The Little Divergence

Summary : A “great divergence” between the economies of Western Europe and East Asia had unambiguously occurred by 1800. However, there’s a growing body of opinion that this was preceded by a “little divergence” (or “lesser divergence”?) which might have started as early as 1200. I argue that the pre-modern “little divergence” was probably real, but that doesn’t mean it happened because of a modern growth process — a sustained rise in the production efficiency of the divergent economies.

[Warning : This blogpost is mostly about how data on incomes from the pre-modern period are constructed. I’ve done my best to minimise details, but I cannot guarantee it won’t be as boring as atonal music performed with a spoon.]

(1)

The “little divergence” may now be close to a consensus view amongst economic historians both in Europe and the United States. In a way it’s a reaction to the revisionist book by Kenneth Pomeranz, The Great Divergence, which argued that Chinese and Western European economies had been fairly comparable as late as 1800. Pomeranz and the “California School of Economic History” are themselves the culmination of the “global systems” macro-histories exemplified by Fernand Braudel. Pomeranz then set off a cascade of dense elaborations by historians of Asia. Before Pomeranz and the Asian revisionism, most histories had pegged the start of the divergence between the two coasts of Eurasia to about 1500 or 1600. But in countering the Pomeranz revisionism, economic historians ended up pushing back the divergence to the High Middle Ages !

These two charts (source) encapsulate the little divergence :

The modern growth of Northwestern Europe after 1800 is now deemed a mere acceleration — albeit a very great acceleration — of an almost millennium-long trend. So people may marvel at the technological sophistication and scientific cleverness of the Song or the Ming or the Bling Dynasty, but in the final, brute number-crunching of per capita incomes, the wretched peasants of Western Europe had shot right past all of them.

Such views are now embedded in the popular imagination, as evidenced in the Atlantic magazine website from which I extracted those charts, as well as in a Vox article by one of the foremost proponents of the “little divergence” himself. (Examples of blogs using the same data or making similar claims : 1, 2, 3)

In this blogpost I will argue the following :

• While very few economic historians now dispute that East Asia had lower living standards than Europe well before 1800,
• there is no agreement on whether European economies prior to 1800 were “modern” or “Malthusian” ;
• if they were Malthusian, then the “little divergence” is rather trivial and unremarkable.
• Furthermore, the income “data” for years prior to 1200 are mostly fictitious.
• While real data exist after 1200 for Western Europe and China, output estimates are still calculated using assumptions that, were they better understood, would shatter confidence in the enterprise of economic history !

(2) Malthusian or Modern ?

In the Malthusian “biological” or “organic” economy, the level of technology at any given time permitted only a certain number of people to live off any given piece of land. The carrying capacity could vary according to the natural ecology of the land, because some environments are naturally more productive than others. Different peoples also possessed different levels of technology, defined in the widest possible sense as the stock of knowledge about the manipulation of the environment. When a people entered new, empty land, they would reproduce themselves until their population hit the carrying capacity — just like caribou or horse flies.

Of course, people can improve the carrying capacity through technological innovations, but in the premodern world those were very slooooow to happen and very rare in comparison with today.

I don’t want to go into too much detail, because you can read about the Malthusian model anywhere. (There are strong and weak versions.) Suffice it to say for my purposes, under Malthusian assumptions, per capita income was determined exclusively by the birth rate and the death rate.

This does not necessarily mean that the average person was living on the edge of starvation. This is a common misconception. To the contrary, the neo-Malthusian model implies that anything which lowers the birth rate and increases the death rate, will raise the living standards of the average person.  This is why different societies with different fertility practises and mortality conditions had very different income levels.

As far as I can tell, few people dispute that Western Europe was richer (per capita) than East Asia or India well before 1800. Gregory Clark in A Farewell to Alms argued that the daily wage, expressed in terms of wheat-pounds or rice-pounds, was much lower in Asia than Western Europe. But it was also much lower in East Asia and India than in Turkey, Egypt and Poland. Other lines of evidence all point to the same thing : the inhabitants of East Asia and India may have had the lowest living standards on earth before the modern period. Paradoxically, this was a sign of cultural sophistication and/or ecological good fortune, for Asian societies were capable of squeezing more people onto a piece of land than other societies.

It’s now well known that in mediaeval Western Europe women married later than in other parts of the world, and fewer women got married in the first place. This had the effect of reducing fertility rates well below the biological maximum. In East Asia, the female marital age was much lower, but a combination of infanticide, birth-spacing and other factors apparently kept net fertility only a little higher than Western Europe’s. Thus, under Malthusian assumptions, East Asia’s relative poverty is largely to be explained by its lower mortality : life in Western Europe was simply more lethal but richer, whilst more East Asian adults survived and lived longer but more miserably. The differences in mortality could be due to differences in disease prevalence, hygienic practises (such as bathing), medical knowledge or public health knowledge.

So, the question is, was the “little divergence” in living standards between Europe and Asia the result of “modern” or “Malthusian” mechanisms ? That is, was Europe’s income higher than China’s and Japan’s because the Europeans were becoming more efficient at extracting output from land, capital and labour long before 1800 ? Or is it simply that Europe and Asia had different birth and death schedules ?

If it’s the latter, then the “little divergence” is trivial and uninteresting. Or perhaps it’s interesting in the perverse sense that East Asia might have been poorer than Western Europe only because East Asians discovered earlier not to shit on themselves, itself because they understood the commercial and technological value of human foeces.

The previous questions can also be rephrased : was there a rising trend of income in Western Europe over the long run before 1800 ? And was what happened to Europe some time in the 18th century a major break with the past ?

(3) North-Central Italy

Most economic historians are either anti-Malthusians or “moderate” neo-Malthusians who think England and other European countries started slowly escaping their ecological constraints earlier than 1800. A fairly small camp of radical neo-Malthusians maintain a view which can be summarised by Gregory Clark’s assertion for England : “England in 1381, with only 55 percent of the population engaged in farming, was at income levels close to those of 1817”.

There is little dispute that between 1300 and 1850 there was long-run income stagnation in North-Central Italy, which is right now one of the richest regions of Europe. The two following charts are both from Malanima :

In the above, income is represented by the aggregate consumption of goods, which itself is computed, essentially, by {daily wage rate} x {number of working days per year} x {prices of basic goods}, along with (very crucial) weights for these variables — based on theoretical assumptions about how Italians of centuries ago might have switched between goods when prices and wages changed. The number of working days per year is unknown, but Italians are assumed to have behaved much as peasants in the poorest countries today who tend to work more when wages fall and work less when wages rise. Hours of work per day, which are also unknown, are assumed to be constant over time.  (This is not stated explicitly in Malanima, but is true, by implication.) What this means is that when prices were high Italian workers of the past were assumed to just work more days of the week, rather than 4 extra hours a day from Monday to Thursday, in anticipation of the demoralising boney fish on Friday…

For North-Central Italy, there exist adequate data for wage rates, prices of basic goods, and population. That’s actually pretty good, but we think of Italian mediaeval data as pretty solid only because we compare them with the complete unknowns like the Axumite Empire in Ethiopia or ancient Greece. We probably have more information to judge the economic performance of the Soviet Autonomous Republic of Tatarstan under Stalin in the 1930s or Zaire under Mobutu Sese Seko. Yet we think of both as relatively inadequate, because the reference comparison for those would be Eurostat or the BEA.

Individually, many of the assumptions behind the construction of income data seem reasonable, but, taken together, they are a little dodgy. And when you consider that the above income series looks more or less like the wage series below, you begin to wonder, what was all that painstaking computation all about anyway ? North-central Italian wages over the same period :

There’s understandable reluctance to rely exclusively on wages, since the proportion of wages in national income can vary when the capital share (i.e., rent, in this case) varies. Malanima does his best to check his income data against more limited information on rents and production.

Few people dispute his reconstruction of Italian data. The Malthusians have no cause to dispute it since the Italian story fits so nicely with the “biological theory of living standards”. The anti-Malthusians, perhaps, don’t find it implausible that Italy, even north-central Italy, was so stagnant over such a long period. After all, they didn’t start the Industrial Revolution, did they ?

(4) England : Broadberry versus Clark

The argument is largely over England (and, perhaps the Netherlands). And that battle is best encapsulated in this chart of competing estimates of income per capita for England over 600 years [source] :

(The rival sets of economic aggregates are described and compiled in Clark and Broadberry.)

How you view English economic history prior to 1800 — Malthusian or modern — depends on your opinion of the estimate of English income in 1400-1450. If income was high, per Clark, then the time series would look Malthusian. If, however, income was low, per Broadberry, then there was a subsequent long-run trend, which would be consistent with the slow-but-modern view of English economic growth.

Clark’s view is that despite ups and downs England in the mid-18th century was no richer than it was in 1350, and the 1350 standard of living was high by comparison with the rest of the world at the same time or most of Sub-Saharan Africa in the present. That is, England was always fairly well off — because England controlled fertility and had high death rates. Broadberry, by contrast, believes England in 1350 was about as poor as Tanzania today (and poorer still in 1250), but English income rose slowly but reliabily over the next 500 years because farmers, artisans, craftsmen, and merchants were getting slowly more efficient at their tasks.

What accounts for the difference between the two estimates ? Remember, Clark’s income for 1450 is roughly double Broadberry’s. That’s a big gap. Clark, like Malanima, aggregates wage data, but pre-modern England is also much richer territory for the economic historian with its bounty of records about rents, tithes, sheep counts, wills, tax records, etc. Broadberry uses pretty much the same data as Clark, but computes the physical output of goods.

In modern GDP accounting, there are three separate methods of computation which serve as checks on one another : the income approach (incomes received by workers and owners of capital) ; the output approach (the sum of physical output minus inputs in the business & public sectors) ; and the expenditure approach (the sum of spending by households, businesses, and the government). There are smallish discrepancies in the GDP estimates from these three approaches, but they get reconciled plausibly in a predictable way.

But for the Middle Ages, the wage approach has always been more popular because it’s thought to be simpler and more straightforward, involving fewer assumptions. Broadberry himself describes how wages have been the most traditional way income has been calculated by English economic historians :

But the anti-Malthusians are sceptical — incredulous, really — of the wage-based results, because, in Broadberry’s words :

So Broadberry and his team made a truly herculean effort to count the total physical output of the English economy between 1300 and 1800. The description of their methodology makes for an even more boring read than this blogpost, but I have read it so you don’t have to. The next paragraph may be particularly boring, so skip it if you trust my later characterisation of it.

Just to give you an idea of how Broadberry et al. came up with England’s total agricultural output : they compute the percentage of arable land from many sources ; then estimate the percentage of fallow and cultivated land, mostly inferred from probate records ; assume there are no major differences between manorial land and freehold land ; use Clark’s regression estimates of yield per acre based on a sample of farms across counties ; make allowances for part of the crop set aside as seed (not clear how they inferred that) ; also make allowances for crops fed to animals based on samples of what horses and oxen ate in 1300, 1600 and 1800 (OK, they have different samples for oats and pulses…) ; extrapolate output of the agricultural sector by multiplying yield per acre by cultivated arable land for each crop, minus seeds and feed ; estimate the output of the pastoral sector (i.e., herds) by counting sheep from a sample of manorial records and probate inventories ; assume arbitrarily that 90% of cows and sheep produce milk and wool, respectively ; also assume (what looks to me like) arbitrary percentages of slaughter of livestock ; extrapolate all this to national pastoral output by assuming certain proportions between manorial and freehold stocks of animals ; estimate output of hay by assuming each horse ate 2.4 tonnes of hay per year, with the number of horses also estimated from diverse records.

Then the statistically inferred physical count of output is multiplied by price data supplied by, again, Clark. Note all of the physical output data  are highly discontinuous : more plentiful in the 1700s, available only once every century before the 1500s or maybe a few times between 1500 and 1700. Broadberry et al. were very careful and diligent. They even try to check to see if the number of sheep they came up with for any given century was consistent with what England exported.

I won’t get into the nonfarm sector, because the preceding makes the point clear : the chain of assumptions and inferences at each step is iffy enough, but when all is said and done, how can we know to trust the aggregates ?

Normally, you compare the GDP estimates calculated with different methods, but in this case, Clark’s and Broadberry’s are very different, especially for the late Middle Ages. Where, precisely, do they differ ? That is, what statistical adjustment is necessary to harmonise Broadberry’s and Clark’s estimates ? The number of days worked ! In Clark’s data, the number of days worked per worker per year stays within the range of 250-280 days over the course of 550 years :

(Of course, the number of hours worked per worker per year does not even figure in anyone’s calculations, since that is unknowable, even though we really need that information to truly assess the pre-1800 years in the same way we assess the post-1800 years.)

Broadberry does not actually use any of the published days-worked data as shown above. What he does, instead, is impute the days worked from his output estimates. This means, he reconciles his output-based GDP with the wage-based GDP by increasing or decreasing the days worked as necessary to fit his own GDP data. Here are the “imputed” days-worked in Broadberry :

I stress : the third and fourth columns do not contain any values which have been actually observed, or inferred from statistical samples. It’s literally the numbers he needs to make Clark’s wage series “fit” his output series. Broadberry is not being sneaky. He’s quite upfront about his assumptions :

“The second purpose of this paper is to explore the differences between the trends in the real wage and output-based GDP per capita series. The most straightforward way to reconcile the two series is to posit an “industrious revolution”, so that annual labour incomes grew as a result of an increase in the number of days worked, despite the stagnation in the daily real wage (de Vries, 1994).”

The reference is to Jan de Vries, aptly, the author of The Industrious Revolution. For de Vries this revolution was his way of reconciling the increase in luxury goods mentioned in wills starting in the 17th century with the reality of stagnating wages. In the narrative he constructed, early modern households, desiring the new luxury goods made available by global trade and New World expansion, supplied more labour than ever before, including that of wives and children. Broadberry allies himself with this story and extends it deeper into the past, because it’s obviously consistent with his output estimates.

Of course, if incomes increased because people are working longer hours than they had been used to, not working ‘better’, then that’s not inconsistent with a Malthusian story in which the productive efficiency of the economy is stagnant.

I am not suggesting Clark’s estimates are free of tremendous uncertainties. His wage series have been criticised on grounds of representativeness, for example. But I think his methods are more straightforward and he does use observed or sampled values for the basic aggregates. His estimates do not require hypothesising an unobserved massive increase in English working habits between 1450 and 1600.

There are many other critiques and counter-critiques of both sides, as well as ingenious attempts to cross-check Broadberry’s estimates with other kinds of calculations (especially by Karl Gunnar Persson, cf “The End of the Malthusian stagnation thesis”). But I think that’s enough for now !

Addendum-Final note : Just to avoid ambiguity, I state as baldly as I can the point of this post: the pre-modern “little divergences” were probably real, but that doesn’t mean they happened because the divergent economies were smarter or more efficient. Today people assume that higher income implies more technological sophistication. But in the Malthusian world, inhabitants of “smarter” or technologically more advanced societies could be poorer on average than those of less sophisticated societies, because what determined living standards was the balance of birth and death rates.

I think a solid piece of evidence for the Malthusian view is that height in England in the years 1-1800 saw no long-term trend :

Addendum #2: There is now a separate blogpost, “Height in the Dark Ages“, with assesses  living standards in post-Roman Europe using evidence from height.

Addendum #3 : There is now another separate blogpost, “Angus Maddison“, which examines the dubious assumptions behind the pre-1200 income data published by the late Angus Maddison.