibility of the world on the shoulders of the White Man? Who put the Anglo-Saxon in the cockpit of history? Why have all modern great powers hailed from the northern temperate zone? All of these questions can be folded into the question posed in the title of this essay.

There is a sort of consensus among economic historians that the international cross-section of per capita income is roughly a question of the spread of the Industrial Revolution. Countries that industrialized are rich, those that did not are poor. And as countries industrialize they become richer. More precisely, the variation in per capita income is explained by the variation in labor productivity. Countries close the income gap with the rich, industrialized nations when their output per worker catches up with that of the latter; otherwise, they don’t. What needs to be explained then is the cross-section of output per worker. We will return to this question presently.


Figure 1. Source: ILO, author’s computations. We restrict our sample to big countries with populations over 30 million that together account for 4.8 billion of the world’s 7.6 billion people. This excludes all sub-Saharan African countries except Sudan and South Africa.

In the preindustrial world, some places were richer than others but the globe was an order of magnitude less polarized. Living standards were comparable across the core regions of Europe, India, China, and Japan as late as the eighteenth century. Modern standards of living are the result of the Second Industrial Revolution, concentrated in 1890-1940 but extending over 1870-1970, that witnessed the advent and dissemination of key technologies—penicillin, indoor plumbing, electricity, industrial chemistry, and above all, powered machinery. To be sure coal-powered versions of the last were at the center of the cotton textile, steamship and railroad revolutions in Britain in the early-19th century. But mass production with powered machinery did not become generalized well into the 20th century. In either case, the sustained escape from Malthus was the result of a thermodynamic revolution: powered machinery allowed the energy stored in the muscles of man and beast to be supplemented by the energy stored in hydrocarbons. The scale of work that could be performed on the farm and on the factory floor was no longer bounded by the muscle energy of working mammals. And that is what made modern living standards possible; that’s what is responsible for the hockey stick.

The mechanical foundation of modern prosperity raised hopes that that nations that are now poor can industrialize and thereby escape their poverty. Surely there are no insurmountable social or natural obstacles in the acquisition of competence in working with powered machinery? Barriers to cross-border flows of machinery, knowhow, and best-practices are also not insurmountable. Nor certainly is funding; not with the mobilization of modern nation-states. Moreover, low real wages in the poor nations seemingly promise an extraordinary reward to global firms willing to relocate production. Why then has the spread of global industrial production been largely confined to Northeast Asia, Europe, North America, and Oceania? Why have the nations of South America, sub-Saharan Africa, the Middle East, South Asia, Indochina, and Southeast Asia, failed to industrialize before and after independence, and before and after liberalization?

In order to answer this question we have to go to the source of the power. We have to take a closer look at powered machinery. The controlling variable is the (quality-adjusted) rate of production that is achieved by the factory. The secret sauce of powered machinery is the performance of precisely repeated mechanical tasks with great frequency. The repetition is mathematically a harmonic oscillation—the underlying principle of the pendulum. The harmonic oscillator can be thought of as the source of the stability of mechanical movement even at great rapidity. The main difference between the pendulum clock and powered machinery lies in the fact that the rate of the latter is variable and read against the former, even as the former marks the relentless march of time. The game of high productivity is to do this really fast and at scale. It requires clever engineering and factory discipline. More precisely, it requires worker submission to a definite tempo of factory work.

Are the cross-country differentials explained by variation in machinery? or are they explained by the variation in work intensity? In order to disentangle the two we have to look at the cross-country variation in the rate of production with the same powered machinery. That isolates the variation accounted for by factory discipline. What we find in such controlled comparisons is that there is great variation in work intensity—enough to account for the bulk of the gap in output per worker between nations. The breaks are frequent; the machines are left idle for much longer; absenteeism is rife. Even when the worker is at the machine, the pace of work is slower and the work load much lower. Bombay textile workers would mind two spindles in 1920s, where on the same machinery, American workers would mind six. Then as now, in India and across the South, it takes too many workers to do the same amount of work on the exact same machine. Why is that?

We argue that work intensity and factory discipline are functions of the macroclimate of the workers. The globe is polarized the way it is because of the polarization of man’s lifeworld by a merciless sun. Specifically, a harsh sun beats down between the Tropic of Cancer and the Tropic of Capricorn. Work intensity is affected directly by the thermal environment of the factory, as well as indirectly through the epidemiological consequences of the sun’s hostility and the crippling trauma thereby visited upon the inhabitants of the torrid zone. Figure 2 displays two thermal maps of the globe. Left: Number of days of the year the temperature exceeds 20 degrees Celsius. Right: Number of days of the year the temperature exceeds 32 degrees.


Figure 2. Source: Jendritzky and Tinz (2009). Left: days above 20; right: days above 32.

The thermal environment of the factory means frequent breaks are required to cool down. Put simply, work intensity cannot be sustained at the rate of the temperate world with temperatures well beyond the limits imposed by the human thermal balance. Figure 2 shows the maximum temperatures by work intensity recommended by the ISO. Intense work should not be undertaken when the temperature is above 25 degrees Celsius; light work 30 degrees. Above 33 one is at risk of overheating, even if one is at complete rest. In Southeast Asia, Indochina, South Asia, the Middle East, sub-Saharan Africa, and South America, mean temperatures range over 20-40 degrees Celsius. The thermal environment of the factory thus places a sharp and binding limit on the rate and intensity of work performed in a factory.

reference ISO

Figure 3. Source: Kjellstrom et al. (2009).

Not only does the merciless sun make sustained, disciplined factory work incompatible with the human thermal balance, it encourages the proliferation of pathogens, parasites and vectors that sap the strength of the populace of the torrid zone. The mosquito vector, for instance, is endemic to the zone between the January and July 10 degree isotherms displayed in Figure 4. According to the WHO, more than 3.9 billion people in over 128 countries are at risk of contracting dengue, with 96 million cases estimated per year; and malaria causes more than 400,000 deaths every year globally, most of them children under 5 years of age. Other vectors include sandflies, triatomine bugs, blackflies, ticks, tsetse flies, mites, snails and lice.


Figure 4. Source: WHO.

But leading off vectors is misdirected. The issue is not actually vectors but microbial pathology. Germs proliferate luxuriantly in the torrid zone causing a long list of infectious diseases that sap the strength of people already weakened by the scorching sun. Food, culture, behavioral norms, worker behavior are all shaped by the overwhelming need to counter the unrelenting hostility of the heat and the fever. Spicy food, frequent hydration, staying out of the sun, frequent rest, and indeed, minimal physical exertion in the heat—these are adaptations of the people of the torrid zone.

There are limits to human adaptation to the thermal environment. The heat still takes its toll. Childhood infections stunt and cripple the populace. Even people who survive to be healthy adults are periodically put out of action by the deadly germs. But is it reasonable to think that the direct burden of the disease would dominate work intensity on the factory floor? Then how do we make sense of the fact that the strongest correlate of output per worker is the WHO’s measure of per capita years lost to infectious disease?


Figure 5. Source: WHO, author’s computations.

Figure 4 documents the cross-sectional evidence. We have rescaled the observations by per capita income only for visualization; the fit is unweighted. We restrict our sample to 24 countries with more than 30 million people. Together they account for 4.8 billion of the world’s 7.6 billion people. We find that a 1 standard deviation higher infectious disease burden reduces expected output per worker by 0.93 standard deviations with the result that 86 percent of the cross-sectional variation in productivity is explained by the infectious disease burden.

What explains the empirical evidence is the wrath of Ra. The harsh toll of the fever in the torrid zone and efficiency-reducing thermal environment of the factory are both functions of the heat induced by solar radiation. The key to understanding this is to realize that nations are situated animals. They have a specific location on the globe. The zone on which the sun beats mercilessly down on the surface of the earth is a function of latitude that is symmetric across the equator. The distribution of land mass on the surface of the planet is overweight the northern hemisphere; so it comes to us as the ‘north-south’ axis of polarization. But southern Australia, southern New Zealand, the southern trip of Africa are equally pleasant because they too lie in the temperate zone. The gradient of latitude is very significant. But the variable that explains output per worker is the thermal environment. Ra doesn’t need mediators to beat the worker into submission; his wrath is personal; he heats up the worker’s lifeworld himself.

What we have then is a Heliocentric model of global polarization. Given the human thermal balance, the direct effect of solar radiation as mediated by the factory’s thermal environment is sufficient to explain the international cross-section of productivity. Because they are all functions of solar radiation, work intensity, latitude, humidity-adjusted temperature, and disease burden are correlated and priced together into the cross-section of productivity. The controlling variable here therefore is the wrath of Ra.

Ram Rati (1997) has shown that the gradient of latitude explains half the variation in the cross-section of a number of socio-economic variables. Lind (1960) isolated the key problem in his paper titled “The effect of heat on the industrial worker.” See also Axelson (1974) “Influence of heat exposure on productivity.” There is a large physiological literature on heat stress. See Lundgren et al. (2014) for an illuminating case study and in lieu of a literature review.

What is clear is that global polarization is explained by the Heliocentric model. It is telling that the Copernican revolution happened in physiology and not political economy. In the latter discipline, the traditions associated with Malthus, Smith, Marx, and Galton remained trapped in the Latourian rigidity. Who knew that a physiological constraint, the human thermal balance, could bind?

Bandyopadhyaya argued forcefully in Climate and World Order that the macroclimate explained global polarization. He went too far. His remedy called for an intervention to modify the global climate. We have maintained a much more narrow focus in the present study. One clear finding is that air conditioning factories can potentially increase productivity. This should be more carefully investigated via randomized control trials. If they prove as effective as the Heliocentric model suggests, relatively modest investments in air conditioning would have dramatic effects on labor productivity.




The Grand-Strategy of the Giant Sequoias: Lessons for Unipoles and Patient Investors

The immense tree quivered like one in agony, and with a crushing, raging, deafening sound it fell, … breaking into a million pieces.

Eyewitness to the fall of a giant sequoia, 1893.

I stood at General Sherman’s ankle—he is the largest known living organism and one of the oldest—and contemplated a question I was asked long ago by a somewhat philosophical investment manager. What is long-term risk? What is the right measure of risk for a truly patient investor? If you are mandated to ensure survival for longer than a hundred years, preferably forever, what is a good replacement for value-at-risk? VAR may be appropriate for market-based financial intermediaries but is certainly not a good measure of risk for massive real money investors like pension funds and sovereign wealth funds. What is the right measure for such patient investors? I spoke of adverse secular movements in demographics, productivity, sustainability, and so on. But the real answer eluded me since the question was not well-posed. A well-posed replacement for that question is, What would a grand-strategy of immortals look like?

We define a patient investor as one seeking to survive in perpetuity; an immortal, like giant-sequoias. These immense trees don’t die; they fall. They fall like monarchs in periods of extreme instability. Only massive earthquakes, extremely powerful lightning bolts, ultra-hot and tall wild-fires, or men with saws can fell them. Giant-sequoias are not alone; there are plenty of immortal species; species with no finite lifespan. A patient investor is the analogue of the immortal species—while death may occur due to extreme events, the grand-strategy is geared to survive for eternity.

Giant sequoias are some of the oldest living individuals on the planet. General Sherman was born twenty-two centuries ago; around the birth of the Roman Empire; ie the Second Punic War, 218 BCE, a decisive hegemonic war when Rome took over the reins of the Mediterranean Sea from Carthage. Unipoles in general and the Roman Empire in particular can be thought of as immortal as well, at least in grand-strategic terms. Rome’s grand-strategy was to eliminate all rivals through the use of force. It was successful for a while. The Roman Empire can be said to have died at the latest with the fall of the western Roman Empire in 476 CE. Sherman was then around 700 years old. He has been alive for twice as long since, and is still going strong. Some giants are even older than human civilization.


General Sherman Tree, the largest living organism on the planet. Photograph taken by the author in April 2018.

The grand-strategy of the giant-sequoias is the orthogonal complement of the Roman grand-strategy; one I will call benign hegemony. The giant sequoia’s grand-strategy is adapted to wild-fires, earthquakes, squirrels, and men. I will show how that evidence  yields first-order insights for both unipoles and patient investors.

Mature sequoias have yard-thick fire-resistant barks, a layer of fluid right underneath that provides additional protection against fire, a tremendous girth of fire-resistant wood, and no branches below the canopy hundreds of feet above the ground. Only extremely hot ‘canopy fires’ that reach hundreds of feet above the ground can fell a mature sequoia. But these don’t occur naturally in the forest. What happens is the slow accumulation over decades of incendiary material on the forest floor which periodically ignites wild-fires of varying intensity. The sequoias treat wild-fires as opportunities and practice what is called ‘explosive reproduction.’ In the immediate aftermath of a fire, prime substrate soil, suitable for sequoia seeds to grow, gets exposed. And the big trees start producing cones and seeds at a rate that is orders of magnitude higher than in normal times. Sequoias thus harvest forest fires to reproduce. That sounds like an aggressive strategy of expansion. Why would I call it benign hegemony? I call it benign hegemony because of the effect of this grand-strategy on forest dwellers. For after a major wild-fire, with the ground smoking with soot, the only thing left to eat for the animals is sequoia cones and seeds. The sequoias’ explosive reproduction thus provides crucial insurance against catastrophe to forest dwellers.


Note the burnt out base of the big trees. Photograph taken by the author in April 2018.

Protection against earthquakes is provided by the stability of the dead weight of the tree, the tapering profile of the trunk, and an extraordinary root system that grips the face of the earth. A mature giant sequoia weighs two million pounds and stands rigidly upright. The trunk at the base is a hundred feet in circumference and tapers as it goes up to the canopy towering hundreds of feet above the ground. The roots are the most remarkable, if invisible, feature of this organism. For instead of going hundreds of feet into the ground, they go no more than a dozen feet deep. Instead, they spread out over an immense area; often more than a whole acre. The root system grips almost the whole geological formation thus stabilizing the immense mass. The extraordinary root system protects the nutrition-rich top soil of an immense area from erosion, thereby providing further insurance against catastrophe to forest dwellers.

But I believe that the most remarkable thing about the sequoias’ grand-strategy is their adaptation to man. For sequoias have evolved such that their wood is entirely useless to man. Ironically, it is simply too light to be used as timber. But even more strikingly I think, the giant sequoias have through their august stature awed mankind into protecting them. If Ayahuasca can be thought of as trying to control men’s minds, then so can giant sequoias; only much more successfully. For the discovery of the Big Trees was the principal trigger for environmental protection and forest preservation efforts that began in the nineteenth century. Again, the forest benefits as a whole from the sequoias’ strategy of winning hearts and minds with shock and awe.


Photograph taken by the author in April 2018.

The picture of the immortal giants as benign hegemons only intensifies as a we pay closer attention to the ecology of this magnificent species. Every giant sequoia is the territory of a single Douglas squirrel—each resident squirrel vigorously defends its Big Tree. They have a life-span of just five years, so that a mature sequoia may host hundreds of them over thousands of years. The squirrels feed on the sequoia pine cones—which, unlike other pine cones, are soft enough to be eaten—and as they do, drop the seeds to the ground. Thus, the non-explosive half of the sequoias’ reproductive strategy relies on a symbiotic relationship with the Douglas squirrel. The giant provides ample food, shelter, and insurance to the resident squirrel. For its part, the resident squirrel helps the giant procreate in the period between fires.


Photo credit: Ivan Phillipsen.

Giant sequoias also willingly accommodate each other. One often finds a number of them in an imposing posse together, and sometimes in more intimate twos or threes, sharing the same patch of thin top soil. Their root systems get so intricately intertwined that they no doubt stand and fall together. Imagine a cohegemony lasting for three thousand years!

So the grand-strategy of the giant sequoias is best described as benign hegemony. Enjoying a surplus of security, giant sequoias act as guarantors of the forest, providing insurance against catastrophes, literally holding the precarious soil in which they and others can grow, and persuading others around them to leave them in peace for eternity.


Photograph taken by the author in April 2018.

Analogously, a unipole can be said to follow a grand-strategy of benign hegemony when it acts as a security guarantor to the lesser great powers, enforces the removal of the threat of the use of force in great power relations—in particular from the unipole itself; and fosters the peaceful resolution of international disputes through multilateral negotiation. The grand-strategy builds on the surplus of security of the unipole. It dissuades lesser great powers from rearmament by taking responsibility for their security, giving them a seat at the table, and accommodating their vital interests and self-respect. It deals with rising powers with reassurance and accommodation; and seeks a modus vivendi, in full knowledge of assured survival and full appreciation of its own strength and ability to prevail in an extended rivalry. It can be said to be successful if security competition between the great powers vanishes, the lesser great powers follow the lead of the unipole, and rising powers do not seek to revise the status quo by the use of force or the threat thereof.

The United States has not followed the grand-strategy of the Roman Empire in that it did not conquer and eliminate other great powers. For the most part, the United States has followed a grand-strategy of militarized liberal hegemony whereby the US maintained military primacy, accommodated the lesser great powers, acted as their security guarantor, and tamped out security competition among them. But US foreign policy since the Soviet capitulation has gone back and forth between defending the status quo, multilateralism and persuasion on the one hand, and revisionism, unilateralism and imposition on the other.

This bipolar disorder is not so much about bad apples in the White House, as the result of the takeover of the GOP by reactionary elements with an aggressive, ill-thought-out, revisionist foreign policy agenda that has tested the transatlantic alliance before and is testing it again. In other words, hunkering down until 2020 is not enough. The Anglo-Saxon powers have become unreliable partners for Europe. The question facing Europe is whether it can rise up to the challenge and pursue an independent course. A game-changer here, as Adam Tooze suggested, would be for Macron to offer to turn over the French deterrent to Europe. What would the Germans say to that?

Dominance and hegemony are not the same thing. Dominance is the fact of the military preponderance of the unipole. Hegemony is the willingness of lesser great powers to follow the lead of the unipole. If the unipole tries to impose its will on the lesser great powers by leveraging its military power it can be said to follow a grand-strategy of unilateral dominance. Such a grand-strategy may succeed if the lesser great powers still bandwagon with the unipole. They may indeed do so as a result of the tragedy of commons.

But if they resist the unipole, what obtains is dominance without hegemony; a fundamentally unstable situation that structurally incentivizes the lesser great powers to rearm and form balancing alliances against the unipole. The onset of such a regime in world affairs looks like the great big sulk that we are observing across Eurasia after the US walked out of the agreement between Iran and the P5+1 powers.

The giant sequoias have an important lesson for the patient investor as well. It is based on the crucial observation that a state of the world that is catastrophic for impatient investors, but not for patient investors, is an extraordinary opportunity for the latter. Just as a giant sequoia goes into explosive reproduction mode in response to a wild-fire, a patient investor should go into a wholesale buying frenzy in response to a major crash in asset prices. An aggressive counter-cyclical investment strategy, one that maximizes exposure to risk assets in states of the world that are catastrophic to impatient investors such as recessions, wars, and financial busts, and slowly sheds that exposure when asset prices boom, would not only yield superior long-term returns but also provide insurance to markets by providing a floor for asset prices.


What Exactly Happened on Vol Monday?

The return of market volatility on Monday, 5 February 2018, was dramatic. The 20 point jump in VIX, a traded measure of expected stock market volatility—best thought of as the price of insurance against a market crash—was the largest daily increase since the 1987 stock market crash.


Daily returns on the VIX and the S&P 500.

A number of leveraged volatility-linked exchange-traded products (ETPs) were implicated in the market commentary that followed. But a clear cut picture was hard to discern. The following forensic analysis by the Bank of International Settlements’ Quarterly Review clarified the dynamic at play:

Issuers of leveraged volatility ETPs take long positions in VIX futures to magnify returns relative to the VIX – for example, a 2X VIX ETP with $200 million in assets would double the daily gains or losses for its investors by using leverage to build a $400 million notional position in VIX futures. Inverse volatility ETPs take short positions in VIX futures so as to allow investors to bet on lower volatility. To maintain target exposure, issuers of leveraged and inverse ETPs rebalance portfolios on a daily basis by trading VIX-related derivatives, usually in the last hour of the trading day.…Given the historical tendency of volatility increases to be rather sharp, such strategies can amount to “collecting pennies in front of a steamroller”.…

Given the rise in the VIX earlier in the day, market participants could expect leveraged long volatility ETPs to rebalance their holdings by buying more VIX futures at the end of the day to maintain their target daily exposure (eg twice or three times their assets). They also knew that inverse volatility ETPs would have to buy VIX futures to cover the losses on their short position in VIX futures. So, both long and short volatility ETPs had to buy VIX futures. The rebalancing by both types of funds takes place right before 16:15, when they publish their daily net asset value. Hence, because the VIX had already been rising since the previous trading day, market participants knew that both types of ETP would be positioned on the same side of the VIX futures market right after New York equity market close. The scene was set.

There were signs that other market participants began bidding up VIX futures prices at around 15:30 in anticipation of the end-of-day rebalancing by volatility ETPs (Graph A2, left-hand panel). Due to the mechanical nature of the rebalancing, a higher VIX futures price necessitated even greater VIX futures purchases by the ETPs, creating a feedback loop. Transaction data show a spike in trading volume to 115,862 VIX futures contracts, or roughly one quarter of the entire market, and at highly inflated prices, within one minute at 16:08. The value of one of the inverse volatility ETPs, XIV, fell 84% and the product was subsequently terminated.

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Source: Bank of International Settlements, Quarterly Review, March 2018.