Karl Gunnar Persson,
Department of Economics, University of Copenhagen
The End of the Malthusian Stagnation Thesis
Abstract (26 April 2010 version)
The view that second millennium European economies exhibited Malthusian stagnation of
real income per head before the Industrial Revolution was long conventional wisdom
sometimes referred to as the ‘Postan’ thesis. It has been revitalized by the publication of
Gregory Clark’s A Farewell to Alms (2007). This note challenges orthodoxy, new and old, by
discussing Gregory Clark’s recent critical appraisal (2009a) of Angus Maddisons’s oeuvre and
an accompanying research paper (2009b). Since the publication of Angus Maddison’s
Contours of the World Economy (2007), which suggested slow growth, a new crop of
reconstructions of European national income accounts are circulated, so far mostly as
reports from research in progress. These , occasionally tentative, estimates suggest slow
but significant growth or stagnation at income levels above any meaningful conceptualization
of Malthusian subsistence stagnation.
Furthermore I demonstrate that the Malthusian stagnation thesis is incompatible with
recorded changes in consumption and occupational patterns as well as with other
acknowledged characteristics of European pre-industrial development.
I finally focus attention on England, by far the best documented of pre-industrial European
economies. A ‘revealed productivity and income growth’ accounting formula based on an
Engel type consumption function is developed and applied using new occupational data for
England. It is possible to confirm the results of slow pre-industrial income growth advanced
in Broadberry, Campbell, Klein ,van Leuven and Overton (2010a), but with a different
methodology.
1
1.Lies, damned lies and historical national income accounts.
Gregory Clark, the University of California economic historian, is not known to please the
authors he is occasionally reviewing in the academic journals. A sample of quotes from a
long review in Journal of Economic History (2009, 69,4, 1156-61) of Angus Maddison’s most
recent book, Contours of the World Economy 1-2030, (2007) confirms that observation:
‘All the numbers Maddison estimates for the years before 1820 are fictions, as real as the
relics peddled around Europe in the Middle Ages. Many of the numbers for the years 1820,
1870, and 1913 are equally fictive. Just as in the Middle Ages there was a ready market for
holy relics to lend prestige to the cathedrals and shrines of Europe – Charlemagne secured
for the cathedral in Aachen, his capital, the cloak of the Blessed Virgin, and the swaddling
cloths of the infant Jesus – so among modern economists there is a hunger by the credulous
for numbers, any numbers however dubious their provenance, to lend support to the model
of the moment. Maddison supplies that market.’
And Maddison is finally relegated to the untouchables:
‘For the reason given above, however, any economist with enough street savvy to resist
fabulous riches offered by unknown Nigerians over the internet will equally want to steer
clear of these estimates.’
Even those of us who routinely deflate Greg Clark’s statements to give them sense are
curious to know what crimes Angus Maddison have committed in his guilt by association
to internet fraudsters. It turns out that Maddison’s major crimes are two: (1) He
underestimates initial income in Europe , say in year 1 or year 1000, and as a consequence
(2) he suggests that there was slow positive growth in Europe in the second millennium
up to the Industrial Revolution. Clark believes that nothing much happened to the alleged
already high level of real per capita income at the dawn of civilization , that is since the
hunter gatherers some 10000 years ago. In A Farewell to Alms (2007) Greg Clark famously
argued that there was near stagnation (stationary variations in the long run) of average real
income from the time of hunters and gatherers, who made their frescos in the caves to
Fillipino Lippi, who did his in the Brancacci Chapel in Florence at the end of the 15th century,
and until the times of Adam Smith.
Maddison believes that most European economies with primitive agricultural technology
and low division of labour had an income per head at or slightly above 400 so called
international dollars in 1990 prices, henceforward called $PPP, in year 1 and year 1000,
which is slightly above the absolute poverty line, the ‘bare bones subsistence’, as
conventionally measured at 355 $PPP. The core of the Roman Empire, Italy, for which there
is some documentation (Maddison 2007, pp 43-59) is ascribed an income of 809
international dollars by Maddison in year 1. Maddison and others (most recently Milanovic,
Lindert and Williamson 2009 ) who have estimated Roman income do not have much to
work on. A pioneering study was made by R.W. Goldsmith (1984). Recent attempts include
R. C. Allen (2007) and W. Schneidel and S. J. Friesen(2009). Results indicate higher income
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in the core part (Italy) of the Empire and a decline setting in after the split of the Empire.
The average income in the Empire was lower. Estimates vary between 1.3 and 1.8
subsistence income units at 355 or 400$PPP. There are several indications that income fell
in the second half of the first millennium. Allen’s estimate of the real wage of an unskilled
worker is not much above the subsistence income by year 300. Population declined, the
monetization of the economy became feeble, cities were abandoned and trade declined.
Byzantium, which developed from East Rome fared much better than Western Europe in
the second half of the first millennium. B. Milanovic (2006) estimated income per head to
some 700 $PPP in year 1000. An educated guess is that income was on average lower in
Western Europe at that time.
Is Maddison right or wrong about these early days with little or no direct documentation?
We will perhaps never know exactly, but the archaeological evidence does not indicate
that, say, Sweden or other economies in the European periphery came close to the
sophistication of Rome in year 1. As for myself I have not as yet discovered a Forum
Romanum in my backyard here in Malmö, southern Sweden, which is, however, rich in
archaeological stone age finds and an occasional Roman coin. By definition Swedish income
could not be (much) below 400$ PPP and it was certainly below the income of Italy both in
year 1 and year 1300, and below Byzantium in year 1000. Olle Krantz ( 2004) offers an
estimate for Sweden around 1571 and suggests a GDP per head of 860 $PPP, that is at
about the average Roman income 1500 years earlier according to Maddison. Available data
seem to suggest that income per head in Europe in the first millennium, also in the more
advanced areas, was considerable lower than before the Industrial Revolution.
2.Conjectures and refutations
No one discussing these matters should ignore the considerable margin of error attached to
the numbers, which like other non-fiction statements, are open to serious scholarly debate
and potential refutation. There are now a large number of initiatives to reconstruct
historical national accounts and five years from now we will know much more. Judging from
the new work in progress there will be a considerable upward shift of the estimated income
levels, compared to Maddison’s estimates for the second millennium up to 1800 but it is not
obvious that rates of growth will be much different .
The new tentative attempts to estimate national income such as Álvares-Nogal and Prados
de la Escosura (2009), Broadberry, Campbell, Klein, van Leuven and Overton ( 2010a),
henceforward Broadberry et als, Buyst (2009), Krantz (2004), Malanima (2009), van Leuwen
and van Zanden (2009) all suggest that income in , say, 1600 was well above ‘bare bones
subsistence’ at 355$PPP. Growth trajectories differed from stationarity at a high level in
some cases, Italy and Spain , to modest (irregular) growth, the Netherlands and
England/Great Britain, and from a lower starting point, Sweden. The new estimates are
compared with Maddison’s income per head in 1990 international dollars in Table 1 below.
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Table 1. Income per head in selected European economies 1500-1820. Maddison (M)
estimates compared to New. 1990 international dollars.
1500M
New
1600M
New
1700M
New
1820
New
England/GB
714
(UK)
1134
974
(UK)
1167
1250
(UK)
1540
1706
(UK)
2193(GB)
Spain
661
1295
853
1382
853
1230
1088
1205#
Netherlands/ 761
1320
1381
2253
2130
1782
1838
1886
1644
1100
1302
1100
1398
1117
1445
824
860*
977
1198
1009
Holland
Italy
1100
Sweden
695
Notes:.# Income in Spain in the 1820 column is from 1800.*Swedish income per head in
1600 is for 1571.Income per head before the Black Death estimated to c.900 in Holland and
England.
Sources: Broadberry, Campbell, Klein, van Leuven and Overton (2010a) Table 24 and the
sources provided therein, see text and references. Maddison(2007) Table A.7.
The high income levels revealed by the new estimates, the New columns in Table 1, are
significant revisions of Maddison’s estimates and Clark obviously has scored a point in
attacking Maddison for underestimating pre-industrial income levels in the second
millennium. However the new estimates must sit uncomfortably with a professed
Malthusian like him because the levels recorded are far above any meaningful notion of
Malthusian subsistence. Modern Malthusians take care in pointing out that subsistence
income should not be interpreted literally as a ‘bare bones’ or absolute subsistence at ,say,
355 or at 400 $PPP which permit survival and restricted productive effort, but little else.
The question arises: how much can the Malthusian subsistence income diverge from the 355
or 400 target? We normally define a Malthusian equilibrium as characterized by constant
population, and by implication subsistence income should be the income level associated
with zero population growth. However at the income per head levels recorded in Table 1
above there is positive population growth. Furthermore income levels seem to be
exogenous in the sense that continued population growth did not make income per head
revert to a significantly lower level.
Peter Skott and I demonstrated long ago that Malthusian and Ricardian conditions , that is
when population growth is positively linked to income and generates diminishing returns,
are compatible with equilibria with sustained population growth and constant, above
subsistence income per head (Persson 1988, chapter 3 and Skott’s appendix to that
chapter). The Malthusian ,subsistence equilibrium usually discussed in the literature is but a
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special case where the rate of technological progress is zero. Once you admit for a positive
rate of technological progress the economy can settle at an income above ‘bare bones’
subsistence and have positive population growth. The equilibrium level of income depends
on the interplay between the rate of technological progress and diminishing returns. That
model is in fact compatible with the results shown in Table 1 where you observe differences
in levels of income across nations. The results reported in Table 1above suggest per capita
income levels three times the 400 dollars mark in 1600 for England, Spain and Italy and 5
times for the Netherlands. An increase in the level of income can be explained by an
increase in the rate of technological progress. A fall in income can result from stronger
diminishing returns. Diets were varied, except for the very poor, with a respectable share
of ‘expensive’ calories from dairy products and meat. Furthermore an increasing share on
non-food producers in the labour force reveals that household’s expenditure on
manufactured goods and services were substantial and in some cases increasing. Households
apparently made choices revealing a trade off between the number and quality
(nourishment) of children as well as between children and other goods, which Malthusians
usually associate with the demographic transition in the 19th century.
Finally Malthusians tend, implicitly, to think of a one-sector (agricultural) economy so when
population increases the land/labour ratio will necessarily fall generating diminishing returns.
However, in the pre-industrial epoch an increasing share of the labour force is active in
non-agrarian professions. As will be documented below the agrarian sector employs about
60 per cent of the labour force in 1600 and then falls to just about 40 per cent in 1760,
before the Industrial Revolution. In the same period the annual increase in population was
0.27 per cent. These numbers actually indicate that the agricultural labour force , and by
implication the land/labour ratio were both constant.
To sum up: Maddison’s pioneering estimates for second millennium Europe are in a process
of careful revision most likely leading to a substantial upward shift in income per head
estimates. The major European economies, not necessarily all, seem to have broken the
Malthusian fetters before the Industrial Revolution and had probably already started the
divergence process with India and China in the middle of the second millennium.
3. Squaring the circle.
We have just demonstrated divergent views regarding levels and trends in income in preindustrial Europe. The estimates of Broadberry et als ( 2010a) suggest a trend growth of
real income per head in England of 0.17% in the 1270-1600 period and 0.37 % in the 17001750 period. These estimates do not differ much from Maddison’s, but his are associated
with lower levels of per capita income. The approach that Broadberry et als have taken is a
reconstruction of national income from the output side. However, Clark does not detect a
positive trend in approximately the same period in his estimate for England, in which
national income is determined from the income side. In principle income and output
approaches should land at the same results. They do not. And therefore we have a problem!
5
I will offer an alternative approach that can be called a ’revealed productivity and income
growth estimate’ using changes in consumption pattern which can be derived from observed
changes in the occupational structure. I will exploit new data provided by Clark and
Broadberry et als and others on levels and changes in occupational structure. My results
support the revisionist stance of Broadberry et als and the results are in line with other
commonly acknowledged indicators, or shall we call it circumstantial evidence, of economic
progress in pre-industrial Europe and England.
Almost all serious scholars agree on the following four statements concerning European
economic history in the second millennium before the Industrial Revolution:
1. ‘The variety of commodities and services as well as professions increased due to the
introduction of new commodities.
2. ‘Over time excess mortality due to harvest shocks fell or disappeared’
3. ‘The non-food producing labour force increased as a share of the total labour force.’
4. ‘The monetization of economies and the sophistication of financial intermediation
increased.’
But here consensus ends.
The stagnationist claim is hardly compatible with any of these statements. It is plausible that
income growth is accompanied by the introduction of new goods (de Vries 2008, Hersh
and Voth 2010). The fall in the incidence of excess mortality ( Campbell and O’Gráda 2010)
in subsistence crises suggests that at least the very poor most vulnerable had experienced
an improvement in living standards. I will explore the implication of statement 3 , that is the
secular rise in the non-agrarian labour force. If the share of the non-food producing labour
force increases it is likely that the share of food in total consumption will fall. However, in a
population not very far away from subsistence level at the beginning of the second
millennium it is unlikely that non-food consumption increases as a share of total
consumption if income is not increasing. This observation is linked to Engel’s law in which
consumption of food as a share of total income falls as income per head increases. The
marginal propensity to consume food is probably low but it is positive! Statement 1 is
closely linked to statement 3 in that the growth of the urban sectors widens the variety of
commodities and services offered, say, new commodities like printed books, fine fabrics,
optical instruments including eye-glasses, colonial imports and new services such as banking,
insurance, art, show-business, (Shakespeare!) and higher learning. The number of
occupations in London more than tripled from 1300 to about 700 in 1700 . (Persson 2010)
Pessimism about the evolution of real income per head in the long run is nurtured by real
day wage data which, for Europe, indicate large variations over time but no positive trend
until the (late) 18th century. But day wage data are notoriously elusive and most inferences
from that type of data to income are based on the controversial assumptions that days
worked per year and participations rates were constant.
6
If workers were on a backward bending supply curve, for which there is empirical support
(Allen and Weisdorf 2009, Dyer 1989, Persson 1984), then increasing day wages would
reduce number of days worked, and vice versa. That condition implies a dampening effect
of changes in day wages on income per head. Clark maintains that from the end of the 16th
century and until the Industrial Revolution the increase in days worked was modest. He
supposes that days worked remain constant at 300 over the pre-industrial period. There is
however evidence of a substantial decline in the high day wage era in the 15th century and
days worked might be as low as 200 per year. This was a period of frequent holidays, many
of which disappeared in the 16th and 17th centuries in Protestant and Catholic societies alike.
The days worked by women and children might be increasing through cottage industry and
proto-industrialization effects especially in areas near urban centres, where a diversified
demand improved employment opportunities. By and large an increase in urbanization might
boost demand for these formerly underemployed categories. This is what the ‘de Vriesian’
literature ( de Vries 2008) on ‘industrious revolution’ is about, although it is dismissed as
without foundation by Clark (2009a, 1160).
It is worth looking more closely at Clark’s estimate of wages and income per head (Clark
2009b). Below we show the two essential graphs, reproduced here with permission from
the author. Surprisingly, from the priors advanced above, there is little difference between
real wage movements and real income movements. A closer scrutiny of the estimates
explain why that is so. First, workers are assumed to work a constant number of days over
time. Second the participation rate is also assumed to be constant. Third, the share of wages
in total income is surprisingly high, around 65 per cent. Finally property income is not linked
to wages in a systematic way. Rents sometimes move with and sometimes against wages.
This amounts to saying that real income was driven mainly by changes in day wages.
A substantial share of the labour force was self-employed and there is little or no income
data on that particular group. It is not clear to me how the income earned by this group is
recorded in Clark’s national income reconstruction. Even economies with a large estatemanaged agricultural sector, like England, was dominated by self-employed peasants as
owner occupiers or leaseholders in the Medieval period. It was previously believed that this
sector was less efficient than estate-managed agriculture but this view has been challenged in
recent decades.
Certain results stand out as fairly controversial and implausible, for example, that income
per head around 1200 and 1450, two medieval peaks interrupted by a sharp drop, was not
attained until early 19th century and that peak income in the mid 15th century was not
matched until the mid 19th century. As noted above excess mortality due to harvest failures
were more pronounced in the medieval period (Campbell and Ò’Gráda 2010) but if we are
to believe Clark that period experienced the twin peaks of pre-industrial income per head.
The prolonged low income period stretching from the end of the 16th century to the end of
the 18th century is in fact a period which experienced the introduction of new goods, say
books and accompanying eyeglasses and a wide variety of colonial commodities, it is the
birth of the scientific efforts leading to modern science. It is also a period of increasing
7
urbanization. Most important of all, of course, the Clarkian estimates do not reveal an
increase in income per head in the pre-industrial period but only very strong fluctuations.
This view fits the Malthusian stagnation thesis well because income per head can only
increase above its equilibrium subsistence level in a transitory manner. Any increase in
income will generate its own destruction by excessive population growth.
Although Clark’s reconstruction of English national income is an admirable project the
results do not differ substantially from deriving income per head just using day wage data
and assuming a constant share of wages in national income.
8
Figure 1. Real wages in England 1200-1850. 1860/69 = 100. Source: Clark 2009b.
Figure 2. Real income per head in England 1200-1850. 1860/69 =100. Source: Clark 2009b.
Certain results stand out as fairly controversial and implausible, for example, that income
per head around 1200 and 1450, the twin medieval peaks, was not attained until early 19th
9
Broadberry et als (2010a) reconstruct national income from output data and come to
results fundamentally different from Clark. The graphs below, reproduced with permission
from the authors, show the real income per head and we can trace a slow, but not
unbroken, positive trend which continues in the 18th century, The yearly growth rate is 0.17
per cent per year between 1270 and 1700 and 0.37 per cent per year between 1700-1760.
The trajectory of GDP per head revealed in these estimates are more in line with what we
would expect from a consideration of the four consensus statements discussed above.
The two contending estimates agree that there is an increase in real income per head from
1300 to the mid 15th century although the increase is much larger in Clark’s estimate, or
more than a doubling. The two sets of estimates also record a setback after the 15th century
peak but it is broken in the mid 16th century in the estimates by Broadberry et als and from
then on you can discern a positive trend in growth. Clark’s estimates display near stagnation
of income per head from the mid 16th to the mid 17th century.
10
Figure 3. Real GDP per capita in England, 1270-1710. (1700=100) Source Broadbery et als
(2010a), Figure 10. Check S.N. Broadberry’s webpage for updates.
Figure 4. British real GDP per capita, 1700-1850. (1850 = 100). Source: Broadberry et als
2010, Figure 12. Check S.N. Broadberry’s webpage for updates.
The two contending estimates agree that there is an increase in real income per head from
1300 to the mid 15th century although the increase is much larger in Clark’s estimate, more
It will be demonstrated that we can infer productivity and ultimately real income per head ,
11
Can we find some alternative method of measuring income which can be the arbiter
between these conflicting estimates? Yes, we can?
It will be demonstrated that we can infer productivity and ultimately real income per head
changes from observed changes in the occupational structure of the economy. A fall in the
agrarian labour force as share of the total labour force is causally linked to increasing labour
productivity and income per head.
The argument that increasing production and consumption of ‘industrial’ commodities as a
share of total consumption reveal increasing income has strong empirical support and forms
the basis for Engel’s law – although it was first shown to apply in cross sections. You can call
it a ‘revealed productivity and income growth’ estimate.
The first attempt to make inferences to income and productivity from the changes in
consumption pattern as revealed by occupational and production patterns was performed
by Tony Wrigley (1967). His accounting framework was very simple and assumed a closed
economy and a marginal propensity to consume food at zero. A more general accounting
framework which permitted international trade in food, income differentials between
agriculture and industry and positive marginal propensity to consume food was developed
by Persson(1988,1991). My method cannot determine levels but only changes in labour
productivity over time or gaps (ratios) across nations or regions. You can, in other words
get an index of output and income per producer at a given point in time relative to income
in a base year = 1. If you have a reliable benchmark estimate it is of course possible to
interpolate back to an estimated initial income level. The Persson method needs little data,
in particular it will not rely on wage, property income or output data at all.
The Persson method is essentially a simple general equilibrium model derived from the
national income identity combined with an Engel’s law consumption function. We think of an
economy with two sectors, an agrarian sector denoted by the subscript a and an non-foodproducing sector, denoted by i. The labour force 𝐿
is measured in units of workers but
we cannot control for number of days per year which might change over time. With 𝐿 =
𝐿𝑎 + 𝐿𝑖 national income is
𝑌 = 𝐿𝑎 𝑞𝑎 𝑝𝑎 + 𝐿𝑖 𝑞𝑖 𝑝𝑖
𝑞𝑎 is output (value added) per agrarian and 𝑞𝑖 output per ‘industrial’ or non-food
producing labour. 𝑝𝑎 is price of agrarian goods 𝑝𝑖 is price of ‘industrial’ goods.
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The method I propose, the ‘revealed labour productivity and income growth’ method, infers
productivity and income changes from changes in occupational structure triggered off by
changes in consumption patterns. It is a well established fact, called Engel’s law, that
expenditure on food falls as a share of total income with increasing income if
𝑐𝑦 = 𝑏 + 𝑚𝑦
The consumption function above indicates that the average consumption of food, 𝑐, of
income per worker , 𝑦, falls since 𝑏 is a constant and 𝑚, the marginal propensity to
consume food (1 > 𝑐 > 𝑚>0). In case there is zero net import of food, as in the period
under consideration here, there is an upper-bound limit of 𝑚 set as 1 > 𝑙𝑎𝑚𝑖𝑛 ≥ 𝑐 > 𝑚>0).
In a ‘steady state’ with balanced agricultural trade 𝑚 is strictly smaller than 𝑙𝑎𝑚𝑖𝑛 which is
the value that 𝑙𝑎 takes at the end of the period under investigation. See Appendix for a
proof.
This change in expenditure patterns when income increases will of course also affect the
occupational structure in a more or less proportional way. The decline of agricultural
employment as a share of total employment is associated with the fact that the rising
income levels permit a larger share of total income to be spent on non-essentials or
‘industrial’ goods.
The demand for food is equal to supply
𝐿𝑏 + 𝐿𝑎 𝑚𝑞𝑎 + 𝐿𝑖 𝑚𝑠𝑞𝑎 = 𝐿𝑎 𝑞𝑎 + 𝑀𝑎 − 𝑋𝑎
In the identity above 𝑠 is the skill premium of ‘industrial’ labour over farm workers and 𝑀𝑎
and 𝑋𝑎 is import and export of food respectively. It is important to control for net exports
of food because it is possible that an increasing number industrial producers do not reveal
increased domestic food production but imports of food paid for by industrial goods.
The logic of the argument is that as the labour force in agriculture shrinks fewer farming
households have to feed more non-farming households which they can do only if they
produce more per worker.
In the Appendix we derive the accounting formula shown below. The intuition is this. If we
observe a decrease in the share of the food producing labour force it reflects a change in
consumption patterns related to an income increase which causes the expenditure on food
to fall as a share of total expenditure. A few things have to be controlled for, however, like
foreign trade and the relative income of the non-food producers.
(𝑏⁄𝑞𝑎0 ) 𝑞𝑎1 𝑙𝑎0 (1 − 𝑚) − 𝑚𝑙𝑖0 𝑠0 + 𝑘0 𝑙𝑎0
=
=
(𝑏⁄𝑞𝑎1 ) 𝑞𝑎0 𝑙𝑎1 (1 − 𝑚) − 𝑚𝑙𝑖1 𝑠1 + 𝑘1 𝑙𝑎1
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𝑙𝑎 is the share of agrarian workers of total labour force of and 𝑙𝑖 the share of non-food
producers, 𝑚 is the marginal propensity to consume food, 𝑠 is the non-agrarian skill
premium and 𝑘 and import of food variable, which would be negative in a case of net
exports of food. 0 and 1 are time subscripts. The numeraire in which income is measured is
units of food.
The formula above gives an index-number of labour productivity in agriculture, 𝑞𝑎1 , with
𝑞𝑎0 = 1. But having derived 𝑞𝑎1 it is easy to estimate average income per economically
active person, 𝑦𝑎1 .
𝑦𝑎1 = 𝑙𝑎1 𝑞𝑎1 + 𝑙𝑖 𝑠1 𝑞𝑎1
𝑦𝑎 differs from income per head 𝑦𝑎ℎ𝑒𝑎𝑑 because the entire population is not economically
active, that is
𝑦𝑎ℎ𝑒𝑎𝑑 = 𝑒𝑦𝑎
𝐿
where 𝑒 is 𝑃 .
If 𝑒 is increasing over time then income per head will consequently rise faster than income
per worker. 𝑦𝑎ℎ𝑒𝑎𝑑 is an expression of real income but expressed in terms of food units.
National income estimates, however, express real per capita income as the income in terms
ℎ𝑒𝑎𝑑
of a basket of goods. The formal expression of what we denote 𝑦𝑟𝑒𝑎𝑙
is detailed in the Appendix but the intuition is give here. The growth of real income
expressed in units of food is identical the to real income in terms of a basket of goods if the
price of food changes exactly as the price of the basket. However, if, say the price of food
increases relative to the other items in the basket then the increases in real income as
conventionally measured is larger than the real income measured in terms of food units,
because a unit of food buys more other goods. What we experience here is equivalent to a
terms of trade improvement of the agrarian sector. If, on the other hand, the price of food
falls relative to the price of the basket of goods then the real income falls relative to the
estimate of income measured in food units.
A straightforward interpretation of the results must control for the employment in each
sector of workers providing intermediate goods. Unfortunately existing data do not give us
a clear-cut distribution of the labour force in this respect. But the view that a shift of labour
to the industrial sector was driven by a demand from the agrarian sector of industrial
intermediate goods, that is equipment , is not plausible. In the pre-industrial period it is not
intermediate goods produced in the non-agrarian sector, such as machinery and chemical
fertilizers, which are prominent in the present era, that drive output growth. It is rather
new knowledge gained by trial and error, selection of better varieties of seed corn, regional
14
specialization, better rotation including the introduction of nitrogen fixing plants and, finally,
greater work effort. The differentiation of output permitted by proximity to urban centres
with diversified demand relieved households from the curse of seasonal unemployment.
Growth in output per labourer was typically larger than growth per hour of labour. The
agrarian sector also ‘exports’ intermediate goods to the industrial sector, wool for the
woollen industry and grain for the breweries , for example. Lacking precise information
these general considerations lead to the assumption that the share of the total labour force
producing intermediate ‘industrial’ goods for the agrarian sector and the share of the total
labour force in the agrarian sector that produces intermediate goods for the industrial
sector are both constant, although they can differ between sectors. That argument
amounts to saying that the changes in occupational distribution of the labour force is driven
by changes in demand for final goods only. Over time as the agrarian share of total
employment falls this assumption implies that the share of the agrarian labour forces that
produces intermediate goods, raw materials, for the ‘industrial’ sector increases while the
share of ‘industrial’ employment that produces final consumer goods increase. This is
consistent with the view that urban professions specialize in new services and goods in the
final goods market and intermediate goods for the ‘industrial’ sector. One of the
acknowledged characteristics of urban agglomerations is that they are clusters of interlinked
producers.
Let us now turn to a discussion that aims at giving plausible values to the variables and
parameters in the accounting formula specified above.
Most scholars, including Clark, agrees agree that the share of the labour force in the nonagrarian sector increases but he questions, with good reason, the accuracy of urbanization
ratios as a proxy for the share of the non-food producing labour force. Measurements of
urbanization usually include only cities above 10.000 inhabitants or in some cases 5000.
However, there were numerous agglomerations with a population between 500 to 5000
inhabitants which were essentially sites of producers of non-agrarian commodities and
services. Clark suggests instead an alternative series based on occupational data from wills.
This series from England has a much higher non-food producing labour force by the end of
the 16th century than suggested by the urbanization data for England, around 40 per cent by
the end of the 16th century and beginning of the 17th century. It then increased to a stable
level around 54 per cent already in the middle of the 18th century. The high non-food
producing labour force already by 1600 suggests an income level far above any meaningful
notion of a subsistence income, in my view. Broadberry and van Leuwen (2010 b, Table 13 )
have also revised their occupational data using Poll Tax returns and Muster Rolls and, like
Clark, they have substantially increased the estimate of the non-agricultural labour force
relative to earlier estimates based on urbanization ratios. The non-food producing labour
force , according to Broadberry and van Leuwen, is surprisingly large, 38.5 per cent already
by the end of the 14th century and although it had increased only slightly by the beginning of
the 16th century it was much higher in 1700, 54 per cent and 61 per cent in 1759.
15
The marginal propensity to consume agricultural goods 𝑚, is difficult to measure.
Conventional measures tend to overstate it because what is measured is the demand for
processed food which has a considerable ‘industrial’ value added content. Since the
estimation method we use is sensitive to the level of 𝑚 and given the lack of firm empirical
foundation as regards its true value I will proceed, not by giving it some best guess value, but
rather to see what the implied level must be to be consistent with the contending estimates
of economic growth. That procedure will give us a chance to discuss the plausibility of the
alternative views of the pre-industrial economy as one of slow growth or stagnation.
The available empirical information of pay differentials records a substantial and fairly
constant gap. I take 𝑠, the per capita income gap between the non-food producing labour
force and the agrarian labour force to be 1.5. The motivation is that the non-food producing
classes included professionals of all sorts with comparatively high wages. It also seems as if
the number of days worked was higher in the non-agricultural sector because work was not
determined by the seasonal cycle as in agriculture. Furthermore the day wage records
suggest a wage gap in favour or non-agricultural workers of at least 50 per cent. Clark
reports a rather stable skill premium of non-agricultural workers to farm workers of about
50 percent since in the pre-industrial period. (Clark 2009b, Table 1).
We can sum the deliberations in the preceding paragraphs in Table 2.
Table 2. Accounting data 1381-1759.
1381
1700
1759
𝑙𝑎
0.615
0.459
0.391
𝑙𝑖
0.385
0.541
0.609
𝑚
< 𝑐 = 0.52
< 𝑐 = 0.36
< 𝑐 = 0.3
𝑠
1.5
1.5
1.5
0
0
0
𝑘
Note: 𝑐 is derived in the Appendix. Sources: Occupational data from Broadberry et als,
(2010) Table 13, other sources see text. Occupational estimates from 1381 based on Poll
Tax records, the 1700 and 1749 estimates from contemporary ‘social tables’.
Using the data summarized in Table 2 will be sufficient for an estimate of an index of output
per labourer in the agrarian sector relative to the base year 1381. Having arrived at that
index number we can calculate growth rates of agrarian labour productivity over time.
Under simplifying assumptions we can also estimate real income per head growth. To do so
we need, however, to assume that relative prices , food vs. other goods, are constant and
that the participation rate does not change. See Appendix equations 16-17 for details. It
turns out that real income per head increases slightly faster than labour productivity in
agriculture. That does not imply that labour productivity (necessarily) increases faster in the
16
‘industrial’ sector but it is simply a structural effect due to the fact that over time an
increasing share of the total work force is employed in the ‘industrial’ sector which enjoys
higher real wages. The growth of income per head, under the assumptions stated above, will
be only marginally larger than growth of labour productivity, typically in the order of 0.02
percentage points.
The first question is whether the stagnation thesis can be upheld given the large increase in
the non-agricultural labour force, and by implication the large increase in per capita
consumption of non-agricultural goods. Let us first see if such an increase is consistent with
a stable Engel-type consumption function, that is with 𝑚 constant over time and lower than
0.3 which is the value of 𝑐 in 1759
Since the implied growth of income will be higher the higher 𝑚 is we let the value be
extremely low at 0.01. Even under these conditions growth in income per head will be
considerable, at 0.15 per cent per year, as reported in Table 3 and the use of a more
conservative estimate of the fall in the agricultural employment favoured by Clark does not
fundamentally alter the implied growth.
The conclusion is that the Malthusian stagnation thesis is not consistent with the observed
changes in the occupational structure unless you assume that there is a huge shift in
consumer preferences over time in favour of non-agricultural goods. Such a shift is highly
improbable in a Malthusian context, because consumers are supposed to use a smaller share
of their constant and low income for food expenditures because of increased taste for nonfood commodities. While consumer preferences might change as new commodities enter
the market, as suggested by the adherents of an industrious revolution, it is not likely that
substantial changes in the expenditure pattern will occur at fairly low and constant income.
Table 2 reveals that the changes in average expenditure were, indeed, substantial since
average expenditure on agricultural goods, 𝑐 , fell from 52 to 30 per cent between 1381 and
1759.
Next step is to determine the marginal propensities to consume food which are broadly
consistent with the growth estimates provided by Broadberry et als (2010). It turns out that
the marginal propensities are far below the maximum suggested in Table 2. If anything the
low displayed as consistent with the growth record in Table 3 might nurture a suspicion
that the Broadberry et als estimates actually have a downward bias. But as suggested above
we know too little about the true value of 𝑚 to make definitive statements. Be as it may,
given the low marginal propensity to consume agricultural goods the economy seems to be
in a state exploring the welfare gains of new commodities beyond those needed for survival.
17
Table 3. Growth of agricultural labour productivity and real income in England 1381-1759.
Per cent per year.
1381-1759
Growth of agrarian
labour productivity
Growth of real
income per head
Comments
0.13
0. 15
Assuming an
implausibly low
0.10*
1381-1700
0.18
1700-1759
0.75
0.4
0.2
𝑚=0.01
𝑚=0.20
𝑚=0.20
0.44
𝑚=0.10
* The growth rate of income per head using the alternative higher estimate of agricultural
share in 1750/60 at 0.47 favoured by Clark (2009b). The estimates are fairly robust as to
variations in s. Assuming that the pay differential is falling from a 50 per cent pay gap to a 25
percent gap so that 𝑠 falls from 1.5 to 1.25 the implied growth will be smaller by 0.020.03 percentage points.
A word of caution must be inserted here. When we talk about increases in labour
productivity it is not output per day worked but per worker. It is likely that a part of the
increase in output per workers is caused by an increase in days worked per year. But also in
case we assume days worked increased a great deal, say, from 225 to 300 days, less than
half of the output increase can be explained and the rest must be caused by labour
productivity in the precise sense, that is output per hour worked.
4. Conclusion
Observed changes is English occupational structure over the second millennium reflect
changes in the consumption pattern which is linked to the introduction of new goods,
increased foreign trade, and, in the spirit of Engel’s law, a substantial increase in real income
per head. The observed changes in consumption and occupational patterns are incompatible
with the Malthusian stagnation thesis.
18
The sources of the revealed income increase are probably a combination of more hours or
days worked per employed and an increase in labour productivity. By implication, the results
presented here suggest that we need to take a second look at real day wage series. Are
these series representative? Where does the large group of self-employed fit in? These
questions must be asked because it is hard to reconcile the increasing labour productivity,
strictly defined, which is documented here with the widely held view that real wages were
stagnating.
Note: Comments from participants at the MEHR seminar at the University of Copenhagen and
‘Högre seminariet’ at University of Gothenburg have been very useful. Carl Johan Dalgaard read a
revised version and suggested several improvements. I am responsible for remaining flaws.
Appendix 1
Notation. 𝑎 is agrarian sector and 𝑖 is non-agrarian sector. 𝑞 is output per economically
active person and 𝑝 is price.
Total labour force, 𝐿, is 𝐿 = 𝐿𝑎 + 𝐿𝑖 (1)
National income 𝑌 is
𝑌 = 𝐿𝑎 𝑞𝑎 𝑝𝑎 + 𝐿𝑖 𝑞𝑖 𝑝𝑖 (2)
Dividing (1) through with 𝐿 yields 𝑦, per household income
𝑦 = 𝑙𝑎 𝑞𝑎 𝑝𝑎 + 𝑙𝑖 𝑞𝑖 𝑝 (3)
𝑖
We define
𝑦𝑎 =
𝑦
𝑝𝑎
(4) and 𝑝 =
𝑝𝑖
𝑝𝑎
(5) and divide(3) through with 𝑝𝑎
𝑦𝑎 = 𝑙𝑎 𝑞𝑎 + 𝑙𝑖 𝑞𝑖 𝑝 (6)
𝑦𝑎 is income per economically active person expressed in units of food.
The Engel type consumption function is
𝑐𝑦𝑎 = 𝑏 + 𝑚𝑦𝑎 (7)
In (7) 𝑐 is average consumption of food which falls as income is increasing. 𝑏> 0 is a constant
and 𝑚 is the marginal propensity to consume food, 1 > 𝑐 > 𝑚>0. There is an upper-bound
limit on 𝑚 as discussed in the text. The ‘industrial’ skill premium is 𝑠 =
and income per non-agrarian or ‘industrial’ labour is 𝑞𝑖 𝑝 = 𝑠𝑞𝑎 (9)
19
𝑞𝑖 𝑝
𝑞𝑎
(8)
Aggregate demand of food is equal to supply
𝐿𝑏 + 𝐿𝑎 𝑚𝑞𝑎 + 𝐿𝑖 𝑚𝑠𝑞𝑎 = 𝐿𝑎 𝑞𝑎 + 𝑀𝑎 − 𝑋𝑎 (10)
In (10) 𝑀𝑎 is import and 𝑋𝑎 is export of food. Net import of food per household is
𝑛=
𝑀𝑎 −𝑋𝑎
𝐿
(11)
Divide (10) through with 𝐿𝑞𝑎 and rearrange will yield
𝑏
𝑞𝑎
= 𝑙𝑎 (1 − 𝑚) − 𝑚𝑙𝑖 𝑠 +
𝑛
𝑞𝑎
(12)
𝑛
It turns out that it is difficult to estimate
𝑞𝑎
directly while it is easier to estimate a variable
𝑘 as net imports of food as a fraction of total domestic production of food
𝑀𝑎 −𝑋𝑎
𝐿𝑎 𝑞𝑎
=
𝑛
𝑙𝑎 𝑞𝑎
= 𝑘 (13)
Therefore 𝑘𝑙𝑎 can be substituted for
𝑏
𝑞𝑎
𝑛
𝑞𝑎
in (12) above and it can be rewritten
= 𝑙𝑎 (1 − 𝑚) − 𝑚𝑙𝑖 𝑠 + 𝑘𝑙𝑎 (12´)
We can now derive an index of household output in the agricultural sector at time 1
relative to output at time 0.
(𝑏⁄𝑞𝑎0 )
𝑞𝑎1
(𝑏⁄𝑞𝑎1
𝑞𝑎0
=
)
=
𝑙𝑎0 (1−𝑚)−𝑚𝑙𝑖0 𝑠0 +𝑘0 𝑙𝑎0
𝑙𝑎1 (1−𝑚)−𝑚𝑙𝑖1 𝑠1 +𝑘1 𝑙𝑎1
(14)
The formula above gives an index-number of 𝑞𝑎1 with 𝑞𝑎0 = 1. But having derived 𝑞𝑎1 it
is easy to estimate average income per economically active person, 𝑦𝑎1 .
𝑦𝑎1 = 𝑙𝑎1 𝑞𝑎1 + 𝑙𝑖 𝑠1 𝑞𝑎1 (15)
𝑦𝑎 differs from income per head 𝑦𝑎ℎ𝑒𝑎𝑑 because the entire population is not economically
active, that is
𝑦𝑎ℎ𝑒𝑎𝑑 = 𝑒𝑦𝑎 (16)
where 𝑒 as before is
20
𝐿
𝑃
.
Income per head expressed in terms of units of food is different from real
income as conventionally measured as the command over a basket of goods,
ℎ𝑒𝑎𝑑
which we denote 𝑦𝑟𝑒𝑎𝑙
. Real income per head is simply the ratio of food price
to the price, 𝑝𝑏 , of the basket of goods, say, a consumer price index multiplied
with the real income in terms of food units,
𝑝
ℎ𝑒𝑎𝑑
𝑦𝑟𝑒𝑎𝑙
= 𝑝𝑎 𝑦ℎ𝑒𝑎𝑑
(17)
𝑎
𝑏
We will now prove that in an economy with balanced trade in agricultural
goods it holds that 𝑚<𝑙𝑎 as long as 𝑠 ≥ 1.
Consumption of food is equal to production, that is
𝑐(𝐿𝑎 𝑞𝑎 + 𝐿𝑖 𝑠𝑞𝑎 ) = 𝐿𝑎 𝑞𝑎 (18)
Divide through with 𝐿𝑞𝑎 yields
𝑐(𝑙𝑎 + 𝑙𝑖 𝑠) = 𝑙𝑎 which implies
𝑐=
𝑙𝑎
𝑙𝑎 +𝑙𝑖 𝑠
(19).
From (19) it is clear that since 𝑙𝑎 + 𝑙𝑖 = 1 and if 𝑠 = 1 then 𝑐= 𝑙𝑎 and if s>1
then 𝑐< 𝑙𝑎 . From (7) it is obvious that 𝑚< 𝑐 where 𝑐 is the average
expenditure on agricultural goods and hence 𝑚 will be strictly smaller than 𝑙𝑎 .
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