End of Malthusian Stagnation Thesis

8/7/2019 End of Malthusian Stagnation Thesis

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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 realincome per head before the Industrial Revolution was long conventional wisdom sometimesreferred to as the Postan thesis. It has been revitalized by the publication of Gregory Clarks

A Farewell to Alms (2007). This note challenges orthodoxy, new and old, by discussing GregoryClarks recent critical appraisal (2009a) of Angus Maddisonss oeuvre and an accompanyingresearch paper (2009b). Since the publication of Angus Maddisons Contours of the WorldEconomy(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 atincome levels above any meaningful conceptualization of Malthusian subsistence stagnation.

Furthermore I demonstrate that the Malthusian stagnation thesis is incompatible withrecorded changes in consumption and occupational patterns as well as with otheracknowledged characteristics of European pre-industrial development.

I finally focus attention on England, by far the best documented of pre-industrial Europeaneconomies. 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 inBroadberry, Campbell, Klein ,van Leuven and Overton (2010a), but with a differentmethodology.


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1.Lies, damned lies and historical nationalincome accounts.

Gregory Clark, the University of California economic historian, is not known to please theauthors he is occasionally reviewing in the academic journals. A sample of quotes from a longreview inJournal of Economic History(2009, 69,4, 1156-61) of Angus Maddisons most recentbook, 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 relicspeddled around Europe in the Middle Ages. Many of the numbers for the years 1820, 1870, and1913 are equally fictive. Just as in the Middle Ages there was a ready market for holy relics tolend prestige to the cathedrals and shrines of Europe Charlemagne secured for the cathedralin 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, anynumbers 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 resistfabulous riches offered by unknown Nigerians over the internet will equally want to steer clearof these estimates.

Even those of us who routinely deflate Greg Clarks statements to give them sense are curiousto know what crimes Angus Maddison have committed in his guilt by association to internetfraudsters. It turns out that Maddisons major crimes are two: (1) He underestimates initialincome in Europe , say in year 1 or year 1000, and as a consequence (2) he suggests thatthere was slow positive growth in Europe in the second millennium up to the IndustrialRevolution. Clark believes that nothing much happened to the alleged already high level of realper capita income at the dawn of civilization , that is since the hunter gatherers some 10000years ago. InA Farewell to Alms (2007) Greg Clark famously argued that there was nearstagnation (stationary variations in the long run) of average real income from the time ofhunters 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 andlow division of labour had an income per head at or slightly above 400 so called internationaldollars in 1990 prices, henceforward called $PPP, in year 1 and year 1000, which is slightlyabove the absolute poverty line, the bare bones subsistence, as conventionally measured at355 $PPP. The core of the Roman Empire, Italy, for which there is some documentation


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(Maddison 2007, pp 43-59) is ascribed an income of 809 international dollars by Maddison inyear 1. Maddison and others (most recently Milanovic, Lindert and Williamson 2009 ) whohave estimated Roman income do not have much to work on. A pioneering study was madeby R.W. Goldsmith (1984). Recent attempts include R. C. Allen (2007) and W. Schneidel and S.

J. Friesen(2009). Results indicate higher income 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 areseveral indications that income fell in the second half of the first millennium. Allens estimate ofthe 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 abandonedand trade declined. Byzantium, which developed from East Rome fared much better thanWestern Europe in the second half of the first millennium. B. Milanovic (2006) estimatedincome per head to some 700 $PPP in year 1000. An educated guess is that income was onaverage lower in Western Europe at that time.

Is Maddison right or wrong about these early days with little or no direct documentation? Wewill 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 ofRome in year 1. As for myself I have not as yet discovered a Forum Romanum in my backyardhere in Malm, southern Sweden, which is, however, rich in archaeological stone age findsand an occasional Roman coin. By definition Swedish income could not be (much) below400$PPP and it was certainly below the income of Italy both in year 1 and year 1300, and belowByzantium in year 1000. Olle Krantz ( 2004) offers an estimate for Sweden around 1571 andsuggests 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 Europein the first millennium, also in the more advanced areas, was considerable lower than before theIndustrial Revolution.

2.Conjectures and refutations

No one discussing these matters should ignore the considerable margin of error attached tothe numbers, which like other non-fiction statements, are open to serious scholarly debate andpotential refutation. There are now a large number of initiatives to reconstruct historicalnational accounts and five years from now we will know much more. Judging from the newwork in progress there will be a considerable upward shift of the estimated income levels,compared to Maddisons estimates for the second millennium up to 1800 but it is not obviousthat rates of growth will be much different .

The new tentative attempts to estimate national income such as lvares-Nogal and Prados dela Escosura (2009), Broadberry, Campbell, Klein, van Leuven and Overton ( 2010a),henceforward Broadberry et als, Buyst (2009), Krantz (2004), Malanima (2009), van Leuwenand van Zanden (2009) all suggest that income in , say, 1600 was well above bare bones


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subsistence at 355$PPP. Growth trajectories differed from stationarity at a high level in somecases, 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 Maddisonsincome per head in 1990 international dollars in Table 1 below.

Table 1. Income per head in selected European economies 1500-1820. Maddison (M) estimatescompared 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/

Holland

761 1320 1381 2253 2130 1782 1838 1886

Italy 1100 1644 1100 1302 1100 1398 1117 1445

Sweden 695 824 860* 977 1198 1009

Notes:.# Income in Spain in the 1820 column is from 1800.*Swedish income per head in 1600 isfor 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 thesources 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, aresignificant revisions of Maddisons estimates and Clark obviously has scored a point in attackingMaddison for underestimating pre-industrial income levels in the second millennium. Howeverthe new estimates must sit uncomfortably with a professed Malthusian like him because thelevels recorded are far above any meaningful notion of Malthusian subsistence. Modern

Malthusians take care in pointing out that subsistence income should not be interpreted literallyas a bare bones or absolute subsistence at ,say, 355 or at 400 $PPP which permit survival andrestricted productive effort, but little else. The question arises: how much can the Malthusiansubsistence income diverge from the 355 or 400 target? We normally define a Malthusianequilibrium as characterized by constant population, and by implication subsistence incomeshould be the income level associated with zero population growth. However at the incomeper head levels recorded in Table 1 above there is positive population growth. Furthermore


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income levels seem to be exogenous in the sense that continued population growth did notmake income per head revert to a significantly lower level.

Peter Skott and I demonstrated long ago that Malthusian and Ricardian conditions , that iswhen population growth is positively linked to income and generates diminishing returns, are

compatible with equilibria with sustained population growth and constant, above subsistenceincome per head (Persson 1988, chapter 3 and Skotts appendix to that chapter). TheMalthusian ,subsistence equilibrium usually discussed in the literature is but a special case wherethe rate of technological progress is zero. Once you admit for a positive rate of technologicalprogress the economy can settle at an income above bare bones subsistence and havepositive population growth. The equilibrium level of income depends on the interplay betweenthe rate of technological progress and diminishing returns. That model is in fact compatible withthe 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 400dollars mark in 1600 for England, Spain and Italy and 5 times for the Netherlands. An increasein the level of income can be explained by an increase in the rate of technological progress. Afall in income can result from stronger diminishing returns. Diets were varied, except for thevery 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 thathouseholds expenditure on manufactured goods and services were substantial and in somecases increasing. Households apparently made choices revealing a trade off between thenumber 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 whenpopulation 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 percent of the labour force in 1600 and then falls to just about 40 per cent in 1760, before theIndustrial 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 theland/labour ratio were both constant.

To sum up: Maddisons pioneering estimates for second millennium Europe are in a process ofcareful 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 fettersbefore the Industrial Revolution and had probably already started the divergence process withIndia and China in the middle of the second millennium.

3. Squaring the circle.


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We have just demonstrated divergent views regarding levels and trends in income in pre-industrial Europe. The estimates of Broadberry et als ( 2010a) suggest a trend growth of realincome per head in England of 0.17% in the 1270-1600 period and 0.37 % in the 1700-1750period. These estimates do not differ much from Maddisons, but his are associated withlower 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 apositive trend in approximately the same period in his estimate for England, in which nationalincome is determined from the income side. In principle income and output approaches shouldland at the same results. They do not. And therefore we have a problem!

I will offer an alternative approach that can be called a revealed productivity and incomegrowth estimate using changes in consumption pattern which can be derived from observedchanges in the occupational structure. I will exploit new data provided by Clark and Broadberryet als and others on levels and changes in occupational structure. My results support therevisionist stance of Broadberry et als and the results are in line with other commonlyacknowledged indicators, or shall we call it circumstantial evidence, of economic progress inpre-industrial Europe and England.

Almost all serious scholars agree on the following four statements concerning Europeaneconomic history in the second millennium before the Industrial Revolution:

The variety of commodities and services as well as professions increased due to theintroduction of new commodities.

Over time excess mortality due to harvest shocks fell or disappeared The non-food producing labour force increased as a share of the total labour force. 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 thatincome growth is accompanied by the introduction of new goods (de Vries 2008, Hersh andVoth 2010). The fall in the incidence of excess mortality ( Campbell and OGrda 2010) in

subsistence crises suggests that at least the very poor most vulnerable had experienced animprovement in living standards. I will explore the implication of statement 3 , that is thesecular rise in the non-agrarian labour force. If the share of the non-food producing labourforce increases it is likely that the share of food in total consumption will fall. However, in apopulation not very far away from subsistence level at the beginning of the second millenniumit is unlikely that non-food consumption increases as a share of total consumption if income isnot increasing. This observation is linked to Engels law in which consumption of food as a share


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of total income falls as income per head increases. The marginal propensity to consume food isprobably low but it is positive! Statement 1 is closely linked to statement 3 in that the growthof the urban sectors widens the variety of commodities and services offered, say, newcommodities like printed books, fine fabrics, optical instruments including eye-glasses, colonialimports 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 about700 in 1700 . (Persson 2010)

Pessimism about the evolution of real income per head in the long run is nurtured by real daywage data which, for Europe, indicate large variations over time but no positive trend until the(late) 18th century. But daywage data are notoriously elusive and most inferences from thattype of data to income are based on the controversial assumptions that days worked per yearand participations rates were constant.

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 reducenumber of days worked, and vice versa. That condition implies a dampening effect of changesin day wages on income per head. Clark maintains that from the end of the 16th century anduntil the Industrial Revolution the increase in days worked was modest. He supposes that daysworked remain constant at 300 over the pre-industrial period. There is however evidence of asubstantial decline in the high day wage era in the 15 th century and days worked might be as lowas 200 per year. This was a period of frequent holidays, many of which disappeared in the 16thand 17th centuries in Protestant and Catholic societies alike. The days worked by women andchildren might be increasing through cottage industry and proto-industrialization effectsespecially in areas near urban centres, where a diversified demand improved employmentopportunities. By and large an increase in urbanization might boost demand for these formerlyunderemployed categories. This is what the de Vriesian literature ( de Vries 2008) onindustrious revolution is about, although it is dismissed as without foundation by Clark (2009a,1160).

It is worth looking more closely at Clarks estimate of wages and income per head (Clark2009b). Below we show the two essential graphs, reproduced here with permission from theauthor. Surprisingly, from the priors advanced above, there is little difference between realwage movements and real income movements. A closer scrutiny of the estimates explain whythat is so. First, workers are assumed to work a constant number of days over time. Secondthe participation rate is also assumed to be constant. Third, the share of wages in total incomeis surprisingly high, around 65 per cent. Finally property income is not linked to wages in asystematic way. Rents sometimes move with and sometimes against wages. This amounts tosaying that real income was driven mainly by changes in daywages.

A substantial share of the labour force was self-employed and there is little or no income dataon that particular group. It is not clear to me how the income earned by this group is recorded


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in Clarks national income reconstruction. Even economies with a large estate-managedagricultural sector, like England, was dominated by self-employed peasants as owner occupiersor leaseholders in the Medieval period. It was previously believed that this sector was lessefficient 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 perhead around 1200 and 1450, two medieval peaks interrupted by a sharp drop, was not attaineduntil early 19th century and that peak income in the mid 15th century was not matched until themid 19th century. As noted above excess mortality due to harvest failures were morepronounced in the medieval period (Campbell and Grda 2010) but if we are to believeClark that period experienced the twin peaks of pre-industrial income per head. The prolongedlow income period stretching from the end of the 16th century to the end of the 18th century isin fact a period which experienced the introduction of new goods, say books and accompanyingeyeglasses and a wide variety of colonial commodities, it is the birth of the scientific effortsleading to modern science. It is also a period of increasing 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 thesiswell because income per head can only increase above its equilibrium subsistence level in atransitory manner. Any increase in income will generate its own destruction by excessivepopulation growth.

Although Clarks reconstruction of English national income is an admirable project the resultsdo not differ substantially from deriving income per head just using daywage data and assuminga constant share of wages in national income.


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Figure 1. Real wages in England 1200-1850. 1860/69 = 100. Source: Clark 2009b.


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Figure 2. Real income per head in England 1200-1850. 1860/69 =100. Source: Clark 2009b.


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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

Broadberry et als (2010a) reconstruct national income from output data and come to resultsfundamentally different from Clark. The graphs below, reproduced with permission from theauthors, show the real income per head and we can trace a slow, but not unbroken, positivetrend which continues in the 18th century, The yearly growth rate is 0.17 per cent per yearbetween 1270 and 1700 and 0.37 per cent per year between 1700-1760. The trajectory of GDPper head revealed in these estimates are more in line with what we would expect from aconsideration of the four consensus statements discussed above.

The two contending estimates agree that there is an increase in real income per head from1300 to the mid 15th century although the increase is much larger in Clarks estimate, or morethan a doubling. The two sets of estimates also record a setback after the 15th century peak butit is broken in the mid 16th century in the estimates by Broadberry et als and from then on youcan discern a positive trend in growth. Clarks estimates display near stagnation of income perhead from the mid 16th to the mid 17th century.


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Figure 3. Real GDP per capita in England, 1270-1710. (1700=100) Source Broadbery et als(2010a), Figure 10. Check S.N. Broadberrys webpage for updates.


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Figure 4. British real GDP per capita, 1700-1850. (1850 = 100). Source: Broadberry et als 2010,Figure 12. Check S.N. Broadberrys webpage for updates.


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The two contending estimates agree that there is an increase in real income per head from1300 to the mid 15th century although the increase is much larger in Clarks estimate, more Itwill be demonstrated that we can infer productivity and ultimately real income per head ,

Can we find some alternative method of measuring income which can be the arbiter betweenthese conflicting estimates? Yes, we can?

It will be demonstrated that we can infer productivity and ultimately real income per headchanges from observed changesin the occupational structure of the economy. A fall in theagrarian labour force as share of the total labour force is causally linked to increasing labourproductivity and income per head.

The argument that increasing production and consumption of industrial commodities as ashare of total consumption reveal increasing income has strong empirical support and forms thebasis for Engels law although it was first shown to apply in cross sections. You can call it arevealed productivity and income growth estimate.

The first attempt to make inferences to income and productivity from the changes inconsumption pattern as revealed by occupational and production patterns was performed byTony Wrigley (1967). His accounting framework was very simple and assumed a closedeconomy and a marginal propensity to consume food at zero. A more general accountingframework which permitted international trade in food, income differentials between

agriculture and industry and positive marginal propensity to consume food was developed byPersson(1988,1991). My method cannot determine levels but only changes in labourproductivity over time or gaps (ratios) across nations or regions. You can, in other words getan index of output and income per producer at a given point in time relative to income in abase year = 1. If you have a reliable benchmark estimate it is of course possible to interpolateback to an estimated initial income level. The Persson method needs little data, in particular itwill not rely on wage, property income or output data at all.


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The Persson method is essentially a simple general equilibrium model derived from the nationalincome identity combined with an Engels law consumption function. We think of an economywith two sectors, an agrarian sector denoted by the subscript a and an non-food-producingsector, denoted byi. The labour force is measured in units of workers but we cannot controlfor number of days per year which might change over time. With = + national income is

is output (value added) per agrarian and output per industrial or non-food producing labour.is price of agrarian goodsis price of industrial goods.

The method I propose, the revealed labour productivity and income growth method, infers

productivity and income changes from changes in occupational structure triggered off bychanges in consumption patterns. It is a well established fact, called Engels law, thatexpenditure on food falls as a share of total income with increasing income if

The consumption function above indicates that the average consumption of food,, of incomeper worker falls since is a constant and , the marginal propensity to consume food>0). In casethere is zero net import of food, as in the period under consideration here, there is an upper-bound limit of set as >0). In a steady state with balanced agricultural trade is strictly smaller

than which is the value that takes at the end of the period under investigation. See Appendixfor a proof.

This change in expenditure patterns when income increases will of course also affect theoccupational structure in a more or less proportional way. The decline of agriculturalemployment as a share of total employment is associated with the fact that the rising incomelevels permit a larger share of total income to be spent on non-essentials or industrial goods.

The demand for food is equal to supply

In the identity above is the skill premium of industrial labour over farm workers and and isimport and export of food respectively. It is important to control for net exports of foodbecause it is possible that an increasing number industrial producers do not reveal increaseddomestic food production but imports of food paid for by industrial goods.


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The logic of the argument is that as the labour force in agriculture shrinks fewer farminghouseholds have to feed more non-farming households which they can do only if they producemore 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 inconsumption patterns related to an income increase which causes the expenditure on food tofall as a share of total expenditure. A few things have to be controlled for, however, like foreigntrade and the relative income of the non-food producers.

is the share of agrarian workers of total labour force of and the share of non-food producers,is the marginal propensity to consume food, is the non-agrarian skill premium and and importof food variable, which would be negative in a case of net exports of food. and are timesubscripts. The numeraire in which income is measured is units of food.

The formula above gives an index-number of labour productivity in agriculture, , with = 1. Buthaving derived it is easy to estimate average income per economically active person, .

differs from income per head because the entire population is not economically active, that is

where is .

If is increasing over time then income per head will consequently rise faster than income perworker. 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 of a basket ofgoods. The formal expression of what we denote

is detailed in the Appendix but the intuition is give here. The growth of real income expressedin units of food is identical the to real income in terms of a basket of goods if the price of foodchanges exactly as the price of the basket. However, if, say the price of food increases relativeto the other items in the basket then the increases in real income as conventionally measured is


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larger than the real income measured in terms of food units, because a unit of food buys moreother goods. What we experience here is equivalent to a terms of trade improvement of theagrarian sector. If, on the other hand, the price of food falls relative to the price of the basketof 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 sectorof workers providing intermediate goods. Unfortunately existing data do not give us a clear-cutdistribution of the labour force in this respect. But the view that a shift of labour to theindustrial sector was driven by a demand from the agrarian sector of industrial intermediategoods, that is equipment , is not plausible. In the pre-industrial period it is not intermediategoods produced in the non-agrarian sector, such as machinery and chemical fertilizers, whichare prominent in the present era, that drive output growth. It is rather new knowledge gainedby trial and error, selection of better varieties of seed corn, regional specialization, betterrotation including the introduction of nitrogen fixing plants and, finally, greater work effort.The differentiation of output permitted by proximity to urban centres with diversified demandrelieved households from the curse of seasonal unemployment. Growth in output per labourerwas typically larger than growth per hour of labour. The agrarian sector also exportsintermediate goods to the industrial sector, wool for the woollen industry and grain for thebreweries , for example. Lacking precise information these general considerations lead to theassumption that the share of the total labour force producing intermediate industrial goodsfor the agrarian sector and the share of the total labour force in the agrarian sector thatproduces intermediate goods for the industrial sector are both constant, although they candiffer between sectors. That argument amounts to saying that the changes in occupationaldistribution 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 theagrarian labour forces that produces intermediate goods, raw materials, for the industrialsector increases while the share of industrial employment that produces final consumer goodsincrease. This is consistent with the view that urban professions specialize in new services andgoods in the final goods market and intermediate goods for the industrial sector. One of theacknowledged characteristics of urban agglomerations is that they are clusters of interlinkedproducers.

Let us now turn to a discussion that aims at giving plausible values to the variables andparameters in the accounting formula specified above.

Most scholars, including Clark, agrees agree that the share of the labour force in the non-agrarian sector increases but he questions, with good reason, the accuracy of urbanizationratios as a proxy for the share of the non-food producing labour force. Measurements ofurbanization usually include only cities above 10.000 inhabitants or in some cases 5000.However, there were numerous agglomerations with a population between 500 to 5000inhabitants which were essentially sites of producers of non-agrarian commodities and services.


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Clark suggests instead an alternative series based on occupational data from wills. This seriesfrom England has a much higher non-food producing labour force by the end of the 16th centurythan suggested by the urbanization data for England, around 40 per cent by the end of the 16thcentury and beginning of the 17th century. It then increased to a stable level around 54 per centalready 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 myview. Broadberry and van Leuwen (2010 b, Table 13 ) have also revised their occupational datausing Poll Tax returns and Muster Rolls and, like Clark, they have substantially increased theestimate of the non-agricultural labour force relative to earlier estimates based on urbanizationratios. The non-food producing labour force , according to Broadberry and van Leuwen, issurprisingly large, 38.5 per cent already by the end of the 14th century and although it hadincreased only slightly by the beginning of the 16th century it was much higher in 1700, 54 percent and 61 per cent in 1759.

The marginal propensity to consume agricultural goods, is difficult to measure. Conventionalmeasures tend to overstate it because what is measured is the demand for processedfoodwhich has a considerable industrial value added content. Since the estimation method we useis sensitive to the level of and given the lack of firm empirical foundation as regards its truevalue I will proceed, not by giving it some best guess value, but rather to see what the impliedlevel must be to be consistent with the contending estimates of economic growth. Thatprocedure 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 constantgap. I take , the per capita income gap between the non-food producing labour force and theagrarian labour force to be 1.5. The motivation is that the non-food producing classes includedprofessionals of all sorts with comparatively high wages. It also seems as if the number of daysworked was higher in the non-agricultural sector because work was not determined by theseasonal cycle as in agriculture. Furthermore the day wage records suggest a wage gap in favouror non-agricultural workers of at least 50 per cent. Clark reports a rather stable skill premiumof non-agricultural workers to farm workers of about 50 percent since in the pre-industrialperiod. (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

0.615 0.459 0.391

0.385 0.541 0.609


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< = 0.52 < = 0.36 < = 0.3

1.5 1.5 1.5

0 0 0

Note: 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 perlabourer in the agrarian sector relative to the base year 1381. Having arrived at that indexnumber we can calculate growth rates of agrarian labour productivity over time. Undersimplifying 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 theparticipation rate does not change. See Appendix equations 16-17 for details. It turns out thatreal income per head increases slightly faster than labour productivity in agriculture. That doesnot imply that labour productivity (necessarily) increases faster in the industrial sector but it issimply a structural effect due to the fact that over time an increasing share of the total workforce is employed in the industrial sector which enjoys higher real wages. The growth ofincome per head, under the assumptions stated above, will be only marginally larger thangrowth 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 thenon-agricultural labour force, and by implication the large increase in per capita consumption ofnon-agricultural goods. Let us first see if such an increase is consistent with a stable Engel-typeconsumption function, that is with constant over time and lower than 0.3 which is the value ofin 1759Since the implied growth of income will be higher the higher is we let the value be extremelylow at 0.01. Even under these conditions growth in income per head will be considerable, at0.15 per cent per year, as reported in Table 3 and the use of a more conservative estimate ofthe fall in the agricultural employment favoured by Clark does not fundamentally alter theimplied 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 consumerpreferences over time in favour of non-agricultural goods. Such a shift is highly improbable in aMalthusian context, because consumers are supposed to use a smaller share of their constantand low income for food expenditures because of increased taste for non-food commodities.While consumer preferences might change as new commodities enter the market, as suggestedby the adherents of an industrious revolution, it is not likely that substantial changes in theexpenditure pattern will occur at fairly low and constant income. Table 2 reveals that the


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changes in average expenditure were, indeed, substantial since average expenditure onagricultural goods, , fell from 52 to 30 per cent between 1381 and 1759.

Next step is to determine the marginal propensities to consume food which are broadlyconsistent 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 lowdisplayed as consistent with the growth record in Table 3 might nurture a suspicion that theBroadberry et als estimates actually have a downward bias. But as suggested above we knowtoo little about the true value of to make definitive statements. Be as it may, given the lowmarginal propensity to consume agricultural goods the economy seems to be in a stateexploring the welfare gains of new commodities beyond those needed for survival.

Table 3. Growth of agricultural labour productivity and real income in England 1381-1759. Percent per year.

Growth of agrarianlabour productivity

Growth of realincome per head

Comments

1381-1759 0.13 0. 15

0.10*

Assuming animplausibly low

1381-1700 0.18 0.2

1700-1759 0.75

0.4 0.44


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* The growth rate of income per head using the alternative higher estimate of agricultural sharein 1750/60 at 0.47 favoured by Clark (2009b). The estimates are fairly robust as to variations ins. Assuming that the pay differential is falling from a 50 per cent pay gap to a 25 percent gap so

that falls from 1.5 to 1.25 the implied growth will be smaller by 0.02-0.03 percentage points.

A word of caution must be inserted here. When we talk about increases in labour productivityit is not output per day worked but per worker. It is likely that a part of the increase in outputper workers is caused by an increase in days worked per year. But also in case we assume daysworked increased a great deal, say, from 225 to 300 days, less than half of the output increasecan be explained and the rest must be caused by labour productivity in the precise sense, thatis 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 foreigntrade, and, in the spirit of Engels law, a substantial increase in real income per head. Theobserved changes in consumption and occupational patterns are incompatible with theMalthusian stagnation thesis.

The sources of the revealed income increase are probably a combination of more hours ordays worked per employed and an increase in labour productivity. By implication, the resultspresented here suggest that we need to take a second look at real day wage series. Are theseseries representative? Where does the large group of self-employed fit in? These questionsmust 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

Hgre seminariet at University of Gothenburg have been very useful. Carl Johan Dalgaard read a

revised version and suggested severalimprovements. I am responsible for remaining flaws.

Appendix 1

Notation. is agrarian sector and is non-agrarian sector. is output per economically active

person and is price.

Total labour force, is = + (1)

National income is

(2)


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Dividing (1) through with yields , per household income

(3)

We define

(4) and (5) and divide(3) through with

(6)

is income per economically active person expressed in units of food.

The Engel type consumption function is

(7)

In (7)is average consumption of food which falls as income is increasing. > 0 is a constant andis the marginal propensity to consume food, >0. There is an upper-bound limit on as discussedin the text. The industrial skill premium is (8)

and income per non-agrarian or industrial labour is (9)

Aggregate demand of food is equal to supply

(10)

In (10) is import and is export of food. Net import of food per household is

(11)

Divide (10) through with and rearrange will yield

(12)

It turns out that it is difficult to estimate directly while it is easier to estimate a variable as

net imports of food as a fraction of total domestic production of food

(13)

Therefore can be substituted for in (12) above and it can be rewritten

(12)

We can now derive an index of household output in the agricultural sector at time 1 relative to

output at time 0.


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(14)

The formula above gives an index-number of with = 1. But having derived it is easy toestimate average income per economically active person, .

(15)

differs from income per head because the entire population is not economically active, that is

(16)

where as before is .

Income per head expressed in terms of units of food is different from real incomeas conventionally measured as the command over a basket of goods, which wedenote . Real income per head is simply the ratio of food price to the price, , ofthe basket of goods, say, a consumer price index multiplied with the real incomein terms of food units,

(17)

We will now prove that in an economy with balanced trade in agricultural goods

it holds that < as long as .Consumption of food is equal to production, that is

(18)

Divide through with yields

which implies

(19).

From (19) it is clear that since and if = then = and if s>1 then < . From (7) it isobvious that < where is the average expenditure on agricultural goods and hencewill be strictly smaller than .


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End of Malthusian Stagnation Thesis

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