Economic Markets Follow Terrain and Transport Technology, Not Fixed Grid Cells

Economic analysis often divides the world into latitude-longitude cells. But people do not make decisions inside equal-sized cells, Stephen Haber and Jordan Horrillo argue. They make them within markets whose reach depends on terrain, waterways, and the technologies available to move goods. A cell stays the same size over time; a market can expand or contract as those conditions change. Treating fixed cells as the units of analysis can therefore obscure the geography of the economic relationships researchers want to measure.

Haber and Horrillo’s proposed alternative is to define a market as the area reachable from a point under a specified transport technology and energy budget. The method makes market boundaries respond to the surface of the Earth and to the capabilities of the people moving goods. Markets can overlap, and that overlap provides a way to measure connections between places rather than treating each location as isolated.

They apply the method to a historical question: how much can the geography of markets help explain the distribution of cities in Eurasia and Africa around 1800? Their starting point is that city locations and populations offer one way to reconstruct the distribution of economic activity before satellite night-light data became available. Haber described night lights as a rough indicator of cities, not a precise substitute for economic activity. The satellite record reaches back only to the 1990s, limiting its use for long-run historical comparisons.

The researchers assembled a dataset of cities with at least 20,000 inhabitants in 1700 and 1800. They drew on online datasets, historical and archaeological research, specialist encyclopedias, historical dictionaries, and colonial gazetteers. Undergraduates collected records, which the researchers then audited city by city. Haber emphasized that this historical work required substantial manual effort and that the records become less reliable the farther back in time they go.

For the main application, the researchers focus on Eurasia and Africa. Haber described the distribution of cities there in 1800 as the outcome of millennia of trade, migration, and technological diffusion. They set aside the Americas and Australia because, in their account, those regions had been technologically isolated from much of that transfer until the arrival of Europeans. This is a scope choice for the analysis, not a claim that the Americas lacked cities: Haber pointed to Mexico City, which had a large population before European arrival, as a case where local food production and transport by canoe could support urban concentration.

The model asks how far a deliberately spare set of assumptions can go. People need food; cities need to be supplied with staple foods from places that can grow them; and cities and rural areas exchange manufactures and services. The researchers do not claim that geography alone determines city growth. They test how much of the observed pattern can be predicted from the physical conditions for producing and moving food, before incorporating other forces.

Haber and Horrillo place 41,435 market origins about 60 kilometers apart across Eurasia and Africa. They snap origins to nearby historically navigable water where appropriate. They also shift points within 10 kilometers of tsetse-fly endemicity to outside the affected area. From each origin, the model calculates how far one metric ton of bulk goods—grain is the example Haber gave—could travel before using up an energy budget of 40 megajoules.

The model chooses the most efficient combination of three transport modes: a horse-drawn wagon, a human porter, and a boat. The 40-megajoule budget is intended to be interpretable: Haber described it as the energy required to move a one-ton load by horse and wagon for 50 miles on flat, dry ground. As the load moves, the model accounts for the energy cost of gravity, friction, and drag. The market boundary is where the budget runs out.

A map illustrates why the resulting boundaries differ from uniform cells. A modeled market around Paris covers about 121,700 square kilometers. Rivers, access to the Channel, and relatively flat terrain allow movement by boat and wagon across a broad area, reaching into neighboring countries and toward London. Kayseri, in Turkey, has a market of about 19,500 square kilometers: without navigable water and with mountains to the south and east, movement depends more heavily on wagons. Nshenge, the capital of the Kuba Kingdom in what is now the Democratic Republic of Congo, has a modeled market of about 473 square kilometers under the same energy budget.

Haber connects Nshenge’s small market to the transport constraints associated with tsetse flies. Animal trypanosomiasis kills horses, mules, donkeys, and oxen, ruling out wheeled transport. Goods carried away from a river must therefore be transported by people, quickly exhausting the energy budget. Nshenge lies near, but not on, a river; Haber noted that its hilltop location served defense. The market estimate describes the reach of bulk-goods transport under the model’s assumptions, not the kingdom’s political or cultural importance.

The method’s boundaries are not independent. Markets can overlap, and their origins are close enough that their modeled reaches can include one another. Haber argued that this is a conceptual advantage over grid cells: the model can represent the extent to which markets connect. But it also complicates analysis, because overlapping units cannot simply be treated as independent observations.

The transport assumptions are specific to the eighteenth century. Haber described the model as using boats comparable to those associated with Lewis and Clark, wagons, and human porters. Boats can move over the sea, but the model uses the less efficient river-transport technology even for seaborne commerce. Haber said this choice was meant to bias the analysis against the idea that easy access to trade promoted city growth. The technology inputs can be changed—for example, by adding railroads or removing horse-drawn transport—but results under a different technology would answer a different question.

Geography is thus conditional on what people can do with it. To approximate eighteenth-century navigability, the researchers use modern terrain slopes but reconstruct navigable water with historical obstructions in mind. They remove rivers frozen for more than six months a year and restore obstacles such as rapids, waterfalls, marshes, and sandbars where these no longer appear on modern maps. The Congo, for example, is treated as unnavigable between the Malebo Pool near Kinshasa and the coast because of rapids and waterfalls. The researchers also add natural harbors, using a 1953 U.S. Navy study, a 1940s study of Africa, and reference data for the Caspian Sea.

To estimate how much staple food could be produced, they use GAEZ 4.0 and USDA data. Horrillo added traditional flood irrigation in arid regions, including the Sahel, the Indus Valley, and the Nile. Each market is characterized by its area, natural harbors, staple-food potential, and urban population. For city locations, the researchers also adjust present-day coordinates when necessary: historical city centers often sat near navigable water, while modern coordinates—typically associated with a city hall—may not preserve that relationship.

The model starts from a basic constraint: people must eat. To sustain people who specialize in work other than farming, a city must be supplied with staple food. In the researchers’ account, rural areas send food to cities, while cities exchange manufactures and services with rural areas and with other cities. Clusters of cities, they infer, indicate economic development emerging through markets.

In the base results, large urban populations tend to appear where market area, staple-food productivity, and harbor access are all toward the high ends of their distributions. The relationships are not treated as linear. The researchers use random forests, a method that can accommodate interactions and thresholds, because they expect a large market, productive land, and harbors to matter in combination rather than through a single straight-line relationship.

Market area does the most predictive work in the base model, followed by caloric productivity and then harbor density. The reported relationships are positive, but they vary in shape. For market area, the model predicts little change in urban density across smaller markets, then a sharper increase above a threshold. The harbor relationship is smoother: the first few harbors appear to matter more than later additions. These are patterns in the model’s predictions, not isolated estimates of the effect of changing one feature while holding the history of a city fixed.

The base model’s held-out R² is 0.48. In other words, the reported fit on markets set aside for testing is about 0.48. Its highest-predicted markets are concentrated: the top 10 percent take up 15.5 percent of Old World land and contain 80.9 percent of 1800 urban population. Including the next 10 percent raises the share of urban population covered to 89.2 percent.

Haber and Horrillo also tested whether their results depended on northwestern Europe. They removed regional blocks and reran the analysis. Fit fell most when northwestern Europe was removed, but Haber said it fell by about 25 percent. He also noted that removing the northern block, including Moscow, improved the fit. The results therefore depend in part on the strongest-performing region, but the presentation does not claim that the model’s explanatory fit is unchanged when that region is removed.

The predicted map shows three large clusters: East Asia, South Asia, and a broad area running from northwestern Europe through the Mediterranean toward the Black Sea. A smaller cluster appears among the Hausa city-states in West Africa. Central Africa has few cities in the historical dataset, and the model’s small market extents there provide one proposed explanation for that pattern. The researchers also acknowledged visible mismatches. The model predicts more urban development than appeared in places such as New Guinea, Madagascar, and Botswana. Conversely, it does not capture some Silk Road cities, including Samarkand and Tashkent, or cities in central Iran.

The model’s limitations are part of what makes those mismatches informative. It does not include disease vectors, food storage, weather shocks, defensive advantages, or historical persistence. It does not model the local development of transport technologies or other inventions. Haber said the list of possible explanations for cities is effectively open-ended; the authors wanted to begin with a parsimonious model rather than attempt to include them all. He also stressed that excluding other technologies from the model does not mean that societies outside Europe lacked technologies or human capital.

Some exchanges exposed how hard it is to interpret the model as a history of particular cities. The origins are points laid across the landscape, not city centers selected because a city already existed there. Paris’s modeled market, for example, is drawn from the nearby origin point used by the researchers, not from a claim that Paris occupied the single location with the largest possible market. A participant raised the possibility that a defensible site helped determine where Paris began. Haber agreed that the model does not resolve why a particular site was chosen; it estimates the market reach associated with locations under its assumptions.

Because markets overlap, the researchers cannot count population in every market as if each were an independent observation. London and Paris provide a clear example: each market reaches territory included in the other. To handle this, Haber and Horrillo repeatedly draw samples of 400 markets in which no two markets overlap. Within any one sample, a population is assigned to only one market. Different draws use different constellations of markets, so the analysis can cover the full set without placing overlapping markets together in the same estimation sample.

They create 6,000 draws. Markets are split into two strata at the 85th percentile of market area, with large markets placed first. Of the draws, 4,800 train the random forest, with one tree per draw; 1,200 are held out. The reported fit is the average R² across those held-out draws. The presentation describes stable performance between training and test draws as evidence that the model is not simply fitting a particular set of markets. It also reports that removing regional blocks does not eliminate the broad pattern, although removing northwestern Europe causes the largest decline in fit.

The sampling design addresses overlap within each draw; it does not make the markets themselves non-overlapping in the underlying geography. Rather, it gives the researchers a way to estimate relationships across repeated samples while avoiding the double counting that would occur if they placed every overlapping market in the same model at once.

The same overlaps that complicate the base analysis also allow the researchers to define a market’s network. If a market’s extent reaches another market’s origin, that origin counts as a neighbor. Paris has 103 accessible neighboring market origins. Land reachable through those neighboring markets, beyond Paris’s own market, makes up the first ring; the next ring extends through the neighbors’ neighbors. Paris’s second-degree network is large, while Kayseri has far fewer linked markets and Inhambane has none.

These rings are a way to estimate spatial lags: characteristics of connected markets that may matter for a market’s development. Local food production and transport matter because the city itself must be supplied. More distant connected markets may matter for trade in manufactures and services or for the circulation of ideas and technology. The network measure does not assume that food for a city comes from every market in its wider network.

Adding neighboring geography raises the reported holdout fit from about 0.48 to 0.52. The researchers then add population in neighboring markets in 1700, alongside the geography. Their rationale is that a neighboring market’s physical conditions and the presence of an established city may both matter for growth in 1800. They do not present the lagged population measure as a solution to the causal or simultaneity questions raised in discussion. One participant suggested that contemporaneous population might be part of the phenomenon rather than a problem to eliminate; Horrillo agreed that the cities may influence one another, while saying the researchers also wanted to understand the direction of the relationship.

With first-degree neighbors and their 1700 population included, the model explains about 60 percent of the variance; the reported fit reaches 0.63 by the third ring and then largely stops increasing. The researchers interpret this as evidence that nearby markets matter most. In the model, the first rings add information, while more distant rings contribute little beyond them.

The network model’s top 10 percent of predicted markets occupy about 13 percent of the land and contain 82 percent of urban population. The broad clusters and the Hausa city-state cluster remain visible. The nonlinear relationships between local market size, food productivity, and urban density also remain. Adding neighboring population makes established urban presence more predictive, but it does not remove the importance of the local market’s capacity to feed a city.

The authors also use the network to describe market integration. Their map shows transport corridors in western Europe, East Asia, Indonesia, and Papua New Guinea, while Central Africa ranks among the least integrated regions except along tributaries of the Congo. These results describe connections under the model’s 1800 transport assumptions. The mismatch in New Guinea became a point of discussion: its local geography and agriculture did not translate into the urban development predicted by the simplest account. Haber suggested that distance from other market clusters and omitted factors such as malaria could help explain the gap; the authors did not present those explanations as resolved.

The authors repeatedly distinguished their historical model from a forecast of current development. It assumes eighteenth-century transport technologies and does not incorporate modern freight, container shipping, air travel, or communications. Asked whether the results implied that investment in Africa was futile, Horrillo said the model offered no such advice. Haber likewise cautioned that the map could not establish what present-day geography or development prospects look like.

The limits are consequential. The model omits fishing, despite discussion of cod and northern European ports, and it does not include food storage, which Horrillo said could help explain why some places could develop secondary products and others could not. It also does not account for how defense might influence the choice of a city site, or for how technologies and institutions change across places. Haber and Horrillo described these as questions for further work, including a broader project on how geography may shape institutions and human capital over time.

A discussion of Singapore illustrated why the technology boundary matters. Singapore was small in the model’s 1800 setting, but its position on the Strait of Malacca later supported a role as a hub for trade. Haber compared such a hub to an airport: goods traveling between distant places may be offloaded and redistributed rather than carried directly from their origin to their final destination. The example shows how later transport networks can change the value of a location; it does not demonstrate that the model predicts which places will become modern hubs.

The method’s broader claim is more limited than a general theory of development, but relevant beyond this historical application. Markets can be measured as contiguous areas conditioned on terrain, technology, and the cost of moving goods. Their overlap can then be used to represent connections between markets. The authors argue that this offers an alternative to treating fixed grid cells as the natural units of spatial economic analysis, while leaving open how much additional explanatory power comes from history, institutions, disease, storage, and technological change.