Were railways indispensable for urbanisation?evidence from England and Wales

Dan Bogart∗, Xuesheng You†, Eduard Alvarez‡, Max Satchell§, and Leigh Shaw-Taylor¶

Draft: November 19 , 2018‖

Abstract

England and Wales underwent a remarkable urbanisation during the railway erain the nineteenth century. Yet this economy was already industrialised with well-developed transport infrastructure prior to railways. This raises the question of whetherrailways were indispensable for urbanisation over the medium and long term. In thispaper, we examine the population growth e�ects of being close to railway stationsversus being close to turnpike roads, inland waterways, and ports. Our estimatesshow that being within a short commuting or shipping distance to all infrastructuressigni�cantly increased a locality's population growth from 1841 to 1891. The same istrue for population growth from 1891 to 2011. Across numerous speci�cations, we �ndthat railways had the largest growth e�ects, but turnpike roads and inland waterwayshad signi�cant e�ects too, and even more so for ports. Our estimates contribute to adeeper understanding of the spatial patterns of growth during the industrial revolutionand the e�ects of transport infrastructure on long-run urbanisation.

Keywords: Urbanisation, railways, transport, spatial reorganizationJEL Codes: N4, O18, R11

∗Corresponding author. Associate Professor, Department of Economics, UC Irvine, dbogart@uci.edu†Research Associate, Faculty of History, University of Cambridge, xy242@cam.ac.uk‡Senior Lecturer, Economics and Business, Universitat Oberta de Catalunya, ealvarezp@uoc.edu§Research Associate, Dept. of Geography, University of Cambridge, aems2@cam.ac.uk¶Senior Lecturer, Faculty of History, University of Cambridge, lmws2@cam.ac.uk‖Data for this paper was created thanks to grants from the Leverhulme Trust (RPG-2013-093), Transport

and Urbanization c.1670-1911, NSF (SES-1260699), Modelling the Transport Revolution and the IndustrialRevolution in England, the ESRC (ES 000-23-0131), Male Occupational Change and Economic Growth inEngland 1750 to 1851, and ESRC (RES-000-23-1579) the Occupational Structure of Nineteenth CenturyBritain: Grant. We thank Walker Hanlon, Gary Richardson, Petra Moser, Kara Dimitruk, Arthi Vellore,William Collins, Jeremy Atack, Alan Rosevear, and Elisabet Viladecans Marsal for comments on earlierdrafts and seminar participants at UC Irvine, UC San Diego, NYU, Florida State, Trinity College Dublin,Queens Belfast, the University of Los Andes, Vanderbilt, and EHA Meetings. We also thank Cran�eldUniversity for share their soils data.

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1 Introduction

Improvements in transport infrastructure can substantially change trade and travel pat-

terns. However, it is not obvious that transport improvements, even large ones, signi�cantly

change urbanisation. Population may continue to cluster around older transport infras-

tructures that remain in use or get transformed to new uses through technological change.

In this paper, we use the lens of history to examine how a large-scale transport improve-

ment�the railway�changed the population geography of England and Wales relative to

previous infrastructures. There is a broader literature on whether railways were crucial (or

even indispensable) to economic development in the nineteenth century and over the longer-

run.1 England and Wales is an interesting case because it was already industrialised when

railways started spreading in the 1830s. It had large secondary employment compared to

other economies and was more urbanised with high levels of migration.2 This economy also

had well developed transport infrastructure before railways, including a large network of

ports, roads, navigable rivers, and canals.

There is a long-standing debate on the impact of railways in England and Wales. One

argument is that canals, roads, and ports helped determine the location of new urban

centers in the eighteenth century and these centers persisted into the railway era. A related

argument is that shipping and inland water transport remained competitive with railways on

bulky-low value goods, like coal, and hence continued to in�uence the location of population.

The opposing argument notes that railways generally provided superior transport services

compared to preexisting modes. This view sees railways as shaping location within major

urban centers, including their suburbs.3

We examine the medium and long-run population growth e�ects of being within a short

commuting or shipping distance to railway stations versus being within the same distance to

turnpike roads, inland waterways, and ports. We use a new data set with local populations

in every decennial census year from 1801 to 1891 and in 2011. Our new spatial units are

consistent across time and are 15 square km on average. They are similar to parishes and

townships, the smallest places reported in the British Census.4 We also incorporate GIS

data on railway lines and stations, turnpike roads, ports, and inland waterways. Most of

1For example, see foundational papers by Fogel (1964) and Fishlow (1965). For more recent studies seeBerger and En�o (2015), Hornung (2015), Jedwab, Kerby, and Moradi (2015).

2See Shaw-Taylor and Wrigley (2014) for an overview of occupational structure and urbanisation. SeeRedford (1976) and Long 2005) for studies on migration.

3See Hawke (1974), Dyos and Aldcroft (1974), Simmons (1986), Leunig (2006), Crafts and Mulatu (2006),Armstrong (2009), Kellet (2012), Maw (2013), Crafts and Wolf (2014).

4Unfortunately, our population data do not include Scotland or Ireland, and thus we cannot make �rmstatements about the UK.

these networks are observed between 1830 and 1860, but for some we have earlier dates. The

networks are created from historical maps and allow us to measure the distance between

units and infrastructure with great precision. Finally, we add geographic characteristics,

like elevation, ruggedness, soils, rainfall, temperature, coastline, and coal.

Our main speci�cation is a long-di�erence, where unit population growth from 1841 to

1891 is regressed on indicators for being within 2 km of infrastructures. 2 km corresponds to

30 minutes walking distance, which is approximately the average commuting time in devel-

oped economies today.5 The baseline speci�cation also includes geographic and structural

controls, like population density and occupational shares c.1840, pre-trends in population

growth, along with registration district �xed e�ects. Registration districts are about 250

square km on average and encompass our spatial units. That implies we are controlling for

unobservable factors common to all units within a relatively small area.

We further address endogeneity of railways using propensity score matching and instru-

mental variables (IV). For the IV, we construct a Least Cost Path (LCP) connecting large

towns in 1801 and incorporating the added costs of building railways over rugged terrain.

Proximity to the LCP is a good instrument because it identi�es units that were close to

stations mainly because they were near favorable routes for connecting large towns.6

Our �rst main �nding is that proximity to railway stations had a large e�ect on pop-

ulation growth between 1841 and 1891. This result is consistent across all speci�cations,

including IV. In our preferred speci�cation, being within 2 km of a railway station increased

unit population growth by 15.9 percentage points (pp) over 50 years, or an increased growth

rate of 0.3% per year. To put this estimate into perspective, the total population in Eng-

land and Wales increased by 79 pp between 1841 and 1891. The average population growth

across all units was 1 pp, which is equivalent to a 0.02% annual growth rate.

Our second main �nding is that proximity to pre-rail infrastructures also had a large e�ect

on population growth between 1841 and 1891. Being within 2 km of an inland waterway

(turnpike road) increased population growth by 5.6 pp (3.8 pp). We also �nd that being

within 4 km of a port increased population growth by 15.5 pp, which is similar to railways.

Separating the e�ects across time reveals that railways had a much larger e�ect than

inland waterways and turnpike roads from 1841 to 1871. Railways were a strong substitute

for roads and inland waterways initially, but by 1891 the latter gained new users like om-

5The US census reports that commuting times in US cities average 26.1 minutes. See U.S. Census Bureau,2012-2016 American Community Survey 5-year estimates.

6Our methodology draws on the so-called inconsequential place approach and other studies which leastcost paths as instruments for infrastructure. See Chandra and Thompson (2000), Michaels (2008), Faber(2014), and Lipscombe et. al. (2013).

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nibuses and steamboats. Port e�ects are largest from 1841 to 1871 and less signi�cant by

1891. Coastal shipping was highly productive in the mid-1800s and was crucial in supplying

London's coal. But coastal shipping increasingly lost its market share to railways and only

some ports gained from international shipping.

The third main �nding is that units within a short distance to all infrastructures con-

tributed to higher population growth between 1891 and 2011. The long run e�ects are

sizable. A one standard deviation change in proximity to 1851 railway stations accounts for

0.161 standard deviations of growth. The same for ports, turnpike roads, and inland water-

ways are 0.078, 0.044, and 0.065 standard deviations. Together our results show that railways

were the most important driver of long-run urbanisation among the historic infrastructures.

However, railways were not indispensable for all growth because pre-rail infrastructures also

made signi�cant contributions.

There is a remaining question as to whether units close to infrastructures pulled popu-

lation from areas more distant and grew at their expense. In extensions, we use units more

than 10 km from infrastructures as the control group. For railway stations, we �nd more

growth between 0 and 6 km distance, but there was no di�erence in growth for units between

6 to 10 km from stations. Thus, we do not �nd any evidence that railways contributed to

relative population declines just beyond the commuting zone measured by 6 km. Neverthe-

less, we still think railways pulled population near stations. There are two reasons. First,

migration rates were very high in nineteenth century England (Long 2005). Second, we use

additional data sources to show that proxies for migration, like the Irish born population

percentage, increases more near railway stations. Also, fertility, another driver of population

growth, decreases more near railway stations.

The previous �ndings raise another question: did railways or other infrastructures reor-

ganize population with little impact on productivity? In extensions, we provide evidence

railways increased population growth by 25 pp for units at the 75th percentile of 1841 pop-

ulation density, 15 pp for units at the 50th percentile, and 8 pp at the 25th percentile. The

same is true for inland waterways, although to a lesser extent. This heterogeneity suggests

that railways and waterways attracted migrants to localities that were more productive.

Some supporting evidence suggests moving a worker from a unit in the 50th to the 85th per-

centile of population density increased their wages by 6.8%. Over the longer term, we think

the higher population and productivity near early infrastructures attracted new investments

and technologies and hence attracted even more migrants during the twentieth century. In

other words, infrastructure, technology, and migration were reinforcing processes.

Our results contribute to a broader literature on the spatial patterns of growth during

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the industrial revolution. A wide range of factors are discussed like endowments, markets,

and human capital.7 Our new data set can test many growth channels. Here we show that

transport infrastructures had signi�cant e�ects on population growth. But our analysis and

data also document the importance of other factors like coal, climate, and ruggedness.

We also add to the large literature on railways and nineteenth century growth.8 Perhaps

our main contribution is to reemphasize the importance of comparing railways with inland

waterways, roads, and ports. Modal substitution and complementarity are central to the

analysis of any transport improvement.

Finally, our study contributes to the literature on infrastructure and urbanisation in

contemporary contexts.9 Over the last 50 years there has been a dramatic rise in urbanisation

across the world. Given the signi�cant social and economic implications, it is useful to look

at history. The English and Welsh case shows that multiple infrastructures can evolve and

in�uence urbanisation long into the future.

2 Background on transport infrastructure

England and Wales (EW) had a well-developed transport network long before its railway

network grew. Figure 1 shows the length of turnpike road, inland waterway, and railway

networks from 1700 to 1890.10 In this section, we discuss each of these networks and ports.

As early as 1680 EW had about 12,000 km of main roads.11 But they were in poor

condition and local governments, then in charge, had little capability to improve them. As

an alternative, EW turned to using tolls and non-governmental organizations called turnpike

trusts. Their powers came from an act of parliament. Acts named local landowners and

merchants to serve as trustees. Parliament o�ered little in subsidies. Locals purchased

bonds to �nance improvements and were repaid using toll revenues.

The �rst trusts generally improved the main roads already in place. Later trusts extended

the road network and transformed dirt paths into roads suitable for wheeled tra�c. As �gure

1 shows the turnpike network grew from about 8000 km in 1750 to about 38,000 km in 1830.

7See Fernihough and Hjortshøj O'Rourke (2014), Crafts andWolf (2014), Klein and Crafts (2012), Becker,Hornung, and Woessmann (2011).

8For previous studies on English and Welsh railways see Hawke (1974), Leunig (2006), Casson (2013),Gregory and Marti Henneberg (2010), Alvarez et. al. (2013), and Heblich, Redding, and Sturm (2018),who focus on London. For other countries see Berger and En�o (2015) for Sweden, Tang (2014, 2017) forJapan, Hornung (2015) for Prussia, Atack, Bateman, Haines, and Margo (2010), Attack and Margo (2011),Donaldson and Hornbeck (2016), and Hodgson (2018) for the US, and Donaldson (2014) for India.

9See Redding and Turner (2015) for an overview. Some papers of related interest include Duranton andTurner (2012), Faber (2014), Jedwab et. al. (2015), Storeygard (2016), and Baum-Snow et. al. (2017).

10Network maps are available at https://www.campop.geog.cam.ac.uk/research/projects/transport/data/11These are documented in Ogilby's Britannia Atlas. See Satchell (2017) for a description of these roads.

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Figure 1: Evolution and size of infrastructure networks in England and Wales 1700-1890

Sources: see data section.

At their peak there were approximately 1000 di�erent trusts. They managed all main roads,

although some turnpike roads could be considered secondary in importance.12

Many users of turnpike roads obtained transport services from public carriers and coach-

ing companies. How did they bene�t from turnpike roads? Transport costs could have

increased because of the tolls and the localism of trusts, but that did not happen.13 The

shift to �y-by-night services and stagecoaches with steel springs meant that passenger travel

times fell substantially between 1750 and 1820. Real freight rates also fell by over 40% as

wagons got bigger and load sizes increased. The growing use of stagecoaches and wagons

led to the concentration of economic activity around turnpike roads.14

Turnpike trusts faced a crisis when railways were widespread. The �nances of many

trusts deteriorated and most stop functioning by the 1870s (see their decline in �gure 1).

Responsibility for maintaining turnpike roads passed to newly formed highway districts and

county councils.

The inland waterway network developed at the same time as turnpike roads. Around

1700 EW had a large system of navigable rivers including the Thames, Severn, Great Ouse,

12For a summary see Bogart (2017).13For a summary of the e�ects of turnpike trusts see Bogart (2005).14See Bogart (2009) and Pawson (1977) for this evidence.

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and Trent (Willan 1964). River navigations, or improved rivers which bypassed di�cult

sections, were added between 1700 and 1750. Canals or arti�cial waterways were built

between 1760 and 1830. Like turnpike roads, river navigations and canals were authorized

by acts of parliament (Bogart 2017). Acts granted authority to companies and included

procedures to negotiate the purchase of land. Most canals required many investors and were

organized as joint stock companies.

By 1830 there were several long-distance canals linking important centers. One example

is the Leeds and Liverpool Canal, which connected the leading woolen and cotton textile

towns. Another example is the Grand Junction Canal, which shortened the waterway dis-

tance between London and Manchester. Independent carriers were hired by individuals and

�rms to provide freight services on canals. Like road carriers, they relied on horsepower to

draw their boats. Nevertheless, the e�ciency of hauling over water brought low cost trans-

port to inland regions. Canals were especially important in the movement of coal.15 As one

illustration, the price of coal in Manchester fell by half after the completion of the nearby

Bridgewater Canal in 1761. Some historians argue that canals led to the development of

inland industrial centers by providing cheap fuel (Maw 2013, Crafts and Wolf 2014).

There was also signi�cant investment in ports. It is estimated there were 391 acres of wet

dock space and 50 harbors in 1830. By contrast, England had no wet docks and a handful

of harbors in 1660 (Pope and Swann 1960). The ports of Liverpool and London provide two

illustrations. In Liverpool, dock acreage increased 11-fold between 1710 and 1830, including

the �rst commercial wet dock. The investment was �nanced by Liverpool merchants who

wanted to facilitate the import of cotton and foodstu�s. London was a center for domestic

and international trade, but there was little investment in its ports between 1700 and 1799.

Then there was a dock building boom from 1799 to 1825 which transformed the capacity of

the capital port (Dyos and Aldcroft 1974, p. 58).

Port infrastructures complemented improvements in shipping technology. After 1800

sailing vessels became larger and more durable with metaled hulls. Sails and rigging also

improved. One indication is the greater speeds achieved by sailing vessels in the early 1800s

(Solar 2013). The arrival of the steamship was even more revolutionary, although its impact

was delayed until the 1860s. Before that steamships were expensive and not as cost e�cient

as sailing ships (Dyos and Aldcroft 1974, p. 257). Improvements in engine e�ciency, steel

hulls, and propellers eventually turned the tide. Steamship capacity exceeded sail for the

�rst time in 1883. Steamships would go on to revolutionize trade and travel across the

oceans (Pascali 2017). However, coastal sailing vessels continued at many ports (Armstrong

15See Turnbull (1987) and Bogart, Lefors, and Satchell (forthcoming) for a discussion of canal carriers.

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2009, Langton and Morris 2002).

The �rst steam powered rail service open to the public came in 1825 in the northern

coal mining region between Stockton and Darlington. In 1830, the Liverpool and Manch-

ester railway opened to facilitate passenger tra�c. The rail network expanded dramatically

following the `Mania' of the mid-1840s. The signi�cance of the Mania can be seen in Figure

1 through the growth of track mileage. By 1851 regional rail networks had formed around

the large towns in addition to trunk lines connecting larger towns.16

Railways were built and operated by joint stock companies. They provided passenger

and freight services directly to customers. Passengers accounted for most revenues initially,

but after 1850 freight accounted for more. One of the most di�cult challenges facing railway

companies was their high construction costs. A key factor was the route of their lines. A

distinction was made between the �original line,� which often aimed to connect large trading

towns, and the �branch lines,� which linked smaller towns to the original lines. Railway

companies preferred original lines whenever possible. One promoter advised the following,

�stick to the original line; keep down the capital and let competing schemes do their worst�

(quoted in Simmons 1986, p. 271).

Railway's impact on the EW economy is often emphasized by historians. Dyos and

Aldcroft (1974, p. 229) argue that urban growth was the most `conspicuous product of

railway development.' Their impact seems to have grown over time as regulations forced

railway companies to provide transport to lower socioeconomic groups. The Cheap Trains

Act of 1883 made daily workman's trains mandatory and led to lower commuting fares.

Despite the popular view that railways were economically crucial, there is a debate as

to whether they signi�cantly changed the location of population and economic activity.

Central to this debate is the degree of substitution or complementarity between railways

and preexisting modes. We now turn to this issue.

3 Modal substitution and complementarity

In this section, we de�ne how transport modes can be substitutes or complements and

we brie�y examine evidence from the literature. The standard mode choice model considers

a traveler or shipper who has N transport options (i.e. modes).17 Each mode has a set of

attributes like the fare, travel time, and convenience. A traveler will also have an idiosyn-

cratic preference yielding an individual utility from each transport mode Ui. The traveler

will choose mode i if Ui>Uj for all j 6= i.16For the literature on the mania see Casson (2009), Odlyzko (2010), Campbell and Turner (2012, 2015)17See Small (2013) for an overview of transport demand.

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Modal substitution occurs if the demand for transport mode i decreases when the fare or

travel time of another mode j decreases. Consider a case where a new mode is better than

existing modes on all attributes. Only those travelers with a high idiosyncratic demand will

use the old mode. Every other will shift to the new. We call this `complete' substitution.

There is another case where the new transport mode is better on some attributes. Say

the new mode o�ers lower travel time than an existing transport mode, but its fare is larger.

In that case, there will be some travelers that shift to the new because they value time more

and others will continue to use the old because they are more fare sensitive. We call this

`partial' substitution. It implies both modes co-exist in a market. High �xed costs can also

lead to co-existence because it prevents a mode from being available to all travelers. In this

case, one could observe two modes in use even though one is better on all attributes.

Transport modes can also be complements, which means the demand for transport mode

i increases when the fare or travel time of another transport mode j decreases. In one case,

di�erent transport modes are links in the same journey. Introducing better attributes on

one link, increases the demand on all links. Complementarity can also arise if the new

mode increases overall transport demand. Here there will be more travel by those who value

attributes of the old.

What does the literature say about substitution and complementarity concerning rail-

ways in EW? It appears railways were a complete substitute for long distance road transport.

Railways o�ered faster services at less than half the fares and freight rates. As a result, long-

distance coaching and road freight services were largely displaced by the 1850s.18

There is a counter-argument that railways could not be built everywhere due to �xed

costs. This allowed some short-distance road transport to continue. There was also inno-

vation in road. The omnibus spread in the mid 1800s. It carried more passengers at lower

fares than coaches of old. Highway districts and county councils also assisted by improving

the former turnpike roads (Dyos and Aldcroft 1974, p. 241).

The standard view is that most canals failed to compete with railways on long distance

tra�c because of their slow speed. Some tried to compete on cost, but the lack of coordi-

nation led many canal companies to sell out to railways. In 1883 half of inland waterway

mileage was leased or owned by railway companies. The remaining canals served short dis-

tance tra�c in industrialised areas. There is some evidence for a canal revival after the

1870s. New regulations helped by requiring canals to publish through rates on long distance

journeys and by limiting railway control. The application of steam power to canal boats

18Between 1845 and 1850, the number of passenger journeys by rail increased by 117%, and again by 65%between 1850 and 1855 ( Mitchell 1998).

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was another factor (Boughey and Had�eld 2012).

Railways are thought to have been a partial substitute for coastal shipping. For example,

railways gained in the biggest market�the transport of coal to London. In 1850, 98.4% of

coal imported into London came by coastal ship. By 1870 the rail share was 55.7% and

in 1880 it was 62%.19 Armstrong (2009) argues that steamships halted the further decline

in coastal shipping. However, the extent to which the two modes co-existed is debatable

because many ports came under the authority of railways (Dyos and Aldcroft 1974).

In the case of international shipping, railways were a complement. There was a tremen-

dous growth in foreign trade from the 1840s, especially in grain (O'Rourke 1997). Sailing

ships and then steamships transported the grain from the Americas, India, and Russia to

EW, where it was transported inland by rail. Hawke (1970, p. 128) estimates that imports

represented more than half of all wheat hauled by English railways in 1865. Some would

even argue that railways and shipping created the world grain market together.

4 Theoretical and empirical frameworks

Our main goal is to identify the relative importance of rail versus pre-rail infrastructures

in nineteenth century population growth in EW. This section discuss how we adapt common

theoretical and empirical frameworks for our research question. Redding and Turner (2015)

summarize a theoretical model, which links transport infrastructure and location of economic

activity. They show equilibrium population in any location is increasing in the quality of its

commuting technology and its �rm and consumer market access. Consumer market access

is measured by the variety of goods available and the trade costs of shipping those varieties

to the location. Firm market access is a weighted sum of �rm demands and depends on the

cost of shipping goods to other markets. Better transport infrastructure plays a role in this

model by reducing trade costs and hence increasing market access for some locations. Better

infrastructure also reduces commuting time and hence increases e�ective units of labor.

Reading and Turner (2015) argue that a fairly standard regression speci�cation provides

a reduced form version of the model. City i population in year t, Yit, is regressed on a

measure of transport infrastructure access, such as an indicator for connection to a highway

network dit, plus time-varying controls and location and time speci�c �xed e�ects. Duranton

and Turner (2012) adapt a similar speci�cation to incorporate a partial adjustment process

where population growth is a function of the di�erence between a city's actual population

and its equilibrium or target population. The estimating equation becomes

19These �gures are reported in Hawke (1970, p. 168).

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yit+1 − yit = λyit + adit + cxit + εit (1)

where the left hand-side variable yit+1− yit is the log di�erence in city population between tand t+1. The right hand side includes the log of initial population yit , indicators for being

connected to a transport network dit, and controls xit.

Speci�cation (1) is appealing for our study because we can estimate the growth impacts of

railways, turnpikes, ports, and waterways by including indicator variables for being within a

short commuting or shipping distance of these infrastructures. If the railway was a complete

substitute for say canals, then we should expect zero e�ect for the inland waterway indicator

all else equal. The reason is that all shippers, outside of idiosyncratic types, would have

preferred using railways. Over time individuals should migrate from areas with canals to

areas with railway stations leading to population growth near the latter. By contrast, if

railways were a partial substitute say for canals, then being near inland waterways should

contribute to some growth. Users that preferred cheap water transport would migrate to

areas with rivers or canals and users that preferred the speed of railways would migrate to

stations.

There are two limitations to speci�cation (1). First, the indicator variable for infras-

tructure access does not account for network structure. Some studies address this issue by

estimating market access, or population-weighted inverse trade costs between all locations

(see Donaldson and Hornbeck 2016). We do not follow the market access approach because

it estimates trade costs for a single user type. In our case, multiple users appear to be

important. Also, the market access approach identi�es the e�ects of trade costs without

di�erentiating by infrastructure type. Therefore, the methodology does not easily lend itself

to identifying the e�ects of railway stations, roads, inland waterways, and ports.20

Second, speci�cation (1) cannot account for spatial reorganization. Localities just beyond

a short commuting distance of infrastructures may not be a clean control group for localities

within the commuting distance. They are potentially treated by infrastructure and could

lose population. Therefore, estimates based on (1) identify di�erences in relative growth, not

absolute growth. Below we address this issue further by studying di�erent control groups

and by looking at migration proxies near railways. We also examine heterogeneity according

to initial population density.

20Also as our data includes population for 9489 units, we would need to calculate trade costs for morethan 45 million unit-pairs. That presents a major computational issue.

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5 Data

Our population data come from British censuses, available every decade starting in

1801. They are digitized at the smallest census place level (e.g. parishes and townships)

up to 1891.21 The census published the same for occupational counts starting in the early

nineteenth century. The counts for 1851 and 1881 are available through the Integrated

Census Micro data project (Schürer and Higgs 2014). The census places with population

and occupations from 1801 to 1891 are not always the same across time. To address boundary

changes, researchers at Cambridge University have created consistent spatial units between

1801 and 1891 and linked them with census population data.22 Using similar techniques, we

create 9489 consistent units mapping population from 1801 to 1891 and male occupations

from 1851 to 1881.23 We call these `units' for short. Units are 15 square km on average

and they belong to a larger jurisdiction called registration districts. There are 616 unique

registration districts in our data and they average 250 square km.

Very long-run outcomes are studied by merging our 9489 historical units with 34,753

Lower Super Output Areas (LSOAs) with population in 2011.24 We use the intersect function

in ArcMap applied to the boundary lines of LSOAs and the boundary lines of our units.

The population variables are expressed in natural log di�erences over time (see table 1).

The mean 1841 to 1891 log di�erence is 0.01, which implies a mean population growth of

1 percentage point between 1841 and 1891. The mean is low in part because some units

in central London experienced large population declines due to out-migration of residents.

Overall there was an increase in urbanisation. The share of the population living in units

with at least 400 persons per square km increased from 42% in 1841 to 68% by 1891.

Our infrastructure data includes GIS shape�les for turnpike roads in 1830, inland wa-

terways in 1680 and 1830, and railway lines and stations in every census year starting in

1831.25 We also have GIS data on the main roads in 1680 as surveyed by John Ogilby.26 In

all cases, the networks are created using historical sources, improving their accuracy.

21The Cambridge Group for the History of Population and Social Structure kindly provided this data.22For details see https://www.campop.geog.cam.ac.uk/research/occupations/datasets/catalogues/documentation.23Ms Gill Newton, of the Cambridge Group, developed the Python code for Transitive Closure as part

of the research project `The occupational structure of Britain, 1379-1911' based at the Cambridge Group.Xuesheng You implemented this code for this particular paper.

24O�ce for National Statistics ; National Records of Scotland ; Northern Ireland Statistics and Re-search Agency (2017): 2011 Census aggregate data. UK Data Service (Edition: February 2017). DOI:http://dx.doi.org/10.5257/census/aggregate-2011-2.

25See Rosevear et. al. (2017), Martí-Henneberg et. al. (2017a, b),and Satchell, Shaw-Taylor, and Wrigley (2017a, b). For a description seehttps://www.campop.geog.cam.ac.uk/research/occupations/datasets/catalogues/documentation

26For a description of the 1680 Ogilby roads data see Satchell (2017).

11

For ports we draw on a list provided in The Shipowner's and Shipmaster's Directory pub-

lished in 1842. This source identi�es 247 ports in use. It also describes whether loading

occurred on the beach and water depths at spring and neap tides. Our baseline model

considers all 247 ports regardless of their features. Thresholds for water depth yielded less

precise results. We also use a source published in 1787, which lists the main ports in 1680

(see Alvarez et. al. 2017).

To analyze infrastructures, a straight line is drawn from the center of each unit to its

nearest station, road, waterway, and port. The unit center corresponds to the market square

if it had a town or the centroid if the unit had no town.27 The mean distance to an 1851

station is 10.4 km (see table 1). The mean distance to a waterway or turnpike road in 1830

was less at 7.2 and 1.9 km. As expected, mean distances to ports were greater, but given

that England had such a large network of ports in 1842 the average was only 30.2 km. We

use these distances to calculate indicators for being close to infrastructures.

An important fact concerns the spread of railway stations over time. In 1841, 1851, and

1861, 4.6%, 13.6% and 19.7% of units had a railway station within 2 km. By 1881 29.9% of

units had railway stations within 2 km.

The geographic data include variables for being on exposed coal�elds, being on the coast,

ruggedness, average rainfall, average temperature, an index for wheat suitability, and the

share of land in 10 di�erent soil types.28 We call these `�rst-nature' variables following the

literature in economic geography (see Fujita et. al. 2001). Coastal is identi�ed using an

intersection of the seacoast with unit boundaries. The ruggedness measures include average

elevation within units, the average elevation slope, and the standard deviation in elevation

slope. See appendix A.2 for details. Rainfall, temperature, and wheat suitability come from

FAO.29 Of special signi�cance, Satchell and Shaw Taylor (2013) identify those areas with

exposed coal bearing strata (i.e. not overlain by younger rocks). Exposed coal�elds were

more easily exploited by early nineteenth century technology compared to concealed coal.30

27We identify if a market existed at some point between 1600 and 1850. This ap-plies to 746 of the 9489 units. It should be noted that little error is introduced by us-ing the market or the centroid since units are so small. For a description of towns seehttps://www.campop.geog.cam.ac.uk/research/occupations/datasets/catalogues/documentation

28Soils data (c) Cran�eld University (NSRI) 2017 used with permission. The 10 soil categories are basedon Avery (1980) and Clayden and Hollis (1985). They include (1) Raw gley, (2) Lithomorphic, (3) Pelosols,(4) Brown, (5) Podzolic, (6) Surface-water gley, (7), Ground-water gley, (8) Man made, (9) peat soils, and(10) other. See http://www.landis.org.uk/downloads/classi�cation.cfm#Clayden_and_Hollis. Brown soilis the most common and serves as the comparison group in the regression analysis.

29See the Global Agro-Ecological Zones data at http://www.fao.org/nr/gaez/about-data-portal/agricultural-suitability-and-potential-yields/en/. We selected low input and rain fed for wheatsuitability.

30For a description see https://www.campop.geog.cam.ac.uk/research/occupations/datasets/catalogues/documentation

12

Table 1: Summary statisticsVariable Obs. Mean Std. Dev. Min Max

Population growth variables

Ln di�. population 1841 to 1891 9489 0.010 0.513 -3.079 4.874

Ln di�. population 1891 to 2011 9488 0.545 0.965 -4.202 5.617

Infrastructure variables

Distance to rail station in 1851 km 9489 10.45 11.065 0.021 73.12

Distance to LCP km 9489 11.86 16.548 0.000 116.3

Distance to inland waterway 1830 km 9489 7.231 6.501 0.000 48.38

Distance to turnpike road 1830 km 9489 1.983 2.458 0.000 22.47

Distance to port 1842 km 9489 30.20 22.81 0.059 99.71

Indicator distance to rail station in 1851

8% of our units are on exposed coal�elds.

We have another set of unit-level variables called `second-nature' factors. These include

distance to one of the ten largest cities in 1801, log population density in 1841, and 1851 male

occupational shares in �ve categories: (1) tertiary, (2) agriculture, (3) secondary, (4) min-

ing/forestry, and (5) unspeci�ed.31 Population density in 1841 varied signi�cantly, although

much was concentrated near large cities, like Manchester and London. Male occupational

structures also exhibit concentration in 1851, especially in secondary employment. The top

1% of units accounted for 57% of male secondary employment in 1851.32

Figure 2 shows the kernel density estimates for the distribution of population growth

from 1841 to 1891 depending on whether units are within 2 km of various infrastructures.

The �rst panel clearly shows that units within 2 km of 1851 railway stations tended to have

higher growth than units more than 2 km from 1851 stations. There were some exceptions

however as growth was sometimes negative for units within 2 km of stations as indicated

by the longer left tail. Panels b to d show a similar pattern for being within 2 km of 1830

inland waterways and turnpike roads and 1842 ports. Hence there is some initial evidence

that railways were one of several infrastructures increasing population growth in the second

half of the nineteenth century.

6 Main results

In this section, we estimate how population growth was a�ected by infrastructures. We

begin by analyzing the following `long di�erences' speci�cation:

yi1891 − yi1841 = β1Iraili1851 + β2Ipre−raili1840 + γxi + εi (2)

where yi1891−yi1841 is the natural log di�erence. The initial year 1841 is chosen because therewere few railway stations open in 1831. 1891 is the last year for which we have historical

data.

One main explanatory variable is Iraili1851 equal to one if unit i is within 2 km of a railway

station in 1851 and 0 otherwise. 1851 is chosen because the rail network underwent its

largest 10-year expansion in the 1840s. As robustness, we check whether station proximity in

earlier or later years changes the conclusions. 2 km is chosen because it takes approximately

30 minutes to walk 2 km. We think 30 minutes represents a typical commute time for

31Here we follow the primary, secondary, and tertiary (PST) coding system described in detail in ShawTaylor et. al. (2014) and Wrigley (2015). We do not code female occupations because there is less agreementin the literature (see You 2014).

32For more details on occupational structure see Shaw-Taylor and Wrigley (2014).

14

Figure 2: The distribution of population growth and infrastructure access

Sources: see text.

individuals who worked near the station or for �rms carting their goods to the station for

quick delivery. However, this assumption is based on limited data, and therefore in a later

section, we consider greater distances.33 Other main explanatory variables are included in

Ipre−raili1840 . They are three indicators identifying whether a unit is within 2 km distance from

turnpike roads, inland waterways, and ports.

There are two sets of control variables included in xi. The �rst nature controls are

listed in table 1 except for the square of temperature and rainfall, which allow for non-linear

e�ects in climate variables. The second nature controls are also listed in table 1. The

log of 1841 population density accounts for the regularity that initially dense units tend

to grow less. The 1851 male occupational shares address the possibility that areas more

specialized in agriculture grow less. Note that roads and canals built in the 1700s may have

33In support of this assumption, Heblich, Redding, and Sturm (2018) use data from a single London �rmto show that 90% of workers lived within 5 km of their residence from 1857 to 1877.

15

caused development by 1841. Therefore, speci�cations with second nature controls hide

some of their e�ects. However, they capture persistent e�ects of roads and canals in the era

supposedly dominated by railways.

Our list of control variables is large, but even so there are some factors that cannot

be measured. We use several approaches to address unobserved heterogeneity. First, we

include registration district �xed e�ects. Districts are approximately 250 square km, and

within such an area there were factors a�ecting growth that are similar across units. Our

second approach recognizes that even within a district there could be unobservable factors

correlated with infrastructures. Some can be captured by a variable for population growth

in the decades before railways. Other approaches include panel regressions, propensity score

matching, and instrumental variables. These approaches are discussed in the next section.

The main coe�cient estimates for equation 2 are shown in table 2. The standard errors

are clustered on registration districts. In column (1), the only explanatory variable is the

indicator for units within 2 km of 1851 stations, which is associated with 24.5 higher log

points of population growth (approximately 28 percentage points or pp). Column (2) adds

indicators for pre-rail infrastructures. Being within 2 km of inland waterways and turnpike

roads has positive and signi�cant e�ects on population growth equal to 9.1 and 6.4 log points

respectively. Being within 2 km of ports is associated with 13.9 higher log points of growth

but the coe�cient is not precisely estimated.

We now consider speci�cations that include more controls. Column (3) in table 2 adds

the �rst nature controls. The estimates for these additional variables are not shown to

save space. Interested readers should consult table 10 in appendix A.3.34 The coe�cients

for railways, turnpike roads, and inland waterways change little. In fact, the estimates

become more precise. But the estimate for ports falls substantially and becomes close to

zero. Examining this speci�cation more closely we �nd that being coastal is correlated with

being within 2 km of a port. We will return to the impact of ports later. The speci�cation

in column (4) adds second nature controls. The estimates are broadly similar except the

railway coe�cient increases in magnitude and the turnpike and inland waterways coe�cients

decrease. The latter makes sense because some of road and waterway's contribution is being

captured by population density in 1841 and occupational shares in 1851. The speci�cation in

column (5) adds 616 district �xed e�ects (FEs). The coe�cients on infrastructures decline

but they remain signi�cant. The speci�cation in (6) adds a control for unit population

growth from 1801 to 1831. The results are nearly identical diminishing concerns about

34Of most importance we �nd that units with coal have 36.7 higher log points population growth from1841 to 1891.

16

pre-trends.

In our preferred model (5), being close to stations increased the annual growth rate by

0.3%, while being close to inland waterways increased the annual growth rate by 0.1%. In

terms of beta coe�cients, a one standard deviation increase in the station variable increases

population growth by 0.106 standard deviations. A one standard deviation increase in the

inland waterway and turnpike variables increased population growth by 0.046 and 0.035

standard deviations. These results imply that in terms of explaining population growth,

being close to railways was more important. Nevertheless, it is striking that roads and

inland waterways had quantitatively signi�cant e�ects even after accounting for railways

and other factors.

Table 2: Access to infrastructures and local population growth: baseline estimates

Dep. var.: unit pop. growth 1841 to 1891 (1) (2) (3) (4) (5) (6)

coe� coe� coe� coe� coe� coe�

variable (std. err.) (std. err.) (std. err.) (std. err.) (std. err.) (std. err.)

Indicator dist. to rail station in 1851

to railway lines were generally close to stations.

A third alternative speci�cation includes an indicator if the unit had more than one

station. For reference 2.4% of units had more than 1 station in 1851. The results in table 11

appendix A.3 show these units had 27 log points higher growth compared to units without

any stations. The coe�cients for one station, inland waterways and turnpike roads are

similar to before. These �ndings make sense since greater station density o�ered more local

and long-distance connections.35

A fourth alternative examines the e�ects of infrastructures over di�erent periods. We

regress population growth from 1841 to 1861 on the same variables including all controls.

The same is done for growth from 1841 to 1871 and so on up to 1841 to 1891. The e�ects of

infrastructure could diminish with time, in which case the coe�cient should stay the same

or increase slightly as the time frame increases. The results are reported in table 3. The

e�ects of railways diminished little. In the speci�cation for 1841 to 1861, the 0.074 coe�cient

implies a 0.35% higher annual growth rate. For 1841 to 1891, the coe�cient 0.159 implies a

0.30% higher annual growth rate.

The e�ects of turnpikes and inland waterways are small and insigni�cant from 1841 to

1871. This era marked the peak of railway in�uence as turnpike and canal companies failed

to compete. However, after 1871 their impact becomes larger and more signi�cant. These

�ndings suggest that turnpike roads and inland waterways were put to new uses after 1871.

The estimated e�ects of ports diminish with time. For example, being within 2 km of

ports increases the annual growth rate by 0.33% up to 1861 and by 0.18% up to 1891. These

�ndings are consistent with (1) shipping playing an important role in the mid-nineteenth

century and (2) railways eventually making inroads into markets previously dominated by

coastal shipping.

35In another related speci�cation, we use log meters of 1851 railway line per square km, log meters of1830 turnpike road per square km, and log meters of 1830 waterway per sq km. The results show a similarimportance of railways. Railways density has a beta coe�cient of 0.144, waterway density has a betacoe�cient of 0.026, and turnpike road density has a beta coe�cient of 0.04.

18

Table 3: Access to infrastructures and local population growth over di�erent periods

Dep. var.: unit pop. growth in 1841 to 61 1841 to 71 1841 to 81 1841 to 91

(1) (2) (3) (4)

coe� coe� coe� coe�

variable (std. err.) (std. err.) (std. err.) (std. err.)

Indicator dist. to rail station in 1851

Table 4: Matching estimator for e�ect of distance to railway stationsUnits within 2km 1851 stations (1 vs. 0)

Covariate Standardized di�erences�raw Variance ratio�raw

Ln pop. per sq. km 1841 1.071 8.184

Has exposed coal 0.291 2.123

Share of 1851 male emp. in agric. -1.137 1.753

Ln di�erence pop. 1831 and 1801 0.230 2.517

N 9,489

Covariate Standardized di�erences�matched Variance ratio�matched

Ln pop. per sq. km 1841 0.007 1.010

Has exposed coal -0.020 0.938

Share of 1851 male emp. in agric. 0.004 0.922

Ln di�erence pop. 1831 and 1801 -0.016 1.153

N 9,485

Units within 2km 1851 stations (1 vs. 0)

Av. Ln di�, pop. 1891 and 1841 Di�. in means�raw data Di�. in means�matched data

(standard error) (robust standard error)

0.010 0.244 0.206

(0.015)*** (0.022)***

N 9,489 9,485

Notes: * p

line connecting them with another town above 5000. But not all large town-pairs would

be connected. Existing levels of trade and communication were often lower between distant

towns or towns of moderate size. A pro�t-seeking promoter would see little value in building

a railway to connect them. We use a simple gravity model (GM) to calculate the relative

value of connecting any town-pairs each with a population above 5000. The equation for

town pairs i and j is GMij =PopiPopjDistij

, where Distij is the straight line distance between

town i and j.

Next we identi�ed a least cost path (LCP) connecting town pairs above a threshold

GMij > 10, 000.38 We assume that in considering their routes, railway companies tried to

minimize the construction costs considering distance and elevation slope. We use construc-

tion cost data for railways built in the 1830s and early 1840s. We also measure the distance

of the lines and total elevation changes between towns at the two ends of the line. The

construction cost is then regressed on the distance and the elevation change to identify the

parameters (the details are in appendix A.1). Based on this analysis we �nd a baseline

construction cost per km when the slope is zero and for every 1% increase in slope the

construction cost rises by three times the baseline (costperkm = 1 + 3 ∗ slope%). Next, weuse this formula to identify the LCP connecting our town pairs above the threshold. The

result is a network of candidate railway lines.

The LCP network is shown in the right of �gure 3. The left shows the real railway

network in 1851. The overlap is fairly high. Locations close to the LCP are also generally

close to railway stations because they were so numerous along the line.

We use an indicator for being within 2 km of the LCP as our instrument for within 2 km

of stations. The exclusion restriction requires that the instrument only a�ects population

growth between 1841 and 1891 through its e�ect on station access. We think this assumption

is plausible under two conditions. First, units containing the town nodes used to construct

the LCP are excluded. They were clearly targeted by railways for their size and possibly

their growth potential. Second, the regression model should contain distance to pre-rail

infrastructures as control variables. If omitted, then one might worry the instrument a�ects

growth partly through road and waterway access.

We provide a `plausibility check' for the exclusion restriction by testing whether less

than 2 km from the LCP is correlated with unit population growth between 1801 and 1831.

The results are shown in table 5. Note in all speci�cations we exclude 364 units within 2

km of the town nodes used to construct the LCP. The standard errors are always clustered

38The 10,000 threshold is arbitrary, but as shown below this threshold does a good job predicting thelocation of lines and stations.

21

Figure 3: The rail network in 1851 and the least cost path (LCP) network

Sources: see text.

on the registration district. In column (1), being within 2 km of the LCP is positively

and signi�cantly associated with higher population growth from 1801 to 1831. Columns (2)

and (3) show the same result holds after including district FEs and �rst nature controls.

The conclusion changes in column (4), which adds pre-rail infrastructure controls. In this

speci�cation, being within 2 km of the LCP is not signi�cantly associated with higher

population growth from 1801 to 1831. In column (5) we add second nature controls and

the results are unchanged. Similar speci�cations use decade population growth (e.g. from

1811 to 1821) as dependent variables. The results are reported in the appendix A.3 table

12. None �nds a large and signi�cant e�ect from being within 2 km of the LCP.

22

Table 5: Pre-trend tests for the validity of instrument distance to LCP

Dep. var.: unit pop. growth 1801 to 1831 (1) (2) (3) (4) (5)

coe� coe� coe� coe� coe�

variable (std. err.) (std. err.) (std. err.) (std. err.) (std. err.)

Distance to LCP for railways

Table 6: Railway stations and population growth: IV estimates

Dep. var.: unit pop. growth 1841 to 1891 OLS IV rail IV rail IV rail, road, water, and port

(1) (2) (3) (4)

coe� coe� coe� coe�

variable (t-stat) (t-stat) (t-stat) (t-stat)

Indicator distance to 1851 railway station

growth potential in the absence of railways.

The �nal IV speci�cation instruments for all infrastructure variables (column 4). The

Kleibergen-Paap F statistic is smaller in this case, so these results need to be interpreted

with caution. The estimated e�ect of being close to stations is very similar, suggesting

our estimate for railways is not a�ected by endogeneity of turnpike roads, waterways, and

ports. These results also show that units close to ports and turnpike roads grow signi�cantly

more even in the IV model. The e�ect of inland waterways are close to zero, but the same

is true in the previous IV speci�cations (see columns 2 and 3 in table 6). Overall the IV

results further con�rm the importance of at least three infrastructures for nineteenth century

growth (ports, turnpikes, and railways).

8 Reorganization and Heterogeneous e�ects

Our analysis thus far does not account for spatial reorganization. Yet there is some

evidence it mattered. One of the leading historians argues "the railway did not necessarily

produce growth in population or business. It might take people or business away (Simmons

1986 p. 16)." Redding and Turner (2015) propose a method to identify reorganization e�ects.

They suggest de�ning a control group more distant from infrastructure and to compare them

with a set of `treated' groups nearby. In our setting one might expect that units just beyond

the 1.5 or 2-hour commuting distance to infrastructures (6 or 8 km) might lose population

due to out-migration to closer units. To identify such an e�ect, we use units beyond 10 km

as the control group. This approach is not perfect because we don't know if units 10 km

away from infrastructures are truly una�ected. Nevertheless, this approach yields insights

on the relative growth e�ects of infrastructure at varying distances up to 10 km.

We estimate a model with �ve distance bins to stations, inland waterways, and ports: 0

to 2, 2 to 4, 4 to 6, 6 to 8, and 8 to 10 km. For turnpikes, around 1% of units were more

than 10 km so we continue to use the simple indicator for being less than 2 km as the only

treatment. The results are reported in table 7. Units 0 to 2 km, 2 to 4 km, and 4 to 6

km from 1851 stations all have higher population growth relative to units more than 10 km

from stations. We also �nd that population growth is not signi�cantly di�erent from zero

in units between 6 and 10 km from stations.

25

Table 7: Population growth at varying distances from infrastructures

coe� coe� coe�

variable (std. err.) variable (std. err.) variable (std. err.)

rail station

and the infant mortality rate (number of children born per 1000 that died before their �rst

birthday) at the sub-registration district level at each decennial census from 1851.40 Sub-

districts are 70 square km on average and equal about 4 or 5 of our units. There is also

data at the sub-district level on the percentage of the population that is Irish born and the

number of working age men per 100 working age women. The percentage born in Ireland

is a good indicator of in-migration. The sex ratio is more subtle. A decline in working age

males to females is thought to have been caused by greater in-migration of young women to

work as servants. Of course, this assumes women are more mobile than men, which is not

true in all cases.

To make use of this data we need to match sub-districts across time. Unfortunately, the

sub-districts are not always spatially consistent. We matched sub-districts in 1851 and 1861

based on name and total land area. At this step, we lose about 8% of sub-districts due to

boundary and name changes. We also link our earlier units to sub-districts to identify which

had at least one railway station in 1851. This second step reduces our sample to about 75%

of all sub-districts based on inconsistency in names.

Table 8 reports speci�cations that regress the change in demographic or migration vari-

ables from 1851 to 1861 on an indicator for having at least one station in 1851.41 Panel A

report speci�cations for the change in fertility. Column (1) includes only the station vari-

able. It shows the fertility rate decreased more in sub-districts with stations. On average

fertility rates change by -0.014 and therefore the coe�cient -0.048 is fairly large. Column

(2) adds a quadratic in sub-district latitude and longitude. The coe�cient on stations is

similar. Column (3) adds county �xed e�ects. Now the coe�cient decreases in size and is

no longer signi�cant. If anything, these results go against population growth near stations

being caused by higher fertility.

Panels B, C, and D analyze changes in infant mortality, the % Irish born, and the male

to female ratio respectively using the same speci�cations. Railways do not have a signi�cant

e�ect on infant mortality in any speci�cation. Changes in the % Irish born are positively

associated with stations in the �rst two speci�cations without county �xed e�ects. The

average change in % Irish born is 0.102 percentage points, indicating a fairly large e�ect

40This data comes from Populations Past. https://www.populationspast.org/imr/1861/#7/53.035/-2.895. This data has been produced by the 'Atlas of Victorian Fertility Decline' project (PI: A.M. Reid) withfunding from the ESRC (ES/L015463/1), using an enhanced version of data from Schurer, K. and Higgs, E.(2014). Integrated Census Microdata (I-CeM), 1851-1911. [data collection]. Colchester, Essex: UK DataArchive [distributor]. SN: 7481, http://dx.doi.org/10.5255/UKDA-SN-7481-1. Dataset last updated: 24thMay 2018.

41We also use the data to run a regression of sub-district population growth from 1851 to 1861 on anindicator for having at least one station in 1851. The results are reported in table 13 appendix A.3. Theycon�rm our earlier conclusion that being near railway stations increased population growth.

27

from stations. Changes in the male to female ratio are negatively associated with railway

stations in the �rst two speci�cations, but again the estimate is not signi�cant with county

�xed e�ects. Overall these results support the argument that railways grew population

through in-migration with the caveat that the estimates are not always precise.

Table 8: Stations, demography, and migration: estimates for sub-districts

Panel A ∆ fertility rate Panel B ∆ inf. mortality rate

(1) (2) (3) (4) (5) (6)

coe� coe� coe� coe� coe� coe�

variable (t-stat) (t-stat) (t-stat) (t-stat) (t-stat) (t-stat)

Indicator for station in 1851 -0.0487** -0.0662*** -0.0284 0.0348 -0.0296 -0.237

(0.0232) (0.0226) (0.0219) (0.282) (0.290) (0.402)

Quadratic in lat. and long. No Yes Yes No Yes Yes

County �xed e�ects No No Yes No No Yes

N 1,568 1,568 1,568 1,360 1,360 1,360

Panel C ∆ % Irish born Panel D ∆ male to female ratio

(7) (8) (9) (10) (11) (12)

coe� coe� coe� coe� coe� coe�

variable (t-stat) (t-stat) (t-stat) (t-stat) (t-stat) (t-stat)

Indicator for station in 1851 0.141** 0.127*** 0.0540 -1.130** -1.248** -1.045

(0.0533) (0.0445) (0.0494) (0.519) (0.486) (0.681)

Quadratic in lat. and long. No Yes Yes No Yes Yes

County �xed e�ects No No Yes No No Yes

N 1,591 1,591 1,591 1,340 1,340 1,340

Notes: * p

Figure 4: Heterogeneity with initial population density

Sources: see text.

The estimates show that being close to railway stations had a signi�cantly larger growth

e�ect for units with medium to large population density. To illustrate, we plot our predicted

population growth for units between the 5th and 95th percentiles in 1841 population density.

One prediction is for units less than 2 km from 1851 stations and the other is for units more

than 2 km from stations (see �gure 4). Railways have their largest e�ect for population

densities between the 75th and 90th percentiles. The increase in population was around 25

percentage points for these units. At the 50th percentile railways increased population by

around 16 pp. To put these �gures into perspective, a unit at the 85th percentile of 1841

population density was 183% more populous than a unit at the 50th percentile. How did this

density matter? Leunig and Crafts estimate that doubling a town's population increased its

wages by 11% in 1868.43 Using this �gure, if railways reallocated population from the 50th

to the 85th percentile then it would raise their wages by 20%�a signi�cant change.

We use a similar methodology to test for an interaction e�ect between proximity to inland

waterways and 1841 population density. The predictions are summarized in the right-hand

panel of �gure 4. They also show bigger e�ects on units around the 75th percentile. It

appears that inland waterways also had productivity enhancing e�ects on migrants.

9 Persistence results

We have shown that units within a short commuting or shipping distance of infrastruc-

tures c.1840 a�ected population growth in the nineteenth century. Now we want to know if

they a�ected population growth in the twentieth century and up to the present. This issue

43See Crafts and Leunig, 'Transport improvements'.

29

is related to the impact of adopting railways at an early stage. Previous studies show that

some infrastructures, like railways, have signi�cant persistent e�ects.44 If turnpike roads,

waterways, and ports also have signi�cant persistent e�ects then this would cast further

doubt on railways being indispensable for all urbanisation.

Persistence is tested using our historical units merged with Lower Super Output Areas

(LSOAs) in 2011. We estimate the following `very' long di�erences speci�cation

yi2011 − yi1891 = β1Iraili1851 + β2Ipre−raili1840 + γxi + εi (4)

where the dependent variable yi2011−yi1891 measures the log di�erence in population 1891 to2011. The variables Iraili1851 and I

pre−raili1840 are indicators for being within 4 km of mid-nineteenth

century infrastructures.

The results are reported in table 9. Column (1) includes 1841 population density as a

control along with all the others in table 1. Column (2) shows a similar speci�cation but

replaces 1841 with 1891 population density as a control. The results are similar. In (1)

being within 4 km of 1851 railway stations increases population growth by 29.4 log points

from 1891 to 2011, or 0.21% higher annual growth. The coe�cients also reveal that being

within 4 km of turnpike roads and inland waterways increased annual growth by 0.10%. The

same for ports increased annual growth by 0.18%. The beta coe�cients show that railways

explain more of the variation in population growth (0.14 for railways compared to 0.058,

0.045, and 0.066 for waterways, turnpikes, and ports). Perhaps more striking is how much

growth is explained by the pre-rail infrastructures. While we cannot trace out exactly why

pre-rail matters so much up to the present, it is likely their uses evolved with the modern

era. For example, inland waterways are now seen as amenities in many areas.

44See Bleakley and Lin (2011), Redding, Sturm, and Wolf (2011), Garcia-López et. al. (2015), Jedwaband Moradi (2016).

30

Table 9: Infrastructure access and population growth over the very long run

Dep. var.: unit pop. growth 1891 to 2011 (1) (2)

OLS OLS

coe� coe�

variable (std. err.) (std. err.)

Indicator distance to 1851 railway station

Previous studies have not been able to identify the e�ects of all infrastructures and not at a

disaggregated level. Using our preferred OLS estimates, a counterfactual calculation implies

that if no units were within 2 km of railways then aggregate population growth would have

been 20% lower between 1841 and 1891. A di�erent counterfactual implies that if no units

were within 2 km of railways, waterways, or turnpike roads then aggregate growth would

have been 35% lower.

Third, we provide evidence that railways mainly grew population by attracting migrants.

Higher fertility near stations, another candidate mechanism, is rejected by the data. How

then did railways grow the economy beyond providing a new transport mode with better

attributes? Railways increased productivity by moving the population from low to high

density areas, where agglomeration was present.

Fourth, we show that population growth in England and Wales between 1891 and 2011

was in�uenced by infrastructures in the mid-nineteenth century. This suggests the policy

decisions made today regarding transport infrastructure will have e�ects on urbanisation for

decades, perhaps even centuries.

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A Appendices:

A.1 The least cost path instrument

In this appendix, we describe the instrument for distance to railway stations. The �rst

step is to select the nodes of the hypothetical network and then which nodes will become

origins and destinations connected by the least cost path (LCP). The candidate nodes are all

the towns with a population over 5,000 inhabitants in 1801. These were the major population

centers. Each pair of towns, both with a population above 5000, is a potential origin and

destination for railway lines. A gravitational model selects the origins and destinations that

will be connected based on an approximation for the value of trade between the potential

origin and destination. We assume the value of connecting an origin and destination pair is

given by GMij =PopiPopjDistij

, where GMij is the gravitational potential between town i and j,

Popi is the 1801 population of town i, and Distit is the straight line distance between i and

j. We chose the town pair i and j as origins and destinations in our LCP if GMij > 10, 000.

The second step is to identify the LCP connecting our nodes. The main criteria used

to plan linear projects is usually the minimization of earth-moving works. Assuming that

the track structure (composed by rails, sleepers and ballast) is equal for the entire length,

it is in the track foundation where more di�erences can be observed. Thus, terrains with

higher slopes require larger earth-moving and, in consequence, construction costs become

higher (Pascual 1999, Poveda 2003, Purcar 2007). The power of traction of the locomotives

and the potential adherence between wheels and rails could be the main reason. Besides,

it is also important to highlight that having slopes over 2% might imply the necessity of

building tunnels, cut-and-cover tunnels or even viaducts. The perpendicular slope was also

crucial. During the construction of the track section, excavation and �lling have to be

balanced in order to minimize provisions, waste and transportation of land. Nowadays,

bulldozers and trailers are used, but historically workers did it manually. It implied a direct

linkage between construction cost, wages and availability of skilled laborers. In fact, it is

commonly accepted in the literature that former railways were highly restricted by several

factors. The quality of the soil, the necessity of construction tunnels and bridges or the

interference with preexistences (building and land dispossession) were several. Longitudinal

and perpendicular slope were the more signi�cant ones and we focus on these below.

39