Urbanisation in Post-Apartheid South Africa∗

Jan David Bakker, Christopher Parsons and Ferdinand Rauch

December 1, 2015

PRELIMINARY AND INCOMPLETE

Abstract

Under apartheid, black South Africans were severely restricted in their choiceof location and many were forced to live in homelands. They were free to migrateafter apartheid. Given gravity, a town nearer to the homelands can be expected toreceive a larger inflow of people than a town further away. We use this exogenousvariation to study the effect of migration on urbanisation and the distribution ofpopulation. In particular, we test if the inflow of migrants led to displacement,path dependence, or agglomeration in the destination area. We find evidence forpath dependence in the aggregate but substantial heterogeneity in town density.Using quantile regressions we show that in areas with high population growthrates migration leads to displacement of incumbents. We also find that in ruralareas the exogenous migration shock leads to displacement of incumbents, while inurban areas the causal effect is more consistent with path dependence. Hence anexogenous population shock leads to an increase of the urban relative to the ruralpopulation. This finding is consistent with standard models used in economicgeography and the migration literature. It suggests that exogenously createdmigration can drive medium run urbanisation.

JEL Codes: R12, R23, N97, O18Keywords: Economic geography, migration, urbanisation, exogenous population shock,path dependence, South Africa

∗We thank Daniel de Kadt who shared census data from 1991. We thank Matteo Escudé, JamesFenske, Doug Gollin, Vernon Henderson, Leander Heldring, Daniel Kaliski, Lu Liu, Chris Roth, LudvigSinander, Andrea Szabo, Tony Venables, Helene Verhoef, Johannes Wohlfart, and the participants ofthe ‘Urbanisation in developing countries’ seminar at the University of Oxford for helpful commentsand discussions.

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1 Introduction

Consider the following thought experiment: What happens if a policy maker exogenouslyincreases the population of a random town? There are three possibilities, the townmay stay at this increased population level, it may revert back to its original level or itmay find itself on a new groth trajectory and even grow further. Which of the threereactions is observed may vary with the size of the original town, and on the size of theshock. Understanding this question would help to shed light on the nature of cities, thegrip of economic equaliziing forces on the size and location of cities, the distrtributionof population in space, and ultimately the planability of the economic distribution ofthe population.

Using quasi-experimental evidence to study the effect of domestic migration on thedistribution of population in post-apartheid South Africa, this paper addresses preciselythese questions. Under the apartheid regime, the black South African population wasseverely restricted in its mobility and large parts of the population were forced tolive in so-called homelands and townships. En-route to the democratic transition in1994, these massive restrictions were lifted in June 1991 and black South Africans wereallowed to move freely for the first time since the foundation of the state of SouthAfrica in 1910. This generated substantial domestic migration flows that further pushedurbanisation dynamics during the 1990s and 2000s (see Figure 1 below). We are ableto identify the exogenous effect of this positive migration shock on the distributionof population in South Africa under the assumption that people behave according togravity. That is, we assume that the cost of migration increases with distance such thatall else equal, a town that is closer to a homeland receives a bigger inflow of previouslymobility-restricted black migrants. Since the location of the homelands resulted froma long historical process starting in the 18th century (Lapping, 1986), it is plausibleto assume that their location conditional on covariates is quasi-random with respectto economic conditions today. Hence assuming gravity and conditional quasi-randomlocation, we can use distance to the nearest homeland as an exogenous instrument formigration.

It is self-evident that the population level of a town that experiences an exogenous mi-gration shock could theoretically evolve in only three ways. First, the town’s populationcould shrink back towards the initial population level, i.e. mean-revert. Such a reactionwould be consistent with an optimal urban network of relative city sizes, where relativesizes might be driven by locational fundamentals. Secondly, the town’s population couldjust remain at the new population level and not adjust endogenously to the shock. Inthis case, the distribution of city sizes would be path dependent. And third, the city

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could grow further, agglomerating population. This would be consistent with a theoryof multiple equilibria, where an initial population shock moves the town on a new popu-lation trajectory growth path from one equilibrium and into another. All three processeshave very different policy implications. If the urban system is an optimal network, thenonly permanent policies will influence the long-run city size. In the second and thirdcase, temporary policies will also have a permanent effect on the population distribution.

Our empirical results suggest that the aggregate population distribution is highlypath dependent. There is some indication of agglomeration effects, but these are onlymarginally significant. However, once we look at urban and rural areas separately, wefind that the population level in areas with low initial population density exhibits meanreverting behaviour, i.e. migrants displace incumbents. In urban areas, there is someevidence for agglomeration effects, but we cannot statistically reject a path dependentdevelopment in the long run. This suggests that a positive exogenous population shockgenerates a ‘Matthew effect’ (‘those who have will be given’), as densely populatedareas gain population relative to sparsely populated areas from an exogenous migrationshock. A ‘Matthew effect’ is consistent with a simple two-sector economic geographymodel where agricultural production in rural areas exhibits decreasing returns to labour,while the urban economy features increasing returns, or at least strictly less decreasingreturns to labour than in rural areas. A similar result also emerges in standard modelsused in the migration literature that feature complementarities between high- andlow-skilled labour in urban, but not in rural areas. An additional finding is that theimpact of migration decreases with population growth, i.e. an exogenous migrationinflow generates more displacement in faster-growing areas. In such areas the levelof private and public infrastructure is low relative to the level of population becauseinfrastructure investments do not materialize instantaneously. This relative lack ofinfrastructure increases rents and congestion costs and thereby induces displacement.

We modify the model of optimal city sizes by Henderson (1974) in order to infer theshape of the agglomeration function from the empirical findings. In this modifiedversion, agents’ utility is equal to the difference between the agglomeration functionand the congestion cost curve. Assuming that the congestion cost curve is increasingand convex in population, we relate the empirical results to the functional form of theagglomeration curve. The path-dependent evolution of the population level suggeststhat the agglomeration curve has a slope similar to the congestion cost curve as afunction of population density. This implies that an exogenous increase in populationdoes not significantly affect the utility level of incumbents and suggests that thereare infinitely many equilibria for the distribution of population in space. The mean

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reversion in the population level in rural areas suggests that the congestion cost curveis steeper than the agglomeration curve at least for the relevant population levels.

These results have important policy implications. Since positive population shocks havea permanent effect on the distribution of population in space, temporary policies thatinduce out-migration from some areas can influence the long-run distribution of citysizes. Such policies also affect the long-run distribution of population between ruraland urban areas. Since the population level in increases by more in urban than in ruralareas, policies that induce migration also generate urbanisation. This suggests thatpolicy makers are able to promote urbanisation and engineer the growth of metropolitanareas through encouraging higher levels of migration. Conversely, policies that impedemigration will hinder urbanisation.

The remainder of this paper is organised as follows. Section 2 discusses the relatedliterature. In Section 3 we illustrate the historical development of South Africa andprovide evidence for the quasi-random location of the homelands. Section 4 introducesthe theoretical thought experiment that serves as a framework for the empirical analysispresented in Section 5. The heterogeneous responses to a positive population shock arediscussed in Section 6. Section 7 concludes.

2 Related literature

This work relates to at least four broader strands of literature. First, the literatureinvestigating the determinants of the uneven distribution of population in space. Second,the related literature on the relationship between city size and population growth. Third,we contribute to the growing literature on post-apartheid South Africa and, fourth, ourfindings also relate to questions of migration within labour economics.

After Auerbach (1913) observed that the size distribution of cities follows a power law,there have been many attempts to explain this persistent empirical regularity (oftenreferred to as Zipf’s Law, after Zipf (1949)). Following the theoretical work by Gabaix(1999) who showed that Zipf’s Law emerges naturally if cities have equal relative growthrates (Gibrat’s Law), an extensive empirical literature on the distribution of populationhas developed. In their seminal study on Japan, Davis and Weinstein (2002) find thatthe dispersion of population is highly path-dependent and argue that this is due to theimportance of locational fundamentals. They show that even after massive destructionand death caused by the nuclear bombs, Hiroshima and Nagasaki rapidly returned to

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their pre-war growth path. Studies by Brakman et al. (2004) for post-war Germany andby Miguel and Roland (2011) for Vietnam arrive at similar results. However, they areunable to distinguish between the effects of path-dependence due to state-dependence(i.e. the presence of factors of production) and the importance of the initial naturaladvantage. That is, it is unclear whether the growth path was due to first natureadvantages such as coast lines and rivers, or to second nature factors such as sunkinvestments in infrastructure and housing, and other positive externalities of economicactivity. Bleakley and Lin (2012) analyse the development of former portage cities inthe United States. Portage cities had a unique natural advantage in the 19th centuryas their location provided a critical link to overseas trade. But this relative advantagehas disappeared due to technological progress, particularly the development of therailway system which made domestic water transport more expensive compared to landtransport. This allows them to disentangle the state-dependence and natural advantageeffect, since continuing agglomerations at these locations cannot be explained by theimportance of natural advantage. They find that former portage locations still maintaintheir historical importance and are not in decline relative to other cities. This suggeststhat path-dependent behaviour is induced by sunk investments and local agglomerationeconomies rather than natural advantage. In addition, their findings emphasise theimportance of sunk investments in a world of increasing returns to scale where multipleequilibria emerge naturally. Thus, agents face an initial coordination problem of whereto co-locate. Bleakley and Lin argue that the natural advantage of portage cities servedas an initial selection mechanism of this coordination problem while the persistence iscaused by the high pay-off to locate at existing agglomerations due to increasing returnsto scale. This explanation is consistent with recent results from local positive populationshocks from German refugees after World War II that were highly persistent and couldnot be explained by locational fundamentals (Schumann, 2014). We contribute tothis literature in multiple ways. First, to the best of our knowledge this study is thefirst to analyse a large scale positive population shock. Most of the literature, such asDavis and Weinstein (2002), Brakman et al. (2004) and Miguel and Roland (2011) hasstudied negative population shocks in the context of wars. This allows us to add a newimportant angle to the existing literature. The studies of war destruction find evidenceof path-dependence but cannot isolate whether this is driven by natural fundamentals,sunk investments, social networks or gains from agglomerations. Bleakley and Lin(2012) provide evidence that it is not driven by locational fundamentals, but cannotdistinguish between the other factors. Since we analyse a positive population shock,incoming migrants do not have social networks or private sunk investments, whichallows us to isolate the effect of gains from agglomeration. Second, we provide evidencefrom a credible natural experiment that is well-identified with a much larger sample

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than most studies in this literature. Third, we am the first to provide evidence fromAfrica, a region that is amongst the most rapidly urbanising regions in the world, andthe continent on which such policies related questions matter most. Fourth, many ofthe previous studies focus only on urban areas, whereas we are able to look at bothrural and urban areas and the differences between these two.

There is a large existing literature in urban economics and economic geography on therelationship between population growth and the size of cities (e.g. Black and Henderson(2003), Eeckhout (2004), Duranton (2007), and Rossi-Hansberg and Wright (2007)).The majority of empirical studies finds that urban systems tend to obey Gibrat’s Lawand that city size is uncorrelated with population growth, while some studies do finddepartures from Gibrat’s Law even for cities (Soo (2007), González-Val et al. (2013), andHolmes and Lee (2010)). Michaels et al. (2012) emphasise the importance of structuraltransformation for urbanisation. In their long-run study of population growth in theUnited States from 1880 to 2000, they find that areas with high initial populationdensity obeyed Gibrat’s Law, i.e. subsequent population growth was uncorrelated withinitial population density. The increasing dispersion in the distribution of populationwas driven by heterogeneous growth rates for areas with intermediate densities. Up toa threshold of 7 people per km2, population growth rate and initial population densityare negatively correlated. For areas with an initial density of 7-55 people per km2,they are positively correlated. They show that their result is driven by the differencesin agriculture’s initial share in production and structural transformation that shiftedemployment away from agriculture. Those areas that did not experience a shift awayfrom agriculture stagnated in terms of population growth. Our contribution to thisresearch is two-fold. Most importantly, there are no studies in this line of research thatlook at exogenous population shocks and whether an urban system experiencing sucha shock reverts back to Gibrat’s Law. Secondly, we are able to show how areas reactdifferently depending on the initial population density and thereby highlight differencesbetween rural and urban areas in the aftermath of an exogenous population shock.Further work based on this study will be able to look at how the reaction to a positivepopulation shock varies with the initial economic structure. This could shed light onthe underlying mechanisms why some areas experience agglomeration effects after apositive population shock, while others mean-revert.

We also contribute to the evolving literature that utilises exogenous variation generatedby apartheid policy to study the development of South Africa since 1994. Most closelyrelated to this study is recent work by de Kadt and Sands (2014) who use variationin geographical features and the corresponding limits to re-integration to estimate the

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effect of segregation on interracial trust. Dinkelman (2013) studies the effect of droughtexposure during childhood in the former homelands on later disabilities and Dinkelman(2011) estimates the economic effects of rural electrification. De Kadt and Larreguy(2014) look at the influence of traditional leaders in the former homelands on votingbehaviour. While there have been descriptive studies on domestic migration (Kok et al.,2005), this is the first piece of research to study a causal effect of domestic migrationflows emerging after the end of apartheid.

The identification strategy in this paper could also be used to study the effects ofmigration on income, wages and induced migration decisions of incumbents. Importantcontributions in this area include Card (1990), Friedberg (2001), Borjas (2003), Peters(2015), Sarvimäki et al. (2009) and Ottaviano and Peri (2012). However, for concisenessof this study, it will place less emphasis on this strand of research that could providequestions for future research.

3 Historical Background

Today, around two-thirds of South Africa’s total population live in urban areas whichmakes it one of the most urbanised countries in Africa. However, the process of urban-isation in South Africa is very different from other African countries. In the secondpart of the 20th century, it was shaped by the apartheid policy of the National Partygovernment (1948-1994). Apartheid, literally meaning “apart-ness”, was by its verynature a spatial concept (Christopher, 2001). The government aimed at total separationof the black and non-black population at every level. This reached from installingtwo town hall bathrooms to segregating city quarters and creating native reserves, theso-called homelands (or ‘bantustans’) that were to become independent states for theblack population.

Segregation and mobility restrictions imposed on the black population had a longtradition in South Africa dating back to at least the 18th century (Lapping, 1986).However, the policies that took shape after 1948 are unique in their aim to achievecomplete spatial and social segregation by mobilising significant government resourcesand the will to move and displace large amounts of people. The support for apartheidpolicies in the run-up to the 1948 elections especially among poor white South Africanswas driven by the increasing black urbanisation rate during the preceding decades.These dynamics in turn were structurally driven by the expansion in manufacturing andthe labour shortages caused by World War II (Ogura, 1996). It was generally believed

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that the problem of white poverty was linked to increasing black urbanisation. TheNative Economic Commission (1930-32) provides an example as it explicitly namesblack urbanisation as a cause for greater levels of unemployment among low-skilledwhite people (Beinart, 2001, p.122). Therefore, one of the main goals of the apartheidpolicies was to stop and reverse black urbanisation, or to put it in the words of theStallard Commission (1922): ‘The Native should only be allowed to enter urban areas,[...], when he is willing to enter and to minister to the needs of the white man, andshould depart therefrom when he ceases so to minister.’ (Feinstein, 2005, p.152).

In order to control the movement of the black population, the government restrictedtheir rights to own land and their legal ability to settle down where they wished. Theliterature distinguishes two dimensions of separation, ‘urban apartheid’ and ‘grandapartheid’ (Christopher, 2001). Urban apartheid aimed at creating separate quartersfor the black population that was allowed to stay permanently in urban areas. Grandapartheid aimed at moving the majority of the black population - that was not neededas labourers in white urban areas - to the native reserves.

The three main measures to implement ‘grand’ and ‘urban apartheid’ were the GroupAreas Act (1950), the Pass Laws Act (1952) and the Population Registration Act(1950). The latter assigned a population group to each citizen, which largely defined anindividual’s political and social rights. The Group Areas Act assigned a native reserveto each black population group and enabled the government to remove people thatwere not living in the area assigned to their population group. In order to control thepopulation flow and black urbanisation flows in particular, the government relied ona pass system. The Pass Laws Act forced every black African to carry an internalpassport at all times.1 If a black African could not present his passport documentinghis permission to be in a certain region, he was subject to arrest by the police.

[Table 1: Black population rural/urban/Bantustan from SPP around here]

These laws were strictly enforced and had a huge impact on the distribution of popula-tion in space and in particular on the process of urbanisation. According to the SurplusPeople Project (1985),2 the South African government forcefully relocated at least 3.5million people between 1960 and 1983. Additionally, several hundred thousand arrestswere made every year under the pass laws (Beinart, 2001, p.158f). Table 1 displays the1It built on pre-apartheid legislation such as the Natives Urban Areas Act from 1923 and NativesUrban Areas Consolidation Act from 1945 that forced every black man in urban areas to carry passesat all times.

2The Surplus People Project was a non-governmental organisation that documented the forced removalthrough the apartheid government.

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share of the black population living in urban and rural areas within South Africa, andthe homelands from 1950 to 1980. While the proportion living in urban areas in SouthAfrica stayed roughly constant over these 30 years, the proportion living in rural areasdecreased by around 15%, and the population of the homelands increased accordingly.This created areas with urban population densities in the homelands. These areas canonly be classified as urban in terms of population densities, but not in terms of publicservice delivery or industrial development. This ‘dislocated urbanisation’ (Beinart,2001), driven by government decisions instead of economic fundamentals, providesevidence for the substantial impact that the apartheid policies had on the distribution ofpopulation. Overall, while apartheid policies failed to reverse the level of urbanisation ofblack South Africans, they were able to stop the trend towards increasing urbanisationdriven by economic growth, and instead channel urbanisation dynamics away from(white) cities towards the homelands.

[Table 2: Urbanisation under apartheid around here]

Table 2 shows the share of the population living in urban areas during apartheid bypopulation group. The three non-black population groups were already much moreurbanised in 1951, and by 1991 around 90% of the non-black population lived in urbanareas. The black population was predominantly living in rural areas in 1951 andurbanised until 1991, but remained significantly less urbanised than the other threepopulation groups. As emphasised before, this urbanisation was severely influencedby government policies that kept the black population out of urban areas in ‘white’South Africa and engineered urbanisation in the homelands. During the 1990s, levels ofurbanisation increased rapidly (see Figure 1). Given that the non-black population wasalmost entirely urbanised in 1991, this is evidence for large domestic migration flows ofthe black population .

[Figure 1: General Urbanisation figures from Turok (2012) around here or Todes et al.2012]

Given the historical development of South Africa and the native reserves outlined above,two main concerns arise regarding the proposed research design, which is to use distanceto the nearest homeland as an instrument for migration. One concern is that thelocation of homelands is non-random and that these could have for instance been placedclose to big industrial centres to serve as labour reservoirs. However, there are reasonsto assume that the location of the homeland was exogenous with respect to economicconditions and driven by other factors. To dispel doubts that the homelands could have

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been located for economic reasons, we will first illustrate how the initial allocation in1913 was not driven by economic concerns. We will then show that subsequent policymeasures that reallocated the amount of land for different population groups were notdriven by economic concerns either.

The homelands established under apartheid (see Figure 2) built on areas that weredesignated as native reserves under the Native Land Act in 1913. The land that wasdesignated as reserves made up 7% of the overall area of South Africa and was largelyinhabited by the black population, as the government was unwilling to expropriatewhite farmers. Hence the land allocation in 1913 did not move large amounts of landbetween the different population groups but merely legally consolidated the distributionof land that had emerged mostly through European conquest of African land (Neame,1962, p.40f). Since land was mostly conquered for agricultural purposes, the Africanreserves have a relatively low quality of land. In 1913, South Africa was mainly anagricultural economy with only two important industries - gold mining around Johan-nesburg and diamond mining around Kimberley. These industries had established asystem of migrant labour. They found it optimal to change their entire workforce ona regular basis - every three or six months - and wanted to keep the families of theworkers out of the city in the reserves. This allowed firms in these industries to paylower wages because the families of the workers were assumed to work on the familyfarm in the reserves, and they were able to send sick or injured workers back to thereserves where their tribe would take care of them (Lapping, 1986, p.26). This suggeststhat there was no need for specifically located labour reservoirs when the homelandswhere established. Therefore, no significant economic considerations appeared to havemotivated the location of homelands, except for perhaps agricultural factors.

[Figure 2: Map of homelands around here]

The 1936 Land Act and following initiatives by the government aimed at consolidatingthe native territories into bigger, more coherent land masses in order to make themviable as independent states. There were no attempts to relocate them for economicreasons. One possible economic reason would be the proximity of cheap labour. In-stead of relocating the homelands, the government created black townships such asSoweto to serve as labour reservoirs. However, if a homeland was conveniently located,many inhabitants commuted to work in white cities (KwaMashu and Umlazi in thehomeland KwaZulu provide an example). Therefore, there were no incentives to relo-cate homelands as other ways to increase the pool of cheap labour were more convenient.

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Another concern when analysing the switch from the constrained equilibrium for theblack population under apartheid to the unconstrained equilibrium is whether thisconstraint was binding. There are several observations that suggest that the constraintwas indeed binding and that the switch to an unconstrained equilibrium was a significantshock to the distribution of population. First, the homelands were much poorer thanother parts of South Africa. In 1985, GDP per capita in the homelands varied between600 and 150 Rands, an order of magnitude below the 7,500 Rand estimated for therest of South Africa (Christopher, 2001, p.93). Second, while more than 90% of whitesand Indians lived in urban areas in 1986, less than 60% of blacks did, and we observea large jump in urbanisation starting in the 1990s. Third, while keeping blacks outof the urban areas was one of the major goals of apartheid policy, the absolute levelof black population in ‘white’ urban areas increased nevertheless. This suggests thatstrong urban attraction pulled blacks into urban areas, while apartheid reduced therate of urbanisation (Feinstein, 2005, p.157).

4 Theoretical Foundation

This section describes the three hypotheses that guide the empirical analysis below,and outlines how they have different implications for the shape of the agglomerationcurve in a modified Henderson (1974) model.

There are three ways how the population level of a region can react to an exogenouspositive migration shock: (i) it can shrink back towards its initial level; (ii) it can stayat the new population level; or (iii) it can grow further. These three behaviours can beconceptualised in the following theoretical framework:

Hypothesis 1: The population of the region shrinks below its new, back towards itsold population level (Mean Reversion).

The population of the region should shrink back towards its initial size if it is part of anoptimal network of constant relative city sizes. An optimal network of relative city sizeswould emerge if locational fundamentals were the main drivers of the location of citiesas argued by Davis and Weinstein (2002). In this case, the migrants displace incumbents.

Hypothesis 2: The region stays at its new population size, i.e. its population does notchange endogenously after the exogenous shock (Path Dependence).

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The population level of a region does not change if urbanisation and the distribution ofpopulation are highly path dependent (Bleakley and Lin (2012), Michaels and Rauch(2013)). Path dependence can arise for various reasons. Firstly, path dependence can becaused by sunk investment such as housing (Glaeser and Gyourko, 2005), which couldexplain that the distribution of population in Japan has been highly path dependentover millennia (Davis and Weinstein, 2002). However, since migration after apartheidconstitutes a positive rather than a negative population shock for the destination area,this logic does not apply. In this setting, path dependence could arise if the utility ofincumbents is unaffected by the increase of population, or if there are high costs ofmoving for incumbents relative to gains from migration.

Hypothesis 3: The population of the region grows by more than the initial exogenousshock (Agglomeration).

In a world of multiple equilibria due to increasing returns, following benchmark modelsof economic geography (e.g. Krugman (1991)), a city can grow further if the initialmigration shock induces a shift between equilibria. If the population exogenouslyincreases above a threshold that fosters the development of new industries, this maychange the economic structure of an area significantly. It could also affect the productiontechnology which might increase labour demand and/or wages. Multiple equilibria arisebecause increasing returns create an incentive for agents to co-locate.

These three hypotheses can be conceptualised in a modified version of the Henderson(1974) model. In the model, agents derive utility from locating in a certain area. In equi-librium, there cannot be any gains from moving locations such that utilities of all agentshave to be equal. This determines the equilibrium allocation of the population. Whilein the original Henderson model utility is derived from consumption, in this versionutility stems from the difference between the agglomeration (A(N)) and the congestioncost curve (C(N)), which are both functions of population density (N).3 Thereforespatial utility in region i is defined as: U(N i) = A(N i)− C(N i). The agglomerationcurve summarises the consumption gains from higher varieties as well as the higherwage resulting from productivity gains due to agglomeration effects. The congestioncost curve is determined by rents and commuting costs. The population allocationequilibrium is determined by the indifference condition that the spatial utility fromlocating in a certain area has to be equalised across all K areas: U(N1) = ... = U(NK).When assuming a certain functional form for one of the two functions, we can infer char-

3In the context of this stylised model, we use changes in the population level and changes in populationdensity interchangeably, since we consider a fixed amount of space.

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acteristics of the shape of the other function from the three hypotheses outlined above.There are no intuitive guidelines on the shape of the agglomeration curve as a functionof population density A(N). The agglomeration function could be non-monotonic, asnew industries might emerge that replace other industries when the population levelcrosses a certain threshold, which could lead to significant changes in the structure ofthe local economy. For the congestion cost curve C(N) on the other hand, given finitespace, it is plausible to assume that it is increasing (C ′(N) > 0) in population density,convex (C ′′(N) > 0), and tends to infinity after a certain population density thresholdhas been reached (limN−→N̄C(N) −→∞).

Given these assumptions on the congestion cost function, different shapes for the ag-glomeration function follow from the three hypotheses outlined above. The definitionof equilibrium implies that the utility across locations has to be equal before the shockhits. The population movements as a reaction to the exogenous shock then again haveto equalise the utility across locations to attain a new equilibrium.

[Figure 2: Three graphs as illustrations of theory]

In order to simplify the analysis within this framework, we look at the effect of a localpopulation shock such that only some areas are treated by a shock, while the populationof others remains unchanged. In the empirical analysis, all areas are treated by apopulation shock with varying intensity depending on distance to the homelands, butthe implications of the analysis do not depend on this simplifying assumption. Theutility level in the initial equilibrium is denoted by U(N0). U(NS) denotes the utilitylevel after the shock, and U(N1) is the utility level of the new equilibrium after agentshave adjusted their locational decisions. By the definition of equilibrium, U(N0) andU(N1) have to be equal across all locations (treated and control), while U(NS) is notrelated to an equilibrium and can therefore vary across locations.

The population level mean reverts (Panel A in Figure 34) if the utility at the newpopulation level U(NS) is below the utility in the initial equilibrium U(N0) that can beattained in the untreated areas. Agents will move from the treated areas to the controlareas until the utilities are equalised across both types of locations U(NT

1 ) = U(NC1 ),

which leads to a reduction of population below NS. For the shape of the agglomerationfunction, this implies that its slope has to be locally smaller than the slope of thecongestion cost function. The evolution of population is path dependent (Panel B)if the utility at the population level after the shock is equal to the utility in the

4Note that the graphs only display the evolution of population in treated areas.

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initial equilibrium U(N0) = U(NS). This implies that there are no gains from movingbetween control and treatment areas and therefore no endogenous adjustment of locationdecisions takes place, such that the new population level is an equilibrium populationlevel: NS = N1. Since the difference between agglomeration and congestion functionat N0 is equal to the difference at NS, the slopes of the two functions between N0 andNS have to be equal. If this property holds globally, then there exist infinitely manyequilibria of the spatial distribution of population. In the case of agglomeration (PanelC), agents move from control areas to treated areas. This implies that there have tobe gains from migration such that the utility level after the shock has to be above theutility in the initial equilibrium: U(N0) < U(NS). However, utility cannot be strictlyincreasing in population between N0 and NS because that would imply the existence ofgains from migration at N0. The existence of such gains would contradict the definitionof equilibrium, such that N0 could not be an equilibrium. Therefore, for N0 to be anequilibrium, utility has to be non-monotonic, which implies the existence of multipleequilibria for the spatial distribution of population. In order for the utility function tobe non-monotonic, the slope of the agglomeration function has to be non-monotonic.5

5 Empirical Analysis

5.1 Data

In order to empirically test the three hypotheses, we make use of a unique geographi-cally referenced South African census dataset. It contains observations for the years1991, 1996, 2001 and 2011 at the ward level and hence bridges across the democratictransition in 1994. This dataset consists of two parts. Firstly, it contains publiclyavailable census data aggregated to the ward level for the censuses in 1996, 2001 and2011. This allows us to distinguish between the short-, medium- and long-run effectsof the exogenous population shock. Secondly, it contains data from the last censusunder the apartheid government in 1991. De Kadt (2015) obtained a partial enumeratorarea (lowest census tract with 30,000 observations) map from 1991 from StatisticsSouth Africa, combined it with the 100% sample of the census made available online byDataFirst at the University of Cape Town and aggregated it to the 2011 ward level.This last census was implemented in March 1991. This timing is crucial as the NativeLand Act, the Population Registration Act and the Group Areas Act were repealedin June 1991. The Pass Laws Act was already repealed in 1986. While identificationwould be cleaner if data from before 1986 were available, this is not a major impediment

5Note that the functional form displayed in Panel C is just one example of a broad class of possibleagglomeration functions. In particular, it is not necessary for the slope of A(N) to be locally negativefor the existence of multiple equilibria.

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to the identification strategy. Given that the Group Areas Act and the PopulationRegistration Act were still in place, the black population was still severely constrainedin its choice of residence until June 1991. Unfortunately, the data from 1991 doesnot cover the entirety of South Africa. One general drawback of the dataset is thatit does not cover the homelands. This does not affect the analysis since we only lookat areas outside the homelands. Another more relevant drawback is that there area few areas that are not covered within South Africa (see Figure 6 in the appendix).This is due to two reasons. Firstly, Statistics South Africa only has a partial map ofthe census enumeration areas in 1991. Therefore, part of the census data cannot begeographically referenced. Secondly, due to violent turmoil at the time, some areas couldnot be visited by enumerators and no data are available on a granular level.6 However,while this reduces the number of observations and therefore the statistical power in theempirical analysis, it should not introduce any inconsistencies in the parameter estimates.

[Table 3: Summary statistics around here]

5.2 Identification

I want to test the effect of exogenous migration on the distribution of population. Inorder to do so, we use distance to the nearest homeland as an instrument for migrationflows. For distance to be an appropriate instrument for migration, it has to be both validand informative. Distance is an informative instrument for migration if it is partiallycorrelated with migration conditional on other covariates. It is a valid instrumentif it only affects the population growth through its effect on migration, and is thusuncorrelated with the error term in the second stage regression.

The validity of the instrument relies on the conditional quasi-random allocation ofhomelands which has been argued for extensively in Section 2. The assumption is likelyto be violated for the areas adjacent to the homelands as they are likely to be affectedby economic spillovers from the neighbouring homeland in a variety of ways that arenot related to the cost of out-migration from the homelands. To adjust for this problem,we exclude areas within 10 km from the homelands as a robustness check, to ensurethat the estimates are not driven by local economic spillovers.

The informativeness relies on the assumption that people migrate according to gravitybecause the cost of migration increases in distance. Migration according to gravity

6This information was obtained in correspondence with Helene Verhoef (Manager at the GeographyDivision of Statistics South Africa).

15

would imply that a town that is closer to the homelands ceteris paribus receives moremigrants than a town that is further away. The gravity assumption is quite a commonassumption in the migration literature7 and the informativeness can be tested empiri-cally by looking at the partial correlation between instrument and endogenous variable.The informativeness of distance as an instrument depends crucially on the level offixed effects chosen, since the level of fixed effects affects the variation in the data.As can be seen from Table 10 in the appendix, the informativeness of the instrumentdecreases almost monotonically in the granularity of the fixed effects. This is quite anintuitive result. For example, when using municipality level fixed effects, the identifyingvariation of the instruments explains in which part of Johannesburg migrants are goingto settle. This is likely to be uncorrelated with distance to homelands especially forurban areas. Therefore we face the trade-off between accounting for unobservablesat a local level and retaining sufficient identifying variation to have an informativeinstrument. We use the province level fixed effects in order to maintain sufficient identi-fying variation while accounting for potential differences in policies at the province level.8

A useful way to test the exclusion restriction, i.e. whether the distance to the nearesthomeland only influences population growth through migration, would be through aplacebo exercise. A placebo exercise measures the impact of the treatment variable whenthere is no treatment. For example, if the treatment is a government program in certaindistrict starting in year t, the estimated treatment effect in year t− 1 should be zero.This ensures that the estimated treatment effect is actually the causal effect of the treat-ment. In this case, a placebo would require finding areas with varying distance to thenearest homeland that did not receive any immigration. For these areas, the effect of dis-tance should be zero if distance only affects overall population growth through migration.

Due to lack of necessary data, we were not able to implement possible placebo exercises.One possibility is to use areas such as Orania in the Northern Cape that are still white-only areas and hence did not receive black immigration, but there are only very few ofthese. In addition, these white-only communities of traditionalist Afrikaners are unlikelyto be comparable to the rest of South Africa in 1991. Alternatively, attitudes thatinhibit black immigration could be proxied through voting behaviour under apartheid,but no geographically referenced election data is available prior to 1994. Another wayof creating a placebo test could be to calculate the cost of migration using data onroads and railways, and creating a sub-sample of areas where the cost of migration isuncorrelated with the distance measure. However, this placebo has the problem that

7For example, Peri (2012) uses distance to the Mexican border as an instrument for the intensity ofmigration to different US states.

8Provinces are equivalent to states in the US.

16

this difference does not only affect the intensity of migration, but also other potentialspillovers from the homelands.

5.3 Estimation

In order to estimate the causal effect of migration on the distribution of population, weestimate the following system using two-stage least squares (2SLS):

BlackPopGri,t = α2 + log(distancei)π + Xi,1991γ2 + δp + υm (1)

∆Ni,t−1991 = α1 + ̂BlackPopGri,tβ + Xi,1991γ1 + δp + εm (2)

where ∆Ni,t−1991 denotes overall or non-black annualised absolute population growthin ward i between 1991 and t. We include controls for population groups, populationdensity, education, gender ratio, employment and income (Xi,1991) and province-levelfixed effects (δp) (see Table 3). The errors are clustered at the municipality level. Theward level is the lowest geographical level that can be tracked over time and municipali-ties are the lowest level of local government. Distance is defined as the distance to thenearest homeland measured from centroid to centroid. Since no measure of domesticmigration is available in the census data sets, we use annualised black populationgrowth conditional on fixed effects and covariates as a proxy for black migration.9 Wealso include a dummy for Cape Town as the municipality is a special case in terms oflocation, politics and demographics, and hence migration patterns. The Western Capewas the only province where the African National Congress did not come first in thegeneral elections in 1994. Until today, it has not achieved the political dominance inthe province or the municipality of Cape Town that it has in the rest of the country. Interms of demographics, there is a much higher white and especially coloured populationin Cape Town than anywhere else in the country. Most importantly, there is a lot ofcircular migration from the Eastern and the Northern Cape into Cape Town. Thesemigration dynamics in particular are quite distorting for the identification strategy, andaccordingly including a dummy for Cape Town significantly increases the predictivepower of the instrument.

9This is commonly used as a proxy when no data on migration status is available, e.g. Czaika andKis-Katos (2009).

17

5.4 Linking theory and the variable of interest in the empiricalestimation

This study intends to test the three hypotheses outlined in Section 4, so it is crucial tolink the predictions from the hypotheses to the parameter of interest β. We define thevariables in order to be able to assign the following interpretations to the estimatedvalue of β. If the underlying process was driven by mean reversion, then the effect ofthe exogenous population shock as measured by β would be below one and decreasingover time, as the shock gets distributed through the urban system. In the case of pathdependence, β would be expected to be equal to one in all periods. In the agglomerationscenario, β would be above one and increasing over time since population agglomerationsmight not materialise immediately (see Table 4 for a summary).

[Table 4: Linking estimated parameters to theoretical hypotheses aroung here]

To be able to assign these theoretical interpretations to the estimated parameters, wehave to avoid percentage growth rates in the endogenous variable and in the dependentvariables in the second stage. Using percentage growth rates would result in the followingexpression for β:

βperc = (Pt − P1991)/P1991

(Bt −B1991)/B1991= B1991

P1991

∆Pt

∆Bt

(3)

where Pt denotes overall population and Bt black population in period t. The two arelinked through the identity Pt = Bt +NBt where NBt is nonblack population in periodt. This definition of β depends on the initial share of black population in each ward(B1991

P1991). Since this is not constant and varies across wards, it is impossible to assign the

interpretation outlined above to the coefficient βperc. Therefore we will refrain fromusing percentage growth rates and use an alternative definition βalt which is independentof the initial fraction of the black population:

βalt = (Pt − P1991)/P1991

(Bt −B1991)/P1991= P1991

P1991

∆Pt

∆Bt

= ∆Pt

∆Bt

(4)

This alternative definition of β is equal to the absolute change in overall populationrelative to the change in black population. If the overall population increases by lessthan one to one, i.e. migrants displace incumbents (Hypothesis 1), then β will besmaller than one. β will be equal to one if there is no endogenous adjustment and theoverall population just grows by the amount of migrants received (Hypothesis 2). If theoverall population increases more than one to one after an exogenous migration shock

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(Hypothesis 3), then β will be bigger than one.

6 Results

6.1 Baseline results

This section describes the results of the empirical investigation. Table 5 summarisesthe main results and Table 6 provides further results from different sub-samples asrobustness checks. Each cell of the tables summarises one regression, e.g. each cellin the first row summarises the causal partial effect of annualised exogenous migra-tion of African population between 1991 and 1996 on the overall annualised absolutepopulation growth rate between 1991 and 1996. Before moving on to interpreting theestimated coefficients of interest, we will discuss a number of results. The difference ofthe parameters in Columns (1) and (2) in Table 5 sums up to one. This is a mechanicaleffect stemming from the fact that we use absolute population growth.10 This resultholds exactly in the OLS specifications, and approximately in the 2SLS estimations(Columns (3) and (4)). Therefore, the effect of the non-black population is omittedfor all other regressions and the subsequent discussion. We report confidence intervalsbased on Conley (1999) standard errors that account for spatial correlation for PanelA (1991-1996).11 These confidence intervals are more precise than those based oncluster-robust standard errors in all specifications that include fixed effects. Thereforewe only use the more conservative cluster robust standard errors for the remainingspecifications. The Angrist and Pischke (2009) F-statistic12 of the first stage is wellabove the rule of thumb threshold of 10 for all baseline specifications and most ofthe robustness specifications. The exceptions are the robustness checks in Columns(1)-(6) that only use sub-samples and Column (7) where the wards are aggregated tomunicipalities such that the sample reduces to 201 observations (the corresponding firststage regressions for Tables 5 and 6 are reported in Tables 11 and 12 in the appendix).These weak instrument problems only arise for the short period between 1991-1996and we will not discuss these parameter estimates as they are quite imprecise whenusing weak instrument robust confidence intervals (Anderson and Rubin, 1949).13 The

10β = ∆Pt

∆Bt= ∆NBt+∆Bt

∆Bt= ∆NBt

∆Bt+ 1

11Conley provides a procedure to estimate the covariance matrix of the estimator that is consistent forany arbitrary spatial dependence.

12In the one instrument and one endogenous variable case, the AP F-statistic is equivalent to thetraditional F-statistic in the first stage. When using several instruments and endogenous variablesthe traditional F-statistic cannot distinguish between well-identified models and under-identifiedmodels where one instrument has explanatory power for all endogenous variables while the otherinstruments have no predictive power. The AP F-statistic accounts for this problem.

13The Anderson-Rubin test statistic corresponding to the confidence intervals does not depend on thestrength of identification and is therefore robust to weak identification (Stock et al., 2002)

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increased explanatory power over the longer time horizons is consistent with the factthat migration decisions only adjust intermittently to a change in policy such as theend of apartheid.

In the OLS regression, we cannot reject the null hypothesis that the coefficient isdifferent from one in the short-run (1991-1996). For the two subsequent periods onthe other hand, the coefficient estimates are well below one. This suggests that blackpopulation growth occurred in areas with low non-black population growth and viceversa. These results should not be interpreted causally since the result could be drivenby black migration displacing non-black incumbents or non-black migration displacingblack incumbents. It could also follow from non-black out-migration from certain areasthat encourages black in-migration due to low rents and vice versa. The baselineresults from the two-stage least squares estimation (Columns (3) and (4)) suggestthat the coefficient is not different from one such that there is no causal effect fromexogenous black migration on aggregate migration decisions of non-black incumbents atany horizon. This result is robust to excluding controls. Once we exclude fixed effects,the estimated coefficients are bigger than one for the short- and medium run, but notdifferent from one in the long-run. Since the coefficient is not different from one inmost of the specifications and never different from one in the long-run, there is strongevidence that an exogenous population shock is absorbed without endogenous reactionof the population level. The results suggest that the effect of an exogenous populationshock on the aggregate long-run equilibrium of the population distribution is consistentwith the theoretical notion of path-dependence (Hypothesis 2). This corroborates thedynamics found by Bleakley and Lin (2012) for fall line cities in the US and Michaelsand Rauch (2013) for Roman cities in France and Britain.

In addition to the baseline regressions, we report several regressions based on differentsub-samples as robustness checks (Table 6). We include a dummy for Johannesburg inColumn (1) as the biggest metropolitan area and industrial centre to ensure that it isnot driving the results. As outlined above, we exclude areas close to the homelands,since for these distance to the nearest homeland could affect them not only throughmigration, but also through local economic spillovers (Column (2)). We also excludeareas with a low share of white population in 1991 because the migration restrictionsunder apartheid might have been less binding for these areas (Columns (3) and (4)).As a further robustness check, we exclude the areas in the upper tail of the distancedistribution in Column (5) to ensure that the high number of observations in the uppertail (see Figure 5 in the appendix for the distribution of the instrument) does notskew the results. In Column (6) we report results using district instead of province

20

fixed effects. We also aggregate wards up to the municipality level and run a separateregression to test whether the results are robust to using a different level of aggregation(Column (7)).

[Table 5: Baseline regression results]

The robustness results from different sub-samples reported in Table 6 (Columns (1)-(5))corroborate the findings of the baseline specification. While there are some specificationswhere we can reject that the coefficient is equal to one at the 10% level, this does nothappen at several horizons for the same specification. In order for such departures fromone to be consistent with a theory of multiple equilibria (Hypothesis 3), they wouldhave to be above one at all horizons and especially in the long-run.

Another interesting result is that the estimates are different when using district levelfixed effects (Column (6)). In this case, the coefficient of interest is below one atall horizons, which is consistent with a theory of an optimal urban network whereexogenous population shocks induce displacement. This difference could arise from thechanges in the identifying variation, which depends on the level of fixed effects. In eightmetropolitan areas, the district level is equivalent to the municipality level, such thatusing district level fixed effects most likely eliminates the variation picked up by theinstrument, as distance to the nearest homeland does not vary much within an urbanmunicipality. Therefore, the identification stems mostly, if not exclusively, from ruralareas. We will return to this point in Section 6.2 when we look at heterogeneity andprovide further evidence for this interpretation. Another possible interpretation couldbe that the greater granularity of fixed effects brings out more of an attenuation biasfrom measurement error when using population growth as a proxy for migration. Theintuition behind this result is that more granular fixed effects reduce the residual varia-tion in the error term such that the residual variance due to measurement error increasesin relative terms (Angrist and Krueger, 1999, p.1291f). When using municipalitiesas a level of analysis, the estimated coefficient are also clustered around one (Column (7)).

Overall, there is strong evidence for path dependence (Hypothesis 2). There are somemarginally significant departures from one, but these departures are never observed intwo periods for a given specification, and mostly found for the medium-run and onlyonce for the long run. These results suggest that, in the aggregate, there is no strongevidence for multiple equilibria and a non-monotonic agglomeration curve. There is alsono evidence for mean-reverting behaviour of the population level except when districtfixed effects are used. The evidence in favour of path-dependence is consistent with an

21

agglomeration function that has the same slope as the congestion function or high costsof migration as found by Imbert and Papp (2014) for temporary labour migration inIndia. This implies that there are many, possibly infinite, equilibria for the populationallocation in space.

[Table 6: Robustness baseline regression results]

6.2 Heterogeneity

This Section discusses how the causal effect of migration on population growth variesacross different dimensions of interest. First, we will discuss how a positive populationshock affects areas differently depending on their current population growth rate: i.e.does the population level react differently in areas where the population is growingrapidly compared to those with low population growth? And secondly, we will inves-tigate how the causal effect varies with initial population density: i.e. how does theeffect differ between densely populated urban and sparsely populated rural areas?

With respect to differences in the existing population growth rate, theory would suggeststronger displacement effects in areas that are faster-growing because of a low level ofinfrastructure relative to population. Rents and congestion costs can be reduced byinvestments in private and public infrastructure. Since the effects of such investmentsare inertial, i.e. they do not materialise instantaneously, the level of infrastructure willbe lower relative to the population if the population growth rate is high. Therefore, rentsand congestion costs are higher in places where the population is currently increasing,compared to similar places without population growth. Since ceteris paribus an increasein the congestion cost curve reduces the utility from locating in an area, this shoulddecrease the level of population for this area.

[Figure 3: Quantile regressions around here]

The results presented in Figure 4 show an almost monotonic decline in the causaleffect of migration on population growth with increasing population growth for alltime horizons.14 These results are consistent with the theory that areas currentlyexperiencing a high level of population growth are much more prone to displacementbecause of high congestion costs and rents, due to inertia in the adjustment of private

14The results were estimated using the Stata implementation of the instrumental variable quantileregression provided by Chernozhukov et al. (2012). This package uses a parametric version of thecontrol function method for quantile instrumental variable regressions suggested by Lee (2007).

22

and public investment.

Secondly, we are interested in how the causal effect varies with initial population density.In this case, theory does not provide clear guidance. Due to the convexity of the costcurve, the causal effect of migration could be decreasing in initial population densitybecause the additional costs generated by new migrants reduce the utility level ofincumbents. At the same time, Michaels et al. (2012) show that long-run populationgrowth in the US is smaller for low initial population densities and increases withpopulation density after a cut-off of 7 people per km2. Such a result would be consistentwith an agglomeration curve that is much steeper in urban than in rural areas. Thiscould suggest that in densely populated areas, exogenous migration leads to a biggerincrease in population than in less densely populated areas.

[Table 7: Summary statistics of interaction terms around here, if included]

In order to estimate how the effect of a positive population shock varies across initialpopulation densities, we use two different specifications. First, we add a linear interac-tion term between predicted black population growth and log population density in1991 to the baseline regression. In order to ensure identification, we create a secondinstrument interacting distance with initial population density (see Table 7 for summarystatistics). The results reported in Table 8 suggest that there is a positive relationbetween initial population density and the causal effect of migration on the level ofpopulation (the corresponding first stage regressions can be found in Table 13 in theappendix). In the baseline specification, the interaction term is statistically differentfrom zero at the 5% level for all time horizons and for 2001 even when choosing asignificance level of 1%. When we drop the province level fixed effects in order toincrease identifying variation, the estimates are even more significant. This suggeststhat areas with high initial population density experience a larger population growthfrom the same exogenous migration shock than areas with lower initial populationdensity.

[Table 8: Regression results of linear interaction term around here]

Secondly, we run the baseline regression for the sub-sample with low and high initialpopulation density separately. Since we do not have data classifying the areas intorural and urban, we use low population density as a proxy for rural areas and highdensity proxies for urban areas. A high population density is defined as being abovean initial logged population density of 4. This cut-off is chosen for several reasons.

23

Michaels et al. (2012) find that for their sample, the growth rate decreases with ini-tial population density in the interval of (0,2), while it increases in the interval (2,4)and is uncorrelated for population densities above 4. Since obeying Gibrat’s Law isgenerally considered a feature of urban and not rural areas, using logged populationdensity of four as the cut-off appears a sensible decision, especially since due to limiteddata availability, we cannot separately investigate the interval from 0 to 2. In thatsense, the decision is also driven by statistical concerns. We provide evidence for differ-ent cut-off values in Table 15 in the appendix and the results do not change qualitatively.

The results of the regressions using the different sub-samples are reported in Table 9.Most of the first stage AP F-statistics for 1996 are well below the cut-off of 10 for 1996and the reported weak identification robust confidences intervals suggest that no preciseparameter estimation is possible. Therefore we will ignore the results of these onlyweakly identified parameters in the subsequent discussion of the results. The estimatedcoefficients for rural areas at the remaining horizons are consistently below one (Column(1)), while the point estimates for urban areas are above one (Column (2)). However,these differences are not statistically significant and there are only marginal departuresfrom one in a statistical sense. In order to increase identifying variation, we re-runthe regressions without province level fixed effects (Columns (3) and (4)). Using thisadditional variation, we can reject that the coefficients for rural and urban areas areequal at all conventional significance levels with t-statistics of −3.45 for 2001 and −3.82for 2011.15 We can also reject that the coefficient for rural areas is equal to one forboth time horizons and for urban areas for 2001.

[Table 9: Subsample regressions for different population densities]

The results of both specifications indicate that the population dynamics induced by apositive population shock differ between less densely populated rural areas and highlypopulated urban areas. Hence in rural areas, a positive population shock leads todisplacement of incumbents such that the population level mean reverts even thoughthe new population level is significantly above the initial level.16 In urban areas, theeffect of a positive population shock is significantly bigger than in rural areas. For somespecifications, the effect is even significantly bigger than one. Overall, the population

15This holds under the assumption that the covariance between the estimators is zero. Since weestimate the same model on different sub-samples, it is hard to imagine how the covariance betweenthe estimators could be negative. As the t-statistic increases in the covariance, setting it to zero is aconservative assumption.

16The mean reverting behaviour of the population level in rural areas is consistent with the argumentthat the coefficients in the regression with district fixed effects (Table (6), Column(6)) are onlyidentified off variation in rural districts.

24

dynamics in urban areas appear to be driven by path dependence or agglomeration.The fact that the population of more densely populated areas increases relative to lessdensely populated areas could be interpreted as a ‘Matthew effect’17 of an exogenouspopulation shock. In general terms, a ‘Matthew effect’ describes a situation where ‘therich get richer and the poor get poorer’.18 In this case, areas rich in population gainover-proportionally from a positive population shock.

In the context of the modified Henderson model presented in Section 4, this resultsuggests that the shape of the agglomeration function is different between urban andrural areas for the relevant population levels. In rural areas the gains from agglomerationare below the increased congestion cost if the population increases exogenously. Inurban areas, the gains from an increase in population seem to be equal to the additionalcosts. Therefore, the gains from agglomeration seem to be much bigger in urban areasthan in less densely populated rural areas.

These heterogeneous gains from agglomeration arise in a simple two-sector economicgeography model. The agricultural sector produces food using a fixed endowment ofland and labour under a technology with decreasing returns to labour.19 The industrialsector, consisting of manufacturing and services, produces consumption goods usingcapital and labour with external agglomeration economies. Labour is perfectly mobileacross sectors and locations. Areas with low population density are predominantlyagricultural, while urban areas are predominantly industrial. If an exogenous populationshock hits both urban and rural areas, the marginal product of labour decreases inrural areas and generates displacement effects because the real wage decreases. Thisdynamic arises naturally from the assumption that there is only a fixed amount ofland available for agricultural production. In urban areas, an increase in the labourforce generates higher investment in capital (assuming a constant real interest rate).Therefore, the marginal product of labour does not fall and might even increase due toexternal economies of scale. This generates agglomeration effects or a path-dependentevolution of population in urban areas.

A similar result emerges in a standard model used in the migration literature (e.g. Borjas(1999) and Kremer and Watt (2006)) that distinguishes between low- and high-skilled17‘For unto every one that hath shall be given, and he shall have abundance: but from him that hathnot shall be taken even that which he hath.’ Matthew 25:29, (American Bible Society, 1999).

18Similar dynamics have been discovered in various fields such as the philosophy of science (Merton,1968), education (Adams, 1990) and individual career dynamics (Petersen et al., 2011). In economicsit is well established in the new new trade literature where big firms gain over-proportionally fromtrade liberalisation (Mrázová and Neary, 2013).

19Capital could be included as an additional factor in production but does not change the resultingdynamics and is therefore omitted.

25

labour used in production in urban areas. The production in rural areas only useslow-skilled labour and the fixed amount of land as inputs with the same technologyas above. In urban areas, low- and high-skilled labour are used as complements inproduction with a constant returns to scale technology. In this framework, the popu-lation shock we analyse in the data is best approximated by an increase of unskilledlabour, since the apartheid government only provided a bare minimum of schooling tothe black population (Feinstein, 2005, p.159f). In the model, an increase in unskilledlabour increases the wage for high-skilled labour and the rents for capital. If the supplyof capital is elastic, this leads to an increase in capital and an inflow of skilled workerssuch that all factor prices return to their initial equilibrium values. Therefore, anexogenous increase in the number of unskilled workers attracts skilled workers suchthat the population level of urban areas experiences agglomeration and a shift towardsa new equilibrium.

If initial population density is a good proxy for the economic structure, these modelscan explain the different responses of urban and rural areas to an exogenous migrationshock.20

7 Conclusion

We study the effect of an exogenous migration shock generated by the abolishment ofmovement restrictions for the black population on the distribution of population inSouth Africa. There are three ways in which an area can react to an exogenous popula-tion shock that arise from different theories describing the distribution of population inspace. The population level of an area could mean revert towards its initial level, itcould remain at the new population level (path dependence) or it could grow further, i.e.agglomerating population, suggesting the existence of multiple equilibria. Using a modi-fied Henderson model and assuming an increasing and convex congestion cost curve, weare able to infer the shape of the agglomeration function from these different predictions.

The empirical results suggest that in the aggregate, the reaction of the population levelis consistent with path dependence. There are some deviations that suggest agglomer-ating behaviour, but those are only marginally significant. For the modified Hendersonmodel, where the spatial utility is equal to the difference between the agglomeration andcongestion cost curve, this implies that the two curves have a similar slope such thatmany, possibly infinitely many equilibria of the distribution of population in space exist.

20Adding additional data on the economic structure in 1991 is a promising avenue for further research.

26

This has important policy implications. Since the population level of a region behavesaccording to path dependence, a temporary policy measure that induces migration canpermanently change the distribution of population.

We also study how the response to an exogenous population shock is heterogeneousacross areas with different population growth rates. In areas where the populationis growing quickly, an identical exogenous migration shock induces a smaller increasein the level of population than in areas with less population growth. This can beexplained by the inertial effects of investment in private and public infrastructure. Thelevel of infrastructure relative to population is lower in those areas that experiencehigh population growth, increasing congestion costs. This implies that an exogenouspopulation shock leads to a relative increase in population in those areas that do nothave high endogenous growth rates.

Additionally, we find that the reaction of an area to an exogenous population shockvaries with the initial population density. In rural areas with low initial populationdensity, the effect of an exogenous population shock is significantly smaller than inurban areas with high population density. The population level in rural areas displaysmean reverting behaviour which suggests that migrants displace incumbents. In urbanareas, the dynamics of the population level are consistent with agglomeration and pathdependence. In the context of the modified Henderson model, this result shows that theagglomeration curve in rural areas is much more concave than in urban areas. Theseresults are consistent with a simple economic geography model where production in ruralareas features decreasing returns to labour due to a fixed endowment of land usable foragricultural purposes. A steeper agglomeration function in urban areas also emerges ina standard model from the migration literature that features complementarities betweenlow- and high-skilled labour in urban, but not in rural areas. If an exogenous populationshock hits both rural and urban areas, these different dynamics increase the shareof the population living in cities. Exogenous migration, thus, generates urbanisation.From a public policy perspective, this is of vital importance because it suggests thaturbanisation can be engineered by public policies that induce migration. In futurework, it will be important to differentiate between the models that can account for thisheterogeneous effect in order to better understand whether complementarities betweenskilled and unskilled labour or increasing returns in production drive these urbanisationdynamics.

27

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31

A Tables and figures that will be in the main text

Table 1: Share of black population living in different areas (1950-1980)

Year Urban areas Rural areas Homelands1950 25.4 34.9 39.71960 29.6 31.3 39.11970 28.1 24.5 47.41980 26.7 20.6 52.7Source: Surplus People Project (1985, p.18)

Table 2: Share of urbanised population by population group (1951-1991)

Year White Coloured Indian Black1951 78 65 78 271960 84 68 83 321980 88 75 91 491991 91 83 96 58Source: Beinart (2001, p.355)

32

Figure 1: Urban share of the national population (%), 1911-2001

Data from Turok (2012), red vertical lines mark the apartheid regime of the National Party (1948-1991)

Figure 2: Homelands (Bantustans) established under apartheid

33

Figure 3: Modified Henderson model with gains from agglomeration andcongestion costs

(a) Mean reversion (b) Path dependence

(c) Agglomeration and multiple equilibria

34

Table 3: Summary statistics for included variables

(1) (2) (3) (4) (5)VARIABLES N mean sd min maxExcluded instrument

log distance 2,015 4.128 1.555 0.0529 6.746Endogenous variables

∆Black Population (1991-1996) 2,015 -1.134 16.08 -407.4 0.199∆Black Population (1991-2001) 2,015 0.0288 0.0438 -0.254 0.0999∆Black Population (1991-2011) 2,015 0.0171 0.0227 -0.202 0.0498

Dependent variables∆Total Population (1991-1996) 2,015 -1.755 21.67 -513.2 0.200∆Total Population (1991-2001) 2,015 0.0318 0.0560 -0.330 0.1000∆Total Population (1991-2011) 2,015 0.0203 0.0270 -0.203 0.0500∆Nonblack Population (1991-1996) 2015 -.6248145 9.351218 -225 .1910352∆Nonblack Population (1991-2001) 2015 .0030771 .0331965 -.327572 .0953673∆Nonblack Population (1991-2011) 2015 .0032292 .0151794 -.2007937 .0469471

Province fixed effectsEastern Cape 2,015 0.0988 0.298 0 1Free State 2,015 0.106 0.308 0 1Gauteng 2,015 0.172 0.377 0 1KwaZulu-Natal 2,015 0.140 0.347 0 1Limpopo 2,015 0.0625 0.242 0 1Mpumalanga 2,015 0.0973 0.296 0 1North West 2,015 0.0759 0.265 0 1Northern Cape 2,015 0.0754 0.264 0 1Western Cape 2,015 0.172 0.378 0 1

35

Table 3 - continued

(1) (2) (3) (4) (5)VARIABLES N mean sd min maxControl variables (from 1991 census in logs)

Gender ratio 2,015 3.898 56.70 0.189 2,286Population group ratio 2,015 0.280 0.321 0 1Population density 2,015 4.490 2.740 -6.256 10.21Total population 2,015 8.218 1.280 0.693 10.65Black population 2,015 6.602 2.126 0 10.27Employed 2,015 7.182 1.399 0 9.970Unemployed 2,015 4.909 1.532 0 8.474Not economically active 2,015 7.598 1.377 0 10.09No schooling 2,015 6.778 1.270 0 9.627Some primary schooling 2,015 6.731 1.316 0 9.132Finished primary school 2,015 5.345 1.299 0 8.374Some secondary schooling 2,015 6.743 1.420 0 9.748Finished secondary school 2,015 5.890 1.679 0 9.666Higher education 2,015 3.401 1.953 0 8.767No income 2,015 7.549 1.369 0 10.15Income: R1-499 2,015 3.583 1.475 0 7.296Income: R500-699 2,015 3.197 1.367 0 6.649Income: R700-999 2,015 3.690 1.358 0 7.032Income: R1000-1499 2,015 4.511 1.371 0 7.412Income: R1500-1999 2,015 4.488 1.370 0 7.271Income: R2000-2999 2,015 5.083 1.438 0 7.731Income: R3k-4k 2,015 5.012 1.410 0 8.144Income: R5k-6k 2,015 4.612 1.399 0 8.054Income: R7k-9k 2,015 4.717 1.513 0 8.425Income: R10k-14k 2,015 4.817 1.593 0 9.123

Table 4: Linking estimated parameter to theoretical hypotheses

β ρ

Mean reversion β < 1 ρ < 0Path Dependence β = 1 ρ = 0Agglomeration β > 1 ρ > 0β is the parameter from equation (2)ρ = βt − βt−1 = ∆βt

36

Table 5: OLS and 2SLS baseline regressions

(1) (2) (3) (4)OLS 2SLS

Population growth Nonblack growth Population growth Nonblack growth

Panel A: Population growth rates (1991-1996)∆Black Population 1.232∗∗∗ 0.232∗∗∗ 1.171∗∗∗ 0.171

(0.0694) (0.0693) (0.233) (0.233)FS AP F-Stat - - 4.81 4.81

Panel B: Population growth rates (1991-2001)∆Black Population 0.836∗∗∗ -0.164∗∗∗ 1.237∗∗∗ 0.237∗

(0.0349) (0.0349) (0.109) (0.109)FS AP F-Stat - - 34.40 34.40

Panel C: Population growth rates (1991-2011)∆Black Population 0.837∗∗∗ -0.163∗∗∗ 1.159∗∗∗ 0.159

(0.0322) (0.0322) (0.0986) (0.0986)FS AP F-Stat - - 40.34 40.34

Province fixed effects Yes Yes Yes Yes

Controls Yes Yes Yes Yes

Observations 2015 2015 2015 2015

Notes. This Table displays estimates of equation (2) in the text. Each cell presents estimates from aseparate regression. The baseline sample consists of all wards inside South Africa for which 1991 data isavailable. The standard errors are clustered on the municipality level. There are 201 clusters. Columns (1)and (2) are estimated using OLS and columns (3)-(6) are estimated using 2SLS where the natural log ofdistance to the nearest homeland is used to instrument for absolute annualised black population growth inthe relevant time period divided by initial overall population. The outcome variable is absolute annualisedoverall or non-black population growth in the relevant time period divided by initial overall population.The relevant time periods are 1991-1996 in Panel A, 1991-2001 in Panel B and 1991-2011 in Panel C.Controls include variables on education, income, population group, population density and employment in1991. There are nine provinces for which fixed effects are included. The estimated coefficients for the firststage regressions are reported in the appendix. Coefficients that are significantly different from one atthe 90% level of confidence are marked with a *; at the 95% level, a **; and at the 99% level, a *** incolumns (1),(3),(5) and (6). In columns (2) and (4) they denote statistical significant departures fromzero. 95% confidence intervals are in brackets.

37

Table 6: 2SLS regressions using different sub-samples

(1) (2) (3) (4) (5) (6) (7)Dummy forJohannesburg Drop within 10 km Drop < 5% white Drop < 10% white Drop distance ≥ 6 District

fixed effectsMunicipalitylevel

Panel A: Population growth rates (1991-1996)∆Black Population 1.176∗∗∗ 1.113∗∗∗ 0.953∗ 0.953∗ 1.138∗∗∗ 0.903 0.948∗∗∗

(0.228) (0.190) (0.413) (0.439) (0.233) (0.599) (0.168)FS AP F-Stat 4.96 5.10 2.58 2.15 4.47 2.14 8.22

Panel B: Population growth rates (1991-2001)∆Black Population 1.236∗∗∗ 1.347∗∗∗ 1.276∗∗∗ 1.453∗∗∗ 1.147∗∗∗ 0.886∗∗∗ 1.082∗∗∗

(0.104) (0.181) (0.151) (0.187) (0.0974) (0.110) (0.216)FS AP F-Stat 38.09 16.37 31.10 21.01 34.77 37.72 13.46

Panel C: Population growth rates (1991-2011)∆Black Population 1.160∗∗∗ 1.300∗∗∗ 1.234∗∗∗ 1.385∗∗∗ 1.068∗∗∗ 0.835∗∗∗ 0.986∗∗∗

(0.0947) (0.160) (0.155) (0.205) (0.0935) (0.0930) (0.278)FS AP F-Stat 43.10 20.22 26.31 17.34 39.36 39.01 17.79

District fixed effects No No No No No Yes No

Province fixed effects Yes Yes Yes Yes Yes No Yes

Controls Yes Yes Yes Yes Yes Yes Yes

Observations 2015 1738 1340 1130 1661 2015 203

Notes. This Table displays estimates of equation (2) in the text for different sub-samples. Column headings denote sub-sample used in each specification.Each cell presents estimates from a separate regression. The standard errors are clustered on the municipality level. There are 201 clusters. All columns areestimated using 2SLS where the natural log of distance to the nearest homeland is used to instrument for absolute annualised black population growth in therelevant time period divided by initial overall population. The outcome variable is absolute annualised overall population growth in the relevant time perioddivided by initial overall population. The relevant time periods are 1991-1996 in Panel A, 1991-2001 in Panel B and 1991-2011 in Panel C. Controls includevariables on education, income, population group, population density and employment in 1991. There are nine provinces for which fixed effects are included.The estimated coefficients for the first stage regressions are reported in the appendix. Coefficients that are significantly different from one at the 90% level ofconfidence are marked with a *; at the 95% level, a **; and at the 99% level, a ***. 95% confidence intervals are in brackets.

38

Figure 4: Quantile regression results for the population growth rateNote: The values of the first two percentiles for 1996 were extremely high (8 and 2),probably due to weak IV issues, therefore we just but in 1 for both to make the picturereadable [Jan]

Notes. This Figure shows the results of an instrumental variable quantile regression following themethodology proposed by Lee (2007). The effect of predicted black population growth on overallpopulation growth (β) is displayed for different quantiles of the population growth distribution.

B Tables and figures for the actual appendix

Figure 5: The distribution of the excluded instrument

(a) Full sample (b) Without Cape Town

Notes. Histograms of log distance to the nearest homeland.

39

Table 7: 2SLS regressions with linear interaction term

(1) (2)With fixed effects Without fixed effects

Panel A: Population growth rates (1991-1996)∆Black Population 2.003 -5.439

(1.400) (11.28)

∆Black Population × -0.139 0.891log population density 1991 (0.205) (1.526)

FS AP F-Stat: ∆Black Population 0.06 0.03FS AP F-Stat: Interaction term 0.06 0.03

Panel B: Population growth rates (1991-2001)∆Black Population 0.969∗∗∗ 0.907∗∗∗

(0.127) (0.0937)

∆Black Population × 0.0923∗∗∗ 0.0814∗∗∗

log population density 1991 (0.0343) (0.0307)

FS AP F-Stat: ∆Black Population 52.94 102.02FS AP F-Stat: Interaction term 30.56 38.07

Panel C: Population growth rates (1991-2011)∆Black Population 0.911∗∗∗ 0.734∗∗∗

(0.132) (0.0937)

∆Black Population × 0.0687∗∗∗ 0.0555∗∗

log population density 1991 (0.0259) (0.0244)

FS AP F-Stat: ∆Black Population 42.97 89.20FS AP F-Stat: Interaction term 35.49 41.95

Province fixed effects Yes No

Controls Yes Yes

Observations 2015 2015

Notes. This Table displays estimates of equation (2) in the text withan additional interaction term. Each cell presents estimates from aseparate regression. All columns are estimated using 2SLS. Absoluteannualised black population growth divided by overall population andthe same term interacted with log population density in 1991 are theendogenous variables. Log distance to the nearest homeland and logdistance to the nearest homeland × log population density in 1991 areused as instruments for the endogenous variables. The outcome variableis absolute annualised overall population growth in the relevant timeperiod divided by initial overall population. The relevant time periodsare 1991-1996 in Panel A, 1991-2001 in Panel B and 1991-2011 in PanelC. The standard errors are clustered on the municipality level. There are201 clusters. Controls include variables on education, income, populationgroup, population density and employment in 1991. There are nineprovinces for which fixed effects are included. The estimated coefficientsfor the first stage regressions are reported in the appendix. Coefficientsthat are statistically significant at the 90% level of confidence are markedwith a *; at the 95% level, a **; and at the 99% level, a ***. 95%confidence intervals are in brackets.

40

Table 8: Separate baseline regressions for urban and rural sub-samples

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

Urbanareas

Ruralareas

Urbanareas

Panel A: Population growth rates (1991-1996)∆Black Population -1.870 1.404∗∗∗ 26.95 1.385∗∗∗

(6.613) (0.205) (138.2) (0.507)FS AP F-Stat 0.40 3.55 0.03 0.80

Panel B: Population growth rates (1991-2001)∆Black Population 0.951∗∗∗ 1.496∗∗∗ 0.828∗∗∗ 1.353∗∗∗

(0.108) (0.335) (0.111) (0.140)FS AP F-Stat 57.41 9.63 61.33 15.05

Panel C: Population growth rates (1991-2011)∆Black Population 0.835∗∗∗ 1.314∗∗∗ 0.607∗∗∗ 1.048∗∗∗

(0.118) (0.216) (0.119) (0.0937)FS AP F-Stat 26.64 13.45 50.66 27.84

Province fixed effects Yes Yes No No

Controls Yes Yes Yes Yes

Observations 884 1131 884 1131

Notes. This Table displays estimates of equation (2) in the text for different sub-samples. Rural areas are defined as areas with a log population density below fourin 1991. Urban areas are defined as areas with a log population density abovefour in 1991. Column headings denote sub-sample used in each specification.Each cell presents estimates from a separate regression. The standard errorsare clustered on the municipality level.All columns are estimated using 2SLSwhere the log of distance to the nearest homeland is used to instrument forabsolute annualised black population growth in the relevant time period dividedby initial overall population. The outcome variable is absolute annualisedoverall population growth in the relevant time period divided by initial overallpopulation. The relevant time periods are 1991-1996 in Panel A, 1991-2001 inPanel B and 1991-2011 in Panel C. Controls include variables on education,income, population group, population density and employment in 1991. Thereare nine provinces for which fixed effects are included. The estimated coefficientsfor the first stage regressions are reported in the appendix. Coefficients thatare significantly different from one at the 90% level of confidence are markedwith a *; at the 95% level, a **; and at the 99% level, a ***. 95% confidenceintervals are in brackets.

41

Table 9: Summary of first stage regressions for the baseline specificationswith different fixed effects

(1) (2) (3) (4)No FE Province FE District FE Municipality FE

Panel A: Population growth rates (1991-1996)log distance 0.0661 -1.015∗ -0.799 -0.517

(0.22) (-2.19) (-1.46) (-1.04)

Panel B: Population growth rates (1991-2001)log distance -0.00735∗∗∗ -0.00752∗∗∗ -0.00726∗∗∗ -0.00375∗

(-8.13) (-5.86) (-6.14) (-2.04)

Panel C: Population growth rates (1991-2011)log distance -0.00409∗∗∗ -0.00359∗∗∗ -0.00413∗∗∗ -0.00217∗

(-9.31) (-6.35) (-6.25) (-2.43)Level ofFixed effects

No Province District Municipality

Controls Yes Yes Yes Yes

Observations 2015 2015 2015 2015

Notes. This Table displays estimates of equation (1) in the main text. Col-umn headings denote different specification. Each cell presents estimatesfrom a separate regression. The standard errors are clustered on the munici-pality level. There are 201 clusters. All columns are estimated using OLSwhere the natural log of distance to the nearest homeland is the variableof interest. The outcome variable is absolute annualised black populationgrowth in the relevant time period divided by initial overall population.The relevant time periods are 1991-1996 in Panel A, 1991-2001 in Panel Band 1991-2011 in Panel C. Controls include variables on education, income,population group, population density and employment in 1991. There arenine provinces for which fixed effects are included. The estimated coefficientsfor the first stage regressions are reported in the appendix. Coefficientsthat are statistically significant at the 90% level of confidence are markedwith a *; at the 95% level, a **; and at the 99% level, a ***. t-statistics inparentheses.

42

Table 10: Summary of first stage regressions corresponding to Table 5

(1)Black population growth

Panel A: Population growth rates (1991-1996)log distance -1.015∗

(-2.19)

Panel B: Population growth rates (1991-2001)log distance -0.00752∗∗∗

(-5.86)

Panel C: Population growth rates (1991-2011)log distance -0.00359∗∗∗

(-6.35)

Fixed effects Yes

Controls Yes

Observations 2015

Notes. This Table displays estimates of equation (1) in the maintext. Each cell presents estimates from a separate regression. Thestandard errors are clustered on the municipality level. There are 201clusters. All columns are estimated using OLS where the natural logof distance to the nearest homeland is the variable of interest. Theoutcome variable is absolute annualised black population growth inthe relevant time period divided by initial overall population. Therelevant time periods are 1991-1996 in Panel A, 1991-2001 in Panel Band 1991-2011 in Panel C. Controls include variables on education,income, population group, population density and employment in1991. There are nine provinces for which fixed effects are included.The estimated coefficients for the first stage regressions are reportedin the appendix. Coefficients that are statistically significant at the90% level of confidence are marked with a *; at the 95% level, a **;and at the 99% level, a ***. t-statistics in parentheses.

43

Table 11: Summary of first stage regressions corresponding to Table 6

(1) (2) (3) (4) (5) (6) (7)Dummy forJohannesburg Drop within 10 km Drop < 5% white Drop < 10% white Drop distance ≥ 6 District

fixed effectsMunicipalitylevel

Panel A: Population growth rates (1991-1996)log distance -1.026∗ -1.119∗ -1.026 -1.124 -1.066∗ -0.799 -1.035

(-2.23) (-2.26) (-1.61) (-1.47) (-2.11) (-1.46) (-1.40)

Panel B: Population growth rates (1991-2001)log distance -0.00781∗∗∗ -0.00726∗∗∗ -0.00845∗∗∗ -0.00741∗∗∗ -0.00777∗∗∗ -0.00726∗∗∗ -0.00678∗∗

(-6.17) (-4.05) (-5.58) (-4.58) (-5.90) (-6.14) (-4.65)

Panel C: Population growth rates (1991-2011)log distance -0.00375∗∗∗ -0.00374∗∗∗ -0.00341∗∗∗ -0.00315∗∗∗ -0.00356∗∗∗ -0.00413∗∗∗ -0.00322∗∗∗

(-6.57) (-4.50) (-5.13) (-4.16) (-6.27) (-6.25) (-5.24)Level ofFixed effects

Province Province Province Province Province District Province

Controls Yes Yes Yes Yes Yes Yes Yes

Observations 2015 1738 1340 1130 1661 2015 201

Notes. This Table displays estimates of equation (1) in the main text. Column headings denote different specification. Each cell presents estimatesfrom a separate regression. The standard errors are clustered on the municipality level. There are 201 clusters. All columns are estimated using OLSwhere the natural log of distance to the nearest homeland is the variable of interest. The outcome variable is absolute annualised black populationgrowth in the relevant time period divided by initial overall population. The relevant time periods are 1991-1996 in Panel A, 1991-2001 in Panel Band 1991-2011 in Panel C. Controls include variables on education, income, population group, population density and employment in 1991. There arenine provinces for which fixed effects are included. The estimated coefficients for the first stage regressions are reported in the appendix. Coefficientsthat are statistically significant at the 90% level of confidence are marked with a *; at the 95% level, a **; and at the 99% level, a ***. t-statistics inparentheses.

44

Table 12: First stage regressions of specification with linear interactionterm corresponding to table 8

(1) (2) (3) (4)With province fixed effects Without fixed effects

∆Black pop growth∆Black pop growth× log populationdensity 1991

∆Black pop growth∆Black pop growth× log populationdensity 1991

Panel A: Population growth rates (1991-1996)log distance -2.363∗∗ -15.28∗∗ -0.930∗∗ -6.299∗∗

(-2.41) (-2.09) (-2.08) (-2.06)

log distance × logpopulation density 1991 0.288∗ 1.969∗ 0.216∗ 1.538∗

(1.91) (1.78) (1.66) (1.66)

Panel B: Population growth rates (1991-2001)log distance -0.0102∗∗∗ 0.0117 -0.0101∗∗∗ 0.0155∗∗

(-7.21) (1.43) (-10.36) (2.39)

log distance × logpopulation density 1991 0.000581∗∗ -0.00718∗∗∗ 0.000603∗∗∗ -0.00725∗∗∗

(2.55) (-5.14) (3.01) (-5.64)

Panel C: Population growth rates (1991-2011)log distance -0.00413∗∗∗ 0.00771∗ -0.00473∗∗∗ 0.00743∗∗

(-5.91) (1.92) (-8.41) (2.03)

log distance × logpopulation density 1991 0.000115 -0.00442∗∗∗ 0.000139 -0.00439∗∗∗

(1.01) (-5.74) (1.36) (-6.03)

Province fixed effects Yes Yes No No

Controls Yes Yes Yes Yes

Observations 2015 2015 2015 2015

Notes. This Table displays estimates of equation (1) in the main text. Column headings denotedifferent specification. Every two rows present estimates from a separate regression. The standarderrors are clustered on the municipality level. There are 201 clusters. All columns are estimatedusing OLS where the natural log of distance to the nearest homeland and the same term ×log population density in 1991 are the variables of interest. The outcome variable are absoluteannualised black population growth divided by initial overall population × log population densityin 1991 and absolute annualised black population growth divided by initial overall population in therelevant time period divided by initial overall population. The relevant time periods are 1991-1996in Panel A, 1991-2001 in Panel B and 1991-2011 in Panel C. Controls include variables on education,income, population group, population density and employment in 1991. There are nine provincesfor which fixed effects are included. The estimated coefficients for the first stage regressions arereported in the appendix. Coefficients that are statistically significant at the 90% level of confidenceare marked with a *; at the 95% level, a **; and at the 99% level, a ***. t-statistics in parentheses.

45

Table 13: First stage regressions for rural and urban sub-samples corre-sponding to Table 9

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

Urbanareas

Ruralareas

Urbanareas

Panel A: Population growth rates (1991-1996)log distance -0.199 -1.612∗ 0.0285 0.545

(-0.63) (-1.88) (0.17) (0.89)

Panel B: Population growth rates (1991-2001)log distance -0.0125∗∗∗ -0.00446∗∗∗ -0.00970∗∗∗ -0.00523∗∗∗

(-7.58) (-3.10) (-7.83) (-3.88)

Panel C: Population growth rates (1991-2011)log distance -0.00426∗∗∗ -0.00269∗∗∗ -0.00411∗∗∗ -0.00314∗∗∗

(-5.16) (-3.67) (-7.12) (-5.28)

Province fixed effects Yes Yes No No

Controls Yes Yes Yes Yes

Observations 738 989 738 989

Notes. This Table displays estimates of equation (1) in the main text. Columnheadings denote different specification. Rural areas are defined as areas witha log population density below four in 1991. Urban areas are defined as areaswith a log population density above four in 1991. Column headings denotesub-sample used in each specification. Each cell presents estimates from aseparate regression. The standard errors are clustered on the municipality level.There are 201 clusters. All columns are estimated using OLS where the naturallog of distance to the nearest homeland is the variable of interest. The outcomevariable is absolute annualised black population growth in the relevant timeperiod divided by initial overall population. The relevant time periods are1991-1996 in Panel A, 1991-2001 in Panel B and 1991-2011 in Panel C. Controlsinclude variables on education, income, population group, population densityand employment in 1991. There are nine provinces for which fixed effects areincluded. The estimated coefficients for the first stage regressions are reportedin the appendix. Coefficients that are significantly different from one at the90% level of confidence are marked with a *; at the 95% level, a **; and at the99% level, a ***.

46

Table 14: Sub-sample regressions for different definitions of rural and urban

Cutoff 3 Cutoff 3.5 Cutoff 4 Cutoff 4.5 Cutoff 5

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Rural Urban Rural Urban Rural Urban Rural Urban Rural Urban

Panel A: Population growth rates (1991-1996)∆Black Pop -181.5 1.389∗∗∗ -5.254 1.443∗∗∗ -1.870 1.404∗∗∗ 0.611 1.491∗∗∗ 1.187∗∗∗ 1.320∗∗∗

(5300.5) (0.197) (18.08) (0.219) (6.613) (0.205) (0.581) (0.277) (0.412) (0.169)FS AP F-Stat 0.00 4.45 0.16 3.93 0.40 3.55 2.44 2.02 4.78 1.64

Panel B: Population growth rates (1991-2001)∆Black Pop 0.858∗∗∗ 1.309∗∗∗ 0.868∗∗∗ 1.483∗∗∗ 0.951∗∗∗ 1.496∗∗∗ 1.057∗∗∗ 1.342∗∗∗ 1.137∗∗∗ 1.355∗∗∗

(0.136) (0.187) (0.111) (0.291) (0.108) (0.335) (0.121) (0.297) (0.119) (0.367)FS AP F-Stat 41.67 15.12 55.72 11.27 57.41 9.63 47.99 11.79 34.60 9.46

Panel C: Population growth rates (1991-2011)∆Black Pop 0.783∗∗∗ 1.150∗∗∗ 0.737∗∗∗ 1.327∗∗∗ 0.835∗∗∗ 1.314∗∗∗ 0.933∗∗∗ 1.289∗∗∗ 1.030∗∗∗ 1.304∗∗∗

(0.125) (0.135) (0.120) (0.210) (0.118) (0.216) (0.113) (0.238) (0.120) (0.276)FS AP F-Stat 23.19 19.72 25.40 15.52 26.64 13.45 25.41 13.59 21.12 12.66

Province FE Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Observations 692 1323 799 1216 884 1131 976 1039 1064 951

Notes. This Table displays estimates of equation (2) in the text for different sub-samples. Different values of logpopulation density in 1991 are used as cut-off between rural and urban areas. Column headings denote sub-sampleused in each specification. Each cell presents estimates from a separate regression. The standard errors areclustered on the municipality level. There are 201 clusters. All columns are estimated using 2SLS where the naturallog of distance to the nearest homeland is used to instrument for absolute annualised black population growthin the relevant time period divided by initial overall population. The outcome variable is absolute annualisedoverall population growth in the relevant time period divided by initial overall population. The relevant timeperiods are 1991-1996 in Panel A, 1991-2001 in Panel B and 1991-2011 in Panel C. Controls include variableson education, income, population group, population density and employment in 1991. There are nine provincesfor which fixed effects are included. The estimated coefficients for the first stage regressions are reported in theappendix. Coefficients that are significantly different from zero at the 90% level of confidence are marked with a *;at the 95% level, a **; and at the 99% level, a ***. 95% confidence intervals in brackets.

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