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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 $PPP. The core of the Roman Empire, Italy, for which there is some documentation (Maddison 2007, pp 43-59) is ascribed an income of 809 international dollars by Maddison in year 1. Maddison and others (most recently Milanovic, Lindert and Williamson 2009 ) who have estimated Roman income do not have much to work on. A pioneering study was made by R.W. Goldsmith (1984). Recent attempts include R. C. Allen (2007) and W. Schneidel and S. J. Friesen(2009). Results indicate higher income 2 in the core part (Italy) of the Empire and a decline setting in after the split of the Empire. The average income in the Empire was lower. Estimates vary between 1.3 and 1.8 subsistence income units at 355 or 400$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. 3 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 4 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. 12 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 13 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). 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