The Three Horsemen of Growth: Plague, War and

Urbanization in Early Modern Europe∗

Nico Voigtländer†, Hans-Joachim Voth‡

August 2008

Abstract

How did Europe overtake China? We construct a simple Malthusian model with two sectors, and

use it to explain how European per capita incomes and urbanization rates could surge ahead of Chi-

nese ones. That living standards could exceed subsistence levels at all in a Malthusian setting should

be surprising. Rising fertility and falling mortality ought to have reversed any gains. We show that

productivity growth in Europe can only explain a small fraction of rising living standards. Population

dynamics – changes of the birth and death schedules – were far more important drivers of the long-

run Malthusian equilibrium. The Black Death raised wages substantially, creating important knock-on

effects. Because of Engel’s Law, demand for urban products increased, raising urban wages and at-

tracting migrants from rural areas. European cities were unhealthy, especially compared to Far Eastern

ones. Urbanization pushed up aggregate death rates. This effect was reinforced by more frequent wars

(fed by city wealth) and disease spread by trade. Thus, higher wages themselves reduced population

pressure. Without technological change, our model can account for the sharp rise in European urban-

ization as well as permanently higher per capita incomes. We complement our calibration exercise with

a detailed analysis of intra-European growth in the early modern period. Using a panel of European

states in the period 1300-1700, we show that war frequency can explain a good share of the divergent

fortunes within Europe.

JEL: E27, N13, N33, O14, O41

Keywords: Malthus to Solow, Long-run Growth, Great Divergence, Epidemics, Demographic Regime

∗We would like to thank Steve Broadberry, Antonio Ciccone, Nick Crafts, Angus Deaton, Matthias Doepke, Jordi Galı́, Oded

Galor, Bob Hall, Tim Kehoe, Nobu Kiyotaki, Ron Lee, Ed Prescott, Diego Puga, Albrecht Ritschl, Nancy Stokey, Michèle Tertilt,

Jaume Ventura, David Weil, and Fabrizio Zilibotti for helpful comments and suggestions. Seminar audiences at Brown University,

Humboldt University, the Minnesota Macro Workshop, Pompeu Fabra, UC Berkeley, Princeton, and Zürich University provided

useful feedback. We thank Morgan Kelly for sharing unpublished results with us. Mrdjan Mladjan provided outstanding research

assistance. Financial support by the Centre for International Economics at UPF (CREI) is gratefully acknowledged.
†UCLA Anderson School of Management, 110 Westwood Plaza, Los Angeles, CA 90095. Email: nico.v@anderson.ucla.edu
‡Department of Economics, Universitat Pompeu Fabra, c/Ramon Trias Fargas 25-27, E-08005 Barcelona, Spain. Email:

voth@mit.edu

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1 Introduction

In 1400, Europe’s potential for growth must have seemed limited. The continent was politically frag-

mented, torn by military conflict, and dominated by feudal elites. Literacy was low. Other regions, such

as China, appeared more promising. It had a track record of useful inventions, from ocean-going ships to

gunpowder and advanced clocks (Moykr 1990). The country was politically unified, and governed by a

career bureaucracy chosen by competitive exam (Pomeranz 2000). Few if any of the variables that predict

growth in modern-day data would suggest that Europe’s starting position was favorable.1

By 1700 however, and long before it industrialized, Europe had pulled ahead decisively in terms of per

capita income – an early divergence preceded the ”Great Divergence” that emerged with the Industrial

Revolution (Broadberry and Gupta 2006, Diamond 1997).2 By this date, England’s per capita income

was more than twice that of China or India, European silver wages were often markedly higher, and

Western European urbanization rates were more than double those in China (Broadberry and Gupta 2006,

Maddison 2001). This early divergence matters in its own right. It laid the foundations for the European

conquest of vast parts of the globe (Diamond 1997). More importantly, it may have contributed to the

even greater differences in per capita incomes that followed. In many unified growth models, a gradual or

temporary rise of per capita income is crucial for starting the transition to self-sustaining growth (Galor

and Weil 2000, Hansen and Prescott 2002). There is growing evidence that a country’s development in the

more distant past is a powerful predictor of its current income position (Comin, Easterly and Gong 2006).

Voigtländer and Voth (2006) develop a model in which greater industrialization probabilities are the direct

consequence of higher starting incomes.3 If we are to understand why Europe achieved the transition from

”Malthus to Solow” before other regions of the world, understanding the initial divergence of incomes is

crucial.

In this paper, we identify the early divergence a new puzzle, and argue that its solution can help

explain why the most advanced parts of Europe in terms of income were far ahead of the rest of the

world by 1700 already. The early modern divergence in per capita incomes represents a major puzzle for

Malthusian models because per capita incomes should not be able to rise substantially above subsistence

for an extended period. Before industrialization, the ’fertility of wombs’ was necessarily greater than the

’fertility of minds.’ Galor (2005) estimates that TFP grew by no more than 0.05-0.15% p.a. in the pre-

industrial era. Over a century, productivity could increase by 5-16%. Maximum fertility rates per female,

by contrast, are around 7. Even with only 3 surviving children per woman, a human population growing

unconstrained would quadruple after 100 years.4 In a Malthusian regime, past generations should have

always ”spent the great gifts of science as rapidly as it got them in a mere insensate multiplication of the

common life” (in the words HG Wells).5

1For a recent overview, see Barro (1997), Bosworth and Collins (2003), and Sala-i-Martin, Doppelhofer and Miller (2004).
2Pomeranz (2000), comparing the Yangtze Delta with England, argues the opposite. The consensus now is that his revisionist

arguments do no stand up to scrutiny (Allen 2004; Allen, Bengtsson, and Dribe 2005; Broadberry and Gupta 2006).
3Allen (2006) has argued that high wages of artisans in Britain before 1800 were responsible for skill-replacing technological

change during the Industrial Revolution.
4Assuming a generation length of 25 years.
5Wells (1905). Galor and Weil (2000) assume that the response of fertility to incomes is delayed. Hence, a one-period acceler-

ation in technological change can generate higher incomes in the subsequent period, and a sequence of positive shocks can lead to

sustained growth. While this solves the problem in a technical sense, it is unlikely to explain why fertility responses did not erode

real wage gains over hundreds of years.

2



Nonetheless, living standards in many European countries increased markedly during the early mod-

ern period. Maddison (2007) estimates that Western European per capita incomes grew by more than

30%, and aggregate incomes still more between 1500 and 1700.6 His data are imperfect, but knowledge-

able contemporary observers such as Adam Smith detected the same trend: ”the annual produce of the

land and labour of England... is certainly much greater than it was a little more than a century ago at

the restoration of Charles II (1660)... and [it] was certainly much greater at the restoration than we can

suppose it to have been a hundred years before.”7 How could such a marked rise be sustained over such a

long period, despite the potential for rapid population growth to erode all gains quickly?

We argue that the impact of the Black Death in Europe was key. Western Europe’s unique set of

geographical and political starting conditions interacted with the plague shock to make higher per capita

living standards sustainable. In a Malthusian regime, lower population spells higher wages. Because

the shock was very large, with up to half of the population dying, land-labor ratios and wages increased

substantially. These real wage gains were so large, and concentrated in such a brief period of time, that

they could not be reversed quickly by population growth. Wages remained high for more than one or two

generations, and were partly spent on manufactured goods. Most of this production took place in cities.

Because early modern European cities were death-traps, with mortality far exceeding fertility rates, they

would have disappeared without steady in-migration from the countryside. Thus, the extra demand for

manufactures pushed up average death rates, making higher incomes sustainable. We capture these key

elements in a simple two-sector model. Effectively, Engel’s law ensured that the plague’s positive effect

on wages did not wear off entirely as a result of higher fertility and lower mortality. Because changes in

the composition of demand increased urbanization rates, average death rates became permanently higher,

implying lower population pressure. Welfare may not have increased, but wages reached a permanently

higher level.

This ’benign’ direct effect of urbanization was reinforced because city wealth fueled early modern

Europe’s endemic warfare. Between 1500 and 1800, the continent’s great powers were fighting each

other on average for nine years out of every ten (Tilly 1990). Cities also acted as nuclei for long-distance

trading networks. Both war and trade spread epidemics. The more effectively they did so, the higher

death rates overall were, and the more readily a rise in incomes and in the urban share of the population

could be sustained. In this way, the Horsemen of the Apocalypse jointly produced higher incomes. In

contrast to numerous papers identifying a negative (short-run) effect of wars, civil wars, disease, and

epidemics on growth in economies today,8 we argue that these factors effectively acted as ’Horsemen of

Growth.’

The great 14th century plague also affected China, as well as other parts of the world (McNeill 1977).

Why did it not have the same effects there? We argue that two factors were crucial. Chinese cities

were far healthier than European ones, for a number of reasons involving cultural practices and political

conditions. We examine these in more detail below. Also, political fragmentation in Europe ensured

continuous warfare once the growing wealth of cities could be tapped by belligerent princes. This was

the case after 1400. China, on the other hand, was politically unified, except for brief spells of turmoil.

There was no link between city growth and the frequency of armed conflict. Hence, a very similar shock

6Maddison estimates that total real GDP doubled in the same period.
7Smith, 1776 (1976), pp. 365-66.
8Murdoch and Sandler (2002), Hoeffler and Reynal-Querol (2003), Hess (2003).

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did not lead to permanently higher death rates; per capita incomes could not rise.

The mechanism presented in this paper is not the only one that can deliver a divergence in per capita

incomes without technological change. In addition to high death rates, Europeans curtailed birth rates.

In contrast to many other regions of the world, socio-economic factors, and not biological fertility, de-

termined the age at first marriage for women. This is what Hajnal (1965) termed the European Marriage

Pattern. In our calibrations, we find that fertility restriction can explain part of the European advantage,

but that the mortality effects identified in our model account for most of the ”First Divergence”.

We are not the first to argue that higher death rates can have beneficial economic effects. Clark (2007)

highlighted the benign effect of higher death rates on living standards. He also concluded that Englishmen

in 1800 lived no better than ancestors on African savannah.9 Young (2005) concludes that Aids in Africa

has a silver lining because it reduces fertility rates, increasing the scarcity of labor and thereby boosting

future consumption. Lagerlöf (2003) also examines the interplay of growth and epidemics, but argues for

the opposite causal mechanism. He concludes that a decline in the severity of epidemics can foster growth

if they stimulate population growth and human capital acquisition. Brainard and Siegler (2003) study the

outbreak of ”Spanish flu” in the US, and conclude that the states worst-hit in 1918 grew markedly faster

subsequently. Compared to these papers, we make three contributions. First, we use the Malthusian model

to explain rising wages, not stagnation. Second, we are the first to demonstrate how specific European

characteristics – political and geographical – interacted with a large mortality shock to drive up incomes

over the long run. Also, we calibrate our model to show that it can account for a large part of the ”First

Divergence” in the early modern period. Finally, we use a panel dataset on urbanization, incomes, and

wars in Europe to explain divergent fortunes within Europe itself.

Other related literature includes the unified growth models of Galor and Weil (2000), and Galor and

Moav (2003). In both, before fertility limitation sets in and growth becomes rapid, a state variable grad-

ually evolves over time during the Malthusian regime, making the final escape from stagnation more and

more likely. In Galor and Weil (2000) and in Jones (2001), the rise in population which in turn produces

more ideas is a key factor; in Galor and Moav (2003), it is the quality of the population.10 Cervellati and

Sunde (2007) argue that mortality decline from the 19th century onwards was an important element in the

transition to self-sustaining growth, by reducing fertility and increasing human capital formation. Hansen

and Prescott (2002) assume that productivity in the manufacturing sector increases exogenously, until

part of the workforce switches out of agriculture. Our model abstracts from technological change during

the Malthusian era, and emphasizes changes in death rates as a key determinant of living standards. One

of the key advantages is that it can be applied to the cross-section of growth outcomes. In contrast, the

majority of existing unified growth papers implicitly use the world as their unit of observation.

We proceed as follows. The next section provides a detailed discussion of the historical context.

Section 3 introduces a simple two-sector model that highlights the main mechanisms. In section 4, we

calibrate our model and show that it captures the salient features of the ”First Divergence”. We also

compare the effect of the European Mortality Pattern to the consequences of fertility restriction. In section

5, we provide empirical evidence for our hypothesis. We show that increasingly frequent military conflict

can explain much of the growing income differences within Europe. The final section summarizes our

9This point does not stand up to scrutiny. On all traditional measures English wages by 1800 were unusually high, compared to

both Britain’s own history and those in other countries (Allen 2001).
10Clark (2007) finds some evidence in favor of the Galor-Moav hypothesis, with the rich having more surviving offspring.

4



findings.

2 Historical context and background

Our story emphasizes three elements that can explain the ”First Divergence”: the impact of the plague, the

peculiarities of European cities, and interaction effects with the political and geographical environment.

In this section, we first assemble some of the evidence suggesting that European per capita income growth

during the early modern period was unusually rapid, and then discuss the three central elements in our

model.

The First Divergence

That Europe pulled ahead of the rest of the world in terms of per capita living standards is now widely

accepted. While Pomeranz (2000) argued that farmers in the Yangtze delta in China earned the same wage

in terms of calories as English farmers, there is now a broad consensus that overturns this argument. First,

better data strongly suggest that English wages expressed as units of grain or rice were markedly higher.

Broadberry and Gupta (2006) calculate Chinese grain-equivalent wages were 87% of English ones by

1550-1649, and fell to 38% in 1750-1849. Second, since foodstuffs were largely non-traded goods, they

are a poor basis for comparison. Silver wages were much higher in Europe than in China. According to

Broadberry and Gupta, they fell from 39% of the English wage to a mere 15%.11 Finally, urbanization

rates have been widely used as an indicator of economic development (Acemoglu, Johnson and Robinson

[subsequently AJR] 2005). This indicator shows that Europe overtook China at some point between 1300

and 1500, and then continued to extend its lead (figure 1).

[Insert Figure 1 here]

The beneficial effect of the Black Death on real wages is well-documented. The wage figures for

England by Phelps-Brown and Hopkins (1981) and by Clark (2005) suggest that wages broadly doubled

after 1350. When these gains were reversed, and how much, is less clear. The older Phelps-Brown

and Hopkins series suggests a strong decline. Clark (2005) shows that wages fell back from their peak

somewhat, but except for crisis years around the English Civil War, they remained about fifty percent

above their 1300 level.12 In this sense, the existing wage series offer qualified support to the optimistic

GDP figures provided by Maddison (2007).

Not all of Europe did equally well. Allen (2001) found that real wage gains for craftsmen after the

Black Death were only maintained in Northwestern Europe. In Southern Europe – especially Italy, but

also Spain – stagnation and decline after 1500 are more noticeable. Described as the ’Rise of Atlantic

Europe’ by AJR (2005), the North-West overtook Southern Europe in terms of urbanization rates and out-

put. Yet for every single European country with the exception of Italy, Maddison estimates that per capita

11While Broadberry and Gupta’s figures for the second period are partly influenced by values from the early 19th century, when

industrialization was already under way, it is clear that observations for the 18th century alone would also show a marked advantage.
12What matters for the predictions of the Malthusian model is per capita output, not wages as such. National income in the

aggregate will be equivalent to the sum of wages, rents, and capital payments. Since English population surpassed its 1300 level in

the eighteenth century, it is likely that rental payments were higher, too.

5



GDP was higher by 1700 than it had been in 1500. This indirectly suggests that standard Malthusian

predictions did not hold during the period. Maddison assumes that subsistence is equivalent to approx-

imately $400 US-Geary Khamy dollars. Even relatively poor countries like Spain and Portugal had per

capita incomes more than twice as high in 1700. At this stage, every single European country had been

above the threshold for centuries, often by 50 percent or more. And yet, population growth did not reverse

these real wage gains. This is the puzzle that we seek to explain. We do so in a way that allows us to

capture the main reasons for intra-European divergence.

The Plague

The plague arrived in Europe from the Crimea in December 1347. Tartar troops besieging the Genoese

trading outpost of Caffa suffered from the disease. In an early example of biological warfare, the Tartars

used trebuchets to throw disease-infected corpses over the city wall. Soon, the defenders caught the

disease. It spread with the fleeing Genoese along the main trading routes, first to Constantinople, then

to Sicily and Marseille, then mainland Italy, and finally the rest of Europe. By December 1350, it had

reached the North of England and the Baltic (McNeill 1977).

Mortality rates amongst those infected varied from 30 to 95%. Bubonic and pneumonic forms of the

plague both contributed to surging mortality. The bubonic form was transmitted by fleas and rats carrying

the plague bacterium (Yersinia pestis). Infected fleas would spread the disease from one host to the next.

When rats died, fleas tried to feast on humans, infecting them in the process. In contrast, pneumonic

plague spread from person to person, via the tiny droplets transmitted by the coughing of the infected.

Transmission and mortality rates were particularly high for the pneumonic form of the plague.

There appear to have been few differences in mortality rates between social classes, or between rural

and urban areas. Some city-dwellers tried to escape the plague, by withdrawing to country residences, as

described in Boccaccio’s Decamerone. It is unclear how often these efforts succeeded. Only a handful

of areas in the Low Countries, in Southwest France and in Eastern Europe were spared the effects of the

Black Death.

We do not have good estimates of aggregate mortality for medieval Europe. Most estimates put pop-

ulation losses at 15 - 25 mio., out of a total population of approximately 40 mio. people. Approximately

half of the English clergy died, and in Florence and Venice, death rates have been estimated as high as

60-75% (Ziegler 1969).

City Mortality

European cities were deadly places. In 1841, when large inflows of labor had put particular pressure on

urban infrastructures, life expectancy in Manchester was a mere 25 years. At the same time, the national

average was 42, and in rural Surrey, 45 years. While available figures are not as precise, early modern

cities were probably just as unhealthy. Life expectancy in London, 1580-1799, fluctuated between 27

and 28 years (Landers 1993). Nor were provincial towns much more fortunate. York had similar rates

of infant mortality.13 In France, the practice of wet-nursing (sending children from cities for breast-

feeding to the countryside) complicates comparisons. A comprehensive survey of rural-urban mortality

13Galley 1998. There is not enough data to derive life expectancy. Since infant mortality is a prime determinant, it was probably

in the same range.

6



differences estimates that in early modern Europe, life expectancy was approximately 50 percent higher

in the countryside than in cities (Woods 2003).

No such differential probably existed in China. Some mortality estimates have been derived from

the family trees of clans (Tsui-Jung 1990), using data from the 15th to the 19th century. Chinese infant

mortality rates were lower in cities than in rural areas, and life expectancy was higher. While the data

is not necessarily representative, other evidence lends indirect support. For example, life expectancy in

Beijing in the 1920s and 1930s was higher than in the countryside. Members of Beijing’s elite in the 18th

century experienced infant mortality rates that were half those in France or England (Woods 2003).

In Japan, where some data for 18th century Nakahara and some rural villages survives, city dwellers

lived as long as their cousins in the countryside. Some recent evidence (Hayami 2001) on adult mortality

questions if Far Eastern cities were indeed healthier than the countryside, as some scholars have argued

(Hanley 1997; Macfarlane 1997). What is clear is that on balance, the evidence favors the hypothesis

that there was no large urban penalty in China and Japan. Principal reasons probably include the transfer

of ”night soil” (i.e., human excrement) out of the city and onto the surrounding fields for fertilization,

relatively high standards of personal hygiene, and a diet rich in vegetarian food. Since the proximity of

animals is a major cause of disease, all these factors probably combined to reduce the urban mortality

burden in the Far East.

Differences in the way cities were built also added to relatively high urban mortality in Europe. In

the words of one prominent urban historian, in ”1600, just as in 1300, Europe was full of cities girded

by walls and moats, bristling with the towers of churches.” (DeVries 1976). In China, city walls were

widely used throughout the early modern period, partly because of their symbolic value for administrative

centers of the Empire. Since the country’s unification under the Qin Dynasty in the third century BC, the

defensive function of city walls declined. With relative ease, houses and markets spread outside the city

walls.14 Because Far Eastern cities could easily expand beyond the old fortifications, city growth did not

push up population densities in the same way as in Europe.15 This is likely to have reduced overcrowding

and kept mortality rates low.

In many European countries, regulations further ensured that manufacturing activities and market

exchange was largely a monopoly of the cities.16 In China, periodic markets in the countryside served the

same function. This reduced relative urbanization rates (Rozman 1973). Finally, European cities offered

a unique benefit not found in other parts of the world – a chance to escape servitude. As a general rule,

staying within the city walls for one year and one day made free men out of peasants bound to the land

and their lord. In contrast, as one leading historian put it, ”Chinese air made nobody free”.17

14In some cases, the new suburbs would also be enclosed by city walls (Chang 1970).
15Barcelona is one extreme example. After the 1713 uprising, the Bourbon kings did not allow the city to expand beyond its

existing walls until 1854. As industrial growth led to an inflow of migrants, living conditions deteriorated considerably (Hughes

1992).
16Some scholars have argued that ”proto-industrialization”, i.e., early forms of home-based manufacturing, often located in the

countryside, were an important feature of early modern European growth (Ogilvy and Cerman 1996). This view is not widely

accepted (Coleman 1983).
17Mark Elvin, cited in Bairoch (1991).

7



Wars, Trade and Disease

The available data on deaths caused by military operations in the early modern period is sketchy.18 Dis-

eases spread by armies were far more important than battlefield casualties and the deaths of siege victims

in determining mortality rates. While individual campaigns could be deadly, armies were too small, and

their members too old, to influence aggregate mortality rates significantly.19

The ”Great Plague” of 1347-48 was not the last to strike Europe. Less well-known is the fact that the

Black Death of Middle Ages was followed by a wave of deadly outbreaks that only peaked in the early

modern period. As shown in figure 2, the number of plague epidemics more than quadrupled between

the 14th and the 17th century – from about 150 outbreaks per decade after the ”Great Plague” to a peak of

705 in 1630-40. The frequency of outbreaks declined only in the late 17th century and dropped below 50

outbreaks per decade in the 18th century, which occurred mostly in Eastern Europe. The last incidents in

Western Europe were plague outbreaks in Austria (1710) and Marseille (1720). Warfare and the outbreak

of diseases were closely linked. The Black Death had originally arrived with a besieging Tartar army in

the Crimea. Early modern armies killed many more Europeans by the germs they spread than through

warfare. Isolated communities in the countryside would suddenly be exposed to new germs as soldiers

foraged or were billeted in farmhouses. The effect could be as deadly as it had been in the New World,

where European diseases killed millions (Diamond 1999). In one famous example, it has been estimated

that a single army of 6,000 men, dispatched from La Rochelle to deal with the Mantuan Succession,

spread plague that may have killed up to one million people (Landers 2003). Population losses in the

aggregate could be heavy. The Holy Roman Empire lost 5-6 mio. out of 15 mio. inhabitants during the

Thirty Years War; France lost 20% of its population in the late 16th century as a result of civil war. As late

as during the Napoleonic wars, typhus, smallpox and other diseases spread by armies marauding across

Europe proved far deadlier than guns and swords.

[Insert Figure 2 here]

For the early and mid-nineteenth century, we have data that allows us to gauge the orders of magnitude

involved. In the Swedish-Russian war of 1808-09, mortality rates in all of Sweden doubled, almost

exclusively through disease. In isolated islands, the presence of Russian troops – without any fighting –

led to a tripling of death rates. During the Franco-Prussian and the Austro-Prussian wars later in the 19th

century, non-violent death rates increased countrywide by 40-50% (Landers 2003). Both background

mortality and the impact of war were probably lower at this late stage than during the early modern

period. Warfare was less likely to spread new germs, since in areas touched by troop movements were

now integrated by extensive road, canal, and railway networks. The figures for the Thirty Years War and

for 16th century France however also imply that mortality rates rose above their normal rate by 50 to

100%.

Early modern warfare, with its need for professional, drilled troops, Italian-style fortifications, ships,

muskets and cannons was particularly expensive – money formed the sinews of power (Brewer 1991,
18Landers (2003) offers an overview of battle-field deaths.
19Since infant mortality was high, by the time men could join the army, many male children had died already. This makes it less

likely for military deaths to matter in the aggregate. Lindegren (2000) finds that military deaths only raised Sweden’s death rates by

2-3/1000 in most decades between 1620 and 1719, a rise of no more than 5%. Castilian military deaths were 1.3/1000, equivalent

to 10 percent of adult male deaths but no more than 3-4% of overall deaths.

8



Landers 2003, Tilly 1990). To make war, princes needed access to liquid wealth. Silver from the Indies

allowed Philip II of Spain to fight in every year of his reign except one. Elsewhere, the growth of cities

provided the kind of easily mobilized wealth that could be spent on mercenary armies – either directly,

through taxation, or through sovereign borrowing. With the growth of urbanization in early modern

Europe, the financial means for fighting more, fighting longer, and in more a deadly fashion became more

easily accessible.

China in the early modern period saw markedly less warfare than Europe. We calculate that even on

the most generous definition, wars and armed uprisings only occurred in one year out of five, no more

than a quarter of the European frequency. Not only were wars fewer in number. They also produced

less of a spike in epidemics. Europe is geographically subdivided by rugged mountain ranges and large

rivers, with considerable variation in climatic conditions. China overall is more homogenous in geo-

graphical terms. While rugged in many parts, major population centers were not separated by as many

geographical barriers as in Europe. The Yangtze River’s climate is markedly different to that of the Yel-

low River, and early settlers migrating from the North experienced high mortality rates in the South. Yet

differences within Europe, from the North of Finland to the shores of Sicily and Ionia, were substantially

greater. Also, average distances between population centres were large, and travellers had to traverse

more mountainous terrain. The history of epidemics in China suggests that by 1000 AD, disease pools

had become largely integrated (McNeill 1976). Since linking semi-independent disease pools through

migratory movements pushes up death rates in a particularly effective way, it may also be that in every

armed conflict, similar troop movements produced less of a surge in Chinese death rates than in Europe.20

Compared to warfare, trade in early modern Europe was a less effective, but more frequent cause of

disease. This is why quarantine measures became frequent throughout the continent. The last outbreak

of the plague in Europe occurred in Marseille in 1720. A plague ship from the Levant, with numerous

sufferers on board, was first quarantined, only to have the restriction lifted as a result of pressure by

merchants. It is estimated that 50,000 out of 90,000 inhabitants died in the subsequent outbreak (Mullett

1936). Since trade increases with per capita incomes, the positive, indirect effect of the initial plague on

wages created additional knock-on effects. These combined to raise mortality rates yet further. Finally,

there were interaction effects between the channels we have highlighted. The effectiveness of quarantine

controls, for example, often declined when wars disrupted administrative procedure (Slack 1981). All

these factors in combination ensured that, after the Black Death, European death rates increased, and

stayed high, in a way that is unlikely to have occurred in China.

3 The Model

This section presents a simple two-sector model that captures the basic mechanisms determining pre-

industrial living standards. The economy is composed of N identical individuals who work, consume,

and procreate. NA individuals work in agriculture (A) and live in the countryside, while NM agents live in

cities producing manufacturing output (M ), both under perfect competition.21 For simplicity, we assume

20We are indebted to David Weil for this point. Weil (2004) shows the marked similarity of agricultural conditions in large parts

of modern-day China.
21During the early modern period, a substantial share of manufacturing took place outside cities – a process called ”protoindustri-

alization” by some. We abstract from it since cities still grew, and our key mechanism remains intact, even if some of the additional

9



that wages are the only source of income. Agents choose their workplace in order to maximize expected

utility, trading greater risks of death in the city for a higher wage. Agricultural output is produced using

labor and a fixed land area. This implies decreasing returns in food production. Manufacturing uses labor

only and is subject to constant returns to scale. Preferences over the two goods are non-homothetic and

reflect Engel’s law: The share of manufacturing expenditures (and thus the urbanization rate NM/N )

grows with income.

Population growth responds to per-capita income. Higher wages translate into more births and lower

mortality. Therefore, the economy is Malthusian – per capita income stagnates close to the subsistence

level, keeping most people at the edge of starvation (the ”positive” Malthusian check). With stagnat-

ing technology, death rates equal birth rates, and N is constant in equilibrium. Technological progress

temporarily relieves Malthusian constraints; population can grow. In the absence of ongoing produc-

tivity gains, however, the falling land-labor ratio drives wages back to their original equilibrium level.

Per-capita income is thus self-equilibrating.

An epidemic like the plague has an economic effect akin to technological progress: it causes land-

labor ratios to rise dramatically. This leaves the remaining population with greater per-capita income,

which translates into more demand for manufactured goods. As a consequence, urbanization rates have

to rise. In the absence of productivity growth and shifts in the birth or death schedules, subsequent

population growth pulls the economy back to its earlier equilibrium – there is no escape from Malthusian

stagnation.

However, in our model, the ”Horsemen of Death” start to ride high after the plague: Wars become

more frequent. City mortality is high. Increasing trade, linking the urban nuclei, spreads disease, as do

wars. As these become a permanent feature of the early modern European economy, the death schedule

shifts upwards. We argue that this mechanism captures an important element of the European experience

in the centuries between the Black Death and the Industrial Revolution. The new long-run equilibrium

has higher birth and death rates, but also increased per capita incomes and a higher share of the population

living in cities.

3.1 Consumption

Each individual supplies one unit of labor inelastically in every period. There is no investment – individ-

uals i use all their income to consume agricultural goods (cA,i) and manufactured goods (cM,i). At the

beginning of each period, agents choose their workplace in order to maximize expected utility. Agents’

optimization therefore involves two stages: The choice of their workplace and the optimal spending of

the corresponding income. We consider the latter first.

In the intra-temporal optimization, each individual takes workplace-specific wages wi, i = {A, M}
as given and maximizes instantaneous utility.22 The corresponding budget constraint is cA,i + pMcM,i ≤
wi, where pM is the price of the manufactured good. The agricultural good serves as the numeraire.

Before individuals buy manufactured goods, they need to consume a minimum quantity of food, c. We

refer to c as the subsistence level. Below it, individuals suffer from hunger, but do not necessarily die

demand translated into growth for non-urban manufactured goods.
22In the following, the subscripts A and M not only represent agricultural and manufacturing goods, but also the locations of

production, i.e., countryside and cities, respectively.

10



– mortality increases continuously as cA falls below c. While consumption is below c, any increase in

income is spent on food. Preferences take the Stone-Geary form and imply the composite consumption

index:

u(cA, cM ) =

{
(cA − c)αc1−α

M , if wi > c

β(cA − c), if wi ≤ c
(1)

Where β > 0, as specified below. Given wi, consumers maximize (1) subject to their budget constraint. In

a poor economy, where income is not enough to ensure subsistence consumption c, the starving peasants

are unwilling to trade food for manufactured goods at any price. Thus, the demand for urban labor is zero

and there are no cities. All individuals work in the countryside: NA = N , while cA = wA < c.

When agricultural productivity is large enough to provide above-subsistence consumption wA > c,

expenditure shares on agricultural and manufacturing products are:

cA,i

wi
= α + (1− α)

(
c

wi

)

pMcM,i

wi
= (1− α)− (1− α)

(
c

wi

)
(2)

Once consumption passes the subsistence level, peasants start to spend on manufacturing products. These

are produced in cities, which grow as a result. If income increases further, the share of spending on

manufactured goods grows in line with Engel’s law, and cities expand. The relationship between income

and urbanization is governed by the parameter α. A higher α implies more food expenditures and thus

less urbanization at any given income level.

3.2 Production

All agricultural goods are homogenous, and are produced under constant returns and perfect competition.

The same is true of manufactured goods. In the countryside, peasants use labor NA and land L to produce

food. The agricultural production function is

YA = AANγ
AL1−γ (3)

where AA is a productivity parameter and γ is the labor income share in agriculture. Suppose that there

are no property rights over land. Thus, the return to land is zero and agricultural wages are equal to the

output per rural worker:

wA = AA

(
L

NA

)1−γ

= AA

(
l

nA

)1−γ

(4)

where l = L/N is the land-labor ratio and nA = NA/N is the labor share in agriculture, or rural

population share. Since land supply is fixed, increases in population result in a falling land-labor ratio

and ceteris paribus in declining agricultural wages. Manufacturing goods are produced in cities using the

technology

YM = AMNM (5)

where AM is a productivity parameter. Manufacturing firms maximize profits and pay wages wM =

pMAM . The manufacturing labor share nM is identical to the urban population share.

11



3.3 Migration

Migration decisions reflect utility maximization of individuals. We suppose that they move (if at all) at

the beginning of every period t, such that migrating individuals arrive at their workplace before produc-

tion starts at time t. In early modern Europe, death rates in cities were substantially higher than in the

countryside (dM > dA). High urban wages compensated for the elevated mortality risk. In order to set

up the corresponding optimization problem, we first derive the indirect utility of consumers from (1) and

(2):

ũ(wi, pM ) =
(

1
pM

)1−α

αα (1− α)1−α (wi − c) (6)

Note that this equation is valid only if (wi > c), which is the more interesting case on which we concen-

trate from now on. Individuals maximize expected utility in each period, where (1 − di) is the survival

probability when working at place i = {A,M}. We define the (hypothetical) utility associated with

death as the one corresponding to zero consumption: ũ(0, pM ) = −βc, as implied by (1). For the

following steps it is convenient to define β ≡ (1/pM )1−α
αα (1− α)1−α.23 The optimization problem

is then:

max
i={A,M}

{(1− di) ũ(wi, pM ) + di ũ(0, pM )} (7)

This setup implies that the city and countryside expected utility levels are equal whenever no migration

is desired. In this case, (7) yields:

(wM − c) =
(1− dA)
(1− dM )

(wA − c) +
dM − dA

1− dM
c (8)

Since dM > dA, wages in the city are higher than in the countryside.24 If (8) holds with equality, no

migration occurs. When the LHS is larger than the RHS, the urban wage premium outweighs the excess

mortality in cities, thus attracting rural workers. The rising urban labor supply then causes the relative

wage to drop until equality is re-established. The opposite workplace decisions restore the equilibrium

when the RHS is larger than the LHS. These dynamics can immediately correct minor shocks to relative

productivity or population NA and NM . If shocks are large, like the plague, migration must be large to

re-establish equality in (8). In this case, cities grow less than would be predicted by the baseline model

as it takes time to construct urban infrastructure – Rome was not built in a day. We discuss this case in

detail in section 3.5.

Figure 3 illustrates the basic income-demand-urbanization mechanism of our model. If the rural wage

(horizontal axis) is below subsistence (normalized to c = 1), the starving population does not consume

any manufacturing goods. Cities do not exist (zero urbanization, left axis), and there are no workers

employed in manufacturing (zero urban wages, right axis). Cities emerge once peasants’ productivity is

high enough for consumption to rise above subsistence. At this stage, urban consumption also becomes

important, driven by city workers who produce manufacturing output. As productivity increases further,

urbanization and consumption (both urban and rural) grow in tandem.

23This definition is made without loss of generality. Any negative number associated with the utility level of death serves to

obtain a positive city wage premium – the more negative, the higher the premium. Our choice of β ensures that the relative price of

urban goods does not directly influence the location decision. This simplifies the subsequent analysis.
24If rural income is too small to ensure consumption above subsistence (wA ≤ c ), equation (8) does not hold and there is no

migration, since all agent work in agriculture.

12



[Insert Figure 3 here]

3.4 Population Dynamics

Birth and death rates depend on real p.c. income. Since there is no investment, units of consumption

serve as a measure of real income: c•,i = cA,i + cM,i for i = {A,M}.25 Substituting from (2) into this

expression yields:

c•,i = αwi + (1− α)c +
(1− α)

pM
(wi − c) (9)

Individuals at location i procreate at the birth rate

bi = b0 · (c•,i)ϕb (10)

where ϕb > 0 is the elasticity of the birth rate with respect to real income. Note that c•,i = c if wi = c.

We choose c = 1, so that b0 represents the birth rate at subsistence income. Before the Black Death,

location-specific death rates fall with income and are given by

dA = min{1, d0 · (c•,A)ϕd}
dM = min{1, d0 · (c•,M )ϕd +4dM} (11)

where ϕd < 0 is the elasticity of the death rate with respect to real income and 4dM represents city

excess mortality; d0 is the countryside death rate at subsistence income.

A poor economy with little urbanization has neither long-range mobility due to trade nor means for

warfare; germ pools remain isolated and mortality is only driven by individual rural income as given

by (11). Higher p.c. income after the plague simultaneously spur trade and wars. Liquid wealth in

cities funds wars and attracts traders. Military casualties mount. Armies as well as merchants continu-

ously spread pathogenic germs to cities and countryside. These factors raise background mortality. In

combination, this is what we call the ’Horsemen effect’, h. Because it is driven by growing income

and urbanization, we use the urbanization rate nM as a proxy for its strength. To capture the positive

relationship between urbanization and the ’Horsemen effect’, we calculate h as:

h(nM ) =

{
0, if nM ≤ nh

M

min{δ nM , hmax}, if nM > nh
M

(12)

where δ > 0 is a slope parameter, hmax represents the maximum additional mortality due to the ’Horsemen

effect’, and nh
M is the threshold urbanization rate where the effect sets in.26 The role of the plague in our

model is to introduce germs and to push p.c. income to levels where nM > nh
M . To kill, germs need to

be spread. This is why the plague can produce a long-term effect. It combines a new disease with higher

incomes, which translates into greater mobility (through both warfare and more trade). Only if higher

mobility spreads epidemics, background mortality increases and alleviates the population pressure.
25We calibrate our model such that the initial relative price is pM,0 = 1. Thus, wi,0 = cA,i,0 + cM,i,0. Real income in

period t is therefore given in terms of the prices in period 0. A simplified approach would have birth and death rate as functions of

nominal income wit = cA,it + pM,t cM,it, not taking into account changes in the relative price pM . Because the latter changes

substantially with the land-labor ratio, we choose the real income approach.
26A more detailed justification for nh

M > 0 is that it indicates a minimum income level that cannot be expropriated, containing

food for elementary nutrition as well as basic cloth and tools produced in city manufacturing. Once this threshold is passed, taxation

yields the means for warfare and arouses the Horsemen.

13



Before we analyze equilibria, we derive population growth from economy-wide fertility and mortality

rates. Average fertility evolves according to (10), using the workforce shares nA and nM as weights:

b = nAbA + nMbM (13)

The same method yields average death rates from (11) and (12), depending on whether or not the Horse-

men ride.

d =

{
nAdA + nMdM , if nM ≤ nh

M

nAdA + nMdM + h, if nM > nh
M

(14)

Increasing real income has an ambiguous effect on mortality: Larger c•,i translates into lower death rates

in (11). On the other hand, manufacturing demand rises with income, driving more people into cities

where mortality is higher. Moreover, in the presence of the ’Horsemen effect’, urbanization (proxying for

the spread of epidemics through trade and wars) also implies larger overall background mortality. The

aggregate impact of productivity on mortality depends on the model parameters (as shown in section 4.1).

Population growth equals the difference between the average birth and death rate: γN,t = bt − dt.

The law of motion for aggregate population N is thus

Nt+1 = (1 + bt − dt)Nt (15)

Births and deaths occur at the end of a period, such that all individuals Nt enter the workforce in period

t.

3.5 Equilibria

Equilibrium in our model is a sequence of factor prices, goods prices, and quantities that satisfies the intra-

temporal and workplace optimization problems for consumers and firms. In this section, we analyze the

economy without technological progress. The long-run equilibrium is characterized by stagnant popula-

tion, labor shares, wages, prices, and consumption. All depend on how the birth and death rates respond to

income. Figure 4 visualizes the schedules. Peasants’ real income c•,A is shown on the horizontal axis.27

Relatively low death rates give rise to equilibrium A: a poor economy with below-subsistence income

(c•,A ≤ c) where all individuals work in agriculture. The long-run level of consumption is independent

of productivity parameters; it only depends on the intersection of b and dL. For purposes of illustration,

assume that there is a one-time major innovation in agriculture, augmenting AA in equation (4). The

rising wage shifts c•,A to the right of point A, such that population grows (b > dL). Consequently, the

land-labor ratio l declines. So do wages, which eventually drives the economy back to equilibrium A.

Land per worker is therefore endogenously determined in the long-run equilibrium.

[Insert Figure 4 here]

In the absence of continuous technological progress, there are two ways for achieving a permanent

rise in per-capita income.28 First, a permanent decline in birth rates. The European Marriage Pattern had

27Provided that there is demand for manufacturing products, urban income is proportional to its rural counterpart, as shown in

Figure 3.
28Continuous technological progress constantly pushes consumption to the right of point A, with increasing population and

falling l always pulling it back. The equilibrium is thus located to the right of the intersection of b and d and is characterized by

14



such an effect, with delayed marriage for some women and permanent celibacy for others. Alternatively,

a permanent rise in mortality can boost incomes. This is the channel we focus on. Higher death rates (dH )

imply lower population in equilibrium and therefore higher income, as represented by point B in Figure

4.29 While total population is constant in point B, there must be perpetual migration from the countryside

to cities in order to compensate for city excess mortality.

Points A and B in Figure 4 are long-run equilibria with endogenous population size. For a given

technology AA, productivity is fixed in the long-run. At any one point in time, output per capita is

driven by the endogenously determined land-labor ratio. During the transition to long-run equilibrium,

population dynamics influence the land-labor ratio and thus output per worker. In the following, we

analyze these dynamics. We first concentrate on the economy with below-subsistence consumption where

individuals struggle for survival and produce only food in the countryside. Next, we turn to the economy

with consumption above c, accounting for constraints to migration due to city congestion during the

transition process.

The Economy with Below-Subsistence Consumption

In order to check whether overall productivity (determined by AA and the land-labor ratio) is sufficient to

ensure above-subsistence consumption, we construct the indicator ŵ, assuming that all individuals work

in agriculture. Equation (3) then gives the corresponding per-capita income:

ŵ ≡ YA(N)
N

= AA

(
L

N

)1−γ

(16)

If ŵ ≤ c, all individuals work in agriculture (NA = N ) and spend their entire income on food. Since

there is no demand for manufacturing goods, the manufacturing price is zero. This implies zero urban

wages and zero population. Economy-wide fertility and mortality are thus equal to the rural levels given

by equations (10) and (11).30 Finally, there is no migration. In order to derive the long-run equilibrium,

we calculate birth and death rates according to the equations in section 3.4. The intersection of the

two schedules (point A in Figure 4) determines equilibrium income, which we can use to derive the

corresponding population size N from (16).

Above-Subsistence Consumption and Unconstrained Migration

If ŵ > c, agricultural productivity is high enough for consumption levels to rise above subsistence.

Following (2), well-nourished individuals spend part of their income on manufacturing goods. To produce

them, a share nM of the population lives and works in cities. In each period, individuals choose their

profession and workplace based on their observation of income and mortality in cities and the countryside.

Productivity increases lead to more manufacturing demand and spur migration, which occurs until (8)

holds with equality. For small productivity changes, migration is minor and cities can absorb enough

consumption stagnating at a higher level. Consumption can grow continuously only if technological change outpaces the falling

land-labor ratio – a highly unrealistic scenario given the observed productivity growth of about 0.1% p.a. before the Industrial

Revolution.
29Note that the death schedules dL and dH become flatter when consumption passes the subsistence level. This is because richer

agents also demand manufacturing products such that part of the population lives in cities, where mortality is higher (4dM > 0).
30Note that the ’Horsemen effect’ is zero because nM = 0.

15



migrants to establish this equality immediately. We refer to this case as equilibrium with unconstrained

migration. Goods market clearing together with equations (2), (3), and (5) implies

AANγ
AL1−γ = α [(wA − c)NA + (wM − c)NM ] + cN (17)

pMAMNM = (1− α) [(wA − c)NA + (wM − c)NM ] (18)

Solving for the expression in brackets in (18), plugging it into (17), and substituting wM = pMAM yields

αwM (1− nA) + (1− α)c = (1− α)AAnγ
Al1−γ (E1)

This equation contains two unknowns: nA and wM . We find an expression for the latter by using the

equality in (8), as implied by unconstrained migration. Substituting (4) into (8) and rearranging gives:

(wM − c) =
(1− dA)
(1− dM )

[
AA

(
l

nA

)1−γ

− c

]
+

dM − dA

1− dM
c (E2)

We now need dA and dM as functions of nA and wM . Plugging (9) into (11), with wA substituted from

(4) and pM = wM/AM , we obtain:

dA = d0

[
αAA

(
l

nA

)1−γ

+
1− α

wM
AM

(
AA

(
l

nA

)1−γ

− c

)
+ (1− α)c

]ϕd

+ h(1− nA) (E3)

dM = d0

[
αwM +

1− α

wM
AM (wM − c) + (1− α)c

]ϕd

+4dM + h(1− nA) (E4)

The last term in (E3) and (E4) represents the ’Horsemen effect’ as a function of the urbanization rate

nM = 1 − nA. For a given population size N we now have a system of 4 equations [(E1)-(E4)] and 4

unknowns (nA, wM , dA, and dM ) that we solve numerically. Given these variables, it is straightforward

to calculate the urbanization rate nM , rural wages wA from (4), and workplace-specific real income (or

consumption) c•,i from (9). Finally, workplace-specific birth rates are given by (10).

All calculations up to now have been for a given N . For small initial population, births outweigh

deaths and N grows until diminishing returns bring down p.c. income enough for b = d to hold. The

opposite is true for large initial N . To find the long-run equilibrium with constant population, we derive b

and d from (13) and (14). We then iterate the above system of equations, deriving Nt in each period t from

(15), until the birth and death schedules intersect (point B in Figure 4). The long-run equilibrium level of

population depends on the productivity parameters AA and AM , and on the available arable surface, L.

Under unconstrained migration, expected utility in each period is identical for peasants and manufac-

turing workers. Rural and urban population is given by NA = nAN and NM = nMN , respectively. But

is there migration in the long-run equilibrium? To answer this question, Figure 5 shows the workplace-

specific death rates as a function of real income.31 We calibrate city excess mortality including the effects

of war and trade as 4dM = 1.5%. Equilibrium death rates in cities are higher than in the countryside.32

Birth rates, on the other hand, are similar in both workplaces.33 With stagnant total population and no
31As in Figure 3, we use peasants’ consumption to represent real income. Urban income is a multiple of rural income, as implied

by (8). Each point on the horizontal axis therefore corresponds to an urban real income level c•,M > c•,A. Note that for c•,A < c,

urban death rates are not defined since all individuals work in the countryside.
32The higher real income of manufacturing workers drives down dM according to (11). However, this income effect is overcom-

pensated by the higher background mortality in cities4dM .
33With an urban wage premium (relative to subsistence) in the range of 30% and birth rate elasticity ϕb = 1.41, as in our baseline

calibration, bM and bA deviate by less than 0.05%.

16



migration, NM would therefore decline continuously. This implication of our model is in line with the

widely-established historical finding that early modern European cities would have disappeared without

a constant inflow of population.

[Insert Figure 5 here]

Congestion and Constrained Migration

Major changes in the urban-rural income differential provide substantial incentives for migration. How-

ever, the short-term capacity of cities to absorb migrants is limited because new dwellings and infrastruc-

ture must be provided. Building new houses and enlarging cities was one of the costliest undertakings in

the early modern economy. Too many migrants caused over-crowding, making further migration to the

cities unattractive. In the interest of simplicity, we capture congestion effects with an upper limit to the

growth rate of cities, ν.34 When shocks are large, and wage differentials are substantial, this constraint

becomes binding. It then takes time until population shares reach their long-run equilibrium levels nLR
A

and nLR
M .

Let N?
A,t and N?

M,t be the number of individuals living in the countryside and cities, respectively, at

the beginning of period t before migration occurs. This ’native’ population is determined by workplace-

specific fertility and mortality in the previous period:

N?
i,t = (1 + bi,t−1 − di,t−1)Ni,t−1 (19)

where Ni,t−1 is the number of agents that live at workplace i = {A,M} during period t − 1, after

migration has taken place. Let Mu
t be the level of migration necessary to (immediately) establish long-

run population levels NLR
i = nLR

i N in period t, i.e., the migration that would take place if it were

unconstrained:

Mu
t = N?

A,t −NLR
A = NLR

M −N?
M,t (20)

There are two ways to calculate Mu
t , since migration out of agriculture (first term in (20)) must equal

migration into cities (second term). Mu
t is positive if migration goes from the countryside to cities, i.e.,

if the number of native peasants is larger than the optimal long-run rural population, and negative if

migration takes the opposite direction. Next we derive the growth of city population that occurs when

migration is unconstrained, reaching the long-run equilibrium instantly.35

νt ≡ Mu
t

N?
M,t

=
NLR

M −N?
M,t

N?
M,t

=
nLR

M − n?
M,t

n?
M,t

(21)

The magnitude of Mu
t , and thus the likelihood that congestion constrains migration, is the larger the

more the long-run population distribution deviates from actual values. If νt exceeds the upper bound for

migration to the urban centers, the constraint ν becomes binding. The number of migrants under this

34Migration in the opposite direction plays no role in our model because any income increase (following the plague or techno-

logical progress) makes cities more attractive than the countryside via the manufacturing demand channel.
35More precisely, this is the growth rate of city population due to migration only. We implicitly assume that urban offsprings do

not contribute to congestion because they live with their parents, at least in the short run. In this specification, the growth rate of ν

is equal to the growth of the urbanization rate – a fact that we will use to calibrate ν.

17



constraint is given by M c
t = νN?

M,t, that is, urban population grows at the rate ν. Together with (19),

this gives the law of motion for workplace-specific population with constrained migration:

NA,t = N?
A,t − νN?

M,t

NM,t = N?
M,t + νN?

M,t (22)

The agricultural workforce in period t is thus composed of rural offspring and surviving peasants from

t− 1, less the ones migrating to cities (until congestion makes these places unattractive). The city popu-

lation consists of surviving manufacturing workers and urban offspring, augmented by migrants from the

countryside.

The equilibrium values of wages, prices, and income under constrained migration are derived from

the location-specific workforce given by (22). Rural wages follow from (4), while (E1) can be re-arranged

to recover urban wages:

wM =
1− α

α(1− nA)
[
AAnγ

Al1−γ − c
]

(23)

Manufacturing products are sold at pM = wM/AM . Workplace specific real income, fertility, and mor-

tality are then calculated from (9), (10), and (11), respectively.

4 Calibration and Simulation Results

In this section we calibrate our model and simulate it with and without the additional mortality that comes

from urbanization, trade, and war. We choose parameters in order to match historically observed fertility,

mortality, and urbanization rates in early modern Europe. We then simulate the impact of the plague and

derive the long-run levels of p.c. income and urbanization in the centuries following the Black Death.

Finally, we add to our model the alleviating effect on birth rates that the European Marriage Pattern

provided.

4.1 Calibration

In order to calibrate our model, we follow the procedure outlined in section 3.5: The intersection of birth

and death schedule determines per-capita income and equilibrium population size. Urbanization rates in

Europe before the Black Death were approximately 3%.36 For cities to exist in our model, real incomes

have to be above subsistence, i.e., c•,i > c in the long-run pre-plague equilibrium. For the intersection of

b and d to lie to the right of c, we must have death rates higher than birth rates at the subsistence level, that

is, d0 > b0 in equations (10) and (11). Kelly (2005) estimates the elasticity of death rates with respect to

income, using weather shocks as exogenous variation. We use his estimate for England over the period

1541-1700, ϕb = −0.55, as a best-guess for Europe. Regarding the elasticity of birth rates with respect

to real income, we use his estimate of ϕb = 1.41 for Europe.37 Regarding the level of birth and death

36Maddison (2001) reports 0% in 1000 and 6.1% in 1500; DeVries (1984) documents 5.6% in 1500. Our 3% for the 14th century

is at the upper end of what we expect, given that wages stagnated throughout the millenium before the plague. We deliberately

make this conservative choice, leaving less urbanization to be explained by our story.
37This number is bigger than the estimates in, say, Crafts and Mills (2007), or in Anderson and Lee (2002). Because of the

important endogeneity issues in deriving any slope coefficient, the IV-approach by Kelly is more likely to pin down the magnitude

of the coefficients, compared to identification through VARs or through Kalman filtering techniques.

18



rates, we use 3.5% in the pre-plague equilibrium, corresponding to the cumulative birth rates reported

by Anderson and Lee (2002). This, together with the elasticities and the equilibrium urbanization rate of

3.0%, implies b0 = 3.11% and d0 = 3.53%. As discussed in the historical overview section, we estimate

that death rates in European cities were approximately 50% higher than in the countryside. This implies

a (conservative) value of 4dM = 1.5%.

Scale does not matter in our model. Solely the productivity parameters AA,t and AM,t, together with

the land-labor ratio lt, determine individual income. Thus, for any equilibrium p.c. income derived from

the intersection of b and d, we can calculate the corresponding population N .38 We choose parameters

such that initial population is unity (N0 = 1). This involves the initial productivity parameters AA,0 =

0.462, AM,0 = 1.080, and L = 8, where land is fixed such that its hypothetical rental rate is 5%.39 Our

calibration also implies the desired urbanization rate nM,0 = 3.0% and a price of manufacturing goods

that is equal to the price of agricultural products, i.e., pM,0 = 1.40

For the baseline model, we use the labor income share in agriculture γ = 0.6. This is similar to the

value implied by Crafts (1985), and it is almost identical with the average in Stokey’s (2001) calibrations.

We normalize the minimum food consumption c to unity. For low income levels, all expenditure goes to

agriculture. With higher productivity, manufacturing expenditure share and urbanization grow in parallel.

To derive this relationship, we pair income data from Maddison (2007) with urbanization rates from

DeVries (1984). In the model, the responsiveness of urbanization to income is governed by the parameter

α. Figure 6 plots urbanization rates in England in the early modern period against per capita income. The

latter is normalized to unity for the pre-plague period. Note that at this point nM = 3% in the model,

as calibrated above. Rising incomes went hand-in-hand with higher urbanization rates. Our calibration,

derived with a model parameter of α = 0.55, traces out a similar increase. The simulation consistently

shows slightly higher urbanization rates for a given income level. This is deliberate – urbanization is an

imperfect proxy for the production of non-agricultural goods, as many authors have emphasized (Wrigley

1985).

[Insert Figure 6 here]

In the centuries before 1700, labor productivity grew at an average rate of roughly 0.05-0.15% per

year (Galor 2005). We use an exogenous growth rate of agricultural and manufacturing TFP, AA and AM ,

of τ = 0.1% in our simulations with technological progress. In order to quantify the upper bound for

city growth, reflecting congestion in our model, we use DeVries’ (1984) urbanization data for 1500-1800.

The largest observed growth rate of urbanization in Europe over this period is ν = 0.38% between 1550

and 1600.

After the Black Death, the ’Horsemen effect’ comes into play. Means for warfare and trade grow with

p.c. income, and greater mobility leads to an ongoing dispersion of germs. According to equation (12),

the Horsemen are at work when the urbanization rate nM is larger than the threshold level nh
M . We choose

38For example, rural population is implicitly given by (4), and is the larger (for a given wage wA) the more land is available. We

calculate the long-run equilibrium by solving the system (E1)-(E4) and iterating over population until b = d. This procedure gives

the long-run stable population as a function of fertility and mortality parameters, productivity, and land area.
39Recall that we assume no property rights to land. The size of L is therefore not important for our results – it could also be

normalized to one and included in AA. We leave L in the equations for the sake of arguments involving the land-labor ratio.
40Other values of this variable, resulting from different AM,0 relative to AA,0, do not change our results.

19



nh
M = 3.5%, which is above the pre-plague urbanization rate. The ’Horsemen effect’ begins to play a role

only if city wealth becomes large enough to support the cost of warfare. Below nh
M , city income is too

low to be taxed or expropriated, serving merely to provide elementary nutrition and basic manufacturing

goods.41 Once the threshold is passed, the ’Horsemen effect’ increases linearly in the urbanization rate

until it reaches its maximum.42 In order to calibrate the maximum impact of the Horsemen channel on

mortality, we use data on war-related deaths and epidemics from Levy (1983). His data show that, in a

typical year, more than one European war was in progress – there were 443 war years during the period

1500-1800, normally involving three or more powers. Since it is the movement of armies, and not just

military engagements that caused death, we count the territories of combatant nations as affected if they

were the locus of troop movements. Combined with demographic data in Maddison (2007), we obtain the

percentage of European population affected by war between 1500 and 1700.43 Figure 7 shows that this

measure grows from about 12% in 1500 to roughly 50% around 1700, and decreases in the 18th century.44

The population share affected by wars mirrors the trend in the number of plague outbreaks shown in

figure 2, as it should if wars were one of the main factors spreading disease in early modern Europe.

In times of war, death rates nationwide could rise by a factor of 1.5 to 2 (see the discussion in section

2). Given equilibrium death rates of over 3%, this implies an additional 1.5-3 percent under warfare.

With more than one third of the European population affected by warfare throughout the 17th century, we

derive a war-related ’Horsemen effect’ of 0.5-1 percent, and use the mid-point of this interval, 0.75 in the

calibration. To this we add a guestimate of 0.25%. This is motivated by the spread of disease through

additional trade, which was also facilitated and encouraged by the wealth of cities. Overall, our best

guess for the maximum size of the ’Horsemen effect’ is therefore hmax = 1% . This value is reached in

the first half of the 17th century. The Thirty Years War was particularly savage, and saw troop movement

from many countries, over a very wide area, and for an extended period (Levy 1983). Urbanization rates

reached 8% in the 17th century (DeVries, 1984). The implied slope parameter of the Horsemen function

is therefore δ = hmax/(0.08− nh
M ) = 0.222. Table 1 summarizes the calibrated parameters.

[Insert Figure 7 here]

[Insert Table 1 here]

4.2 Plague and Equilibrium without ’Horsemen Effect’

The left panel of figure 8 shows the pre-plague long-run equilibrium according to our baseline calibration.

The fertility and mortality schedules intersect at a rate of 3.5% for each, while 3% of the population live

41Recall that city wages and urbanization rates grow in tandem (figure 3) such that one serves as an indicator for the other.

Total taxable surplus income (above subsistence) may not have increased as much as per capita income due to population losses.

However, what matters for the ability to fight wars is the relative position of powers. If population losses are symmetric, higher per

capita incomes can translate into greater war-fighting ability.
42Our long-run results would be the same if the ’Horsemen effect’ reached its full strength immediately after the plague. However,

our modeling choice provides more historical realism during the transition – warfare and death rates increased only gradually with

urbanization in early modern Europe.
43Linear interpolation is used for the years where no population data are available.
44The AJR (2005) dataset shows a similar if less pronounced trend over time. For the calibration, we use the more precise

measure of population affected by warfare derived from the Levy data. Where comparability of results is key, as in the regression

analysis below, we use the AJR data instead.

20



in cities. The economy is trapped in Malthusian stagnation in point E. One-time increases in productivity

lead to higher income and therefore population growth. As a consequence, the land-labor ratio falls and

drives per-capita income back to its long-run equilibrium value.

[Insert Figure 8 here]

The effect of a one-time technological improvement on p.c. income is similar to the impact of the

plague in our model: While the former raises TFP, the latter increases the land-labor ratio. Both result

in higher wages, according to (4). The right panel of figure 8 shows the effect of the Black Death when

all model parameters are unchanged. Before the plague, population and urbanization stagnate in the

absence of technological progress. The Black Death in our calibration reduces population by 40%. As

an immediate consequence, wages and p.c. consumption rise. Urbanization rates increase more slowly

because cities cannot immediately grow to their new equilibrium size. In the aftermath of the plague,

population grows because the economy is now situated to the right of the long-run equilibrium in point

E, with fertility higher than mortality. The falling land-labor ratio eventually drives the economy back

to E, with all variables returning to their pre-plague values. We argue that this describes the Chinese

experience. Things look different in the presence of the ’Horsemen effect’, which is unique to Europe.

4.3 Long-run Equilibria with ’Horsemen Effect’

If the shock is large enough, like the Great Plague, city wealth generates more trade and provides the

means for more wars. The economy can converge to a new equilibrium with higher mortality, but also

larger p.c. income and urbanization. The left panel of figure 9 shows the two stable equilibria, E and H,

and an unstable equilibrium, U. Initially, the economy is in E, and all variables remain unchanged in the

absence of technological progress. In order to initiate the transition from E to H, a shock to population (or

productivity) must be large enough to push the economy beyond U, where Horsemen-augmented death

rates exceed birth rates.45 We argue that early modern Europe underwent such a transition.

Following the plague, p.c. incomes surged. Surviving individuals and their descendants were sub-

stantially better off than their ancestors before the plague. This is in line with historical evidence: It took

until the 19th century for wages to recover their post-plague peak (Clark 2005). The demand for urban

goods made cities grow, fostering trade and providing the means for warfare. Enhanced mobility con-

stantly spread epidemics and therefore raised mortality. The size of this ’Horsemen effect’ grew together

with urbanization until the 17th century, as shown in figures 2 and 7, and captured by (12) in our model.

The economy converges to the Horsemen equilibrium (point H) in the aftermath of the Great Plague.

This equilibrium is characterized by higher birth and death rates (about 4.2%) and higher urbanization

(8.5%). The corresponding dynamics are shown in the right panel of figure 9. Our story can explain the

rising urbanization rates in early modern Europe in the absence of technological change. However, in

this reduced form it predicts falling population, which contradicts the observed trend. Next, we allow

for slowly growing productivity. We find that technological progress can explain rising population, but

cannot account for increasing urbanization. The latter is explained largely by the ’Horsemen effect.’

45With ongoing technological progress the argument is similar. Continuous technological progress implies rising population at

stagnant p.c. income. If death rates rise sufficiently because of the Horsemen, income grows while population can grow or fall. We

analyze this case below.

21



[Insert Figure 9 here]

4.4 Technological Progress and Model Fit

Technological progress in premodern times alone is not enough to escape from the Malthusian trap. While

a growing population eventually reverses the benefits of one-time inventions, ongoing progress implies

higher, but still stagnating, long-run p.c. income. Its effects are thus similar to a permanent outward

shift of the death schedule. Our calibrations also suggest that the effect in early modern Europe was

markedly smaller than the effect of death rates. Technology pushes p.c. income up, and population

growth responds, offsetting any gains. This corresponds to a long-run equilibrium in point T in the

left panel of figure 10, where the birth rate exceeds the death rate and technological progress is exactly

offset by the falling land-labor ratio.46 The right panel of figure 10 illustrates the orders of magnitude

involved. The rate of technological change before the Industrial Revolution was low, approximately 0.1%

(Galor 2005). For purposes of illustration, progress is assumed to set in after 50 periods of stagnating

technology. As the figure shows, this raises the urbanization rate by less than 2%. Note that this is an

extreme scenario where the economy jumps from complete stagnation to continuous inventions. The

corresponding increase of urbanization is thus an upper bound for the impact of technology on individual

income. Therefore, technological progress cannot be a candidate to explain the rise of Europe in the early

modern period.

[Insert Figure 10 here]

Next, we investigate the fit of our model, including the ’Horsemen effect’ and the observed rate of

technological progress.47 We begin simulations in 1000 AD in order to show both the pre- and post-plague

fit of the model. While the ’Horsemen effect’ alone can account for almost all the observed increase in

European urbanization (see figure 9), technological progress is responsible for the growth in population.

Figure 11 shows the simulation results together with the data. Our model performs well in reproducing

both population growth and urbanization.

[Insert Figure 11 here]

4.5 The European Marriage Pattern

Europeans curtailed fertility in an important way - by delaying marriage for most women, and ensuring

that a high proportion never married.48 This pattern is known as the European Marriage Pattern (EMP),

and only evolved West of a line from Triest to St. Petersburg. In a normal Malthusian setting, increasing

fertility should have eroded all gains in living standards quickly. Lower birth rates for a given income have

46Equation (3) with constant p.c. income (and thus constant agricultural labor share) implies that population grows at the rate

τ/(1− γ) in the long-run equilibrium.
47We allow technology to grow at τ = 0.1% throughout the simulation. The model is calibrated to yield the same initial values

as above for population, urbanization, fertility, mortality, and relative prices (as given in the lower part of table 1). Intuitively, this

technology-progress adjusted calibration corresponds to shifting the death schedule downwards by τ/(1−γ) in figure 10. The new

equilibrium T is then the same as the previous E.
48This went hand in hand with very low rates of bastardy.

22



a similar effect to higher background mortality: both alleviate population pressure and reduce the land-

labor ratio in equilibrium. Average realized fertility rates in early modern Europe were approximately

equal to those in China, despite markedly higher living standards (Clark 2007). At Chinese income

levels, European fertility would have been much lower because of fertility restriction. In figure 12, 17th

century China would be close to point E. This suggests that English fertility, because of the EMP, would

have been 0.75% below the corresponding value for China - with equal incomes. We do not know when

the European marriage pattern emerged. Some authors have argued that the plague was critical (Van

Zanden and deMoor 2007). If so, then some of the increase in European incomes after 1350 has to be

attributed to the plague’s impact on fertility.

Births in England were probably unusually responsive to economic conditions (Lee 1981, Wrigley

and Schofield 1981). England was also ahead of the European average in terms of incomes and city

growth: p.c. income grew by 75% between 1500 and 1700, and urbanization rates more than quadrupled

from 3% to over 13% (and 20% in 1800) (Maddison 2007, DeVries 1984). We now investigate the EMP’s

contribution to income and city growth in our model. We assume that birth rates are not responsive to

income before the Black Death, so that ϕbefore
b = 0. After the plague the EMP emerges, it shifts the birth

schedule downwards by 1%. This corresponds to a 30% drop relative to the pre-plague equilibrium. We

deliberately assign a potentially large role to the EMP, as to ensure that we do not exaggerate the role of

the ’Horsemen effect.’ The EMP also makes birth rates responsive to income such that ϕafter
b = 1.4, as in

the baseline calibration.49

[Insert Figure 12 here]

Figure 12 shows the EMP simulation results. In the absence of the ’Horsemen effect’, the shift and tilt

of the birth schedule move the economy from the pre-plague equilibrium E to the EMP equilibrium. Part

of the downward-shift is compensated by the positive response of birth rates to growing income after the

plague. The ’Horsemen effect’ creates an additional rise in urbanization (equilibrium H+EMP). Instead

of an urbanization rate of 3%, we predict a rate of 8.5% based on the rotated fertility schedule. The rise

from 8.5 to 14 percent is due to the ’Horsemen effect.’ Both effects appear to be equally important, and

together they match the observed increase in England’s urbanization rate. This underlines the importance

of the ’Horsemen effect’ for increasing living standards in early modern Europe – in continental Europe,

where the EMP was weaker, the Horsemen contribution was possibly even more significant.

5 Empirical Evidence

In this section we provide empirical evidence that underlines the importance of the ’Horsemen of Growth’–

the rise in mortality that results from more wars, more cities, and more trade. We demonstrate that this

mechanism can help us explain divergence within Europe, between a dynamic North-Western region and

a stagnant Southern one. While urbanization rates and wages declined in the latter, they rose in the former

after 1500. The ”Rise of Atlantic Europe”, emphasized by AJR (2005) is captured by our model, but it is

49The corresponding parameter values are bbefore
0 = 0.0344 and bafter

0 = 0.0244. With all other parameters unchanged, this

implies again an equilibrium urbanization rate of 3% before the plague.

23



observationally equivalent to the rise of the most belligerent and war-torn parts of Europe.50 We extend

the dataset used by AJR (2005), who show that Atlantic trade was a driver of European growth, both

directly, and indirectly through its effect on institutional quality. Our results suggest that warfare was also

a key determinant of income levels in Europe until 1700. Since war itself killed few people, we argue

that this effect is driven by the epidemics that fighting and the movement of armies spread. We also show

that the effect is causal, by pinning down the part of variation in war frequency driven by geographical

factors. In the following, we quickly describe our data sources and then turn to the regressions – first

using a cross-section and then panel data for early modern Europe.

5.1 Data

We use two indicators for European development: urbanization and per capita GDP. Both measures gen-

erally go hand in hand. AJR (2002b) present time-series and cross-section evidence for a close association

between urbanization and per capita income before as well as after industrialization. 51 Urbanization can

therefore be used as a proxy for GDP per capita. AJR (2005) derive urbanization rates by dividing the

urban population numbers of Bairoch et al. (1988) by the population estimates of McEvedy and Jones

(1978).52 The former dataset includes information on all 2,200 European cities which had 5,000 or more

inhabitants at some time between 800 and 1800. From 800 until 1700 there are estimates for every 100

years, and then for every 50 years through 1850. Since Bairoch et al. (1988) emphasize that estimates

before 1300 are rough and unreliable, we do not include these figures in our sample. We use the data

between 1300 and 1700 to derive our baseline results. In addition, as a consistency check, we use urban-

ization data from DeVries (1984). His data cover all cities with at least 10,000 inhabitants. As a result,

DeVries’ urbanization estimates are generally lower, but the pattern over time is similar. The higher relia-

bility of these data comes at a cost: DeVries’ data only start in 1500 and cover primarily Western Europe.

Following AJR (2005), we use estimates of GDP per capita from Maddison (2001). His estimates start

in 1500 and are available for 1600, 1700, and 1820. Especially before 1820, the figures are more akin

to educated guesses. We therefore think of the GDP data as an additional robustness check. Our main

results use urbanization data between 1300 and 1700 from Bairoch et al. (1988).

War frequency is also adopted from AJR (2005) who derive the number of years of war in the preced-

ing 50 or 100 years from Kohn (1999). These data exclude civil wars and colonial wars outside Europe.

Using the average war frequency over the preceding period allows for a new equilibrium to emerge, af-

ter the short-term upheaval of warfare itself. We use two geographical variables as instruments for war

frequency in early modern Europe. First, the average aerial distance of a country’s capital to the capitals

of the great powers: Spain, France, England, Austria, the Ottoman Empire, and Russia.53 Our second

50We think of the data exercise as an indirect test of our hypothesis regarding the origins of European ascendancy. Since a simple

empirical analysis of Europe vs. China would essentially leave us with a regression based on N=2, we use a panel on intra-European

divergence to demonstrate the importance of the channels we identify.
51One reason for this finding is that only areas with high agricultural productivity and a developed transportation network could

support large urban populations (Bairoch, Batou and Chèvre, 1988, Ch. 1; DeVries, 1976, p. 164).
52All country-level data are derived for borders as of 2001.
53What constitutes a great power can be debated. Great powers according Kennedy (1988) also include Sweden and the United

Provinces. For our purposes, the country in question has to be a major military player for the entire period. Prussia, which emerges

as a great power after 1700, is not part of the set for this reason. Sweden declines as a major power after the Thirty Years War.

The United Provinces are not politically independent before the 17th century. To calculate distance, we use aerial distances between

24



instrument is the altitude of capitals. Both variables reflect geographically-determined protection against

potential aggressors – the first through distance and the second through a natural defense against foreign

powers. Since our instruments capture the geographically determined part of the variation in war fre-

quency, they are particularly appropriate for our argument – geographical ease of access will also benefit

the third of our Horsemen, trade. The data confirm the prediction that low-lying countries close to the

major powers suffered many more wars – both our instrumental variables are negatively correlated with

war frequency (see below).

5.2 Estimation Strategy

We have argued that in a Malthusian setup, the ’Horsemen of Growth’ drive up death rates and therefore

lead to higher steady state income and urbanization rates. The calibration of the ’Horsemen effect’ im-

plied that diseases, spread mainly by warfare, provide the largest contribution to rising death rates. Trade

is another factor raising mobility and spreading disease. While we cannot account directly for the flow of

goods across early modern Europe, our geography-based instruments for warfare will capture part of the

mobility channel. Consequently, warfare together with its geography-based instruments should account

for the main impact of the ’Horsemen of Growth’ on urbanization and per capita income in early modern

Europe. We test this idea using regressions of the following form:54

uj,t = β warj,t + dt + δj + γ Xj,t + εj,t (24)

where uj,t is the urbanization rate in country j at time t (or alternatively log per capita income), warj,t

denotes war frequency, the dt’s are year effects and the δj’s denote country effects. Xj,t is a vector of

other covariates, including Western Europe dummies, measures of Atlantic trade and institutions, religion,

latitude and Roman heritage. Finally, εj,t is a disturbance term.

Ideally, we would also want to check the channel through which the ’Horsemen of Growth’ work

their wonders – population. However, this is hard to identify. On the one hand, more wars and mobility

increase living standards in a Malthusian setup by spreading diseases and reducing population. On the

other hand, this direct negative effect on population is at least partially offset by the positive response of

birth rates to income. In addition, higher income leads to more demand for manufacturing goods, which in

turn can raise productivity, supporting greater populations.55 Consequently, while the ’Horsemen effect’

on living standards is positive (figure 9), its impact on population is ambiguous. We therefore restrict our

analysis to the former.

5.3 Cross-Section

We begin by analyzing a cross-section of growth in early modern Europe, where the dependent variable

in (24) is the change in urbanization or per-capita income, and the explanatory variables are averaged

capitals (in kilometers) are obtained from http://www.indo.com/distance/. Just like country borders, country capital are as of 2001,

with the exception of Turkey, where Istanbul is used instead of Ankara since the capital at the time, Edirne, was closer to Istanbul.
54Urbanization plays an ambiguous role in our estimation strategy. It is the dependent variable, capturing per capita income

levels. It is also one of the factors driving up death rates. Fortunately, the bias arising from this is small. Our calibration has shown

that excess city mortality has a negligible effect on aggregate death rates.
55While technological progress alone is not enough to significantly increase incomes, it can substantially affect population growth

(see figure 10).

25



over the corresponding period.56

OLS Regressions

First, we examine simple correlations. Figure 13 shows that a higher war frequency between 1300 and

1700 is associated with a larger increase in urbanization. The same holds for per capita income, which is

available from 1500 on.57 Columns 1-4 of table 5 show that the correlation is highly significant and robust

to excluding the great powers themselves, or the Netherlands which are unusually rich and afflicted by

numerous conflicts. The same pattern emerges when we run the regression without population weights

or when including Atlantic coast-to-area as a measure for the potential for Atlantic trade, as suggested by

AJR (2005).

[Insert Figure 13 here]

[Insert Table 2 here]

IV Regressions

Wars and urbanization growth could be related for reasons other than the mortality channel. For

example, fast growing countries may have the means (and incentives) for warfare, implying a reverse

causality. We therefore need instruments that explain a country’s war frequency but do not influence

growth through channels other than the spreading of diseases. We use geographical variables such as

the average distance to great powers and the altitude of a country’s capital. We expect both variables to

lower the probability of warfare, and to make long-distance trade more difficult. While distance to great

powers offers protection from conflict through distance to potential aggressors, altitude of a country’s

capital proxies for ruggedness. This directly lowers the risk of invasion. Two examples illustrate this

point. Both Switzerland and the Netherlands are on average about 1,200 km away from great powers.

However, Switzerland is protected by mountains – a protection that the Netherlands lack because of their

sea-level altitude. This is reflected in the war frequencies of both countries between 1300 and 1700: 0.14

vs. 0.56 wars per year on average. Table 3 shows that this relationship holds, on average, for the entire

sample.58 War frequency between 1300 and 1700 is highest for countries that are close to great powers

and have relatively low-lying capitals, and it is smallest for countries with the opposite characteristics.

War frequency is intermediate for the two mixed cases close/high and distant/low. In order to allow

for non-linearity in the distance-altitude relationship, we include the interaction between both variables.

Finally, we also use a dummy variable for the five great powers in the first stage regressions.59

[Insert Table 3 here]
56This also has the advantage of indirectly serving as a check on our data for the biases identified by Bertrand, Duflo, and

Mullainathan (2004), who argue that difference-in-difference estimators tend to understate standard errors. Since our fixed effects

regressions below are open to this criticism, we use the cross-sectional evidence – as suggested by Bertrand et al. – to check how

sensitive our results potentially are.
57Maddison (2001) provides data also for 1200, but these are rough guestimates – the reported p.c. income is the same for all

European countries (400 international Geary-Khamis dollars).
58Results are very similar when using the median.
59This captures the effect of the great power status itself on warfare. Including these dummies improves the fit at the first stage.

However, all cross-sectional and panel results are robust to excluding the dummies.

26



Columns 6 and 7 of table 2 report the results of our IV estimation.60 The first-stage results reported in

the lower part of the table confirm our choice of instruments: both distance to great powers and altitude

lower the frequency of war, while great power status itself has the opposite effect. The interaction term is

positive and significant, which is also intuitive. Note that from column 6 the marginal effect of distance to

great powers on war frequency is given by d(war)/d(distance) = −.566 + .0018 altitude. Therefore,

distance is the more decisive as a protection against warfare the lower a country’s capital. Neither instru-

ment endogeneity nor weak instruments appear to be a concern: While the p-values of the overidentifying

restriction are far from the level at which one would reject instrument endogeneity, the F -statistic for the

instruments is well above 10, which is often used as a rule-of-thumb for instrument quality.61

The second-stage results in columns 6 and 7 represent the causal impact of war frequency on urban-

ization over the period 1300-1700. The coefficients are highly significant and positive, but slightly lower

than in the OLS specifications. This is what we would expect, given that warfare may in part respond

positively to greater riches. AJR (2005) argue that access to the Atlantic was an important determinant

of growth in Western Europe relative to Eastern Europe. We confirm their finding, obtaining a large co-

efficient for coastline. In order to compare the importance of warfare and Atlantic trade for European

urbanization on average, we multiply the coefficients in column 7 with the corresponding explanatory

variable’s population-weighted average. Average European urbanization grew by 3.3 percent between

1300 and 1700.62 About 3/4 of this increase is due to war frequency (weighted average .55), while less

than 1/5 is due to Atlantic trade, proxied by the coastline-to-area ratio (weighted average .005). How-

ever, Atlantic trade is as important as warfare for explaining cross-country variation within Europe: A

one standard deviation increase in Atlantic coastline (0.011) is associated with a 1.5% increase in the

urbanization rate between 1300 and 1700. Similarly, a one standard deviation increase in war frequency

(0.304) implies a 1.4% rise in urbanization over the same period. Taken at face value, the ’Horsemen of

Growth’ can account for a good deal of Europe’s rise, while Atlantic trade explains some of the rise of its

North-Western part.

All results presented so far have used the urbanization rates calculated by AJR (2005) for the period

1300-1700. In Appendix 1 we show that our results are robust to using urbanization rates from DeVries

(1984) for the period 1500-1700.

GDP as dependent variable

In order to check the robustness of our cross-section results to alternative development indicators, we

also use per capita income. Since these figures are only available from 1500 on, we use the change in

60Throughout the empirical section we use the kernel-based heteroskedastic and autocorrelation-consistent (HAC) 2-step GMM

estimation technique, and follow Newey and West (1994) to select the bandwidth. This approach is more efficient than traditional 2-

stage least square estimation. When using the latter, the magnitude of our results does not change, but standard errors are generally

larger – although the high significance of the warfare variable remains mostly unaffected. There is an argument in the literature that

the continuous updating estimator (CUE) due to Hansen, Heaton, and Yaron (1996) can gain further efficiency. We check our main

results using the CUE and find very similar magnitudes and standard errors.
61The quality of our instruments, as indicated by Stock and Yogo’s (2002) test, is very close to the highest level, indicating 5%

maximal IV relative bias.
62This relatively small increase results from the high initial urbanization rates in 1300 in the AJR (2005) dataset, which counts

cities from 5,000 inhabitants on. According to the urbanization data from DeVries (1984) – counting only cities with more then

10,000 inhabitants – average European urbanization grew by about 4% over half the time span, between 1500 and 1700. For

North-Western Europe this figure is even larger – about 7 percent.

27



log GDP per capita between 1500 and 1700 as the dependent variable. The results presented in table

4 confirm the ones found above for urbanization.63 War frequency correlates positively with per capita

GDP growth, and the IV regressions indicate a positive causal relationship. While the sign is ’right’ in

all specifications, standard errors are relatively larger, such that the results for GDP per capita are less

significant than the ones for urbanization. This is likely driven by the more noisy data on per capita

income.

Average per capita GDP in Europe grew by 0.26 log points (or about 30%) between 1500 and 1700.

Based on the coefficients in column 7 of table 4, warfare can explain 27 percent of this increase over time,

and Atlantic coastline another 15 percent. Finally, both variables are important drivers of cross-sectional

variation: If war frequency (Atlantic coastline) increases by one standard deviation, per capita income

growth goes up by .05 (.09) log points.

[Insert Table 4 here]

5.4 Panel

One concern in the cross-sectional analysis is that country-specific characteristics could drive both war-

fare and development. We now address this issue by turning to a panel, which allows us to control for

country fixed effects. As for the cross-section, we start with urbanization as the dependent variable, and

then turn to GDP per capita to check the robustness of our results.

Urbanization as dependent variable

Table 5 presents the panel regressions for country-level urbanization. Data are available in 100 year

intervals between 1300 and 1700. The pooled OLS regression in the first column shows a strong posi-

tive correlation between war frequency and urbanization. All remaining specifications use instruments

for warfare. The panel structure requires an extension of the set of instruments. The ones used so far

– distance to great powers, altitude, distance x