Population History, Climatic Adaptation, and Cranial Morphology

Physical anthropology in general and craniology in particular have quite a sordid history. The size of the skull was of great interest to scientific racialists, who seized on minor differences in averages as evidence of differential capacity of the “races” for civilization. As we have shown before and we shall see again in what follows, race gives us a very poor handle on cranial morphology, and human morphology more generally. This does not mean that there is little systematic variation; that all variation in between individuals within populations. To the contrary, human morphology is geographically patterned. Situated local populations or demes differ systematically and significantly from each other, generating smooth geographic clines. In particular, as the next figure shows, our species obeys Bergmann’s rule—bigger variants are found in colder climes.  


Source: Ruff (1994)

Of course, skull size and body size scale together. We can read this off the US military anthropometric database. So we should expect the bigger people of colder climes to have bigger skulls as well. Indeed, if Ruff’s thermoregulatory theory is right, particular features of skull morphology should be adapted to the macroclimate even more than the postcranial skeleton (the bit below the head).  

It is easy enough to recover the monotonic relationship between climatic variables and cranial measurements. But there is a very serious problem. Suppose that we can rule out nutritional and other environmental influence, say because we know the parameter is very slow-moving. That does not mean that all systematic variation in that parameter is then due to the bioclimate. For it may instead be due to random drift. Indeed, we know that founder effects, isolation-by-distance, and genetic drift can generate geographic clines that confound the bioclimatic signal. There is mounting evidence that human morphology, just like the human genome and linguistic diversity, contains a strong population history signal. 

Population history signals in DNA, RBC polymorphisms, and craniometrics are congruent.

Segments of DNA under selection do not preserve the signal from population history well; the bit not under selection—”junk DNA”—does. Similarly, information on population history can be recovered from traits of cranial morphology that are neutral, ie not under selection. Scholars have used genetic distance to control for population history in order to recover information on bioclimatic adaptation from morphology. In what follows, I will show how we can use cranial morphology itself to the same effect.

Howells Craniometric Dataset contains 82 linear measurements 2,524 skulls from 30 populations located in five continents. We will be working exclusively with that data. Let us begin with skull size. The five continental “races” that Wade thinks are real—one each for Europe, Africa, Asia, Australia, and the Americas—explain 6 percent of the variation in skull size. Moreover, not even one of the mean differences between said “races” is statistically significant. See Table 1. 

Table 1. Mean cranial capacity by continental “race”.
ContinentMale meantStatStd
Source: Howells Craniometric Dataset. Estimates in Italics are insignificantly different from the global mean at the 5 percent level. 

While demes are lumpy, they can’t be called races; there are tens of thousands of them. And though races are useless fictions, demes or situated local populations are very useful fictions. Put another way, demes are to anthropology what particles are to physicists and representative rational agents are to economists. Recall the tyranny of distance over land before the late-nineteenth century. Under such conditions as prevailed well into the ethnographic present, populations were situated locally and isolated from nearby and far away demes; the latter more than the former and smoothly so. Dummies for the demes alone explain 44 percent of the variation. What needs to be explained is this systematic component. 

In order to understand variation in skull size we first note that Binford’s Effective Temperature (ET, estimated as a linear function of latitude) is a strong correlate of skull size (r=-0.547 for men, r=-0.472 for women) and orbital size, ie the size of the eye socket (r=-0.464 for men, r=-0.522 for women). See the top panel of next figure. Moreover, as you can see the bottom-left graph, orbital size is a strong predictor of skull size (r=0.506); raising an intriguing pathway of selective pressure that ties cranial variation not to thermal parameters but to variation in light conditions. Still, the bottom-right graph shows that ET is correlated with skull size even after controlling for orbital size. 

If we consider only the systematic component, orbital size alone explains half the variation in skull size. So we should try to understand variation in this mediating variable as well. 

A straightforward way to extract the population history signal is to isolate morphological parameters that are uncorrelated with climatic variables and use these to construct a neutral phenotypic distance measure. We identity 14 linear measurements in the dataset that are uncorrelated or very weakly correlated with ET. Assuming that these are neutral traits not under selection, we use them to compute phenotypic distance from the San. (We use Pearson’s correlation coefficient between standardized 14-vectors for the San and each of the 30 populations as our measure of phenotypic distance.) Basically we are using the fact that the San are known to have been the first to diverge from the rest of us so that the degree of correlation in these neutral measures contains information on the genetic distance between the two populations. We also know that genetic distance is proportional to geographic distance from sub-Saharan Africa due to our specific population history. So if our measure is capturing population history, it should be correlated with geographic distance. The next figure shows that this is indeed the case. 

If we are right about our reasoning, we are now in a position to decompose morphological variation into neutral, bioclimatic and non-systematic factors. We begin with our estimates of pairwise correlation between our neutral factor (phenotypic distance from San) and ET on the one hand and selected morphological variables on the other. 

Table 2. Spearman’s correlation coefficients.
  Skull sizeOrbital sizeCranial IndexNasal Index
Source: Howells Craniometric Dataset. Estimates in Bold are significant at the 5 percent level. 

We see that Cranial Index (head breadth/head length) is uncorrelated with both ET and Neutral, while orbital size and skull size are strongly correlated with both. Interestingly, the Nasal Index (nasal breadth/nasal length) is a strong correlate of ET but not our neutral factor, implying that nasal morphology contains a strong bioclimatic signal and a weak population history signal. These results are only suggestive however. In order to nail down the bioclimatic signal we must control for population history and vice-versa. 

Table 3. Spearman’s partial correlation coefficients.
  Skull sizeOrbital sizeCranial IndexNasal Index
Neutral controlling for ETMen-0.533-0.6090.2210.260
ET controlling for neutralMen-0.584-0.513-0.0800.584
Source: Howells Craniometric Dataset. Estimates in Bold are significant at the 5 percent level.

We see that both population history and bioclimatic signals are present in skull size and orbital size; neither is present in the Cranial Index; and only the bioclimatic signal is present in the Nasal Index. This is consistent with known results in the field. Not just the Nasal Index but a bunch of other traits in facial morphology exhibit a strong bioclimatic signal, suggesting strong selective pressure on the only part of the human body exposed to the elements even in winter gear and even in the circumpolar region. 

Table 4 shows the percentage of variation explained by phenotypic distance from the San and ET. We see that Neutral and ET explain roughly 11 percent of the variation in skull size and orbital size each; neither explains CI; and ET explains 15.6 percent of the variation in the Nasal Index. More than three-fourths of the variation in these variables in not explained by either. 

Table 4. Apportionment of individual craniometric variation.
 Skull sizeOrbital sizeCranial IndexNasal Index
Source: Howells Craniometric Dataset. OLS-ANOVA estimates after controlling for sex. 

Table 5 displays the portion of systematic (interdeme or interpopulation) variation explained by population history and ET. Interestingly, the population history signal is stronger than the bioclimatic signal for systematic variation in skull size and especially orbital size. Neutral phenotypic distance from the San, our population history variable, explains 35 percent of the systematic variation in orbital size and 28 percent in skull size. ET explains 22 percent in both. Population history and ET explain more than half the systematic variation in both size variables. ET explains 27 percent of the systematic variation in the Nasal Index likely reflecting morphological adaptation to the macroclimate. The less said about the Cranial Index the better. 

Table 5. Apportionment of systematic craniometric variation.
 Skull sizeOrbital sizeCranial IndexNasal Index
Source: Howells Craniometric Dataset. OLS estimates adjusting for sex-ratio.

Remarkably, both ET and population history’s average share is more than a sixth but shy of a fifth, adding up to 37 percent of systematic variation of all four variables. If we drop the Cranial Index and average the other three morphological variables, they explain 24 percent of the variation each. In the horse race between population history and ET, we have a draw. The balance is more uneven in cranial size variables where population history has the upper hand. What happens if we introduce race dummies? 

Table 6. Apportionment of systematic craniometric variation.
 Skull sizeOrbital sizeCranial IndexNasal Index
Europe dummy4.1%0.0%0.7%7.0%
Asia dummy0.0%0.0%16.5%6.1%
America dummy0.0%3.4%0.2%3.9%
Pacific dummy0.3%0.9%0.9%0.5%
Source: Howells Craniometric Dataset. Estimates in bold are significant and those in italics are insignificant at the 5 percent level. OLS estimates adjusting for sex-ratio.

We see that race is pretty much a useless fiction. It gives us no handle at all on craniometric variation. The best we can say is that Asian heads are more globular. Interestingly, ET and population history exchange rankings in explaining orbital size after controlling for race. But the overall picture is unchanged. 

In order to be sure than we are not picking up spurious correlations, we fit linear mixed-effects models. We allow for random-effects by deme and admit fixed-effects for sex and race. We report the number of continental race dummies (out of four) that are significant in each regression. 

Table 6. Linear mixed-effects model estimates.
 Skull sizeOrbital sizeCranial IndexNasal Index
Sex dummyYesYesYesYes
Deme random effectYesYesYesYes
Number of race dummies significant0012
Source: Howells Craniometric Dataset. Estimates in bold are significant at the 5 percent level.

Our main results are robust to the inclusion of random effects for demes. The Cranial Index is bunk. The Nasal Index contains a strong bioclimatic signal but an insignificant population history signal. The gradients of ET and phenotypic distance from the San are significant for skull size and orbital size. Note that the sex dummy is always significant due to dimorphism—the dimorphism index for skull size in the dataset is around 1.15. But race dummies are rarely significant. Indeed, of the 16 dummies for race in the above regressions only 3 were significant. And these had mostly to do with “the wrong latitude problem”: New World population morphology can be expected to be adapted to the paleoclimate of Siberia so that it is not surprising that the coefficient parameter of the dummy would absorb that systematic error. 

The results presented above are congruent with known results from dental, cranial, and postcranial morphology. The basic picture that is emerging suggests that some skeletal traits are developmentally-plastic so that they reflect health status (eg stature, femur length); some are selectively neutral (eg temporal bone, basicranium, molars) so that they can be used to track population history; and finally, some have been under selection and likely reflect bioclimatic adaptation (eg, nasal shape, orbital size, skull size, pelvic bone width). 

In the 1990s and the early 2000s there was a sort of panic in physical anthropology related to genetics. The genomic revolution threatened to put people out of business. But it has become increasingly clear that the genomic revolution has turned out to be a dud. Most efforts to tie phenotypic variation to genomic variation have failed utterly. So far the best use of DNA for understanding human variation has turned out to be just a fancy version fingerprinting. So if you have ancient DNA samples, you can track population history. It has since been shown that morphological variation itself can be used to track population history just as effectively as DNA markers. With the advent of new techniques such as geometric morphometrics, the resurgence of interest in understanding morphological variation, and the manifest failure of DNA as the key to understanding variation in human morphology, we are truly in the midst of an unannounced golden age in physical anthropology. 

In lieu of references: See the splendid work by, among others, Brace (1980), Beals (1983, 1984), Ruff (1994), Relethford (2004, 2010, 2017), Roseman (2004), Harvati and Waever (2006), von Cramon-Taubadel (2014), and Betti et al. (2010). 



When Was the Industrial Revolution?

Metrics of everyday living standards are problematic. Commonly used economic statistics like real median income, real median household consumption, real per capita income et cetera rely on fallible national economic statistics. Above all, National Income Accounting may be blind to integral aspects of the standard of living. Accounts may be fudged by governments in countries with weak independent institutions. Finally, such statistics rely on judgements encoded in adjustments for representative consumption bundles, purchasing power and effective exchange rates. Of course, the entire enterprise relies quite heavily on assumptions about the plausibility of reducing human well-being to consumption bundles.

Anthropometric alternatives such as stature and BMI are confounded by morphological adaptation to the paleoclimate. Bigger bodies generate more heat so that situated populations adapted to warmer climes tend to be smaller than those adapted to colder climes in accordance with Bergmann’s rule. This means that the cross-sectional variation of stature and BMI cannot be interpreted straightforwardly as reflecting differences in everyday living standards. However, time-variation in anthropometric measures (and the cross-section of dynamic quantities) can be usefully interpreted as measuring changes in living standards. To wit, the Dutch-Indian difference in contemporary stature is less reliable than the Dutch-Indian difference in gains in stature (say, over the past century).

Actuarial alternatives are more promising. Mortality and morbidity data capture health insults that are directly indicative of net nutritional status. Since the latter is an irreducibly joint function of disease environment and nutritional intake, it goes to the heart of everyday living standards. Actuarial alternatives such as life expectancy are not confounded by adaptation to the paleoclimate since there is no equivalent of Bergmann’s rule for life history variables. Instead variables such as life expectancy capture contemporaneous environmental burdens—epidemiological and thermal—that are indeed of interest to those investigating variation in living standards.

Table 1a. Effective Temperature and Living Standards.
Effective Temperature PCGDP Stature (cm) Life Expectancy
ET < 14 23,537 174 76
14 < ET < 16 12,526 171 73
ET > 16 8,439 167 68
Source: Clio Infra, Binford (2001), author’s computations. Population-weighted means for N=99 countries. 

The above differences in the variables explain why Stature (r=-0.736, p<0.001) is a stronger correlate of Effective Temperature (ET) than Life Expectancy (r=-0.360, p<0.001) and PCGDP (r=-0.378, p<0.001). It also explains why controlling for income, ET is uncorrelated with Life Expectancy (t-Stat=-1.5) but not stature (t-Stat=-8.0). Whatever causal effect ET has on Life Expectancy is explained by variation in per capita income. This is not true of stature presumably because ET is correlated with variation in the paleoclimate which is causally related to stature and other body size variables via Bergmann’s rule.

Screen Shot 2018-11-10 at 12.50.06 AM.png

Parenthetically, we note that if we use Binford’s thresholds for storage (ET=15.25) and terrestrial plant dependence (ET=12.75), then we obtain a version of Table 1a that is less effective at partitioning modern societies by living standards. See Table 2b below. The map above displays Binford’s thresholds.

Table 2b. Effective Temperature and Living Standards.
Effective Temperature PCGDP Stature (cm) Life Expectancy
ET < 12.75 22,012 174 75
12.75 < ET < 15.25 24,164 174 78
ET > 15.25 8,781 167 68
Source: Clio Infra, Binford (2001), author’s computations. 

ET is a linear function of absolute latitude (r=-0.944, p<0.001). ET is meant to capture the basic thermal parameter of the macroclimate. Together temperature, precipitation and topography (elevation, terrain, soil, drainage) structure the ecology of situated populations in the ethnographic present just as they did in prehistory. Economic history, prehistory, and anthropology are not as far from each other as they seem. But we have digressed far enough. Let us return to living standards in Britain.


If you accept my argument that life expectancy is the best measure of everyday living standards we have, then the transformation of British living standards can be dated quite precisely. The essence of the Malthusian Trap was that real gains in living standards could not be sustained. Given the energetic constraints of preindustrial economies, population growth wiped them out. Thus we find that forty was a sort of rough upper bound on British life expectancy under the Malthusian Trap. The British Industrial Revolution, 1760-1830, had no discernable impact on British Life Expectancy. It is only in 1870 that British life expectancy begins to pull away from forty. Fifty was only breached in 1907; sixty in 1930; seventy in 1950; and eighty in 2000. Britons could expect to live twice as long at the end of the 20th century as in 1870 or 1550. 20 of the 40 years in life expectancy gained over the past 150 years were gained in the 40 year period 1910-1950; 10 have been gained in the 68 years since 1950; and 10 were gained in the first 40 years of the secondary revolution, 1870-1910. 1910-1950 is the hockey-stick that takes you from the turn of the century classical to the mid-century modern.


The evidence from stature is also consistent with this periodization. The problem with using body size variables like stature is that, unlike life expectancy, we don’t have a Malthusian ballpark against which to judge modern morphology. As I explained, European body size over the very long run is explained by population history. European gracialization (shrinking bodies) and decephalization (shrinking brains) since the medieval period is an active area of investigation, although still poorly understood.

body_sizeHowever, time-variation of stature in the ethnographic present can be interpreted as measuring time-variation in everyday living standards. That is all we really need to date the departure. And that too points to the last quarter of the nineteenth century as the beginning of the divergence. Most of the gains in stature were concentrated in the period 1920-1960, corroborating the finding from British life expectancy. The hockey-stick is a story of the early-twentieth century.


The empirical evidence from both anthropometric and actuarial metrics suggest that it is time to cut the British Industrial Revolution down to size. It is time to recognize it for what it was: a “revolution” largely confined to cotton textile manufacturing that pointedly failed to transform everyday living standards in Britain. The real departure came with the secondary industrial revolution, 1870-1970, that was not confined to Britain but a rather transatlantic affair. It witnessed the generalized application of machinery powered by fossil fuels to perform work everywhere from farms to factories. More generally, it is characterized above all by the increasingly ubiquitous application of science and technology to concrete problems.

But there was much more at play than technology and knowhow. For it involved a massive integration of the globe that, as Geyer and Bright put it, destroyed the capacity of the world’s macroregions to sustain autonomous histories. This onset of their ‘global condition’ takes places in the middle decades of the nineteenth century. The key to this transformation was rail. Sail was competitive with steam on the open ocean through the nineteenth century. The topology of the world economy thus couldn’t have been transformed by cheap and efficient transport by steam ships because sailing ships were already cheap and efficient.

The disconnectedness of the world economy was not a function of weak connections between macroregions. Instead it was local; defined by the tyranny of distance in the interiors of the great landmasses of worlds old and new. Until the advent of rail, transport over land was prohibitively expensive; condemning lands far from waterways to insulation. The sea-borne world economy was correspondingly limited to the maritime world. A larger, more integrated and more intrusive world economy emerged with rail that allowed the bounty of the interior to be sold on the world market. The international division of labor that emerged on this iron frame had much more bite than the one that characterized the world economy confined to the maritime world.

Ghost acres had little bearing on the British kitchen table until the late-nineteenth century. To be sure, Britons had been addicted to imported drug foods (sugar, tea, coffee, tobacco) from slave plantations for centuries. But as late as 1870, only 10 percent of British meat was imported. By 1910, Britain was importing 40 percent; largely beef from Argentina and lamb from New Zealand. The ghost acres finally increased the proportion of high quality foods in the British diet. Recall that beef is extraordinarily land-intensive. In the present day US, according to a recent study, producing one calorie (Mcal=1000 kcals) of beef requires 147 square meters of land compared to just 5 square meters for chicken and pork. Since land productivity was considerably lower than today, beef must have been even more land-intensive that it is today. The ghost acres were thus absolutely necessary for the transformation of British diets and therefore British living standards.

So Pomeranz is right about the ghost acres but wrong about the timing. Ghost acres did not transform British diets until the last quarter of the nineteenth century. As I suggested in the great British meat trade, the transformation of British living standards required not only the opening of the American interior but also an instance of definite technical solutions that make up the secondary/real industrial revolution: in this case solving the problem of transoceanic mechanical refrigeration. Chicago could not monopolize the British beef trade in 1880s and in the 1900s Argentina could not replace the US as a supplier in the British beef trade without the chilling solution. So I am not saying that rail was sufficient. What I am saying is that rail was necessary. Moreover, the British beef trade was ultimately based on the harvesting of great pastures in the interior of the New World. This required rail not only in the Anglo newlands but also in Argentina.

The opening of the interiors also required great migrations from the two Anglo oldlands. It also required the expulsion of native populations with great violence. In the American West, not only was there great military resistance by the horse cultures of the Great Plains Indians; during the mid-nineteenth century, the Sioux acted as a great power equal to the United States in Great Plains diplomacy and warfare. As Richard White notes,

In a sense, the Fort Laramie Treaty marked the height of Sioux political power. … With the Sioux and their allies so thoroughly dominating the conference, the treaty itself amounted to both a recognition of Sioux power and an attempt to curb it. But when American negotiators tried to restrict the Sioux to an area north of the Platte, Black Hawk, an Oglala, protested that they held the lands to the south by the same right the Americans held their lands, the right of conquest: “These lands once belonged to the Kiowas and the Crows, but we whipped those nations out of them, and in this we did what the white men do when they want the lands of the Indians.”

The warfare between the northern plains tribes and the United States that followed the Fort Laramie Treaty of 1851 was not the armed resistance of a people driven to the wall by American expansion. In reality these wars arose from the clash of two expanding powers–the United States, and the Sioux and their allies. If, from a distance, it appears that the vast preponderance of strength rested with the whites, it should be remembered that the ability of the United States to bring this power to bear was limited. The series of defeats the Sioux inflicted on American troops during these years reveals how real the power of the Tetons was.

Sioux power, like that of the other Great Plains Indians, was based on the bountiful but precarious foundations of the horse trade and bison herds in the middle decades of the nineteenth century. The last of the bison herds were wiped by the locust of white hunters looking for hide in 1871-1875. But the decline of Sioux power was slow; they still managed to wage pitched battles against the US army into the last decade of the nineteenth century. So the expulsion of native populations was very far from an automatic process.

But even after native resistance was overcome, settlers had to clear the land. And so on … the point being that a whole lot more was ultimately involved in the transformation of British living standards that was not in place until the last quarter of the nineteenth century. Indeed, it only came together by the turn of the century. That’s why the hockey-stick is a story of the early twentieth century.


Anglo-Saxon Population History and World Power

The German Empire would not be proclaimed until next January, but it was forged in Bismarck’s splendid war against France in 1870. That was also the last year in which Germany would be more populous than the United States. Germany was born in relative demographic decline as a result of the settlement of the American West. In 1870, Greater Britain (Britain, Canada, and Australia—we don’t have data for New Zealand and South Africa)’s population was 37.0m, France’s population was 38.4m, America’s 40.2m, and Germany’s 40.8m. 1870 is really the crossover point of the population scissors. The populations of all four were roughly around 40m in 1870. Over the next forty years, while France’s grew by a mere 7 percent, Greater Britain’s grew by 53 percent, Germany’s by 58 percent. But both were dwarfed by America’s 131 percent. By 1910, France, Greater Britain, Germany, and the US weighed in at 41.2m, 56.5m, 64.6m, and 92.8m respectively.

The stagnation of the French population, the fact that Greater Britain expanded demographically nearly as much as Germany, and German demographic decline relative to the United States, all came to weigh heavily on the world question at the turn of the century. This was especially so because all four great powers were roughly at the technological frontier by the turn of the century. Although the United States had clear leadership, the secondary industrial revolution occurred in all four poles (and beyond). Germany in particular was a major center of innovation in the mechanical arts, leading in many sectors, eg industrial chemistry, heavy industry, and catching up in many where the Americans had led, eg automobiles.

Population in millions
Greater Britain United States Germany France
1870 37.0 40.2 40.8 38.4
1880 41.2 50.5 45.1 39.0
1890 45.5 63.3 49.2 40.0
1900 50.4 76.4 56.0 40.6
1910 56.5 92.8 64.6 41.2


Life expectancy is a good measure of everyday living standards. The next figure shows that by this measure, improvement in German living standards accelerated around 1890. But there was no relative improvement in Germany’s position because the Atlantic powers themselves hit the toe of the hockey-stick at the same time. The Anglo-Saxons opened up a gap with France as well. No one was as rich as them or lived as long.


The evidence from stature is even more daunting from the perspective of an aspiring world power. Americans still towered over Germans. Greater Britain and Germany remain close throughout, although with a British edge. France, which was closer to the Anglo-Saxons in life expectancy, lagged behind even though it too participated in the onset of the hockey stick.


Note that we have defined the average stature of Greater Britain as the population weighted average of British, Canadian, and Australian means. If you unpack Greater Britain, it turns out that Canadians and especially Australians enjoyed a definite settler premium. See next figure. American supremacy in stature is therefore not surprising. Britons would finally become taller than Americans for the first time in 1930. But that is a story for another day. Instead of unpacking Greater Britain, the challenge is to expand it to encompass not just New Zealand and White British subjects in southern Africa, but Greater Britain in a thick sense: as the predominance of the British diaspora in the offshore world. Proximately what was required was to monopolize prime temperate land in Anglo-Saxon hands; in order to do that, what was required was the take-off of self-reproducing settler colonies; preferably junior geopolitical allies of Belich’s Anglo oldlands (see the schematic map) that could thus anchor the world position of the two Anglo-Saxon great powers.


Screen Shot 2018-10-31 at 3.24.26 AM

From Belich, Replenishing the Earth.

I still haven’t finished reading Belich’s Replenishing the Earth: the Settler Revolution and the Rise of the Anglo-World, 1783-1939, so I will hold my judgement of the first three-fourths of the book. I will say that his description of the wildcat banking and asset price bubbles of the Anglo-Saxon frontier is excellent. I also agree with him that explosive colonization was a bubble by construction. One went all in when one went to settle a fledgling colony. Things worked themselves out once enough talent showed up. Speculators abounded. Increasingly massive boom-bust cycles whipsawed the frontier. Boom towns expanded at prodigious rates; driven by investment booms, unregulated bank lending, furious speculation, and attendant asset price bubbles amid extraordinarily elevated rates of settler arrivals. At the heart of Settlerism itself was a Ponzi scheme; the Anglo-Saxon folie a famille in two senses. As the Anglo-Saxon madness of course. But also the self-accelerating aspect of settler success itself. The booms were in a fundamental sense self-igniting. They solved the problem of coordination through faith. Not just faith in God. But faith in the colony. The frontier attracted the believer like a magnet.

In the American West, there were three major medium term cycles that peaked in 1837, 1857, and 1873. (The last of the great booms peaked in 1893 and 1907.) After each of these busts, Belich argues, the West was re-colonized, reoriented to point towards to metropole; peripheralized via a vertical division of labor—Cincinnati would no longer produce books and periodicals (88,000 books were published in the town in the three months of 1831, Belich reports) but pork and grain; New York would supply the books and periodicals. Fair trade or not, this was the construction process of the Weltwirtschaft.

The topology of the world had been transformed by Anglo-Saxon settlement. Britain’s decline relative to Germany has been overestimated. If we consider the product of life expectancy and population as the measure of war potential instead of GDP which is a product of per capita GDP and population, Britain kept pace with Germany all the way. (We know the picture that emerges from income: Britain’s per capita GDP was 25 percent larger than Germany’s in 1900).


France was guaranteed to be a member of any balancing coalition against Germany. The real question was Anglo-German relations. Given the Anglo-Saxon stranglehold on the maritime world-economy, their naval mastery, and their settlement of all available prime temperate land, there was no solution to the problem of wrestling world control away from Anglo-Saxon hands. Fisher’s ‘five keys that lock up the world’ were Anglo-Saxon property by the time the German Empire was proclaimed. So the German bid to be one of the four world policeman was thwarted by the difficulty of dethroning Great Britain, the Franco-Russian alliance and the problem of two-front war, and above all, the settlement of the American West and the rise of the United States.

Population history is crucial to the Franco-German story, the Anglo-German balance, the rise of the United States to global mastery, and the cul-de-sac of German navalism. But was there no viable path for Germany to become a world power? The missed opportunity of 1905 points in the right direction. Above all, Germany needed to achieve military hegemony on the continent. Russia was out of business and France lay exposed. Navalism came to bite not only in 1914 but also in 1905 when the Kaiser decided to wait for a more favorable naval balance.


How was the German question resolved?

Sovereignty is always shaped from below, and by those who are afraid  — Michel Foucault

Marc Trachtenberg’s A Constructed Peace: The Making of the European Settlement, 1945-1963, won the George Louis Beer Prize as well as the Paul Birdsall Prize.[1] It remains highly regarded in the field. Trachtenberg argues convincingly that the German question was at the heart of postwar international politics and its resolution was the key to the establishment of a stable international system. Since the great powers disagreed so profoundly on what was to be done with Germany and put a great deal of importance on that question, a stable pattern of East-West relations could not obtain until the German question had been settled one way or the other. As long as the German question remained unresolved, the specter of general nuclear war hung over East-West relations. Once it was resolved, the basic parameters of the bipolar world fell into place, East-West relations were stabilized, and the Cold War in effect came to an end.[2]

The entire future of Germany was open for reconsideration when postwar planning began during the war.[3] Was Germany to pay reparations? Was it to be deindustrialized and turned into an agrarian country to reduce its power as envisioned in the Morgenthau Plan? Was Germany to be broken up into smaller statelets? Into two, three, or four pieces? Under whose sphere of influence were these pieces to fall? Who was going to control the Ruhr? Even after they had been agreed upon, were the occupation zones to be run separately by each occupying power as it wished? What was to be their socio-economic system? Were all non-fascist political parties to be tolerated in all zones? Or were the zones merely temporary and a unified German state was to be resurrected? And if so, was the Germany army to be reconstituted? And if German power was to be restored, was Germany going to be neutral or an ally of one of the three great powers?

Given the centrality of the German question to his account of the European postwar settlement, it is perplexing to find Trachtenberg begin his narrative at war’s end, some two years after official three-power negotiations began. A number of important decisions on the German question were in fact hashed out during the war; above all, the territorial division of Germany into occupation zones. The first steps in that direction were taken at the Moscow Conference in October 1943.[4] The British circulated a draft agreement on the zones of occupation on January 15, 1944.[5] On February 18, 1944, the Soviets accepted the British proposal for the eastern zone apparently without bargaining.[6] Why Stalin would accept a division that gave him control of the agrarian third of Germany is not clear.

So Trachtenberg is not interested in how the German question was resolved per se. What Trachtenberg does instead is mobilize it to explain why East-West relations took so long to stabilize. Secretary of State James Byrnes, ‘the real maker of American foreign policy during the early Truman period,’ we are told, pressed for ‘a spheres of influence settlement in Europe’ that the Soviets could get behind, whereby ‘each side would have a free hand in the area it dominated, and on that basis the two sides would be able to get along with each other in the future.’[7]

But a settlement of this sort did not come into being, not until 1963 at any rate. Why was it so long in the coming? Why did the division of Europe not lead directly to a stable international order?[8]

Trachtenberg’s answer is that profound disagreements on the German question prevented the emergence of a stable order. The Soviets were implacably opposed to the resurrection of German power, especially a nuclear-armed Germany, particularly one allied to the West. The US did not want an independent Germany. But the defense of Western Europe ultimately required the reconstitution of the German army. In the end, despite the fact that the Soviet Union had almost single-handedly defeated Hitler, the US was able to get its way on the German question. In effect, the US managed to impose its preferred outcome on the Soviet Union. Why?

Although Trachtenberg does not come right out and say it, the short answer is that the US leveraged its nuclear superiority to get its way on the German question. The first great confrontation was triggered by the introduction of a common currency into the three Western zones in 1948. It meant in effect the creation of a West German state. It is this that triggered the Berlin Crisis. At the time the United States enjoyed a nuclear monopoly, and according to Trachtenberg, ‘as long as it was a question of purely one-sided air-atomic war’ the US was ‘sure to win in the end’.[9] The West could thus afford to stand firm in the face of Soviet pressure. And the Soviets backed down once it became clear that the United States was prepared to go all the way to general nuclear war in order to defend the West’s position in West Berlin.

America responded to the loss of nuclear monopoly in 1949 with an enormous buildup of air-atomic forces. By 1952 the Strategic Air Command had emerged as a war-winning first-strike weapon. It was in this context that the resurrection of the German army was put on the table. Stalin responded by sending the famous March 1952 Note suggesting that the Soviets would be willing to accept a unified Germany with free elections and even a capitalist economic system as long as it was guaranteed to be neutral. The West dismissed the offer as a mere ploy. Trachtenberg, following Gaddis, concurs.[10] But many serious scholars of Soviet foreign policy have argued that the offer was in earnest.[11]

A series of increasingly hostile confrontations occurred in 1958-1962 culminating in the Cuban Missile Crisis, when Khrushchev, emboldened by the Soviet acquisition of ICBMs capable of reaching US cities, decided to force a showdown on the question of the introduction of tactical nuclear weapons into the German army. Astonishingly, Trachtenberg devotes less than three pages to this final confrontation over the German question, concluding that the US ‘laid down an ultimatum’ and the USSR ‘acceded’ without explaining why.[12] As Trachtenberg himself had argued elsewhere,

It really does seem that “we had a gun to their head and they didn’t move a muscle”—that their failure to make any preparations for general war was linked to a fear of provoking American preemptive action. … The effect therefore was to tie their hands, to limit their freedom of maneuver, and thus to increase their incentive to settle the crisis quickly.[13]

The picture that emerges thus calls for a major revision of the account presented in the monograph, one that pays attention to the balance of strategic power as it came to weigh on international politics at crucial moments in the resolution of the German question, 1942-1963.


[1] Trachtenberg, Marc. A Constructed Peace: The Making of the European Settlement, 1945-1963. Princeton University Press, 1999.

[2] Except for a brief revival under Reagan in the early 1980s. See Stephanson, Anders. “Cold War Degree Zero.” Uncertain Empire: American History and the Idea of the Cold War (2012): 19-50.

[3] This paragraph is adapted from an earlier essay that appeared on my blog.

[4] Mosely, Philip E. “The occupation of Germany: New light on how the zones were drawn.” Foreign Affairs 28, no. 4 (1950): 580-604, p. 580.

[5] Ibid, p. 589. Of course, the British awarded the Ruhr to themselves.

[6] Ibid, p. 591.

[7] Trachtenberg, p. 4.

[8] Ibid.

[9] Trachtenberg, p. 89.

[10] Ibid, p. 129.

[11] See Willging, Paul Raymond. “Soviet foreign policy in the German question: 1950-1955.” (1975): 1199-1199, and references therein.

[12] Trachtenberg, p. 352-355.

[13] Trachtenberg, Marc. History and strategy. Princeton University Press, 1991, p. 259.


Testing Krugman’s It Theory of Global Polarization

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

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

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

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

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


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

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


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


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


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


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

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


The figure incorrectly states that the sample is restricted to the low income group. It is not. This is the full sample. 

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


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

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

\text{growth}=-0.3028+0.0710\times log(PCGDP)_{i,t}-0.0039\times log(PCGDP)_{i,t}^2.

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


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



An Irredeemable Miscalculation?


The grim details of the extrajudicial torture-execution of the Post columnist are now clear. The most astonishing fact to emerge is that MBS did not even bother to cover his tracks. Instead of sending expendable killers-for-hire to maintain plausible deniability, the standard operating procedure for kinetic intelligence operations, MBS sent men from his own personal security detail to assassinate the journalist.

2017 imprisoned

Journalists imprisoned. Source: CPJ.

Killing journalists is not a new trick for mafia states. On average a journalist is killed every week, according to the Committee to Protect Journalists. Some 44 have already been killed this year, although that number does not include Khashoggi.


Of the 1,323 journalists reported killed since 1992, 912 have been killed since the Iraq War began in 2003; including 159 Iraqi journalists and 110 Syrians. Outside these two warzones, the greatest rate of scribe killing is in the Philippines, followed by Algeria, Pakistan, Russia, Somalia, Colombia, India, Mexico, and Brazil. The next graph shows the notorious double-digits scorers in the CPJ database.


We can think of the number of scribes killed as measuring to what degree the state formation approximates a mafia state. This is not exactly right because the 1,323 total scribe killings since 1992 include some 131 involving criminal gangs, as when the Chicago mafia gets rid of a pesky reporter with the understanding of the local judge and politician. More generally, only 1,083 killings can be attributed to specific actors. The next table shows the breakdown. It’s clear that the vast bulk of the killings are ordered by political or military authorities.

Attributed killings of journalists.
Killer Number Share
Government 194 18%
Military 242 22%
Political 436 40%
Paramilitary 62 6%
Mob 14 1%
Criminal 135 12%
Total 1,083 100%
Source: CPJ.

So it cannot possibly be the case that the prestige media is up in arms about the mere killing of a journalist. Why then does it look like MBS has his feet to the fire? And why does it look like his days are numbered? Are they? What precisely can be done about MBS? and more generally, the Saudis?

What the extraordinary opprobrium in the Western press reflects, I think, is Said’s Orientalism in reverse. What was so egregious about the Khashoggi business was not that he was a scribe. It was that he was a columnist at the Washington Post. Indeed, he probably thought that his association with a prestige paper in the United States made him bulletproof. Put bluntly, the implicit norm said: You can kill a journalist in your backyard, especially one writing in the vernacular. And if you’re going to kill a prominent critic who is known internationally, you better have plausible deniability. But you can’t kill a card-carrying member of the Western Press, especially not without even a fig leaf of deniability. So MBS miscalculated badly. It may be because he has always lived in the Kingdom and has no first-hand experience of the rigidity of the liberal-democratic discourse in Western civil society.

Now what? What is the West to do with MBS? Must he go? Oh it can be arranged. And if you are thinking of European dependence on gulf crude, there are operational solutions to the problem of stabilizing oil prices. There is no need to occupy Saudi cities and the vast bulk of Saudi territory. All you need is to secure a small portion of the eastern province. US forces can secure the oil fields in the gulf with a light force, as a joint Anglo-Saxon plan had it in the 1970s, and as someone, probably Kissinger (Grey Anderson tells me that Edward Luttwak admitted to having authored the article in 2004) wrote about anonymously in Harper’s at the time of the Arab embargo. Since all of Saudi oil sits under a zone of Shiite predominance, the political problem can be solved by working with Iran just as the United States has to already in the arc of weakness that stretches from the gulf to the Levant. The micro-oil monarchies of the gulf are already under US protection. They would have to move closer. We cannot allow the Saudis to mediate between the United States and the Trucial States.


But knowing that the United States can secure the oil fields without putting many boots on the ground is an insurance policy, not the proposed strategy. The Policy Tensor has been suggesting for a long time that the United States ought to follow a more even handed policy in the gulf. Indeed, it would not hurt to ditch Saudi Arabia for Iran. To put it bluntly, Iran dwarfs the gulf region in warmaking potential. The United States shot itself in the foot by destroying the garrison state built by Saddam. The result of US debacle is that Iran is now the most influential power in southwest Asia. Iran understands that the US is capable and willing to confront Iranian foreign policy in the gulf region and in southwest Asia as a whole. But it is also true that the United States has little choice but to work with Iran on regional questions. I think it is obvious that rolling back Iranian influence in Syria and Iraq is a fool’s errand.Iran is a natural ally of the West in the fight against salafi jihadism. The US needs a working relationship with Iran; better still, would be a genuine partnership with Iran.

I think there has been increasing cooperation in US-Iranian relations, each has gained an increased appreciation of the other’s strength by fighting side-by-side against Isis. What needs to be recognized now is the congruence of interests between Iran and the West. Because Iran is the potential region hegemon of gulf region, it is best to have good working relations. It makes for stable relations to have potential regional hegemons invested in the status quo.  As Huntington observed, the world is uni-multipolar. The United States is the only state in the world that can project power system wide. But geopolitics is regional. In order to run the different regions of the world, at the minimum, the United States has to reach an understanding with China in east Asia, India in south Asia, Iran in southwest Asia, Russia across Eurasia, and Germany in Europe. This is particularly true under conditions of mutually-assured destruction.


What requires particular attention is gulf terror finance. Whether or not we contain Saudi Arabia more generally, terror finance from the gulf has to stop. Frankly, this requires eyeballs and interdiction by law enforcement in international financial flows from and to the gulf. Congress should fund this right quick and subject enforcement to oversight. But the real problem with Saudi Arabia is not restricted to terror finance even in the narrow sense of the war on terror. For Saudi Arabia is the world capital of salafism. Thousands of little religious schools run by the Saudis dot the Old World from Kosovo to Indonesia, where every attendant is at risk of recruitment by salafi jihadists. These schools are the breeding ground in which salafi jihadism grows. More generally, the propagation of salafism is the principal driver of jihadism. If we are serious about the fight against salafi jihadism, we must arm-twist the Saudis to roll-back their global network of salafi madrasas.

These are all matters of elementary security policy for the United States. But should Saudi Arabia be contained? What exactly would containment entail? Sanctions? Air strikes? I do not believe any of that is required. A simple threat of US abandonment would be enough to concentrate minds in the Kingdom. For if abandoned by the United States, the Kingdom would be faced with a vastly stronger power across the gulf without any security solutions. My proposal is not to jump to containment yet.

If the West were to act jointly, it would inform the Saudi authorities—once the intelligence is verified—that MBS has to go. He would be persona non grata. If the Saudis want to hold on to him even though there are thousands of princes waiting in line for the throne, it will be awkward for a while. But the West could very well stand firm on this. MBS just cut it too close to the bone.

Whether or not the Saudis ought to be subjected to sanctions depends on whether or not they are willing to cooperate in a major reorientation of Saudi policy (on terror finance, the madarsa network, and MBS). It would be best if the Saudis marginalized MBS without US intrigue. Although even intrigue would be better than having to deal with Saudi Arabia without talking to its de facto leader for whatever time it takes for the Saudis to come around.

Here’s how the unipolar world works. If there is a Nash equilibrium in international politics that the United States lays down and insists on, eg Washington Naval Conference of 1922, then a stable order can be secured. But this does not mean that Europe does not have a say. Indeed, the Europeans could unilaterally contain MBS. By declaring him persona non grata and opposing this administration on gulf policy, Europe can prepare the ground for when adults are back in Washington. This is already underway in the sense that the Europeans are working with the Iranians to pushback against the US reneging on the nuclear deal. Merkel would be wise to take this opportunity to extend the pushback to MBS.

When adults are back in Washington, one could move ahead in leaning harder on Saudi Arabia. But two things must be recognized. This is not just about Khashoggi and not just about MBS. This is above all an opportunity to reconsider Western gulf policy tout court. Why is the West containing Iran and arming the Saudis when core Western interests are closer to the former than the latter?



Wage Growth Predicts Productivity Growth

Tip of the hat to Ted Fertik for bringing Servaas Storm’s unpacking of total-factor-productivity growth (TFP) to my attention. Storm shows that TFP can be regarded mechanically as a weighted sum of the growth rates of labor and capital productivity, roughly in a 3:1 ratio in that order. TFP, of course, is a measure of our ignorance. It nudges us to look inside firms, ie the supply side. This leads down the path to situated communities of skilled practice, ie Crawford’s ‘ecologies of attention.’ But perhaps it is better to work directly with labor productivity, certainly if Storm is right. Some say that high wages incentivize firms to invest in labor-saving innovations thereby increasing labor productivity. This is certainly consistent with the standard microeconomics view of firm behavior in that they are expected to do whatever it takes to get a competitive advantage in the market. A straightforward implication of this hypothesis is that real wage growth ought to predict productivity growth. We’ll see what the evidence has to say about this presently. But let us first note the policy implications of the theory.

The fundamental challenge of contemporary Western political economy is how to restore economic dynamism. The first-best solution to the rise to China is for the West to maintain its technical and economic lead. Similarly, the first-best solution to political instability and the crisis of legitimacy is a revival in the underlying pace of economic growth. So far no one has offered a credible solution; Trump’s tariffs, nationalist socialism á la Streeck, restoration of high neoliberalism á la Macron, are all small bore. But if the hypothesis that a significant causal vector points from real wage growth to productivity growth holds, then a bold new Social Democratic solution to the fundamental challenge of Western political economy immediately becomes available.

What I have in mind is a new mandate for central bankers. To wit, Congress should mandate the Federal Reserve to maximize real median wage growth subject to monetary and labor market stability. Until now central banks have targeted labor market slack as understood in terms of employment and inflation. But the real price of labor (more precisely, productivity-adjusted real median wage) is also an excellent measure of labor market slack. The hypothesis implies that targeting productivity-adjusted real median wage growth could restore productivity growth; perhaps dramatically. My suggestion is consistent with social democracy’s concern with distributional questions as well as with standard central banking practice. So if the result holds, it’s very useful indeed.

We start of by checking that real wage growth predicts productivity growth in the United States. The correlation is large and significant (r=0.531, p<0.001). This is suggestive. Wages_productivity.png

In order to systematically investigate this question we interrogate the data from the International Labor Organization (ILO). The ILO provides estimates of real output per worker, unemployment rate, and the growth rate of real wages. We restrict our sample to N=30 industrial countries since wage growth has diverged so significantly between the slow-growing advanced economies and fast-growing developing countries. We estimate a number of linear models and collect our gradient estimates in Table 1.

We begin in the first column that reports estimates for the simple linear model that explains productivity growth by 1-year lagged real wage growth. In the second column, we introduce controls for a temporal trend and lagged productivity growth. This sharply reduces our estimate for the gradient suggesting that the estimate reported in column 1 was inflated due to autocorrelation. We introduce country-fixed effects (ie country dummies) in column 3, which modestly reduces our estimate of the gradient. Instead of country fixed-effects, in the fourth column, we control for the unemployment rate, which turns out to be significant and which very modestly increases our gradient estimate. In the last two columns we introduce random effects for country and year. What this means is that instead of dummies for each country and year which is equivalent to having fixed intercepts by country and year, we admit the possibility that the intercept for a given country and year is random.

Table 1. Linear mixed-effect model estimates.
Intercept Yes Yes Yes Yes No No
Trend No Yes Yes Yes Yes Yes
AR(1) No Yes Yes Yes Yes Yes
Country fixed-effect No No Yes No No Yes
Unemployment Rate (lagged) No No No Yes Yes Yes
Real wage growth (lagged) 0.233 0.136 0.104 0.140 0.108 0.100
standard error 0.037 0.042 0.046 0.042 0.037 0.044
Country random effect No No No No Yes Yes
Year random effect No No No No Yes Yes
Source: ILO. Estimates in bold are significant at the 5 percent level. Dependent variable is real output per worker at market exchange rates. The number of observations is 480. 

We note that the gradient for lagged real wage growth remains significant across our linear models even after controlling for a temporal trend, lagged term for the dependent variable, lagged unemployment rate, country fixed-effects, and random effects for country and year. We can thus be fairly confident that real wage growth predicts productivity growth across the industrial world. The next step would be to embed this in a macro model to interrogate the viability of real median wage growth targeting by central banks.