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 :

littledivergence2littledivergence1

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, 23)

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 :

malanimagdp

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 :

italywages

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] :

clarkbroadberry

(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 :

“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 :

workdays

(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 :

imputeddaysworked

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 :

height england 1-1800


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.

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24 Responses to The Little Divergence

  1. I have been alerted to this blogpost by Nick Szabo. He appears to have constructed “isoclines” that relate food production per worker with what he calls “human population per natural global hectare” :

    He explains the latter as the “human population per area of land adjusted for natural (but not artificial) variability in its potential to support human food production.”

    I find that incomprehensible. But he continues : “Such an adjusted area is typically called by ecologists a “global hectare” and my phrase “natural global hectare” represents a hypothetical measure of this independent of all human labor and capital improvements”.

    He explains that as the isocline shifts right, a “given unit of labor is producing more human nutrition from the same global hectare” than previously. This sentence I understand perfectly, but I still don’t know whether the variable captured in his X-axis actually measures what he says is being measured, since Szabo does not provide his data sources or his method of computation. But the computation does seem to be a purely ecological one, in which the only measure of interest is the number of workers (regardless of the amount of time it takes them) required to produce a given output of food per given input of land. It seems to lack the economic sense of output per unit of labour-time or output per unit of capital input, all of these things being crucial in the comparison of modern growth with pre-industrial growth.

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  2. Paul says:

    Thanks for this. The mention of the church at the end of the post reminds me you that you promised to delve into gothic building some time ago. Still waiting…

    If I am not mistaken, Broadberry and his collaborators think there was also an Asian Little Divergence, in which Japan got steadily richer (though from a very low baseline) after 1500 while China didn’t. If true, and if the NWEuro Little Divergence is also true, it is highly suggestive that modern growth was not as recent, sudden, and shallow rooted as Pomeranz claims.

    Clark is of course very different to Pomeranz: they may agree it was recent and sudden, but Pomeranz thinks the cause was luck, whereas Clark thinks it very deep rooted.

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  3. On Gothic, well, there are ~600 words on the topic (plus a few illustrations) that had been part of the Creativity of Civilisations blogpost but I removed it because it was not organically connected with that topic. Right now those 600 words seem thin and more like an aside. As it stands those words do illustrate one principle I wanted to push but I want to research another topic (related to Boethius) but I haven’t had time.

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  4. If true, and if the NWEuro Little Divergence is also true, it is highly suggestive that modern growth was not as recent, sudden, and shallow rooted as Pomeranz claims.

    Well, I believe the pre-modern “little divergences” were probably real, but that doesn’t mean they happened because of modern growth processes (a sustained rise in production efficiency). They might have happened because of changes in the Malthusian balance of natality and mortality. The Broadberry versus Clark dispute strongly suggests that the Malthusian process could have been the driver of the “little divergence” at least in England.

    “Broadberry and his collaborators think there was also an Asian Little Divergence, in which Japan got steadily richer (though from a very low baseline) after 1500 while China didn’t.”

    The “surprising wealth of Tokugawa Japan” was part of the Japan revisionism from the 1980s and early 1990s, well before Pomeranz let alone Broadberry. The revisionists back then argued that Japan’s development started earlier than the Meiji restoration. They argued impressionistically about the vitality of the merchant class in pre-Meiji Japan. Of course they never asked whether this was really the start of a modern growth process, or a simple change in the Malthusian balance of natality and mortality. Right now the Broadberry mafia have raised the estimates of Japanese income prior to the 1870s in order to flesh out the “Asian little divergence” but I haven’t really looked into those yet. But all these “little divergences” smell like projecting modern growth processes untenably into the past…

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  5. I’ve added my usual edit-addendum-clarification at the end of the blogpost.

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  6. I’ve posted (separately) an addendum to this post, focusing on pre-1200 data and the work of Angus Maddison, along with some quick observations about the “Dark Ages”.

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  7. T. Greer says:

    “under Malthusian assumptions, per capita income was determined exclusively by the birth rate and the death rate ; and it is not possible to have both higher income per capita and higher population in the long run.”

    OK, so I want to be clear I understand you on this point before I proceed. Should I take this to mean that if living standards and population grew at the same time then the society in question is not experiencing Malthusian growth?

    By extension, if it can be showed that living standards and population increased in a given period – say, pre-modern England or wherever – then you would describe this as ‘Modern growth’?

    *I suppose one might also include that rising living standards were not simply the result of conquest, loot, or theft.

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  8. Yes and no. Population & wage/income correlations are actually an indirect test of the Malthusian model. You can only say any given pattern is consistent or inconsistent. The definitive test of whether the “little divergence” took place because of a “modern” or “Malthusian” process is to check the growth of efficiency over time. But you must first know income in order to measure efficiency, and income for the first industrialiser is the issue that’s being disputed !

    (More on this at the end of the comment.)

    I have focused on the fairly narrow Broadberry versus Clark debate for a reason. The wider debate on Malthusianism is more complicated and more abstract. In order for you to stake an informed position it would require you to get into the minutiae.

    There are stong-form and weak-form Malthusian models, as well as tweaks on both. In the weaker forms, people modify their fertility (and even mortality) behaviour consciously in response to changes in income. Then the question turns to whether these responses are short- or long-term. There’s also the issue of lag time — how long it takes for fertility/mortality changes to take effect in reaction to income. There’s also the question of fertility/mortality responses being different in cities and in the countryside. And there’s also the question of the magnitude of the response changing over time.

    Most economic historians are agreed that the strong form is probably untrue, although some will argue that it was more accurate deeper in the past.

    The difference between radical and moderate Malthusians is essentially on the timing of the transition from weak-form Malthusian to modern. Moderates are largely agreed that things looked quite weak-form Malthusian until about 1600-50, depending on country. Radicals take it further to about 1800-50, depending on country. Those two centuries may seem like not a lot, but they are two very crucial centuries !

    In this blogpost I deliberately sketched a “semi-weak” form with the time element left vague — mainly for ease of presentation & comprehensibility. Again, my purpose was not to explain the Malthusian model, but to talk about how income data get constructed, with just enough about Malthusianism to make my point.

    For heuristic reasons, I also made the difference between “Malthusian” and “modern” growth processes very stark. But it’s possible — in fact, likely — that there was a transition period in which the relationship between people’s fertility/mortality behaviour and income growth weakened over time. For example, say in 1300-1400, the almost imperceptible increase in the economy’s efficiency gets reflected entirely in extra fertility (more income, more babies); but (again, hypothetically) in 1650-1700, the somewhat more perceptible increase in efficiency gets reflected in a smaller fertility response. There’s some evidence for this.

    But the scholarly work checking all this out would make for an even more boring blogpost than the one on how income estimates get done ! So I focused on what I thought was more straightforward — income — as a way of advising caution before concluding that the “little divergence” was all that.

    Back to efficiency. I think in FTA Clark said the efficiency of the English economy grew by ~0.2% per year in 1600-1750.

    Today, the annual growth rate of efficiency (*) since 1973 in the developed countries has been about 1%. (It was 2% in 1945-73 for the United States, which explains at least a part of the wage stagnation.)

    (*) = growth in output relative to all inputs including labour, capital, land, materials, energy, etc. (though land today is a negligeable component).

    So 0.2% per annum might not seem all that bad. But look :

    The LEVEL of efficiency in the English economy 1200-1800, with 1860s = 100.

    Taken from : http://www.researchgate.net/publication/228455000_Interpreting_English_Economic_History_1200-1800_Malthusian_Stasis_or_Early_Dynamism

    The rising trend in 1600-1760 was merely reversing the declining trend in the previous 150 years !

    The “radical” interpretation of the above is : there’s no clear sign of a definitive break until 1800. Maybe the uptick after 1600 was a long-term trend change, as moderates prefer to think, but radicals say you can’t prove that from the time series. Which is why there’s this huge research into the demographic responses to the apparent cyclicality in the time series. But so far there are no clear answers.

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  9. NOTE : the data underlying the above chart involve a crucial assumption. In order to be able to express the productivity level of 1200-1800 in terms of the 1860-70 level, Clark had to assume 10 hours worked per day worked for the period 1200-1800. Hours worked data are estimable only starting from the mid-19th century. So this computation from 2006 started a big debate on working hours in the premodern period. There’s some evidence that working hours fluctuated a lot. But, to my eyes, the limited evidence can imply some of those swings depicted by Clark in the time series might not have taken place, i.e., that the time series might have been stagnant, not even cyclical !

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  10. T. Greer says:

    ” You can only say any given pattern is consistent or inconsistent.”

    This leads to the bigger question I am moving towards. If all measures based off of income-which can only be constructed upon some large and perhaps untenable assumptions-are simply consistent or inconsistent with the pattern, then it makes sense to broaden the evidence stream and seek out other possibly measures of productivity and living standards, no?

    You’ve already utilized a similar approach to the problem in your ‘addendum’ post with the biological standard of living data. (I actually have some doubt about using the bio. standard of living data to measure wealth per capita in agricultural societies, but that is not the point of this query so I’ll set that aside for the moment). But lets say we were able to develop a few other ways to approach household wealth and/or productivity over the centuries. If it appeared from these measures that living standards were raising in spite of population growth, would this be – in your eyes – convincing evidence for a “little divergence”?

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  11. But people are already investigating other lines of evidence on the standard of living. And I don’t know why you don’t like heights.

    Let’s get one thing straight : the WAGE evidence is straightforwardly consistent with Malthusianism. It’s the people who favour the little divergence who construct income estimates that are at variance with the much more solida data on wage. True, wages are not the full extent of income, because they do not include capital income, but capital income was even more likely to be concentrated at the top centuries ago than today !

    Here are some charts from anther notable radical Malthusian, the Israeli economist Oded Galor http://ideas.repec.org/h/eee/grochp/1-04.html :

    The height chart is from http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1084883

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  12. TGreer is giving me new material for future blogposts. I want to illustrate something to TGreer. I drew this up by hand very quickly :

    The above represents the “trade-off” between population and living standards. D>B means deaths exceed births. This is neither a cross-section nor a time-series. A country can be located on different points on the curve at different times. Now, the slope also matters, I’ve made it gently non-linear. A straight line would mean a constant level of trade-off between living standards and wages. A curved line implies the amount of trade off between living standards and population is different (increasing or decreasing, not constant) along the length of the curve.

    A change in the economy’s efficiency that’s big enough NOT to be eaten up by population growth would be depicted as a shift in the above curve, like this :

    I’ve drawn the shift as a parallel movement of the line, but the slope of the curve can change with the shift. In fact, the full transition from Malthusian to modern might be depicted like this :

    I have yet to see Malthusian dynamics depicted like the above. I looked before I drew it myself, but I didn’t see it anywhere.

    Now, take a chart with actual data, with a moderate Malthusian’s interpretation of them for the Netherlands :

    The above is an interpretation of the data points on the chart using the type of curves I drew by hand above. Here is an interpretation for England :

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  13. T. Greer says:

    Hey Pseudo, I apologize for not getting back on this; I was in transit earlier this week and had to put all of the internet conversations I was having on hold.

    1. On biological standard of living — I have no problem with height data persaye. It is a great ‘objective’ measure of well-being. I think, however, it is a poor proxy for “wealth” production/consumption or any of the measures we normally use to measure these things in a per-capita fashion.

    Take, for example, 6th century Europe. We know from the biological data that over the century heights “increased astonishingly.” It seems clear that 6th century Europeans were a healthier lot than their Roman predecessors. But the evidence (as seen here, for example, or in Bryan Ward Perkin’s book, is unambiguous: the fall of the Roman empire was an economic disaster that reduced European production by an order of magnitude.

    A similar point could be made about the neolithic transition. Hunter-gatherers, by and large, were a healthier lot than agriculturalists. I have never heard anyone suggest they were a wealthier lot as well.

    1. When I suggested alternate ways of measuring living standards this was the first measure I was thinking about. I’ve been meaning to blog about that paper for almost a year now and have never got around to it, so I might as well let you have at it. Wat do you think of ‘respectability ratios’ built on market basket consumption?

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  14. T. Greer says:

    Seems one of my links did not go through properly. Here is the list of Roman economic-related graphs I attempted to link to above: http://historum.com/ancient-history/43434-rise-fall-ancient-economy.html

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  15. Well, all that deserves a full blogpost as a response — perhaps one on living standards in early & late antiquity in general. But suffice to say for now, one should not confuse the collapse in population & aggregate output, with a collapse in living standards (a per capita measure). Almost everything in http://historum.com/ancient-history/43434-rise-fall-ancient-economy.html is arguing that there was less economic activity in late Roman and post-Roman periods. Of course there was ! That’s the point. So while I like Ward-Perkins’s book, I do not agree it illustrates what you say it does. Ward-Perkins amasses undeniable evidence of a civilisational collapse, but my point is precisely that the crash in production and population might very well have raised average living standards for the remaining (much smaller) population. Height from the 4th to 6th centuries is strong, though not definitive, evidence for that.

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  19. Jim says:

    Taintor in “The Collapse of Complex Cultures” says that living standards in 6th Century Italy were higher than in 5th Century Italy. Life for many people in 6th Century Italy may have been better than it was for similar people in the 5th Century.

    So the collapse of the Western Roman Empire was a mitigated disaster. On the other hand if the Roman Empire had continued longer maybe North Africa today would be part of European civilization with populations speaking Romance languages.

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  21. Note to Billare re http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0105291

    (1)
    That’s ecology and rather different from economics. Econ models production & consumption and (generally) not population which is treated as exogenous. There are however “unified growth models” with endogenous population. More importantly, however, economic theories would attempt to show how the transition from Malthusian to modern happened, with the key assumption that the two worlds have radically different underlying dynamics. In the original and strong Malthusian formulation population expansion is limited by area under cultivation with assumed fixed yield per acre. But the (implicit) assumption for the modern world is, there is no intrinsic inverse relationship between population (or growth) and carrying capacity. Economics generally assumes resource depletion is prevented by consumers modifying their behaviour in response to price signals, or made irrelevant by technological innovation supplying cost-dependent substitutions. (cf Simon-Ehrlich wager)

    (2)
    But as far as I know, ecologists prefer a kind of super-Malthusian model describing all human history, which preserves some long-run inverse relationship between carrying capacity and population, with resource extraction/depletion placing either a static or dynamic limit on expansion of carrying capacity.

    In that paper the OC model discussed has a term with diminishing marginal increases in carrying capacity K converging to 0 after P(t) > arbitrary limit term L. Either the author just doesn’t like that K will only stop growing and can’t actually fall, OR he “needs” K to fall in order to account for the recent population trends. So he builds the CC model that fits the global population data over both the very long run and the recent past, by building into the model the possibility of falling K via resource depletion that’s an exponential function of population size.

    But as far as I can tell the simulation values of K, c and L are determined by the functional form chosen by the author for the CC model and I can’t tell without spending some more time on it whether the carrying capacity curves in Figures 6 and 7 are “real”. By “real” I mean I don’t know after a quick read, whether the population curve that fits the actual population data pretty well, also algebraically implies the carrying capacity curve or whether there are some arbitrary parameters somewhere which are tweaked to produce the carrying capacity curves.

    Finally, regarding the evolutionary implications in the discussion section of the paper, isn’t that just a badly written version of Gregory Clark ?

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