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” may or may not be real, but, either way, that doesn’t mean it happened because of a modern growth process — a sustained rise in the production efficiency of the divergent economies.

{Note 5 July 2017: This post was written in 2014. Since then, Broadberry et al. have come out with a new book, and there have been many new papers touching on the subject of this post. The post is still accurate but it does need updating with new information.}

[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 then set off a cascade of 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 :

Few economic historians now dispute that East Asia had lower living standards than Europe well before 1800,

but there is no agreement on whether European economies prior to 1800 were “modern” or “Malthusian” because…

if GDP per capita is increasing because people are working more hours or days per year, that is not necessarily evidence of “sustained growth”, because there is a limit to increasing labour inputs.

so the early modern growth acceleration might still have happened under a Malthusian regime;

(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 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 ?

(3) North-Central Italy

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 :

For North-Central Italy, there are good data for wage rates, prices of basic goods, and population. So the GDP per capita estimates are constructed from those data, with some assumptions built in.

In the GDP series (the first chart), 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…

The point is this. The GDP per capita estimates are ultimately constructed out of daily wage estimates with many assumptions built into how to transform daily wages into total annual income per capita.

(4) England: Broadberry versus Clark

The Clark-Broadberry dispute is best encapsulated in this chart of competing estimates of income per capita for England over 600 years [source] :

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

How you view English economic history prior to 1800 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 (shockingly) argues 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 — for reasons we will get into a moment.

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 wage data are abundant. Broadberry himself describes how wages have been the most traditional way income has been calculated by English economic historians:

“The quantitative picture of long run economic development in Europe is based largely on the evidence of real wages. In the case of Britain, the standard source is Phelps Brown and Hopkins (1955; 1956), who showed that there was no trend in the daily real wage rates of building labourers from the late thirteenth century to the middle of the nineteenth century, albeit with quite large swings over sustained periods. This view has recently been supported by Clark (2004, 2005, 2007a), who constructs a new price index, refines the Phelps Brown and Hopkins industrial wage series and adds a wage series for agricultural labourers. In addition, Clark (2010) provides new time series for land rents and capital income to construct a series for GDP from the income side. This new series is dominated by the real wage and hence paints a bleak Malthusian picture of long run stagnation of living standards and productivity.”

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

“…there are good reasons to be sceptical about this interpretation of long run economic history [based on wage data], which seems to fly in the face of other evidence of rising living standards, including the growing diversity of diets (Feinstein, 1995; Woolgar, Serjeantson and Waldron, 2006), the availability of new and cheap consumer goods (Hersh and Voth, 2009), the growing wealth of testators (Overton, Whittle, Dean and Haan, 2004; de Vries, 1994), the virtual elimination of famines (Campbell and Ó Gráda, 2011), the growth of publicly funded welfare provision (Slack, 1990), increasing literacy (Houstan, 1982; Schofield, 1973), the growing diversity of occupations (Goose and Evans, 2000), the growth of urbanization and the transformation of the built environment (de Vries, 1984).”

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.)

What Broadberry does 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 more hours and days per year than they had been used to, not working more efficiently, then that’s not inconsistent with a Malthusian story in which the productive efficiency of the economy is stagnant.

In other words, “working more” is not per se evidence of “sustained growth”. (In production function terms, y=AF(L,K)…. L is growing faster, but A is constant, or the growth of A is still low.)

Addendum 18 July 2017: Humphries & Weisdorff finds that, whilst daily wages stagnated after 1650, annual wages or income rose, with the implication that hours and days worked per year rose markedly. This confirms Broadberry et al.’s view. But again, this does not mean England escaped the Malthusian regime in 1650!

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 real, but that doesn’t mean they happened because the divergent economies had achieved greater technical efficiency. Broadberry et al. only claim people worked longer after 1650. Higher income does not necessarily imply more technological sophistication. 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 :