RAILWAYS AND CITIES IN INDIA

A BSTRACT . Using a new dataset on city populations in colonial India, we show that the railroad network increased city size in the period 1881 to 1931. Our baseline estimation approach includes fixed effects for city and year, and we construct instrumental variables for railroad proximity based on distance from a least cost path spanning cities that existed prior to the start of railroad construction. Cities that increased market access due to the railroad grew. The small and heterogeneous effects we find are driven largely by cities that were initially small and isolated.


INTRODUCTION
How did the spread of the railroad shape the size of cities in colonial India? Governments in developing countries today make large investments in transportation infrastructure; in India, for example, the government's flagship road-building program aims to connect more than 175,000 settlements to all-weather roads. 1 Evidence of the impact of these investments, however, is often limited to developed countries and can only consider outcomes over a short time horizon, creating scope for historical evidence to improve our understanding of their effects (Berger and Enflo, 2017;Donaldson and Hornbeck, 2016). The growth of cities is a particular challenge in developing countries like those we consider; the overwhelming bulk of urbanization over the next three decades will occur in Asia and Africa, where congestion, contagion, and other difficulties of density are particularly acute (Bryan et al., 2020). Urbanization in developing countries also displays features distinct from those in developed countries, potentially challenging conventional models of spatial equilibrium (Henderson and Kriticos, 2018;Henderson and Turner, 2020). In this paper, we seek to understand one aspect of the origins of urbanization in South Asia.
We introduce a new dataset on cities of at least 1,000 persons in colonial India. Our data are taken from the 1931 census of India, and cover modern-day Bangladesh, Burma, India, and Pakistan. There are 2,456 distinct cities for which population is reported, and the data cover the years 1881, 1891, 1901, 1911, 1921, and 1931. We have geocoded these data ourselves, and one contribution of this paper is the introduction of this dataset. Our baseline specification is a fixed effects model, estimated using ordinary least squares (OLS). We include fixed effects for city and year, and ask whether proximity to the railroad predicts log population size. Our OLS results suggest a negative elasticity of city size with respect to distance from a railroad that is between -0.017 and -0.019, corresponding to a standardized magnitude of roughly 5% of a standard deviation. So, while railway access spurred city growth in colonial India, the impact of railways on urban geography is less than that estimated in other developing and developed countries.
Because of possible biases in this fixed effects estimation, we employ a number of instrumental variables (IV) strategies. Our principal instrument is based on the use of a least cost path similar to the one constructed by Bogart et al. (2022) for nineteenthcentury England. This path connects pairs of cities that existed prior to the railway that are selected based on their market potential. The paths between them are chosen to minimize construction costs that are parameterized using data on terrain slope at the grid cell level. We use the fact that proximity to this least cost path predicts the speed at which cities gained railway proximity to construct our instrument, and find elasticities that are much larger than our OLS estimates, ranging from -0.113 to -0.191. This difference in magnitudes may be plausibly attributed to the negative selection of certain railway lines, heterogeneous responses to railway connection, and measurement error in railway proximity.
To understand the mechanisms that connect railways to cities in colonial India, we turn first to a major concept that links transportation costs with equilibrium population in several models of economic geography: market access (e.g. Donaldson and Hornbeck (2016); Redding and Sturm (2008)). This is a measure of the access that firms and consumers in a given location have to the firms and consumers in all other locations, scaled down by the costs of reaching these other locations. That is, market access measures the degree to which one city is exposed to supply and demand forces from all other cities. We estimate elasticities of city size with respect to market access that range from 0.385 to 0.628 via OLS and 1.028 and 1.370 via IV. In heterogeneity analyses, we show that railways increased city size most where their impact on market access was greatest: initially smaller and more isolated cities. Similarly, their impact was attenuated for cities with alternative transport links such as ports and rivers, in regions suitable for cash crop (i.e. cotton) cultivation, and where military motives directed railroad placement.
results provide empirical evidence that railways had measurable impacts on the nonagricultural sector of the economy.
In section 2, we provide background on India's cities and railroads and outline the potential conceptual links between them. In section 3, we describe our data. In section 4, we outline our empirical strategy. In section 5, we present our results. Section 6 concludes.
2. BACKGROUND AND CONCEPTUAL FRAMEWORK 2.1. Urbanization in colonial India. Owing in part to their advantages in soil, rainfall, and natural transportation, the floodplains of the Ganges and Indus were historically more urban than peninsular India (Roy, 2011, p. 21). Gujurat too was historically more urban than other regions (Roy, 2011, p. 56), as were the wet, rice-growing areas (Tomlinson, 2013, p. 29). While information on urbanization in India prior to the census of 1872 is limited, Visaria and Visaria (1983, p. 519) cite estimates from Gadgil (1959) that the net growth of urbanization from 1800 to 1872 was negative, with growth in the presidency cities of Calcutta, Bombay and Madras being offset by the decline of older capital towns such as Lucknow. While the region had many urban centres, thousands of which appear in our data, urbanization was low when compared, for example, to Europe (Tomlinson, 2013, p. 3). The fraction of the population living in towns or cities of at least 5,000 was 8.7% in 1872 (Visaria and Visaria, 1983, p. 519);de Vries (1984, p. 76), by contrast, estimates that 10.8% of the population of Western Europe lived in towns of at least 5,000 in 1600. This measure of Indian urbanization increased slowly and without acceleration to 11.1% in 1931 (Visaria and Visaria, 1983, p. 519). 3 Of this urban population in 1931, some 27.4% lived in cities of 100,000 or more (Bose and Bhatia, 1980, p. 50).
In the census reports, colonial officials proposed a wide range of contradictory factors that drove differences in urbanization and its growth across regions of India, including race, rainfall, plague, famines, and accidents of history (Bose and Bhatia, 1980, p. 76). The increases in urbanization that existed over the period 1881 to 1931 were driven largely by rural-urban migration, and not by differences in fertility and mortality (Visaria and Visaria, 1983, p. 521). Many of these migrants were recruited by labor contractors (Gupta, 2015, p. 74). Some of these workers migrated out of caste-based "attached" labor relationships (Roy, 2011, p. 131). Some migrated seasonally (Roy, 2011, p. 136). As a result, the population of India's urban centers was disproportionately male (Visaria and Visaria, 1983, p. 521); female migration was constrained by the need to mind children and land (Roy, 2015, p. 189). Workers might retire to their native villages, creating multi-generational links with urban mills (Wolcott, 2015, p. 200). Urbanization increased in the 1920s, in part due to postwar industrial protection (Visaria and Visaria, 1983, p. 520).
What role did cities play in the Indian economy? In the colonial period, several smallscale industries had a distinctively urban character (Roy, 2011, p. 173-179). Large-scale industry was almost entirely in urban areas (Roy, 2011, p. 183), particularly in Bombay, Madras, Calcutta, Agra, and Kanpur (Roy, 2012, p. 195). Cotton mills in Bombay served export markets, while upcountry mills supplied domestic demand (Rothermund, 2002, p. 68). Colonial cities were also large centers of consumer demand (Tomlinson, 2013, p. 115). In data from Fenske et al. (2022b), the share of the population living in cities of at least 5,000 persons correlates negatively with the share of the population working in agriculture and positively with the share of the population working in industry or services over the period . Cities are, then, an indicator of structural transformation in colonial India, and so we contribute to the literature on transportation infrastructure, structural transformation, and development.
Patterns of urbanization in colonial India show persistence similar to what has been found in other contexts (Bleakley and Lin, 2012;Davis and Weinstein, 2002); many of South Asia's larger cities were already established during the colonial period. Consider the 581 prominent cities of Bangladesh, Burma, India, and Pakistan reported in the World Cities Database. 4 450 of these are within 10 kilometers of a city reported in the 1931 census. Taking the sum of the colonial cities within 10 kilometers as a rough measure of the modern-day city's population in 1931, we estimate an elasticity of contemporary city size of 0.757 with respect to colonial city population, and show the corresponding scatterplot in Figure 1. While the process by which past cities have merged and the presence of modern cities that were outside the borders of colonial India makes this procedure inexact, and while many new cities such as Chandigarh and Islamabad have emerged since the colonial period, it is clear that the relative sizes of the cities that existed in the late colonial period have remained remarkably stable over the past century.
2.2. Railroads in colonial India. In 1853, Governor-General Dalhousie proposed constructing 5,000 miles of railway in India (Rothermund, 2002, p. 32). By 1930, more than 40,000 miles of track had been built (Donaldson, 2018). Several concerns prompted the construction of the railway. Rothermund (2002, p. 32) cites political unification and access to raw cotton. Bogart and Chaudhary (2015, p. 141) claim that commercial viability was paramount until the 1870s, after which military and famine concerns became more important.

FIGURE 1. Persistence of Urban Populations
How did the railway affect the Indian economy? Because engines and coal were imported, Rothermund (2002, p. 33) argues that the railroad did not provide linkage effects that might spur growth in other sectors of the economy. McAlpin (1974) argues that precautionary food storage dampened farmers' substitution towards cash crops. Other writers have claimed that the railroads did matter. It is through these impacts that the railway might be expected to affect city growth and size. Roy (2012, p. 189-190) argues that falling transportation costs benefitted industries, such as cotton textiles, in which India had an advantage; further, money earned in rail-facilitated cotton cultivation was later invested in Bombay mills. Empirical work has found that the extension of the railway system reduced price gaps over space (Andrabi and Kuehlwein, 2010;Hurd, 1975), increased trade and real incomes (Donaldson, 2018), and reduced vulnerability to famine (Burgess and Donaldson, 2017).

Conceptual Framework.
A number of theoretical and structural contributions have noted that a critical link between population and transportation costs in spatial equilibrium is market access (e.g. Allen and Donaldson (2020); Baum-Snow et al. (2020); Donaldson and Hornbeck (2016)). In particular, Redding and Sturm (2008) note two important dimensions of market access: while "firm market access" captures the proximity of firms to demand in all markets, consumer market access captures the access consumers have to the goods produced in all markets. One increases the wages firms can pay, while the other reduces the cost of living. Theoretically, both forms of market access increase equilibrium population in several models of economic geography 8 JAMES FENSKE, NAMRATA KALA, AND JINLIN WEI (Redding and Turner, 2015). Empirically, market access has had substantial power to explain the impacts of transportation costs on economic outcomes -serving even as a sufficient statistic for the impacts of transportation networks in some contexts (Redding and Rossi-Hansberg, 2017). This importance of market access in the literature will motivate our focus on market access measures in our empirical analysis. Beyond this core mechanism of greater market access, a number of papers have identified other related channels that could link transportation infrastructure to urbanization and the growth of cities. 5 These include factor mobility and the ability of rural labor to access external labor markets Banerjee et al., 2020;Bogart et al., 2022;Morten and Oliveira, 2016), consumption cities in resource-exporting countries (Gollin et al., 2016), complementarity with market-oriented minority communities (Jedwab et al., 2017;Johnson and Koyama, 2017), relaxation of the land constraint on the growth of large cities (Dittmar, 2011a;Nagy, 2020), structural change (Fajgelbaum and Redding, 2022), towns that serve as trading stations for agricultural products (Jedwab and Moradi, 2016), and better conditions for manufacturing production (Atack et al., 2011;Hornbeck and Rotemberg, 2019). If transportation infrastructure leads to the spatial concentration of production, output can fall in peripheral areas connected to the network (Faber, 2014).
In the specific context of colonial India, other effects of the railways identified in other studies, such as price convergence (Andrabi and Kuehlwein, 2010), reduced famine mortality (Burgess and Donaldson, 2010), greater agricultural incomes (Burgess and Donaldson, 2017), and human capital (Chaudhary and Fenske, 2020) may also have acted as supporting mechanisms through which railways facilitated urbanization. While we will not be able to test for all of these supporting or ancillary mechanisms in our empirical analysis, we will use the variables available to us in order to test for heterogeneous responses to railway access -for example, by initial city size or by access to alternative transportation modes -that will allow us to evaluate the degree to which some of these reinforce or attenuate our main effect of interest.
3. DATA 3.1. Indian Cities. We have digitized data on city populations from the 1931 Census of India. These cover modern-day Bangladesh, Burma, India, and Pakistan. In particular, for each provincial volume of the census, these are reported in Table 4 of the section  containing the Imperial Tables. There are 2,456 distinct cities in the data, and populations are reported for the years 1881, 1891, 1901, 1911, 1921, and 1931. The Census itself states that these data cover cities with populations of at least 1,000 persons, and indeed only 80 of 14,736 possible entries report populations less than 1,000. 2,043 of 14,736 possible entries are missing in the original data and likely reflect years in which these settlements had populations of less than 1,000. For consistency, then, we code as missing all observations of populations less than 1,000. We have located latitude and longitude coordinates for all but three cities in these data, using GeoHack and Google Earth as our principal sources. 6 Because these data are all taken from the 1931 Census, the original data assigns these to the districts that existed in 1931. We do not, then, need to address the creation, dissolution, or modification of districts and their boundaries over time. However, for consistency with how the Census reports data on total district populations, we have collapsed some districts into aggregate units. 7 Cities, similarly, are aggregated into a single unit if the populations of their constituent parts are not reported separately. For example, Dehra Dun urban, suburban, and cantonment are treated as the single city Dehra Dun, because separate populations are not reported prior to 1921. Where the populations of constituent units are consistently reported separately in the original data (for example, Barrackpore, North Barrackpore, and Barrackpore Cantonment), we treat these as separate observations.
In Table 1 we report summary statistics for the cities in our data. The number of cities for which populations are reported rises from 1,786 in 1881 to 2,429 in 1931. The summary statistics reflect that, on average, city populations grew moderately from 1881 to 1931. Of the cities for which populations are reported in 1881, the population mean was 13,113 in 1881. This rises to 15,951 for the 2,429 cities reported in in 1931. The largest city in 1881 was Bombay, with a population of 773,196. By 1931, Calcutta was the largest city, with a population of 1,196,734. The standard deviation of city sizes also grew over time, from 32,882 to 46,175. We present maps of city populations for 1881 and 1931 in Figures 2 and 3.
Creation of these data is one of the contributions of this paper, and it is our hope that these data will be of use to other researchers. Existing work in both economics and economic history has used similar data on cities for other parts of the world. It has been used, for example, to proxy for development (Acemoglu et al., 2005;Bosker et al., 2013;Hornung, 2015;Wrigley, 1985). City populations have been used to assess the importance, among other variables, of the printing press (Dittmar, 2011b), the Protestant 6 The three cities we have not been able to locate are Raswas (Bhopal District), Qadirabad (Aurangabad District) and Kodaikal (Raichur District).  reformation (Cantoni, 2015), medieval universities (Cantoni and Yuchtman, 2014), and the French Revolution (Acemoglu and Cantoni, 2011).

10001-50000
3.2. Railroads. In order to assess the impact of the expansion of the colonial railway system on the growth of Indian cities, we have followed a procedure similar to that in Donaldson (2018) in order to construct a polyline shapefile of the Indian railway system in which the opening date is known for each segment. We begin with the 1934 edition of History of Indian Railways Constructed and In Progress. For each of the roughly 2,000 railway lines listed, we record the opening dates and identify start points and end points, again mostly using GeoHack and Google Earth. We then take a polyline file of the modern Indian railway from www.gadm.org. We fracture this polyline using the start and end points of the colonial railway segments. We assign each railway line from History of Indian Railways Constructed and In Progress the polyline segments between its start and end points. If a polyline segment belongs to several railway lines, we assign it to the railway line that opens the earliest. There are some railway lines that are in the History of Indian Railways Constructed and In Progress that are not in the modern map of railroads, such as that between Nidamangalam and Manargudi. We add these to the polyline file using straight lines. Some of these lines that are not in the modern map of railroads are very short (e.g. "Bhagalpur Kachery To Bhagalpur Station, E.I. Ry."). We ignore these short lines.
We plot the railway maps we obtain for 1881 and 1931 using Figures 4 and 5. While there was already a substantial railroad network in place by 1881, it became much more dense by 1931. Comparing these maps with Figures 2 and 3, the relationship between expansion of the railroad and city growth over the 1881 to 1931 interval is not obvious. The railway system did expand into regions in which rapid city growth is visible, such as Punjab and Assam, but the railway system was also built up substantially in areas that saw much slower urban growth, such as Rajasthan and Uttar Pradesh.

Additional variables.
We create data on a number of geographic controls. At the city level, the correlates we consider are latitude, longitude, log distance to a major river, and log distance to coast. We compute these distances using ArcMAP, using polylines of rivers and the coastline taken from www.naturalearthdata.com.
The other geographic correlates we consider are originally available as raster data, and so we compute them at the district level rather than individually for each city. To match raster points to districts, we begin by converting the map of districts from the 1931 census to a shapefile. Because this map has a low resolution, we are concerned that this will lead to measurement error for geographic controls, particularly for small or irregularly shaped districts. We address this by identifying all modern-day third-level administrative divisions (e.g. tehsils) that intersect these historic districts, and averaging over the raster points within this set of units. For example, historic Agra district is merged to the Agra, Bah, Fatehabad, Khairagarh, and Kiraoli tehsils of modern Agra district, as well as the Etmadpur and Firozabad tehsils of modern Firozabad district.
In particular, we include ruggedness, malaria, altitude, precipitation, temperature, and suitability for dryland rice, wetland rice, wheat and cotton as additional correlates. Ruggedness is from Nunn and Puga (2012) and captures the roughness of the terrain. 8 Our measure of malaria is that originally created by Kiszewski et al. (2004). 9 We have used altitude data that are originally taken from the CGIAR's SRTM30 dataset. 10 We rely on the FAO-GAEZ data portal for means of precipitation, temperature, and suitabilities for specific crops. 11 There are three additional variables that we will consider in our tests for possible heterogeneous responses to railway access, but that we do not treat as controls in our baseline specification: presence of a medieval port, proximity to events during the Indian Rebellion of 1857, and exposure to famines. For medieval ports, we take the list of ports from Jha (2013) and code a dummy for whether a city in our data is within 10 kilometers of a city on this list. For events during the Rebellion of 1857, we begin with the list of events in Jaques (2007), as geocoded by Dincecco et al. (2020). We code a city as exposed to the Rebellion if an event occurred within 20 kilometers -roughly the range an army can cover in one day. We code famine events using the lists and maps of major nineteenth century famines from Srivastava (1968). These provide information at the district-by-year level on the existence of a famine and have previously been used by Donaldson (2010, 2017). We code a city as exposed to a famine if there was a famine in its district within the previous decade, i.e. the time period between observations of city populations.

EMPIRICAL STRATEGY
4.1. Fixed Effects. Our main empirical specification is a fixed effects model. For city i in year t, we use OLS to estimate: In equation (1), the variable P i,t is the population of city i in census year t, where kilometers. Because the city fixed effects will remove any time-invariant geographical controls, we follow the same procedure as in several studies where time-varying historical control variables are difficult to obtain (e.g. Juhász (2018); Waldinger (2022)) and interact our controls x i,0 with the year fixed effects. The baseline controls we include in x i,0 are latitude, longitude, log distance to river, log distance to coast, ruggedness, malaria, altitude, precipitation, temperature, and suitability for dryland rice, wetland rice, wheat, and cotton. We cluster standard errors by city.
The identifying variation in this specification comes from comparing the change over time in a city's size as it gains proximity to the railway network, over and above common trends in population growth given by the year fixed effects. Time-invariant variables that predict how a city gained proximity to the railway over time will not confound these estimates unless they predict differential trends in city growth rather than differing levels of city size.
There are, however, reasons why these fixed effects estimates could be biased. These include reverse causation, differential trends in potential city growth, measurement error in railway proximity, and time-varying variables that correlate with railway proximity. Such omitted variables could include, for example, colonial investments such as canals insofar as these are not consequences of the railway network. Because of this possible bias, we employ a number of instrumental variables specifications.

Instrumental Variables.
In order to mitigate possible omitted variables bias, we employ a number of alternative instruments for ln RailwayDistance i,t and estimate equation (1) using instrumental variables. Our main instrument is based on work by Bogart et al. (2022) for the United Kingdom. It takes as its base the distance between each city in our data and a least cost path that connects cities that existed in India before the beginning of railway construction. The cities the least cost path connects are selected based on market potential, and so were more likely to be connected to the railway network.
The cities data in the census go back only to 1881, while the first railway line reported in History of Indian Railways Constructed and In Progress (Victoria Terminus To Thana), opens in 1853. To find a set of cities that predate the Indian railway, we turn to Chandler and Fox (1974). They do not report data in tabular format, but instead provide a list of cities and estimates of their populations at various dates that differ across cities. We have identified 97 cities in British India (including Burma) that Chandler and Fox (1974) list as having a population of at least 10,000 in 1850, in "c. 1850," or in the closest years before and after 1850 that are reported.
We construct our least cost path in three steps, following Bogart et al. (2022). First, we begin with the subset of 76 Indian cities whose populations are recorded in Chandler RAILWAYS AND CITIES IN INDIA 15 and Fox (1974) in the mid-nineteenth century, before 1853 (the start of railway construction), and that also appear in the census. We then compute the market potential of any pair of cities as G ij = P opulation i ×P opulation j Distance ij , where P opulation i and P opulation j are the populations of each city, and Distance ij is the distance between them in kilometers.
The second step is to create least cost paths connecting this set of market pairs. Rather than using straight lines to connect cities, we follow Bogart et al. (2022) and create paths between cities that minimize the cost of construction. We begin with raster data on slope at the grid cell level. 12 We parameterize the cost of any hypothetical line crossing a cell by letting the cost of construction increase by a factor of three for every 1 percentage point increase in the slope of a cell. That is, if the cost of crossing a flat grid cell is 1, the cost of crossing a cell with a slope of x% is 1 + 3 × x. For example, the cost of crossing a cell with a slope of 2% is 7. This again follows Bogart et al. (2022), and is based on the relationship they estimate between construction costs and elevation change for 36 non-London railways during the nineteenth century in England. These costs are unitless, and the choice of unit will not affect the optimal route placement since the least cost path will minimize costs expressed in any unit.
The third step is to select from this set of least cost paths a subset that is to be included in the data. We sort each pair of towns by market potential G ij , and select routes until the total length of the least cost path network is as large as the actual railway network in 1881. The resulting hypothetical railway network is shown in Figure 6.
This hypothetical network resembles the early stages of the network that was actually constructed, and so proximity to this least cost path predicts how quickly the cities in our data -including the vast majority that are not recorded in Chandler and Fox (1974) gained access to the railway network. Cities closer to this least cost path became closer to the railway network in earlier years.
Once this least cost path is constructed, we use it to construct an instrumental variable. We compute the distance in kilometres of each city in the data to this least cost path. We then use the interaction the log of (one plus) distance to this least cost path with year (i.e. t) to instrument for ln RailwayDistance i,t . We make two notes here. First, because the cities are treated as a set of points with zero area, and the railways are treated as a set of lines with zero thickness, no city has zero distance from the railway. However, the least cost path is built to connect a subset of these city points. As a result, some have zero distance from the least cost path. This motivates the use of the log of one plus distance rather than simply log distance in the instrument. 12 We work with grid cells that are 180m × 180m at the equator. Our underlying data source is Shuttle Radar Topography Mission with a resolution of 90 metres (SRTM 90). This is the same underlying source used in Bogart et al. (2022). We aggregate the raster data to a resolution of 180 metres because South Asia's vast size makes computations with 90 metre cells computationally demanding.

FIGURE 6. Least Cost Path
Second, because distance from the least cost path is time-invariant, it is collinear with our city fixed effects. Hence, interacting this with year to construct our instrument bases identification on how proximity to the hypothetical plan predicts differential time trends in railroad proximity. In 1881, cities distant from the least cost path were distant from the railroad. Over time, this relationship flattened as railroads expanded closer to cities more distant from the least cost path. It is the flattening of this relationship that we exploit for exogenous variation in our instrumental variables analysis.
The exclusion restriction here is the assumption that linear trends in population predicted by distance from the least cost path are uncorrelated with the unobserved timevarying determinants of city size that remain once city fixed effects, year fixed effects, and the differential nonlinear time trends predicted by our control variables have been partialled out. One example of a violation of this restriction would be if pre-existing trade routes followed similar least cost paths and predicted not only greater population levels at the start of our data, but also differential trends in growth after 1881. We will show below, however, that our main results are almost unchanged when controlling for roads, canals, and other historic trade routes.
In addition to our principal instrumental variable, we construct three alternative instruments for robustness, based on alternative least cost paths. Two of our three alternative least cost paths are based on alternative scenarios from Bogart et al. (2022).

RAILWAYS AND CITIES IN INDIA 17
These scenarios allow terrain slope to have differing effects on the costs of construction. In the first alternative, which we call A1, the cost of building across a grid cell is equal to one plus its slope: 1 if it is flat, 2 if the slope is 1%, 3 if it is 2%, and so forth. We cap the cost of crossing any one cell at 51. This corresponds to what Bogart et al. (2022) call "Scenario 1," and allows for a less convex relationship between terrain slope and construction cost than in their baseline. The second alternative, which we call A2, corresponds to what Bogart et al. (2022) call "Scenario 3." This scenario assumes that any cell with a gradient greater than 6% requires a tunnel, and so caps costs at 19. Our third alternative least cost path, which we call A3, is similar to the baseline scenario in Bogart et al. (2022), but based on data from data on Indian construction costs. We take data from Bogart and Chaudhary (2013) on the real value of capital of 21 Indian railway companies from 1851 to 1912. We assume that the value of capital of a railway line in year t is equal to the construction costs of all the branches that have been finished by year t. Combining these data with the lengths and accumulated slopes of railway lines in the years 1861, 1871, 1881, 1891, 1901 and 1911, we can then estimate the relationship between cost and elevation change for each line i using the following regression, based on Bogart et al. (2022): Here, Length i is measured as the number of raster cells crossed, while Slope i is the total slope of the line, in percentage points. Our estimates suggest thatβ 2 ≈ 0.6β 1 . We then replace the cost parameterization of 1 + 3 × x with 1 + 0.6 × x when computing the cost of any given line.
For each of these three alternative least cost paths, we again take the interaction the log of (one plus) distance to the path with year as an alternative instrument for ln RailwayDistance i,t . 4.3. Market access. The existing literature on economic geography stresses market access as the critical link between equilibrium population and transportation costs. As an alternative to our main empirical specification, which considers physical proximity to a railway, we can estimate: All terms here are defined as in (1), except that we have replaced RailwayDistance i,t with M arketAccess i,t . Whereas physical proximity to a railway measures whether a city has access to a railway, market access measures the sizes of the markets that each city is JAMES FENSKE, NAMRATA KALA, AND JINLIN WEI connected to, deflated by the costs of reaching them. We follow Donaldson and Hornbeck (2016) and define market access as: Here, the market access for city i in year t depends on the costs of reaching each other city j in year t, τ i,d,t , and the population of each other city j in year t, P j,t . This is a close approximation of the market access measures that emerge as sufficient statistics for transportation infrastructure in structural models of economic geography (e.g. Donaldson (2018); Eaton and Kortum (2002); Redding and Sturm (2008)).
To compute market access, we need three quantities: τ i,j,t , θ, and P j,t . We compute τ i,j,t , the cost of travel between any city i and any other city j, by following Donaldson (2018). We compute least cost paths connecting any two cities i and j in the data. Transportation modes allowed in these routes include wagons, coastal shipping, rivers, and railways. Connections to oceanic transportation routes are only accessible via ports.
Normalizing the cost of shipment by railways to 1, the relative costs of travel by wagons, coastal shipping, and rivers are 2.375, 6.188, and 2.250, respectively. These are based on estimates in Donaldson (2018). For θ, we will take 1 as our baseline, and report alternative values of 3.6 7.8, and 8.28. The baseline value follows the original parameterization in Harris (1954), and the alternatives come from Donaldson and Hornbeck (2016), Eaton and Kortum (2002), and Donaldson (2018). 8.28 is the preferred value from Eaton and Kortum (2002), while the mean result in Donaldson (2018) is 7.80. We will show below that lower values of θ have more predictive power in our data. City sizes P j,t are reported in our data, and for this calculation we assume that the population of a city is 0 if it is not recorded in the census in any specific year. Note that τ i,j,t will only change over time due to the expansion of the railway network. As with equation (1), we will estimate (4). We will use both OLS and IV, and we will employ the same instruments for ln M arketAccess i,t that we used for that we used for ln RailwayDistance i,t .

RESULTS
In this section, we present our estimates of equations (1) and (4). We begin by presenting results connecting distance from the railway to city size, before then presenting results in which we use market access to measure a city's connection to the transportation network. We explore the heterogeneity of our results, and report our principal robustness checks. Table 2, we present OLS and IV estimates of equation (1). The first column reports OLS estimates without controls, while the second column interacts baseline geographic characteristics with our year fixed effects. Columns (3) and (4) present analogous specifications for our instrumental variables estimates. The corresponding first stage estimates are in columns (5) and (6). Note that we divide the instrument by 1,000 in order to ease the presentation of coefficients. Note that there are fewer observations in our IV estimations because we purposefully exclude the nodes of the least cost paths -this focuses identification on cities that were connected to the railway, incidentally based on their proximity to a path connecting two other cities.

Distance from railroad. In
Our OLS estimates suggest an elasticity of city size with respect to railway proximity that is negative, but that is not large. These range from −0.017 to −0.019. Put differently, a one standard deviation reduction in distance from the railroad increases city size between 4.47% and 5.06% of a standard deviation. Similarly, the share of city growth that is explained by railway proximity is small -the R 2 net of fixed effects before controls are added is less than 1%. Our instrumental variables estimates are larger in magnitude. Here, the implied elasticities range from −0.113 to −0.191, and the effect sizes expressed in standard deviations range from -29.8% to -50.3%.
There are a number of possible reasons why our IV results are larger than our OLS results. One explanation would be a bias towards zero due to omitted variables that predict railway proximity but that retard city growth. Variables that predict absence of a railway and favor city growth would have the same effect. Chaudhary and Fenske (2020) discuss several motives for railway placement in colonial India that could create this type of bias, including "protective" lines that connect famine-prone areas to the transportation network, lines from Delhi towards Afghanistan built for military purposes, lines connecting ports to cotton-growing regions that were likely to remain agricultural, and lines connecting small hill stations that British officials used as summer retreats.
Another potential explanation is the difference between the local average treatment effect estimated by IV and the average treatment effect for the whole population of cities. That is, treatment effects may be larger for compliers than for the full sample. We will show below in Table 4 that the impact of a railway is attenuated by a number of city characteristics. Critically, these include an above-median population in 1881 and proximity to the railway in 1881. The instrumental variables approach places more weight on compliers -cities that gained access to railways earlier because of their proximity to the least cost path. If these cities are less likely to have characteristics that attenuate the effects of railways, this would inflate the IV estimates relative to the OLS estimates. In addition, some cities close to the least cost path will have already been connected to the railway before 1881, and so their proximity to the railway will not change during the sample period.
Another possible explanation would be attenuation bias due to measurement error in railway proximity. Narrowly, treating railways as polylines and cities as massless points will lead to mis-measurement of the distance of cities from railways, and this will be exacerbated by changes over time in the locations of cities and of specific railway lines. Conceptually, it is possible that physical proximity does not fully capture the dimensions of the railway network that are most important and so mismeasures these. We will show below in Table 3 that the inflation of coefficients when moving from OLS to IV estimates using market access measures is smaller than in Table 2, which is consistent with this interpretation.
Another possibility would be weak instruments. We do not believe this is a likely explanation: the Kleibergen-Papp F statistics in our regression are greater than 70, well above the conventional cutoff of 10. Yet another possible explanation would be violations of the exclusion restriction. Given our baseline inclusion of both city and year fixed effects, and since we show below that we obtain similar magnitudes with alternative instruments, we believe this is unlikely to explain the difference between OLS and IV estimates. Table 3, we report OLS and IV estimates of equation (4), where we now use market access to measure how a city is exposed to the railway network. In columns (1) and (2) we report OLS estimates with and without controls, respectively. In columns (3) and (4) we present our analogous IV results. Columns (5) and (6) show first stage estimates. Finally, columns (7) and (8) report our OLS estimates using an alternative measure of market access that follows Donaldson and Hornbeck (2016). Using equation (3) to compute market access, we now exclude any markets j that are within 100km of a given city. We call this new measure "access to distant markets." This isolates a component of market access that is unlikely to be affected by unobserved factors that correlate with the construction of railways close to the city i for which market access is measured. We treat this as an alternative to instrumental variables in generating exogenous variation in market access.

Market access. In
Our OLS estimates suggest an elasticity of city size with respect to market access of between 0.385 and 0.628. Expressed as a standardized effect size, this suggests that a one standard deviation increase in market access would increase city size by 22.2% to 36.2% of a standard deviation. The IV results are larger in magnitude, corresponding to an elasticity between 1.028 and 1.370, and a standardized effect size between 59.3% and 79.0% of a standard deviation. Using access to distant markets as an alternative measure gives estimates larger than the OLS estimates in columns (1) and (2), but smaller than RAILWAYS AND CITIES IN INDIA 21 the IV estimates in columns (3) and (4). Here, the elasticities range from 0.579 to 0.886, and the standardized effect sizes range from 25.3% to 38.7%. These results give us additional evidence on the difference between the OLS and IV coefficients in Table 2. The IV results remain larger than the OLS results when using market access, but the degree of inflation is less. This is still consistent with negative selection of cities into railway access, but suggests the problem of attenuation bias due to measurement error is larger when using the log of distance from the railway rather than market access as a measure of exposure. The larger elasticities and standardized effects obtained using access to distant markets are further evidence that OLS estimates may be biased downwards due to negative selection. The first stage F statistic is much larger in the market access regressions, suggesting that weak instruments do not explain the divergence of the OLS and IV estimates, and that distance from the least cost path is a better predictor of time trends in market access than of time trends in proximity to the railway network. We will show below in Table 4 that many of the same variables that predict differential response to railroad proximity also predict differential response to market access, suggesting again that compliers may differ from the average city and that this may explain the divergence between OLS and IV estimates.

Heterogeneity.
To explore the channels by which railway access increased city size in India, we use Table 4 to test whether seven variables predict heterogeneous responses: greater city size in 1881, suitability for cotton cultivation, presence of a medieval port, having a river within 2 kilometers, experiencing an event related to the Indian Rebellion of 1857 within 20 kilometers, being above-median distance from the railway system in 1881, and exposure to the famines of the nineteenth and early twentieth centuries.
We report OLS estimates of both equation (1) and equation (4), augmented to include the interaction between the relevant measure of railway access (log distance from a line or market access) with the possible source of heterogeneity. In all cases except one, the source of heterogeneity is time-invariant and so it is absorbed by the city fixed effects. The exception is famine exposure. Because this is time-varying, we also include it as a control but do not report the coefficient.
Columns (1) and (2) of Table 4 allow the impact of railways to vary for cities that are above median size in 1881. This will capture the degree to which railways reinforced existing agglomeration or allowed smaller cities to grow. Note that we can only perform this test on the sub-sample of cities that have populations reported in 1881, which reduces sample size in these columns. The interaction is positive when we use the log of railway distance to measure proximity and negative when we use market access, suggesting that the effects of railways are attenuated in the set of cities that are already large in 1881. This implies that railways led to city growth not by reinforcing existing agglomeration, but by letting smaller cities grow. One possible reason for this pattern is greater congestion problems in larger cities. In columns (3) and (4) of Table 4, we perform a related test and divide our sample by median distance from a railway in 1881. Cities above median distance from a railway will have typically had the lowest levels of market access at the start of our data series. Across specifications, it is clear that the effect sizes are largest for these most initially isolated cities. Indeed, using distance from a railway as a measure of access, it appears as though greater proximity only increased city size for the initially most isolated cities. This further reinforces our interpretation that railways increased market access for initially small and isolated cities, rather than reinforcing the advantages of initially large and more connected locations.
In columns (5) and (6) of Table 4, we examine the possible differential response of former medieval ports. These ports may capture both historical prosperity or the predetermined presence of alternative transportation links. If railways substitute for other forms of transportation, their effects could be mitigated in these cities. This would be similar to what Okoye et al. (2019) find in Nigeria. By contrast, if connecting sea-borne trade hubs to a railway reinforces network externalities, their impacts could be greater. Across specifications, the coefficient signs suggest attenuation, but they are not significantly different from zero in three of four cases. This provides little evidence, then, of network externalities as the main driving force behind our results.
Columns (7) and (8) of Table 4 consider a related dimension of heterogeneity -proximity to a river. Our use of a 2 kilometer threshold here follows earlier versions of Bogart et al. (2022). Our logic here resembles that in the previous test: like a port, a river may substitute for a railway, attenuating its impact, or it may reinforce network externalities. In the specification that employs physical proximity, the presence of a river significantly attenuates railway access. This does not appear to be the case when we use the market access measure of railway connection. This again provides little evidence of a major role for network externalities or reinforcement of existing agglomeration in accounting for our main results.
Columns (9) and (10) of Table 4 consider possible heterogeneity by suitability for cotton cultivation. In particular, we create a dummy equal to one for cities located in districts with above-median cotton suitability. Especially during the civil war in the United States (1861-65), British officials in India believed railways could ensure a reliable supply of cotton for use by the textile industry in Britain (Thorner, 1951(Thorner, , 1955. While these districts may have become more specialized in cash crop agriculture due to the railways, limiting urbanization, secondary towns that served the farming sector may still RAILWAYS AND CITIES IN INDIA 23 have grown in these regions. In three of four relevant specifications, cotton suitability appears to attenuate the impact of railroads. This suggests that the agglomeration effects due to services that serve the agricultural sector, such as those Jedwab and Moradi (2016) find in Ghana, are less important in the Indian case.
In columns (11) and (12) of Table 4, we test whether cities that were connected to the railway for military reasons responded differently. Particularly after the Sikh wars of the 1840s, the British were concerned that railways would be needed to move troops to politically unstable regions (Hurd, 1983;Parliamentary Papers, 1854). We use spatial variation in the Indian Rebellion of 1857, which occurred only shortly after the start of railway construction and for which there is rich data on the locations of major events, to measure military motives for railway construction. Across specifications, the coefficients suggest an attenuating effect of Rebellion exposure; cities that were connected to the railroad for reasons other than economic potential responded less in terms of city growth.
Finally, in columns (13) and (14) of Table 4, we consider cities that were vulnerable to famine and that were connected to a railway. Particularly after the 1870s, the British constructed railway lines that could aid in famine relief for famine-prone areas (Hurd, 1983;Parliamentary Papers, 1854). Across specifications, we find coefficient signs suggesting that railways had smaller effects on city sizes in these areas, but these heterogeneous responses are not significant at conventional levels using the market access measure.
In sum, then, our results are consistent with the railway increasing the size of Indian cities through a market access channel. The heterogeneous results we find suggest that railways increased city growth by facilitating the growth of smaller and initially isolated cities, rather than reinforcing existing agglomeration effects. We do not find evidence that secondary towns serving the cotton sector nor reinforcement of network externalizes in port and river trade help explain the result. The impacts were attenuated where railways were built for military reasons, though we find no similar evidence for famines.

Principal Robustness Checks.
Here, we discuss the robustness of our results. We begin by showing the robustness of our results on the proximity of railways to alternative functional forms. In Figure 7, we show that the relationship between log city size and log distance from a railroad is approximately linear. We begin by residualizing the data on log population and log distance from a railroad relative to the fixed effects for both city and year. We then show a binned scatterplot of these partial residuals against each other. While the best quadratic fit of these data is not perfectly linear, the curvature is slight. This validates our baseline log-log specification in Equation (1). in Ghana in 1931 (Jedwab andMoradi, 2016) and 0.37 standard deviations in Kenya in 1962 (Jedwab et al., 2017). Bogart et al. (2022) find in their OLS estimates that the change in population between 1851 and 1891 was 16.6 log points greater for localities of England with a railway station in 1851. Their IV estimate of the same effect is 34.9. In nineteenth century Prussia, panel estimates in Hornung (2015) suggest that railway connection raised city size by 7.7 log points.
Our estimates are generally smaller than those noted above. While none of these studies directly reports an elasticity of city size with respect to distance from a railway, our OLS elasticity estimates from Table 2 imply that a colonial Indian city would need to become very distant from a railroad to experience the same reduction in size predicted by disconnection in the studies above. For example, for population to fall 23.4 log points as in Berger and Enflo (2017), a city would need to be (100 × 0.234/0.017) 1376 log points further from a railway according to our estimates in column (2). Similarly, while Atack et al. (2010) find that urbanization increased by 3.7 percentage points relative to a baseline mean of 6.7% in US counties that gained rail access during the 1850s, the coefficients we estimate in Table 5 are much smaller relative to the outcome mean of 9.02. So, across these disparate estimates, it is clear that our estimates of the impact of railway proximity for colonial India are smaller than in other contexts. One exception is that our estimates of the elasticity of city size with respect to market access are larger than those, ranging from 0.08 to 0.13, that Jedwab and Storeygard (2022) find in their study of cities in Africa since 1960.
There are a number of possible reasons for our smaller magnitudes compared to much of the literature. One is that, in contrast to early twentieth century Africa and the United States before westward expansion of white migrants, the population density of India was already relatively high and many urban centers existed that predated the railway. The capacity of the railway to reset the urban network will, then, have been less in India. Further, the slow growth of urbanization in India, outlined in Section 2, means there is less urban growth to be explained in our data.
In Figure 8, we take an even more general approach to distance bands. We again estimate equation (1) by OLS, but now we replace ln RailwayDistance i,t with a full set of dummies for falling within distance bands of the railroad. We use bands that are 10 kilometers wide up to a distance of 120 kilometers, and then use bands of 120-150 km and 150-200 km due to the sparsity of cities at these greater distances. We plot the coefficient estimates and 95% confidence intervals from this regression in the Figure. In this estimation, cities immediately adjacent to a railway are a bit more than 25 log points larger in population. This declines as distance from the railway increases, flattening out at distances greater than 100 kilometers. Coefficients are larger in this exercise than in FIGURE 8. Log city size by distance from railroad the first two columns of Table 5, as the set of baseline cities against which these coefficients are to be compared is now much more distant from a railway -at least 200, rather than at least 20 kilometers.
We also use Table 5 to consider a more subtle issue of functional form: the possible influence of outliers due to cities that are very close to a railway line. At very low distances, the logarithmic transformation can rapidly approach negative infinity. We show that this does not drive our main results, replacing observed values of railway distance below a cutoff with the cutoff itself. We consider four cutoffs: 1m, 1km, 2km, and 5km. This is a procedure similar to winsorizing. In columns (3) through (6) of Table 5, we show that the results from this exercise give coefficients very similar to those from Tables (1) and (2) of Table 2 -possible outliers very close to railway lines do not drive our results.
In Table 6, we consider the robustness of our market access results. We begin by changing the value of θ in equation 3. Often referred to as the "trade elasticity," this parameter governs the speed at which access to a market declines as transportation costs increase. Greater values of θ imply a more rapid decline in market access for a given increase in transportation costs. Following Donaldson and Hornbeck (2016), we consider three alternatives to our baseline value of 1 -3.6, 7.8, and 8.28, which lie within the typical range of gravity estimates reported in the meta-survey by Head and Mayer RAILWAYS AND CITIES IN INDIA 27 (2014). In columns (3) through (8) of Table 6, it is clear that these do not change the general conclusion that greater market access due to the expansion of the railway network increases city size. Quantitatively, the elasticity estimates, standardized magnitudes, and the "within" R 2 measure of goodness of fit net of city and year fixed effects all fall as θ increases. The impact of market access on city size, then, is smaller when compared with columns (1) and (2) of Table 3. The fundamental parameters underlying θ differ between demandside and supply-side derivations of structural gravity models, and so lower values of θ are consistent with a number of interpretations (Head and Mayer, 2014). These include lower substitutability of goods in consumption, and greater heterogeneity across consumers or producers.
In the second panel of Table 6, we show that an alternative parameterization of our market access measure gives results that are qualitatively similar to those in Table 3. Recall that, in our baseline computation, we normalized the cost of shipping on railways to 1, and set the relative costs of travel by wagons, coastal shipping, and rivers to 2. 375, 6.188, and 2.250, following Donaldson (2018). In panel 2, we adopt the alternative relative costs of 4.5, 2.25, and 3.0, respectively. This alternative parameterization also follows Donaldson (2018), is based on his estimates of colonial freight rates, and gives results that, while again qualitatively similar to our baseline, are also quantitatively smaller, whether interpreted as elasticities or in standardized magnitudes.
In the bottom panel of Table 6, we again turn to our alternative measure of market access that exploits changes in access to distant markets. Here, we show the robustness of this measure to alternative values of the trade elasticity, θ. We consider the same alternatives as before: 3.6 7.8, and 8.28. Columns (1) and (2) reproduce the baseline results from Table 6. For greater values of θ, the qualitative conclusion of a positive impact of market access on city size remains. As with our baseline measure of market access, the estimated elasticities and standardized coefficients fall as θ increases.
As evidence that our results are not driven by correlation between the railroad network and alternative transportation networks or other colonial investments, we use Table 7 to show that our main results survive controlling for roads, canals, and historic trade routes. The Schwartzberg (1978) "Historical Atlas of South Asia" provides maps of roads and canals in three benchmark years: 1872, 1901, and 1931. These are derived J o u r n a l P r e -p r o o f Journal Pre-proof 28 JAMES FENSKE, NAMRATA KALA, AND JINLIN WEI from a larger underlying set of maps and atlases. 13 We have converted these to shapefiles and computed the (log) distance of each city in our data from the nearest road and from the nearest canal in each of these years. We control in the table for these distances in the most recent year. Similarly, Raychaudhuri (1982) provides a map of seventeenth century trade routes. This is based on a large number of primary and secondary textual descriptions of trade, with Deloche (1968) as the main cartographic source. We include the interaction of distance from these routes, because they are time-invariant, with the year fixed effects. We add these as controls to the table as well. While cities closer to the least cost path were also closer to historic trade routes and to roads, controlling for these measures of access to alternative transportation does little to our results.

Alternative Mechanisms.
Our results are consistent with railroads increasing city size primarily through a market access channel. Where did additional urban residents come from? The secondary historical literature suggests that cities in colonial India grew largely from rural-to-urban migration, and not through greater fertility or lower mortality in cities (Visaria and Visaria, 1983, p. 521). That is, people migrated from villages too small to exist in the sample into the cities in the data. In every census year from 1881 to 1931, less than 12% of the total population lived in the cities of at least 1,000 persons that appear in our data. This rural-urban migration is likely to have occurred primarily within districts. We consider here three alternative channels: inter-district migration, income, and fertility. We are, however, limited by the nature of the historical sources. While our data on city populations cover more than 2,400 cities, many key variables that could be used to test these mechanisms are reported only at the district level, have not been digitized from the colonial census, or are not available in all census years. So: our samples in these analyses overlap only partially with our baseline sample. On inter-district migration, note first that Chaudhary and Fenske (2020) have shown that the share of persons living in a given district in a census year that were born in other districts did not respond to railways over the period 1901-1911. Second, we find no evidence that railway connection increased a district's total population. In Table 8, below, we estimate: 13 Chief among these are: Bartholomew, J. (c. 1930 Here, our outcome variable is ln P d,t , the natural log of population P in district d in year t. Rail d,t captures district railway access, which we measure in two ways: as a dummy for whether the district is intersected by a railway, and market access at the district level. The specification includes district fixed effects (δ d ) and year fixed effects (η t ). We also include the same controls as in our city-level regressions, aggregated to the district level, and interacted with year fixed effects (x ′ d,0 η t ). We cluster standard errors by district. Results, in Table 8, show no significant correlation between rail access and total district population.
On income, Donaldson (2018) has provided district-level estimates of rural income for some of the district-year observations in our panel. We show in Table 8, however, that controlling for this measure of income in the city-level specification from equation 4 does little to diminish the coefficient on market access. On fertility, we follow Wanamaker (2012) and construct a proxy using the ratio of children to women of childbearing age. These district-level data come from Fenske et al. (2022a) and our outcome variable is defined as the (log) ratio of children under 10 to women aged 10-40. We find little evidence in Table 8 that this measure of fertility responds to railways.

Additional Robustness Checks.
We report a number of additional robustness exercises in the appendix.
In Table A1, we show the robustness of our results to alternative sample restrictions, specifications, and estimators. In columns (1) through (4) of the first panel, we report results using both railway proximity and market access, but discarding any cities that remained distant from a railroad -more than 100 km -throughout the entire sample period. The results are largely unchanged. Our results are not, then, driven by these possible outliers. In columns (5) through (8) of the first panel, we discard modern-day Burma from the results. This too does little to affect the results, showing that our results hold for the core regions of what is conventionally considered to be colonial India.
In columns (1) through (4) of the second panel of Table A1, we rule out the possibility that cities that are reported despite having populations below 1,000 are driving our results. We truncate all populations below 1,000. Results are again very similar to our baseline. In columns (5) through (8) of the second panel, we make this same truncation, but use a tobit estimator to account for the fact population is bounded below by 1,000. This too does little to our main results. Here, we gain observations by treating cities whose populations are not yet reported as if they are 1,000.
In columns (1) through (4) of the third panel of Table A1, we take an alternative approach to showing that cities with populations below 1,000 do not drive the result. We recode missing observations to 1,000. Results are similar to our baseline. Recoding these instead to 500 -in columns (5) through (8) -again changes little.
In columns (1) through (4) of the fourth panel of Table A1, we discard possible outliers -those in the top and bottom 1% of the sample by statistical influence onβ. Finally, in columns (5) through (8) of the bottom panel, we include fixed effects for district × year. This focuses identification on cities observed in the same district in the same year with differing degrees of railway access. Here too, the results are similar to our baseline results, suggesting that time-varying unobservables at the district level do not explain our results.
In Tables A2 and A3, we show that alternative instrumental variables give results similar to our baseline estimations. The construction of these alternative instruments has been described in more detail above in Section 4.2. Table A2 shows both first and second stage results using the log of distance from a railway to measure a city's railroad access. Table A3 does the same using market access. In both tables, columns (1) and (2) show results in which we continue to use our baseline least cost path to construct our instrument, but now we interact distance from the path, rather than its logarithm, with year.
Columns (3) and (4) use least cost path "A1", in which the cost of construction rises more rapidly with terrain slope than in our baseline. Columns (5) and (6) use instead the least cost path "A2," in which construction costs are capped at high slopes due to the use of tunnels. Columns (7) and (8) use least cost path "A3," based on Indian construction costs.
Across both tables, a general pattern emerges. Each of these least cost paths is a strong predictor of the speed with which cities gained access to the railway network, measured either with physical proximity or with market access. Similarly, our second stage results are similar to our baseline results in Tables 2 and 3, suggesting our results are not driven by the selection of one possible IV strategy relative to another.
Finally, in Table A4, we expand on the district × year fixed effect specifications reported in Table A1. In particular, we show that our market access results continue to hold in this specification using alternative values of both θ -the trade elasticity -and of the relative costs of transportation. In the top panel, we use the same alternative values of θ as in Table 6: 3.6 7.8, and 8.28. In the bottom panel, we replace our baseline relative costs of travel (2.375, 6.188, and 2.250 for wagons, coastal shipping, and rivers, relative to rail) with the same alternatives that we reported in Table 6: 4.5, 3.0 and 2.25. (1) (2) Main controls are latitude, longitude, log distance to river, log distance to coast, ruggedness, malaria, altitude, precipitation, temperature, and suitability for dryland rice, wetland rice, wheat and cotton. *** indicates significance at the 1% level, ** at 5% and * at 10%.

ln(Population) ln(Population)
Above-median initial size -0.0488 -0.0500 -0.0494 -0.0479 Note: Standard errors clustered by city are reported in parentheses. Main controls are latitude, longitude, log distance to river, log distance to coast, ruggedness, malaria, altitude, precipitation, temperature, and suitability for dryland rice, wetland rice, wheat and cotton. *** indicates significance at the 1% level, ** at 5% and * at 10%. Distances below the minimum distance are recoded to equal the minimum distance.  Note: Standard errors clustered by city are reported in parentheses. Main controls are latitude, longitude, log distance to river, log distance to coast, ruggedness, malaria, altitude, precipitation, temperature, and suitability for dryland rice, wetland rice, wheat and cotton. *** indicates significance at the 1% level, ** at 5% and * at 10%.

ln(Population) ln(Population)
J o u r n a l P r e -p r o o f

ln(Population) Without Roads and Canals With Roads and Canals
Note: Standard errors clustered by city are reported in parentheses. Main controls are latitude, longitude, log distance to river, log distance to coast, ruggedness, malaria, altitude, precipitation, temperature, and suitability for dryland rice, wetland rice, wheat and cotton. *** indicates significance at the 1% level, ** at 5% and * at 10%. (1)

ln(Population)
Note: For district-level regressions, standard errors clustered by district are reported in parentheses. For city-level regressions, standard errors clustered by city are reported in parentheses. Main controls are latitude, longitude, log distance to river, log distance to coast, ruggedness, malaria, altitude, precipitation, temperature, and suitability for dryland rice, wetland rice, wheat and cotton. *** indicates significance at the 1% level, ** at 5% and * at 10%.

Districts
Cities Districts