Policy Research Working Paper 8636
Backyarding
Theory and Evidence for South Africa
Jan K. Brueckner
Claus Rabe
Harris Selod
Development Economics
Development Research Group
November 2018
Policy Research Working Paper 8636
Abstract
This paper explores the incentives for backyarding, an job access for backyarders raising land rent by increasing
expanding category of urban land-use in developing coun- their willingness-to-pay, the analysis then predicts that the
tries that has proliferated South Africa. The theoretical extent of backyarding will be higher for parcels with good
model exposes the trade-off faced by the homeowner in job access. This hypothesis is tested by combining a sat-
deciding how much backyard land to rent out: loss of yard ellite- based count of backyard dwellings per parcel with
space consumption in return for a gain in rental income. job-access data. The empirical results strongly confirm the
Under common forms for preferences, the homeowner’s prediction that better job access increases the extent of
own-consumption of yard space falls as land rent increases, backyarding.
causing more land to be rented to backyarders. With better
This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the
World Bank to provide open access to its research and make a contribution to development policy discussions around the
world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors
may be contacted at jkbrueck@uci.edu, clausrabe@hotmail.com and hselod@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
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Backyarding: Theory and Evidence for South Africa
by
Jan K. Brueckner
University of California, Irvine
Claus Rabe
Independent Consultant, Cape Town, South Africa
Harris Selod
The World Bank, Washington, DC
October 2018, revised February 2019
Keywords: informal housing; backyard housing; job access; South Africa
JEL codes: R14, R21, R31
Backyarding: Theory and Evidence for South Africa
by
Jan K. Brueckner, Claus Rabe and Harris Selod∗
1. Introduction
Governments in most countries in the world have pursued housing subsidy schemes designed
to make land and housing more aﬀordable to targeted beneﬁciaries. In the cities of developing
countries, where informal housing is widespread, these programs aim to facilitate access to
formal housing for low-income households who would otherwise live in slums. The programs
often consist of the provision of individual houses, a generous approach that builds political
support among the beneciaries. Because subsidized housing schemes are run by government
agencies, they must comply with formal housing norms and often end up providing plots that
are signiﬁcantly larger than what beneﬁciaries would have demanded if support came in the
form of supplementary income. In the absence of legal transferability of the allocated plots
(which often cannot be resold for a number of years), a likely consequence is overconsumption
of space by current occupants along with land misallocation and sprawl at the city level.
South Africa oﬀers a graphic example of consumer responses to a housing program with
such features. A land-use practice known as “backyarding” has proliferated in South Africa,
and it also appears to be expanding in other developing countries. Under this practice, the
owner of a (typically subsized) formal house rents a portion of his yard area to occupants who
live in a dwelling constructed either by formal or informal methods (yielding a backyard shack
in the latter case). The presence of backyarding indicates that existing subsidized homeowners
view their yard areas as excessive at prevailing land rents, encouraging them to reduce their
consumption of yard space in return for cash.
Despite its emergence as the fastest growing housing type in South Africa, backyarding
remains poorly understood. Moreover, it represents a unique mixture of informal and formal
land-tenure modes that has not yet been recognized in the economics literature on housing
in developing countries. The present paper adds to the literature on housing markets in the
1
developing world by providing an economic analysis of backyarding, developing a theoretical
model whose predictions are then tested empirically.1 By improving our understanding of
the backyarding phenomenon, the paper also helps to guide the formulation of government
housing programs in the developing world, mainly by the exposing consequences of giving poor
households more housing than they can reasonably use.
An appreciable share of South Africa’s population, particularly the urban population,
lives in backyard dwellings. According to Statistics South Africa, the number of households
living in either formal or informal dwellings in backyards has increased from 1.135 million in
2011 (7.3% of the country total), to 1.835 million in 2016 (12.5% of the total). Backyarding is
predominantly an urban phenomenon, with 84.2% of households that live in backyard dwellings
residing in urban areas (as deﬁned by Statistics South Africa as of 2011). Households living in
backyards constituted 8.9% of urban households in 2011, rising to 13.4% by 2016. In contrast,
the number of households living in informal settlements declined both in absolute and relative
terms, from 9.8% of urban households in 2011 to 8.7% in 2016.
The durability of housing capital limits the adjustment of urban densities as population
growth raises housing demand, and backyarding can be viewed as an eﬃcient way of over-
coming this limitation. With the durable housing stock ﬁxed in the short run, backyarding
allows an incremental increase in housing supply without the need to redevelop existing struc-
tures at higher densities, an adjustment that might take decades to unfold. The backyarding
phenomenon may also indicate that yard areas in government-subsidized housing, where back-
yarding is most common, were too large from an overall eﬃciency perspective, with backyarding
providing a correction to this original misallocation of resources.2 These ideas could be illus-
trated formally, but doing so is beyond the scope of the paper (the argument is clear intuitively
in any case).
The theoretical model developed in the paper depicts the homeowner’s backyarding choice,
where the amount of yard area rented to backyard households is chosen.3 In making this choice,
the homeowner trades oﬀ rental income against the loss of yard space for his own consumption.
A higher land rent raises the “price” to the homeowner of a unit of yard-space consumption
(the forgone income from renting it), generating the usual income and substitution eﬀects of
2
a price change. But the resulting negative eﬀect of rent on own-consumption of yard space is
oﬀset by an additional positive eﬀect that arises through an increase in the homeowner’s “full
income” (non-rental income plus income from renting the entire yard area). As a result, the
eﬀect of land rent on the amount of land rented out, and thus on the extent of backyarding,
is ambiguous in general. A similar ambiguity arises in the labor-leisure choice, where a higher
wage raises full income along with the price of leisure. This ambiguity is not present, however,
when the homeowner’s preferences take the Cobb-Douglas form or the more-general CES form
(as long as the elasticity of substitution is reasonably high). In these familiar cases, a higher
rent decreases yard-space consumption, raising the amount of yard area rented out and thus
the extent of backyarding.
With backyarders willing to pay more for land near employment centers, the rent they oﬀer
rises with job access, which then tends to raise the extent of backyarding, given the positive
connection between the yard area rented out and the rent level. But better job access also
raises the homeowner’s income net of commuting cost, which tends to reduce his willingness to
rent out yard space. However, under the assumption that homeowner and backyarder earnings
diﬀer only through their extent of labor market attachment, it is shown that the net eﬀect of
job access on backyarding is positive, an eﬀect that constitutes the main empirical prediction of
the model. While the prediction may seem natural, being similar to usual association between
population density and job access in urban models, the existence of the opposing eﬀects of job
access on rent and homeowner net income means that the prediction is by no means automatic.
The paper’s empirical work adds to a large empirical literature on housing in developing
countries, but there is little precedent for the actual empirical exercise that we carry out and
thus little direct connection to any previous paper.4 The empirical work is mainly devoted
to testing the job-access prediction, and it relies on a number of data sets sourced from Cape
Town’s city government. The ﬁrst data set comes from digital aerial photography and high-
resolution satellite images, which give point locations of buildings along with an associated
land-use classiﬁcation per building, including informal uses. We overlaid these spatial data on
a digital map of land-parcel contours from the City of Cape Town’s cadastre, yielding a count
of the number of backyard dwellings per land parcel. After various exclusions, our data set
3
consists of 551,421 sample parcels. Backyarding usually involves a single dwelling, but many
land parcels have multiple backyard structures.
Two additional data sets are combined in order to measure job access. The ﬁrst con-
tains employment counts by transportation zone within Cape Town. With almost 1,800 zones
delineated, employment across space is ﬁnely measured. The additional data set consists of
origin-destination matrices showing commute travel times between each pair of Cape Town
transportation zones, with separate matrices for diﬀerent modes. After assigning parcels to
transportation zones, this travel time information is used to compute several gravity-type job-
access measures for each parcel in the sample. Then, using a Poisson regression, the parcel-level
backyarding count is regressed on a job-access measure and several additional covariates. The
results strongly support the model’s prediction that the extent of backyarding rises with job
access.
The paper is organized as follows. Section 2 presents background information on the
backyarding phenomenon. Section 3 presents the theoretical analysis, and section 4 describes
the data sources. Section 5 describes the empirical framework and presents summary statistics,
while section 6 presents the empirical results. Section 7 oﬀers conclusions, showing the broader
implications of the analysis by noting the emergence of backyard structures as a partial remedy
for housing unaﬀordability in high-cost US cities, with a similar trend emerging in Europe.
2. Background information on backyarding
2.1. General features
Backyarding usually occurs on a small scale, rarely involving more than one or two self-
contained dwellings constructed in the back yard of a formal dwelling. Whether constructed
from permanent or non-permanent building materials, these self-contained units are distinct
from secondary dwellings (e.g., ﬂatlets) developed in compliance with planning regulations. By
sharing external services such as water taps, electricity connections and outside toilets with
the landlord in return for rent, the overall quality of accommodation for backyard residents is
signiﬁcantly better than that available in informal settlements (Beall, Crankshaw and Parnell,
2003). The photograph in Figure 1 shows a parcel in Cape Town’s Gugulethu township with
4
two backyard shacks, with the main house seen on the left.
The proliferation of backyard dwellings in Cape Town corresponds closely to the roll-out of
government-subsidized and fully serviced housing properties, where surplus yard space created
the opportunity for additional one- or two-room structures to be developed by the landlord,
to accommodate family or earn rent.
2.2. Backyarding in Council housing
The earliest occurrence of the backyarding phenomenon can be traced to the roll-out of
Council housing during the 1950s and 1960s, which was intended to accommodate migrant labor
of black African and mixed descent during the height of Apartheid. Rental housing for families
of mixed descent oﬀered enough backyard space for tenants to supplement their incomes by
building additional dwellings to accommodate relatives, who paid in kind (rather than through
rent). Units assigned to black African households were of a highly standardised “matchbox”
design: a free-standing, single-storey house with an internal ﬂoor space of between 40 and
44m2 , situated on a plot of at least 100m2 (Beall et al., 2003). In black African townships,
these dwellings were typically intended to accommodate paying tenants rather than relatives
(Lemanski, 2009). These distinctions, however, weakened with time.
Turok and Borel-Saladin (2016, p. 11) describe backyarding as a “safety valve to absorb
the pressure of popular demand to access urban livehoods”. As a result, in contravention
of planning legislation, municipal authorities adopted a laissez-faire stance as backyarding
grew during the 1970s and 1980s. This trend accelerated further following the relaxation of
Apartheid-era inﬂux-control laws during the 1980s, which precipitated the ﬁrst major wave of
urbanization in South Africa. By 1994, 87% of houses in two large black African townships in
Cape Town contained shacks constructed in the backyard (Lemanski, 2009). In one of them,
Gugulethu, the number of backyard dwellings (9981) outnumbered formal houses (8156) (Lee,
2005).
2.2. Backyarding in RDP housing
The second, larger wave of backyarding expansion occurred following the ambitious public
housing program launched after the country’s ﬁrst democratic elections in 1994. Under the
5
auspices of the Reconstruction and Development Program (RDP) and its successor, Breaking
New Ground (BNG), the State constructed over a million fully serviced houses across South
Africa. Following a standard format with a 40m2 dwelling on a serviced residential land
parcel averaging 160m2 in size, the roll-out of so-called “RDP houses” greatly expanded the
opportunity for backyarding throughout urban areas.
2.3. Landlord and tenant incentives
The improvement in living conditions enjoyed by the RDP household was rarely accom-
panied by an improvement in its economic prospects. In fact, the peripheral location and
dormitory nature of the sprawling RDP housing settlements often resulted in poor job acces-
sibility. In response, housing recipients became landlords by erecting and then renting out
informal dwellings in their backyards. In doing so, they successfully exploited one of the few
resources at their disposal: space (Govender, Barnes, and Pieper 2011).
Why do poor people live in backyard dwellings, dependent on landlords and liable for rent,
rather than moving to an informal settlement and experiencing an independent and rent-free
lifestyle? The principal reasons appear to include better access to services, better locations,
a reduced threat of eviction, and greater personal safety (Tshangana, 2014, Lemanski, 2009).
For poor households dependent on irregular and informal employment, backyard dwellings of-
fer a degree of locational ﬂexibility in response to economic opportunities not available with
static residence in a peripheral, dormitory RDP settlement (Lemanski, 2009). Such locational
ﬂexibility is particularly attractive to newly urbanized residents seeking job opportunities (Le-
manski, 2009). Perhaps counter-intuitively, both oﬃcial statistics and case studies conﬁrm
that the economic and educational proﬁles of backyard dwellers are superior to those of their
landlords (Govender et al., 2011). In addition, 2011 Census data analysed by Rabe (2017)
show that backyard dwellings in Cape Town are more likely to contain a single person, and
less likely to contain more than four persons, than the average dwelling in the city, consis-
tent with the view that backyard households are more mobile than the general population.
Moreover, a study of backyarding in Greater Soweto (Johannesburg) indicated that backyard
tenants are signiﬁcantly younger than their landlords (36 vs. 56 years for household heads)
and more likely to be foreign immigrants (Beall et al., 2003).
6
3. Theory
The section develops a theoretical model and derives hypotheses on backyarding patterns.
These predictions are then tested in the empirical analysis.
3.1. Model
In the model, the characteristics of the existing formal house are taken as given, having been
determined under the RDP program or by other past formal housing development decisions.
The ﬁxed ﬂoor space of an existing house is denoted q and the yard area is denoted y . With
a single-storey house, the formal lot size is then q + y . Letting y denote the consumption
yard space, which may be less than y, and c denote nonhousing consumption, the formal
homeowner’s well-behaved utility function is u(c, y, q). Let I denote the homeowner’s income
net of any commuting cost and let r denote land rent, which may depend on location (sections
3.3 and 3.4 below analyze locational eﬀects). Then, assuming the house is owned outright, so
that no current payments are required, the budget constraint is
c = I + r (y − y ), (1)
where r(y − y ) is the income from renting out yard space.5 Note that the rented space equals
the size y of the yard minus own-consumption y , which is multiplied by land rent r to get
rental income. Observe also that this formulation assumes that, by renting out less than his
total yard area, the formal homeowner can still enjoy the beneﬁts of some open space around
his house. Substituting (1) into the utility function, while recognizing that ﬂoor space stays
ﬁxed at q , utility can be written as
u(I + r(y − y ), y, q). (2)
Utility in (2) is maximized by choice of y , and the ﬁrst-order condition is
uy
MRS ≡ = r, (3)
uc
7
where subscripts denote partial derivatives and MRS denotes the marginal rate of substitution
between yard space and c. This condition says that the MRS is set equal to the opportunity
cost of yard space, namely, the rent forgone by consuming an extra square foot of y . The
next section carries out comparative-static analysis of the decision problem, showing how the
yard-space choice depends on the parameters of the problem, most importantly r and I .
3.2. Comparative-static analysis
Note ﬁrst that, if the MRS exceeds r when y equals y , so that the value of the ﬁrst rented
unit of yard space exceeds its opportunity cost, then no yard space is rented, with y = y.
Conversely, if the MRS is less than r when y = 0, then every marginal unit of yard space
is valued at less than the opportunity cost, so that the entire yard is rented out. Assuming
that neither of these conditions holds, so that an interior solution obtains, comparative-static
analysis can then be carried out.6 Totally diﬀerentiating (3) with respect to y , I , r, y , and q
yields
(−MRSc r + MRSy )dy + MRSc dI + (MRSc (y − y ) − 1)dr + rMRSc dy
+ MRSq dq = 0, (4)
where the subscripts denote the partial derivatives of MRS .
It is straightforward to show that the term multiplying dy (−MRSc r + MRSy ≡ Ω) is neg-
ative when the utility function has strictly convex indiﬀerence curves.7 In addition, normality
of y implies MRSc > 0, so that the absolute indiﬀerence-curve slope (given by MRS ) becomes
steeper moving vertically toward higher c’s in the (y, c) plane (y is on the horizontal axis).
Then, as an increase in I or an increase in y shifts the budget constraint (1) upward in parallel
fashion, the tangency between the steepening indiﬀerence curve and the constraint will move
to the right. Thus, using (4),
∂y MRSc ∂y rMRSc
= − > 0, = − > 0, (5)
∂I Ω ∂y Ω
8
so that higher homeowner income or a higher y causes more yard space to be consumed. Less
yard space is therefore rented out when income increases, with y − y falling, although y − y
could rise or fall when y increases, given that both y and y increase.
Using (2), the eﬀect of higher land rent on y is given by
∂y MRSc (y − y ) − 1
= − > (<) 0. (6)
∂r Ω
The eﬀect of r is thus ambiguous, with either more or less yard space consumed as rent rises.
The reason is that the usual negative substitution and income eﬀects of a higher rent (captured
respectively by the −1 and −MRSc y terms in the numerator of (6)) are oﬀset by an additional
positive income eﬀect that arises because the “full income” of the consumer (I + ry) rises with
r (captured by the MRSc y term). This ambiguity is similar to the one that arises in analysis
of the labor-leisure choice, where a higher wage raises full income while also increasing the
price of leisure.
The ambiguity can be seen in Figure 2, which shows the change in the budget line when
r increases. If y = y in (1), then c = I holds regardless of the value of r, so that the bottom
endpoint of the budget line is ﬁxed at (y, I ). If y = 0, then c = I + ry , so that the c intercept
of the budget line rises when r increases, with the line rotating clockwise. Depending on how
rapidly the indiﬀerence-curve slope increases moving vertically (or on how large MRSc is),
the indiﬀerence-curve tangency could move either to the right or left as a higher r rotates
the budget line upward. The ﬁgure shows the latter case, where y falls. Note that, while
the steepening of the budget line is the same as in the usual case of a price increase for the
good measured on the horizontal axis, the diﬀerence in Figure 2 is that the budget line rotates
upward around its ﬁxed lower endpoint rather than downward around a ﬁxed vertical intercept.
This upward rotation generates the additional income eﬀect that is not present in the usual
case.
The sign of the r derivative in (6) can be checked for speciﬁc utility functions. With
Cobb-Douglas preferences (u = cα y γ q θ ),
γ I
y = +y , (7)
α+γ r
9
so that y decreases with r. With CES preferences (u = [δcβ + (1 − δ − µ)y β + µq β ]1/β ),
k I
y = +y , (8)
r σ −1 + k r
where k > 0 is a constant and σ = 1/(β + 1) > 0 is the elasticity of substitution (equal to
1 in the Cobb-Douglas case). Using (8), it can be shown that y decreases with r provided
that the elasticity of substitution does not lie too far below unity.8 Therefore, as long as the
consumption goods are reasonably substitutable, y decreases with r, so that higher rent causes
more yard space to be rented out (y − y rises).
Finally, using (4), the eﬀect of q on y is given by
∂y MRSq
= − > (<) 0, (9)
∂q Ω
with sign of MRSq being ambiguous. MRSq depends on two cross-derivatives of the utility
function, uyq and ucq , which are ambiguous in sign and depend on the nature of the comple-
mentarities between the pairs of goods.
3.3. Job access and backyarding
The land rent r on which the formal homeowner bases his backyarding decision is deter-
mined by the willingness-to-pay of renters. Let M denote renter income, and let T x denote
commuting cost from a location x miles from the employment center (T is cost per round-trip
mile per period). Then M − T x is the renter’s disposable income, which supports nonhousing
consumption C and housing consumption Q (upper case letters denote renter values). Note
that with a single-storey backyard structure, Q is equal to the amount of backyard land rented.
Assuming that backyarders do not acquire open space for themselves, their well-behaved
utility can be written V (C, 0, Q), with the Y argument set equal to zero. The renter’s bud-
get constraint is C = M − T x − rQ, and substituting in V , the ﬁrst-order condition for
choice of Q is VQ /VC = r. In addition, rent must vary across locations x to insure loca-
tional indiﬀerence among renters. Renter utility must therefore be spatially uniform, with
V (M − T x − rQ, 0, Q) = v holding, where v is a constant. Together, this condition and the
10
ﬁrst-order condition determine Q and r as functions of the model parameters, most importantly
x and v , as in the standard urban model (see Brueckner (1987)). Totally diﬀerentiating the
uniform-utility condition and then substituting the ﬁrst-order condition yields the standard
condition ∂r/∂x = −T /Q, indicating that rent falls moving away from the employment center.
This conclusion can be used to investigate the spatial pattern of backyarding. Suppose for
the moment that the formal homeowner does not commute to work, so that I is independent
of x. Suppose also that ∂y/∂r < 0, as in the Cobb-Douglas and high-σ CES cases. Then, with
r falling as x increases and y inversely related to r, it follows that y increases with x, so that
homeowners consume more yard space, renting out less, farther from the employment center.
In other words, dy/dx = (∂y/∂r)(∂r/∂x) > 0.9
The analysis is more complex if the formal homeowner is also a commuter, in which case
I = m − tx, where m is wage income and t is commuting cost per mile per period for the
homeowner. Now, both I and r fall with x, so that the derivative
dy ∂y ∂I ∂y ∂r
= + (10)
dx ∂I ∂x ∂r ∂x
+ − +
is ambiguous in sign. Some clarity can be gained in the Cobb-Douglas case, where y depends
on the ratio I/r = (m − tx)/r (see (7)). Diﬀerentiating this ratio with respect to x,
dy t m − tx ∂r t m − tx T t m − tx T
− − = − + = −1 , (11)
dx r r2 ∂x r r2 Q r rQ t
θ
where means “same sign.” Since rQ = θ + α (M − T x) in the Cobb-Douglas case (where
V (C, 0, Q) = C αQθ , the term in parenthesis in (11) equals
θ + α (m − tx)/t
− 1, (12)
θ (M − T x)/T
To sign (12), suppose that income and commuting-cost diﬀerences arise only because home-
owners and renters make diﬀerent numbers of commute trips, showing diﬀerent degrees of
11
attachment to the labor market (with renters presumably (see Tshangana (2014)), but not
necessarily, making more trips). Accordingly, suppose that each group earns income w per trip
and has cost s per mile per trip, while renters make F trips and homeowners make f trips.
Then (m − tx)/t = f (w − sx)/fs = F (w − sx)/F s = (M − T x)/T . The second ratio term
in (12) thus equals 1, and since (θ + α)/θ > 1, (12) is positive and hence dy/dx > 0 holds in
(11). Summarizing yields
Proposition 1. If preferences are Cobb-Douglas and if income and commuting-cost
diﬀerences between homeowners and renters arise only because of diﬀerent numbers of
commute trips (indicating diﬀerent degrees of attachment to the labor market), then
homeowners rent out more backyard space at locations with better job access.
This conclusion would hold, of course, under other conditions that make (12) positive. It
should be noted that, while the predicted positive association between backyarding and job
access may seem natural, reﬂecting usual link between population density and job access in
urban models, it reﬂects a more subtle combination of forces given the opposing eﬀects of job
access on rent and homeowner income. Therefore, Proposition 1 is by no means an automatic
conclusion.
It is also interesting to note that, with minor amendments, the model developed so far
would also apply to a homeowner’s decision to rent out one or more rooms in his owner-
occupied house. The trade-oﬀ is then between the lost use of ﬂoorspace in the house and the
gain from rental income. Therefore, the analysis could provide insight into rentals of this type
in the cities of the developed world, including the use of services like Airbnb.
3.4. Determination of equilibrium land rents
While the preceding analysis involves the slope of land rent as a function of x, the level of r
remains to be determined. This level depends on the renter utility level v , which is determined
by an equilibrium condition stating that the renter population, denoted N , ﬁts in the available
space.
To develop this condition, let r(x, v ) and Q(x, v ) denote land rent and renter housing
consumption as functions of x and v (dependencies noted above). It is easily seen that ∂Q/∂x >
0, as in the standard urban model, and that ∂r/∂v < 0 and ∂Q/∂v > 0. In addition, let
12
y (r(x, v ), m − tx) denote the homeowner’s yard consumption as a function of r and I . Then
the renter population density at distance x from the employment center is
[y − y (r(x, v ), m − tx)] 1
D(x, v ) ≡ . (13)
Q(x, v ) q+y
The ﬁrst ratio term in (13) equals the number of backyarders per formal dwelling, given by
yard space rented out (y − y ) divided by land area per backyard dwelling (Q).10 The second
ratio is formal dwellings per unit of total land area (recall that q + y is formal lot size). If
dy/dx > 0, then the number of backyarders per formal dwelling decreases with x since the
numerator of the ﬁrst ratio in (13) is decreasing in x and Q is increasing in x. With the
second ratio constant, renter population density then falls as distance to the center increases.
It is important to note that the ﬁrst pattern (a decline in backyarders per parcel as distance
increases) is the basis for the empirical work, which uses a count of backyard dwellings.
Let [x0, x1 ] denote the range of locations where backyard space is available. Then, assuming
a circular city, the equilibrium condition that determines the utility level v is
x1
2πxD(x, v )dx = N. (14)
x0
In standard fashion, the LHS of (14) is the number of renters ﬁtting in the available backyard
space, equal to the integral of renter population density times total land area over the relevant
distance range. Note that this condition reﬂects the assumption that backyard land has no
alternative use aside from occupancy by renters, implying that the entire range of potential
locations will be occupied. As a result, the urban boundary condition usually seen in urban
models is not present.11
Comparative-static analysis based on (14) can show the eﬀect of parameters such as N on
the utility level v . Since ∂D/∂v < 0, it follows that v must fall when the renter population N
rises. With ∂r/∂v < 0, rent then rises at all locations, reﬂecting the greater demand pressure
from a larger renter population. With ∂y/∂r < 0, yard space rented out then rises, helping to
eliminate the excess demand for housing due to the larger N .
13
4. Data sources
As explained in the introduction, the paper relies on three data sets to explore the link
between backyarding and job access: a count of backyard dwellings per parcel drawn from
satellite data, job data at the level of transportation zones, and origin-destination trip-time
matrices. The sources of these data sets are described below.
The satellite data, provided by GeoTerraImage (Pty) Ltd. is contained in the Building
Based Land Use spatial data set, which provides a land-use classiﬁcation per building. The
data are captured from digital ortho-corrected aerial photography and/or high-resolution ortho-
rectiﬁed satellite images. It diﬀerentiates between 17 classes of residential structures, including
formal residential, informal residential and backyard structures. We overlaid the aerial GTI
data on a map containing individual parcel contours from the City of Cape Town’s cadastre
records, thus generating a count of backyard structures per parcel for 2014.12
Employment at the transportation-zone level for 2013 is estimated as part of the City of
Cape Town’s Land Use Model. The land-use model estimates the number of jobs by applying
workplace density assumptions to the internal ﬂoor space of various types of non-residential
buildings, as measured by the city’s Valuation Department in its non-residential valuation
processes. The preliminary results per transport zone are reconciled with citywide job numbers
(by occupation) as published in the Statistics South Africa Labour Force Survey.
The origin-destination matrix for commute-trip times is an output of the City of Cape
Town’s four-step travel demand model, known as the EMME model. These four steps are
(1) trip generation, (2) trip distribution, (3) mode choice and (4) route assignment. EMME
was designed by INRO Consultants at the University of Montreal and adopted by the City
of Cape Town in 1991. The model implements an equilibrium route assignment based on the
distribution of trip origins and destinations in relation to the transport network and modal
choice. On this basis, it estimates travel volumes, average trip distances and travel times
between each transport zone, for each mode of transport, for the morning peak. The model
is calibrated by means of General Household Transport Surveys, on-board surveys and cordon
counts.
14
5. Empirical framework, variables, and summary statistics
The sample consists observations on 551,412 parcels in Cape Town, with the variable count
denoting the number of backyard dwellings for the parcel. This count variable is a reasonable
proxy for the amount y of yard area devoted to backyarding. The sample was derived from
a larger data set consisting of more than 850,000 observations by dropping parcels whose size
was above the 70th percentile in the distribution of sizes, equal to 762m2 , a value that is over
ﬁve times the size of a typical RDP lot. This restriction eliminates about 255,000 observations,
reducing the sample to 595,000, with the loss of only about 1,000 observations with backyard
dwellings (thus allowing a better focus on the backyarding phenomenon). Deletion of observa-
tions outside a broad residential property type eliminates an additional 30,500 observations,
with missing data accounting for the rest of the reduction in the sample size.
Table 1 shows the frequency distribution of the count variable. Most observations (over
418,000) have no backyard dwellings, while about 98,000 have one dwelling and about 26,500
have two. Sample parcels have as many as 8 backyard dwellings, although the frequencies are
low beyond 4 dwellings.13 The map in Figure 3 shows the distribution of backyarding across
Cape Town, with the counts shown being generated from aggregations of transportation zones,
and Figure 4 shows a neighborhood view.
Table 2 shows the distribution of backyarding across Cape Town’s zoning categories. While
the vast majority of the observations are within residential categories, a relatively small num-
ber of observations appear in other categories, which the restriction to the broad residential
property type did not eliminate. Note that observations in these categories also exhibit back-
yarding. As can be seen, the great majority of the parcels with backyard dwellings are in
two categories: Single Residential 1 and Single Residential 2, known as SR1 and SR2. The
second of these categories, SR2, is known to contain mostly RDP dwellings.14 Smaller but
still appreciable numbers of parcels with backwarding are in the General Residential 1 and 4
categories.
Given the count nature of the dependent variable count, we estimate a Poisson regression
model. The density function for a Poisson random variable is e−λi λz
i /zi !, where zi is the value
i
of the variable for observation i and λi is the expected value of the variable, which depends on
15
the explanatory variables. Assuming a log-linear model, λi = exp(ω gi ), where ω is a coeﬃcient
vector and gi is the vector of explanatory variables.
Four explanatory variables appear in the regressions. Two are dummy variables for the
SR1 and SR2 zoning categories, which are more likely to contain parcels with backyarding
than other categories (the variables are sr1 and sr2). The third variable is a job-access
measure, explained further below. The fourth is parcel area, equal to the parcel area in
square meters. At ﬁrst, one might expect that larger parcels would contain more backyarders,
but the likelihood that larger parcels have higher-income homeowners, who are less likely to
rent to backyarders, can reverse this expectation. Recall from (5) that y depends positively
on y as well as on income I and rent, so that y (·) in (13) can be rewritten as y (r, I, y). But
assuming that I is increasing in y (being written I (y)), the amount of yard space rented out
is y − y = y − y (r, I (y), y). The total derivative of this expression is then
d(y − y ) ∂y ∂y ∂I
= 1 − − . (15)
dy ∂y ∂I ∂y
Since ∂y/∂y > 0, the sign of the ﬁrst two terms is ambiguous (as noted earlier), but since
∂y/∂I > 0, the remaining term is negative if ∂I/∂y > 0, as assumed. While the overall eﬀect
of y remains ambiguous, this inverse association between I and y thus increases the likelihood
that (15) is negative and that backyarding rises as y falls. Therefore, a negative coeﬃcient for
parcel area may well emerge.15
The job-access variables are computed using the trip-time origin-destination matrix, which
is based on transportation zones (almost 1800 in number), along with data on zone-level jobs.16
We use two job counts: total jobs in a zone, and jobs in the lowest income category among the
four categories tabulated. The ﬁrst job-access measure takes a gravity form, with access from
zone i given by Ai = j jobsj /timeij , where timeij is trip time from zone i to zone j and
either total or low-income jobs is used. The other access measure is the number of either total
or low-income jobs within X minutes of zone i, where X = 45, 60, 90, 120. Trip times are for
two diﬀerent alternate modes: minibus/taxi, which are small buses that constitute the main
commute mode for low-income South Africans, and regular bus. The job-access variables are
thus denoted
16
jobs K X B, where K = total, lowinc, X = grav, 45, 60, 90, 120, B = taxi, bus,
with an example being jobs total 45 taxi (grav denotes the gravity measure). The map in
Figure 5 shows the distribution of low-income jobs across Cape Town, with the counts again
based on aggregations of transportation zones.
Table 3 contains the summary statistics for the variables. The mean value of count equals
0.323, reﬂecting the large number of zeroes in Table 1, the mean of parcel area is 302.22m2 ,
and the mean distance of parcels from the Cape Town CBD is 21.1 km. The job-access measures
show that jobs within X minutes of a parcel rise with X and that the low-income job access
values are smaller than those for total jobs, both as expected. Even though minibus/taxi is a
more popular mode for low-income residents, Table 1 shows that job access by bus is uniformly
better than by minibus/taxi (only two X values, 45 and 60 minutes, are used for bus).
Before proceeding to the results, it should be noted that identiﬁcation issues are unlikely
to arise in the estimation. Although job and residence locations are simultaneously determined
at an aggregate level, a fact that would be taken into account in studying the link between
job access and residential patterns using highly aggregated spatial data, simultaneity between
the current job-access measures and the backyarding count variable is not a concern. Since
our job-access measures depend on the job location pattern across the entire metropolitan
area, whereas the count variable captures backyarding choices on individual parcels, reverse
causality from backyarding to job access will not be present. Job-access endogeneity could
arise if taxi service to areas with substantial backyarding were to oﬀer more-direct routings
to job sites (routes from sparse areas may detour to collect additional passengers, reducing
the access measures). Even though we do not ﬁnd this argument convincing, it is possible in
principle to address it by replacing the trip-time gravity measure jobs lowinc grav taxi with
a gravity measure based on straight-line distance, which removes any routing endogeneity (see
below). Finally, another source of endogeneity would be sorting of landlords across areas with
diﬀerent job access according to their propensity to rent to backyarders. However, the model
already controls for an important landlord-related variable, parcel size (a proxy for income).
A related point is that, while it might be desirable to control for other locational factors
17
such as access to stores and public services, such data were unavailable. Use of transportation-
zone ﬁxed eﬀects is, of course, not possible given that such variables would be perfectly corre-
lated with the job-access measures.
6. Results
Since distance to the CBD is a standard measure of job access, it is useful to start by
investigating the connection between backyarding and distance to Cape Town’s CBD. If CBD
distance is a good job-access measure, then backyarding should fall as distance increases. The
approach is to run an ordinary least-square (OLS) regression that has count as the depen-
dent variable and uses dummy variables for various 5-mile distance ranges as the explanatory
variables, an approach that allows ﬂexibility in the count/distance relationship. The results
are shown in graphical form in Figure 6. As can been seen, backyarding is mostly increasing
with distance to the CBD, in contrast to the predictions of the model. When the sample is
restricted to SR1 and SR2 parcels, where most backyarding occurs, the relationship is approx-
imately U-shaped beyond an initial short range where no backyarding is present (Figure 7),
again in contrast to the model predictions.
After inspecting the maps in Figures 3 and 5, these results come as no surprise. Figure 3
shows that little backyarding occurs near the CBD, even though it contains an appreciable con-
centration of low income jobs. Backyarding instead seem to be occurring near the substantial
job concentrations that exist outside the CBD, which are clearly seen in Figure 5. To measure
the attractive force of these job concentrations, we use the superior job-access measures from
Table 3 along with the other variables that are likely to aﬀect backyarding: sr1, sr2, and
parcel area. All of these explanatory variables are used in Poisson regressions, which are
better suited than OLS to the discrete nature of the count variable. These regressions are
estimated with coeﬃcient standard errors clustered at the transportation-zone level, an appro-
priate procedure given that the job-access variables are zone speciﬁc, thus not varying across
parcels within a zone. Failure to cluster the standard errors leads to very large t-statistics that
greatly overstate the true precision of the estimates.
Table 4 shows the Poisson regressions using the access measures for total jobs and the
18
minibus/taxi mode. The coeﬃcients for parcel area are all negative and strongly statisti-
cally signiﬁcant regardless of which access variable is used, showing that backyarding is more
common for smaller parcels where the homeowner’s income is likely to be lower, as argued
above. The coeﬃcients of the sr1 and sr2 dummy variables are also positive, indicating that
backyarding is more common for these property types, as already seen in Table 2. Note that
the sr2 coeﬃcient is more than double the size of the sr1 coeﬃcient, reﬂecting the greater
backyarding incidence for SR2 versus SR1 properties.
Turning to the job-access variables, the estimated coeﬃcients of all the variables except
jobs total 120 taxi are positive and statistically signiﬁcant, showing that better job access
indeed raises the extent of backyarding. These ﬁndings show the importance of controlling for
parcel size along with SR1 and SR2 status in isolating the job-access eﬀect. The insigniﬁcance
of the 120-minute access coeﬃcient probably reﬂects the long trip time, which, by allowing
access to most of the city’s jobs regardless of the parcel location, yields too little access variance
across parcels to generate a signiﬁcant eﬀect.17
Table 5 shows the Poisson results using the access measures for low-income (as opposed to
total) jobs and the minibus/taxi mode. The results are similar to those in Table 4 except that
the 90-minute job access coeﬃcient is now only marginally signiﬁcant, at the 8% rather than
the 5% level. Nevertheless, the lesson of this table is again that better job access increases the
extent of backyarding, as predicted by the theory.18
Table 6 shows the results using selected job-access measures for the bus mode and both
total and low-income jobs (the gravity, 45- and 60-minute variables are used). While the
parcel area and sr1 and sr2 coeﬃcients show little change, three of the job-access coeﬃcients
are now insigniﬁcant (both gravity coeﬃcients, as well as the 60-minute total-job coeﬃcient).
This pattern may make sense given the lower reliance of low-income Cape Town residents on
bus transportation relative to the minibus/taxi mode.
Table 7 shows results when the sample is restricted to SR1 and SR2 parcels, where back-
yarding is most common, using the same job access variables as in Table 6, but with taxi in
place of bus. The parcel area coeﬃcients are all again negative and signiﬁcant, while the sr2
coeﬃcient is positive (SR1 parcels are now the default). Five of the six job-access variables
19
have signiﬁcant coeﬃcients, with the jobs total grav taxi coeﬃcient marginally signiﬁcant
at the 6% level. Again, the lesson is that better job access spurs backyarding.19
If the sample is restricted to just SR2 parcels, the coeﬃcient of parcel area becomes pos-
itive. This outcome makes sense given that Census data show SR2 areas as mostly composed
of black households with presumably similar incomes, weakening the assumed correlation be-
tween parcel size and income. With parcel size no longer a good proxy for income, the oﬀsetting
parcel-size eﬀect (the ability of larger parcels to accommodate more backyarders) is able to
dominate.
The marginal eﬀects of the variables are shown in Table 8, using the regression from Table
5 with access variable jobs lowinc 60 taxi. The table shows the hypothetical change in the
explanatory variable along with the percentage change in the expected number of backyarders.
A 50m2 reduction in the parcel size (from a mean of 302) leads to a 10% increase in the
expected number of backyarders, while a 38,000 increase in the job-access variable (equal to
one standard deviation from Table 3) leads to an 11% increase in the expected number of
backyarders. Changing a parcel from non-SR1,SR2 status to SR1 or SR2 status raises the
expected number of backyarders by 61% or 220% respectively. The marginal eﬀects from the
other regressions are similar in magnitude.
To get a sense of the meaning of these percentage changes, recall that the mean of the count
variable is 0.323. The 11% increase in the expected number of backyarders due to improved
job access translates almost exactly into 11% of this mean, or 0.035. The implication is that
the job-access improvement leads approximately to an extra 1/30th of a backyarder per parcel,
or a new backyarder for every 30th parcel. The impact of the 50m2 decrease in parcel area
(which yields a 10%, as opposed to 11%, increase in the expected number of backyarders) is
very similar.
7. Conclusion
This paper explores the incentives for backyarding, an expanding category of South African
land-use. In doing so, the paper provides the ﬁrst treatment in the economics literature of a
new category of land-use in developing countries, which represents a unique mixture of informal
20
and formal tenure modes. The theoretical model exposes the trade-oﬀ faced by the homeowner
in deciding how much backyard land to rent out: loss of yard space consumption in return
for a gain in rental income. Higher rent raises the opportunity cost of own-consumption of
yard space (depressing it), but the gain in rental income from higher rent has the opposite
eﬀect, leading to an ambiguous net impact of rent on consumption. Under common forms
for preferences, however, the homeowner’s own-consumption of yard space falls as land rent
increases, causing more land to be rented to backyarders. Better job access, which raises the
land rent backyarders are willing to pay, then tends to lead to more backyarding, but it also
raises the homeowner’s income net of commuting cost, which leads to less backyarding. Under a
natural assumption, the net eﬀect is an increase in backyarding, leading to a predicted positive
association between job access and the extent of backyarding. This result matches the usual
connection between job access and population density in urban models, but it comes from a
subtler combination of eﬀects.
This hypothesis is tested by combining a satellite-based count of backyard dwellings per
parcel with job-access data, which come from job data at the level of transportation zones
together with an origin-destination matrix showing trip times between zones. The empirical
results strongly conﬁrm the prediction that better job access increases the extent of back-
yarding. In addition, the estimated inverse relationship between backyarding and parcel size
suggests that lower homeowner income (associated with small parcels) may spur backyarding,
as also predicted by the model.
Thus, using information from a number of remarkable data sets, the paper provides unique
insights into a land-use practice that is mostly absent in developed Western countries, even
though it bears some resemblance to room rentals by homeowners under an Airbnb-style ar-
rangement. An understanding of the forces that drive the backyarding phenomenon, particu-
larly the link to job access, is potentially useful to South African city planners as they attempt
to manage the evolution of their urban areas. For example, transport policies that increase
job access would lead to more backyarding in the aﬀected areas, while policies that raise em-
ployment for homeowners would reduce it. Planners should also recognize that, even though
backyarding may be technically illegal and often unsightly, it generates short-run eﬃciencies
21
by raising the density of land-use in response to higher housing demand, without the need for
wholesale redevelopment of the housing stock (an adjustment that would occur over a longer
period).
The paper’s exploration of the backyarding phenomenon suggests possible adjustments to
housing subsidy policies in South Africa and other developing countries, highlighting the conse-
quences of giving poor households more housing than they can use. Where policies have taken
this form, however, the paper suggests that facilitating the development of a rental market for
backyard structures is a smart way to allow poor homeowners to generate supplementary in-
come while at the same time increasing the private supply of aﬀordable housing and densifying
cities.
Finally, although the focus has been on a developing country, the paper may have relevance
for housing aﬀordability issues in the US. Construction and rental of formal backyard dwellings
could be a way of raising homeowner incomes while easing housing shortages in areas with high
housing costs. This possibility echoes the growing “yes in my backyard” movement evident in
cities such as New York, Los Angeles and San Francisco. In California, the demand for more-
aﬀordable forms of housing led to a 2016 state law easing building-permit delivery for backyard
structures (known in the US as accessory dwelling units or ADUs), and an increasing number
of state and local governments are envisioning similar legislation.20 Thus, there are reasons to
believe that the South African pattern could be a rising phenomenon that will become common
in many diﬀerent contexts, from similar shack structures in the cities of low-income countries
to more comfortable mini-houses in the expensive cities of the developed world.
22
Photo: M. Friedman
Figure 1: Backyard shacks
23
I + r1ȳ
I + r0ȳ
I
ȳ y
Figure 2: The effect of a rent increase
24
Source: GeoTerraImage, Building Based Land Use Figure 3: Location of backyarders
data set, 2014, and City of Cape Town
25
Source: GeoTerra Image, Building Based Land Use data
set, 2014, and City of Cape Town
Figure 4: Neighborhood View
26
Source, Land Use Model, City of Cape Town, 2013 Figure 5: Location of low-income jobs
27
Figure 6: Backyarders as a function of CBD distance
0.7
0.6
0.5
Number of Bacakyarders
0.4
0.3
0.2
0.1
0
0 5 10 15 20 25 30 35 40 45
Distance to CBD
28
Figure 7: Backyarders as a function of CBD distance--
SR1, SR2 parcels
1
0.9
0.8
0.7
Number of Bacakyarders
0.6
0.5
0.4
0.3
0.2
0.1
0
0 5 10 15 20 25 30 35 40 45
Distance to CBD
29
Table 1: Backyard Count Frequency
Count Frequency Percent Cumulative
0 418,754 75.94 75.94
1 98,037 17.78 93.72
2 26,532 4.81 98.53
3 6,174 1.12 99.65
4 1,471 0.27 99.92
5 349 0.06 99.98
6 78 0.01 100.00
7 15 0.00 100.00
8 11 0.00 100.00
Total 551,421
30
Table 2: Backyarding Frequency Across Zoning Categories
Backyarding?
Zoning Category No Yes Total
Agricultural 180 19 199
Community 1: Local 91 18 109
Community 2 : Regional 84 3 87
General Business 1 564 53 617
General Business 2 136 14 150
General Business 3 15 0 15
General Business 4 209 32 241
General Business 5 51 1 52
General Industrial 1 19 1 20
General Industrial 2 66 2 68
General Residential 1 55,593 8,079 63,672
General Residential 2 14,573 434 15,007
General Residential 3 1,938 0 1,938
General Residential 4 15,397 4,278 19,675
General Residential 5 270 0 270
General Residential 6 1 0 1
Limited Use Zone 76 8 84
Local Business 1 47 2 49
Local Business 2 584 24 608
Mixed Use 1 8 0 8
Mixed Use 2 801 14 815
Mixed Use 3 29 0 29
Open Space 2 : Public 370 56 426
Open Space 3: Special 18 0 18
Rural 125 35 160
Single Residential 1 (SR1) 236,552 48,573 285,125
Single Residential 2 (SR2) 90,488 70,995 161,483
Transport 1 23 2 25
Transport 2 314 19 333
Utility 132 5 137
Total 418,754 132,667 551,421
31
Table 3: Summary Statistics
VARIABLE Obs. Mean Std. Dev. Min Max
count 551,421 0.323 0.658 0 8
parcel area 551,421 302.22 178.84 0.133 762.0
distance 551,421 21.1 9.1 0.656 50.3
jobs total grav taxi 551,621 19,243.3 6,826.5 0.219 54,145.8
jobs total 45 taxi 551,621 48,378.6 64,973.5 0 428,155.0
jobs total 60 taxi 551,621 137,525.4 145,485.6 0 684,519.0
jobs total 90 taxi 551,621 510,719.0 402,339.0 0 1,465,416.0
jobs total 120 taxi 551,621 1,008,236.0 557,354.9 0 1,792,191.0
jobs lowinc grav taxi 551,621 4,950.6 1,828.8 0.055 12,928.8
jobs lowinc 45 taxi 551,621 13,026.9 15,398.6 0 88,227.0
jobs lowinc 60 taxi 551,621 37,047.4 37,804.8 0 175,237.0
jobs lowinc 90 taxi 551,621 132,308.0 99,766.4 0 362,607.0
jobs lowinc 120 taxi 551,621 252,799.8 138,135.0 0 444,484.0
jobs total grav bus 552,098 22,653.1 10,771.7 0.219 66,785.0
jobs total 45 bus 552,098 117,217.0 128,940.0 0 712,153.0
jobs total 60 bus 552,098 286,031.3 299,390.5 0 1,235,940.0
jobs lowinc grav bus 552,098 5,705.7 2,650.9 0.055 16,348.9
jobs lowinc 45 bus 552,098 31,427.8 32,871.7 0 165,619.0
jobs lowinc 60 bus 552,098 75,176.1 74,187.2 0 291,930.0
32
Table 4: Eﬀect of Job Access by Taxi on Backyard Count (Total Jobs)
VARIABLES (1) (2) (3) (4) (5)
parcel area -0.00170** -0.00182** -0.00184** -0.00180** -0.00175**
(-6.896) (-7.477) (-7.508) (-7.334) (-6.875)
sr1 0.443* 0.498* 0.482* 0.464* 0.449*
(2.355) (2.541) (2.519) (2.446) (2.331)
sr2 1.159** 1.228** 1.192** 1.169** 1.163**
(6.052) (6.074) (6.157) (6.063) (5.942)
jobs total grav taxi 0.0201**
(2.873)
jobs total 45 taxi 0.00141*
(2.552)
jobs total 60 taxi 0.000672**
(2.894)
jobs total 90 taxi 0.000214*
(2.050)
jobs total 120 taxi 8.48e-05
(0.915)
Constant -1.780** -1.466** -1.469** -1.479** -1.457**
(-7.741) (-7.033) (-7.428) (-7.440) (-6.658)
Observations 551,421 551,421 551,421 551,421 551,421
Robust z-statistics in parentheses
** p<0.01, * p<0.05
33
Table 5: Eﬀect of Job Access by Taxi on Backyard Count (Low Income Jobs)
VARIABLES (1) (2) (3) (4) (5)
parcel area -0.00164** -0.00183** -0.00182** -0.00177** -0.00175**
(-6.685) (-7.563) (-7.484) (-7.170) (-6.766)
sr1 0.430* 0.487* 0.475* 0.458* 0.452*
(2.312) (2.548) (2.508) (2.411) (2.330)
sr2 1.110** 1.197** 1.162** 1.155** 1.161**
(5.780) (6.165) (6.022) (5.938) (5.887)
jobs lowinc grav taxi 0.0887**
(3.336)
jobs lowinc 45 taxi 0.00747**
(3.760)
jobs lowinc 60 taxi 0.00271**
(2.981)
jobs lowinc 90 taxi 0.000808
(1.774)
jobs lowinc 120 taxi 0.000307
(0.784)
Constant -1.831** -1.482** -1.468** -1.478** -1.450**
(-8.321) (-7.471) (-7.595) (-7.415) (-6.615)
Observations 551,421 551,421 551,421 551,421 551,421
Robust z-statistics in parentheses
** p<0.01, * p<0.05
34
Table 6: Eﬀect of Job Access by Bus on Backyard Count
VARIABLES (1) (2) (3) (4) (5) (6)
parcel area -0.00184** -0.00188** -0.00187** -0.00183** -0.00187** -0.00187**
(-7.354) (-7.523) (-7.423) (-7.352) (-7.442) (-7.378)
sr1 0.496** 0.524** 0.513** 0.498** 0.530** 0.516**
(2.619) (2.786) (2.748) (2.635) (2.838) (2.764)
sr2 1.204** 1.228** 1.221** 1.210** 1.230** 1.224**
(6.345) (6.528) (6.516) (6.396) (6.581) (6.536)
jobs total grav bus 0.00518
(1.242)
jobs total 45 bus 0.000734*
(2.263)
jobs total 60 bus 0.000258
(1.794)
jobs lowinc grav bus 0.0246
(1.334)
jobs lowinc 45 bus 0.00320*
(2.356)
jobs lowinc 60 bus 0.00117*
(2.002)
Constant -1.499** -1.480** -1.460** -1.526** -1.501** -1.478**
(-7.247) (-7.715) (-7.691) (-7.193) (-7.878) (-7.809)
Observations 551,421 551,421 551,421 551,421 551,421 551,421
Robust z-statistics in parentheses
** p<0.01, * p<0.05
35
Table 7: Eﬀect of Job Access by Taxi on Backyard Count, RS1 and RS2 parcels
VARIABLES (1) (2) (3) (4) (5) (6)
parcel area -0.00176** -0.00190** -0.00189** -0.00173** -0.00188** -0.00186**
(-6.870) (-7.506) (-7.355) (-6.770) (-7.463) (-7.289)
sr2 0.706** 0.737** 0.702** 0.682** 0.701** 0.682**
(6.420) (6.759) (6.482) (6.155) (6.513) (6.145)
jobs total grav taxi 0.0144
(1.902)
jobs total 45 taxi 0.00224**
(4.365)
jobs total 60 taxi 0.000713**
(3.060)
jobs lowinc grav taxi 0.0585*
(2.201)
jobs lowinc 45 taxi 0.00784**
(4.167)
jobs lowinc 60 taxi 0.00237**
(2.627)
Constant -1.198** -0.994** -0.977** -1.216** -0.984** -0.968**
(-5.932) (-7.742) (-7.833) (-6.476) (-7.848) (-7.773)
Observations 446,608 446,608 446,608 446,608 446,608 446,608
Robust z-statistics in parentheses
** p<0.01, * p<0.05
36
Table 8: Marginal Eﬀects
% Eﬀect on expected
VARIABLE Change number of backyarders
parcel area 50m2 decrease 10% increase
sr1 increase from 0 to 1 61% increase
sr2 increase from 0 to 1 220% increase
jobs lowinc 60 taxi 38,000 increase (1 std. dev.) 11% increase
37
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Footnotes
∗ We thank the City of Cape Town, where Claus Rabe was formerly employed, for access to
the data used in this paper. We are also grateful to Peter Ahmad, Dr. Edward Beukes,
Hugh Cole, Rob McGaﬃn, Janet Gie, Jaco Petzer, Prof. Ivan Turok, Carol Wright, and
Dr. John Spotten for useful discussions, to Matt Freedman, Mariaﬂavia Harari, Vanessa
Nadalin and Elisabet Viladecans-Marsal for comments, and to Basile Pfeiﬀer for research
assistance. Funding from DFID under the World Bank’s Strategic Research Program is
gratefully acknowledged.
1
Selod and Tobin (2018) oﬀer a related analysis that explores a tenure-security continuum
oﬀered by diﬀerent kinds of property rights in Mali.
2A Brazilian colleague pointed out that slum residents in Brazil will sometimes rent out the
rooftop of their house for construction of an additional informal dwelling, an alternative
approach to raising neighborhood density.
3 Among other theoretical work on housing in developing countries, some focuses on squatting,
with contributions by Jimenez (1984), Hoy and Jimenez (1991), Turnbull (2008), Brueckner
and Selod (2009), Brueckner (2013a), and Shah (2014) (see Brueckner and Lall, 2015, for a
survey). Theoretical papers on informality more generally include Brueckner (1996), Heikkila
and Lin (2014), Cavalcanti, da Mata and Santos (2018), Posada (2018), Cai, Selod and
Steinbuks (2018), and Selod and Tobin (2018).
4 For other empirical work on housing in developing countries by economists, see Follain, Lim
and Renaud (1980), Follain and Jimenez (1985), Friedman, Jimenez and Mayo (1988), Lan-
jouw and Levy (2002), Field (2005), Kapoor and le Blanc (2008), Galiani and Schargrodsky
(2010), Hidalgo, Naidu, Nichter and Richardson (2010), Feler and Henderson (2011), Marx,
Stoker and Suri (2013), Brueckner (2013b), Cavalcanti et al. (2018).
5 The cost of constructing the informal backyard dwelling, which is assumed to negligible, is
ignored.
6 It could be argued that extreme poverty will always push the homeowner to a corner so-
lution, where the entire backyard is rented out. However, even for poor households, the
resulting congestion on the parcel could be undesirable, making retention of some yard area
worthwhile.
7 The derivative of MRS moving downhill along an indiﬀerence curve is MRSc (∂c/∂y )+ MRSy ,
41
where ∂c/∂y is the change in c as y increases. Since ∂c/∂y equals −MRS , which in turn
equals −r from (3), the expression above equals Ω. For the indiﬀerence curve to become
ﬂatter moving downhill along it (for the curve to be convex), MRS must fall, or Ω < 0.
8 Thederivative of (8) with respect to r has the same sign as kyrσ (1 − σ ) − kIσrσ−1 − k 2 I ,
where k = (δ/(1 − δ − µ))−σ . This expression is positive for σ ≥ 1 and for a range of σ
values below 1.
9 If ∂y/∂r > 0 holds, this pattern would be reversed.
10 Note that the model allows the number of backyard renters per formal homeowner to be a
fractional value, ignoring the integer requirement.
11 The equilibrium condition in (14) ignores other informal housing in the city. To take such
housing into account, suppose that inferior access to utilities in non-backyard informal hous-
ing leads to a rent discount, with rent given by r(x, v ) = r(x, v ) − ρ. In response to this
lower rent, informal land consumption outside the backyard area will be Q(x, v ), larger than
Q(x, v ). Let D (x, v ) = 1/Q(x, v ) denote non-backyard informal population density, and let
x > x0 and x ≤ x1 denote the outer and inner ranges of the non-backyard informal area,
which includes land outside the backyard area and possibly inside of it as well (closer to
the job center). Then the population ﬁtting inside the backyard and non-backyard informal
x x
areas equals the LHS of (14) plus x 0 2π D (x, v )dx + x1 2π D (x, v )dx. The new equilibrium
condition requires that this amended expression equals N , which now denotes the overall
informal population. Assuming that x is exogenous, so that the informal sector does not
compete with the formal housing sector located inside x for access to land (as in Brueckner,
1996), only one additional equilibrium condition is needed. This condition says that informal
rent at the edge x of the city equals the agricultural rent ra , so that r(x, v ) = ra . Together,
these two conditions determine x and v . Comparative-static analysis based on these equi-
librium conditions yields the same conclusions regarding backyard housing as those coming
from (14).
12 The aerial data do not give a formal/informal distinction for backyard structures, but GTI
assigns these categories based on broad neighborhood patterns. Backyard structures in
well-to-do neighborhoods with large houses are assumed to be formal (i.e., “granny ﬂats”),
whereas backyard structures in poor neighborhoods containing small houses are assumed to
be informal.
13 An alternative, but dispreferred, backyarding measure is backyarding “density”, or count
divided by parcel area.
42
14 The longer names for SR1 and SR2 are “Single Residential: Conventional Housing” and
“Single Residential : Incremental Housing,” respectively. There is no consolidated spatially
enabled database of public housing delivered over the last few decades, but “Incremental
Housing” (SR2) is a good proxy for land parcels with such housing.
15 This analysis holds the size q of the main dwelling ﬁxed as y varies, so that parcel area q + y
varies in step with y. Suppose instead that larger yards are associated with larger dwellings,
with q = ρy. Then the derivative of y with respect to parcel area equals 1/(1 + ρ) times
dy/dy . But dy/dy now includes a new term capturing the eﬀect of q on y , with the RHS of
(15) now including −(∂y/∂q)(∂q/∂y ) = −ρ∂y/∂q. Given (9), this expression is ambiguous
in sign. However, the negative income eﬀect in (15) still provides a force that tends to make
backyarding fall as parcel size rises.
16 The backyard count variable is generated for 990 of these transportation zones, with the
omitted zones lying outside the low-income areas that contain informal backyard structures.
17 To address the routing-endogeneity concern discussed earlier, we ran Poisson regressions with
gravity job-access measures based on straight-line distance rather than travel time, one for
total jobs and one for low-income jobs. The job-access coeﬃcients in both regressions are only
marginally signiﬁcant, but we view this outcome as reﬂecting the inferiority of the distance-
based variables rather than as evidence of endogeneity. Indeed, regressions of the various
trip-time job-access measures on the distance-based measure show weak relationships.
18
The qualitative results in Tables 4 and 5 are unchanged when the job-access measures are
computed using the natural logs of total and low-income jobs.
19 Land value data per square meter for vacant residential land has been derived from the City
of Cape Town 2015 Valuation Roll. Average land value is computed for transport zones with
a representative sample of vacant residential properties (designated as E04 by the City of
Cape Town Valuation Department). When this land-value measure is used in place of the
job-access variable in the Poisson regressions, the results are unsatisfactory. However, since
these land values show little relationship to job access for SR1 and SR2 parcels, it appears
that they do not capture the willingness-to-pay for land of backyarders, perhaps being more
representative of the formal land market. As a result, the land-value data are not very useful
in testing the hypotheses suggested by the theory.
20 Los Angeles is also considering a $75,000 subsidy for construction of ADUs intended for
rental to homeless people. For websites tracking the California experience with ADUs as
well as parallel developments in Paris, see
https://www.curbed.com/2018/1/16/16897014/adus-development-us
https://www.businessinsider.com/granny-flat-law-solution-california-
43
affordable-housing-shortage-2017-3
https://www.csmonitor.com/World/Europe/2018/0301/Nonprofit-group-builds-
tiny-homes-for-refugees-in-Parisian-private-gardens
44