Policy Research Working Paper                       8764




Migration and Urbanization in Post-Apartheid
               South Africa
                              Jan David Bakker
                              Christopher Parsons
                               Ferdinand Rauch




Development Economics Vice Presidency
Strategy and Operations Team
March 2019
Policy Research Working Paper 8764


  Abstract
 Although Africa has experienced rapid urbanization in                              Drawing upon this exogenous variation, the authors study
 recent decades, we know little about the process of urban-                         the effect of migration on urbanization in South Africa.
 ization across the continent. The paper exploits a natural                         While they find that on average there is no endogenous
 experiment, the abolition of South African pass laws, to                           adjustment of population location to a positive popula-
 explore how exogenous population shocks affect the spatial                         tion shock, there is heterogeneity in these results. Cities
 distribution of economic activity. Under apartheid, black                          that start off larger do grow endogenously in the wake of
 South Africans were severely restricted in their choice of                         a migration shock, while rural areas that start off small do
 location and many were forced to live in homelands. Fol-                           not respond in the same way. This heterogeneity indicates
 lowing the abolition of apartheid they were free to migrate.                       that population shocks lead to an increase in urban relative
 Given a migration cost in distance, a town nearer to the                           to rural populations. Overall, the evidence suggests that
 homelands will receive a larger inflow of people than a more                       exogenous migration shocks can foster urbanization in the
 distant town following the removal of mobility restrictions.                       medium run.




 This paper is a product of the Strategy and Operations Team, Development Economics Vice Presidency. It is part of a
 larger effort by the World Bank to provide open access to its research and make a contribution to development policy
 discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/
 research. The authors may be contacted at ferdinand.rauch@economics.ox.ac.uk.




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                                                       Produced by the Research Support Team
       Migration and Urbanization in Post-Apartheid

                                       South Africa∗

         Jan David Bakker, Christopher Parsons, Ferdinand Rauch




JEL Codes: R12, R23, N97, O18

Keywords: Economic geography, migration, urbanization, natural experiment




   ∗
    Jan David Bakker is a Phd student at the University of Oxford (email:
jan.bakker@economics.ox.ac.uk), Christopher Parsons is Associate Professor at the University
of Western Australia (email: christopher.parsons@uwa.edu.au), Ferdinand Rauch (corresponding
author) is Associate Professor at the University of Oxford (email: ferdinand.rauch@economics.ox.ac.uk).
We gratefully acknowledge the support of the Africa Research Program on Spatial Development of
Cities at Oxford and the London School of Economics funded by the Multi Donor Trust Fund on
Sustainable urbanization of the World Bank and supported by the UK Department for International
Development. We thank Daniel de Kadt and Melissa Sands who shared census data from 1991.
We thank Frederic Giraut and Celine Vacchiani-Marcuzzo who shared the Dysturb dataset. We
are grateful to Matteo Escudé, James Fenske, Doug Gollin, Vernon Henderson, Leander Heldring,
Daniel Kaliski, Daniel de Kadt, Lu Liu, Chris Roth, Ludvig Sinander, Andrea Szabo, Tony Venables,
Helene Verhoef, Johannes Wohlfart and seminar participants at Oxford, the Economic Geography and
International Trade Research Meeting 2017 and the Annual Bank Conference on Africa 2016 for useful
comments and discussion.
1     Introduction


Africa is the least urbanized continent, but its urbanization rate is catching up. The

pace of urbanization is remarkable and the continent is due to overtake Asia as the

fastest urbanizing region of the world within a decade (United Nations, 2014). Managing

the challenges of this rapid transformation represents is a key policy challenge and yet

the evidence base, particularly in the case of Sub-Saharan Africa, remains limited. One

central question for policy makers is to what degree this process can be managed by

policy as opposed to being determined by fundamentals alone.


To illustrate this issue, consider a town experiencing an exogenous migration shock.

Theoretically it can evolve in just three ways. First, the town’s population could shrink

back to the initial population level, i.e. mean-revert. Such a reaction would be consistent

with an optimal urban network of relative city sizes, where relative sizes might be driven

by location fundamentals. Secondly, the town’s population could simply remain at the

new increased population level and not adjust endogenously to the shock. In this case,

the distribution of city sizes would be path dependent. Thirdly, the city could grow

further. This would be consistent with a theory of agglomeration eﬀects and multiple

equilibria, where an initial population shock moves the town onto a new population

trajectory growth path from one equilibrium to another. If city sizes behave according

to the ﬁrst scenario, policies to aﬀect the location of people would be ineﬀective, while

in the other two, policies that induce migration can in turn aﬀect urbanization.


In this paper, we study how cities in South Africa behave having been exposed to

exogenous population shocks following the abolition of apartheid. Under the apartheid



                                            2
regime, the black South African population was severely restricted in its mobility.

Large parts of the population were forced to live in so-called homelands and townships.

En-route to the democratic transition in 1994, these restrictions were lifted and in

June 1991 black South Africans could move freely. Substantial internal migration

ﬂows resulted, which led to increased urbanization during the 1990s and 2000s (see

Figure 1 below). We use the fact that the locations of the homelands resulted from a

long historical process beginning in the 18th century (Lapping, 1986), which makes it

plausible that, conditional on covariates, their location is quasi-random with respect

to economic conditions today. Assuming the subsequent migration outﬂows from the

homelands behave according to some migration cost in distance, we are able to exploit

the exogenous variation from this positive migration shock to identify the eﬀect of

increased internal migration on the distribution of population in South Africa. In

other words, assuming migration costs increase with distance, ceteris paribus, a town

physically located nearer to a homeland is assumed to have received a larger inﬂow of

previously mobility-restricted black migrants.1 Hence, while the homelands are crucial

to our empirical design, we do not study the development of population within the

homelands.


Our main ﬁndings are threefold. First, we show that the distance to homelands is a

strong predictor of black population growth in the years following the end of apartheid

(i.e. our “ﬁrst stage”). Second, we show that on average, an exogenous increase

in population in a town leads to an increase in population by just that amount, in

the medium to long run. This suggests that on average, the population distribution

follows a path dependent process. Third, we ﬁnd heterogeneous responses to exogenous
1
Even if the distance cost of migration are small, there would be a distance coeﬃcient if migrants
“radiate” from their origin (Rauch, 2016).


                                               3
population shocks across rural and urban areas. Population levels in areas with initially

high population densities experience further agglomeration, i.e. exogenous immigration

leads to population growth. Only in rural areas do we continue to ﬁnd path dependence.2

This suggests that a positive exogenous population shock generates a ‘Matthew eﬀect’

(‘those who have will be given’), as densely populated areas gain population relative to

sparsely populated areas. We further investigate this heterogeneity by examining how

the eﬀect varies with both initial population density and the reduced form magnitude

of the shock. For a given initial density, a larger shock leads to higher endogenous

population growth. This is consistent with the idea that a signiﬁcant shock is required

to push a locality from its current equilibrium onto a new trajectory. These results

imply that policies aiming to foster migration can further trigger urban agglomeration

forces in high density areas.


South Africa’s history lends itself to studying our research question and the country

maintains excellent census data, both before and after Apartheid. One important

limitation of the census data however, is that after apartheid many changes were

made to various geographical and other deﬁnitions, which limits the comparability of

our data before and after 1994, although the population data can be matched with

some conﬁdence on a level as ﬁne as wards. Another drawback of our data on the

regional level is that it does not identify internal migrants explicitly, so we have to infer

diﬀerences in migration as diﬀerences in population growth conditional on covariates

that account for diﬀerences in fertility and mortality. A third shortcoming is that

no reliable information for population in homelands is available. For our purposes,


2
    While standard models of trade and urbanization typically do not predict path dependence, recent
    studies that have found path-dependent behavior for small and medium sized towns include Bleakley
    and Lin (2012) and Michaels and Rauch (2018).


                                                   4
information from outside homelands is suﬃcient. Hence we are unable to pinpoint the

underlying micro-mechanisms driving our results.


The remainder of this paper is organized as follows. Section 2 details the historical

development of South Africa thereby providing evidence for the quasi-random location of

the homelands. Section 3 discusses the related literature and introduces the theoretical

thought experiment that serves as a framework for the empirical analysis presented in

Section 4. The heterogeneous responses to a positive population shock are discussed in

Section 5, and section 6 concludes.




2     Historical Background


Around two-thirds of South Africa’s total population live in urban areas, making it

one of the most urbanized countries in Africa. In the second half of the 20th century,

urbanization in South Africa was shaped by the apartheid policy of the National Party

government (1948-1994). Apartheid - literally meaning “apart-ness” - was by its very

nature a spatial concept (Christopher, 2001). The government aimed to completely

separate the black and non-black populations.3 Policies ranged from installing two

town hall bathrooms to segregating city quarters and creating native reserves, the

so-called homelands (or ‘bantustans’) that were to become independent states for the

black population.


Segregation and mobility restrictions imposed on the black population had a long

tradition in South Africa dating back to at least the 18th century (Lapping, 1986). The

3
 We use the same terminology for racial categories as the census, namely ‘Black’ or ‘African’, ‘Colored’,
‘Asian/Indian’, and ‘White’, where the last three categories make up to the ‘Non-black’ category.


                                                   5
support for apartheid policies in the run-up to the 1948 elections, especially among poor

white South Africans, resulted from the increasing black urbanization rate during the

preceding decades. These dynamics derived from the expansion of manufacturing and

labor shortages resulting from World War II (Ogura, 1996). It was generally believed

that the problem of white poverty was linked to increasing black urbanization. The

Native Economic Commission (1930-32) provides an example as it explicitly names

black urbanization as a cause for greater levels of unemployment among low-skilled

white people (Beinart, 2001, p.122). One of the main goals of the apartheid policies

was therefore to prevent and reverse black urbanization, or to put it in the words of the

Stallard 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, and

should depart therefrom when he ceases so to minister.’ (Feinstein, 2005, p.152). The

policies that took shape after 1948 were therefore unique in aiming to achieve complete

spatial and social segregation and were achieved by mobilizing signiﬁcant government

resources and displacing large numbers of black South Africans.


In order to control the movement of the black population, the government restricted

blacks’ rights to own land and their legal ability to settle where they wished. The

literature distinguishes two dimensions of separation, ‘urban apartheid’ and ‘grand

apartheid’ (Christopher, 2001). Urban apartheid aimed at creating separate quarters

for that part of the black population that was allowed to stay permanently in urban

areas. Grand apartheid rather aimed at moving the majority of the black population -

that was not needed as laborers in white urban areas - to native reserves.


The three main measures to implement ‘grand’ and ‘urban apartheid’ were the Group



                                           6
Areas 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 an

individual’s political and social rights. The Group Areas Act assigned a native reserve

to each black population group and enabled the government to remove people that were

not living in the area assigned to their population group. To control population ﬂows

and black urbanization in particular, the government relied on a pass system. The Pass

Laws Act forced every black African to carry an internal passport at all times.4 If a

black African could not present their passport demonstrating their right to be in a

particular region, they were subject to arrest.


These strictly enforced laws signiﬁcantly constrained the distribution of population in

space as well as the process of urbanization. According to the Surplus People Project

(1985),5 the South African government forcefully relocated at least 3.5 million people

between 1960 and 1983. Additionally, several hundred thousand arrests were made

every year under the pass laws (Beinart, 2001, p.158f). Table 1 displays the share

of the black population living in urban and rural areas within South Africa and the

homelands from 1950 to 1980. While the proportion living in urban areas in South

Africa stayed roughly constant over the three decades, the proportion living in rural

areas decreased by around 15%, while the homelands experienced a commensurate

increase. These movements resulted in densely populated areas in the homelands that

can be deﬁned as urban in terms of population densities, but not in terms of public

service delivery or industrial development. This ‘dislocated urbanization’ (Beinart,


4
   It built on pre-apartheid legislation including the Natives Urban Areas Act from 1923 and Natives
  Urban Areas Consolidation Act from 1945, which forced every black man in urban areas to carry
  passes at all times.
5
  The Surplus People Project was a non-governmental organization that documented forced removals
  through the apartheid government.


                                                 7
2001), driven by government decisions instead of economic fundamentals, provides

evidence of the substantial impact that the apartheid policies had on the distribution of

population. Overall, while apartheid policies failed to reverse the level of urbanization of

black South Africans, they were able to stop the trend towards increasing urbanization

driven by economic growth and instead channel urbanization dynamics away from

(white) cities and towards the homelands.


Table 1 shows the share of the population living in urban areas during apartheid

by population group. The three non-black population groups were already far more

urbanized in 1951 and by 1991 around 90% of the non-black population resided in

urban areas. The black population was predominantly living in rural areas in 1951

and urbanized until 1991, but remained signiﬁcantly less urbanized than the other

three population groups. As previously emphasized, this urbanization was heavily

inﬂuenced by government policies that kept the black population out of urban areas

in ‘white’ South Africa and engineered urbanization in the homelands. During the

1990s, urbanization rapidly increased (see Figure 1). Since the non-black population

was almost entirely urbanized in 1991, this is evidence of large domestic migration ﬂows

of the black population.


Given the historical context, two main concerns arise regarding the proposed research

design, which uses distance to the nearest homeland as an instrument for migration.

First, that the location of homelands is non-random and that these could have for

instance been located nearer to large industrial centers to serve as labor reservoirs.

Secondly, that the constraint on internal mobility was binding.


The homelands established under apartheid (see Figure 2) were conﬁned to areas


                                             8
designated as native reserves under the Native Land Act in 1913. This land comprised

7% of the overall area of South Africa and was already largely inhabited by the black

population at the time, as the government was unwilling to expropriate white farmers.

Hence the land allocation in 1913 failed to transfer large tracts of land between the

diﬀerent population groups and merely legally consolidated the distribution of land that

had emerged predominantly through the European conquest of African land (Neame,

1962, p.40f). Since land was largely conquered for agricultural purposes, the African

land reserves were of relatively low quality.


In 1913, South Africa was predominantly an agricultural economy with just two

important industries - gold mining around Johannesburg and diamond mining around

Kimberley. These industries established a system of migrant labor. Both found it

optimal to change their entire workforce on a regular basis - every three to six months

- and wanted workers’ families to remain in reserves. This allowed ﬁrms to pay low

wages since the workers’ families were supposed to ﬁnd alternative work in the reserves

(e.g. subsistence farming) which also reﬂected the (very low) opportunity cost of

the worker. Additionally, they were able to send sick or injured workers back to the

reserves where their tribe would take care of them (Lapping, 1986, p.26). This suggests

that there was no need for speciﬁcally located labor reservoirs when the homelands

where established. Therefore, no signiﬁcant economic considerations appeared to have

motivated the location of homelands, except for perhaps agricultural factors.


The 1936 Land Act and subsequent Government initiatives aimed at consolidating native

territories to make them viable as independent states. There were no attempts to relocate

them for economic reasons. One possible economic reason would be the proximity



                                            9
of cheap labor. Instead of relocating the homelands, the government created black

townships such as Soweto to serve as labor reservoirs. If a homeland was conveniently

located, many inhabitants commuted to work in white cities (KwaMashu and Umlazi

in the homeland KwaZulu provide an example). There were therefore no incentives to

relocate homelands as alternative ways to increase the pool of cheap labor proved more

convenient.


A second concern when analyzing the switch from the constrained equilibrium for the

black population under apartheid to the unconstrained equilibrium, is whether this

constraint was binding. There are several observations that suggest that the constraint

was indeed binding and that the switch to an unconstrained equilibrium was a signiﬁcant

shock to the distribution of population. First, the homelands were much poorer than

other parts of South Africa. In 1985, GDP per capita in the homelands varied between

600 and 150 Rands, an order of magnitude below the 7,500 Rand estimated for the rest

of South Africa (Christopher, 2001, p.93). Secondly, while more than 90% of whites

and Indians lived in urban areas in 1986, less than 60% of blacks did, and we observe

a large jump in urbanization starting in the 1990s. Thirdly, while keeping blacks out

of urban areas was one of the major goals of apartheid policy, the absolute level of

the black population in ‘white’ urban areas nevertheless increased. This suggests that

strong urban attraction pulled blacks into urban areas, while apartheid reduced the

rate of urbanization (Feinstein, 2005, p.157).




                                          10
3    Related Literature


This paper relates to a number of literatures, in particular to the increased interest

in cities and urban planning from the perspective of economic development. While

urbanization already plays a central role in many of the seminal contributions in the

early development economics literature (see for example Lewis (1954), Ranis and Fei

(1961), Harris and Todaro (1970)), there have been a number of recent empirical and

theoretical contributions studying the determinants of urbanization, as well as its eﬀect

on economic growth. Recent work by Henderson (2005) suggests that urban growth may

be a necessary condition for GDP growth. Potts (2012) and Gollin et al. (2016) draw

upon census data and economic theory to show the importance of natural resources

as a determinant of city sizes in Africa, and raise questions about diﬀerences between

urbanization in Africa and elsewhere.


We add to this literature by studying how the urban system in South Africa reacts to

an exogenous population shock. The main policy question we address here is the degree

to which population ﬂows within a country can be managed in the medium to long

run. To illustrate this policy question, consider a town of initial population N0 , in a

country with no population growth, that is given an exogenous population increase of ∆

to N0 + ∆ people. There are only three ways in which the population of this town can

respond in the long run. First, there could be mean reversion to the original relative

population level, such that the long run population is smaller than N0 + ∆. Secondly,

there could be a random walk process that generates path dependence, such that the

long run expected value of the size of the town is now N0 + ∆. Thirdly, it could be

that the additional population generates agglomeration eﬀects and triggers a process in


                                           11
which it gains a long run population greater than N0 + ∆.


These three possibilities can be captured in an economic model following Henderson

(1974), as demonstrated recently by Bleakley and Lin (2015). Let us consider a simple

version of these models here to illustrate the key point.


In this model, agents derive utility from locating in particular areas. In equilibrium,

there cannot be any gains from mobility, such that the utilities of all agents have to

be equal across locations. Utility stems from the diﬀerence between the agglomeration

(A(N )) and the congestion cost (C (N )) curves that are both functions of population

density (N ).6 Spatial utility in region i is deﬁned as: U (N i ) = A(N i ) − C (N i ). The

agglomeration curve summarizes the consumption gains from a greater number of

varieties as well as higher wages resulting from productivity gains due to agglomeration

eﬀects. The congestion cost curve is determined by rents and commuting costs. The

population allocation equilibrium is determined by the indiﬀerence condition that the

spatial utility from locating in a certain area has to be equalized across all K areas:

U (N 1 ) = ... = U (N K ). When assuming a particular functional form for one of the two

functions, we can infer characteristics of the shape of the other function from the three

hypotheses outlined above.


There are no intuitive guidelines as to the shape of the agglomeration curve as a function

of population density A(N ). The agglomeration function could be non-monotonic, as

new industries emerge to replace others when the population level crosses some threshold.

This could result in signiﬁcant changes in the structure of the local economy. For the

congestion cost curve C (N ) on the other hand, given ﬁnite space, it is plausible to

6
    In the context of this stylized model, we use changes in the population level and changes in population
    density interchangeably, since we consider a ﬁxed amount of space.


                                                     12
assume that it is increasing (C (N ) > 0) in population density, convex (C (N ) > 0)

and tending to inﬁnity after a certain population density threshold has been reached

        ¯ C (N ) = ∞). Given these assumptions on the congestion cost function,
(limN −→N

diﬀerent shapes for the agglomeration function follow from the three hypotheses outlined

above.


The deﬁnition of equilibrium implies that the utility across locations has to be equal

before the shock hits.7 Population movements reacting to the exogenous shock again

have to equalize the utility across locations to attain a new equilibrium. In the empirical

analysis, all areas are treated by a population shock with varying intensities that depend

upon their geographical proximity to the homelands. The utility level in the initial

equilibrium is denoted by U (N0 ). U (NS ) is the utility level after the shock and U (N1 )

is the utility level of the new equilibrium after agents have adjusted their location

decisions. By the deﬁnition of equilibrium, U (N0 ) and U (N1 ) have to be equal across

all locations (treated and control), while U (NS ) is not related to an equilibrium and

can therefore vary across locations.


The population level mean reverts (Panel A in Figure 3)8 if the utility at the new

population level U (NS ) is below the utility in the initial equilibrium U (N0 ) that can be

attained in the untreated areas. Agents move from treated areas to the control areas until

                                                               T         C
the utilities are equalized across both types of locations U (N1 ) = U (N1 ). This leads to

a reduction of population below NS . This implies that the slope of the agglomeration

function has to be locally shallower than the slope of the congestion cost function. The
7
  We are implicitly assuming that ‘white’ South Africa was in spatial equilibrium before the positive
  population shock. However, this is obviously not the case given ‘urban apartheid’ and the movement
  restrictions imposed on the non-white population within South Africa. Since these restrictions were
  in place in all of ‘white’ South Africa they are orthogonal to the population treatment and so we
  abstract from them in the model for simplicity.
8
  Note that the graphs only display the evolution of population in treated areas.


                                                 13
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 initial equilibrium U (N0 ) = U (NS ).

This implies that there are no gains from moving between control and treatment areas

and that therefore there is no endogenous adjustment of location decisions, such that

the new population level is an equilibrium population level: NS = N1 . Since the

diﬀerence between the agglomeration and congestion functions at N0 is equal to the

diﬀerence at NS , the slopes of the two functions between N0 and NS have to be equal.

If this property holds globally, then there are inﬁnitely many equilibria of the spatial

distribution of population. In the case of agglomeration (Panel C), agents move from

control areas to treated areas. This implies that gains from migration exist, such that

the utility level after the shock has to be greater than the utility in the initial equilibrium:

U (N0 ) < U (NS ). Utility could not be strictly increasing in population between N0 and

NS however, because that would imply the existence of gains from migration at N0 .

The existence of such gains would contradict the deﬁnition of an equilibrium, such that

N0 could not be an equilibrium. For N0 to be an equilibrium therefore, utility has to be

non-monotonic, implying the existence of multiple equilibria for the spatial distribution

of population. In order for the utility function to be non-monotonic, the slope of the

agglomeration function has to be non-monotonic.9 This model demonstrates the three

possible cases between which we aim to distinguish in this paper. Since the local slope

of agglomeration and congestion function determine which case applies, the model also

suggests that the reaction might be diﬀerent at towns of diﬀerent initial population

densities and motivates us to study heterogeneity along this dimension. It is clear that

understanding the slope of these curves is of central importance to policy makers trying
9
    Note that the functional form displayed in Panel C is just one example of a broad class of possible
    agglomeration functions. In particular, it is not necessary for the slope of A(N ) to be locally negative
    for the existence of multiple equilibria.


                                                      14
to adjust the size of cities and towns.


This setup relates to a large empirical literature that studies how exogenous shocks to

cities aﬀects the long-run development of aﬀected areas. Studying the population of

Japan, Davis and Weinstein (2002) ﬁnd that population tends to mean-revert after a

shock thereby concluding that location fundamentals play an important role. Studies

by Brakman et al. (2004) for post-war Germany and by Miguel and Roland (2011)

for Vietnam arrive at similar results using destruction resulting from wars. Bleakley

and Lin (2012) analyse path dependence by studying the development of towns that

experienced a negative shock to their fundamentals. Their main result is that former

portage cities maintained their historical importance, a ﬁnding consistent with recent

results from local positive population shocks from German refugees after World War

II that were highly persistent and could not be explained by location fundamentals

(Schumann, 2014). Using the same natural experiment, Peters (2017) shows that income

per capita, overall manufacturing employment and the entry of new plants are positively

correlated with refugee inﬂows in Germany after World War II.


We contribute to this literature in several ways. First, our study is the ﬁrst to analyze a

large scale and indeed positive population shock. The aforementioned studies analyzing

the eﬀects of war, ﬁnd evidence of path-dependence but cannot isolate whether this is

driven by natural fundamentals, sunk investments, social networks, capital unaﬀected

by shocks, or gains from agglomerations. Bleakley and Lin (2012) provide evidence that

it is not driven by location fundamentals, but cannot distinguish between other factors.

Since we analyze a positive population shock in which incoming migrants have neither

social networks nor private sunk investments, we are able to isolate the eﬀect of gains



                                            15
from agglomeration. Second, we provide evidence from a credible natural experiment

that is well-identiﬁed and are able to draw upon a much larger sample in comparison

with most studies in this literature. Third, we are the ﬁrst to provide evidence from

Africa, a region that is amongst the most rapidly urbanizing regions in the world, the

continent in which such policies related questions matter most. Fourth, many of the

previous studies focus solely upon urban areas, whereas we are able to look at both

rural and urban areas and the diﬀerences between the two.


There are other studies that exploit the exogenous variation resulting from apartheid

policies to study the development of South Africa after 1994, see for example de Kadt

and Sands (2016), de Kadt and Larreguy (2018) and Dinkelman (2011, 2017). We

are the ﬁrst to use this natural experiment to study the causal economic eﬀect of

internal migration and how it eﬀects the distribution of population across space. This

paper, thereby, adds quasi-experimental evidence to the literatures that examine the

determinants of the uneven distribution of population across space and the relationship

between city size and population growth (e.g. Black and Henderson (2003), Eeckhout

(2004), Duranton (2007), Rauch (2013) and Rossi-Hansberg and Wright (2007)). 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 (often referred

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 growth

rates (Gibrat’s Law), an extensive empirical literature on the distribution of population

has developed. The majority of empirical studies ﬁnd urban systems tend to obey

Gibrat’s Law and that city size is uncorrelated with population growth, while others ﬁnd

departures from Gibrat’s Law even for cities (Soo (2007), González-Val et al. (2013), and


                                           16
Holmes and Lee (2010)). Michaels et al. (2012) emphasize the importance of structural

transformation for urbanization. In their long-run study of population growth in the

United States from 1880 to 2000, they ﬁnd that areas with high initial population

density obeyed Gibrat’s Law, i.e. subsequent population growth was uncorrelated with

initial population density. Our research contributes to this literature by demonstrating

the heterogeneous reaction of towns of diﬀerent size to a population shock.




4    Empirical Analysis


Data


In order to empirically test the three hypotheses, we make use of a unique geographically

referenced South African census dataset. It contains observations for the years 1991,

1996, 2001 and 2011 at the ward level and hence bridges across the democratic transition

in 1994. This dataset consists of two parts. First, it contains publicly available census

data aggregated to the ward level for the censuses in 1996, 2001 and 2011 provided by

Statistics South Africa. This allows us to distinguish between the short-, medium- and

long-run eﬀects of the exogenous population shock. Secondly, it contains data from

the last census under the apartheid government in 1991. De Kadt and Sands (2016)

matched a partial enumerator area map from the census in 1991 with the 100% sample

of the individual level census data made available by DataFirst 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 Native Land Act, the Population Registration

Act and the Group Areas Act were repealed in June 1991.


                                           17
While the Pass Laws Act had already been repealed in 1986 and although identiﬁcation

would be cleaner if data from before 1986 were available, this timeline does not pose a

major threat to our identiﬁcation strategy. This is because the Group Areas Act and

the Population Registration Act were still in place, and as such the black population

was still severely constrained in its choice of residence until June 1991.10




Identiﬁcation


Distance to the nearest homeland is used as an instrument for migration ﬂows in order

to causally identify the eﬀect of migration on population distribution. Figure 4 shows

that the relationship between this distance and population growth between 1991 and

2011 is strongly negative, both at short and longer distances. In this ﬁgure we pool

neighboring observations into discrete bins to improve clarity. We specify 100 bins in

total, which puts around 20 observations into each bin. The log linear speciﬁcation

seems a good ﬁt for the data. The validity of the instrument relies on the conditional

quasi-random allocation of homelands, which has been argued for in Section 2. The

assumption may be violated for areas adjacent to the homelands however, as they are

likely to be aﬀected by economic spillovers from the neighboring homeland in a variety

of ways that are not 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

10
     The data from 1991 does not cover the entirety of South Africa. One general drawback of the dataset
     is that it does not cover the homelands. This does not aﬀect the analysis since we only look at
     areas outside the homelands. Another more relevant drawback is that there are a few areas that are
     not covered within South Africa (see Figure 7 in appendix B). This is due to two reasons. First,
     Statistics South Africa only has a partial map of the census enumeration areas in 1991. Therefore,
     part of the census data cannot be geographically referenced. Secondly, due to violent turmoil at the
     time, some areas could not be visited by enumerators and no data are available on a granular level.
     This is potentially beneﬁcial for our analysis since we exclude areas with high racial tension, which
     could otherwise bias our results. So, while this reduces the number of observations and therefore the
     statistical power in the empirical analysis, our parameter estimates will remain consistent.


                                                    18
check to ensure that the estimates are not driven by local economic spillovers.


For our instrument to be informative, the cost of migration has to increases substantially

with distance, which would imply that a town located nearer to the homelands ceteris

paribus receives more migrants than a town further away. This assumption, consistent

with the gravity framework, is a common assumption in the migration literature and the

informativeness can be tested empirically by looking at the partial correlation between

the instrument and the endogenous variable.11 The informativeness of distance as an

instrument crucially depends upon the level of ﬁxed eﬀects chosen, which aﬀects the

variation in the data. As shown in Table 9 in appendix B, the informativeness of the

instrument decreases almost monotonically in the granularity of the ﬁxed eﬀects.12

A trade-oﬀ therefore exists between accounting for local unobservables and retaining

suﬃcient identifying variation, in order to ensure that our instrument remains informa-

tive. We include province level ﬁxed eﬀects in order to account for diﬀerent trends and

policies across provinces while allowing for suﬃcient spatial variation.13




Estimation


To estimate the causal eﬀect of migration on the distribution of population, the following

system is estimated using two-stage least squares (2SLS):




11
   For example, Peri (2012) uses distance to the Mexican border as an instrument for the intensity of
   migration to diﬀerent US states.
12
   This is intuitive, since for example when using municipality level ﬁxed eﬀects, the identifying variation
   of the instruments explains in which part of Johannesburg migrants are going to settle. This is likely
   to be uncorrelated with distance to homelands especially for urban areas.
13
   Provinces are equivalent to states in the US.


                                                    19
                   B
                 ∆Ni,t −1991 = α2 + log (distancei )π + Xi,1991 γ2 + δp + υm                      (1)

                                     B
                 ∆Ni,t−1991 = α1 + ∆Ni,t −1991 β + Xi,1991 γ1 + δp +         m                    (2)




where ∆Ni,t−1991 denotes overall population growth in ward i between 1991 and t and

  B                                         14
∆Ni,t −1991 denotes black population growth.   Our controls include: population groups,

population density, education, the gender ratio, employment and income (Xi,1991 ) and

province-level ﬁxed eﬀects (δp ) (see Table 2). The errors are clustered at the municipality

level.15 The ward level is the lowest geographical level that can be tracked consistently

over time and municipalities are the lowest level of local government. Distance is deﬁned

as the distance to the nearest homeland measured from centroid to centroid. Since no

measure of domestic migration is available in the census data, black population growth

conditional on ﬁxed eﬀects and covariates is used as a proxy for black migration.16 A

dummy variable for Cape Town is also included as the municipality is a special case in

terms of location, politics and demographics and hence migration patterns. The Western

Cape was the only province where the African National Congress did not come ﬁrst in

the general elections in 1994. Until today, it has not achieved the political dominance in

the province or the municipality of Cape Town that it has in the rest of the country. In

terms of demographics, there is a much higher white and especially colored population

in Cape Town, more than anywhere else in the country. Most importantly, there is a


14     B
   ∆Ni,t −1991 is deﬁned as absolute growth of the black population from 1991 to year t divided by the
   overall population in t, where t corresponds to 1996, 2001 or 2011. ∆Ni,t−1991 is deﬁned similarly
   using overall instead of black absolute population growth.
15
   Using Conley (1999) standard errors to account for spatial correlation yields similar results.
16
   As has been used previously as a proxy for migration status, see for example Czaika and Kis-Katos
  (2009).


                                                 20
lot of circular migration from the Eastern and the Northern Capes into Cape Town.

These migration dynamics potentially distort our identiﬁcation strategy such that we

include a dummy for Cape Town, which signiﬁcantly increases the predictive power of

our instrument. The results are robust to not including a dummy for Cape Town.




Linking theory and the variable of interest in the empirical

estimation


In order to test the three competing hypotheses outlined in Section 3, it proves crucial

to link the predictions from the hypotheses to the parameter of interest β . If the

underlying process was driven by mean reversion, then the eﬀect of the exogenous

population shock as measured by β would be less than one and decreasing over time,

as the shock dissipates through the urban system. In the case of path dependence, β

would be expected to be equal to one in all periods. In the agglomeration scenario, β

would be signiﬁcantly greater than one.


In order to assign these theoretical interpretations to the estimated parameters, we

have to avoid using percentage growth rates in the endogenous variable and in the

dependent variables in the second stage. Using percentage growth would make the

shock a function of the share of black population that already lives in the area, which

makes the interpretation we are looking for impossible. Therefore we instead deﬁne

our variables of interest as absolute growth rates relative to the overall population in

period t where t corresponds to 1996, 2001 and 2011. We incorporate this normalizing

factor since the size of the population shock should be measured relative to the overall

population rather than in absolute terms to get a good understanding of its impact.

                                          21
Pre-trends


Given the empirical setting of this exercise we expect the population growth eﬀects

to take place after 1994, but not before. A natural test is to see if indeed population

growth is independent of the distance to homelands before 1994. Our dataset does

not cover any year other than 1991 in the period pre-1994, and so we can’t use it for

this purpose. Instead we use the Dysturb dataset (Giraut and Vacchiani-Marcuzzo,

2013), a dataset that maps population in comparable units over time in South Africa.

Dysturb provides data at two diﬀerent levels of aggregation, ‘urban agglomeration’

(UA) and ‘magisterial district’ (MD). We use the UA dataset because unlike the MD

the units used here are deﬁned consistently over time. In Table 3 we regress population

growth on the distance to homelands variable. In columns 4, 5 and 6 we control for

initial population, in the ﬁrst three columns we do not. In columns 1 and 4 we use all

units with non-missing data in 1980 and 1991. In columns 2 and 5 we use all units

with non-missing data in 1991 and 2001. In columns 3 and 6 we use all units with

non-missing data in 1980, 1991 and 2001 to make sure the diﬀerence in coeﬃcients

between columns is not driven by sample selection. The table shows that we ﬁnd the

expected negative correlation between distance to the homeland and population growth

for 1991-2001, but not for 1980-1991.




                                          22
5     Results


Baseline results


Table 4 summarizes the main results and Table 5 provides further results from diﬀerent

sub-samples as robustness checks. Each cell of the tables summarizes one regression.17

Before moving on to interpreting the estimated coeﬃcients of interest, we will discuss a

number of results. The Angrist and Pischke (2009) F-statistic of the ﬁrst stage is well

above the rule of thumb threshold of 10 for all speciﬁcations for the medium and long

horizon.18 Weak instrument problems only arise for the short period between 1991-1996

and we will not discuss these parameter estimates. The increased explanatory power

over the longer time horizons is consistent with the fact that migration decisions only

adjust intermittently to a change in policy, such as the end of apartheid.


In the OLS regression (Table 4, Column 1), we cannot reject the null hypothesis

that the coeﬃcient is diﬀerent from one in the short-run (1991-1996). For the two

subsequent periods on the other hand, the coeﬃcient estimates are well below one.

This suggests that black population growth occurred in areas with low population

growth of the incumbent population and vice versa, since if there was no reaction by the

incumbent population an increase in population by one would lead to a coeﬃcient of

one mechanically. These results should not be assigned a causal interpretation however,

since the result could be driven by unobserved shocks that induce black in-migration

and white out-migration or vice versa jointly. The baseline results from the two-stage
17
   I.e. each cell in the ﬁrst row of Table 4 summarizes the causal partial eﬀect of exogenous migration
   of black population between 1991 and 1996 on the overall population growth rate between 1991 and
   1996.
18
   The corresponding ﬁrst stage regressions for Tables 4 and 5 as well as the other main tables shown
   here are reported in the online appendix.


                                                  23
least squares estimation suggest that the coeﬃcient is not diﬀerent from one at any

horizon such that there is no causal eﬀect from exogenous black migration on aggregate

migration decisions of non-black incumbents. This is evidence that an exogenous

population shock is absorbed without an endogenous reaction of the population level.

The results suggest that the eﬀect of an exogenous population shock on the aggregate

long-run equilibrium of the population distribution is consistent with the theoretical

notion of path-dependence (Hypothesis 2). We note that coeﬃcients estimated for

1991-2001 and 1991-2011 are not statistically diﬀerent from one another, which could

suggest that the migration transition period had converged to a new steady state not

long after 2001.


In addition to the baseline regressions, we report several regressions based on diﬀerent

sub-samples as robustness checks (Table 5). We include a dummy for Johannesburg in

Column 1 as the largest metropolitan area and industrial center to ensure that it is not

driving the results. In Column 2 we remove the dummy variable for Cape Town that

we usually include, which does not signiﬁcantly aﬀect results. In Column 3 we include

separate ﬁxed eﬀects for all the metropolitan areas in our sample, which again does not

seem to change our results signiﬁcantly. As outlined above, we exclude areas close to the

homelands, since for these localities, distance to the nearest homeland could aﬀect them

not only through migration, but also through local economic spillovers (Column 4). We

also exclude areas with a low white population share in 1991 because the migration

restrictions under apartheid might have been less binding for these areas (Columns 5

and 6). As a further robustness check, we exclude the areas in the upper tail of the

distance distribution in Column 7 to ensure that the high number of observations in

the upper tail of the distance distribution does not skew the results. In Column 8 we


                                           24
report results using district instead of province ﬁxed eﬀects. We also aggregate wards

up to the municipality level and run a separate regression to test whether the results are

robust to using a diﬀerent level of aggregation (Column 9). These robustness tests using

diﬀerent sub-samples as reported in Table 5 corroborate our baseline ﬁndings since

none of the coeﬃcients signiﬁcantly deviates from one. When comparing the timing of

the eﬀect, both the coeﬃcients and statistical power seem fairly similar for the periods

1991-2001 and 1991-2011. The short run result for 1991-1996 is weaker, both in the

ﬁrst stage statistical power and in the magnitude of the second stage result. This might

suggest that the migration took longer than the ﬁrst year after apartheid to converge,

while the new equilibrium was largely reached by 2001, and so did not change to 2011.


One concern is that fertility or mortality diﬀerences may inﬂuence these results. To

investigate these concerns we repeat the entire exercise from in Table 5 for people of

working age population only. These results are in Table 6. Here we deﬁne working age

as the population that is aged between 15 and 64. All coeﬃcients are similar to their

counterpart in Table 5.


In our main regressions we measure population growth on the right hand side in the

same time period as on the left hand side. This may be measured with noise if the

incumbent population only reacts to the population shock with a lag as opposed to

instantaneously. In order to make sure that these potential dynamics do not distort our

results, we test for them in an alternative speciﬁcation. Table 7 reports the result of a

speciﬁcation where we run the ﬁrst stage for black population growth for the period

1991 to 2001 and the second stage for overall population growth for the period 2001

to 2011. Intuitively, this regression picks up whether an exogenous population shock



                                           25
during the period 1991 to 2001 aﬀects overall population growth in the subsequent

period. In this speciﬁcation a coeﬃcient equal to 0 indicates path dependence while a

coeﬃcient smaller or larger than 0 indicates mean reversion or multiple equilibria. The

fact that none of the coeﬃcients in Table 7 is signiﬁcantly diﬀerent from 0 indicates

that the dynamic response is also consistent with path dependence.


Overall, the empirical results provide strong evidence for path dependence (Hypothesis

2). These results suggest that, in the aggregate, there is no evidence for multiple

equilibria and a non-monotonic agglomeration curve or mean-reverting behavior. The

evidence in favor of path-dependence is consistent with an agglomeration function that

has the same slope as the congestion function or high costs of migration as found by

Imbert and Papp (forth) for temporary labor migration in India. This corroborates the

dynamics found by Bleakley and Lin (2012) for fall line cities in the US and Michaels

and Rauch (2018) for Roman cities in France and Britain.




Heterogeneity


This Section discusses how the causal eﬀect of migration on population growth varies

across two dimensions, the initial population density or level of urbanization of an area,

and the size of the exogenous population shock.


First, we are interested in how the causal eﬀect varies with initial population densities.

In this case, theory does not provide clear guidance. Due to the convexity of the cost

curve, the causal eﬀect of migration could be decreasing in initial population density

because the additional costs generated by new migrants reduce the utility level of



                                           26
incumbents. At the same time, Michaels et al. (2012) show that long-run population

growth in the US is smaller for low initial population densities and increases with

population density after a cut-oﬀ of 7 people per km2 . Such a result would be consistent

with an agglomeration curve that is much steeper in urban than in rural areas. This

could suggest that in densely populated areas, exogenous migration leads to a larger

increase in population than in less densely populated areas.


In order to estimate how the eﬀect of a positive population shock varies across initial

population densities, we deﬁne dummy variables for high initial population densities

and for high initial shares of urbanized households. The results reported in Table 8

show that there is a positive and signiﬁcant interaction between high initial densities

and population shocks. This suggests that areas with high initial densities experience a

signiﬁcant endogenous inﬂow of population as a reaction to the exogenous population

shock while others do not. This eﬀect exists in the medium and long-run but is

economically stronger in the medium run for population density. It looses signiﬁcance

in the long-run for the share of urbanized households. The results of both speciﬁcations

indicate that the population dynamics induced by a positive population shock diﬀer

between less densely populated rural areas and highly populated urban areas. While we

cannot reject path dependence for rural areas, there is a signiﬁcant and positive eﬀect

in urban areas suggesting that an exogenous population shock leads to endogenous

immigration. This is suggestive evidence for the existence of multiple equilibria within

urban areas.


We show the eﬀects graphically in Figure 5, which corresponds closely to Panel C in

Table 8. We aggregate observations into bins to increase clarity, we specify 100 bins



                                           27
in total for each of the two plots. While low density places show no reaction to the

migration shock, and so follow path-dependence, in high density places we see evidence

of agglomeration economies: Inﬂows of people lead to the rest of the population to

positively react.


We next consider the size of the population shock as an additional dimension of

heterogeneity. So we estimate how overall population growth varies with the size of the

shock and initial population density. In order to do so, we combine the deciles of the

two distributions and estimate 100 distinct conditional means:




                10   10
   ∆Ni,2011 =              βj,k 1[if P opdeni,1991 in decile j ] × 1[if distancei in decile k ]
                j =1 k=1


                + γ Xi,1991 + δp +       m                                                        (3)




The βj,k s are the coeﬃcients of interest and estimate how conditional population growth

varies by the deciles of the initial population density distribution and the size of the

shock distribution. The size of the shock is measured using the reduced form, i.e.

distance to the nearest homeland. While the estimates do not provide the same clear

cut causal evidence as the two stage least squares approach they are indicative as to how

the eﬀect of the exogenous population shock varies with the size of the shock and the

initial density. The results displayed in Figure 6 suggest that for a given initial density

an increase in the size of a shock results in a higher population growth rate. This is in

line with the idea that it requires a substantial shock to switch between equilibria.


The fact that the population of more densely populated areas increases relative to less

                                                  28
densely populated areas could be interpreted as a ‘Matthew eﬀect’19 of an exogenous

population shock, where areas rich in population gain over-proportionally from a positive

population shock.


In the context of the modiﬁed Henderson model presented in Section 3, this result

suggests that the shape of the agglomeration function is diﬀerent between urban and

rural areas for the relevant population levels. In rural areas, the gains from agglomeration

are below the increased congestion cost if the population increases exogenously. In

urban areas, the gains from an increase in population seem to be equal to the additional

costs. The gains from agglomeration therefore seem to be much larger in urban areas

than in less densely populated rural areas.


While the simple model easily accommodates this heterogeneity in the agglomeration

and congestion cost curves across diﬀerent initial population densities, it remains silent

on its origin. There a number of ways this heterogeneity can be microfounded. Such an

agglomeration function emerges naturally in a two-sector economic geography model

or labor market models that distinguish high- and low-skilled workers with diﬀerent

production technologies in urban and rural labor markets. Consider a simple economic

geography model where the agricultural sector produces food using a ﬁxed endowment

of land and labor under a technology with decreasing returns to labor. The industrial

sector, consisting of manufacturing and services, produces consumption goods using

capital and labor with external agglomeration economies. Labor is perfectly mobile

across sectors and locations. Areas with low population densities are predominantly

agricultural, while urban areas are predominantly industrial. If an exogenous population


19
     ‘For unto every one that hath shall be given, and he shall have abundance: but from him that hath
     not shall be taken even that which he hath.’ Matthew 25:29, (American Bible Society, 1999).


                                                   29
shock hits both urban and rural areas, the marginal product of labor decreases in rural

areas and generates displacement eﬀects because the real wage decreases. This dynamic

arises naturally from the assumption that there is only a ﬁxed amount of land available

for agricultural production. In urban areas, an increase in the labor force generates

higher investment in capital (assuming a constant real interest rate set in world markets).

Therefore, the marginal product of labor does not fall and might even increase due to

external economies of scale. This generates agglomeration eﬀects or a path-dependent

evolution 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-skilled

labor used in production in urban areas. The production in rural areas only uses low-

skilled labor and the ﬁxed amount of land as inputs with the same technology as above.

In urban areas, low- and high-skilled labor are used as complements in production

with a constant returns to scale technology. In this framework, the population shock

we analyze in the data is best approximated by an increase of unskilled labor, since

the apartheid government only provided a bare minimum of schooling to the black

population (Feinstein, 2005, p.159f). In the model, an increase in unskilled labor

increases the wage for high-skilled labor and the rents for capital. If the supply of

capital is elastic, this leads to an increase in capital and an inﬂow of skilled workers

such that all factor prices return to their initial equilibrium values. Therefore, an

exogenous increase in the number of unskilled workers attracts skilled workers such

that the population level of urban areas experiences agglomeration and a shift towards

a new equilibrium.




                                            30
6     Conclusion


We study the eﬀect of an exogenous migration shock generated by the abolition of

migration restrictions for the black population on the distribution of population in South

Africa. There are three ways in which an area can react to an exogenous population

shock that arise from diﬀerent theories describing the distribution of population in

space. The population level of an area could mean revert towards its initial level, it

could remain at the new population level (path dependence) or it could grow further,

i.e. agglomerating population, suggesting the existence of multiple equilibria. The

empirical results presented in this paper suggest that in the aggregate, the reaction of the

population level to an exogenous population shock is consistent with path dependence.

This potentially has important policy implications. If the population level of a region is

path dependent, a temporary policy measure that induces migration can permanently

change the distribution of population.


Additionally, we ﬁnd that the reaction of an area to an exogenous population shock

varies with the initial population density. In rural areas with low initial population

densities, the eﬀect of an exogenous population shock is signiﬁcantly smaller than

in urban areas with high population densities. In urban areas, the dynamics of the

population level are consistent with agglomeration. We provide evidence that for a

given initial population density a larger exogenous population shock leads to more

endogenous immigration. In the context of the modiﬁed Henderson model, this result

shows that the agglomeration curve in rural areas is much more concave than in urban

areas and it also suggests that it’s slope is non-monotonic. These results are consistent

with a simple economic geography model in which production in rural areas features


                                            31
decreasing returns to labor due to a ﬁxed endowment of land usable for agricultural

purposes. A steeper agglomeration function in urban areas also emerges in a standard

model from the migration literature that features complementarities between low- and

high-skilled labor in urban, but not in rural areas. If an exogenous population shock

hits both rural and urban areas, these diﬀering dynamics increase the share of the

population living in cities.




                                         32
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                                         37
A      Tables and ﬁgures


A.1      Figures

Figure 1: Urban share of the national population (percent), 1911-2001




                   Source : Authors’ own work based on data from Turok (2012).
      Note : Vertical dashed lines mark the apartheid regime of the National Party (1948-1991)




                                                38
      Figure 2: Homelands (Bantustans) established under apartheid




Source : Authors’ own work. Bantustan boundary data from the Directorate: Public State Land
Support via Africa Open Data




                                            39
Figure 3: Modified Henderson model with gains from agglomeration and
congestion costs
         (a) Mean reversion                                 (b) Path dependence




                    (c) Agglomeration and multiple equilibria




                              Source : Authors’ own work.




                                          40
                                     Figure 4: First stage




Note : Relationship between distance to the homelands and black population growth, conditional on
controls for education, income, population group, population density and employment in 1991 and
province ﬁxed eﬀects. Data are collapsed into 100 bins, representing roughly 20 wards each.
Source : Authors’ analysis based on South African census data.




      Figure 5: Population reaction for high and low density places




Note : The ﬁgure displays the relationship between the predicted growth in the black population between
1991 and 2011 and its impact on non-black population growth over the same period, distinguishing
between initially low and high density locales. These results are analogous to the results in Panel C of
Table 8.
Source : Authors’ analysis based on South African census data.




                                                  41
Figure 6: The effect of initial density and size of shock for population
growth




Note : This ﬁgure displays the βj,k coeﬃcients resulting from estimating equation (3) in the main text.
The size of the shock increases along the x-axis. It starts oﬀ with the highest decile of the distance
distribution going to the decile with the lowest values (i.e. those closest to a homeland). Similarly,
the ﬁrst value on the y-axis corresponds to those wards in the lowest decile of the initial population
density distribution while the last one contains the highest decile. The z-axis displays diﬀerences in
the conditional mean of population growth in the period 1991-2011.
Source : Authors’ analysis based on South African census data.




                                                 42
A.2    Tables

Table 1: Descriptive statistics on the population distribution (in percent)

         Distribution of black                         Share of urbanised population
      population across area types                       across population groups
    Year Urban Rural Homelands                 Year   White Colored Indian Black
    1950     25.4      34.9        39.7        1951    78       65      78      27
    1960     29.6      31.3        39.1        1960    84       68      83      32
    1970     28.1      24.5        47.4        1980    88       75      91      49
    1980     26.7      20.6        52.7        1991    91       83      96      58
    Source : Surplus People Project (1985, p.18)




                                               43
              Table 2: Summary statistics of included variables

                                                (1)      (2)       (3)      (4)      (5)
VARIABLES                                        N      mean       sd       min      max
Excluded instrument
   log distance                               2,093     4.092     1.564    0.0529    6.746
Endogenous variables
   ∆Black Population (1991-1996)              2,093     -1.081   20.75     -615.4     0.200
   ∆Black Population (1991-2001)              2,093     0.0310   0.0381    -0.200     0.100
   ∆Black Population (1991-2011)              2,093     0.0179   0.0207    -0.168    0.0499
Dependent variables
   ∆Total Population (1991-1996)              2,093 -1.787        29.81      -829     0.200
   ∆Total Population (1991-2001)              2,093 0.0348       0.0417     -0.358   0.1000
   ∆Total Population (1991-2011)              2,093 0.0214       0.0213     -0.168   0.0500
   ∆Nonblack Population (1991-1996)           2,093 -0.709        18.51     -773.8    0.192
   ∆Nonblack Population (1991-2001)           2,093 0.00380      0.0211     -0.294   0.0960
   ∆Nonblack Population (1991-2011)           2,093 0.00354      0.00989   -0.0669   0.0425
Province fixed effects
   Eastern Cape                               2,093     0.100     0.301      0         1
   Free State                                 2,093     0.0994    0.299      0         1
   Gauteng                                    2,093      0.172    0.378      0         1
   KwaZulu-Natal                              2,093     0.145     0.352      0         1
   Limpopo                                    2,093     0.0674    0.251      0         1
   Mpumalanga                                 2,093     0.102     0.302      0         1
   North West                                 2,093     0.0726    0.260      0         1
   Northern Cape                              2,093     0.0717    0.258      0         1
   Western Cape                               2,093      0.170    0.375      0         1
Source : Authors’ analysis based on South African census data.




                                               44
                                      Table 2 - continued

                                       (1)     (2)        (3)       (4)               (5)
VARIABLES                               N     mean        sd        min               max
Control variables (from 1991 census in logs)
   Male share                        2,093    0.506     0.0826       0                 1
   Population group ratio            2,093    0.275     0.321        0                 1
   Population density                2,093    4.647      2.478    0.0148             10.40
   Total population                  2,093    8.282      1.197     0.693             10.45
   Black population                  2,093    6.712     1.997        0               9.944
   Employed                          2,093    7.261      1.306       0               9.635
   Unemployed                        2,093    4.977      1.389       0               8.183
   Not economically active           2,093    7.665      1.258       0               9.925
   No schooling                      2,093    6.864      1.154       0               9.317
   Some primary schooling            2,093    6.807      1.188       0               9.135
   Finished primary school           2,093    5.414      1.168       0               8.255
   Some secondary schooling          2,093    6.792      1.333       0               9.585
   Finished secondary school         2,093    5.952      1.578       0               9.404
   Higher education                  2,093    3.442      1.899       0               8.283
   No income                         2,093    7.618     1.250        0               9.932
   Income: R1-499                    2,093    3.655     1.391        0               7.349
   Income: R500-699                  2,093    3.266      1.285       0               6.852
   Income: R700-999                  2,093    3.775      1.246       0               6.952
   Income: R1000-1499                2,093    4.610      1.246       0               7.594
   Income: R1500-1999                2,093    4.604      1.228       0               7.489
   Income: R2000-2999                2,093    5.188      1.302       0               7.856
   Income: R3k-4k                    2,093    5.111      1.280       0               7.953
   Income: R5k-6k                    2,093    4.706      1.259       0               8.084
   Income: R7k-9k                    2,093    4.786      1.396       0               8.357
   Income: R10k-14k                  2,093    4.874      1.498       0               9.125
Source : Authors’ analysis based on South African census data.
Note : Log distance is the distance to the nearest homeland in logs. All population growth variables
are deﬁned as absolute population growth in the relevant time period divided by overall population.
Male share is the share of males in the overall population and population group ratio the share
of white population. All other demographic variables are the log of the number of people falling
within a given category (e.g. “Finished primary school” is the log of the size of the population that
has ﬁnished primary shool and no further education).




                                                45
                           Table 3: Pre-trend regressions

                    (1)          (2)           (3)           (4)          (5)            (6)
                  ∆pop80,91    ∆pop91,01     ∆pop91,01     ∆pop80,91    ∆pop91,01      ∆pop91,01
log (dist)         -0.002       -0.017∗∗∗     -0.018∗∗      -0.001       -0.018∗∗∗     -0.020∗∗∗
                  (0.0095)      (0.0066)      (0.0072)     (0.0096)      (0.0066)      (0.0071)
log (pop80 )                                                0.009
                                                           (0.0097)
log (pop91 )                                                             -0.020∗∗∗     -0.023∗∗∗
                                                                         (0.0072)      (0.0080)
Observations         160           207          158           160           207           158
Source : Authors’ analysis based on South African census data.
Notes : Sample varies according to data availability for diﬀerent periods. The sample in columns 3
and 6 consists of observations with data for both periods. Robust standard errors in parentheses.
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 ***. dist measures the distance to the nearest
homeland in km, pop measures population and ∆pop measures absolute population growth divided
by population in the latter period.




                                                46
           Table 4: OLS and 2SLS baseline regressions

                              (1)                          (2)
                              OLS                         2SLS
                       Population growth            Population growth
Panel A: Population growth rates (1991-1996)
∆Black Population             1.126                       0.360
                            (0.0814)                     (0.862)
FS AP F-Stat                    -                         2.52
Panel B: Population growth rates (1991-2001)
∆Black Population            0.899∗                       1.061
                            (0.0393)                     (0.115)
FS AP F-Stat                    -                         29.98
Panel C: Population growth rates (1991-2011)
∆Black Population           0.895∗∗∗                      0.993
                            (0.0236)                     (0.0873)
FS AP F-Stat                    -                         42.95
Province ﬁxed eﬀects           Yes                         Yes
Controls                       Yes                         Yes
Observations                  2093                        2093

Notes. This Table displays estimates of equation (2) in the text. Each cell
presents estimates from a separate regression. The baseline sample consists of
all wards inside South Africa for which 1991 data is available. The standard
errors are clustered on the municipality level and presented in parentheses.
There are 201 clusters. The outcome variable is absolute overall population
growth in the relevant time period divided by overall population. ∆Black
population is deﬁned as absolute growth of the black population from 1991 to
year t divided by the overall population in t. The relevant time periods t 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 in 1991. There are nine provinces for which ﬁxed eﬀects are
included. The estimated coeﬃcients for the ﬁrst stage regressions are reported
in appendix B. Coeﬃcients that are signiﬁcantly diﬀerent from one at the 90%
level of conﬁdence are marked with a *; at the 95% level, a **; and at the 99%
level, a ***.
Source : Authors’ analysis based on South African census data.




                                     47
                                              Table 5: 2SLS regressions using different sub-samples

                                 (1)              (2)              (3)               (4)           (5)            (6)             (7)           (8)          (9)
                             Dummy for       No dummy for     Dummies for all    Drop within    Drop < 5%     Drop < 10%     Drop distance    District   Municipality
                            Johannesburg      Cape Town        metro areas         10 km          white          white           ≥6             FE          level
     Panel A: Population growth rates (1991-1996)
     ∆Black Population          0.360           0.373               0.315            0.615         23.37          20.75           0.345         -0.652     0.814∗∗∗
                               (0.861)         (0.850)             (0.909)          (0.442)       (32.85)        (25.53)         (0.853)       (1.926)      (0.058)
     FS AP F-Stat               2.52            2.53                2.32              1.36          0.25          0.31            2.61           1.67        10.27
     Panel B: Population growth rates (1991-2001)
     ∆Black Population          1.069           1.072               1.034            1.066         1.169          1.231           1.008         0.948       1.039
                               (0.112)         (0.132)             (0.134)          (0.189)       (0.144)        (0.173)         (0.108)       (0.084)     (0.154)
     FS AP F-Stat               32.23           22.96               26.65            12.51         30.67          25.55           30.55         34.68       11.17
     Panel C: Population growth rates (1991-2011)
     ∆Black Population          1.000            1.007              0.957            1.046         1.049          1.062          0.9726         0.870       0.926
                               (0.086)         (0.0992)            (0.115)          (0.131)       (0.139)        (0.146)         (0.088)       (0.077)     (0.151)
48




     FS AP F-Stat               44.67           32.52               31.28            20.69         31.09          28.89           42.81         36.59       12.91
     District ﬁxed eﬀects         No               No                No               No            No             No              No           Yes           No
     Province ﬁxed eﬀects         Yes              Yes               Yes              Yes           Yes            Yes             Yes           No          Yes
     Controls                     Yes              Yes               Yes              Yes           Yes            Yes             Yes          Yes          Yes
     Observations                2093             2093              2093             1790           1374          1137            1730          2093         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 and presented in parentheses. There are 201
     clusters. All columns are estimated using 2SLS where the natural log of distance to the nearest homeland is used to instrument for absolute black population
     growth in the relevant time period divided by the overall population. The outcome variable is absolute population growth in the relevant time period divided
     by the overall population. ∆Black population is deﬁned as absolute growth of the black population from 1991 to year t divided by the overall population in t.
     The relevant time periods t 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 in 1991. There are nine provinces for which ﬁxed eﬀects are included. The estimated coeﬃcients for the
     ﬁrst stage regressions are reported in appendix B. Coeﬃcients that are signiﬁcantly diﬀerent from one at the 90% level of conﬁdence are marked with a *; at
     the 95% level, a **; and at the 99% level, a ***. 95% conﬁdence intervals are in brackets.
     Source : Authors’ analysis based on South African census data.
                                         Table 6: 2SLS regressions using working-age population only

                               (1)           (2)            (3)              (4)             (5)           (6)            (7)           (8)         (9)         (10)
                                         Dummy for        No Cape        Dummies for     Drop within    Drop < 5%     Drop < 10%     Drop dist.   District   Municipality
                             Baseline
                                        Johannesburg    Town dummy       metro areas       10 km          white          white         ≥6           FE          level
     Panel A: Population growth rates (1991-1996)
     ∆Black Population       1.311         1.339             1.305           1.175          1.480          1.433          1.694         1.272       1.026        1.128
                            (0.206)       (0.212)           (0.227)         (0.242)        (0.383)        (0.315)        (0.479)       (0.206)     (0.182)      (0.361)
     FS AP F-Stat            17.27         17.76             14.07           14.45          7.06           14.05           8.46         15.91       18.01        4.46
     Panel B: Population growth rates (1991-2001)
     ∆Black Population       1.070         1.076             1.085           1.048          1.060          1.189          1.254         1.020      0.945         1.032
                            (0.120)       (0.118)           (0.139)         (0.143)        (0.196)        (0.157)        (0.185)       (0.116)    (0.0862)      (0.187)
     FS AP F-Stat            30.50         32.49             22.85           27.03          11.84          28.83          24.73         30.84       34.50        9.32
     Panel C: Population growth rates (1991-2011)
     ∆Black Population       0.990        0.996             1.006            0.947          1.021          1.055          1.067        0.931       0.876         0.918
                            (0.0803)     (0.0787)          (0.0919)         (0.107)        (0.125)        (0.134)        (0.140)      (0.0805)    (0.0788)      (0.175)
49




     FS AP F-Stat             42.36       43.38             31.55            31.37          19.32          31.24          28.54        41.98        36.75        11.53
     District ﬁxed eﬀects      No            No               No              No             No             No             No            No         Yes           No
     Province ﬁxed eﬀects      Yes           Yes              Yes             Yes            Yes            Yes           Yes           Yes          No           Yes
     Controls                  Yes           Yes              Yes             Yes            Yes            Yes           Yes           Yes         Yes           Yes
     Observations             2093          2093             2093            2093           1790           1374           1137          1730        2093          203

     Notes. This Table displays estimates of equation (2) in the text using working-age population rather than overall population for diﬀerent sub-samples. This includes
     everyone aged 15 to 64. 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 and presented in parentheses. There are 201 clusters. All columns are estimated using 2SLS where the natural log of distance
     to the nearest homeland is used to instrument for absolute black population growth in the relevant time period divided by the overall population. The outcome
     variable is absolute population growth in the relevant time period divided by the overall population. ∆Black population is deﬁned as absolute growth of the black
     population from 1991 to year t divided by the overall population in t. The relevant time periods t 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 in 1991. There are nine provinces for which ﬁxed
     eﬀects are included. The estimated coeﬃcients for the ﬁrst stage regressions are reported in appendix B. Coeﬃcients that are signiﬁcantly diﬀerent from one at the
     90% level of conﬁdence are marked with a *; at the 95% level, a **; and at the 99% level, a ***. 95% conﬁdence intervals are in brackets.
     Source : Authors’ analysis based on South African census data.
Table 7: Alternative specification using different time periods

                                     Full sample          Working-age population
                              (1)             (2)          (3)            (4)
                           ∆ Overall      ∆ Non-black   ∆ Overall     ∆ Non-black
                           population      population   population     population
   ∆Black Population          0.167          0.0319        0.246          -0.035
   (1991 - 2001)             (0.139)         (0.484)      (0.153)        (0.045)
   FS AP F-Stat               29.97             29.97      30.50          30.50
   Province ﬁxed eﬀects        Yes              Yes         Yes            Yes
   Controls                    Yes              Yes         Yes            Yes
   Observations               2093              2093        2093          2093

   Notes. This table reports 2SLS results. In the second stage we regress diﬀerent
   population growth measures for the period 2001 - 2011 on predicted black
   population growth in the previous period (1991 - 2001). In the ﬁrst stage we
   instrument black population growth using distance to the nearest homeland as in
   the baseline speciﬁcation. The outcome variable is absolute population growth
   in the relevant time period divided by the overall population. ∆Black population
   is deﬁned as absolute growth of the black population from 1991 to 2001 divided
   by the overall population in 2001. Controls include variables on education,
   income, population group, population density and employment in 1991. There
   are nine provinces for which ﬁxed eﬀects are included. Standard errors are
   clustered at the municipality level and presented in parentheses. 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 are in brackets.
   Source : Authors’ analysis based on South African census data.




                                           50
Table 8: Heterogeneity with respect to the initial population density
and level of urbanization

                                                          (1)                    (2)
                                                 High population density   High urban share
                                                        dummy                  dummy
       Panel A: Population growth rates (1991-1996)
       ∆Black Population                                  1.026                 -6.333
                                                         (1.425)               (11.35)
       High initial urban share dummy ×                                         7.589
       ∆Black Population                                                       (11.56)
       High initial population density dummy ×            0.509
       ∆Black Population                                 (1.133)
       FS AP F-Stat: ∆Black Population                    0.81                   0.07
       FS AP F-Stat: Urban interaction                      -                    0.07
       FS AP F-Stat: Density interaction                  0.45                     -

       Panel B: Population growth rates (1991-2001)
       ∆Black Population                                  1.106                 1.002
                                                         (0.138)               (0.111)
       High initial urban share dummy ×                                        0.178∗∗
       ∆Black Population                                                       (0.084)
       High initial population density dummy ×          0.681∗∗
       ∆Black Population                                (0.284)
       FS AP F-Stat: ∆Black Population                   26.54                  36.98
       FS AP F-Stat: Urban interaction                     -                    23.70
       FS AP F-Stat: Density interaction                 18.71                    -

       Panel C: Population growth rates (1991-2011)
       ∆Black Population                                  0.957                 0.986
                                                         (0.092)               (0.082)
       High initial urban share dummy ×                                         0.040
       ∆Black Population                                                       (0.062)
       High initial population density dummy ×          0.348∗∗
       ∆Black Population                                (0.152)
       FS AP F-Stat: ∆Black Population                   44.53                  46.50
       FS AP F-Stat: Urban interaction                     -                    27.49
       FS AP F-Stat: Density interaction                 17.67                    -

       Province ﬁxed eﬀects                               Yes                    Yes
       Controls                                           Yes                    Yes
       Observations                                       2093                  2093

       Notes. This Table displays estimates of equation (2) in the text with an addi-
       tional interaction term. Each column displays one speciﬁcation. The standard
       errors are clustered on the municipality level and presented in parentheses.
       There are 201 clusters. All columns are estimated using 2SLS. Absolute black
       population growth divided by the overall population and the same term in-
       teracted with a dummy for high population density in 1991 or for high urban
       share of households are the endogenous variables. Log distance to the nearest
       homeland and log distance to the nearest homeland times a dummy for high
       population density in 1991 or high urban share of households are used as instru-
       ments for the endogenous variables. An area is deﬁned as having a high initial
       population density if it is among the 25% most dense areas. An area is deﬁned
       as having a high urban share if it is among the areas with the 75% highest
       share of urban households in 1991. The outcome variable is absolute population
       growth in the relevant time period divided by the overall population. ∆Black
       population is deﬁned as absolute growth of the black population from 1991 to
       year t divided by the overall population in t. The relevant time periods t 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 in 1991. There are nine provinces for which ﬁxed eﬀects are
       included. The estimated coeﬃcients for the ﬁrst stage regressions are reported in
       appendix B. Coeﬃcients on the interaction terms 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 ***.     51
       Source : Authors’ analysis based on South African census data.
B     Additional tables and ﬁgures


This appendix contains all the ﬁrst stage regressions corresponding to the tables in the

main paper, as well as one graph discussed brieﬂy in the main text.




                                          52
                                  Figure 7: Missing wards




Note: This map displays all wards in South Africa outside of the former homelands. Those wards with
in red are missing. The former homelands are colored in green.

Source: Authors’ own work using data from the Directorate: Public Sate Land Support via Africa
Open Data.




                                                53
Table 9: Summary of first stage regressions for the baseline specifications
with different fixed effects

                            (1)           (2)            (3)              (4)
                           No FE      Province FE    District FE    Municipality FE
          Panel A: Population growth rates (1991-1996)
          log distance    0.308         -0.940        -0.936              -1.148
                         (0.365)       (0.593)       (0.723)             (0.993)
          Panel B: Population growth rates (1991-2001)
          log distance  -0.007∗∗∗     -0.007∗∗∗     -0.006∗∗∗           -0.003∗∗
                         (0.001)       (0.001)       (0.001)             (0.001)
          Panel C: Population growth rates (1991-2011)
          log distance  -0.004∗∗∗     -0.004∗∗∗     -0.004∗∗∗           -0.002∗∗
                         (0.000)       (0.001)       (0.001)             (0.001)
          Level of
                             No         Province       District       Municipality
          Fixed eﬀects
          Controls          Yes           Yes            Yes              Yes
          Observations      2093          2093           2093             2093

          Note: This Table displays estimates of equation (1) in the main text. Col-
          umn headings denote diﬀerent speciﬁcation. Each cell presents estimates
          from a separate regression. The standard errors are clustered on the
          municipality level and presented in parentheses. There are 201 clusters.
          All columns are estimated using OLS where the natural log of distance to
          the nearest homeland is the variable of interest. The outcome variable is
          absolute black population growth in the relevant time period divided by
          the 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 in 1991. Fixed eﬀects at varying levels are included.
          Coeﬃcients that are statistically signiﬁcant at the 90% level of conﬁdence
          are marked with a *; at the 95% level, a **; and at the 99% level, a ***.
          Standard errors in parentheses.
          Source : Authors’ analysis based on South African census data.




                                              54
Table 10: First stage regressions corresponding to Table 4

                                                 (1)
                                       Black population growth
     Panel A: Population growth rates (1991-1996)
     log distance                               -0.940
                                               (0.593)
     Panel B: Population growth rates (1991-2001)
     log distance                             -0.007∗∗∗
                                               (0.001)
     Panel C: Population growth rates (1991-2011)
     log distance                             -0.004∗∗∗
                                               (0.001)
     Fixed eﬀects                                Yes
     Controls                                    Yes
     Observations                               2093

    Notes. This Table displays estimates of equation (1) in the main
    text. Each cell presents estimates from a separate regression. The
    standard errors are clustered on the municipality level and presented
    in parentheses. There are 201 clusters. All columns are estimated
    using OLS where the natural log of distance to the nearest homeland
    is the variable of interest. The outcome variable is absolute black
    population growth in the relevant time period divided by the 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 in 1991. There are nine provinces for which ﬁxed
    eﬀects are included. Coeﬃcients that are statistically signiﬁcant at
    the 90% level of conﬁdence are marked with a *; at the 95% level, a
    **; and at the 99% level, a ***. Standard errors in parentheses.
    Source : Authors’ analysis based on South African census data.




                                         55
                                 Table 11: Summary of first stage regressions corresponding to Table 5

                                 (1)              (2)              (3)               (4)           (5)            (6)             (7)           (8)           (9)
                             Dummy for       No dummy for     Dummies for all    Drop within    Drop < 5%     Drop < 10%     Drop distance    District    Municipality
                            Johannesburg      Cape Town        metro areas         10 km          white          white           ≥6             FE           level
     Panel A: Population growth rates (1991-1996)
     log distance               -0.949          -0.951              -1.109          -0.806        0.0761         0.106           -1.004         -0.945       -0.948
                               (0.592)         (0.591)             (0.722)         (0.687)        (0.152)       (0.189)         (0.616)        (0.719)      (0.700)
     Panel B: Population growth rates (1991-2001)
     log distance             -0.007∗∗∗       -0.006∗∗∗           -0.006∗∗∗        -0.006∗∗∗     -0.008∗∗∗      -0.007∗∗∗      -0.007∗∗∗      -0.007∗∗∗    -0.006∗∗∗
                               (0.001)         (0.001)             (0.001)          (0.002)       (0.001)        (0.001)        (0.001)        (0.001)      (0.001)
     Panel C: Population growth rates (1991-2011)
     log distance             -0.004∗∗∗       -0.003∗∗∗           -0.003∗∗∗        -0.004∗∗∗     -0.003∗∗∗      -0.004∗∗∗      -0.003∗∗∗      -0.004∗∗∗    -0.003∗∗∗
                               (0.001)         (0.001)             (0.001)          (0.001)       (0.001)        (0.001)        (0.001)        (0.001)      (0.001)
     District ﬁxed eﬀects         No               No                No               No            No             No             No            Yes           No
     Province ﬁxed eﬀects         Yes             Yes               Yes              Yes            Yes           Yes             Yes            No           Yes
56




     Controls                     Yes             Yes               Yes              Yes            Yes           Yes             Yes           Yes           Yes
     Observations                2093             2093              2093             1790          1374           1137            1730          2093          203

     Notes. This Table displays estimates of equation (1) in the main text. Column headings denote diﬀerent speciﬁcation. Each cell presents estimates from
     a separate regression. The standard errors are clustered on the municipality level and presented in parentheses. There are 201 clusters. All columns are
     estimated using OLS where the natural log of distance to the nearest homeland is the variable of interest. The outcome variable is absolute black population
     growth in the relevant time period divided by the 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 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 statistically
     signiﬁcant at the 90% level of conﬁdence are marked with a *; at the 95% level, a **; and at the 99% level, a ***. Standard errors in parentheses.
     Source : Authors’ analysis based on South African census data.
                                 Table 12: Summary of first stage regressions corresponding to Table 6

                                (1)           (2)             (3)               (4)               (5)           (6)            (7)              (8)           (9)          (10)
                                          Dummy for      No dummy for      Dummies for all    Drop within    Drop < 5%     Drop < 10%      Drop distance    District    Municipality
                             Baseline
                                         Johannesburg     Cape Town         metro areas         10 km          white          white            ≥6             FE           level
     Panel A: Population growth rates (1991-1996)
     log distance           -0.003∗∗∗    -0.003∗∗∗          -0.003∗∗∗          -0.003∗∗∗        -0.003∗∗∗     -0.003∗∗∗      -0.003∗∗∗       -0.003∗∗∗      -0.003∗∗∗        -0.004∗
                             (0.001)      (0.001)            (0.001)            (0.001)          (0.001)       (0.001)        (0.001)         (0.001)        (0.001)         (0.002)
     Panel B: Population growth rates (1991-2001)
     log distance           -0.007∗∗∗    -0.007∗∗∗          -0.006∗∗∗          -0.006∗∗∗        -0.006∗∗∗     -0.007∗∗∗      -0.007∗∗∗       -0.007∗∗∗      -0.006∗∗∗        -0.008∗∗
                             (0.001)      (0.001)            (0.001)            (0.001)          (0.002)       (0.001)        (0.001)         (0.001)        (0.001)          (0.003)
     Panel C: Population growth rates (1991-2011)
     log distance           -0.004∗∗∗    -0.004∗∗∗          -0.003∗∗∗          -0.003∗∗∗        -0.004∗∗∗     -0.003∗∗∗      -0.003∗∗∗       -0.003∗∗∗      -0.004∗∗∗    -0.004∗∗∗
                             (0.001)      (0.001)            (0.001)            (0.001)          (0.001)       (0.001)        (0.001)         (0.001)        (0.001)      (0.001)
     District ﬁxed eﬀects       No            No               No                 No               No            No             No              No            Yes              No
     Province ﬁxed eﬀects       Yes           Yes              Yes               Yes              Yes            Yes            Yes             Yes            No              Yes
57




     Controls                   Yes           Yes              Yes               Yes              Yes            Yes            Yes             Yes           Yes              Yes
     Observations              2093          2093             2093               2093             1790           1374          1137            1730           2093             203

     Notes. This Table displays estimates of equation (1) in the main text using working age population. Column headings denote diﬀerent speciﬁcation. Each cell
     presents estimates from a separate regression. The standard errors are clustered on the municipality level and presented in parentheses. There are 201 clusters. All
     columns are estimated using OLS where the natural log of distance to the nearest homeland is the variable of interest. The outcome variable is absolute black
     population growth in the relevant time period divided by the 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 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 statistically signiﬁcant at
     the 90% level of conﬁdence are marked with a *; at the 95% level, a **; and at the 99% level, a ***. Standard errors in parentheses.
     Source : Authors’ analysis based on South African census data.
Table 13: First stage regressions of specification with interaction term
corresponding to table 8

                                     (1)                  (2)               (3)                 (4)

                                                 ∆Black pop growth                       ∆Black pop growth
                             ∆Black pop growth   × high population   ∆Black pop growth   × high urban
                                                 density dummy                           share dummy
 Panel A: Population growth rates (1991-1996)
 log distance                       -1.250∗              -0.821           -1.426∗              -1.388
                                    (0.727)             (0.656)           (0.846)             (0.841)
 log distance × high
                                    1.426               1.564                -                   -
 population density dummy
                                   (1.130)              (1.253)              -                   -
 log distance × high
                                      -                    -               0.710               0.815
 urban share dummy
                                      -                    -              (0.736)             (0.707)

 Panel B: Population growth rates (1991-2001)
 log distance                      -0.007∗∗∗          0.001∗∗∗           -0.009∗∗∗            0.004∗∗
                                    (0.001)           (0.0003)            (0.001)             (0.002)
 log distance × high
                                   0.002∗            -0.004∗∗∗               -                   -
 population density dummy
                                   (0.001)              (0.001)              -                   -
 log distance × high
                                      -                    -             0.003∗∗∗            -0.009∗∗∗
 urban share dummy
                                      -                    -              (0.001)             (0.002)

 Panel C: Population growth rates (1991-2011)
 log distance                      -0.004∗∗∗             0.000           -0.004∗∗∗            0.002∗
                                    (0.001)             (0.000)           (0.001)             (0.001)
 log distance × high
                                    0.001            -0.002∗∗∗               -                   -
 population density dummy
                                   (0.001)              (0.001)              -                   -
 log distance × high
                                      -                    -              0.001∗∗            -0.005∗∗∗
 urban share dummy
                                      -                    -              (0.001)             (0.001)

 Province ﬁxed eﬀects                Yes                 Yes                Yes                 Yes
 Controls                            Yes                 Yes                Yes                 Yes
 Observations                       2093                 2093              2093                2093

 Notes. This Table displays estimates of equation (1) in the main text with an additional interaction
 term. Column headings denote diﬀerent speciﬁcations. The standard errors are clustered on the
 municipality level and presented in parentheses. There are 201 clusters. All columns are estimated
 using OLS where the natural log of distance to the nearest homeland and the same term times
 a dummy for high initial population density or high initial urban share of households are the
 variables of interest. The outcome variable are absolute black population growth divided by the
 overall population times a dummy for high initial population density or high initial share of urban
 households in 1991 and absolute black population growth divided by the 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 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
 statistically signiﬁcant at the 90% level of conﬁdence are marked with a *; at the 95% level, a **;
 and at the 99% level, a ***. Standard errors in parentheses.
 Source : Authors’ analysis based on South African census data.




                                                   58