metadata: authors: 0: author: Fafchamps,Marcel
1: author: Shilpi,Forhad J.
count: Ghana
docna: 0: docna: The Evolution of Built-up Areas in Ghana
            since 1975
docty: Policy Research Working Paper
subtopic: Hydrology,Transport Services,Food Security,International Trade and Trade Rules
teratopic: Agriculture,International Economics and Trade,Transport,Water Resources
abstracts: cdata!: This paper uses high-resolution
            satellite data on the proportion of buildings in a 250x250
            meter cell to study the evolution of human settlement in
            Ghana over a 40-year period. The analysis finds a strong
            increase in built-up area over time, mostly concentrated in
            the vicinity of roads, and also directly on the coast. There
            is strong evidence of agglomeration effects in the static
            sense -- buildup in one cell predicts buildup in a nearby
            cell -- and in a dynamic sense -- buildup in a cell predicts
            buildup in that cell later on, and an increase in buildup in
            nearby cells. These effects are strongest over a radius of 3
            to 15 kilometers. No evidence is found that human
            settlements are spaced more or less equally over the
            landscape or along roads. By fitting a transition matrix to
            the data, this paper predicts a sharp increase in the
            proportion of the country that is densely built-up by the
            middle and end of the century, but there is no increase in
            the proportion of partially built-up locations.
geo_reg_key: 517191,1927320
repnme: repnme: The Evolution of Built-up Areas in Ghana
            since 1975
display_title: The Evolution of Built-up Areas in
            Ghana since 1975
listing_relative_url: /research/2020/07/32208051/evolution-built-up-areas-ghana-1975
topicv3: Agriculture and Food Security m1326205 435,Water m1326522 137,Transport m1326661 135,Trade m1326924 698,Population, Aging and Health m1327736 640
publishtoextweb_dt: 2020-07-01T00:00:00Z
historic_topic: Agriculture,International Economics and Trade,Transport,Water Resources
origu: DEC-Sustainability & Infrastruct (DECSI)
no_of_pages: 55
author_keys: 0: author_key: 165973
1: author_key: 84831
model_extractions: Policy Research Working Paper 9314 The Evolution of Built-up Areas in Ghana since 1975 _Marcel Fafchamps Forhad Shilpi_ Development Economics Development Research Group July 2020
Policy Research Working Paper 9314

# **Abstract**

This paper uses high-resolution satellite data on the proportion of buildings in a 250x250 meter cell to study the evolution of human settlement in Ghana over a 40-year period. The analysis finds a strong increase in built-up area over time, mostly concentrated in the vicinity of roads, and also directly on the coast. There is strong evidence of agglomeration effects in the static sense—buildup in one cell predicts buildup in a nearby cell—and in a dynamic sense—buildup in a cell predicts buildup in that cell later on, and an increase in buildup in nearby cells. These effects are strongest over a radius of 3 to 15 kilometers. No evidence is found that human settlements are spaced more or less equally over the landscape or along roads. By fitting a transition matrix to the data, this paper predicts a sharp increase in the proportion of the country that is densely built-up by the middle and end of the century, but there is no increase in the proportion of partially built-up locations.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at fshilpi@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
The Evolution of Built-up Areas in Ghana since 1975<sup>1</sup> Marcel Fafchamps2 Forhad Shilpi3 JEL Classification : R12, O18, R10, R14

**Keywords:** Human settlement pattern; transition matrix; roads; agglomeration; urbanization forecasts

> 1 We would like to acknowledge Varnitha Kurli for excellent research assistance in extracting all relevant GIS data used in the study.  Our sincere thanks to Brian Blankespoor for his help with the GIS data. We are grateful to the World Bank for funding this research. All views expressed in the paper are those of authors and should not be attributed to the Bank or its affiliates.

> 2 Stanford University, NBER, and IZA. Email: fafchamp@stanford.edu

> 3 The World Bank, 1818 H Street, Washington DC, USA.
# **1 Introduction**

The world population has been growing rapidly. This is particularly true in Africa where the population has multiplied manyfold since the beginning of the 20th century, and is predicted to reach four billion by the end of the 20th (UN 2013). Increases in the African population have spurred urbanization in general, and the emergence of mega-cities of several million inhabitants in many -- if not most -- African countries (Lall, Henderson and Venables 2017). How this rapid expansion of human settlements unfolds over geographical space is of paramount importance for development (e.g., Duranton 2015) and has likely deep consequences on inequality and poverty (e.g., UNDP 2017). While these structural changes create formidable challenges for policy makers, relatively little is known -- beyond the above general observations -- on the process by which urbanization is unfolding in the continent.

The purpose of this paper is to document how the spatial distribution of buildings has evolved over four decades in Ghana. To do this, we take advantage of the recently available Global Human Settlement Layer (GHSL) data from the European Commission, Joint Research Centre, which used machine learning tools to predict the presence of buildings from satellite imagery. At the heart of this study is a panel dataset of 3.8 million rectangle-shaped cells covering the entire territory of Ghana and observed in 1975, 1990, 2000, and 2014. For each of these cells, the GHSL dataset has an ML prediction of the proportion of that cell’s area that is covered by buildings. We regard the existence of buildings as indicating the presence of people and economic activity. Given that we have precise geocoordinates for each cell, we can combine this large dataset with information on roads, humidity, soil types, and proximity to borders and bodies of water.

We start by documenting the evolution of the distribution of land by intensity of construction. Over the period of our study, the average proportion of the country with buildings went from 0.4% in 1975 to 0.8% in 1990, 1.1% in 2000 and 1.8% in 2014. The distribution of built-up area proportions has changed over time. The proportion of cells without buildings has dropped from 98.5% to 93.8% while the number of built-up cells has gone up. When we limit our attention to cells with at least one building, we note an increase in the proportion of built-up cells that are fully built (i.e., with a buildup density of 90% or more): this proportion rises from 7% to 12% of the built-up cells. The rest of the distribution of built-up cells is largely constant over time. To put 1
it differently, we observe an increase in the number of cells with at least one building – i.e., there is entry in the number of built-up cells – and, among those, an increase in the proportion of fully built cells – i.e., some cells exit their semi-built status. Yet despite of entry and exit in the set of semi-built-up cells, the distribution of their buildup density does not change over time.

Next, we compute transition matrices over time and find them to be quite similar. There is clear evidence that once a cell gets built up, it seldom reverts to an unbuilt state, even over a 40 year period and for very low density build-up cells. If Ghana were to continue evolving as it did between 1975 and 2014, there would still be 91.9% unbuilt cells by 2055. But the share of the most built-up areas would increase by 130% -- admittedly from a very low base as a proportion of all cells.

We then look at differences across different geographical and agro-ecological zones of Ghana. We find strong initial differences in built-up density across zones with more buildings in semi-humid areas, and fewer in areas that are waterlogged or steep and locations with humid or hydromorphic soils. Over the 40 years of the study period, many of these areas experience the fastest buildup growth, possibly suggesting that investments were successful in making these locations more attractive for production (e.g., the stabilization of the Volta estuary after the construction of the dam attracted settlement and fishing). Reduction in onchocercosis may have also attracted settlement in humid areas of the north of the country.

Turning to proximity to borders and bodies of water, we find that localities near a body of water inland had the lowest buildup density in 1975, but they experienced a faster than average growth in buildup. In contrast, places near the sea were massively more likely to have buildings at the beginning of the study period, but experienced a steady but smaller-than-average increase in buildup. Places near the land border had fewer buildings throughout the period.

Roads appear to attract a disproportionate share of the increase in build-up over time: 14.24% of cells are at most 1.5km from a road in 1976, yet they attract approximately 62.6% of buildings. The same is true in 1990 when 66.7% of all built-up land is located within 250 meters from a road. This is also true of new construction, except that over time more roads are built such that new buildings between 1975 and 2014 are not all near 1976 roads. Much of the new construction in Ghana between 1975 and 2014 happened over a fairly small fraction of the country’s total area. We also find that new roads tend to be built near already built-up areas.

2
To investigate this further, we compute separate distribution functions and transition matrices for areas located near a road or not. Buildup forecasts based on fitted transition matrices predict a strong increase in fully built-up areas – i.e., towns and cities – but no similar increase in the proportion of cells that are partially built-up. Apart from a small proportion of lowly built cells that seem to correspond to scattered farms, partially built-up areas seem to serve a transitory role as urban areas expand over time. This analysis also confirms that proximity to roads is associated with a much larger increase in future buildup.

We also investigate whether new construction locates near newly built roads. For this purpose, we use the 1975 and 1990 data and compare the new construction in cells that are close to a road in 1986 but not in 1976 to cells that are already close to a road in 1976, and also to cells that not close to a road in either years. We find that proximity to either type of road predicts a larger increase in future buildup – but proximity to a road in 1986 is the more robust predictor. Of course without proper identification we cannot tell whether new construction near a new road is a net addition or whether it displaces construction that would have taken place either near pre-existing roads or far from a road. More research is needed, using quasi-natural experiments if they can be found, such as those used by Banerjee et al., 2012 and by Faber, 2014, among others.

The last part of the analysis examines the evidence regarding agglomeration effects by examining spatial correlograms. Because cells located near a road are so different from those that are not, we conduct the analysis separately. We find in both cases that buidup in a cell predicts more buildup in cells located up to 3 to 5 km. For cells located near roads, there is still some evidence of more buildup up to 40-50 km away. For cells not near a road, the effect fades away faster. We find no evidence that densely built areas tend to be separated by a specific distance, as would be captured by a spike in the spatial correlogram. Over time, the covariogram increases, capturing the general increase in buildup.

This paper contributes to the literature on urbanization and regional development. Data on built-up area at a highly disaggregated level has recently become available (Pesaresi et al. 2016). This has encouraged a newly emerged literature that seeks to make use of this information to explore important economic realities. Bellefon et al. (2018), for instance, use buildup proportion as a way of identifying the edges of cities, arguing that partial buildup identifies sub-urban areas. We adopt a similar philosophy in the sense that we regard building concentration as an indication 3
of a dense human settlement in an urban setting.

Recent literature has shown a substantial impact of transport infrastructure on the geographical concentration of economic activities (Donaldson, 2014; Banerjee et al., 2012; Faber, 2014; Bird and Straub, 2014; Thompson, 2000; Michaels, 2008). Much of this evidence is at a fairly aggregate level, e.g., a city or town. We show that a similar pattern exists for smaller settlements of a radius of a few hundred meters. Jedwab (2014) documents how, in Ghana and Cˆote d’Ivoire, cocoa production spawned many small towns and how these towns survived the gradual westward shift of cocoa plantations that took place over the last century. Our results confirm that buildup is highly persistent: once a building appears in a cell, it is very rare for this cell not to also have a building in subsequent years, even though we cannot say if it is the same one. Moreover, places that are already settled tend to attract additional buildings, meaning that they become a focal point for population growth. The same can be said of roads, in the sense that proximity to a road in 1976 or 1986 is a strong predictor of human settlement in 2014, even when that road has since disappeared.

An intellectually elegant literature, spearheaded by von Thunen in 1826 (1966), argues that human economic activity self-organizes over space into equally spaced settlements. Refinements of this theory have been offered by Chistaller (1933), Henderson (1985), and Fujita et al. (1999). Isard (1956) in particular argued that self-organization of economic activity across space or transport lines should lead to a hierarchy of cities, with big cities serving a large geographical area in goods and services that can profitably be transported over large distances (either physically or over telephone and IT lines), medium-size cities offering goods and services that can profitably be supplied only over shorter distances, and small towns serving a local hinterland in non-tradables and purchasing farm products from the surrounding countryside. Similar ideas have been applied to the distance from which workers are willing to commute, and to study the geographical coverage of shopping malls and grocery stores. Some evidence has been provided that towns and cities are more or less equally spaced from each other – e.g., Jedwab and Moradi (2016) and Jedwab et al. (2017) for African towns along railway lines; and Faber (2014) for Chinese cities along newly built freeways. In both of these cases, however, planning by a government or colonial authority seems to have been influential. We contribute to this literature by investigating whether evidence of equal spacing can be found in a setting that is much more decentralized but nonetheless very dynamic, with a lot of construction happening and new human settlements popping up in many previously unoccupied 4
places. We find no evidence that built-up cells are located at more or less regular distances from each other. The same is true for cells located along a road – where distance better represents travel cost and time using road transport. Why this is the case is unclear: after all, any look at a map or a Google Earth picture indicates that towns are seldom located next to each other. But in practice, small differences in terrain and obstacles to travel seem to offer enough disruption to blur the distance regularity predicted by theory. This is true even in Ghana where the terrain is fairly uniform, compared to other parts of the world, and lacks major rivers other than the Volta.

A related strand of literature has sought to characterized the size distribution of cities, taking Zipf’s Law as starting point (Gabaix 1999, Arshad et al. 2018). While some evidence has been offered that city sizes follow an exponential distribution, more recent evidence has cast doubt on the idea, arguing that the distribution of city sizes diverges from Zipf’s Law when more complete data are used at a higher degree of disaggregation. We contribute to this literature by showing that at the very smallest level – i.e., partial buildup of a small geographical cell, Zipf’s Law certainly does not apply: the log of the buildup proportion of cells is far from forming a linear relationship with the log of the rank of that buildup proportion. We see this as extending earlier work to the lowest level of geographical disaggregation.

We start in section 2 by explaining how the data are constructed. A brief conceptual framework is introduced in Section 3. Empirical results are presented in Section 4.

# **2 Data**

Our main variable of interest _yit_ measures the proportion of a cell _i_ in year _t_ that is covered by buildings, as inferred from a high-definition satellite image of Ghana. This variable comes from the Global Human Settlement Layer (GHSL) data that have been put together by the European Commission, Joint Research Centre. A Mollweide projection was used to divide the earth’s surface into square cells of approximately 250 by 250 meters, which is rather small for an analysis of builtup area. The proportion of buildings on each cell was predicted using a machine learning algorithm trained on observations of actual buildings made on the ground (see Pesaresi et al. 2016 for details). This algorithm predicts buildup in squares of 30x30 meters. These predictions are then aggregated using GIS into 250x250m cells, thereby generating an accurate prediction of the proportion of that 5
cell that has buildings on it. A little over 3.8 million cells are needed to cover the entire area of Ghana.<sup>1</sup> The variable _yit_ exist for four separate years: 1975, 1990, 2000, and 2014. Cells for each of these years have been carefully aligned using detailed GPS coordinates so as to form a panel dataset.<sup>2</sup> Variable _yit_ takes values between 0 and 1, with 0 meaning no building detected in the cell, and 1 meaning the cell is entirely occupied by buildings – i.e., as in a city center.<sup>3</sup> As shown in Table 1, most cells (98.5%) in 1975 are predicted to be unbuilt, which is hardly surprising given that Ghana at the time only had a national population density of 43.9 per square km. Builtup area grows over time as population increases to 119.4 per sqkm in 2014 and Ghana becomes more urbanized (urban population share increasing from 30% in 1975 to 53% in 2014). In 2014, 93.8% of cells were unbuilt.

For each cell _i_ in year _t_ we construct two measures of buildup in the cells surrounding _i_ . The first of these measures is denoted as _yit_<sup>_n_1andistheaveragebuilt-upareainthecellsimmediately</sup> adjacent to _i_ . Since the data is divided into a square grid, each cell on that grid in principle has 8 immediate neighbors, which constitute the set _n_ 1. We thus have: where by an abuse of notation _n_ 1 represents both the set of immediate neighbors and their number. Together with _yit_ , this variable captures the proportion of built-up area in an approximate cell 675 meters wide by 825 meters high (approximately 2025 by 2475 feet).<sup>4</sup> We also construct a variable _yit_<sup>_n_2thatcapturestheaveragebuildupincellsimmediatelyadjacentto</sup><sup>_y_</sup> _it_<sup>_n_1.Thereareinprinciple</sup> 16 cells in set _n_ 2, except in the vicinity of borders and large bodies of water where that number gets truncated. The formula for _yit_<sup>_n_2</sup> is that same as equation (1) but with _n_ 1 replaced by _n_ 2. Together, _yit_ , _yit_<sup>_n_1</sup> and _yit_<sup>_n_2</sup> cover an area 1125 meters wide and 1375 meters wide, roughly 1.55 square kilometers.

> 1In practice, in our data each cell measures approximately 225 meters wide by 275 meters high (approximately 675 by 825 feet or 6.2 hectares) due to Ghana’s location close to the equator.

> 2Aligning satellite photographs with each other and over time was achieved projecting each photograph using the same Mollweide projection.

> 3More precisely, _yit_ = 1 when all its area is covered by impervious surfaces, such as roofs, sidewalks, streets, and courtyards.

> 4Cells located on the border or along the sea or large body of water do not have a full complement of 8 adjacent cells located wholly or partly within Ghana. For these cells, the immediate neighborhood is limited to those cells included in the dataset and the average is adjusted accordingly.

6
We combine data on built-up area with information on agro-ecological zones to capture the wide variety of landscapes and agricultural potential that characterize Ghana.<sup>5</sup> We divide this information into two variables, which do not vary over time. The first of these variables characterizes the humidity of a particular region, i.e., whether moist/dry, semi-humid, or humid. In Ghana as in the rest of West Africa, the rains follows a monsoon pattern and rainfall generally decreases along a North-South gradient, with the North being drier and the South being more humid. There are exceptions to this general pattern, however – the immediate coastal area, for instance, tends to be drier than inland. In the data, humid soils are associated with the entire valley of the Volta river and with the forested region North of Takoradi.

The second agro-ecological variable we construct captures soil quality – going from poor to moderately good to good. There are two additional categories: hydromorphic soil, which is characterized by excess moisture which tends to suppress aerobic factors in soil-building; and soils unsuitable for buildings or agriculture, such as steep soils or soils covered by standing water at least part of the year – these soils require special investments (e.g., terassing, drainage) in order to become usable. Given that Ghana is relatively flat with no mountains and a relatively homogenous physical landscape, we abstract from altitude: whatever variation in altitude there may be, it translates into variation in rainfall and soil quality and is already captured. Information on agro-ecological zones comes from Global Agro-Ecological Zones (GAEZ) 2012 data from FAO. The GAEZ2012 dataset has a resolution of 10km which was overlaid on our square pattern in order to derive relevant values for each cell.

To this data we add longitude and latitude information expressed in decimal degrees, which we normalize to have mean zero and unit variance. A higher value of longitude means more to the West; a higher value of latitude means more to the North. Population density in Ghana is in general higher in the humid South than in the drier North, largely due to the higher agricultural potential and better soils in the South. But there is a lot of local variation, something we aim to capture with our set of agro-ecological and geographical variables.

We also have information about the presence on a cell of a land border, sea border, or large body of water. We drop from the _yit_ database of all the cells outside Ghana, as well as those that are entirely covered by water, since they cannot be built on. This includes lake Volta, a large

> 5The agro-ecological information is missing for some of the cells located at the edges of the map.

7
artificial lake that covers 8,502 square kilometers within Ghana. Some cells are partially outside Ghana, or partially covered in water or by the sea, something we capture with dummies. We also construct a dummy equal to one if there is a large body of water on any of the eight adjacent cells _n_ 1, and another one for the next 16 adjacent cells _n_ 2. This is done to investigate whether proximity to a lake or lagoon attracts human settlement, e.g., if the lake is use to fish or transport goods. The same thing is done for proximity to the sea and to a land border, for similar reasons.

The last piece of information that we integrate into our analysis is road data. For 1976 and 1986 we have information about the location of all roads in Ghana. These roads are classified into four categories, from 1 to 4.<sup>6</sup> Class 1 roads are the highest quality, and class 4 roads the poorest. Typically, a class 1 road is paved and hence usable all year round. In contrast, a class 4 is a dirt track and many of these roads are seasonal. Class 2 and 3 occupy an intermediate position. Road availability in 1976 is of particular interest for our purpose because these roads predate our period of analysis and thus cannot be construed as caused by buildings constructed after 1976. The same can be said of 1986 roads regarding new buildings constructed afterwards.<sup>7</sup> For each cell we construct a dummy _rkit_ equal to 1 if there is a road of class _k_ in cell _i_ in year _t_ = 1976 or _t_ = 1986 and 0 otherwise. We also calculate the proportion of immediately adjacent cells that contain a road of each particular class, which we denote _rkit_<sup>_n_1.Mirroringwhatwedidforbuilt-uparea,we</sup> construct a similar proportion of roads in the _n_ 2 neighborhood of _i_ , which we denote _rkit_<sup>_n_2.</sup>

# **3 Conceptual framework**

The objective of this paper is to make predictions about the evolution of buildup patterns over time at the high level of geographical disaggregation allowed by our data. While we do not attempt to pinpoint where any construction will occur in the future, we wish to uncover patterns that are relevant for regional planning. Indeed, the population of Africa continues to grow at a rapid pace and this will undoubtedly translate into more buildings. Where these buildings locate will have large consequences for public service delivery as well as for economic growth – two issues that we

> 6There is also a class 5 which is labeled ’unknown road’. Our of an abundance of caution, we ignored these roads in our analysis.

> 7We also have data on roads in 2008, divided into primary, secondary, and tertiary roads. Unfortunately, these categories reflect administrative definitions, and they do not overlap with those used in 1976 and 1986, which focus on the physical qualities of the road. Since we are interested in predicting settlement patterns starting in 1975, this data is less relevant and is ignored in most of the analysis.

8
do not examine here but that motivate our analysis.

If we think of Ghana circa 1975, it was a large country with a relatively small, predominantly rural population, and few roads. Where would we expect people – and therefore buildings – to locate? If we abstract from trade and assume each farming household to be self-sufficient, the optimal organization of dwellings is one in which each farmer locates at the center of the land he cultivates so as to minimize travel time to fields. On a homogeneous landscape and without any other influences, this should result in a honey-comb-like spatial distribution of dwellings whereby each farm is located at an equal distance from the others (e.g., von Thunen 1966, Isard 1956). Observationally, this prediction translates into a relatively unimodal distribution of building density per cell. For instance, if each farming household cultivates 6.2 hectares – which is the size of a cell – we expect to observe one farm building on average per cell.<sup>8</sup> In drier locations<sup>9</sup> with poor soils, crops are typically complemented by livestock, which require a larger land base to be fed. Hence, we would expect, other things being equal, farms in the drier Northern part of Ghana to be farther apart. More generally, we expect farms to locate in a tighter lattice pattern in more fertile areas where less cultivated acreage is required in order to subsist. This means that each agro-ecological zone would have a similar farm size and thus a similar unimodal distribution of built-up area, although the mode of the distribution would vary across regions depending on their agricultural productivity.

Countervailing forces may drive rural households to live near each other. One such factor is safety from attacks. While this factor may have been historically relevant given Ghana’s history of slave raiding, it is doubtful that it continues to affect large portions of the territory today. The main reason is that since slavery ended the population of Ghana has expanded a lot, colonizing new land and creating new settlements – so much so that most villages in existence today probably did not exist 100 years ago, let alone in 1804.<sup>10</sup> Another possible factor is the scarcity of water, in which case joint settlement in the proximity to water points may be a relevant consideration, leading to a more concentrated settlement pattern. This should affect the northern part of Ghana

> 8Assuming for instance that the average farmhouse (with side buildings) occupies 200 square meters, this is equivalent to 0.32% of built-up area per cell.

> 9These locations are also less affected by trypanosomiasis, a livestock disease that decimates herds in humid and semi-humid regions of Africa.

> 10An additional factor is the historical practice of slash-and-burn agriculture which requires households to move every few years to clear new land.

9
more than the south. Other local features such as access to fishing resource, or proximity to mines (e.g., Fafchamps, Koele and Shilpi 2017) may similarly lead to the more concentrated settlement. To continue with our earlier example, imagine that farmhouses conglomerate near each other into hamlets of, say, nine households, each of whom cultivates 6.2 hectares. We would observe one cell with a small settlement occupying 2% of its area, surrounded roughly by 8 cells with no building. Again, this predicts a unimodal buildup distribution across cells that contain at least one building. But it also predicts that if _yit >_ 0 in cell _i_ , then _ykt_ = 0 for _k_ within a certain radius of cell _i_ .

What happens to this geographical equilibrium if population grows but technology remains the same? Agriculture must intensify in order to support the increased number of mouths to feed (e.g., Boserup 1961). This reduces farm sizes and, following the logic above, results in tighter distribution of farmhouses or hamlets over the landscape. But they still tend to be equally spaced in order to locate close to their cultivated area. This means that, other things being equal, the unimodal distribution of built-up area shifts to the right – but remains unimodal within agroecological zones. It also predicts a shrinkage of the unbuilt radius around a built-up cell _yit >_ 0 as the rural population expands.

Trade changes these predictions in several ways. Since the work of von Thunen (1826/1966), it is well known that, at the local level, artisans and services tend to agglomerate into a town or village that trades with the surrounding farmers. The size of the town is determined by the area it serves, which itself depends on travel costs for the farmers who purchase goods and services from artisans and sell them their agricultural surplus. The lower travel costs are, the larger the area serviced by the town, and the larger the town. Industries with a larger fixed cost of production (at the firm level or at the industry level) need not be profitable at the level of a single town. They may nonetheless be able to serve several surrounding towns or villages. The larger the fixed costs – or the larger the industry-specific agglomeration effects – the larger the area covered by the industry. High finance is a good illustration of this principle: a handful of cities serve the needs of the whole world. The concentration of some industries into a small number of locations leads to the emergence of large cities, surrounded by a hierarchy of smaller towns and cities that retail their services while producing goods and services for a smaller catchment area (Isard 1956). We therefore expect to observe towns and cities of different sizes (e.g., Gabaix 1999).

Since most people living in towns and cities do not rely on agriculture for their income, this 10
allows a higher concentration of people in one place, something that manifests itself as a concentration of buildings that occupies all the available space in a cell – i.e., _yit_ = 1. The stronger the agglomeration forces are, the more likely it is that high built-up areas are located next to other high built-up area – i.e., _yit_ , _yit_<sup>_n_1</sup> and _yit_<sup>_n_2</sup> are positively correlated. If the boundary of cities is compact, i.e., without low density suburban areas, we expect to observe a number of cells with built-up proportions distributed between 0 and 1. Because the cells intersect with city and town boundaries in a random way, this results in a number of cells split more or less uniformly between built-up and unbuilt areas.

To the extent that economic growth reinforces agglomeration forces more than agricultural productivity, we expect towns and cities to expand and, consequently, the proportion of fully builtup cells to increase, often in close proximity to each other. By Zipf’s Law, we expect that as large cities grow, smaller towns expand as well at more or less the same rate, and new towns appear that did not exist before. It follows that we also expect to find a larger proportion of cell intersecting with city boundaries, that is, cells with 0 _< yit <_ 1. If the distribution of cities of different sizes remains more or less unchanged, this frequency distribution of _yit_ should also remain unchanged over time for intersecting cells 0 _< yit <_ 1, even if their total number increases. However, the ratio between the numbers of intersecting cells and fully built-up cells should fall as urbanization increases. This is because the ratio between the circumference of a city and its area is approximately equal to: where _R_ is city radius. Hence as the radius of cities expands, the ratio falls. These simple predictions form the core of our testing strategy.

# **4 Empirical results**

## **4.1 Descriptive statistics**

We start by showing in Tables 1 to 3 key descriptive statistics for our variables of interest. From Table 1 we see that proportion of empty cells ( _yit_ = 0) fell 98.5% to 93.8% between 1975 and 2014. Averages are essentially identical for _yit_ , _yit_<sup>_n_1and</sup><sup>_y_</sup> _it_<sup>_n_2,whichishardlysurprisingsincetheyaverage</sup> 11
essentially the same cells.<sup>11</sup> The proportion of fully built-up cells ( _yit_ = 1) among built-up cells increased a lot between 1975 and 1990 – from 2% to 6.6%, but does not show any trend after that. We revisit this point more in detail below. We check whether Zipf’s Law applies to built-up area at this micro level. To do this, we sort partially built-up cells by the proportion of cell area that is built up – from largest to lowest. We then plot the log of the rank to the log of the built-up area. Here cells with a built-up proportion close to 1 represent ’cities’ while those with a built-up proportion close to 0 represent the smallest possible town. Results are shown in Appendix Figures A1 (in levels) and A2 (in logs). We find absolutely no evidence of a Zipf’s Law similar to what has been discussed for cities (e.g., Gabaix 1999, Ashrad et al. 2018).

In Maps 1a to 1d, we illustrate what the data looks like for a randomly chosen location in Ghana – the rural town of Yeji. Buildup is color coded, with white meaning no evidence of any building in the cell and black meaning high density buildup – i.e., 90% and above. Intermediate shades of blue and grey correspond to different levels of partial buildup. We see that in 1975 there is very little evidence of buildup – most of Map 1a is empty. But the small settlement of Yeji can be seen in the upper middle of the map. Over time, this initial settlement grows and expands geographically. It also spawns small satellite settlements at more or less random but fairly equally spaced intervals. New settlements also appear farther away from the initial settlement, often in the proximity of a road. But the initial settlement remains the most densely built-up area of the map throughout the 40 years period covered by the data, suggesting some form of preferential attachment/first-mover advantage. Maps 1e and 1f show the same general area as a Google Earth photograph and Google map print, respectively. It is immediately clear that the data contain a wealth of detail about buildup that is hard to see at this level of magnification, but it comes to view under magnification. The picture also reveals the presence of the Volta lake nearby. Some of the roads shown in Map1f correspond to 1975 roads. However, one road running to the west from Yeji seems no longer in use, even though its outline is still visible from the air. Similar map sequences for other parts of Ghana show a similar evolution, at least visually (Maps 2a to f show the evolution of buildup in the coastal town of Takoradi). The rest of the paper is devoted to analyzing these patterns in a formal way.

> 11A small difference arises due to the fact that _yitn_ 1<sup>and</sup><sup>_y_</sup> _it_<sup>_n_2arenormalizedbythesizeoftheneighborhood.This</sup> gives a bit more weight to small neighborhoods in the averages of _yit_<sup>_n_1and</sup><sup>_y_</sup> _it_<sup>_n_2relativeto</sup><sup>_yit_.</sup>

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Road information is presented in Table 2. For 1976 and 1986, the road information we have captures road quality, divided into four categories, plus a small ’quality unknown’ category. At that time, most of the roads included in this list are unpaved. According to these data, the proportion of cells with at least one road was 3% in 1976 and 3.4% in 1986. The 2008 data use a more stringent road definition, according to which 1.8% of cells had at least one road. The 2014 data includes two new categories: highways, which at the time only include on short stretch of motorway/freeway between Accra and a nearby town; and local roads. The meaning of the other three categories also seems to have changed between the two years, precluding a direct comparison. In the analysis we rely heavily on the 1976 data because it captures the predetermined road infrastructure at the beginning of our study period. Averages for road availability in the 8 _n_ 1 and 16 _n_ 2 neighboring cells are not shown to save space but, by construction, they are identical to the cell averages reported here.

In Table 3 we summarize our main time-invariant variables. Longitude and latitude are presented in decimal degrees. They are used to measure the distance between cells in the subsequent analysis. A tiny fraction of cells are on the border with a neighboring country or on the seashore, but 2.7% are partially covered by a water body such as Lake Volta. The predominant soil quality is either poor or moderate, a situation that typifies much of Sub-Saharan Africa and reflects its tropical nature: heavy rainfall combined with high evapotranspiration means considerable leaching of nutrients from the soil. Only 7.4% of soils are categorized as good. There is a small fraction of cells with hydroponic soils, which means they are located in river estuaries or flood plains. Some of these soils can be made fertile, but often at some cost in terms of infrastructure and equipment. Some 5% of cells have land unsuited for traditional agriculture either because they are waterlogged or too steep. Cultivating these soils requires investment in drainage or terracing. In terms of humidity, most of Ghana’s land is classified as sub-humid, which some areas being either drier or more humid. Rainfall typically follows a North-South gradient in western Africa, with more rains along the coast than in the North.<sup>12</sup> There are exceptions, however: coastal areas of Ghana tend to receive less rainfall than those located more inland. The humidity of the soil also depends on its texture. In Ghana, soils in the valley of the Volta river are classified as humid as they tend to

> 12An ordered probit regression of the climate variable on latitude returns a strongly negative coefficient with a pseudo- _R_<sup>2</sup> = 0 _._ 28.

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retain moisture better.

In Table 4 we break down _yit_ by agro-ecological zone and proximity to borders and water. We find strong initial differences in buildup density across zones with, in 1975, more buildings (and hence a higher population density) in semi-humid areas and in areas with humid or hydromorphic soils. Over the study period, however, we observe dramatic changes in relative buildup densities: cells with initially the lowest buildup densities – i.e., areas with soils that humid, hydromorphic, or waterlogged or steep – experience the fastest growth, possibly suggesting that investments were successful in making these soils or locations more productive. Reduction in onchocercosis may have also attracted settlement in these areas.

Table 5 presents a similar breakdown of built-up areas by the presence or not of a road in the cell. Not surprisingly, we find a strong difference in buildup density between cells with and without a road. This difference falls over time however: comparing cells with and without a road in 1976, the difference falls from 8.5 more buildup in 1975 to 6.3 times in 2014. We also note that the new road definitions adopted in the 2014 data match heavily built-up areas much more closely than before, suggesting that this new road nomenclature puts more emphasis on residential streets (e.g., Gonzalez-Navarro and Quintana-Domeque (2016).) and less on dirt roads serving rural communities.

In Table 6 we show buildup proportions in ‘edge cells’, that is, cells that overlap with a land border or a water body. We see that the presence of a water body is in general associated with a much lower buildup density. This may be because the largest inner body of water is a dam lake and hence probably has a water level that varies over time depending on annual rainfall: people don’t want to live right next to it. Land borders also have a lower density than no-edge cells, while cells near the sea have a much higher buildup density, probably reflecting the presence of towns and cities along the coast, but also the fishing communities that launch their fishing boats directly from the beach. We also observe a much faster buildup over time in cells near inner water bodies, probably reflecting the fact that Lake Volta was only completed in 1965 and it probably took time for people to relocate along its permanent shore.

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# **4.2 Buildup frequency distribution**

Next, we look in more detail at the frequency distribution of buildup for cells that are neither empty of buildings or fully occupied by them. Figure 1 shows this distribution for the four data years we have. It is immediately clear that the frequency distribution of partially built cells remains constant over time, even if the proportion of unbuilt cells falls while the proportion of fully built-up cells increases. We then break down this distribution by cells that are located near built-up areas and cells that are not, i.e, by whether _yit_<sup>_n_2</sup><sup>_>_0 or = 0.Unsurprisingly perhaps, we find that isolated</sup> built-up cells only have a small fraction of built-up area: half of them are less than 4% built up, which is equivalent to having at most a 50 _m_<sup>2</sup> (550 square feet) structure on them; three quarters of them have structures covering at most 83 _m_<sup>2</sup> or 915 square feet. In contrast, half of built-up cells in the vicinity of other built-up cells have structures covering 106 _m_<sup>2</sup> or more – with a fairly even distribution of _yit_ across the entire spectrum of built-up proportion, a finding in line with the idea that these cells correspond to the edges of towns and cities. This pattern suggests that population growth at the aggregate level is not associated with a densification of all areas simultaneously. Rather, what we observe is a fall in the proportion of empty cells, an increase in the proportion of densely built cells, and a more or less constant distribution of partially built cells.

To investigate this issue further, we construct the transition matrix _M_ of _yit_ between 1975 and 2014 and, taking the full distribution of _yit_ in 2014 as starting point, we multiply it a couple times by _M_ to produce forecasts of the distribution of built-up area in Ghana around the years 2055 and 2095. These forecasts implicitly assume a constant rate of aggregate population growth, or more precisely the same rate of increase in aggregate buildup across the country. We also calculate the ergodic distribution corresponding to the transition matrix. This distribution is not intended to be a forecast; rather it represents the long-term distributional trend implied by _M_ .

The forecasts are shown in Figure 2, together with the actual built-up proportions in 1975 and 2014. The histogram confirms that the evolution of built-up proportions in Ghana is characterized by a transfer from unbuilt to fully built, with partially built-up cells serving a transitory role. Over the foreseeable future, the calculations forecast 89.5% unbuilt cells circa 2050 and 85% unbuilt cells circa 2100. At the same time, the proportion of very densely built areas (90% built-up or more) will go from 0.9% in 2014 to 3% in 2053 and 6.2% in 2092. We predict no equivalent increase 15
in partially built cells. In other words, the additional population will not spread itself evenly on the land. Rather, it will congregate in cities. Assuming that the historical rate of population growth continues, this represents more than a tripling of dense urban areas in about 40 years, and a multiplication by 7 by the end of the century. Very similar forecast are obtained if we construct the transition matrix using only 1976 and 1986, or 2000 and 2014: the matrices are very similar, and the forecasts as well. Although our forecasts apply to buildings only, they imply a dramatic change in the distribution of population across the country, with an increased concentration in towns and cities without much of a densification of rural areas. To illustrate the magnitude of these changes, an equivalent increase in the population of Accra would imply an increase from 2.2 million in 2014 to 7.3 million people by 2053 and more than 15 million by the end of the century. These are not small changes.

# **4.3 Roads**

In Figures 3a and 3b, we repeat the exercise separately for cells that were close to a road in 1976 and those that were not. We define being close to a road as having at least one of the five categories of roads documented in 1976 either in the cell itself, or in its neighborhood _n_ 1 or _n_ 2. With this definition, 14.24% of cells at most 1.5km from a road in 1976. The year 1976 is chosen because it is close to the starting point of our data. Hence the transition matrices that are constructed on that basis can be seen as predictions based on road conditions existing in 1976. Results show a stark contrast between cells near road or not. Cells near a 1976 road were already less likely to be unbuilt in 1975: 93.7% vs. 99.3% for cells not near a road. This gap increased to 81% vs. 96% in 2014 and is predicted to grow to 61% vs. 90% by the end of the century. Furthermore, the distribution of built-up areas also varies greatly depending on the presence of a road in 1976. In 1975, only 0.05% of cells not near a road had a value of _yit_ in excess of 90%, compared to 0.73% of those near a road. By 2014 the difference was 0.46% vs. 3.71%. By the end of the century, the forecasted difference is 4% vs. 19%. Put differently, by the end of the century nearly 19% of the area within 1.5km of a 1976 road will be nearly fully built up. Of course new roads will be built that can affect that, a point we revisit below. But the main message here is that the early presence of a road is predicted to have long lasting effects on urbanization patterns. Figures 3a and 3b also show that while proximity to a road affects the probability of subsequent buildup, it 16
does not markedly change the distribution of partially built-up cells: while the levels are different between the two figures, the shape of the distribution is similar. This is true even though each transition matrix is estimated from two distinct sets of observations.

Next, we expand on the above analysis to investigate the effect of adding or removing a nearby road. We use the data from 1976 and 1986 since they are comparable. We define four categories: cells not close to a road in either 1976 or 1986; cells close to a 1976 road that no longer existed in 1986; cells close to a road that did not exist in 1976 but was present in 1986; and cells close to a road that existed both in 1976 and 1986. Abandoning a road may signal that the road was no longer economically useful which, if true, should predict less growth and less subsequent buildup. In contrast roads that remained in existence across both years should be correlated with a preexisting and persistent economic usefulness. Hence, we expect them to be most associated with economic activity and thus most likely to attract population and buildup. Roads that were added in 1986 should occupy an intermediate position: they were not initially deemed useful but were added later, perhaps when sufficient funds became available to add less essential roads. For the analysis, we construct four transition matrices from the 1975-2014 data on these four categories of cells. We then predict buildup in 2053 and 2092 as before. To save space, we present in Figures 4a and 4b only the results for unbuilt and fully built cells, respectively. Indeed, as noted earlier, the actual and forecasted distributions of partially build cells are fairly stable across time. We see that, as anticipated, cells near a road are predicted to receive a lot more buildup over time. The buildup forecast is particular strong for locations that had a road in 1986. Whether or not they also had a road in 1976 matters less, contrary to what we expected. Cells near an abandoned road do less well, but still better than cells with no road in either years.

# **4.4 Agglomeration**

Having discussed roads, we now turn to agglomeration effects. We first examine the extent of correlation between built-up levels _yit_ , _yit_<sup>_n_1</sup> and _yit_<sup>_n_2.</sup> To this effect we estimate a simple OLS regression of the form: 17
It goes without saying that the estimated coefficients should not be given a causal interpretation; they simply document the spatial correlation patterns in buildup. The results, shown in Table 7, are very stable across data years: we note a strong contemporaneous correlation between _yit_ and _yit_<sup>_n_1but,conditionalon</sup><sup>_y_</sup> _it_<sup>_n_1,thecorrelationwith</sup><sup>_y_</sup> _it_<sup>_n_2isnegative.Putdifferently,ifweobservehigh</sup> buildup in _n_ 1 and _n_ 2, we would predict a lower buildup _yit_ than if we only observed high buildup in _n_ 1 alone. This potentially suggest that buildups on either side of _n_ 1 are substitutes: if happens in _n_ 2, it is less likely to occur in cell _i_ .

Next, we investigate whether cells in a built-up neighborhood subsequently experience more buildup. We start by estimating a simple OLS regression of the form: where _s_ is a time lag. Results are presented in Table 8 for the six separate regressions. Unsurprisingly, they show a lot of persistence in buildup: the estimated coefficient _β_ 1 is large in all regressions, indicating that past buildup is a strong predictor of future buildup. This predictive power, however, falls with the time gap _s_ : the more distant in the past is _yit−s_ , the smaller the value of _β_ 1, and the smaller is the precision of the prediction, i.e., the _R_<sup>2</sup> . We also notice that, when the time interval _s_ is short, the additional predictive power of _yit_<sup>_n_1and</sup><sup>_y_</sup> _it_<sup>_n_2isrelativelysmall.</sup> As the time interval increases, the coefficients – and thus the predictive power – of _yit_<sup>_n_1and</sup><sup>_y_</sup> _it_<sup>_n_2</sup> increases and, unlike in Table 7, it is positive for both. This is consistent with a process by which much of the diffusion of buildup to neighboring cells occurs over a relatively short time interval of less than 10 to 15 years. Once this diffusion has begun, own past buildup takes over the predictive power of buildup in neighboring cells. This finding is suggestive of some form of hysteresis: once a cell has started to build up, it tends to remain that way, irrespective of neighboring effects.

We confirm this interpretation by estimating a non-parametric version of regression (4) in which the three regressors are replaced by dummies for each of the deciles of the relevant regressors. We also include a vector _Xi_ of time-invariant cell characteristics as controls. These include soil quality and soil humidity categories; latitude, longitude, their cross-product; and dummies for the presence 18
of a body of water, a land border, or a sea border. The estimated regression has the form: where _yit_<sup>_k_</sup> _−_ 1<sup>isadummyequalto1forthe</sup><sup>_k_’thdecileof</sup><sup>_yit−s_,and</sup><sup>_y_</sup> _it_<sup>_kn_</sup> _−_<sup>1</sup> _s_<sup>and</sup><sup>_y_</sup> _it_<sup>_kn_</sup> _−_<sup>2</sup> _s_<sup>arethesameset</sup> decile dummies for _yit_<sup>_n_1and</sup><sup>_y_</sup> _it_<sup>_n_2.Weonlyestimateregression(5)fortheshortestlag</sup><sup>_s_,i.e.,using</sup> 1975 for 1990, 1990 for 2000, and 2000 for 2014. Coefficient estimates for the buildup variables of interest are presented in graphical form in Figure 5. Results by and large confirm earlier findings from Table 8. They also provide some evidence of a stronger lag effect for higher deciles of _yit−s_ , suggesting more persistence for high buildup. Interestingly, we see that the lagged effect of buildup in neighboring cells tends to taper off at high buildup values, suggesting some form of substitution effect perhaps.

We next expand the model to include dummies for different road categories. The estimated regression has the form: where: _rit−s_ is a vector of road availability dummies, one for each road type, at time _t − s_ in cell _i_ ; _rit_<sup>_n_1</sup> _−s_<sup>isavectorofaverageavailabilityofdifferenttypesofroadsinneighborhood</sup><sup>_n_1,and</sup> _rit_<sup>_n_2</sup> _−s_<sup>isthesameforneighborhood</sup><sup>_n_2.Wefocusourattentiononoutcomeyears1990and2000</sup> because for each of them we have comparable road data approximately 14 years earlier, i.e., in 1976 and 1986. Road data for 2008 and 2014 are not comparable to either of these or to each other. Coefficient estimates for _γ_ 1 _, γ_ 2 and _γ_ 3 are presented in Figure 6, for each of the four road categories and each of the two outcome years, 1990 and 2000. Coefficient _γ_ 1 gives the predicted % point increase in buildup if there is a road in the cell 14 years before. Coefficients _γ_ 2 and _γ_ 3 give the predicted % point increase in buildup if neighborhoods N1 and N2, respectively, go from no cell with a road to all cells with a road. We note a lot of similarity between the two regressions in terms of relative magnitude of the coefficients: the presence of a class 1 road in the cell or nearby predicts more buildup 14 years later. For the other three categories, the presence of a road in the cell predicts slightly higher buildup later on, but the presence of a road in the more distant 19
neighborhood N2 has a consistently negative effect on subsequent buildup predictions. A similar negative coefficient is observed in some regressions for neighborhood N1 as well. These findings are again consistent with the existence of a substitution effect in buildup: if the road is in a neighboring cell but not in my cell, my cell is likely to be built-up a decade and a half later – an outcome we would expect if local inhabitants prefer to locate immediately near these smaller roads. When we estimate regression (6) with 2014 buildup _yit_ and the 2008 road data, we find that all the road coefficients but one are positive. The only exception is for the presence of a primary road in the cell itself, which by 2014 may have too much traffic to be an attractive location. The 2008 road data is completely different from the earlier data, however, with very little correlation between the two, thereby making comparisons problematic. The 2014 road data is strongly correlated with buildup in that year, but since it is contemporary to our last data year, it cannot be regarded as a useful predictor.

We also estimate a different version of regression (6) setting _t − s_ = 1975 for lagged buildup and _t−s_ = 1976 for the road data. By regressing each of the subsequent data years 1990, 2000 and 2014 on these initial buildup and road conditions, we examine the delayed predictive effect of buildup and roads over time. Figure 7 summarizes the buildup coefficients in a way similar to Figure 4, the main difference being that now all regressions use the same 1975 buildup data as regressors. The Figure shows clearly that, over time, the predictive effect of past buildup changes. For buildup in neighborhoods N1 and N2, we see a systematic increase in buildup predictions as time passes. This is consistent with some form or preferential attachment – the presence of buildings in the past attracts new buildings later – possibly due to agglomeration externalities. Past buildup in the cell itself varies depending on the original buildup intensity: for heavily built-up cells in 1975, the own-cell predictive effect falls over time. In contrast, cells with less buildup in 1975 see their buildup predictions increase over time. The fall in predictions for heavily built-up cells may suggest some form of congestion, unless it is compensated by buildup in neighboring cells, which makes it harder to move to a nearby cell.

Figure 8 does the same thing for coefficient estimates for _γ_ 1 _, γ_ 2 and _γ_ 3. The interpretation of the coefficients is similar to that in Figure 6, except that we are now comparing the evolution of buildup predictions over time, using roads in 1976 as predictor. We immediately see that the predicted effect of class 1 roads increases massively over time both for the presence of a road in 20
the cell, as well as for road density in neighboring cells. The other three road categories produced similar results: we observe an increasing positive effect of roads in the cell and in the immediate neighborhood N1 on buildup predictions, while road presence in neighborhood N2 has a negative effect that is initially stronger and falls later on. This is consistent with an initial substitution effect that starts to reverse itself as population density increases and moving to a neighboring cell to get near the road becomes harder.

# **4.5 Spatial covariogram**

So far we have been looking at agglomeration effects at fairly close range – i.e., up to 1.5km at most. We found mostly evidence of agglomeration effects, except occasionally when we uncovered patterns suggestive of spatial substitution effects. We now explore this possibility further by broadening the range of distances we consider so as to produce a spatial correlogram of cell buildup. To recall, the spatial correlogram of a spatial variable _z_ plots the average correlation between observations of _z_ for various distances between them. This is in principle achieved by calculating the distance between all possible pairs of observations and then by computing, for each relevant distance interval, the sample correlations between _y_ pairs located within that distance interval from each other. The concept is similar to autocorrelogram in time series analysis, except that it is calculated over distances which, in data like ours, are not limited to integer values.

To do this effectively, we have to overcome the challenge of dimensionality. With nearly 4 million cells, calculating all pairwise distances would generate around 16 trillion observations – a number that far exceeds the computing capacity at our disposal. To implement our plan, we therefore need to resort to a few tricks. The first trick is to focus on the spatial covariogram and simplify the calculation of covariance by focusing on a dichotomous variable _zit ≡ Pr_ ( _yit >_ 0). This means that the sample equivalent of the spatial covariance _E_ [ _zitzjt_ ] at distance _d_ is simply the proportion of cell pairs _ij_ at distance _d_ that are both 1. Our objective is thus to plot a sample estimate of _E_ [ _zitzjt_ ] at various distances _d_ for Ghana. To this effect, we need to construct a representative sample of cell pairs and calculate the proportion of pairs that are both built-up among all sampled pairs.

To achieve this, we divide Ghana into a number of tiles small enough that we are able to construct all the cell pairs in that tile. This is done by creating a grid of 856 equal size tiles that 21
covers all of Ghana.<sup>13</sup> This implies that we are not using all the data at our disposal: pairs of observations that belong to different tiles are not used to construct the correlogram. Since tile boundaries are chosen at regular intervals based on latitude and longitude, they are orthogonal to the phenomenon we study. Hence the resulting sample of cell pairs should be representative. Each of these tiles is an 18 _×_ 18 km square (approximately 26 km in diagonal). It comprises around 5,200 cells and approximately 13.5 million unique cell pairs. We then divide cell pairs into approximately 260 distance bins of 100 meters each. The number of cell pairs in each bin varies with the shape of the tile and the presence of borders and water bodies. We then count, for each distance bin _b_ , the total number of pairs _Nb_ =<sup>�</sup> _ij∈b_<sup>_Cijt_inthatbin–where</sup><sup>_Cijt_=1forcellpair</sup><sup>_ij_andthe</sup> summation is taken over all the cell pairs in bin _b_ . We also count, for each year _t_ and each bin _b_ in each tile _m_ the number of pairs with two built-up cells, that is, two cells _i_ and _j_ in _b_ for which _zit_ = 1 and _zjt_ = 1. This enables us to calculate the share _Sbtm_ of cell pairs in tile _m_ and in distance bin _b_ that are both built up in year _t_ as: Since this is done separately for each tile _m_ , it means that the values of _Sbtm_ can be computed separately tile by tile before assembling them together to cover all of Ghana.

Because country borders and bodies of waterare irregular,<sup>14</sup> the size and shape of each tile varies somewhat and so does the number of cell pairs in each bin of each tile. This means that to reconstruct the country-level covariogram, we need to weight each _Sbtm_ by the number of cell pairs that it represents. To achieve this, we simply regress _Sbtm_ for a given year on distance bin dummies: and weight each observation _Sbtm_ by the number of observations _Nbm_ in bin _b_ of tile _m_ . We then plot, for each year _t_ the predicted values _S_<sup>ˆ</sup> _b_ (they only vary by distance bin _b_ ) and the prediction

> 13In practice, this is achieved as follows. We first identify the extrema of latitude and longitude in Ghana. We then divide the North-South difference into 33 equal intervals. We do the same for the East-West difference. This creates 1,089 blocks, 856 of which cover at least part of Ghana; the rest fall in neighboring countries and are ignored here. We also drop a handful of tiles with a number of cells too small to compute a correlogram.

> 14Plus a small variation in the length of one degree of longitude from North to South Ghana.

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standard errors obtained from the above regression.<sup>15</sup> This process yields a spatial correlogram averaged across all tiles and weighted by the number of cell pairs in each bin of that tile.

The results are shown in Figure 9 for all four years combined. We see that, since the proportion of built-up cells increases over time, the proportion of built-up cell pairs not surprisingly increases as well. Otherwise the spatial pattern is similar across all years: cells located close to a built-up cell are more likely to be built up as well: _E_ [ _zitzjt_ ] falls with distance. The correlation is particularly strong at short distances of up to 3 km, but the pattern is present across the entire distance distribution and, given how tight the confidence intervals are, differences in spatial correlation by distance are significant up to distances of at least 20km. Beyond 20 km, the number of observations in distance bins _Nbm_ drops rapidly, confidence intervals increase in size, and the covariogram becomes unreliable, a point we revisit below.

We repeat the exercise separately for cell pairs both located near a road in 1976, and other cell pairs. Proximity to a road is defined as having a road in the cell itself or in neighborhoods _n_ 1 or _n_ 2 – i.e., as having _rit_ 0, _rit_<sup>_n_1</sup> 0<sup>,or</sup><sup>_r_</sup> _it_<sup>_n_2</sup> 0<sup>_>_0for</sup><sup>_t_0=1976.Theresultingspatialcovariogramisshown</sup> in Figure 10 for all four years of data we have. The general pattern is similar to that observed for all cell pairs, except that the proportion of built-up cells is higher near roads, and thus there are more built-up cell _pairs_ near roads. We also observe the sharply higher spatial correlation at close distances of around 2-3 km. But the spatial correlation in buildup falls less fast near roads than away from roads. This is consistent with our earlier finding that proximity to a road predicts higher buildup independently from proximity to a pre-existing agglomeration, and this effect is distinct from the fact that settlements often are near roads to start with. The spatial covariogram for cell pairs that are not close to roads is very similar to that reported in Figure 9 and is not shown here to save space.

Contrary to what is predicted by the von Thunen (1966) model subsequently expanded by Chistaller (1933) and Isard (1956), we find no strong evidence of a ’bump’ in the covariogram at any specific distance. If farm buildings tended to be spaced equally so as to locate in the middle of their fields, we would expect a spike in the covariogram at the relevant distance. For instance, if each farming households occupies, say, 20 Ha of cultivated land, fallows and pastures, we would

> 15We only show confidence intervals for 1975 and 2014, to keep the graph uncluttered. As is immediately apparent from the graph, confidence intervals are extremely tight.

23
expect farms to be, on average, 500 meters from each other.<sup>16</sup> This would more or less correspond to one farm per cell, and thus a flat spatial correlogram between farm buildings. We also would not expect to find a buildup concentration along roads – which is not what we find. In contrast, if farmers live in villages of, say, 100 households needing each 20 Ha of combined cultivated land, fallows and pastures, each village would require an area of 2,000 Ha, which would imply a spacing of villages each 5 km. If this were the case, we would expect a spike in the spatial correlogram at 5km: the presence of village buildindgs at distance 0 would predict village buildings 5 km away. We do not find evidence consistent with this conjecture – or any equal spacing of villages up to 20 km. We do however find evidence of agglomerations covering an area of up to 3 km in radius – 6 km or 4 miles in diameter. These localities may be larger than simple villages, and they may be located further apart than 20 km. Could there be, therefore, spikes in the spatial covariogram at distances above 20km – something that is possibly suggested by the appearance of a spike at distances slightly above 20km in Figure 10?

To investigate this possibility, we recalculate the spacial covariogram for distances up to 75 km. To do this, we divided Ghana into 86 tiles of roughly 60 _×_ 60 km, with a diagonal distance of over 76km. Because the proportion of built-up cells is low, we are still able to form all built-up cell pairs and to compute<sup>�</sup> _ij∈b,m_<sup>_zjtzjt_forallbutthe3mostdenselybuilt-uptiles.17Wecannot</sup> compute _Nbm_ directly, however, due to computer power requirements. We therefore must proceed differently. The total number _Tm_ of unique cell pairs in each tile is immediately obtainable: it is _Tm_ = _Nm ×_ ( _Nm −_ 1) _/_ 2, where _Nm_ is the number of cells in tile _m_ . What we need is an estimate of how these _Nm ×_ ( _Nm −_ 1) _/_ 2 are divided across distance tiles. Indeed, because tiles vary in shape, the distribution of pairs across distance bins varies across tiles. To construct an estimate of the frequency distribution of cell pairs into distance bins for each tile, we select in each tile a large but manageable random sample of cells. We form all cell pairs among them and calculate the number of pairs in each distance bin _Rbm_ . Let _Rm_ =<sup>�</sup> _b_<sup>_Rbm_bethetotalnumberofcellpairsintherandom</sup> sample for tile _m_ . Since we did not use all cells in the tile, _Rm < Tm_ . The frequency distribution

> 1620 Ha is 200,000 _m_ 2, an area that is contained in a circle with a 250 meter radius. Two such circles would be, on average, roughly 500 meters from each other.

> 17The three omitted tiles each contain a large city and thus a large proportion of built-up cells. This means that the number of built-up cell pairs is too large for us to compute on our computer. These three cities, however, contain little usable information to test the idea that small towns are more or less equally spaced. If anything, including them would probably reduce the likelihood of finding a spike.

24
of distance bins in each tile can nonetheless be approximated as: where _Tm/Rm_ is used to rescale the distribution of weights to match the full size of the tile.

Results comparable to Figures 9 and 10 are shown in Figures 11 and 12, respectively. We see that the reported patterns are very similar to those reported earlier. The fall in buildup correlation that was observed at short distances in Figure 9 is confirmed in Figure 11, and it is seem to continue then flatten our around about 50 km of distance. A similar pattern is shown in Figure 12 for cell pairs located near a road, except that the fall is steeper at short distances and the slope is steeper for longer. The curve also flattens our at around 50 km distance. We also observe that the bump at distances above 20 km in Figure 10 is not a robust result and is probably an artifact of the small number of tiles and cell pairs with observations at those distances. Using larger tiles solves that problem. These results confirm our earlier findings, namely that, across Ghana, human settlements (as proxied by buildings) are not evenly spaced, as theories inspired by von Thunen would predict. This is true across cells in general, but also along roads. We do, however, find strong evidence of agglomeration at short distances, as well as evidence of weak agglomeration forces operating up 50 km away – in the sense that being less than 50 km from a built-up location predict a slightly higher probability of buildup. The figures also confirm that buildings tend to concentrate along roads and near each other.

In the last figure, we perform a similar exercise using small tiles as unit of observation. Since nearly all these tiles include at least one building, we define buildup as being in the top decile in term of buildup, averaged over the whole tile. We then form all tile pairs and conduct the same analysis as in Figures 9 and 11. Distance between tiles is calculated from the tile’s centroid.<sup>18</sup> As we have much fewer observations, we need not put tile pairs into distance bins: we can work directly on the full sample of pairs. Given that nearly all tiles contain at least one road, we ignore that dimension here. Figure 13 shows the result, with distance on the horizontal axis and, on the vertical axis, the share of tile pairs that are both in the top buildup decile. By construction, the horizontal axis is truncated at distances less than 18 km, which is the size of a tile itself. The four

> 18For our purpose, the centroid of a tile is defined as the point with the average longitude and the average latitude of the tile.

25
curves show, for each of the data year, the predictions from a fractional polynomial regression of the share of top decile pairs on distance. If buildup were distributed randomly across space, we should observe a flat curve. This is not what we see: as in Figures 9 to 12 we find evidence of agglomeration, which is strongest at distances up to around 60 km, which is the range of distances covered in Figures 11 and 12. Correlation in high buildup falls after that, but only gradually – suggesting that agglomeration continues to have an effect on buildup even at long distances.

# **5 Conclusions**

Developing countries across the world experienced strong population growth during the last four decades. With population growth, urbanization also picked up pace with half of the developing world’s population now living in urban areas. The accelerated urbanization has received considerable attention in the Africa region where urbanization has not been associated as strongly with economic growth as observed historically in developed countries. Less is however known about how human settlements expanded geographically along with population growth and increased urbanization. In this paper, we use high resolution satellite data on built-up areas within micro-pixels to study the evolution of human settlements in Ghana over a 40 year period.

The empirical analysis of built-up data produces a couple of substantive findings. First, we find a strong increase in built-up area over time, mostly concentrated in the vicinity of roads, and also directly on the coast. The proportion of fully built cells increased substantially at the expense of un-built cells leaving the distribution of partially built-up cells unchanged. We find strong evidence of agglomeration effects both in the static sense – buildup in one cell predicts buildup in a nearby cell – and in a dynamic sense – buildup in a cell predicts buildup in that cell later on, and an increase in buildup in nearby cells. These effects are strongest over a 3 to 15 km radius. Within the distance windows analyzed (upto 60km), we find no evidence that human settlements are spaced more or less equally either over the landscape or along roads. Overall, expansion of human settlements in Ghana occurred mainly at the edge of existing agglomeration of built-up areas. If a similar expansion pattern continues then our analysis based on transition matrices predict a strong increase in fully built-up areas – i.e., towns and cities – but no similar increase in the proportion of cells that are partially built-up. And this increase will be concentrated in a relatively small 26
geographical area around existing agglomerations. These findings have important implications for targeting provision of services in the coming years. Expansion of provision of services in the case of Ghana should be based on its existing concentration of population.

The main finding of the paper that expansion of human settlements happened mostly around the existing built-up areas also raises the question of what lies behind this observed persistence particularly in terms of policies and infrastructure investments. This should be a priority for future research.

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Table 1. Built-up area

|Year|Proportion<br>ofbuilt-up<br>area|Proportion<br>ofbutItup<br>areainNI — <br>cells|Proportion<br>ofbutItup<br> area inN2<br>cells|Shareof<br>cellsthatare <br>empty|Shareofnon-<br> emptycellsthat<br>are fullybuilt-<br>;<br>up|
|---|---|---|---|---|---|
|1975|0.43%|0.43%|0.42%|98.50%|1.96%|
|1990|0.80%|0.80%|0.80%|97.48%|6.61%|
|2000|1.19%|1.19%|1.19%|96.52%|8.41%|
|2014|1.85%|1.85%|1.84%|93.78%|6.70%|

Notes: Total number of observations 1s 3,853,273. N1 cells are the 8 rectangles surrounding the cell. N2 cells are the 16 rectangles surrounding N1 cells. The number of N1 cells is 8 for all but 27,241 cells. The number of N2 cells is 16 for all but 54,324 cells.
Table 2. Presence of roads in a cell

|Road quality|1976|1986|2008|2014|
|---|---|---|---|---|
|Class 1 road|0.61%|0.67%|||
|Class 2? road|0.83%|0.98%|||
|Class 3 road|1.03%|1.15%|||
|Track|0.55%|0.60%|||
|Unknown|0.01%|0.00%|||
|Any road|2.99%|3.35%|||
|Intersection|0.03%|0.04%|||
|Administrative road|definition||||
|Highways|||n.a.|0.00%|
|Primary|||0.63%|0.25%|
|Secondary|||0.36%|1.05%|
|Tertiary|||0.82%|1.66%|
|Local road|||n.a.|0.28%|
|Any road|||1.80%|3.12%|
|Intersection||n|.a.|0.23%|

Note: Number of observations: 3,880,380. Unknown roads in 1976 and 1986 denote a very small proportion of roads of unknown quality. Road quality in 1976 and 1986 does not align with administrative road definitions in 2008 and 2014, which themselves differ as well in spite of the partial similarity in names. Highways in 2014 include a single motorway/freeway from Accra to the nearby city of Tema and is present in 113 cells only. Averages for road availability in the 8 (N1) and 16 (N2) neighboring cells are not shown here to save space. They are essentially identical to the averages reported here since they are averages over essentially the same cells (except far small differences at the edges). Intersections cover all classes of road available in the data.
Table 3. Time-invariant features of cells

||Average|Min|Max|
|---|---|---|---|
|Latitude|7.96|474|11.17|
|Longitude|-1.21|-3.26|1.20|
|Presence ofwater body|2.7%|||
|Presence of land border|0.1%|||
|Presence of sea|0.1%|||
|Number of cells|3,853,273|||
|Soil quality||||
|Poor|38.1%|||
|Moderate|47.8%|||
|Good|7.4%|||
|Hydromorphic|1.7%|||
|Waterlogged/Steep terrain|5.0%|||
|Climate||||
|Moist ordry|17.1%|||
|Sub-humid|70.2%|||
|Humid|12.8%|||
|Numberofcellswithsoilandclimat|3,811,014|||

Notes: Latitude and longitude reported in decimal degrees. Water bodies include rivers, lakes and lagoons. Hydromorphic soils are those affected by water (e.g., river banks, tidal estuaries). Waterlogged soils and steep terrain are those considered unsuitable for agriculture or house construction. Of all the cells covering the area of Ghana, 27,107 are excluded because they are fully covered by water; most of this is Lake Volta.
Table 4. Breakdown of built-up proportion by agro-ecological zones

|||S|oil quality|||So|il humidity||No info|
|---|---|---|---|---|---|---|---|---|---|
|Year||Poor|Moderate|Good|.|ep|Moist/dry|humid|Humid||
|1975|0.55%|0.30%|0.21%|0.41%|0.09%|0.21%|0.47%|0.15%|3.56%|
|1990|0.89%|0.70%|0.43%|0.81%|0.23%|0.37%|0.88%|0.42%|5.88%|
|2000|1.31%|1.08%|0.66%|1.07%|0.29%|0.50%|1.32%|0.66%|8.09%|
|2014|2.03%|1.69%|1.02%|2.71%|0.75%|0.69%|2.07%|1.34%|9.32%|
|N.obs.||1,447,084|1,816,564|282,295|64,568|189,485}|648,635|2,666,937|484,424|53,277|

Table 5. Breakdown of built-up proportion by presence of a road

|Year|Road in|1976|Road in|1986|Road in 2|008|Road in|2014|
|---|---|---|---|---|---|---|---|---|
||No|Yes|No|Yes|No|Yes|No|Yes|
|1975|0.35%|2.94%|0.34%|3.01%|0.37%|3.53%|0.22%|6.84%|
|1990|0.67%|5.21%|0.64%|5.39%|0.70%|6.23%|0.46%|11.44%|
|2000|1.01%|7.15%|0.97%|7.44%|1.05%|8.61%|0.74%|14.96%|
|2014|1.59%|10.00%|1.55%|10.35%|1.66%|12.21%|1.29%|19.17%|
|N.obs.|3,737,881|115,392|3,723,869|129,404|3,783,821|69,452|3,732,420|120,853|

Table 6. Breakdown of built-up proportion by boundary status

||Presence on t|he cell of:||
|---|---|---|---|
|Year<br>Waterbody|Land border|Sea|None|
|1975<br>0.01%|0.27%|30.75%|0.42%|
|1990<br>0.03%|0.52%|49.73%|0.80%|
|2000<br>0.06%|0.70%|60.40%|1.19%|
|2014<br>0.20%|1.11%|61.87%|1.86%|
|N.obs.<br>105,035|4,041|1,978|3,742,297|
Table 7. Correlation in buildup between neighboring cells

||197|5|199|0|200|0|201|4|
|---|---|---|---|---|---|---|---|---|
||Coef.|Std.err.|Coef.|Std.err.|Coef.|Std.err.|Coef.|Std.err.|
|y(n1)|1.3102|0.0008|1.3761|0.0007|1.3953|0.0007|1.3708|0.0007|
|y(n2)|-0.3237|0.0008|-0.3888|0.0008|-0.4060|0.0007|-0.3807|0.0008|
|Intercept|0.0000|0.0000|0.0001|0.0000|0.0001|0.0000|0.0002|0.0000|
|R-square|0.7952||0.8402||0.8666||0.8507||
|N.obs.|3,853,228||3,853,228||3,853,228||3,853,228||

Note: the dependent variable is y. There are no controls included.

Table 8. Correlation in buildup between neighboring cells over time

||199|0|200|0|201|4|
|---|---|---|---|---|---|---|
|Regressors in|1975||||||
|y|0.8691|0.0008|0.7273|0.0013|0.6123|0.0018|
|y(n1)|0.3420|=©0.0016|0.4390|0.0025|0.5221|0.0036|
|y(n2)|0.1605|0.0013|0.4304|0.00271|0.5568|0.0030|
|intercept|0.0022|0.0000|0.0051|0.0000|0.0113|0.0000|
||0.7453||0.5945||0.4352||
||||200|0|201|4|
|Regressors in|1990||||||
|y|||0.8961|0.0007|0.7575|0.0012|
|y(n1)|||0.1839|0.0013|0.3688|0.0024|
|y(n2)|||0.1025|0.0011|0.1477|0.0019|
|intercept|||0.0024|0.0000|0.0082|0.0000|
||||0.812||0.6029||
||||||201|4|
|Regressors in|2000||||||
|y|||||0.8395|0.0008|
|y(n1)|||||0.2505|0.0016|
|y(n2)|||||0.0252|0.0012|
|intercept|||||0.0052|0.0000|
||||||0.7758||

Notes: each panel is a separate regression. The total number of observations is 3,853,228 in each regression.
<!-- Start of picture text --> Figure 1. Distribution of built-up proportion<br>omitting unbuilt and fully built cells<br>12.0%<br>10.0%<br>8.0%<br>6.0%<br>4.0%<br>2.0%<br>0.0%<br>0 10 20 30 40 50 60 70 80 90 100<br>Percentage buildup in the cell<br>Year 1975 Year 1990 Year 2000 Year 2014<br><!-- End of picture text --> Notes: After dropping unbuilt cells (which constitute more than 90% of cells in all years) and the fully built-up cells (which are discussed separately in the text), Figure 1 plots four histograms of the frequency distribution of partially built-up cells by their built-up proportion. The horizontal axis shows the built-up proportion of the cell. The vertical axis shows the proportion of cells in each buildup percentage interval. There is one histogram for each year. To facilitate viewing, each of the four histograms is represented as a colored line and the four histograms are overlaid on top of each other. This is done to facilitate a visual comparison of the frequency distribution across years.
<!-- Start of picture text --> Figure 2. Histogram of built-up proportions<br>omitting unbuilt areas<br>7%<br>6%<br>5%<br>4%<br>3%<br>2%<br>1%<br>0%<br>1-10% 11-20% 21-30% 31-40% 41-50% 51-60% 61-70% 71-80% 81-90% 91-100%<br>1975 (actual) 2014 (actual) 2053 (forecast) 2092 (forecast)<br><!-- End of picture text --> Notes: Figure 2 shows a stacked histogram of the frequency distribution of built-up proportion divided into deciles of buildup proportion in 1975. Fully built cells are included in the top decile. Since an overwhelming proportion of cells are unbuilt in all years, they are omitted from the Figure for the sake of clarity. The 1975 and 2014 values are taken directly from the data. The 2053 and 2092 forecasts are obtained as follows. We first form the decile transition matrix using data from 1975 and 2014 (a 39 year interval). We then project the built-up frequency distribution from 2014 to 2053 and 2092 as two iterations of the transition matrix. The resulting forecasts should be understood as predictions of what the distribution of buildup will look like if the transition matrix remains unchanged. Similar forecasts are obtained if we use transition matrices constructed using different data years. The forecast do not specify which cells will be built.
<!-- Start of picture text --> Figure 3a. Histogram of built-up: cells with roads in 1976<br>omitting unbuilt areas<br>20%<br>1975 (actual) 2014 (actual) 2053 (forecast) 2092 (forecast)<br>18%<br>16%<br>14%<br>12%<br>10%<br>8%<br>6%<br>4%<br>2%<br>0%<br>1-10% 11-20% 21-30% 31-40% 41-50% 51-60% 61-70% 71-80% 81-90% 91-100%<br>Figure 3b. Histogram of built-up: cells w/out road in 1976<br>omitting unbuilt areas<br>5%<br>1975 (actual) 2014 (actual) 2053 (forecast) 2092 (forecast)<br>4%<br>4%<br>3%<br>3%<br>2%<br>2%<br>1%<br>1%<br>0%<br>1-10% 11-20% 21-30% 31-40% 41-50% 51-60% 61-70% 71-80% 81-90% 91-100%<br><!-- End of picture text --> Notes for Figures 3a and 3b: The Figures show a stacked histogram of the frequency distribution of builtup proportions divided into 1975 deciles. In Figure 3a only those cells with a road in 1976 are used in the histograms. Figure 3b does the same thing for cells without a road in 1976. In both Figures, fully built cells are included in the top decile. Since an overwhelming proportion of cells are unbuilt in all years, they are omitted from the Figures for the sake of clarity. The 1975 and 2014 values are taken directly from the data. The 2053 and 2092 forecasts are obtained as follows. We first form the decile transition matrix using data from 1975 and 2014, only using cells with a road in 1976 (for Figure 3a) or those without a road in 1976 (for Figure 3b). We then separately project the built-up frequency distribution from 2014 to 2053 and 2092 as two iterations of the transition matrix. The resulting forecasts should be understood as predictions of what the distribution of buildup will look like in 1976 if the transition matrices remain unchanged. Similar forecasts are obtained if we use transition matrices constructed using different data years. The forecast do not specify which cells will be built.
**Figure 4a. Percent of unbuilt cells depending on roads in '76 and '86**

<!-- Start of picture text --> Figure 4b. Percent of fully built cells depending on roads<br>in '76 and '86<br>25.0%<br>20.0%<br>15.0%<br>10.0%<br>5.0%<br>0.0%<br>1975 2014 2053 2092<br>r76=0 r86=0 r76=1 r86=0 r76=0 r86=1 r76=1 r86=1<br><!-- End of picture text --> Notes: Figure 4a shows the percent of unbuilt cells in various years, conditional on whether the cell had a road in 1976 (r76=1) and a road in 1986 (r86=1). Some cells with a road in 1976 no longer have one in 1986 (e.g., because the road was not maintained or was moved). Figure 4b shows the percent of fully built cells in various years, also depending on whether the cell had a road in 1976 (r76=1) and a road in 1986 (r86=1). Values for 1975 and 2014 are take from the data. Values for 2053 and 2092 are forecasts obtained in the same manner as for Figures 3a and 3b, except that we now use four different transition matrices and four 2014 buildup vectors from which to iterate.
<!-- Start of picture text --> Figure 5. Plot of lagged buildup coefficients<br>90.0%<br>80.0%<br>70.0%<br>y(1975)<br>60.0% y(1990)<br>y(2000)<br>50.0%<br>n1(1975)<br>40.0%<br>n1(1990)<br>30.0% n1(2000)<br>n2(1975)<br>20.0%<br>n2(1990)<br>10.0% n2(2000)<br>0.0%<br>1 3 5 7 9<br>% buildup decile in earlier period<br>impact on buildup proportion<br><!-- End of picture text --> Notes: Figure 5 summarizes the coefficients from three separate regressions. The dependent variable in the three regressions is the proportion of a cell that is built up in 1990, 2000, and 2014 respectively. Each regression includes lagged values of buildup in the cell and in the neighboring cells n1 and n2. The lagged values are for 1975, 1990, and 2000 respectively. Each of the three lagged buildup variables appears in the regression as a series of 10 dummies, one per buildup decile. The Figure shows the estimated decile coefficients in each of the three regressions for (1) buildup in the cell itself [lines y(1975), y(1990) and y(2000)]; buildup in neighboring cells n1 [lines n1(1975), n1(1990), and n1(2000)]; and buildup in neighboring cells n2 [lines n2(1975), n2(1990), n2(2000)]. Each regression also includes the following time invariant regressors: longitude, latitude, and their product [three variables]; soil humidity and soil quality dummies [six variables]; and dummies for the presence of a water body, a land border, or the sea in the cell, the neighboring cells n1 and the neighboring cells n2, respectively [9 variables]. The number of observations in each regression is just shy of 3.8 million. R-squares are 0.799, 0.845 and 0.796, respectively. All coefficients shown here are significant at the 1% or better.
<!-- Start of picture text --> Figure 6. Coefficient of lagged presence of roads<br>2.5%<br>2.0%<br>1.5%<br>1.0%<br>0.5%<br>0.0%<br>In cell In N1 In N2 In cell In N1 In N2 In cell In N1 In N2 In cell In N1 In N2<br>-0.5%<br>Class 1 road Class 2 road Class 3 road Track road<br>-1.0%<br>-1.5%<br>1990 regression 2000 regression<br>Impact on buildup proportion<br><!-- End of picture text --> Notes: Figure 6 summarizes the coefficients from two separate regressions. The dependent variable in the two regressions is the proportion of a cell that is built up in 1990 and 2000, respectively. The Figure shows the coefficients of the presence of a road of a certain class (i.e., category) in the cell, the neighborhood N1 and the neighborhood N2. The road quality ordering is: class 1 (top category), class 2, class 3, and track (bottom category). In the 1990 regression, the road data refers to 1976; in the 2000 regression, the road data refers to 1986. Each of the regressions also includes all the regressors that were present in those for Figure 5. More precisely, each regression includes lagged values of buildup in the cell and in the neighboring cells n1 and n2. The lagged values are for 1975 and 1990, respectively. Each of the three lagged buildup variables appears in the regression as a series of 10 dummies, one per buildup decile. Each regression also includes the following time invariant regressors: longitude, latitude, and their product [three variables]; soil humidity and soil quality dummies [six variables]; and dummies for the presence of a water body, a land border, or the sea in the cell, the neighboring cells n1 and the neighboring cells n2, respectively [9 variables]. The number of observations in each regression is just shy of 3.8 million. R-squares are 0.796 and 0.796, respectively. All coefficients shown here are significant at the 1% or better.
<!-- Start of picture text --> Figure 7. Plot of 1975 buildup coefficients<br>0.8<br>0.7<br>0.6 y(1990)<br>y(2000)<br>0.5<br>y(2014)<br>0.4 n1(1990)<br>n1(2000)<br>0.3<br>n1(2014)<br>0.2 n2(1990)<br>n2(2000)<br>0.1<br>n2(2014)<br>0<br>1 3 5 7 9<br>% buildup decile in 1975<br>Impact on buildup proportion<br><!-- End of picture text --> Notes: Figure 7 summarizes the coefficients from three separate regressions. The dependent variable in the three regressions is the proportion of a cell that is built up in 1990, 2000, and 2014 respectively. Each regression includes the 1975 values of buildup in the cell and in the neighboring cells n1 and n2. Each of the three 1975 buildup variables appears in the regression as a series of 10 dummies, one per buildup decile. The Figure shows the estimated decile coefficients in each of the three regressions for (1) 1975 buildup in the cell [lines y(1990), y(2000) and y(2014)]; 1975 buildup in neighboring cells n1 [lines n1(1990), n1(2000), and n1(2014)]; and 975 buildup in neighboring cells n2 [lines n2(1990), n2(2000), n2(2014)]. Each regression also includes all the road presence dummies for 1976 (see Figure 8) and the following time invariant regressors: longitude, latitude, and their product [three variables]; soil humidity and soil quality dummies [six variables]; and dummies for the presence of a water body, a land border, or the sea in the cell, the neighboring cells n1 and the neighboring cells n2, respectively [9 variables]. The number of observations in each regression is just shy of 3.8 million. R-squares are 0.799, 0.711 and 0.582, respectively. All coefficients shown here are significant at the 1% or better.
<!-- Start of picture text --> Figure 8. Coefficients of the presence of roads in 1976<br>8.0%<br>7.0%<br>6.0%<br>5.0%<br>4.0%<br>1990 regression<br>3.0% 2000 regression<br>2014 regression<br>2.0%<br>1.0%<br>0.0%<br>In cell In N1 In N2 In cell In N1 In N2 In cell In N1 In N2 In cell In N1 In N2<br>-1.0%<br>Class 1 road Class 2 road Class 3 road Track road<br>-2.0%<br>Impact on buildup proportion<br><!-- End of picture text --> Notes: Figure 8 summarizes other coefficients from three separate regressions presented in Figure 7. The dependent variable in the three regressions is the proportion of a cell that is built up in 1990, 2000, and 2014 respectively. The Figure shows the coefficients of the presence in 1976 of a road of a certain class in the cell, the neighborhood N1 and the neighborhood N2. The road quality ordering is: class 1 (top category), class 2, class 3, and track (bottom category). Each regression includes the 1975 values of buildup in the cell and in the neighboring cells n1 and n2. Each of the three 1975 buildup variables appears in the regression as a series of 10 dummies, one per buildup decile (see Figure 7). Each regression also includes the following time invariant regressors: longitude, latitude, and their product [three variables]; soil humidity and soil quality dummies [six variables]; and dummies for the presence of a water body, a land border, or the sea in the cell, the neighboring cells n1 and the neighboring cells n2, respectively [9 variables]. The number of observations in each regression is just shy of 3.8 million. R- squares are 0.799, 0.711 and 0.582, respectively. All coefficients shown here are significant at the 1% or better.
<!-- Start of picture text --> Figure 9. Covariogram of built-up cells - Small tiles<br>S<br>2<br>oO<br>[=i<br>a8<br>Zo<br>><br>Be<br>o<br>s<br>Se<br>So<br>&<br>) 5 10 15 20 25<br>Distance in Km<br>——_ 1975 ——— 1990<br>—— 2000 =————. 2015<br><!-- End of picture text --> <!-- Start of picture text --> Figure 10. Covariogram of built-up cells near a road - Small tiles<br>re] ;<br>oo:<br>>a Na WASLMAR on saraliall . 1<br>2 sii |<br>—o U<br>g<br>e h<br>Qin<br>So<br>fo) 5 10 15 20 25<br>Distance in Km<br>——-_ 1975 ——_ 1990<br>———__ 2000 ——_ 2015<br>————— cl 1975 ———._ cl 1975<br>——— C2015 Cl 2015<br>95%. confidence interval shown for 1975 and 2015<br><!-- End of picture text -->
<!-- Start of picture text --> Figure 11. Covariogram of built-up cells - Big tiles<br>s<br>Ke<br>os<br>o&<br>8S<br>7°<br>7<br>Ss<br>2<br>oS<br>Cc<br>3<br>°<br>"<br>i] Stee<br>0 20 40 60<br>Distance in Km<br>———_ Year 1975 ————_ Year 1990<br>————_ Year 2000 ———— Year 2015<br><!-- End of picture text --> <!-- Start of picture text --> Figure 12. Covariogram of built-up cells near road - Big tiles<br>a<br>Zu<br>fe<br>8<br>ow<br>a<br>S<br>i<br>Ss<br>geSs | |<br>o<br>fe) 20 40 60<br>Distance in Km<br>————_ Year 1975 ————_ Year 1990<br>————__ Year 2000 ————— Year 2015<br><!-- End of picture text -->
Notes: Figure 13 shows, for each distance value between small tiles, the proportion of tile pairs that are both in the top buildup decile. For instance, a value of 2% at distance 50Km means that tile pairs that are both in the top build decile make up 2% of all the cell pairs distant from each other by 50Km. For correlograms are displayed, one for each of the years for which we have buildup data. The four curves show, for each of the data year, the predictions from a fractional polynomial regression of the share of top decile pairs on distance.
<!-- Start of picture text --> Map 1. Buildup of Yeji over time<br>Map 1a. Buildup of Yeji in 1975 Map 1b. Buildup of Yeji in 1990<br>-.9 -.8 -.7 -.6 -.5 -.9 -.8 -.7 -.6 -.5<br>Longitude Longitude<br>Map 1c. Buildup of Yeji in 2000 Map 1d. Buildup of Yeji in 2014<br>-.9 -.8 -.7 -.6 -.5<br>Longitude -.9 -.8 -.7 -.6 -.5<br>Latitude given in Mollweide projection Longitude<br>10.3 10.3<br>10.2 10.2<br>Latitude Latitude<br>10.1 10.1<br>10 10<br>10.3 10.3<br>10.2<br>Latitude 10.2<br>10.1 Latitude<br>10.1<br>10<br>10<br><!-- End of picture text -->
8°05'56.4"N 0°54'10.8"W Imagery ©2020 TerraMetrics, Map data ©2020 2 km
<!-- Start of picture text --> Google Maps<br><!-- End of picture text -->

# Google Maps

<!-- Start of picture text --> NORTHERN REGION OldMakongo<br>: a3S<br>ee<br>s<br>a<br>An.<br>OOS<br>Wy<br>Sawaba<br><!-- End of picture text --> ~~Ld~~
<!-- Start of picture text --> Map 2. Buildup of Takoradi over time<br><!-- End of picture text --> <!-- Start of picture text --> Map 2a. Buildup of Takoradi in 1975 Map 2b. Buildup of Takoradi in 1990<br>-2 -1.9 -1.8 -1.7 -2 -1.9 -1.8 -1.7<br>Longitude Longitude<br>Map 2c. Buildup of Takoradi in 2000 Map 2d. Buildup of Takoradi in 2014<br>-2 -1.9 -1.8 -1.7<br>Longitude -2 -1.9 -1.8 -1.7<br>Latitude given in Mollweide projection Longitude<br>6.3 6.3<br>6.2 6.2<br>Latitude Latitude<br>6.1 6.1<br>6 6<br>6.3 6.3<br>6.2<br>Latitude 6.2<br>6.1 Latitude<br>6.1<br>6<br>6<br><!-- End of picture text -->
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<!-- Start of picture text --> Google Maps<br><!-- End of picture text -->

# Google Maps

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