Agriculture, Transportation and the Timing of Urbanization: Global Analysis at the Grid Cell Level

Agriculture, Transportation and the Timing of Urbanization: Global Analysis at the Grid Cell Level Mesbah J. Motamed Economic Research Service U.S. Department of Agriculture mmotamed@ers.usda.gov Raymond J.G.M. Florax Purdue University VU University, Amsterdam rflorax@purdue.edu William A. Masters Tufts University william.masters@tufts.edu

Agriculture, Transportation and the Timing of Urbanization: Global Analysis at the Grid Cell Level Abstract This paper addresses the timing of a location s historical transition from rural to urban activity. In our simple two-sector model, urbanization occurs sooner when rural productivity is higher or transport costs are lower. We test the model on worldwide data that divide the earth s surface at half-degree intervals into over 60,000 cells. From an independent estimate of each cell s rural and urban population history, we identify the date at which each cell achieves various thresholds of urbanization. Controlling for unobserved heterogeneity across countries through fixed effects and neighbors urbanization using spatial techniques, we find that the date at which each cell passes each urbanization threshold is positively associated with its suitability for cultivation, having seasonal frosts, more access to navigable waterways and lower elevation. Aggregating cells into countries, an earlier urbanization date is linked to higher per capita income today. JEL: C21, N50, O11, O18, R1 Keywords: economic growth, economic geography, urbanization, agriculture 1 Introduction This paper addresses the role of physical geography in the timing and location of urbanization. Our central hypothesis is that, for any given place, higher local agricultural potential and lower physical barriers to transport facilitate the growth of cities and hence economic growth in the associated region. This could help explain late urbanization and the persistence of rural poverty in regions with limited agro-ecological productivity and significant transportation barriers. Our focus on the initial formation and early growth of cities is consistent with new work on the historical roots of economic development (see Nunn (2009)) which provides econometric evidence linking events in the distant past, such as early technology adoption, European colonization and African enslavement, to countries current state of economic development (Comin et al., 2006; Acemoglu et al., 2002; Banerjee and Iyer, 2005; Nunn, 2008). This literature has hypothesized and tested how physical geography might have influenced those events. Most notably, Sokoloff and Engerman (2000) introduce agro-ecological conditions as a determinant of crop choice and hence the location of slavery and inequality in the New World. They argue that climate and soils favorable to sugar, coffee, and tobacco plantations, in contrast to grain crops, favored the concentration of land, and thus wealth, into relatively few hands. Ultimately, this arrangement predisposed the formation of institutions to preserve the power and status of landholding elites, with effects persisting until today. Similarly, Acemoglu et al. (2001) linked disease ecology and the mortality of colonial settlers to the kinds of institutions they established in the New World. Nunn and Puga (2007) consider the multiple and countervailing effects on income of one unusual feature of African geography, ruggedness. One effect is negative as a consequence of ruggedness impact on transport costs and agriculture. This however is dominated by its positive effect, as ruggedness aided a population to resist or escape slave traders raids, the consequences of which can be detected in better institutions today. Jared Diamond s Guns, Germs, and Steel is perhaps the most popular exposition of geography s role in shaping human history (Diamond, 1997). Diamond focuses on soil fertility and the presence of edible plants, potentially domesticated wildlife, and infectious diseases, tracing their role in the development of ancient societies around the world. Olsson and Hibbs (2005), in a direct test of Diamond s hypotheses, use 1

continent size, east-west orientation, climate, and availability of potentially domesticated plants and animals to explain the timing of a region s transition into sedentary agriculture. In their empirical results, they find significant evidence in support of Diamond s hypothesis. Putterman (2008), in an extension of Olsson and Hibbs (2005), refines the analysis by observing these variables effects on population density in the year 1500 as well as on modern-day income, controlling for the transmission of agricultural technologies via migration. Putterman finds that the knowledge and technologies that accrued to populations in their historic lands were carried by later generations to newly settled areas. 1 The analysis in this paper focuses on urbanization, which is a particularly visible and economically important historical event with strongly persistent effects. Urbanization is rarely reversed and usually proceeds cumulatively at a given location. One can think of urbanization in terms of a break from farm households Malthusian dependence on local natural resources to more use of man-made capital, specialization and agglomeration which facilitate the start of modern economic growth (Lucas, 2000). Variation in the timing of such breaks has been linked to differences in institutional quality, total factor productivity, and geography (Ngai, 2004; Gollin et al., 2002). Economic transition itself entails a variety of contemporaneous changes, including rising productivity in both agriculture and manufacturing; sectoral shifts in employment, output and expenditure from agriculture to manufacturing and services; and a demographic transition in mortality, fertility and the age structure of the population (Kuznets, 1973; Williamson, 1988). We focus only on the most visible, and thus best recorded, aspect of economic transition, which is the shift from rural to urban residence. Our approach to economic geography utilizes global grid cell data, disaggregating the whole world into regular cells defined only by their latitude and longitude. To our knowledge, the first paper on economic growth to exploit such data directly is Masters and McMillan (2001), who test a variety of possible influences on cell-level population density, and then aggregate cell-level attributes to the country level to test their relationship with national per capita income growth. More recently, Nordhaus (2006) disaggregates all economic activity into 1 by 1 cells, and finds the level of activity to be highly correlated with climate and topography. Economic data rendered in grid cell units, as opposed to political, administrative, or other geographic regions, offer important advantages for empirical analysis. Such regions are smaller than most countries or even provinces, and thus offer a larger number of distinct observations. The boundaries of each observation are defined arbitrarily in regular intervals of geographic coordinates and not subject to the potential endogeneity of administrative boundaries. 2 The corresponding challenge is to allocate socioeconomic activity across grid cells, with the underlying data originally being collected on the basis of administrative boundaries. Our starting place is a stylized model of urbanization in a closed economy, in which urban growth depends on production of subsistence goods and transport costs in the surrounding countryside. Testing the model with grid cell data, we reject the hypothesis that each cell is in fact an independent observation of closed-economy growth. Such spatial dependence could be due to spatially correlated omitted variables, or interactions between cells through common institutions, trade, migration, investment or other channels (McMillen, 2003). To control for many different types of distance-dependent spatial processes, we use a very general spatial error model (Anselin, 1988). Beyond these controls, each cell s agroclimatic suitability for agriculture still correlates closely with its speed of urbanization, with a particularly strong link at early stages of city growth. Access to low-cost transportation also facilitates urbanization, particularly at later stages. The remainder of this paper is organized as follows. Section 2 motivates the examination of geography s relationship to economic transition. Section 3 introduces the data, Section 4 presents the methods and 1 The papers discussed here all focus on how physical geography might have influenced historical events and institutions. A related but different literature looks at the contemporary effects of geography, including for example the role of access to navigable waterways, frost prevalence, and malarial ecology (Gallup et al., 1999; Masters and McMillan, 2001; Sachs, 2003). Some authors, such as Easterly and Levine (2003), find that geography-related variables influence modern incomes only through their historical effect on institutions. 2 For example, if economically successful societies tend to seek control over locations with attractive geographical features (e.g., access to navigable waterways), their institutions would become correlated with geography even if their initial wealth accumulation was caused by something else. 2

discusses the results, and Section 5 concludes. 2 Motivation 2.1 Transition from Malthusian stagnation to modern growth In the standard literature on economic growth, explanations for the extreme differences in present-day national incomes initially focused on recent growth rates, which were shown to be associated with disparities in national savings rates, technical change, human capital, institutions, and even genetic distances between populations (Solow, 1956; North, 1990; Mankiw et al., 1992; Spolaore and Wacziarg, 2009). More recently, models have focused instead on differences in income levels, which could be primarily driven by the timing of transition from a Malthusian regime of low or zero long-run growth into a modern regime in which higher growth rates are sustained over time (Lucas, 2000). If growth paths within each regime are similar and differences are attributable to the date of transition, then the relevant research question is historical: not what differences exist today, but rather why some places start down the path of modern economic growth earlier than others. Figure 1 suggests that both the start date and the pace of modern growth are important. For each region, the development of per capita income has a clear structural break. 3 Western Europe s income began to rise soon after 1800, Latin America s approximately fifty years later, and Asia about fifty years after that. Africa s income appears to break more gradually, though it certainly occurs at the end of the sequence. Most evidence suggests that per capita incomes grew negligibly prior to industrialization. Over the millennia, human development resulted in considerable population growth but not much improvement in living standards (Birdsall, 1988). Despite constant incomes, however, population growth and the accumulation of knowledge could have changed things so that switching to new technologies eventually became profitable (Galor and Weil, 2000; Hansen and Prescott, 2002; Strulik and Weisdorf, 2008). Such a switch is said to have occurred in eighteenth-century England, perhaps involving changes in property rights (McCloskey, 1972; Clark, 1992; Clark and Clark, 2001), improved soil fertility through animal manure, (Chorley, 1981) or nitrogen-fixing legumes (Allen, 2008), raising farm productivity in a way that could have helped sustain industrialization over time. Improvements in agricultural productivity have long been seen as necessary for the sustained growth of industry (Johnston and Mellor, 1961), typically because of nutrition constraints and Engel s Law (Matsuyama, 1992; Kögel and Prskawetz, 2001; Gollin et al., 2002). This implies that, in a closed economy, low farm productivity traps workers in agriculture. Only when agricultural production per worker rises above subsistence needs can resources shift to non-farm activities. A location s successful agriculture does not, however, guarantee industrialization, especially if manufacturing involves scale economies and transport costs. Krugman (1991) demonstrated how scale economies interact with transport costs to drive agglomerations of firms in a particular place. 4 Murata (2008) links Engel s Law to the spatial location of firms to show that falling transport costs can raise real wages and drive up food consumption. Later, upon satisfying the food requirement, consumption of manufactured goods begins to rise, and ultimately, this spurs agglomeration. Capital accumulation and the use of intermediate goods can accelerate this process, as in the model of Gallup et al. (1999) where lower transport costs help make capital investment more profitable. In this paper we build on the Matsuyama (1992) model of a closed dual-sector economy, modified to include intraregional transport costs for nonfarm activity. In our model the rural sector is defined simply as dispersed activity that occurs close to consumption and produces, among other things, some subsistence goods such as basic foods. The urban sector is agglomerated activity, whose profitability depends, among on other things, on transport costs into and out of the city. We reduce the model to a single period and do 3 The regions are grouped following Maddison et al. (2001), with the exception that we combine east and west Asia into one category from which we exclude Japan. 4 Numerous variations on this original model have appeared since then, including Fujita and Krugman (1995), Fujita et al. (2001) and Puga (1999). 3

20000 15000 Western Europe 1990 international dollars 10000 5000 Latin America Asia 0 Africa 1600 1700 1800 1900 2000 year Figure 1: Regional per capita GDP, 1600-2000 AD. Source: Maddison et al. (2001) Note: Asia category excludes Japan not distinguish between capital accumulation, scale economies or technical change, all of which are captured by a single labor productivity parameter in each sector. This simplified framework leaves just two distinct channels through which physical geography can affect the timing of transition from rural to urban life. First, the timing of transition would be accelerated by higher agricultural productivity, which releases labor and creates purchasing power in rural areas. Second, transition would occur earlier with lower transport costs into or out of the city, which raises the profitability of urban activity. 2.2 The model An area s labor force is divided between rural and urban inhabitants, denoted N r and N u, respectively. Without loss of generality, their sum is normalized to unity (N r + N u = 1) so the number of workers can be interpreted as a share of total employment. For the rural sector, output Y r is only a function of employment and labor productivity, A r : Y r = A r N r, (1) where A r captures everything that might determine rural labor productivity in meeting subsistence needs, including not only institutions and policies, but also climate and soils. The urban product is the numeraire good. Assuming all rural output is valued at similar prices, profits π r are: π r = pa r N r wn r, (2) where p is the price paid to producers, and w is the wage rate paid to labor. For producers of urban goods, output Y u is a function of just productivity A u and labor N u. Y u = A u N u. (3) Urban profits depend not only on productivity and the wage rate but also on transportation costs between the city and the surrounding rural areas: π u = (1 t) A u N u wn u, (4) 4

where π u represents profit, w is the wage paid to labor, and t is transport costs. In this static model, any capital accumulation or scale effects are swept into the productivity parameters and are left unspecified. The model accounts for two possible channels for physical geography to play a role. The first channel is in the form of transport costs t that urban firms must pay to reach people outside the city. The second channel is the agroecological inputs to rural productivity, A r, that help meet workers subsistence needs. 5 Equilibrium between the sectors hinges on both labor migration and goods transport. When workers are mobile and firms are price takers, each sector s labor quantity N adjusts to yield wage equations, which, in competitive equilibrium, are such that the price ratio p of the two goods is: p = (1 t) A m A a. (5) To close the model, we follow Matsuyama (1992) and impose a subsistence constraint for all workers. This takes the form of a minimum consumption requirement for the good produced by rural workers: U (C r, C u ) = ln (C r r) + ln (C u ), (6) where C r represents consumption of agricultural goods, r is the minimum food requirement for subsistence, and C u is consumption of manufacturing. 6 First-order conditions for equilibrium imply that the marginal rate of substitution for rural and urban goods will equal their price ratio: C u C r r = (1 t) A u A r. (7) Since the economy is closed, quantity consumed equals quantity produced, thus: Substituting the production technologies into equation (8) yields: and rewriting N r in terms of N u and simplifying leads to: Solving the above equation for N u and simplifying, we obtain: Y u Y r r = (1 t) A u A r. (8) A u N u A r N r r = (1 t) A u A r. (9) N u (1 t) =. (10) A r (1 N u ) r A r N u = 1 t 2 t (1 rar ). (11) Comparative statics show the effect of a change in agricultural productivity A r on the composition of labor between the two sectors: N u = r 1 t A r A 2 r 2 t. (12) Transport costs t are defined as a fraction between zero and one, so N u / A r > 0, and a rise in agriculture s productivity causes labor to move from agriculture into manufacturing. However, workers do not begin to exit agriculture until the level of A r equals the nutrition requirement r. Beyond that point, higher rural productivity translates into greater urbanization, although at a diminishing rate at higher levels of rural productivity and urbanization. 5 One might also introduce transportation costs within the rural sector, which would delay the formation of cities without otherwise altering our model. 6 This linearized form derives from Cobb-Douglas preferences. 5

Meanwhile, transport costs also matter for urbanization. Differentiating (11) with respect to transport costs t reveals how changes in transport costs affect the allocation of labor between sectors: ) (1 rar. (13) N u t = 1 (2 t) 2 For the derivative to take a negative sign, the second term on the right hand side of the equation must be positive. This condition is met as long as rural productivity exceeds the subsistence requirement: A r > r. (14) Figure 2 summarizes the predictions taken from equation (11) regarding the effect of farm productivity and transportation, including their diminishing effects on urban activity. Both lines in the figure illustrate urbanization s response to farm productivity at a particular level of t, high and low. The figure reflects the constraint that the urban population fraction cannot be negative, and as a result, a kink appears at the point where A r reaches r. Figure 2: Urbanization and agricultural total factor productivity The central testable hypothesis of our model is that higher agricultural productivity and lower transport costs both facilitate urbanization, for all inhabited locations where basic subsistence needs are met. A secondary hypothesis is that, as productivity rises and urbanization proceeds, additional increases in farm productivity have a diminishing effect on further urbanization. 3 Data Our focus in this paper is the variation in geography and climate across continents and regions, exploiting grid cell data on variables that could be associated with either rural productivity or transportation costs. Since these observations are not time-varying, we can test their link to urbanization using the historical date at which each location s urban population passed various thresholds. This approach is consistent with some exogenous source of demographic change or knowledge accumulation that drives urbanization. Our goal is to explain some of the variance across grid cells in the timing of that urbanization. The unit of observation is an arbitrarily-defined geographic region, which in our case are grid cells demarcated by lines at intervals of 0.5 latitude and 0.5 longitude. Such cells are largest at the equator, where each cell covers approximately 3,000 square kilometers. At the Arctic Circle, grid cells are about one-third that size. The total number of such half-degree cells in our dataset is 62,290. 6

Empirically, we are testing T = f (G r, G u ), where T is the year at which a grid cell acquired an urban population of a specific size, G r are the grid cell s geographic correlates of rural productivity, and G u are its geographic correlates of lower transport costs. To permit a causal interpretation of any correlation between T and these geographic features G, we must choose features that are not themselves influenced by urbanization, either directly or indirectly. The strengths and limitations of each regressor are discussed in turn below, after we present the data on urbanization. 3.1 Urbanization Historical data on the location and population of cities have been collected and assigned to grid cells and matched with estimates of the surrounding rural populations by Klein Goldewijk et al. (2010). The authors used a wide range of census figures, historical records, scholarly publications, and interpolations over time and space to construct an internally consistent time series of rural and urban populations for each grid cell, from year 0 to 1600 in century intervals, and from 1700 to 2000 in decade intervals. The details underlying the construction of their data set can be found in Klein Goldewijk et al. (2010) and its supplemental materials. From those data we compute for each cell a time period T defined as the number of years that have passed since year t at which a cell reached a particular urbanization threshold. Thus, T = 2000 t. 7 Urbanization thresholds can then be defined in either of two ways: as the absolute number of urban people in that grid cell, or as the urban fraction of that cell s total population. Our tests compare results using both definitions, at various levels of the threshold. First, in terms of the absolute number of urban people, we follow Acemoglu et al. (2002), who built on Bairoch (1998) and judged urbanization to have started once a location could support over 5,000 urban inhabitants. Since grid cells closer to the equator are larger, we normalize by area and define the Bairoch rule in terms of the smallest cell that supported an urban population greater than 5,000 in the year 2000. That cell turns out to have had a size of 881 square kilometers, so our threshold for the absolute number of urban people is actually 5.67 urban inhabitants per square kilometer. 8 This value is then applied to grid cells of other sizes, offering a consistent measure of economic activity for cross-sectional comparison purposes. For comparison, we also use a lower threshold of one person per square kilometer. At the equator, this corresponds to approximately 3,000 urban inhabitants per grid cell. For robustness, we compare results with the number of urban people against results based on the fraction of people who are urban, for which we follow Williamson (1988) and many others and consider a range of thresholds: 10%, 25%, and 50%. Figure 3 presents the geographic distribution of the duration since transition at the 10% level. Maps for the other thresholds have a similar appearance, and formal summary statistics are presented at the end of this section. The temporal scope and spatial resolution of the data set causes potential inaccuracies in the estimated population values and therefore warrants caution in interpreting the results, particularly with respect to the earlier time periods. However, one should note that the analysis in this paper focuses on urbanization. Ninety-nine percent of all cells that achieved 10% urbanization did so only in the last 400 years, and among the cells that reached 50% urbanization, 99% percent occurred within the past 170 years. In other words, nearly all the historic urbanization outcomes occur in the most recent time periods when records of urban populations were relatively accurate. For this reason, the potential inaccuracy of a particular grid cell s pre-modern population, given that its composition was almost certainly rural, does not meaningfully affect the analysis. Rather, it is the timing of this cell s urban break from its rural past, an event most likely to have occured recently, that matters substantively. 3.2 Cultivation Suitability Index To capture soil and climate conditions associated with rural production of subsistence goods, we start with an index of each grid cell s suitability for cultivation prepared by Ramankutty et al. (2002). These data 7 We use the year 2000 as the base year, since that is the last time period for which data are available. 8 This smallest of all urbanized grid cells lies above the Arctic Circle, along the northern coast of Norway. A threshold of 5,000 urban people divided by its area of 881 square kilometers yields the 5.67 urban people per square kilometer. 7

Figure 3: Number of years since transition to a 10% urban population or greater. Source: Authors calculations from Klein Goldewijk et al. (2010). Darker colors represent a transition occurring longer ago. See Table 1 for details. are constructed from geo-referenced observations covering the number of growing degree days, actual and potential evapotranspiration, soil carbon density and soil ph. The suitability index ranges from zero to one, and is calibrated to the probability that a particular location was actually cultivated in 1992. 9 Figure 4 presents a map of these data. Although the Ramankutty et al. (2002) measure of cultivation suitability is constructed from purely exogenous climatic and geological features of the landscape, the selection and weights on variables in the index are potentially influenced by reverse causality from urbanization. This could arise to the extent that successful urbanization led to greater cultivation intensity of the surrounding areas. The resulting formula might then include variables such as availability of drinking water or drainage that reflect the needs of urban activity as much as rural productivity. In fact, however, the Ramankutty et al. (2002) index includes no such variable. For the variables actually used (temperature, evapotranspiration, soil carbon and soil ph), the only plausible channel of influence on urbanization is through farm productivity. Plotting the Klein Goldewijk et al. (2010) urbanization data against the Ramankutty et al. (2002) cultivation suitability index reveals the correlation between them. Figure 5 shows urbanization rates as a function of cultivation suitability in selected years, for all cells that were actually inhabited in that year, using a local polynomial regression to compute confidence intervals around local means. The resulting lines are empirical versions of Figure 2, without controlling for transport costs or other factors, and omitting the region of uninhabited cells where subsistence needs are not met. The curves shift upward as time passes, as the average urbanization rate for cells at each level of cultivation suitability increases over time. For example, cells with a cultivation suitability index of 0.4 had average urbanization rates that rose to cross the 10-percent threshold around 1950 and passed 30 percent by 2000. It is this upward trend that we exploit in our cross-sectional tests, regressing the number of years since each individual cell crossed various thresholds on that cell s own cultivation suitability index and other factors. 3.3 Transportation costs: distance to navigable waterways Our theoretical model suggests urbanization depends not only on farm productivity but also on low transport costs to support agglomeration. Here, the main geographic variable we use to capture historical transport 9 Probabilities were assigned on the basis of the areal fraction of each grid cell that was observed by remote sensing to be cultivated in that year. 8

Figure 4: Worldwide distribution of land suitability for cultivation. Darker shades represent higher index values. Source: Ramankutty et al. (2002). See Table 1 for details..4 2000.3 rate of urbanization.2 1970 1950.1 1900 1800 0 0.2.4.6.8 1 cultivation suitability index Figure 5: Local polynomial regression of urbanization on cultivation suitability. Note: Shaded regions show 95% percent confidence intervals around each line, fitting a zero degree polynomial, with bandwidths of 0.09, 0.09, 0.09, 0.1, and 0.12 for the years 2000, 1970, 1950, 1900 and 1800 respectively, selected by rule-of-thumb using Stata s lpolyci command. 9

costs is a grid cell s distance from a navigable waterway. Proximity to navigable waterways is captured in two variables. The first measure is distance in kilometers to the coast, calculated from the centroid of each half-degree grid cell to the nearest unbounded sea or ocean. This is presumably most important for transport to and from other regions, to enlarge the market for urban goods and to bring in subsistence goods from elsewhere. The second measure pertains to rivers, for which the Strahler order of streams are observed in each grid cell (Vörösmatry et al., 2000). The Strahler index ranges from 1 to 6, with six representing the largest river into which all tributaries flow and one representing a small stream with no tributaries. We interpret larger order values to reflect greater inherent navigability of a river. This avoids the potential endogeneity that arises when using actual navigability data, which are influenced by human interventions such as dredging, locks, and the design of suitable boats. 3.4 Seasonal frost and elevation The variables described above are complemented by data on seasonal frost, which captures an additional dimension of agricultural productivity, and elevation, which could matter for both agricultural productivity and the cost of transport. For frost, we follow Masters and McMillan (2001) and use a dummy variable to capture whether or not a cell receives frost in winter, after a frost-free summer. This measure is intended to capture a potentially important aspect of temperate as opposed to tropical environments, in which postharvest frosts help control pests and diseases until the next warm season. The prevalence of ground frost is computed from IPCC (2002), as a dummy variable equal to one for cells that receive a significant level of frost in winter, conditional on having no frost in summer. The cutoff we use is 2.11 frost-days per month, corresponding to the threshold estimated econometrically by Funke and Zuo (2003). Combining the cultivation-suitability index with the prevalence of winter frost gives us two plausible measures of agricultural productivity, capturing whether crops are easily grown and whether pests and diseases are easily controlled. A significant correlation between these geographic features of a grid cell and the date at which the grid cell urbanized would be consistent with our model, and with the broader idea that farm productivity plays a causal role in economic transition. We use average grid cell level elevation due to Hijmans et al. (2005) to capture the ease of surface transportation, such as barriers to mobility on foot and using animals or motorized vehicles. More complex measures of topography were considered for this paper, including a grid cell s standard deviation of elevation, its average gradient, and its ruggedness, but these are all highly correlated with average elevation so we ultimately chose the simplest possible measure so as to avoid any concern about endogeneity due to ex-post selection from among a large pool of candidate variables. 3.5 Summary statistics The stylized model described above does not apply to locations that are uninhabited. For this reason, we limit our sample to those grid cells that had at least one inhabitant at some point over the entire time frame. The resulting sample consists of 52,144 grid-cell observations, summarized in Table 1. The dependent variables of interest are the number of years since various thresholds of urbanization were reached. Their maximum values reveal that, at the start of our data about 2000 years ago, some cells had already reached the first threshold of one urban inhabitant per square kilometer. About 200 years later the first cells reached the threshold of having 10 percent of their population in urban areas. The mean date of urbanization, however, was much more recent and many cells have not yet passed any of our five thresholds. 10

Table 1: Summary statistics for all variables a Number of years since cell reached: Mean Std. Dev. Min Max 1 inhabitant per sq. km. 35.29 118.98 0 2000 5.67 inhabitant per sq. km. 18.83 67.23 0 1600 10% urbanization 40.64 102.38 0 1800 25% urbanization 23.51 57.84 0 1100 50% urbanization 11.42 33.50 0 700 cultivation suitability index 0.31 0.32 0.0001 1.00 distance to coast (km) 566.49 525.71 0 2514.70 Strahler order of streams 1.04 1.03 0 6 seasonal frost b 0.41 0.49 0 1 land elevation (meters) 630.84 821.49-29.33 5717.11 Source: Authors calculations from sources detailed in the text. a Total number of observations is 52,144. b Seasonal frost refers to 2.11 or more days per month of ground frost in winter after a summer with less than 3 total days of ground frost. 4 Methodology and results 4.1 Model specification Our basic specification is to regress a grid cell s time since its date of urbanization, as measured by one of the five thresholds listed above, on our geographic variables plus country fixed effects: ln T ij = β 0 + β 1 ln cultiv ij + β 2 ln coast ij + β 3 river ij + β 4 frost ij + β 5 ln elevation ij + δ j + ɛ ij, (15) where T ij represents the number of years elapsed since grid cell i in country j passed the given level of urbanization, cultiv is the cultivation suitability index, coast is the distance from a grid cell s centroid to the nearest unbounded sea or ocean coast, river indicates the presence of a river of Strahler order 4 or greater, frost indicates the presence of frost in winter after a frost-free summer, and elevation is the average elevation of the cell s land area. Country fixed effects are captured by the variable δ j. Grid cells that span more than one country are assigned to the country that occupies the greatest area of the grid cell. To assure consistency, we use a year 2000 map of country borders, even though these borders may not have been in place at the time of each grid cell s urbanization. Absorbing fixed effects in this way makes our estimates refer only to within-country effects. Robustness tests will include regressions without these controls. As described earlier, cells that have not reached a particular urbanization threshold receive zero values for T. 10 In fact, across the different urbanization thresholds, more than two-thirds of the observations have not experienced any urbanization. This outcome can be interpreted in two ways. First, the presently-observed sample may reflect a long-run equilibrium outcome; thus the rural or urban character of a cell is no longer expected to change. Or, alternatively, the outcomes could be understood to reflect a snapshot of a process that is not yet complete. In the future, some of these zero-valued cells may reach some urban threshold, implying a presently negative value of T instead of the observed zero that is reported here. If T is censored at zero, naïve estimation of (15) could therefore involve substantial attenuation bias, which we can address using Tobit regressions as detailed below. Our analytical model and regression specification are highly stylized, omitting a wide range of variables that could lead to bias or inefficiency in estimating equation (15) by ordinary least squares (OLS). Most 10 For purposes of estimation, we assign these cells the value one to permit the log transformation. 11

fundamentally, we use a closed-economy model and only the cell s own values in the model, when we expect there to be at least some interactions between cells that influence each others urbanization rates. To account for this, we employ a spatial autoregressive error model which captures spatial dependence in the error term. 11 y = βx + µ, (16) µ = λw µ + ɛ. In the second equation, the error term µ is a function of its neighbors errors W µ and an additional independent error term ɛ. W is a spatial weights matrix that identifies the immediate neighbors of each observation. 12 The following section presents and discusses the results of the three model specifications: simple OLS, Tobit, and the maximum likelihood spatial error estimator. 4.2 Results and discussion Tables 2 through 6 present the results for the simple OLS, the Tobit estimates along with its associated marginal effects, as well as the spatially explicit estimates, with and without country dummies. Across all specifications, the results reject the hypothesis that urbanization s timing is uncorrelated with our primary geographic variables. Consider, for example, the spatial error model results from Table 5. Based on the coefficient for cultivation suitability in the 10% urbanization model, a one percent increase in cultivation suitability introduces transition nearly 0.219% earlier on average. In other words, doubling a location s cultivation suitability index introduces urbanization ln(2.219 ) or 15% earlier than average. Doubling a location s distance from a coastline postpones its urbanization by 6% on average. Raising a cell s order of streams by one unit and the occurrence of seasonal frost introduce urbanization nearly 18% and 24% earlier, respectively. Across all specifications, we find strong significance for all of our variables, with the exception of elevation in certain specifications and at certain thresholds. 13 In short, grid cells whose land is more suitable for cultivation and are exposed to frost in winter urbanized earlier in history, as did cells that are closer to the seacoast and had more navigable rivers. Results reported above correspond to within-country differences, after controlling for country fixed effects. Those country effects are themselves potentially of interest, since they capture impacts of social, institutional and policy factors beyond the simple distance-dependent effects absorbed in the spatially autoregressive errors. For illustration purposes, country fixed effects for the 25% urbanization threshold are presented in Figure 6. Clearly some of the variation is systematically absorbed by country dummies, which show earlierthan-average urbanization primarily in Northwest Europe, but also the rest of Europe, Scandinavia and the Near East, plus the United States, Argentina and New Zealand. An interesting feature of our results is that certain geographic characteristics decline in importance at higher urbanization levels. Specifically, cultivation suitability, river order, and elevation exhibit smaller coefficients going across columns 1 and 2 of Table 5, as well as columns 3, 4 and 5. 14 These aspects of physical geography are closely linked to the initial formation of urban settlements, up to 10 or 25 percent 11 Alternative specifications such as spatial lags could be imposed and compared using Lagrange Multiplier tests (Anselin et al., 1996), which would allow statistical criteria to drive the choice of specification. Here we deliberately impose the most general specification, to absorb into the spatial error term any unobserved neighborhood characteristics such as shared language, ethnicity, region-specific technology or local institutions. Country-level effects for which national borders define the neighborhood are captured separately by our country fixed effects. 12 Neighbors are defined according to the first order queen criterion of contiguity. In most cases, this denotes the immediate 8 grid cells that surround a cell on the map. This neighborhood of cells corresponds to a square area with sides roughly 161 kilometers in length at the equator. 13 Tests for heteroskedasticity reveal that the variance of the residuals is non-constant, potentially biasing the estimates of the standard errors. We do not, however, report robust standard errors since the standard errors are very small, and our inferences would not change meaningfully. 14 Since the only difference across the specifications is the dependent variable, we constructed the 99% percent confidence interval for the estimated coefficient of each explanatory variable and observed that, across the models, none of the value ranges overlap. This approach offers reasonable assurance that the coefficients differ across models, although this is not a formal statistical test. 12

Table 2: Urbanization and Geography, OLS Dependent variable: no. of years since urbanization 1 inhabitant 5.67 inhabitants 10% 25% 50% per sq. km per sq. km urban urban urban (1) (2) (3) (4) (5) cultivation suitability 0.285 0.197 0.219 0.165 0.092 (0.004) (0.004) (0.005) (0.004) (0.004) distance to coast 0.147 0.148 0.164 0.164 0.144 (0.006) (0.005) (0.007) (0.006) (0.005) order of streams 0.186 0.161 0.200 0.164 0.119 (0.007) (0.006) (0.009) (0.008) (0.007) frost 0.551 0.419 0.472 0.405 0.297 (0.020) (0.017) (0.023) (0.021) (0.018) elevation 0.019 0.030 0.030 0.001 0.013 (0.007) (0.006) (0.008) (0.007) (0.006) constant 2.414 0.525 2.346 1.489 0.757 (0.111) (1.767) (0.126) (0.115) (0.097) R 2 0.37 0.38 0.26 0.25 0.20 Note: n = 52, 144 Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1 All regressions include fixed effects for 186 countries (not shown). of the total population, and have significant but lower correlation with further urbanization beyond that. That relationship is robust across all of our specifications. In the model that controls for spatial errors, however, two of the geographic variables have estimated coefficients that do not vary with the level of urbanization: distance from the coast and the presence of seasonal frost. These geographic factors remain similarly correlated with the timing of urbanization past each successive threshold, suggesting a sustained influence on the continued growth of cities well after their initial formation. Our geographic variables contribution to the start of urbanization is illustrated in Figure 7. Specifically, the figure depicts the spatial distribution of predicted number of log years ago since urbanization reached the 10% threshold, obtained by multiplying each cell s value for cultivation suitability, coastal distance, order of streams, seasonal frost, and elevation by their respective coefficients. (The coefficients for this map are taken from Table 5, the spatial error model with country dummies using the 10% urbanization threshold.) The geographic variables alone predict urbanization to occur earliest in a handful of unsurprising locations: the northern coast of Europe, including Amsterdam, the area around Venice in southern Europe; eastern China around Shanghai; and around Dhaka in South Asia. In the Western Hemisphere, this includes the deltas of the Mississippi River around New Orleans, as well as the Rio de la Plata which terminates at Buenos Aires. Interestingly, the model predicts a large unrealized spatial concentration of early urbanizers around the Caspian Sea, which is classed as a seacoast but had no outlet to the open ocean until completion of the Volga-Don canal in 1952. Africa falls nearly entirely in the later half of the predicted urbanization period. The only grid cell predicted to urbanize early corresponds to the city of Accra in Ghana. Similarly, the interiors of Latin America and South Asia are predicted to lag in urbanization, relative to Europe and the Asian and North American coasts. Locations predicted to experience urbanization last are typically surrounded by deserts, mountains, or permafrost. Population densities in these parts of the world are so sparse that they may ever urbanize. Figure 7 shows that the predicted number of log years ago, based on our five geographic variables, ranges 13

Table 3: Urbanization and Geography, Tobit Dependent variable: no. of years since urbanization 1 inhabitant 5.67 inhabitants 10% 25% 50% per sq. km per sq. km urban urban urban (1) (2) (3) (4) (5) cultivation suitability 1.227 1.274 0.657 0.618 0.551 (0.018) (0.023) (0.013) (0.014) (0.018) distance to coast 0.413 0.588 0.415 0.491 0.614 (0.018) (0.022) (0.017) (0.018) (0.023) order of streams 0.457 0.587 0.448 0.458 0.511 (0.022) (0.026) (0.020) (0.023) (0.028) frost 1.344 1.605 0.964 0.921 0.944 (0.061) (0.078) (0.057) (0.064) (0.081) elevation 0.000 0.019 0.060 0.011 0.071 (0.021) (0.025) (0.020) (0.021) (0.028) constant 2.849 1.625 2.043 0.145 4.977 (0.313) (0.384) (0.316) (0.379) (1.236) R 2 0.34 0.30 0.21 0.21 0.12 Number of censored 35,530 40,654 31,388 35,131 41,034 observations Note: n = 52, 144. Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1 All regressions include fixed effects for 186 countries (not shown). R 2 value is the squared correlation between predicted urbanization date and actual urbanization date. Table 4: Urbanization and Geography, Tobit marginal effects Dependent variable: no. of years since urbanization 1 inhabitant 5.67 inhabitants 10% 25% 50% per sq. km per sq. km urban urban urban (1) (2) (3) (4) (5) cultivation suitability 0.357 0.191 0.281 0.204 0.096 (0.004) (0.003) (0.006) (0.005) (0.003) distance to coast 0.120 0.088 0.178 0.162 0.107 (0.005) (0.003) (0.008) (0.006) (0.004) order of streams 0.133 0.088 0.192 0.151 0.089 (0.006) (0.004) (0.009) (0.007) (0.005) frost 0.391 0.241 0.412 0.304 0.165 (0.018) (0.012) (0.025) (0.021) (0.014) elevation 0.000 0.003 0.025 0.004 0.012 (0.006) (0.004) (0.008) (0.007) (0.005) n = 52, 144 Delta method standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1 Marginal effects are calculated at the variable s mean, conditional on the uncensored observations. 14

Table 5: Urbanization and Geography, spatial error model with country dummies 1 inhabitant 5.67 inhabitants 10% 25% 50% per sq. km per sq. km urban urban urban (1) (2) (3) (4) (5) cultivation suitability 0.266 0.186 0.221 0.173 0.100 (0.007) (0.006) (0.008) (0.007) (0.006) distance to coast 0.078 0.091 0.092 0.122 0.127 (0.009) (0.007) (0.010) (0.009) (0.007) order of streams 0.142 0.119 0.177 0.157 0.122 (0.007) (0.007) (0.008) (0.008) (0.007) frost 0.305 0.253 0.238 0.244 0.210 (0.030) (0.025) (0.033) (0.030) (0.024) elevation 0.120 0.109 0.131 0.073 0.030 (0.011) (0.009) (0.013) (0.011) (0.009) λ 0.585 0.546 0.585 0.530 0.460 (0.005) (0.005) (0.005) (0.005) (0.006) R 2 0.35 0.30 0.31 0.25 0.17 Note: n = 52, 144. Sample excludes all grid cells that lack contiguous neighbors. Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1 All regressions reflect controls for 186 countries (not shown) in terms of deviations from country-level means. Table 6: Urbanization and Geography, spatial error model without country dummies Dependent variable: no. of years since urbanization 1 inhabitant 5.67 inhabitants 10% 25% 50% per sq. km per sq. km urban urban urban (1) (2) (3) (4) (5) cultivation suitability 0.273 0.199 0.215 0.161 0.084 (0.007) (0.006) (0.008) (0.007) (0.005) distance to coast 0.113 0.117 0.126 0.152 0.144 (0.009) (0.008) (0.010) (0.009) (0.007) order of streams 0.145 0.119 0.187 0.169 0.132 (0.008) (0.007) (0.008) (0.008) (0.007) frost 0.363 0.356 0.275 0.319 0.279 (0.029) (0.025) (0.032) (0.029) (0.023) elevation 0.127 0.117 0.142 0.096 0.061 (0.012) (0.010) (0.013) (0.012) (0.009) constant 3.024 2.405 3.325 2.728 1.876 (0.063) (0.055) (0.070) (0.062) (0.050) λ 0.688 0.678 0.666 0.629 0.571 (0.004) (0.004) (0.004) (0.005) (0.005) R 2 0.52 0.49 0.44 0.38 0.30 Note: n = 52, 144. Sample excludes all grid cells that lack contiguous neighbors. Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1 15

Figure 6: Country fixed effects from the spatial error model (25% urbanization) from 0.02 to 2.87, which translates to about one to 18 years. These values are small relative to the full span of our data, but note that the average grid cell urbanized at the 10% threshold only about 40 years ago, so our five variables can account for substantial differences in the timing of urbanization over the relevant time period. 4.3 Transition and modern national income We have shown that physical geography is closely linked to the date at which people move into cities. Recall Figure 1 in which incomes are plotted over time for different regions. A similar pattern holds with urbanization for different geographies. For example, Figure 8 shows the time path of average urbanization rates for the universe of all grid cells that eventually achieved at least 10% urbanization by the year 2000, divided into two samples: one line traces average urbanization for those cells whose cultivation suitability index is above the median value, 0.391, and the other traces the average of all grid cells whose cultivation suitability index is below that value. Figure 8 illustrates the idea that locations with higher agricultural land quality may have, on average, urbanized earlier than areas with lower agricultural land quality. Since urbanization plausibly links geography to modern income, we ask whether the historic date of a country s urbanization matters to income today. Following Olsson and Hibbs (2005) and Putterman (2008), the implicit hypothesis is that the earlier a country was able to urbanize, the higher its present-day income can be. Figure 9 illustrates this possibility, plotting a country s real per capita income against the number of years since any of its grid cells first reached 25% urbanization. 15 There is a strong correlation, and the outliers are themselves of interest: below the regression line are several countries such as China, India and Italy which had early urbanized centers but persistent poverty in hinterland areas. Countries above the line include Luxembourg, Qatar, and Singapore all of which urbanized late but are geographically small and had no lagging hinterland. We test the relationship between national income and cell-level urbanization more formally in a regression framework, again accounting for spatial dependence due to distance-dependent but otherwise unobserved heterogeneity. The dependent variable here is per capita national income at PPP prices in 2000 taken from Penn World Tables (Heston et al., 2006). We regress income on the number of years since at least one of 15 We use the country s first cell to urbanize, rather than the average date of a country s cells, to capture the start of a country s transition wherever it may occur. 16