Angus Maddison

This blogpost examines the dubious assumptions behind Angus Maddison’s pre-1200 income data.

In the blogpost “The Little Divergence” I argued that in charts like this,

littledivergence1

the period 1200-1800 involve uncertainties and conjectures that should make us pause.

But at least the post-1200 figures are based on something. What about those ‘data’ prior to 1200? Those are based on work done by the late Angus Maddison who spent nearly his entire life constructing page after page of statistics on income and population for regions of the world going back to Year 1 of the common era. Since his death Maddison’s work has been continued, refined, and updated by the Maddison Project in the Netherlands. But since Maddison’s original pre-1200 ‘data’ still show up frequently, I want to address those, not the revisions.

Greg Clark, in an unrelentingly scathing review of Angus Maddison, basically argues most of the data are made up. Clark’s comments are pretty harsh, but his conclusion seems inevitable once you actually examine Maddison’s sources.

Maddison’s pre-1820 data are derived from a small set of assumptions, as sketched in Appendix B of The Monitoring the World Economy 1820-1992. And those initial assumptions are rolled over into every subsequent iteration of Maddison’s long-run income histories of the world.

In order to show you what some of these assumptions are, I quote directly from the aforementioned Appendix B, pp 260-261 of that book :

“Before 1500, the element of conjecture in the estimates is very large indeed. The derivation of per capita GDP levels for China and Europe are explained in Maddison (1998a), and the conjectures for other areas are explained below. In all cases GDP is derived by multiplying the per capita levels by the independently estimated levels of population.

Maddison (1998a) contained estimates of Chinese economic performance from the first century onwards. The evidence suggested that per capita GDP in the first century (in the Han dynasty) was above subsistence levels — about $450 in our numeraire (1990 international dollars), but did not change significantly until the end of the 10th century.

“For most of the rest of Asia, it seemed reasonable here to assume that the level of per capita income was similar to that in China and showed no great change from the first century to the year 1000. The $450 level of per capita income assumed here is sufficiently above subsistence to maintain the governing elite in some degree of luxury and to sustain a relatively elaborate system of governance. Japan was a rather special case. In the first century, it was a subsistence economy in course of transition to agriculture from hunting and gathering, and from wooden to metal tools. By the year 1000, it had made some progress but lagged well behind China.

“In Maddison (1998a), pp. 25, 37–38, it was assumed that European per capita income levels in the first century were similar to those in China. Goldsmith (1984) provided a comprehensive assessment of economic performance for the Roman Empire as a whole, and also provided a temporal link, suggesting that Roman levels were about two fifths of Gregory King’s estimate of English income for 1688.

“The West Asian and North African parts of the Roman Empire were at least as prosperous and urbanised as the European component, which warrants the assumption of similar levels of income there.

“Between the first century and the year 1000, there was a collapse in living standards in Western Europe. Urbanisation ratios provide the strongest evidence that the year 1000 was a nadir. The urban ratio of Roman Europe was around 5 per cent in the first century. This compares with zero in the year 1000, when there were only 4 towns with more than 10 000 population (see Maddison, 1998a, p. 35). The urban collapse and other signs of decline warrant the assumption of a relapse more or less to subsistence levels ($400 per capita) in the year 1000.

“For the Americas, Australasia, Africa south of the Sahara, Eastern Europe and the area of the former USSR, I have assumed that more or less subsistence levels of income ($400 per capita) prevailed from the first century to the end of the first millennium.

Since Maddison refers to it constantly in the above, I also quote from his 1998 book on Chinese economic history :

“3. In the first century, at the death of Augustus, the Roman Empire had 23 million inhabitants in Europe, 19.5 million in what became the Byzantine Empire, and 11.5 million in Africa (see Beloch, 1886, p. 507). Goldsmith (1984) produced an extraordinarily erudite, ingenious and ambitious attempt to estimate total and per capita income in the Empire at the time of Augustus. He suggests that per capita product was about two fifths of the British level at the end of the seventeeth century.

Using my 1990 numeraire, this would be around $500. However, the Asian and African parts of the Empire were more urbanised than the Western Empire and Egypt’s irrigated agriculture had much higher yields than those in Europe. The level in the West was therefore lower than the average for the whole of the Empire, and the non–Roman inhabitants of Europe (about 11 million in the first century) were operating near subsistence levels.

In my estimate for European per capita income in the first century (Table 1.3 above), I assumed a $480 level in the Roman part, and a $400 in the non–Roman area — an average of about $450. I assumed that China and Europe operated at about the same per capita level in the first century A.D.”

You can see that the the chain of assumptions one way or another ultimately goes back to the Goldsmith reference, which is an estimation of Roman empire income in the reign of Augustus. From this I also quote the relevant portion :

“2. National product in terms of commodities

“In the face of the inability to express national product in terms of an appropriately constituted basket of commodities and final services the comparison will be limited to two basic commodities.

“The comparison of the gold equivalent of national product per head is arithmetically unequivocal, but economically problematic, because the ratio of the price of the representative basket of commodities and services in terms of gold is very difficult to determine but certainly has changed over time.

“In terms of gold, which was the base of the monetary system of the early Roman Empire, its national product per head of about four aurei, equal to 31 g or about one ounce of gold was higher than those of India and Brazil in the mid-19th century (14 g and 27 g), but substantially lower than those of England in 1688 (over 70 g) or of France and the United States in 1820 (about 100g).8′

“The wheat equivalent of annual national product per head in the early Roman empire of about 125 modii at a price of HS three or close to 850 kg was in the order of one-half the level of England and Wales in 1688, of the United States in 1820 (about 1700 and 2050 kg respectively) and if all less developed countries in 1960 (about 1,500kg) reflecting the high relative price of wheat in imperial Rome.”

Note, Goldsmith says he doesn’t know the Roman price of gold in terms of other commodities. So the finding that the Roman per capita income in terms of gold was 3/5th of English income in 1688 in terms of gold is not “PPP-adjusted”, i.e., not adjusted for the Roman-English differences in the purchasing power of gold. So I don’t know why Maddison honed in on this.

All the same, almost everything in Maddison’s pre-1000 or pre-1200 data emanates from this single assumption ! Therefore, Maddison’s chain of reasoning is as follows :

Universal subsistence income is assumed to be $400 in 1990 dollars. Most of the world in 0-1000 is assumed to fall into either the $400 or the $450 category. The Roman empire income in 1AD (supposedly) ≈ 40% of British income in 1700 ≈ $500 using Maddison’s base => European income of $450 in 1AD ≈ (by assumption) Chinese income in 1AD => (by assumption) rest of Asia about the same as China => (by assumption) little change in income in Asia until 1000, but European income falls below $400 until 1000.

The whole thing is a house of cards. Can you take the data for 1-1000 seriously after reading all that ?

Now, it’s true the Maddison Project has revised Maddison’s data quite a lot, as can be seen from this :

maddproject

The above (expressed in 1990 international dollars) are based on new studies which I haven’t looked at yet. But they look suspiciously like Maddison’s $400 baseline has been ratcheted up to $600, with his assumptions still largely intact… But I don’t know for sure.

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One Response to Angus Maddison

  1. Pingback: The Little Divergence | Pseudoerasmus

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