On the Determinants of Slum Formation∗
Tiago Cavalcanti†
Daniel Da Mata‡
Version: September 30, 2013.
Abstract
This article aims to measure the main determinants of the expansion of informal
settlements. The focus is on how urban poverty, rural-urban migration and land use
regulations impact the growth of slums. We construct a structural general equilibrium model with heterogeneous agents to explain the determinants of slums in urban
areas. The model supports the main empirical evidence regarding slum formation
and it is able to quantitatively assess the role of each determinant of slums growth.
The model is calibrated and estimated to be consistent with several statistics related to the Brazilian urbanization process from 1980 to 2000. We implement several
counterfactual experiments to assess the role of income, migration and land use regulation. We show that these factors explain much of the variation in slums growth
in Brazil between 1980 and 2000. We also perform ex-ante evaluation of the impacts
of slum upgrading interventions and show how policies may have unintended adverse
effects on slum formation.
Keywords: Slums; rural-urban migration; city growth; land use regulations
JEL Classification: O18, O15, R52
1
Introduction
Slums represent a large portion of housing markets in developing countries1 . Although the
definition of slums varies depending on the country, slums are always associated with some
∗
We have benefited from discussions with Toke Aidt, Klenio Barbosa, Thomas Crossley, Petra Geraats,
Chryssi Giannitsarou, Pramila Krishnan, Alice Kuegler, Danilo Igliori, Povilas Lastauskas, Hamish Low,
Diana Motta, Cezar Santos, and Anne Villamil. All remaining errors are of our responsibility.
†
Faculty of Economics, University of Cambridge.
‡
IPEA and Faculty of Economics, University of Cambridge
1
In this paper we will use the words informal housing, slums, and squatter settlements interchangeably.
By and large, slums are characterized by overcrowding, lack of access to basic urban services, and illegal
occupation of land (UN-Habitat (2003)). Squatting means illegal dwelling on a land one does not own
(Jimenez (1985)).
1
sort of deprivation such as insecurity of land tenure, low standards of urban services, and
even non-durable housing structure. According to UN-Habitat (2003), in 2001 more than
30% of the world’s urban population lived in slums. Moreover, UN-Habitat (2003) points
out that slums will rise in the following decades and by 2030 roughly 2 billion people would
live in slums. Despite the increasing number of slums and squatter dwellers around the
world, not much is known about the economic incentives associated with the decision of
dwelling in informal settlements (Brueckner and Selod (2009)).2
This paper studies the determinants of informal housing and investigates the economic
incentives concerning squatting. It also performs ex-ante evaluation of the impacts of policy
interventions on slums. In particular the goal of this paper is to quantify the contribution
of urban poverty, rural-urban migration, and land use regulations to the growth of informal housing. In order to achieve this goal, we construct a structural general equilibrium
model of a city with heterogenous agents to explain the determinants of informal housing
formation. The model supports the main empirical evidence regarding slums formation
and is able to quantitatively assess the role of each determinant of slums growth. The
“structure” of the model is justified by anecdotal evidence and by Microdata from Caju
slum dataset3 from Brazil. The model is calibrated and estimated to be consistent with
several statistics related to the Brazilian urbanization process during the period from 1980
to 2000 (with a focus on the city of São Paulo). We use the Brazilian case to motivate the
analysis and to estimate the model even though the theoretical framework can be applied
to other developing countries. After calibrating and estimating the model, we simulate
several counterfactual events in order to disentangle the impact of specific factors on informal housing growth. We then present policy simulations to verify the impact of policies
that aim to make the formal housing market more accessible to the urban poor.
Data facts from Brazil suggest that the access to formal urban land becomes difficult
to low-income families facing (a) increasing housing demand (due to rapid urbanization
and immigration to cities); (b) economic stagnation, deterioration of real income and
persistent income inequality; and (c) stricter regulations to build. We also present reducedform evidence (using panel data from Brazilian cities) connecting the data facts. Even
though the reduced-form evidence indicate strong correlations regarding the determinants
of slums growth, the regression results do not show the mechanisms through which income,
migration and regulations affect slums formation. The channels are explained by using a
simple general equilibrium model of a city.
The model formalizes the household decision on the type of housing tenure: formal or
2
There is large literature which investigates the determinants of informal production in developing
countries.
3
The municipality of Rio de Janeiro carried out a survey in 2002 and collected data for more than 5,000
people in the “Caju” slum complex. The Caju data was collected to a land titling project in Rio and it is
explained in more details in Appendix A.
2
informal housing. Agents are heterogeneous in respect to their labor productivity and they
derive utility over a non-housing consumption good and housing services. When choosing
between the two tenure modes, an agent faces the following trade-off: if she chooses to
live in an informal settlement she escapes from paying property taxes and from complying
with building regulations, but informal housing is insecure (due to, say, exogenous risks
of eviction and demolition by the government or property theft by other households) and
therefore she incurs (i) a utility discount per housing space and (ii) protection costs. We
model protection costs in the form of foregone labor income: agents must spend part
of her time to be physically present in order to protect the informal plot. The basic
economic mechanism of the model shows that land costs, property taxation, and building
regulations act as barriers that inhibit poor households from entering the formal housing
market. As income grows, the protection costs (forgone labor income) are high enough such
that households are better off living in the formal housing sector. Our model shows that
there is a labor productivity cutoff (associated with the opportunity costs of protecting
the informal plot) separating formal and informal housing agents.
The model includes also zoning constraints that may interfere households’ decisions.
Specifically, according to building regulations set (exogenously) by the local government,
households who choose to live in formal housing units must occupy a minimum lot size
(MLS ). Households unable to meet the minimum lot size requirement are bound to live in
informal settlements. As a result, there is an additional income cutoff that makes formal
housing affordable. We compare the two labor productivity cutoffs which arise from the
model (the one associated with the opportunity costs of protecting the informal plot and
the one that make the MLS affordable) to analyze the cases when MLS regulations are
not enforced. The model points out that man-made regulations may induce more slums.
Housing prices are determined endogenously in the model. In equilibrium, formal
housing cost differs from informal housing cost, in agreement with the literature concerning
price (and rent) differentials between formal and informal housing units (Jimenez (1984);
Friedman, Jimenez, and Mayo (1988)). Even though the model is very stylized, due to
the income heterogeneity assumption there is no closed-form solution for the stationary
equilibrium of the model. As a result, we use a numerical algorithm to compute the
model equilibrium solution. Exogenous shocks (such as income shocks and changing land
regulations) alter the share of households in informal settlements. Comparative statics
exercises on the determinants of slums growth are presented.
The model is calibrated and estimated to be consistent with several statistics related
to the Brazilian urbanization process from 1980 to 2000. Since our model is one of a
city, we use data from the city of São Paulo during the estimation (instead of data for
the entire country). Due to data restrictions, we calibrate some parameters of the model
instead of estimating them. Other parameters were obtained by minimizing a loss function.
3
The estimated parameters of the structural model are obtained via a nested fixed point
algorithm. We use a distance minimization procedure in order to fit the model to the data
from the Brazilian urbanization process. Analogous to moments conditions, we match
predictions of the model to their data counterparts. Thus we obtain the key parameters
that minimize the distance between the predicted (by the model) and the empirical slums
share and other targets. The data stem basically from surveys conducted by the Brazilian
Institute of Geography and Statistics (IBGE ), specially the Population Censuses of 1980,
1991, 2000, and 2010. We discuss the data in greater details in the following section and
in Appendix A.
Our model is able to account for a great part of the variation in slums growth during the
last decades in Brazil. Income level, income inequality, rural-urban migration and zoning
explain much of the variation in slums growth during 1980-2000. Our policy simulations
concentrate in two groups: policies to decrease barriers to formalization and slum upgrading interventions. Our simulations point out that decreasing barriers to formalization has
great impact on slums’ reduction. By contrast, slum upgrading interventions can have unintended adverse impacts as upgrading may turn informal housing “more attractive” (and
induce more people to live in slums). Slum upgrading interventions may change adversely
the incentives regarding the decision to whether dwell in slums. Additionally, we perform
a welfare exercise in order to understand the heterogenous impacts of the simulated policies. The main lessons from the simulations are that (i) one must differentiate groups of
policies and that (ii) average welfare gains are driven mainly by the subpopulation directly
affected by the slum upgrading intervention (even though great part of the population may
be worse off after the policy because of higher housing prices).
In this paper, we define informal housing as housing units characterized by low provision of public infrastructure, lack of property rights and non-compliance with existing
building regulations. In Brazil, there is no official definition of “informal housing”, but a
working definition called “subnormal agglomeration” is obtained from the Brazilian Bureau of Statistics (IBGE) Population Censuses. According to the Censuses, a subnormal
agglomeration satisfies three conditions: (i) a group of at least 50 housing units; (ii) where
land is occupied illegally and (iii) it is urbanized in a disordered pattern and/or lacks basic public services such as sewage or electricity. Therefore, there is a connection between
the definition of “subnormal agglomeration” and the notion of a “slum”. Because illegal
occupation of land plays a central role in the model, we will employ the words informal
housing, squatter and slum as synonymies throughout the paper.4
How do income, migration, and land use regulations impact informal housing forma4
In Brazil, slums are better known as “favelas”, where there is lack of public services and illegal
occupation of government-owned land, marginal land (floodplains or hillsides) or under dispute land.
Another type of informal housing is called “Cortiços”: high-density housing units located in central older
parts of metropolitan areas.
4
tion? Income seems to be one of the main determinants of household location choice
(for example, Glaeser and Kahn (2004) and Kopecky and Suen (2010)). As for the decision of living formally or informally, a higher income level might induce people to live
in formal housing. In our model, individuals with higher ability (and income) tend to
live in formal housing units and this is consistent with findings in the literature (e.g.
Friedman, Jimenez, and Mayo (1988)). In other words, the model is consistent with the
fact that poorer agents are more likely to live in informal settlements.
Rapid rural-urban migration increases the competition for land and drives land prices
up. Migrants facing high land and housing prices find it harder to live in the formal housing
sector. Even current residents suffer from the high prices and might end-up moving to a
informal settlement. UN-Habitat (2003) argues that the rapid and enormous rural-tourban migration intensifies slum formation. Todaro (1969) points out that the relatively
higher incomes of urban areas attract rural migrants into the “congested urban slums”,
while Frankenhoff (1967) argues that slums in Latin American cities act as staging areas
for rural immigrants in search of a better life. In the model, migration increases overall
housing demand and, as a results, housing prices increases. Higher housing prices impact
the decision on the type of housing tenure and may induce people to live informally.
Land use regulations impact housing markets in various forms. Stricter land use regulation increases existing home prices (Hamilton (1978), Quigley and Raphael (2005)).
Regulation affects the cost of housing and consequently housing prices and, as a result,
interfere the decision of whether to live formally or not. Excessive regulation can create
a shortage of urban land to construct, lack of housing supply, higher (formal) housing
prices, and induce informal housing expansion. In sum, inappropriate planning and poor
land use governance could enhance squatting. For instance, in Brazil, a federal land use
law from the late 1970’s stipulated that developers should employ specific construction
parameters. In addition, the same law allowed municipalities to establish their own land
use parameters to promote pro-poor housing programs.5 Lowering national subdivision
regulations may create more affordable housing. However, several municipalities in Brazil
have enacted land use laws with stricter parameters instead (as will be discussed later in
the data facts in Section 2). More stringent land laws mean greater difficulties to construct
and to be located in the formal housing sector. As mentioned above, in the present model,
the minimum lot size impacts households’ decision of tenure type as individuals unable to
meet the minimum housing space requirement must live in informal settlements.
The remainder of this section discusses the related literature and highlights our contribution. The data facts are presented in Section 2. Section 3 presents the model. Section
4 discusses the steps taken to calibrate the model and to estimate its parameters. Section
5
Municipalities are the third level of administrative (autonomous government) division according to
the Brazilian Constitution.
5
5 shows the quantitative analysis to measure the determinants of slums formation and to
perform ex-ante policy simulations. Section 6 contains concluding remarks.
1.1
Literature
This article follows a trend of the literature which estimates the parameters of the model
to explore quantitatively how different policies affect urban phenomena (for instance,
Chatterjee and Carlino (2001), Baum-Snow (2007), Brinkman, Coen-Pirani, and Sieg (2010),
Kopecky and Suen (2010), and Michaels, Rauch, and Redding (2012)). Our paper differs
from these papers in an important way as (to our knowledge) none of the quantitative
papers investigate the issue about informal housing6 .
This paper is also connected to the literature on urban squatting. Protection costs
and defensive expenditures play an important role in studies concerning urban squatting
(for instance, Jimenez (1985), Field (2007), Brueckner and Selod (2009), and Brueckner
(2013)). Field (2007) provides evidence about the importance of the forgone labor income
when agents lack property title. Field (2007), in a study on a titling program carried
out by the Peruvian government, concluded that land titling has a substantial impact
on the number of working hours. In order to protect the informal plot, households may
have to be active and participate in meetings, demonstrations, and other actions. Jimenez
(1985) points out that indeed many squatter communities are well-organized in terms
of motivation and cohesion. Moreover, Brueckner and Selod (2009) models a community
organizer who set pecuniary defensive expenditures to be paid by each household in the
informal housing sector. These expenditure are used by the community leader so as to
avoid evictions. Brueckner (2013) models a rent-seeking community organizer and the
effects of competition among different community organizers. The main differences of this
paper from previous works on urban squatting are mainly two: (i) Firstly, we set up a
general equilibrium model of a city with heterogeneous agents while most papers use a
partial equilibrium analysis or a homogenous agents setting; and (ii) secondly, we not
only derive the qualitative properties of the model, but we also study it quantitatively
by estimating the parameters of the model using evidence from Brazil and implementing
ex-ante policy evaluation. We believe that our findings have far reaching implications for
policies in developing countries.
Finally, our focus on policy evaluation also connects with papers on the effects of slum
upgrading interventions. This literature has focus more on the (ex-post) evaluation of
policies. Examples include the studies on how land title influences outcomes in slums
6
There is large literature which investigates the determinants of informal production in developing
countries. In this literature, given policies and institutions heterogeneous agents choose either to run a
formal or an informal business (e.g. Amaral and Quintin (2006) and Antunes and Cavalcanti (2007)). In
this literature, the entrepreneurial choice of households depend on their entrepreneurial income while in
our model the type of housing choice of households depend on their labor productivity.
6
in Ecuador, Peru and Argentina. Lanjouw and Levy (2002) point out that title raised
properties’ value in Ecuador. In Peru, Field (2005) argues that land title had significant
impact on renovation in slums, while Field (2007) shows that land title increased labor
hours of slum dwellers. In Argentina, Di Tella, Galiani, and Schargrodsky (2007) provide
evidence on how titling programs change household’s beliefs and Galiani and Schargrodsky
(2010) point out that property rights increased housing investment, reduced household
size, and enhanced education of the children. We aim at contributing to this literature
by performing an ex-ante evaluation of key policies on slums. We also show the channels
through which such policies affect households and their housing tenure choices. In this
sense, this paper complements the ex-post literature. This paper provides evidence on the
impacts of slum upgrading policies considering general equilibrium effects. We show how
policies may have unintended adverse impacts on slums formation.
2
Data Facts and Reduced-Form Evidence
In this section we show how the access to (formal) urban land becomes difficult to lowincome families facing increasing housing demand due to rapid rural-urban migration (Fact
1), deterioration of real income and persistent income inequality (Fact 2), and stricter
regulation to build formal housing units (Fact 3). We connect the data facts by presenting
reduced-form evidence for 123 urban agglomerations in Brazil. Data sources and definitions
are shown in Appendix A.
2.1
Data Facts
Fact 1: There has been a rapid urbanization in Brazil during the last decades. Using
data from the Brazilian Population Censuses, Table 1 documents a steady increase in total
population in Brazil from roughly 50 million people in 1950 to over 190 million in 2010.
Moreover, the urban share of population jumped from 36% to 84% in 1950-2010. In other
words, according to the 2010 Population Census less than 16% of the population were in
rural areas. Population is growing basically in cities and Brazil rapidly became an urban
country. It is estimated that urban population growth will continue in the next decades
(UN (2004)). As a result, housing demand will continue to increase in cities.
Fact 2: The surge in urban population has been accompanied by stagnant real incomes
and persistent income inequality (from 1980 to mid 1990s). Figure 1(a) shows the evolution
of real labor income, while Figure 1(b) shows the evolution of income inequality (measured
by the Gini coefficient) from 1980 to 2009. We used a nonparametric local linear smoother
to obtain the “trend” path for the real income and income inequality time series. By
7
Table 1: Population in Brazil: 1950-2010
Year Urban Population
1950
36.2%
1960
44.7%
1970
55.9%
1980
67.6%
1991
75.6%
2000
81.2%
2010
84.4%
Rural Population
63.8%
55.3%
44.1%
32.4%
24.4%
18.8%
15.6%
Total Population
51,944,397
70,070,457
93,139,037
118,562,549
149,094,266
171,279,882
190,755,799
Notes. IBGE, Population Censuses 1950-2010.
mid-2000 real wages did recover the 1980’s values after a sharp drop in the early 1990’s.
Historically, Brazil presented a record of high economic growth during the post-war era
until 1980. The 1980s are known as the “lost decade”, when Brazil’s economic growth
slowed down, after a severe sovereign debt crisis. Brazilian National Accounts show that
Gross Domestic Product (GDP) growth was nearly 10% per year during 1968-1977, while
GDP grew by only 1.6% per year on average during 1981-1990 when the economy lost
its dynamism. Brazil has great regional disparities, but the country as a whole suffered
from the economic recession during the 1980s. Several economic reforms were implemented
during 1990s, but Brazil experienced only limited recovery. Only recently trended growth
has increased. Notice that Brazil presents a very high and persistent income inequality,
although it has recently declined.
Fig. 1: Evolution of Real Income and Income Inequality
Real Income
Income Inquality
750
0.64
Gini Index
Trend: 1981−2009
0.63
700
0.62
650
0.61
0.6
600
0.59
550
0.58
0.57
500
Real Income
Trend: 1981−2009
Trend: 1981−1993
450
400
1980
1985
1990
1995
Year
2000
2005
0.56
0.55
0.54
1980
2010
(a) Real Income
1985
1990
1995
Year
2000
2005
2010
(b) Income Inequality
Notes: Nonparametric local linear smoother used to obtain the “trend” paths. We computed two trends
for real income (one between 1981 and 1993 and the other for 1981-2009) and one trend for income
inequality (for 1981-2009).
Fact 3: The last decades are also associated with the adoption of stricter land use regulations by Brazilian municipalities. A 1979 federal land use law (Federal Law 6,766/79)
stipulated that developers in Brazil must follow federally-mandated construction parame8
ters concerning urban land occupation and subdivision (such as basic infrastructure standards and minimum lot size). One of the construction parameters of the federal land use
law was a minimum lot size of 125 m2 . Federal Law 6,766/79 allowed municipalities to
change the land use parameters to create locally-suitable land use parameters for specific
urbanization projects to build public housing7 . According to Table 2 several municipalities
have enacted their own land use laws, but instead of lowering federal requirements, the
majority of those municipalities established bigger minimum lot sizes. Precisely, out of the
1,482 municipalities that have established their own land use laws, 1,183 established larger
minimum lot sizes.8
Table 2: Number of municipalities adopting local land use laws - from 1979
until 1999 - and the the minimum lot size
Years/Minimum lot size
1979-1983
1984-1988
1989-1993
1994-1999
Total
Up to 125 m2
103
36
60
100
299
More than 125 m2
334
165
280
404
1183
Total
437
201
430
504
1482
Notes. The Federally-mandated minimum lot size is 125 m2 . The second column
shows the number of municipalities that have lot sizes smaller or equal to 125
m2 . The third column the number of municipalities that have adopted stricter
parameters. See appendix A for details.
Fact 4: There has been a rise of slums and slum dwellers in Brazilian cities concomitantly
to (i) the high urban population growth, (ii) the stagnant real income and persistent income
inequality, and (iii) to the stricter land use regulations. Brazilian Censuses data show that
informal housing is steadily increasing in Brazil (see Table 3). Slums data in Brazil stem
from Population Censuses of 1980, 1991, 2000, and 2010. Even though the Censuses data
are capable of capturing the trend of slums growth, the Censuses tend to underestimate
both the amounts of slums units and slum dwellers. The case of São Paulo is illustrative:
according to the 1991 Population Census, there was roughly 650,000 slum dwellers in the
city, while a “Slums Census” carried out the municipality in 1993 had shown that more
than 1,9 million people live in slums. We discuss data on slums in greater details in
appendix A.
7
Previous law regarding land policy did not set national-level construction parameters (Federal Decrees
58/37 of 1937 and 271/67 of 1967). In contrast to these federal decrees, the Federal Law 6,766/79 stipulated
parameters to building housing units in the country.
8
In fact, lowering national subdivision parameter is considered unconstitutional in Brazil. But this
does not rule out the argument concerning the (potential) relationship between municipalities increasing
their minimum lot sizes and slums growth.
9
Table 3: Population, Housing and Slums in Brazil: 1980-2010
123 Urban Agglomerations
Housing units(a)
Slum units(b)
Population(c)
Slum dwellers(d)
% Slums(b/a)
% Slum dwellers (d/c)
1980
1991
14,012,484 20,564,931
476,292
943,667
62,390,783 80,885,091
2,224,164 4,084,051
3.40%
4.59%
3.56%
5.05%
2000
27,126,584
1,488,779
96,951,317
5,775,890
5.49%
5.96%
2010
34,188,992
2,732,576
110,287,840
9,516,899
7.99%
8.63%
Notes. Data from Da Mata, Lall, and Wang (2008) and tabulations from the 2010 Population Census in Brazil. Slum data from the 2010 Census is not directly comparable with that
of other Censuses (IBGE (2011)).
2.2
Reduced-Form Evidence: Correlations
The data facts suggest that changes in income, population and regulation measures may
have important implications for the evolution of informal housing in Brazilian cities. Now,
we present reduced-form evidence that aims at connecting the four stylized facts. We
assume an empirical specification in additively separable form as
yit = µ(Xit ) + !it .
where yit is the share of slum dwellers in city i at year t, Xit are the city-level determinants of slums growth (such as average income, income inequality, urban regulation
measures and rural-urban migration), µ(Xit ) is the mean function, and !it represents the
unobservable determinants of slums growth. We impose a parametric and linear form
for the mean function, i.e., µ(Xit ) = α + β ! Xit . Therefore, the empirical specification is
linear-in-parameters:
yit = α + β ! Xit + !it .
Table 4 shows simple correlations regarding the potential determinants of slums formation at city level: per capita income, income inequality (measured by the Gini coefficient),
urban regulation, and population density. We use panel data for 123 urban agglomerations
in Brazil covering the period 1980-2000.9 The results are for Pooled OLS, but they are virtually the same when we use other panel methods such as random effects (see Appendix C).
Note that a fixed-effects model is unable to estimate the time invariant variable (zoning)
and it is inefficient to estimate the rarely changing variables (such as income inequality
measured by the Gini coefficient). Therefore, we do not estimate the reduced-form by
conventional fixed effects. We also used the fixed-effects vector decomposition proposed by
Plümper and Troeger (2007) and results are similar. Summary statistics for the variables
in the Pooled OLS regressions are in Table 11 in Appendix C.
9
We do not use data for 2010 because slums data from the 2010 Census is not directly comparable with
that of other Censuses (IBGE (2011)).
10
Table 4 shows that there is a positive correlation between slums growth and all four
potential determinants. As shown by the data facts, one expects that greater income
inequality, stricter regulation and greater urban population are associated with more slums.
Notice that after controlling for other factors, mean per capita income is either positive
correlated with slums growth (see columns (iv) and (vii)) or not statistically significant (see
column (v)). One potential explanation is that places with greater per capita income have
higher housing prices that may act as a barrier to enter the formal housing market. We
discuss this issue in our theoretical model, which suggests an ambiguous effect of income
on slums.
Table 4: Reduced-form Evidence: Pooled OLS
VARIABLES
% of Slum Dwellers
(i)
(ln) per capita Income
(ii)
(iii)
(iv)
0.0119***
(0.0029)
0.0156**
(0.0064)
0.235***
(0.0526)
0.0117***
(0.0041)
0.0105**
(0.0045)
Income inequality (Gini index)
0.172***
(0.0482)
Urban regulation
(ln) Population Density
Constant
Observations
R-squared
-0.0430*
(0.025)
-0.0775***
(0.026)
0.0056***
(0.002)
-0.210***
(0.054)
369
0.013
246
0.038
369
0.017
246
0.077
ln # of Slum Dwellers
(v)
(vi)
0.0092
3.507***
(0.0060)
(0.841)
0.257***
35.99***
(0.0507)
(6.991)
0.0102**
1.709**
(0.0039)
(0.704)
0.00636***
(0.0018)
-0.215**
-36.69***
(0.051)
(6.911)
246
0.127
246
0.122
(vii)
2.337***
(0.851)
40.02***
(6.435)
1.444**
(0.702)
1.161***
(0.223)
-37.63***
(6.690)
246
0.216
Notes. Robust standard errors in parentheses. All the regressions are for 123 urban agglomeration in Brazil. The pooled OLS is for 1980,
1991, and 2000. Therefore, there are 369 observations in each regression. The dependent variables are the share of slum dwellers in each
urban agglomeration (columns (i) to (v)) and the log number of slum dwellers (columns (vi) and (vii)). Each urban agglomeration is
formed by more than one municipality - the lowest autonomous administrative entity in the Brazilian federation. The explanatory variable
“urban regulation” is a dummy variable that takes value 1 if the majority of people in the urban agglomeration lives in municipalities
with own land use law. The Gini index is measured only in two year (1991 and 2000), and this explains the 246 observations in regressions
(ii) and (iv).
*** p<0.01, ** p<0.05, * p<0.1
We then perform some robustness checks. We test each determinant separately and
combinations of them (see columns (i) to (vii) in Table 4). Results are also similar when we
use urban population density instead of total population density. We employ two different
dependent variables: % of slum dwellers and the (log) number of slum dwellers in the urban
agglomeration. Besides, we also use geographical controls, such as mean temperature and
precipitation, and results are roughly the same.
The coefficients of the reduced-form results give us the directions of the correlations,
but the exact mechanisms through which income and land regulation affect of slums growth
are unclear. We construct a (tractable) structural model to explain the channels related to
slums formation. Using realistic assumptions, the structural model explains the behavior
of households regarding their decision on what type of housing unit to live: formal or
informal. The model supports the main empirical evidences regarding slums formation
11
and it is able to quantitatively assess the role of each determinant of slums growth. The
model is presented in the next section.
3
The Model
We construct a general equilibrium model of a city to explain the determinants of informal
housing formation. The model includes households with distinct income levels due to
heterogeneous ability choosing their residential tenure mode, i.e., living either in formal
or informal housing. Including informal housing allows the model to explain important
features of housing markets in developing countries. The assumptions of the model are
motivated by anecdotal evidence and by using microdata from a survey carried out by
the Prefecture of Rio de Janeiro in 2002 for more than 5,000 people in the “Caju” slum
complex. The Caju data was collected to a land titling project in Rio and it is explained
in more details in Appendix A.
3.1
The Environment
Households. There is a continuum of households of measure P , each of whom with labor
productivity λ ∈ (0, ∞). The distribution of abilities in this economy follows a continuous
cumulative distribution Υ(λ), where Υ(0) = 0 and limλ→∞ Υ(λ) = 1.
Households have to decide on their housing tenure type: formal or informal housing.
They obtain utility over non-housing consumption (a homogeneous good c) and housing
services (sj ), where j equals F if formal housing and I if informal housing. The utility
function is specified as
U (c, sj ) = c1−α sαj ,
where α ∈ (0, 1) and j = F, I.
For a given level of consumption c, utility derived from formal housing is higher compared to informal housing. Housing service flow (sj ) entails housing space (h), public goods
surrounding the housing unit (g), and a parameter θ (that equals one to formal housing
and less than one to informal housing). We assume that housing service flow is a linear
function, i.e.,

gh if formal housing (j=F),
sj =
θgh if informal housing (j=I),
where θ ∈ (0, 1). The expression θg means that informal housing agents do not reap all
the benefits from public goods provision within the city boundaries. The parameter θ
may be seen as a congestion cost due to live in high density neighborhood (as is typically
the case of slums). Caju’s slum data supports the low provision of public services and
12
high congestion costs in informal settlements: the main complain of Caju’s slum dwellers
is violence (circa 50% of the population stated that violence is the main problem in the
community), while the lack of public services was the third major complain (14%)10 .
Household’s labor income is given by (1 − τ )λw, where w is the average wage of the
city, τ is the labor income tax, and λ is the labor productivity of the household. A household allocates her labor income between non-housing consumption (c), housing services
(s), and a property tax (η). Only households in formal housing pay a property tax η - a
cost associated with being located in the formal housing sector. One can argue that slum
dwellers escape from paying for public utilities such as electricity. Therefore, the parameter η could also incorporate the payment of public utilities by formal housing residents,
while informal housing residents do not pay for such public services. Caju’s slum data
supports the assumptions of no-payment of property taxes by slum dwellers (94.58% of
the households in Caju slum do not pay property taxes), but 92.01% of the residents in
Caju pay electricity bills.
A household has one unit of productive time. If the household decides to live in
the informal sector, she occurs in protection costs (Ψ). We assume that there is a risk
associated with property theft by other households that decided to dwell illegally or even
with eviction and demolition by the government (Field (2007)). Informal housing lacks
property rights and is associated with insecurity due to exogenous risks of eviction and
demolitions by the government. Therefore, if an agent chooses to dwell illegally, she will
spend 1 − Ψ of her time working, i.e., informal housing agents allocate part of their time
to protect their informal plot. This is a reduced form approach to represent the cost of
informality and is particularly useful for our quantitative analysis. The implicit assumption
is that if households living in informal housing do not spend time or resource in protecting
their land, then they will be evicted. This implies that spending such time and resource
is incentive compatible.
We model protection costs in the form of foregone labor income: the agent must spend
part of her time to be physically present in order to protect the informal plot. Precisely,
protection costs are a function of labor productivity and housing space: Ψ(λ, h). The
greater the productivity, the greater the opportunity cost associated with the protection
of the plot; similarly, greater housing space consumption is associated with more time
spending to protect the plot. Protection costs are assumed to be given by the following
expression: Ψ(λ, h) = ψ(1−τ )wλh, where ψ is a constant. Therefore, ψ(1−τ )wλ represents
the protection cost per unit of housing space 11 . The parameter ψ reflects both the penalty
costs and the probability of being caught by the government due to live in a informal
settlement.
10
The second main complain was high housing prices (17%).
Instead of forgone labor, the opportunity cost of informal housing could be modeled as defensive
expenditures paid to, say, a community leader. This assumption would generate similar results.
11
13
Moreover, if households choose to live in formal housing, she must comply with building
regulations. In this paper, a formal housing unit must comply with a specific buildingrelated requirement: the minimum lot size (MLS ). In the model, the MLS is represented
by parameter h, which is exogenously set by the local government.12
In sum, a household faces the following trade-off: if she chooses to live in an informal
settlement she escapes from paying property taxes (η) and from complying with the minimum lot size regulations (h), but informal housing is insecure and therefore she incurs a
utility discount per housing space (θ) and an opportunity cost related to informal housing
(ψ). As a result, the informal housing sector in this paper is related to the general notion
of a slum, where there is insecure land tenure (represented by the opportunity cost ψ),
low infrastructure provision (represented by θ), non-compliance with building regulations
(represented by h).
Notice that parameters θ and ψ may represent other costs of informal housing such as
the adverse effect of lack of job networks for slum dwellers. Specifically, ψ is associated
with any time spent due to living at a slum. For instance, parameter ψ could also represent
some sort of stigma informal housing agents might suffer. Anecdotal evidence on fires in
slums supports the idea that slum dwellers spend extra time on (re)constructions after fire.
In some cases, the same slum is destroyed by fire more than once in a single year: this was
the unfortunate case of Favela Moinho in São Paulo in 201213 . In addition, evidence shows
that after a fire the slum dwellers also suffer from robbery from opportunistic thefts that
try to enter houses taking advantage of the fire despair14 .
Consumption Goods. The homogeneous non-housing consumption good is the economy’s numeraire. Its production takes place in a competitive environment where all
firms have a constant returns-to-scale production function Q(N, K) = BN υ K 1−υ , where
υ ∈ (0, 1) is the labor share in production, N represents units of labor efficiency, K represents units of capital and B is a total factor productivity parameter of the city. Labor
is supplied by households given the wage rate w. Capital, K, is an elastically supplied
factor with rental price r determined outside the city. The optimization problem of the
representative firm operating in this sector is represented by:
π = max{BN υ K 1−υ − wN − rK}.
N,K
12
The minimum lot size is exogenous in the model, i.e., we assume that the city and its households take
the MLS parameter as given. There are cases where building regulations are nationally mandated, such
as in the case of municipalities that followed the Brazilian national law stipulating the minimum lot size
of 125m2 .
13
http://g1.globo.com/jornal-nacional/noticia/2012/09/incendio-em-favela-de-sp-deixa-uma-pessoamorta-e-300-desabrigadas.html
14
http://noticias.bol.uol.com.br/brasil/2012/11/27/incendio-em-favela-de-manaus-deixa-545-familiasdesabrigadas.jhtm
14
N υ
The first-order condition for K is r = (1 − υ)B( K
) , while the first-order condition for L
K 1−υ
is given by w = υB( L ) . Combining both conditions generates the labor demand of the
city:
$ (1 − υ)B % 1−υ
υ
w = υB
.
(1)
r
Equation (1) shows that labor demand is perfect elastic because the rental rate of capital
r is exogenous to the city point of view. As a result, the wage rate w in the model is
determined solely by the labor demand equation. Observe that in equilibrium profits are
zero and firm ownership is unimportant.
Housing. Housing space is produced using land (L) and capital (K): L is available in fixed
supply, while K is elastically supplied with price r. The production function of housing
space is H(L, K) = Lγ K 1−γ , where γ ∈ (0, 1). Land price (pL ) is the same at every unit
of land and is privately owned. Land belongs to a group of absentee landlords who spend
land rents outside the city. Total land cost is pL L, where pL is the land price and L is the
quantity of land.
Developers have the following optimization problem:
Π = max{pLγ K 1−γ − pL L − rK},
L,K
where p is the housing price. Using the first order conditions for this problem, then:
pL = γ(
1
1 − γ 1−γ
) γ pγ .
r
(2)
Housing supply is obtained by manipulating the first-order conditions for this problem:
s
H = Lp
1−γ
γ
$ 1 − γ % 1−γ
γ
r
.
(3)
The model generates a constant price-elasticity housing supply function in the city.
The price-elasticity of housing supply is determined by the parameter γ. Housing price p
is endogenously determined by the equilibrium in the housing market.
Government and Land Law Enforcement. Let e(g) be local government expenditures
and assume that e(g) is linear in the public good g, i.e., e(g) = g. The government finances
expenditures through a property tax rate (η) paid only by formal housing residents and
by a labor income tax (τ ) paid by all workers. Define E F (o) as the measure of households
who live in formal housing units. We will define E F (o) precisely shortly. Government runs
a balanced budget and therefore
g=
&
ηRH hF (λ)dΥ(λ) +
E F (o)
15
&
∞
0
τ wλdΥ(λ),
where RH is the housing rent and hF (λ) is the housing size chosen by each formal housing
household. Property tax η and income tax τ are government parameters. Note that the
local government spending g enters the utility function of all households, but there is a
discount in utility, θ ∈ (0, 1), for informal housing agents.
It has been said that informal housing agents do not pay property taxes. But what
is the reaction of the local government? The land law enforcement is exogenous in the
model. For simplicity, we assume that government spending involves a public good and the
security of land tenure for those household that have opted for dwelling in formal housing
units. Then, only households in the formal housing sector can reap all the benefits from
public expenditure. Some papers model the decision of whether or not execute evictions.
A recent example is Turnbull (2008) where eviction occurs with some probability. In a
different approach, Brueckner and Selod (2009) model a “no-eviction” constraint: in their
model the squatters are organized by a community leader and the cost of evictions is a
function of the size of squatter group and of monetary contributions paid by the squatters.
The larger the size of the squatter group and the monetary payments, the greater is the
expropriation costs. In equilibrium, the eviction cost set by the organizer is high enough to
landowners find eviction unattractive. We follow Brueckner and Selod (2009) by adding
a no-eviction constraint in the model: We implicitly assume that there is a “collective
threat” from all time spent by informal housing agents to protect their plots such that the
government does not have incentives to carry out evictions15 .
3.2
Decision Problems and Properties of the Model
Formal housing problem. Define the vector of prices, policies and institutions by
o = (w, RH , ψ, τ, η, h). Taking w (average city wage) and RH (housing rent) as given,
households who have chosen to live in formal housing solve the following problem:
V F (λ; o) = max [c1−α (gh)α ],
c,h
15
(4)
The assumption that the government is capable of protecting the plot of those who stay in the formal
housing market (and pay property taxes) is central to the present analysis. How come the government is
able to enforce property tax collection, but does not prohibit squatting? Squatting in developing countries
was accompanied by huge rural-urban migration. For instance, in Brazil the urban population was 80
million in 1980 and 160 million in 2010. In 30 years, the urban population growth was equivalent to
the population size of Germany or the combined population of Spain and Canada. In this scenario,
the government may not be able to prevent every single land invasion, specially when there is vacant
land. At the same time, the government cannot guarantee public goods provision and land security for
all new residents and, therefore, those who pay property taxes might be the only ones benefiting from
government actions. Government protection (of plots) could induce “voluntary” payment of property taxes
by households.
16
subject to
c + [RH (1 + η)]h ≤ wλ(1 − τ ),
(5)
h ≥ h ≥ 0,
(6)
c ≥ 0.
(7)
The budget constraint (5) states that expenditures on consumption and housing cannot
be larger than disposable income. Equation (6) means that there is a minimum housing
space that stems from minimum lot size (MLS ) regulations from a zoning constraint in the
city. When equation (6) is not binding, the optimal choice of consumption and housing
for formal households are determined by:
cF (λ; o) = (1 − α)wλ(1 − τ ),
hF (λ; o) = α
(8)
wλ(1 − τ )
.
RH (1 + η)
(9)
Using these two equations into the utility function yields the following value function:
F
Vnb
(λ; o) = αα (1 − α)1−α w(1 − τ )λ[RH (1 + η)]−α g α .
(10)
When equation (6) is binding, we have that
cF (λ; o) = wλ(1 − τ ) − RH (1 + η)h,
(11)
hF (λ; o) = h.
(12)
In this case, the indirect utility function of the household is given by:
VbF (λ; o) = [w(1 − τ )λ − RH (1 + η)h]1−α hα g α .
(13)
Constraint (6) binds only for sufficient small values of λ. Moreover, there is a minimum
H (1+η)h
value of λ, which is equal to λ(o) = Rw(1−τ
≥ 0 such that for any λ < λ(o) the problem
)
of the household living in formal housing is not well defined. Then, for any λ > λ(o) we
have that:
'
(
wλ(1 − τ )
hF (λ; o) = max α
,h .
(14)
RH (1 + η)
The problem of a household choosing formal housing is summarized in the Lemma 1.
Lemma 1 For each o = (w, RH , ψ, τ, η, h) and λ ∈ (0, ∞), we have that V F : (λ, ∞) → (,
H (1+η)h
where λ(o) = Rw(1−τ
≥ 0, such that:
)
i. There exists a productivity level λM LS (o) =
17
RH (1+η)h
αw(1−τ )
≥ λ(o) such that for λ ∈
(λ(o), λM LS (o)) formal housing in independent of income and equal to the minimum
lot size h; and for λ ∈ [λM LS (o), ∞) formal housing is increasing in income;
iii. Moreover, V F (λ; o) is continuous and strictly increasing in λ; and V F (λ; o) =
F
VbF (λ; o) is strictly concave in λ ∈ (λ(o), λM LS (o)) and V F (λ; o) = Vnb
(λ; o) is linear
F
M LS
F
for λ ∈ [λ
(o), ∞). Finally, limλ→+ λ(o) V (λ; o) = 0 and limλ→+ λ(o) ∂V ∂λ(λ;o) = ∞.
Proof. See Appendix B.
The black solid line in Figure 2 displays the value function V F (λ; o).16
Informal housing problem. Taking w and RH as given, households who choose to live
in informal housing solve the following problem:
V I (λ; o) = max[c1−α (θgh)α ],
(15)
c + RH h ≤ wλ(1 − τ ) − Ψ(λ, h),
(16)
Ψ(λ, h) = ψ(1 − τ )wλh,
(17)
c ≥ 0, h ≥ 0.
(18)
c,h
subject to
We used the fact that sj = θgh (i.e., there is a utility discount θ associated with
squatting) and that there is no payment of property taxes (η) if the agent lives in the
informal housing sector. Recall that informal housing tenure implicate in protection costs
and therefore the agent will spend 1 − Ψ(λ, h) of her time working (see right-hand side of
the budget constraint, Equation (16)). This problem leads to the following consumption
and housing demand equations:
cI (λ; o) = (1 − α)wλ(1 − τ ),
hI (λ; o) = α
λw(1 − τ )
.
RH + ψwλ(1 − τ )
(19)
(20)
The indirect utility for households living in informal housing is given by:
V I (λ; o) = αα (1 − α)1−α w(1 − τ )λ[RH + ψw(1 − τ )λ]−α (gθ)α .
16
(21)
In order to save notation, in the graphs we are omitting the vector of prices, policies and institutions
F
(o) in the value functions and endogenous threshold values for labor productivity. Value functions Vnb
(λ; o)
F
F
and Vb (λ; o) are also displayed in this figure. Vnb (λ; o) is represented by the dot dark gray line, while
VbF (λ) is represented by the dash dark gray line.
18
Lemma 2 For each vector o = (w, RH , ψ, τ, η, h), we have that V I : (0, ∞) → (, such
that:
i. Informal housing is increasing with income;
iii. Moreover, V I (λ; o) is continuous, differentiable, strictly increasing, and strictly conI (λ;o)
cave in λ ∈ (0, ∞); in addition, limλ→+ 0 V I (λ; o) = 0, and limλ→+ 0 ∂V ∂λ
=
−α
α
1−α
α
α (1 − α) w(1 − τ )RH (gθ) .
Proof. See Appendix B.
Value function V I (λ; o) is displayed by the solid blue line in Figure 2. Income elasticities of formal and informal housing consumption will be important to determine housing
choices. When the regulation constraint is not binding we can show the following result.
Proposition 3 When λ ∈ (λ(o), λM LS (o)), formal housing has income elasticity of zero;
and for λ ∈ (λM LS (o), ∞), then formal housing has income elasticity of 1. Informal
housing has income elasticity of less than 1.
Proof. See Appendix B.
The result of proposition 3 relates with literature on the lack of incentives to investment
in informal and illegal housing units (Kapoor and le Blanc (2008)). For instance, Field
(2005) points out that housing renovation increased after a land titling program in Peru and
Galiani and Schargrodsky (2010) show that title increased housing investment in Buenos
Aires.
Housing choice. Households will live in formal housing units if V F (λ; o) > V I (λ; o).
The housing type decision can be described by the function Ω(λ; o) where
Ω(λ; o) = arg
max
Ω(λ;o)∈{0,1}
{Ω(λ; o)V F (λ; o) + (1 − Ω(λ; o))V I (λ; o)},
(22)
for λ ∈ (0, ∞). For any vector o define the measure of households who choose to live in a
formal housing by
E F (o) = {λ ∈ (0, ∞) : V F (λ; o) > V I (λ; o)}.
(23)
Let (E F )c (o) denote the complement set of E F (o). Obviously, if λ ∈ (E F )c (o), then
households are living in informal housing.
Assumption 1 Let (1 + η)θ > 1.
19
Assumption 1 guarantees that very poor households would prefer to live in informal
housing than in formal housing when MLS regulations are not binding or h = 0. The
following lemma characterizes the housing choice for a given labor ability in a partial
equilibrium environment in which prices are exogenously given. Later on we will investigate
the qualitative properties of the model in general equilibrium.
Lemma 4 Let Assumption 1 be satisfied. Then for each vector o = (w, RH , ψ, τ, η, h),
there exists a unique λ̄(o), such that for any λ ∈ (0, λ̄(o)) implies λ ∈ (E F )c (o); and for
any λ ∈ (λ̄(o), ∞) implies λ ∈ E F (o). Moreover,
i.
∂ λ̄(o)
∂θ
> 0;
∂ λ̄(o)
∂η
ii.
∂ λ̄(o)
∂w
< 0; and
> 0;
∂ λ̄(o)
∂RH
∂ λ̄(o)
∂ψ
< 0;
∂ λ̄(o)
∂h
≥ 0;
> 0.
Proof. See Appendix B.
Under Assumption 1, inequality V F (λ; o) − V I (λ; o) > 0 defines a unique value, λ̄(o) >
0, for the labor productivity such that households are indifferent between living formally or
informally. In addition for any value of λ ∈ (0, λ̄(o)) households choose to live informally
and for any λ ∈ (λ̄(o), ∞) households prefer to live in formal housing. There are two cases
to be considered. In the first one, productivity level λM LS (o) associated with the minimum
lot size in formal housing (from Lemma 1) is lower than λ̄(o). Then housing regulations
do not interfere in the housing decision of households. This is depicted in Figure 2(a) and
λ̄(o) =
RH
[θ(1 + η) − 1].
ψw(1 − τ )
(24)
In this case, the share of informal housing increases with housing rent (RH ), property
taxes (η), and when the utility cost for informality (high θ) is low. Notice that in this case,
regulation in the MLS has no effect on the share of informal housing.
When λM LS (o) > λ̄(o), then regulation matters for the type of housing tenure decision.
In this case, there will be some agents that will live informally (because cannot comply
with the minimum lot size), even though they would live in the formal housing sector if
such regulations were not in place. This case is depicted in Figure 2(b) for households
with λ ∈ [λ̄nb (o), λ̄(o)), where λ̄nb (o) denotes the ability level such that households were
indifferent between formal and informal housing if there was not MLS regulation in formal
housing. Households with ability λ ∈ [λ̄(o), λM LS (o)) live in formal housing but the size of
their housing choice is constrained by the MLS regulation. In this case, a more restricted
housing regulation (higher value for h) implies a large share of informal housing.
20
Fig. 2: Housing choice.
F
Vnb
(λ)
VbF (λ)
V F (λ)
V F (λ), V I (λ)
V I (λ)
Formal
housing
Informal
housing
0
0
λ λ M LS
λ̄ = λ̄ nb
λ
(a) Non-binding housing regulations. λ corresponds to the lowest productivity value
in which VbF (λ; o) is defined; λM LS is the productivity value such that for any
λ ≤ λM LS the minimum size regulation is binding in the formal sector. Therefore,
F
V F (λ; o) = VbF (λ; o) for λ ∈ (λ, λM LS ) and V F (λ; o) = Vnb
(λ; o) for λ ∈ (λM LS , ∞).
F
The cutoff λ̄nb (λ̄) is the productivity value such that Vnb
(λ; o) > V I (λ; o)
F
I
(V (λ; o) > V (λ; o)) for any λ > λ̄nb .
F
Vnb
(λ)
VbF (λ)
V F (λ)
V F (λ), V I (λ)
V I (λ)
Informal
housing
due to
regulations
Informal
housing
0
0
λ̄ nb
λ
Constrained
formal
housing
M LS
λ̄ = λ̄ b λ
Formal
housing
λ
(b) Binding housing regulations. λ corresponds to the lowest productivity value in
which VbF (λ; o) is defined; λM LS is the productivity value such that for any λ ≤ λM LS
the minimum size regulation is binding in the formal sector. Therefore, V F (λ; o) =
F
VbF (λ; o) for λ ∈ (λ, λM LS ); λ̄nb is the productivity value such that Vnb
(λ; o) >
I
F
I
V (λ; o); λ̄b (λ̄) is the productivity value such that Vb (λ; o) > V (λ; o) (V F (λ; o) >
V I (λ; o)) for any λ > λ̄b .
21
F
When Assumption 1 is not satisfied, then Vnb
(λ; o) > V I (λ; o) for any value of λ ∈
(0, ∞) and informal housing exists only if there is a regulation in the MLS. This will
be similar to the case depicted in Figure 2(b) with the difference that V I (λ; o) will be
F
uniformly lower than Vnb
(λ; o).
3.3
Competitive Equilibrium
In order to complete the analysis of the model it remains to define the competitive equilibrium. The households’ optimal behavior was previously described in detail above as well as
the government budget constraint. It remains, therefore, to characterize the market equilibrium conditions. There are five prices in this economy (w, r, pL , RH , p). We are assuming
that the rental price of capital is determined outside the city boundaries. Therefore, given
r and Equation (1) the wage rate w is also determined. Equilibrium in the asset market
with no uncertainty means that the housing price equals the discounted value of housing
rents: p = RH /r, where RH represents the housing rent and r is the real interest rate (Saiz
(2010)). Equation (2) implies that given r and once we determine p, then land price pL
will be determined. Therefore, we need just one market clearing condition to define the
housing price p and therefore the land price, pL , and housing rent, RH .
Housing market equilibrium. Total housing demand in the informal sector is
I
H (RH ; o, P ) = P
&
λ̄(o)
hI (λ; o)dΥ(λ) = P
0
&
λ̄(o)
α
0
λw(1 − τ )
dΥ(λ),
RH + ψwλ(1 − τ )
where λ̄(o) is the unique productivity cutoff that partitions households into informal and
formal tenures. In the formal sector, total housing demand is
H F (RH ; o, P ) = P
&
∞
hF (λ; o)dΥ(λ) = P
λ̄(o)
&
∞
λ̄(o)
max
'
α
(
wλ(1 − τ )
, h dΥ(λ).
RH (1 + η)
Recall that housing supply is given by Equation (3) and p = RF /r. The housing market
clearing condition can be stated as
P
&
λ̄(o)
0
λw(1 − τ )
α
dΥ(λ) + P
RH + ψwλ(1 − τ )
&
∞
λ̄(o)
max
'
(
1−γ
1−γ $
wλ(1 − τ )
1−γ% γ
γ
α
, h dΥ(λ) = LRH
. (25)
RH (1 + η)
r2
where the left-hand side (LHS) shows the housing demands and the right-hand side (RHS)
shows the total housing supply of the city.
Proposition 5 (Existence and Uniqueness) Let Υ(λ) be a continuous cumulative
∗
distribution for λ ∈ (0, ∞), then there exists a rental housing price level 0 < RH
< ∞
which clears the housing market. Moreover,
22
i. When λM LS < λ̄nb (o), then a sufficient condition for uniqueness is that θ → 1.
ii. When λM LS > λ̄nb (o), then a sufficient condition for uniqueness is that h ≥
η α
.
(1+η) ψ
Proof. See Appendix B.
Therefore, given the properties of the model an equilibrium always exists. It is important to highlight that the conditions for uniqueness are sufficient conditions. Even
when these conditions are not satisfied the equilibrium might be unique. In fact, in most
of the numerical exercises we verify that uniqueness is satisfied. Note that uniqueness
does not mean that the “effective cost” of formal and informal housing units are equal:
for each agent, the cost of a housing unit differs depending on her ability. Specifically,
informal housing is “cheaper” for low-income agents, while formal housing is cheaper for
higher income households (because informality is associated with a high opportunity cost).
Usually, studies argue that formal housing units have higher prices (e.g., Jimenez (1984);
Friedman, Jimenez, and Mayo (1988)). However, others emphasize that an informal housing unit may be even more expensive because of a “premium” associated with urban
freedom17 and future land regularization (Smolka and Biderman (2011)).
Given the equilibrium, we can study the qualitative properties of the model. The
comparative statics of the model are shown by the next proposition. Proposition 6 shows
the impact of several parameters on the share of households living in informal housing and
on the equilibrium rent price.18
Proposition 6 (Comparative statics) Let the conditions for uniqueness be satisfied,
then
i.
ii.
∗
∂RH
∂P
∂ λ̄(o)
∂P
> 0;
> 0;
∗
∂RH
∂L
< 0;
∂ λ̄(o)
∂L
∗
∂RH
∂r
< 0;
> 0;
∂ λ̄(o)
∂r
∗
∂RH
∂θ
> 0;
< 0;
∂ λ̄(o)
∂θ
∗
∂RH
∂w(1−τ )
> 0;
> 0;
∂ λ̄(o)
∂w(1−τ )
∗
∂RH
∂h
! 0;
! 0;
∂ λ̄(o)
∂h
iii. Let λ = eµ+σZ , where Z ∼ N (0, 1). If µ increases, then
increases, then
∗
∂RH
∂σ
! 0;
∂ λ̄(o)
∂σ
∗
∂RH
∂ψ
≥ 0;
∗
∂RH
∂µ
! 0;
∂ λ̄(o)
∂ψ
> 0;
∗
∂RH
∂η
< 0;
∂ λ̄(o)
∂µ
< 0;
∂ λ̄(o)
∂η
> 0;
> 0. If σ
"0
Proof. See Appendix B.
Results of the comparative statics exercises help to explain the directions of the correlations found previously by the reduced-form evidence (section 2). We can observe that
17
The freedom to choose exactly the construction specifications of one’s housing unit.
In this proposition, we consider small variations in the parameters of the model and assume that
the government keeps the same level of public goods. The government budget )constraint is adjusted by
changing the fraction of resources which might be wasted. In this case, g + ∆ = E F (o) ηRH hF (λ)dΥ(λ) +
)∞
τ wλdΥ(λ) and ∆ is adjusted. In the numerical exercises, we will consider the case of changes in
0
policies and institutions which might also change the level of public good provision.
18
23
the equilibrium rental housing price increases with population (P ), interest rate (r), and
disposable income (w(1 − τ )). It also decreases with the supply of land (L), when the utility cost for informality decreases (θ increases), and with property taxes (η). Such results
are quite intuitive. We, however, cannot identify how the rental housing price changes
with protection costs (ψ) and the minimum lot size regulation (h) - it is unchanged when
the MLS regulation is not binding. For instance, when protection costs (ψ) decrease more
households start to live informally and there is an increase in housing units for such households. The demand for formal housing decreases generating an ambiguous effect on the
rental housing price.
The fraction of households living in informal housing increases with a larger population
(P ) - or lower supply of land (L), higher interest rate (r), lower utility cost of living
informally (higher θ), higher property taxes (η), higher MLS regulations if they are binding,
and lower protection costs (ψ). Qualitatively we are not able to identify how the share
of households living in informal housing changes with disposable income. This result
is consistent with Jimenez (1985). When wages increase formal housing become more
affordable and the cost of being a slum dweller increases. Therefore, there is a positive
effect on the share of households living in formal housing. On the other hand, the land
price increases due to higher housing demand and this has a negative effect on the share of
households living in formal housing. Finally, the last item of this proposition applies when
the distribution of labor productivity follows a log-normal distribution. In this case, if there
is a change in the labor productivity distribution such that it stochastically dominates the
previous one, then the rental housing price increases (as well as the equilibrium level of
labor productivity which makes households indifferent between living in informal or formal
housing units). However, the effects of the variance of the labor productivity on the two
endogenous variables of interest are ambiguous.19 Notice that the model is able to explain
the case in which housing informality does not exist.
Proposition 7 Let (1 + η)θ < 1 and h = 0, then (E F )c (o) = ∅.
Proof. See Appendix B.
The comparative statics study how the model parameters affect equilibrium outcomes.
As discussed above, the parameters are: disposable income w(1 − τ ), average labor productivity µ, inequality in labor productivity σ, urban population P , land use regulation h,
protection cost ψ, informality disutility θ, property taxation η, land supply L, labor tax
τ , and real interest rate r. It is possible to partition the parameters into two categories:
determinants of slum formation and policy-parameters, i.e.,
19
For an continuous uniform distribution, we can show that if the variance increases but the mean
remains the same, then the rental housing price increases, as well as the productivity level which makes
households indifferent on the type of house they choose to live.
24
Local and National Policies
,
-*
+
w, µ, σ, P , h, ψ, θ, η, L, τ , r .
*
+,
Determinants
3.4
Extensions
In order to derive the main analytical results and to understand the main determinants of
slum growth, the model was kept at a simple level. Below we discuss two extensions which
might enrich the model. The first extension considers the case of a city with an endogenous
population, such that changes in polices might have an effect on the population size of the
city considered in the analysis. The second extension modifies the model to introduce a
dynamic setting. We show that our analysis would go through in a dynamic environment.
3.4.1
Endogenous Population
The population size is determined exogenously in the model, but a simple modification
suffices to endogenize population size. Let the reservation utility be u∗ (λ). This utility
might represent the value of being in a rural area working in the agricultural sector and
therefore it might be independent of λ, such that u∗ (λ) = u∗ . The endogenous population
size (P̄ ) would be determined by the following spatial condition or participation constraint:
max{V F (λ, o), V I (λ, o)} ≥ u∗ . Since the indirect utility of living in the city is increasing
in income λ, this condition implies that there exists a λu (o) > 0 such that if λ < λu (o),
then households will live in the rural area. Notice that this effect might reduce housing
informality in urban areas. Changes in the parameters of the city will not only change
the informality threshold value λ̄(o), but also the endogenous migration value λu (o) > 0.
This is the case, for instance, when a rise in urban population is generated by a higher
total factor productivity (TFP) in the production function of firms in urban sector visà-vis firms in the rural sector. Higher TFP in the urban area generates wage differential
between urban and rural areas inducing people to move to the urban area. This in turn
might increase slums in urban areas.
3.4.2
Dynamics
Our model is static. This allows us to derive some analytical properties of the model
and to get clear intuition of the main determinants of slum formation. A simple way to
extend the model to a dynamic setting is to use a modified version of the Galor and Zeira
(1993) framework. For instance, we could assume that at each date, there is a continuum
of households with measure P (which might change over time), each of whom with labor
productivity λ ∈ (0, ∞). Each household lives for one period and derives utility from
25
consumption, housing services and bequest left to her offsprings (b! ), such that
U (c, sj , b! ) = c1−α−β sαj (b! )β , α, β ∈ (0, 1), α + β < 1,
and j ∈ {F, I} as before. In this case, total income of a household with labor productivity
λ would be represented by
ω(λ, b) = (1 − τ )wλ + (1 + r)b,
where b is bequest received from parents. A housing unit is assumed to depreciate fully
at the end of the period. Since the model’s period is one generation, the full-depreciation
is not necessarily an unrealistic assumption. The budget constraint in the formal housing
sector would be:
c + [RH (1 + η)]h + b! ≤ (1 − τ )wλ + (1 + r)b.
For the case of informal housing, we would have:
c + RH h + b! ≤ wλ(1 − τ ) + (1 + r)b − ψw(1 − τ )λh.
The rest of the environment (e.g. production technology) is unchanged. Then, decisions
of households will depend on their type (λ, b) instead of λ only. It can be shown that
there exists a ω̄(λ, b; o), such that for any ω ≥ ω̄(λ, b; o) households will live in a formal
housing and for any ω < ω̄(λ, b; o) households will dwell illegally. In addition, ω̄(λ, b; o)
is increasing in λ and b, which implies that ω̄(λ, b; o) defines a curve b̄(λ; o) in the plane
(b, λ), such that ∂ b̄(λ;o)
< 0. In this way, the introduction of dynamics per se does not add
∂λ
any new insight to explain slum formation in developing countries.
New insights to explain informal housing in developing countries can be introduced in a
dynamic framework if some factors can interact with the transmission mechanism of wealth
between generations. One candidate is the credit market. For instance, if houses have to
be paid in advance (before production) and households face a collateral constraint of the
form of φi b with i ∈ {F, I} and φF > 1 and φI = 1, then improvements in the efficiency of
the formal credit market (an increase in φF ) might potentially decrease informal housing.
To fully introduce credit markets we should also consider the case in which households can
either buy or rent formal or informal housing units. We would have to introduce some lifecycle microfoundations to explain why some households choose to buy instead of renting
their houses. Another issue which might be important in a dynamic setting is related to
neighborhood effects in slums. It might be the case that children inherit their parents’
networks and breaking such links might be costly, creating a path dependence in living
in slums. These modifications would provide guidance on whether slums are an entrepôt
to the urban poor or on whether there exists a “housing ladder” from informal to formal
26
tenure. We leave the issue about network effects and the role of credit market for future
work20 and we focus on issues related to urbanization, changes in the wage distribution
and on land regulation policies and institutions.
4
Estimation
The model formalizes the mechanisms through which income, population size, land use
regulations, among other variables, affect housing type decisions. Now we want to determine the magnitude of those factors on slum formation. The parameters of the model are
set to match relevant features of the Brazilian economy in 2000. Since our model is one
of a city, we use data from the city of São Paulo instead of data for the whole country.
We verify the model’s predictions and confront those predictions with the data. Once the
model is estimated to fit the data, the contribution of each factor impacting slums growth
is analyzed through counterfactual exercises (see Section 5).
We need to calibrate 14 parameters generated by the structure of the model and represented by the following vector of parameters.
ξ = {B, υ, µ, σ, α, γ, η, τ, P, L, r, ψ, θ, h}.
The values of the parameters of vector ξ were either selected from existing observations
(“external calibration”) or determined by a distance minimization procedure (“internal
calibration” or estimation). Let ξext be the partition of vector ξ containing eleven parameters to be (externally) calibrated and ξint be the partition of ξ with the additional three
unknown parameters to be estimated.
External Calibration. The vector to be determined by external calibration is given by
ξext = {B, υ, µ, σ, α, γ, η, τ, P, L, r}.
Due to the shortage of empirical literature on slums, in particular applied to Brazil, we
had to select parameters directly from datasets to use in the calibration. We compare the
selected parameters to the ones used in the existing literature for other countries. The
parameters of the external calibration are: city-level productivity (B), labor share in the
production of the consumption good (υ), mean labor productivity (µ), variance of labor
productivity (σ), weight of housing consumption (α), weight of land input (γ - recall that
20
In our application, credit and generational effects do not seem to be chief explanations for slums’
growth. We will calibrate and estimate the model for Brazil and we would like to explain informal housing
growth during two decades. Generational aspects may not be at play because of the short time span.
Besides, data from Brazil’s Central Bank show that total mortgage debt as a share of income in the
country has been historically very low (e.g., it was less than 1% of GDP in the beginning of 2000s). As a
result, credit market also does not seem to be a key factor to explain informal housing in our application.
27
housing supply price-elasticity comes from γ), property tax rate (η), income tax rate (τ ),
total urban population (P ), total land supply (L), and real interest rate (r).
One key aspect of the present numerical exercise is the distribution of labor productivity
(Υ(λ)). In the calibration exercise, we use the fact that the lognormal distribution works
as an approximation to the empirical income distribution (except from its tails). As such,
the distribution of abilities Υ(λ) is set as a doubly-truncated lognormal distribution, i.e.,
we use the (doubly-truncated) lognormal distribution in order to fit the empirical income
distribution21 . We adjust the two parameters of the lognormal distributions to match
moments from the income distribution of São Paulo in 2000, i.e., the artificial income
data is set to match moments of the empirical income data. We use two income data
moments from PNAD (IBGE’s household survey - see IBGE (2002) and appendix A) for
this exercise: mean income (proxy for average labor productivity µ) and ratio of the income
of the household at the 80th percentile to that of the household at the 20th percentile (proxy
for inequality σ). The estimated lognormal distribution provides the income distribution
for the calibration exercise.
The weight of housing consumption in the utility function (α) is set at 0.14. This
value stems from the Household Budget Survey (IBGE (2004)), the main data source on
the distribution of spending of Brazilian households, carried out by IBGE. The Brazilian
values are quite similar to those from other studies (see Davis and Heathcote (2005) and
Davis and Ortalo-Magne (2011)). For instance, Lebergott (1996) reports that historically
the value has been 0.14 for the US.
We set the weight of land input (γ) to be equal to 0.25. The parameter γ can be rewritten as the share of land out of total output given the Cobb-Douglas production function of
the developers. Construction companies listed on the São Paulo Stock Exchange display
information on the price of land compared to the their total sales (both by construction
unit and the total values). Production technology of developers varies because several factors influence the ratio of land prices to total sales, such as whether the land was bought
directly or the company has offer residential units in exchange for the land. However, data
from construction companies in São Paulo indicate that the target value for land price lies
between 25% to 35% of the total output when it comes to residential units.
The property tax rate (η) equals 1%. In São Paulo, property tax varies between 0.8%
and 1.6% of the market value (housing price) of the housing unit. Although there is some
variability, the median and mode rates for residential units were 1%. It is useful to note
that a municipality can adopt a single property tax rate or several rates depending on
the housing value, housing location, etc. For instance, 2/3 of 365 Brazilian municipalities
studied by Carvalho Jr. (2008) adopted a single rate. Besides, note that η multiplies
21
Parker (1999) argues that the lognormal distribution does not adequately fit the tails of the income
distribution. To circumvent this issue, the lognormal distribution is doubly-truncated. We truncate 2,5%
of extreme observations from each tail of the distribution.
28
housing rents (RH ) in the model, so it is necessary to calculate the “effective” property
tax as of housing rents’ values (instead of housing prices). For instance, a tax of 1% on
housing prices is equivalent of a tax of 25% on rents, for a given interest rate of 4% per
year.
Labor income tax (τ ) rate equals to 22%. Income tax are determined by the national
government in Brazil. According to the Brazilian Revenue Service, the effective labor
income tax is 12%22 . There is a social security contribution of 10% on top of labor income
tax, so the parameter τ is set to 0.22.
Parameter P is set to be equal to one in 2000, as well as the total land supply L. We
also need to stipulate the interest rate r. We use the national interest rate since one city
cannot influence the magnitude of the interest rate. Brazil was characterized by high real
interest rates during the 1990s and 2000s. By contrast, annual real interest rates were
very low, sometimes even negative, during the 1970s and 1980s23 . Based on a 30 years
average for Brazil, the interest rate is set to be 4% per annum in real terms. Parameter
υ is the labor share in the production of the consumption good. We set it equal to 0.6,
which is consistent with the estimates provided by Gollin (2002). Given r and υ, we choose
productivity factor B such that the wage rate is equal to 1.
Internal Calibration. Due to the paucity of data, the additional three parameters (from
the partition ξint of vector ξ) were found by minimizing the distance between the model
and the data moments. Therefore, we find the three parameters focusing on selected data
moments (along the lines suggested by Hansen (1982)) instead of focusing on the entire
distribution of the observed variables. Partition ξint is represented by
ξint = {ψ, θ, h},
where ψ represents protection costs, θ represents informality disutility, and h is the minimum housing space. Internal calibration consists of estimating three parameters from ξint
such that the model would match key statistics of the São Paulo’s urbanization process.
We match five predictions of the model to their data counterparts. Recall that the
model is able to generate information on housing tenure choices and on a distribution
of housing space consumption (given that the model has heterogenous agents). The five
predictions used in the matching strategy are: (i) fraction of population in slums; (ii)
housing space inequality (measured by a Gini housing space coefficient); (iii) ratio of the
housing space of the household at the 25th percentile to that of the household at the 35th
percentile; (iv) ratio of housing space at the 45th percentile to that at the 55th percentile;
and (v) ratio of housing space at the 65th percentile to that at the 75th percentile. The
22
Precisely, it is between 0.3% and 12% because of the progressive structure of labor taxation.
According to data from Ipeadata, in 1975-1984 the mean real interest rate was -4%, in 1985-1994 the
average real interest rate was 7%, and during 1995-2004 the rate was 12%.
23
29
idea was to obtain measures of centrality and dispersion from a housing space distribution.
In order to create the slums’ share, we verify the decision rule regarding housing tenure
(represented by Ω(λ; o) in the model) for each agent and then aggregate it to create the
slums share value. After verifying the optimal choices of each agent, it is also possible to
retrieve information on housing space consumption to construct the Gini index and the
housing space ratios. In sum, tenure choice and housing space choice are used as moments
in the minimization procedure.
We use a Method of Moments or Minimum Distance procedure to find the unknown parameters. The nested fixed point algorithm used to compute the parameters has two loops:
the inner loop computes the housing market equilibrium given each parameter value, while
the outer loop searches for optimal parameter values. The distance minimization procedure consists of finding the vector ξˆint that minimizes the distance between the model’s
prediction and the data. By carrying out this procedure, we aim to obtain parameter
values which most closely reproduce key features of the data. The objective is to minimize the quadratic loss function of deviations of predicted moments from their empirical
counterpart (weighted sum of squared errors of model moments and data moments). The
model is overidentified, since the number of parameters in ξint is three and the number of
moments is five.
Let L(ξ) be the quadratic loss function to be minimized, Md be the vector of data
moments, and Mm (ξ) be the correspondent vector of model moments. Formally, we want
to find a ξˆint such that
1
1
ξˆint = arg min L(ξ) = arg min [Mm (ξ) − Md ]! WN [Mm (ξ) − Md ].
ξint
ξint N
N
(26)
where Mm (ξ)−Md is the orthogonality condition and WN is a positive semi-definite weighting matrix. The matrix WN converges in probability to W . It follows that ξˆint is a consistent and asymptotically normal estimator of ξint . In the analysis, we use an optimal
weighting matrix W , which is given by the inverse of the variance-covariance matrix of the
data moments (S)24 , i.e., W = S −1 .
We aim also to determine the precision of the parameter vector ξˆint . To calculate its
standard error we use the following equation:
V (ξˆint ) =
(D! W D)−1 D! W SW D(D! W D)−1
,
N
(27)
where S is variance-covariance matrix of the data moments, N is the sample size, and D
24
There are 5 moments, so the orthogonality condition is a 5x1 matrix and the weighting matrix is a 5x5
matrix. All five data moments are calculated from São Paulo’s microdata. We computed data-moments
variance-covariance matrix S directly from city-level variance-covariance information. The off-diagonal
elements of the matrix S also come from the city-level information.
30
is a gradient matrix equivalent to
∂[Mm (ξ) − Md ] ..
∂Mm (ξ) ..
D=
=
=
.
.
∂ξint
∂ξint ξint =ξ̂int
ξint =ξ̂int

1 (ξ)
∂Mm
 ∂M∂ψ
 m2 (ξ)
 ∂ψ
 ∂Mm3 (ξ)
 ∂ψ
 ∂M 4 (ξ)
 m
 ∂ψ
5 (ξ)
∂Mm
∂ψ
1 (ξ)
∂Mm
∂θ
2 (ξ)
∂Mm
∂θ
3 (ξ)
∂Mm
∂θ
4 (ξ)
∂Mm
∂θ
5 (ξ)
∂Mm
∂θ

1 (ξ)
∂Mm
∂h
2 (ξ) 
∂Mm

∂h 
3 (ξ) 
∂Mm
.
∂h 
4 (ξ) 
∂Mm

∂h 
5 (ξ)
∂Mm
∂h
Equation (27) simplifies to
(D! S −1 D)−1
V (ξˆint ) =
N
when we use the optimal matrix W . We compute the standard error (SE) via
1
SE(ξˆint ) = (diagV (b̂)) 2 .
(28)
Given the structure of the model, we had to consider the following constraints in the
estimation procedure:
• ψ > 0: protection costs must be positive.
• θ > 0: there must be a disutility from dwelling at a informal housing unit.
• θ(1 + η) − 1 > 0: equivalent to assumption 1 from the model.
• h > 0: enforcement of MLS regulations.
Table 5 shows the value of the calibrated and estimated parameters. The internallyestimated parameters have the expected sign and are somewhat precise. The only parameter that its magnitude has a direct economic interpretation is ψ, because θ is a utility-shifter
and h is related to the concept of housing services (which enters the utility function as
well). Field (2007) estimates that in Peru no legal claim to property is associated to a
reduction of 14% in total household working hours. Our estimate for São Paulo is that,
for each housing space unit, the cost of informality is about 16 percent of disposable income. One may consider our forgone time estimate as an upper-bound for the Brazilian
case. The reason is that it is an estimate for São Paulo, where land prices are high and
thus informal households would need to allocate more time for protection. This high value
for protection costs highlights a relevant (and adverse) aspect from slums, since informal
dwellers may need to spend certain amount of time to protect their plot. This estimate
might also represent lost time due to health problems from living around inadequate urban
infrastructure.
Table 6 shows the baseline economy in 2000 (see columns (i) and (ii)). The data
moments for the baseline economy stem from the 2000 Population Census. We need to
obtain data moments on slums’ share and housing space distribution to be consistent with
the 5 moments from the model. The Census has information about whether or not a
31
Table 5: Estimation of the Model: Parameters for the city of São Paulo
External Calibration
Parameter
Description
Values
Source
α
γ
η
τ
P
L
r
υ
B
µ
σ
Preferences: Weight of housing service
Housing: Weight of land input
Government: Property tax rate1
Government: Income tax rate
Urban population size
Land supply
Real interest rate
Labor share in production
Total Factor Productivity
Average labor productivity
Income ratio: 80th percentile to 20th
0.14
0.25
0.25
0.22
1
1
0.04
0.6
0.541
811.12
17.85
POF survey
Construction Companies
São Paulo City Council
Ministry of Finance
Normalized to one
Normalized to one
Central Bank of Brazil
Gollin (2002)
Normalized such that w = 1
PNAD survey
PNAD survey
Internal Calibration
Parameter
Description
Point Estim.
(Std. Error)
Source
ψ
θ
h
Protection costs
Housing Informality Disutility
Minimum Lot Size regulation
0.16 (0.06)
0.91 (0.41)
0.86 (0.22)
Estimation
Estimation
Estimation
1
Notes. Eight parameters were chosen via external calibration. Three parameters were estimated via a distance
minimization procedure (internal calibration).
Equivalent to 1% of the housing price.
32
housing unit is classified as an informal housing unit (“aglomerado subnormal ”), so we use
this information to calculate the share of slums. Table 5 indicates that our parametrization
is able to match the share of slums from the data. To compute the housing space moments,
we use information on the density of people per room (as the Census provides information
on the number of rooms and on the number of people in each housing unit). We constructed
the variable “density per room” and used it as a proxy for size. Four moments were created
from the “density per room” variable: a housing space Gini index and 3 ratios of housing
space for different percentiles. Table 5 indicates that our parametrization is also able to
match the housing space distribution from the data, but with lower precision.
Table 6: Moments: Data and Model
(i)
(ii)
Baseline
Moments
Slums Share (%)
Gini Housing Space
Housing Space: 25th/35th percentile
Housing Space: 45th/55th percentile
Housing Space: 65th/75th percentile
(iii)
(iv)
(v)
(vi)
Comparison/Counterfactual
2000
Data Model
1980
Data Model
1991
Data Model
8.92
0.39
0.85
0.80
0.77
4.07
0.43
0.83
0.88
0.88
7.46
0.42
0.83
0.83
0.78
8.91
0.43
0.80
0.82
0.82
4.68
0.38
0.82
0.84
0.82
7.13
0.41
0.81
0.83
0.80
Notes. Data for São Paulo. Data moments calculated from Brazil’s Population Censuses of
1980, 1991 and 2000. The baseline year is 2000, so the model’s moments for 2000 are obtained
by using the parameters from Table 5. To obtain the model’s moments in 1980 and 1991, we
change three parameters: urban population, average income and income inequality. All other
parameters are used as in 2000 (see Table 5).
Figure 3 compares the housing inequality generated by the fitted model and the one
from the data. Note that the housing space inequality from the model as shown by the
Lorenz curve is higher. One reason for this difference might be due to our data: we are
measuring housing inequality as density per room, but richer households may have several
real estate properties (commercial, a second residential unit, etc) and we are unable to
capture this information from the data. In sum, our data potentially underestimate the
real housing inequality in Brazil. Moreover, according to the data, housing space inequality
in 2000 (0.39) is lower than income inequality (more than 0.5) in the same year. We
mentioned that housing inequality is potentially underestimated by the data, but the model
provides an insight on the comparison between housing and income inequalities: informality
attenuates housing inequality as the informal housing sector allows some agents to consume
more housing space. In the model, a lower-income agent who lives in the informal housing
sector consumes more housing space than she would have consumed in case she was only
33
able to dwell in the formal housing sector. This mechanism of the model provides intuition
on why housing inequality is smaller than income inequality in the data.
Fig. 3: Lorenz Curves: Model vs Data in 2000
1
Model
Data
Perfect Equality
0.9
0.8
Housing space (%)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
Population (%)
0.8
1
Notes. The figure shows three Lorenz curves regarding housing space consumption. The 45-degrees line
represents the case of perfect equality in terms of housing space consumption.
5
Quantitative Analysis
This section comprises three parts. In the counterfactual part we quantify how much of the
growth in slums is accounted by poverty, regulation and migration. In the policy experiments we perform several ex-ante policy simulations. We close the section by presenting a
welfare analysis.
5.1
Counterfactual Analysis
We now carried out several counterfactual experiments to evaluate the determinants of
slums’ formation. A relevant factor has its value fixed in order to assess the role of this
factor on the increase in slums’ share. The counterfactual experiments aim to answer
questions such as: what is the impact of changing land use regulation? What is the
quantitative impact of low income growth, increasing income inequality or rapid ruralurban migration? Our period of analysis is from 1980 to 2000. The 1980s and 1990s
are specially important for counterfactual experiments in Brazil and in São Paulo as the
population in slums increased substantially in the period (see Table 3 in Section 2 and
Table 10 in Appendix A).
34
Specifically, we want to study the contribution of four factors: income level, inequality,
rural-urban migration and urban regulation. The model was initially parameterized for
the city of São Paulo in 2000 (see Section 4). We estimate the parameters for São Paulo
because the model is one of a city. A caveat is that preexisting regulations do not vary
during 1980-2000 in São Paulo25 , although there may be changes in the enforcement of the
zoning law. Therefore, in our specific application, it is difficult to directly examine in the
counterfactual exercises the variable “changing regulation” as the enforcement of zoning
regulations is unobservable (i.e., we do not have data on the evolution of enforcement in
1980-2000). As a consequence, we concentrate on three determinants in the counterfactual
exercise: urban population, average income and income inequality. The contribution of
urban regulation is examined indirectly by the residual difference between the data and the
counterfactual (that may be partly explained by changes in enforcement). To obtain the
counterfactual in 1980, we use the population level, average income and income inequality
as in 1980, and all other parameters keep their values as in 2000 (from Table 5). To obtain
the counterfactual in 1991, we perform similarly: we froze population, income level, and
income inequality as in 1991 and use all other parameters as in 2000.
Table 6 shows the comparison between the slums’ share generated by the counterfactuals and the one from the data for 1980 and 1991 (see columns (iii) and (vi)). The relevant
information from Table 6 is that the model is able to explain much of the variation in
slums’ growth when we fix only three determinants. In 1980, the counterfactual indicates
a slums’ share of 4.68%, while the data show a slums’ share of 4.07%. The enforcement of
land law is assumed to be the same every year, and this may explain part of the residual
difference between the data and the counterfactual result in 1980. Let’s analyze the data
for 1980 to grasp the mechanics of the counterfactual exercise. One one hand, in 1980
population is almost 30% smaller (and so housing rents and prices are smaller as well) and
inequality is 18% lower than in 2000. Less people and less inequality are associated with
fewer people in informal housing. On the other hand, income level is lower and this causes
more informality. In the end, the weight of population and inequality is chief to explain
slum formation as there is a decline in the share of slum dwellers.
We disaggregate and quantify the contribution of each factor in Table 7. We again
change only three variables to generate counterfactuals: income level, income inequality,
and the size of population. We first perform counterfactual exercises shutting down each
determinant of slums growth separately. The counterfactuals are (i) income level as in
1980 (and all other parameters as in 2000); (ii) income inequality as in 1980 (and all
other parameters as in 2000); (iii) urban population as in 1980 (and all other parameters
as in 2000). Then we shut down a combination of the determinants to generate new
25
The city adopted the national urban regulation from the Federal Law 6,766/79 in 1979 and only
changed its urban regulation in the 2000’s.
35
scenarios: (iv) income level and inequality as in 1980, (v) income level, inequality, and
rural-urban migration as in 1980 (as we have done previously in the counterfactual exercise
shown in Table 6). Table 7 shows the results. First, the counterfactuals indicate that
income inequality seems to have the greatest impacts on slums formation vis-à-vis the other
determinants of slums formation. Moreover, rural-urban migration has a sizeable effect on
slums growth. Income level has also a important role in explaining slums formation, but
its impact is not as important as the ones from the other determinants. Note that, when
we shut down all three factor (see the last counterfactual in Table 7), the share of slums
decrease to virtually half. In other words, as mentioned above this indicates that much
of the variation of slums growth during 1980-2000 is accounted for by the three relevant
determinants.
Table 7: Counterfactual Experiments:
Decomposing the Variation in Slums Growth in 1980-2000
Fraction of population
in slums in 2000
Counterfactuals
1.
2.
3.
4.
5.
Average income as in 1980
Income inequality as in 1980
Urban Population as in 1980
Inequality and average income as in 1980
Inequality, average income and population as in 1980
Data
Model
Counter.
8.92%
8.92%
8.92%
8.92%
8.92%
8.91%
8.91%
8.91%
8.91%
8.91%
9.55%
5.73%
7.13%
6.28%
4.68%
Notes. This table details the results from Table 6. Data moments calculated from Brazil’s Population Censuses of 1980, 1991 and 2000. The baseline year is 2000, so the model’s moments for
2000 are obtained by using the parameters from Table 5. To obtain the counterfactuals in 1980,
we modify three parameters (urban population, average income and income inequality) separately
or concomitantly to their values in 1980. All other parameters are used as in 2000 (see Table 5).
5.2
Policy Simulations
In this subsection, we perform different policy simulations. We use our behavioral model
to predict the impact of hypothetical policies. The simulations seek to quantify the exante impact of policies that makes formal housing market more accessible to the urban
poor. By and large, policies towards slums are classified under the umbrella of “slum upgrading” interventions. Upgrading projects include a wide range of interventions. Typical
interventions include a bundle of land titling, provision of basic infrastructure (e.g., water, electricity, and lightning), construction of facilities (schools, health posts), and home
improvement. In the simulations, we focus on a somewhat broader set of interventions
that we split into two categories: apart from slum upgrading interventions, we also study
the effects of policies that decrease barriers to formalization. The simulated policies have
significant impact on the city so as to interfere housing prices (our economy-wide outcome)
36
as is typically the case of large-scale interventions. In fact, our simulations highlight the
importance of considering general equilibrium effects of programs with universal coverage.
In the present analysis, policies on slums impact the housing market of the entire city and
thus influence housing prices within the city boundaries. Therefore, one must consider the
effect on housing prices when analyzing the impacts from large-scale interventions26 .
We simulate 4 policies: reduction in formalization costs, relaxation of urban regulations,
infrastructure provision to informal housing units and a titling program. Recall the basic
trade-off of the model: informal housing agents escape from paying property taxes (η)
and from complying with building regulations (h), but informal housing also means lower
provision of public services (θ) and incurring in defensive costs (ψ). We simulate changes
in each of these four aspects (η, h, θ, and ψ) separately. Firstly, we simulate the impact
of a reduction in real estate taxation η by half, which is a proxy for a reduction in the
cost of housing formalization. Secondly, we simulate the effect of less-strict man-made
regulations through a reduction of 10% in the value of h. Thirdly, we evaluate the effects of
providing better basic infrastructure to informal settlements (by changing θ to 1). Finally,
we simulate the impact of a titling program (represented by a decrease by half in protection
costs ψ).
We focus on an aggregate-level outcome in this subsection: the fraction of population
in slums, which is given by the following relation:
SS =
N
1 5
1{V F (λ, o, ξ(z ! )) ≤ V I (λ, o, ξ(z ! ))},
N i=1
where SS stands for slums’ share, 1{} is an indicator function, ξ(·) represents the vector
of all 14 parameters of the model and z ! the parameter subject to the policy variation.
By calculating the macro effects (via slums’ share), we are able to identify the fraction
of households induced to change from one state (housing tenure) to another due to the
simulated policy.
The aggregate-level effects of the policy scenarios are shown in Table 8. We first discuss
the simulation of a reduction of property taxation. The comparative statics point out that
this will decrease the amount of slums dwellers (recall Proposition 6). The quantitative
exercise shows by how much. According to Table 8, a reduction of property tax η by half
would decrease the informal housing by roughly 1.3 percentage points. Even though the
costs of formal housing is a relevant factor, this result does not discard that other barriers
to formalization (such as urban regulations) cay play a great role in slum formation.
26
Both formal and informal housing sectors contribute to determine the magnitude of housing rents in
the model. Nonetheless, because of the share of slums in the data, housing rents in the simulations are
guided basically by the behavior of the formal housing sector.
37
Table 8: Policy Simulations: Macro Effects
Fraction of population
in slums in 2000
Policy Simulations
1.
2.
3.
4.
Formalization costs: reduction by half
MLS reduction by 10%
Infrastructure Upgrading: Eliminating informal housing disutility
Titling: Reduction of protection costs by half
Data
Model
Simulation
8.92%
8.92%
8.92%
8.92%
8.91%
8.91%
8.91%
8.91%
7.60%
7.95%
9.92%
9.98%
Notes. The table presents four policy simulations. Reduction of formalization costs is a reduction of the parameter
η by half. MLS reductions means a reduction of 10% in h. In the infrastructure upgrading we set θ equals to 1.
Titling means reducing the value of the parameter ψ by half.
The second simulation is associated with a relaxation of urban regulations. The intuition is to reduce the “regulation bundle” in 10%, which means a (concomitant or separate)
relaxation of selected building constraints (minimum lot size, height control, frontage, etc).
Aura and Davidoff (2008) study the effect of an uncoordinated reduction of land use constraints on housing markets and concludes that small jurisdictions changing their land use
constraints would have little effect on the housing market price. Larger effects could come
from coordinated actions among jurisdictions and regions. Our simulation is for the biggest
city in Brazil: we simulate the impact of an overall reduction in regulations supposing that
the entire city is now under a less-severe urban regulation. The relaxation of regulation
has great impact on reducing slums.
We simulate as well the impact of two common policies towards slums: infrastructure
upgrading and titling. By infrastructure upgrading, we mean better infrastructure and
public services. Land titling means a reduction in the likelihood of expropriation by giving
property rights to slum dwellers. Usually, slum upgrading interventions aim to both provide
infrastructure upgrading and titling, but we separate these two aspects to understand the
potential distinct impacts.
We consider the impact of providing infrastructure, while keeping the housing unit still
in the informal sector without land titling. In the model, it means changing informal housing disutility (θ) but keeping protection costs (ψ) in the same level as before. Provision of
infrastructure is represented by setting θ = 1. We verify that setting θ = 1 is associated
with an increase in the number of slum dwellers by 1.1 percentage points. The intuition is
that now informal housing became more attractive because of the better infrastructure. It
means that slum upgrading interventions can have unintended adverse impacts as upgrading may attract more people to live in slums. Upgrading may attract more people to live in
slums because the benefits of living in slums increased: even though there is insecurity in
terms of land occupation, better infrastructure increase utility (given that the household
still do not need to comply with regulation and to pay property taxes).
Simulations are also able to quantify by how much land titling programs impact slum
38
formation. We simulate a decrease in protection costs (ψ), while keeping disutility from
informality as in the baseline economy. In this way, there are still components of “informality”: even with a reduction in protection costs because of the titling scheme, informal
housing agents still suffer from lower utility, do not comply with regulations, and do not
pay property taxes. The ex-post evaluation literature shows that giving property rights to
the urban poor increases housing investments and housing prices (e.g., Lanjouw and Levy
(2002) and Galiani and Schargrodsky (2010)). Our simulations support the claim that
providing (exclusively) more security to informal housing will induce more people to live
in informal settlements. Property rights means reducing the cost of informal housing. It
is a parallel result to the one found previously for the infrastructure upgrading policies.
In the simulations, better infrastructure or property rights increase slums because they
give incentive toward living in informal units. Note that it would be necessary to combine
several policies to extinguish informal housing from the simulations.27
The main lesson from the analysis is that one must differentiate two groups of policies.
By providing better infrastructure or giving property rights, the government is in practice
changing the “type” or “quality” of the informal housing. For example, improving infrastructure by decreasing θ means that the informal housing is becoming “more attractive”
and this explain why more people wants to live in informal settlements. The same reasoning applies to a decrease in defensive expenditures. By contrast, by reducing the cost of
formal housing (e.g., changing regulation and property taxation), the government would
induce households to migrate from informal to formal housing units.
5.3
Welfare
This subsection exploits additional information from the simulated policies regarding welfare impacts. We measure welfare impacts from the simulated policies using the concept
of equivalent variation. The simulated policies are the same ones described in the previous subsection: reduction of formalization costs, changing urban regulation, infrastructure
upgrading, and titling. The magnitude of the changes are similar to those presented previously in Table 8.
One important feature of our welfare analysis is that again we account for general
equilibrium effects. Large-scale interventions may have substantial impacts, so ignoring
27
We also simulated the impacts from a hypothetical cash-transfer program. The properties of model
show that any policy to reduce inequality will reduce the incidence of slums. However, the effectiveness
of the inequality-reducing policies will depend on the size of the informal housing sector in the city. The
intuition is simple: for a given level of inequality, the bigger the informal housing sector is, the greater is the
pressure of housing prices after a cash transfer policy. If housing prices increase greatly after the transfer
policy, the effect of the transfer policy will be diminished. In our baseline city, the informal housing sector
is less than 10%, so inequality-reducing policies have an important impact on slums’ reduction. Cashtransfer simulations are for a 20% percentage increase in income of the bottom decile and this decreases
slums from 8.91% to 6.87% in the simulations.
39
general equilibrium effects may produce misleading evaluations. The size of the intervention influences the impact of the policy as individual response to policies varies when only
his or her constraints changes but also when economy-wide variables changes. Recall that
households are linked in the model through the housing market. Therefore, some agents are
directly affected by the simulated policy, while other are only indirectly affected by policies
through market mechanisms (i.e., through varying housing prices or pecuniary externalities). Take the case of a titling or infrastructure upgrading program: those who receive
the land titling or the infrastructure improvement are directly affected, while the rest of
the agents are affected by the effects on housing demand and housing prices. Similarly,
reducing property taxation has a direct effect on the budget constraint of households living
in formal housing, as well as an indirect effect on all households via housing prices. In the
case of reducing MLS regulation, the direct effect is only on a subset of households (the
ones that switched tenure or had their previous housing space consumption constrained by
the urban regulation), while the indirect effects impact all households via housing prices.
Equivalent Variation. Let “b” represent a baseline policy and “a” represent the alternative policy being evaluated. Let Va and Vb be the individual’s indirect utilities under
policies “a” and “b” respectively. The equivalent variation (EV) is calculated as the percentage change in income such that households enjoy the same level of utility after the
policy as before the policy, i.e.,
Va (λ, o, ξ(z ! )) = Vb (λ(1 + EV ), o, ξ(z)),
where EV is the equivalent variation and ξ(·) represents the vector of 14 parameters of
the model. The the vector of parameter z ! represents the set of parameters with the policy
change.
Results for the EV exercise are shown in Table 9, which reports the average EV for
different policies. While the reduction of property taxation by half is the policy with the
greatest impact on slums only by a small margin (see Table 8 in Subsection 5.2), property
tax reduction has the greatest effect on welfare by a far-reaching margin. This policy
affects directly all households living in formal housing and indirectly informal and formal
households. Therefore, the measure of agents affected directly by this policy is large,
while MLS relaxation, infrastructure and titling affect directly only a small subsample of
households (consequently with a small indirect general equilibrium effect). The average
welfare gains in reducing property tax by half is equivalent to an increase in 1.54 percent
of income relative to the baseline.
Table 9 indicates the average welfare impacts from the simulated policies. However, we
have heterogenous households in the model and then we are able to perform an analysis
40
Table 9: Policy Simulations: Average Welfare Impacts
Policy Simulations
1.
2.
3.
4.
Equivalent Variation (%)
Formalization costs: reduction by half
MLS reduction by 10%
Infrastructure Upgrading: Eliminating informal housing disutility
Titling: Reduction of protection costs by half
1.54%
0.06%
0.27%
0.22%
Notes. The table presents four policy simulations. Reduction of formalization costs is a reduction of the
parameter η by half. MLS reductions means a reduction of 10% in h. In the infrastructure upgrading we set θ
equals to 1. Titling means reducing the value of the parameter ψ by half.
about the distributional welfare effects of each policy. In order to implement such analysis,
it is useful to classify the households into four categories (as described in Figure 2 in
Subsection 3.2): informal housing, informal housing due to regulation, constrained formal
housing and formal housing. The simulated policies will present heterogenous impacts and
those four categories will be useful to understand the main trends.
Figure 4 shows the heterogenous impacts from the simulated policies. We start by
analyzing the reduction of formalization costs (see Figure 4(a)). The direct impact on the
budget constraint means that property tax reduction is associated with a welfare gain on
average (as shown by the average EV of 1.54% from Table 9). Note that property taxation
reduction affects decision of all formal agents who are a large measure of the society and this
causes a great impact on housing prices. As a consequence, the increased aggregate housing
demand means higher housing prices and this impacts negatively the welfare of every single
household. The higher housing price is of second order importance for the majority of
households, but very important to some of them: Figure 4(a) points out that the ones who
suffer the most from higher housing prices are the households with lower labor productivity.
High housing prices act as a barrier that impact more aggressively and adversely low-ability
households with a higher marginal utility of consumption. This reduction in property
tax generates a welfare loss of about 1 percent of income equivalent to the baseline for
households at the bottom of the income distribution. If we had simulated the EV exercise
without general equilibrium effects, no household would have had a negative individual
EV. Although some agents have a negative individual EV, the average EV is still positive
as mentioned above. Lastly, notice that there is a spike in welfare for those individuals
whose tenure choice is modified by the simulated policy. For such households, this policy
can increase welfare by more than 2 percent of consumption equivalent to the baseline
income.
Figure 4(b) displays a distinct welfare pattern for the relaxation of MLS regulations.
MLS regulation affects directly households who are informal due to housing regulations and
households whose (formal) housing consumption is constrained. A relaxation in regulation
means more housing space consumption for those two categories of households (i.e., an
increase in housing demand). Figure 4(b) shows a (i) positive EV for the changing-tenure
41
households and constrained-consumption households and a (ii) slightly negative EV for the
lower and higher abilities agents. For households who are directly affected by this policy,
the average welfare gains can reach about 2 percent of income relative to the baseline.
Note that the negative values are due to the fact that those lower-ability and higherability households are not directly affected by MLS regulations, but they are negatively
affected by higher housing prices. We observe slightly negative values for EV because
housing prices do not increase much after MLS relaxations (as MLS relaxation affects only
a subset of households). The average impact of MLS relaxation turns out to be positive,
even though the welfare of some households are negatively affected by this policy.
Infrastructure upgrading has an average positive impact (an EV of about 0.27%). As
shown in Figure 4(c), the positive impact is specially strong for those households in the
informal housing sector. Contrary to the other policies analyzed so far, it does have a
small positive impact on the rest of the population. The intuition is as follows: an increase
in θ affects the indirect utility of households inducing a switching from formal to informal
housing tenure by some households, but θ does not affect housing space consumption. As a
result, the group of “switchers” to informality (due to ↑ θ) actually reduces housing space
consumption: informal housing is still insecure (because of ψ) and so housing consumption
in the simulated policy is lower than the previous (formal housing) space consumption
in baseline policy. There is an aggregate decline in housing prices because of the lower
housing consumption of the switchers. The lower housing price affects positively the welfare
of the rest of the agents. The result is that there is an aggregate welfare increase after
infrastructure upgrading, even though there is an increase in the number of households
living in slums. For EV for those households affected directly by this policy are almost 3
percent of income equivalent to the baseline.
Finally, titling has an average positive welfare impact of about 0.22% even though
there is an increase in slums’ share. Notice that titling (represented by a decrease in
ψ) influences housing space consumption of the informal housing sector. As a result, a
decline in ψ increases both overall housing demand and housing prices. The result is that
the households indirectly affected by this policy suffer a small negative welfare impact.
The slightly negative effect on some households is more than offset by welfare gains from
households directly impacted by the titling policy (see Figure 4(d)). For the later group,
welfare gains can reach almost 4 percent of income relative to the baseline. A large measure.
42
4
4
3
3
2
2
1
1
EV (%)
EV (%)
Fig. 4: Individual-level Equivalent Variation (EV)
0
−1
−1
−2
−3
0
−2
Formalization costs
0
100
200
300
400
Regulation
−3
500
0
100
200
Ability
(a) Formalization Cost
400
4
4
3
3
2
2
1
1
0
−1
0
−1
−2
−2
Titling
Upgrading
−3
500
(b) MLS relaxation
EV (%)
EV (%)
300
Ability
0
100
200
300
400
−3
500
0
100
200
Ability
300
400
500
Ability
(c) Infrastructure
(d) Titling
4
3
EV (%)
2
1
0
−1
Formalization costs
Regulation
Upgrading
Titling
−2
−3
0
100
200
300
400
500
Ability
(e) All Policies
Notes. The figures show the welfare impact measured by individual-level equivalent variations (EV) from
four policies: reduction in formalization costs, relaxation of MLS regulations, infrastructure provision,
and titling. In each subfigure, the vertical axis displays the EV (as a percentage of the individual
income), while the horizontal axis shows the heterogenous ability (truncated for the first one-third of the
households).
43
We can summarize the main implications of the welfare analysis as follows: (i) even
considering general equilibrium effects, we find an average welfare gain from the simulated
policies; (ii) the positive welfare is guided in most cases by the great welfare gain from the
households directly affected by the policies; (iii) even though some policies increase slums’
share, the same policies may be associated with a positive welfare impact.
6
Conclusion
Informal housing plays an important role in developing countries. This article aims to
measure the main determinants of the informal housing expansion and to evaluate the
impact of policies towards slums. We construct a simple general equilibrium model of a
city to explain the determinants of informal housing formation. The model is calibrated
and estimated to be consistent with several statistics related to the urbanization process
in São Paulo.
Our results show that urban poverty, rural-urban migration and man-made regulations
explain much of the variation in slums’ growth during 1980-2000 in São Paulo. In particular, the results indicate that income inequality has a sizeable effect on slums’ growth.
Our ex-ante policy evaluation points out that (i) decreasing barriers to formalization (e.g.,
“friendly” land-use regulations) has great impact on slums’ reduction, while (ii) slum upgrading interventions can have unintended adverse impacts as infrastructure improvement
and titling may induce more people to live in slums. The main lesson from the analysis
is that one must differentiate two groups of policies. By providing better infrastructure
or giving property rights, the government is in practice changing the “type” or “quality”
of the informal housing. Improving infrastructure and land security means that the informal housing is becoming “more attractive” and this explain why more people may live in
informal settlements.
An important element of the model is the protection cost. Our estimate for protection
costs is high: forgone labor income is approximately 16% per unit of housing space. This
is an upper-bound estimate because it is for São Paulo, where land prices are high and
thus informal households need to allocate more time for protection. This high value for
protection costs highlights a relevant aspect from living in slums: forgone time. Our
estimated parameter shows how a slum is associated with “time lost”: slum dwellers lose
time to protect informal plot, to allocate children to protect the informal plot, to recover
from health problems related from inadequate urban infrastructure (such as diarrhoea),
among other factors. In fact, slum dwellers may lose time simultaneously to protect the
irregular plot or to recover from illness. Moreover, slum dwellers may not fulfill their labor
potential because of stigma attached to the urban poor.
44
The analysis has several policy implications. The analysis points out that regulation
and inequality has great influence on slum formation. Besides, upgrading policies may
change adversely the incentives regarding the decision to whether dwell in slums. Housing
formalization policies may decrease the opportunity cost of informal housing and increase
aggregate welfare. Nevertheless, our simulations indicate that average welfare gains may
be driven by large gains from the subpopulation directly targeted by the policy towards
slums (in detriment of the rest of population that may be worse off after the program).
There are several determinants of slums formation. All factors are directly or indirectly
related to housing affordability. This paper quantifies the impact of three factors: the focus
is on how urban poverty (proxied by real incomes and income inequality), rural-urban
migration, and changing land use regulations impact the evolution of informal housing in
Brazil. In this paper, we concentrate on this three factors but extensions may include other
factors that may explain the formation of slums in developing countries, such as the cost
of infrastructure, human capital formation, and higher fertility rates of poor households.
Another natural extension of this paper would be to explore the spatial impacts of
regulation and other policies within a city. In order to study further the location properties
of the model, it is necessary to endogeneize the city boundaries and verify how land costs
change within the city boundaries. This would be important in order to explain the spatial
configuration of cities in developing countries, where, in terms of residency, the traditional
city center has several empty areas and where the middle-class and rich households live
somewhat closer to the city center compared to the poor households (that live in very
suburb areas). It is a different spatial pattern from what is observed in most developed
countries.
45
References
Amaral, P. S., and E. Quintin (2006): “A competitive model of the informal sector,”
Journal of Monetary Economics, 53(7), 1541 – 1553.
Antunes, A. R., and T. Cavalcanti (2007): “Start up costs, limited enforcement, and
the hidden economy,” European Economic Review, 51(1), 203 – 224.
Aura, S., and T. Davidoff (2008): “Supply constraints and housing prices,” Economics
Letters, 99(2), 275–277.
Baum-Snow, N. (2007): “Suburbanization and transportation in the monocentric
model,” Journal of Urban Economics, 62(3), 405–423.
Brinkman, J., D. Coen-Pirani, and H. Sieg (2010): “Agglomeration externalities
and the dynamics of firm location choices,” Mimeograph, University of Pennsylvania.
Brueckner, J. K. (2013): “Urban squatting with rent-seeking organizers,” Regional
Science and Urban Economics, 43(4), 561 – 569.
Brueckner, J. K., and H. Selod (2009): “A Theory of Urban Squatting and LandTenure Formalization in Developing Countries,” American Economic Journal: Economic
Policy, 1(1), 28–51.
Carvalho Jr., P. H. (2008): “Distributive Effects of Real Estate Property and its
taxation among Brazilian Families,” Working paper n.1417a, Ipea.
Chatterjee, S., and G. A. Carlino (2001): “Aggregate metropolitan employment
growth and the deconcentration of metropolitan employment,” Journal of Monetary
Economics, 48(3), 549–583.
Da Mata, D., U. Deichmann, J. Henderson, S. Lall, and H. Wang (2007):
“Determinants of city growth in Brazil,” Journal of Urban Economics, 62(2), 252–272.
Da Mata, D., S. V. Lall, and H. Wang (2008): “Favelas e Dinâmica das Cidades
Brasileiras,” in Ensaios de Economia Regional e Urbana, ed. by A. Carvalho, C. Oliveira,
J. Mota, and M. Piancastelli, pp. 47–64. Brası́lia: IPEA.
Davis, M. A., and J. Heathcote (2005): “Housing And The Business Cycle,” International Economic Review, 46(3), 751–784.
Davis, M. A., and F. Ortalo-Magne (2011): “Household Expenditures, Wages,
Rents,” Review of Economic Dynamics, 14(2), 248–261.
46
Di Tella, R., S. Galiani, and E. Schargrodsky (2007): “The Formation of Beliefs:
Evidence from the Allocation of Land Titles to Squatters,” The Quarterly Journal of
Economics, 122(1), 209–241.
Field, E. (2005): “Property Rights and Investment in Urban Slums,” Journal of the
European Economic Association, 3(2-3), 279–290.
(2007): “Entitled to Work: Urban Property Rights and Labor Supply in Peru,”
Quarterly Journal of Economics, 122(4), 1561 – 1602.
Frankenhoff, C. A. (1967): “Elements of an Economic Model for Slums in a Developing
Economy,” Economic Development and Cultural Change, 16(1), pp. 27–36.
Friedman, J., E. Jimenez, and S. K. Mayo (1988): “The demand for tenure security
in developing countries,” Journal of Development Economics, 29(2), 185 – 198.
Galiani, S., and E. Schargrodsky (2010): “Property rights for the poor: Effects of
land titling,” Journal of Public Economics, 94(910), 700 – 729.
Galor, O., and J. Zeira (1993): “Income Distribution and Macroeconomics,” Review
of Economic Studies, 60(1), 35–52.
Glaeser, E. L., and M. E. Kahn (2004): “Sprawl and urban growth,” in Handbook
of Regional and Urban Economics, ed. by J. V. Henderson, and J. F. Thisse, vol. 4 of
Handbook of Regional and Urban Economics, chap. 56, pp. 2481–2527. Elsevier.
Gollin, D. (2002): “Getting Income Shares Right,” Journal of Political Economy, 110(2),
458–474.
Hamilton, B. W. (1978): “Zoning and the exercise of monopoly power,” Journal of
Urban Economics, 5(1), 116–130.
Hansen, L. P. (1982): “Large Sample Properties of Generalized Method of Moments
Estimators,” Econometrica, 50(4), 1029–54.
IBGE (2002): Pesquisa Nacional por Amostra de Domicı́lios: several years. Rio de Janeiro,
RJ: Instituto Brasileiro de Geografia e Estatı́stica - IBGE.
(2004): Pesquisa de Orçamentos Familiares: 1986-1987, 1995-1996, and 20022003. Rio de Janeiro, RJ: Instituto Brasileiro de Geografia e Estatı́stica - IBGE.
(2011): Censo 2010: Aglomerados Subnormais, Primeiros Resultados. Rio de
Janeiro, RJ: Instituto Brasileiro de Geografia e Estatı́stica - IBGE.
47
Jimenez, E. (1984): “Tenure Security and Urban Squatting,” The Review of Economics
and Statistics, 66(4), 556–67.
(1985): “Urban squatting and community organization in developing countries,”
Journal of Public Economics, 27(1), 69–92.
Kapoor, M., and D. le Blanc (2008): “Measuring risk on investment in informal
(illegal) housing: Theory and evidence from Pune, India,” Regional Science and Urban
Economics, 38(4), 311–329.
Kopecky, K. A., and R. M. H. Suen (2010): “A Quantitative Analysis of Suburbanization And the Diffusion of the Automobile,” International Economic Review, 51(4),
1003–1037.
Lanjouw, J. O., and P. I. Levy (2002): “Untitled: A Study Of Formal and Informal
Property Rights in Urban Ecuador*,” The Economic Journal, 112(482), 986–1019.
Lebergott, S. (1996): Consumer Expenditures: New Measures and Old Motives. Princeton: Princeton University Press.
Michaels, G., F. Rauch, and S. J. Redding (2012): “Urbanization and Structural
Transformation,” The Quarterly Journal of Economics, 127(2), 535–586.
Parker, S. C. (1999): “The generalised beta as a model for the distribution of earnings,”
Economics Letters, 62(2), 197 – 200.
Plümper, T., and V. E. Troeger (2007): “Efficient Estimation of Time-Invariant and
Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects,”
Political Analysis, 15(2), 124–139.
Quigley, J. M., and S. Raphael (2005): “Regulation and the High Cost of Housing
in California,” American Economic Review, 95(2), 323–328.
Saiz, A. (2010): “The Geographic Determinants of Housing Supply,” The Quarterly Journal of Economics, 125(3), 1253–1296.
Smolka, M. O., and C. Biderman (2011): “Housing Informality: An Economist’s
Perspective on Urban Planning,” in The Oxford Handbook of Urban Economics and
Planning, ed. by K. D. Nancy Brooks, and G.-J. Knaap. Oxford University Press.
Todaro, M. (1969): “A model of labor migration and urban unemployment in less developed countries,” The American Economic Review, 59(1), 138–148.
Turnbull, G. K. (2008): “Squatting, eviction and development,” Regional Science and
Urban Economics, 38(1), 1–15.
48
UN (2004): World Urbanization Prospects: the 2003 Revision / United Nations, Population Division. New York, N.Y.: United Nations.
UN-Habitat (2003): The challenge of slums : global report on human settlements, 2003
/ United Nations Human Settlements Programme. UN-Habitat [and] Earthscan Publications, London ; Sterling, VA :.
49
A
A.1
Appendix: Data
Data Sources and Definitions
The Brazilian Population Censuses (1960 to 2010) and Brazil’s National Survey of Households (PNAD - in Portuguese, Pesquisa Nacional por Amostra de Domicı́lios) provided the
majority of the data used in stylized facts and reduced-form analysis (section 2). While
the Population Censuses take place every decade, PNAD survey is done every year (except
from the years when a Census takes place). Both the Census and PNAD are carried out by
IBGE (Brazilian Bureau of Statistics). The Population Census provided information on
total population, rural population, urban population, slums, and slum dwellers. Annual
income level and income inequality (measured by the Gini coefficient) stem from PNAD.
Price index used to created real income data was the INPC (Consumer National Price
Index) from IBGE.
Data on zoning and urban regulation are from Perfil dos Municı́pios Brasileiros, a
survey conducted yearly by IBGE. We used the 1999 Perfil dataset, the survey that contains
detailed information on zoning measures for each municipality in Brazil. Data on historical
GDP comes from Ipeadata.
Caju slum dataset was collected to provide information for a land titling program
carried out by the housing department of Rio de Janeiro municipality. The Caju dataset
was constructed in 2002 by IETS (Institute for Labor and Social Studies), FIRJAN (Rio’s
Federation of Industries) and SCIENCE (National School of Statistical Science). The land
titling program is called “Favela-Bairro” (literally, Slums-Neighborhood). Caju slum, one
of the first informal settlements in Rio, is located in Rio’s port region. The community had
843 households and the total sample size was 261 households. The Caju community was
located in federal land, so to facilitate the land titling program, the federal government
ceded the land to the municipality of Rio de Janeiro. The local government then sold the
land to the households and invested in infrastructure. The pacification of the Caju slum
took place in 2013. The presence of special Pacifying Police Units (in Portuguese, Unidade
de Polı́cia Pacificadora) started on March 3rd 2013. After being controlled for years by
drug traffickers, the slums in Rio de Janeiro are undergoing a change to make slums safer28
29
. Figure 5 shows the location of Caju slum in Port region in Rio de Janeiro.
Data from Table 3 and the regressions of Table 4 (see section 2) are all for 123 urban
agglomerations. The 123 urban agglomeration comprises more then 800 municipalities in
Brazil. Brazil has experienced several detachment and splits of municipalities, especially
from the 1980’s on (when democracy was restored in Brazil). For instance, there were
3,951 municipalities in 1970, 3,991 municipalities in 1980, 4,491 in 1991, 5,507 in 2000
and 5565 in 2010. The 123 urban agglomerations were constructed so as to comparable
spatial units over time. The construction of the 123 urban agglomerations is detailed in
Da Mata, Deichmann, Henderson, Lall, and Wang (2007).
Data on housing consumption (the parameter α in the utility functions) stems from the
Household Budget Survey (IBGE (2004)) carried out by IBGE. POFs were undertaken in
1987/1988, 1995/1996, and 2002/2003 and they provide detailed information (more than
10,000 expenditure types) about households’ expenditures. POFs are the main data source
28
http://www1.folha.uol.com.br/cotidiano/1240193-ocupacao-no-rio-foi-considerada-a-mais-tranquilanos-quatro-anos-de-upps.shtml
29
http://g1.globo.com/rio-de-janeiro/noticia/2013/03/bandeiras-sao-hasteadas-em-comunidadesocupadas.html
50
Fig. 5: Map of Caju Slum and Rio de Janeiro’s Port Region
(a) Caju Slum
(b) Caju Slum and the Port region
Notes: Map constructed from http://www.censo2010.ibge.gov.br/agsn/.
on the distribution of spending of Brazilian households.
A.2
Slums Data in Brazil
In Brazil, the only national-wide source of city-level slums data is the Brazilian Bureau of
Statistics (IBGE) Population Census. The Population Censuses classifies whether the housing unit is considered an “aglomerado subnormal” (subnormal agglomeration). “Aglomerados Subnormais” classification includes both irregular and illegal units. According to the
Censuses, a subnormal agglomeration satisfies three conditions: (a) a group of at least 50
housing units; (b) where land is occupied illegally and (c) it is urbanized in a disordered
pattern and/or lacks basic public services such as sewage or electricity. Therefore, there
is a connection between the definition of “subnormal agglomeration” and the notion of a
“slum”. Slums in Brazil are better known as “favelas”, where there is lack of public services
and illegal occupation of government-owned land, marginal land (floodplains or hillsides)
or under dispute land. “Cortiços” are high-density housing units located in central older
parts of metropolitan areas.
The most recent data on slums is from the 2010 Population Census. Brazil had
11,425,644 people living in slums (6.01% of the total population). There were 3,224,529
housing units classified as subnormal agglomerations (5.61% of the total housing units).
Slum data from the 2010 Census is not directly comparable with that of other Censuses
(IBGE (2011)).
One issue with the Population Census data is that it underestimates the real number
of slum dwellers in the country. One concern is that the local government is in charge of
defining whether a housing block is classified as subnormal. Another issue is the definition
of a subnormal agglomeration itself. Information on the number of slum dwellers in the
municipality of São Paulo shows the evolution of slums as well as the issues regarding the
measurement of slums in Brazil. Table 10 shows the number of people in slums in São
Paulo according to different sources. In 1973, there were only over 71,000 people living in
slums, while by 1987 roughly 780,000 people were living in slums and by 2010 there were
almost 1.3 million people in slums.
The Population Censuses tend to underestimate the number of people in slums. One
can see this pattern by verifying the slums numbers according to other sources. One
51
reason for the Censuses underestimation is the definition of a subnormal agglomeration
(recall that it must contain at least 50 housing units together). The other sources define
a slum if two or more housing units lack public services and lack land titling. São Paulo
has several small-scale slums (the opposite happens in Rio de Janeiro), and that explain
the underestimated numbers of the several Censuses.
Table 10: Population living in Slums - São Paulo
Source
Year
1973
Cadastro e Censo de Favelas 1975
1987
Eletropaulo
1980
FIPE
1993
1991
CEM
2000
1980
1991
IBGE Population Census
1996
2000
2010
# Pop. in Slums
71,840
117,237
812,764
594,525
1,901,892
891,673
1,160,590
335,334
711,050
749,318
932,628
1,280,400
% Pop. in Slums
1.06%
1.60%
8.90%
7.00%
19,80%
9.24%
11.12%
4.07%
7,46%
7,60%
8.92%
11.42%
Notes. “Cadastro and Censo de Favelas” was done by the Prefecture of São Paulo.
CEM stands for “Centro de Estudos da Metrpole”. In 1996, there was a Population
Count done by IBGE.
52
B
Appendix: Proofs
Lemma 1. Recall that when constraint (6) is binding, we have that:
VbF (λ; o) = [w(1 − τ )λ − RH (1 + η)h]1−α hα g α ,
H (1+η)h
and this problem is defined only when λ ≥ λ(o) = Rw(1−τ
. In addition, we have that
)
formal housing demand is given by
'
(
wλ(1 − τ )
hF (λ; o) = max α
,h .
RH (1 + η)
H (1+η)h
This equation defines λM LS (o) = Rαw(1−τ
> λ(o), such that when λ < λM LS (o), then
)
hF (λ; o) = h which is independent of labor productivity λ; and when λ ≥ λM LS (o), then
)
hF (λ; o) = α Rwλ(1−τ
which is linear in labor productivity.
H (1+η)
F
Continuity of Vnb (λ; o) follows from the Maximum Theorem. Similarly for continuity
F
of VbF (λ; o) at λ > λ(o). Notice that Vnb
(λ; o) = VbF (λ; o) if and only if λ = λM LS (o).
F
Therefore, there is no jump in the function V F (λ; o) = max{Vnb
(λ; o), VbF (λ; o)} and
F
F
V (λ; o) is continuous at λ ∈ (λ(o), ∞). By twice differentiating Vb (λ; o), we can easily
show that this function is strictly concave and therefore so it will be V F (λ; o) for λ ∈
F
(λ(o), λM LS (o)). We can also show that limλ→+ λ(o) V F (λ; o) = 0 and limλ→+ λ(o) ∂V ∂λ(λ;o) =
∞. We also have that
F
Vnb
(λ; o) = αα (1 − α)1−α w(1 − τ )λ[RH (1 + η)]−α g α ,
which is linear in λ.
Lemma 2. The indirect utility for households living in informal housing is given by:
V I (λ; o) = αα (1 − α)1−α w(1 − τ )λ[RH + ψw(1 − τ )λ]−α (gθ)α ,
It is straightforward to show that that V I (λ; o) is continuous and differentiable in λ ∈
(0, ∞), limλ→+ 0 V I (λ; o) = 0. We also have that
∂V I (λ; o)
= αα (1−α)1−α w(1−τ )λ[RH +ψw(1−τ )λ]−α−1 (gθ)α [RH +(1−α)ψw(1−τ )λ] > 0,
∂λ
and limλ→+ 0
∂V I (λ;o)
∂λ
−α
= αα (1 − α)1−α w(1 − τ )RH
(gθ)α . In addition,
∂ 2 V I (λ; o)
= −αα (1−α)1−α w(1−τ )λ[RH +ψw(1−τ )λ]−α−2 (gθ)α α(RH +(1−α)ψw(1−τ )λ)ψw(1−τ ) < 0.
∂λ2
Informal housing demand is
hI (λ; o) = α
λw(1 − τ )
∂hI (λ; o)
αw(1 − τ )RH
⇒
=
> 0.
RH + ψwλ(1 − τ )
∂λ
(RH + ψwλ(1 − τ ))2
∂hF (λ;o)
λ
= 1 if λ > λM LS (o)
∂λ
hF (λ;o)
(λ;o)
λ
also have that ∂hI∂λ
=1−
hI (λ;o)
1+
Proposition 3. Notice that
λ ∈ (λ(o), λ
M LS
(o)). We
and
∂hF (λ;o)
λ
∂λ
hF (λ;o)
1
RH
ψw(1−τ )λ
53
< 1.
= 0 for
∂V F (λ;o)
I
(λ;o)
Lemma 4. Under Assumption 1, we have that limλ→+ 0 ∂V ∂λ
> limλ→+ 0 nb∂λ . Then,
F
given that V I (λ; o) is strictly concave in λ ∈ (0, 1) and Vnb
(λ; o) is linear in λ ∈ (0, 1),
I
F
then V (λ; o) crosses Vnb (λ; o) from above in only one value of λ > 0. Denotes this value
by λ̄nb (o), where
RH
λ̄nb (o) =
[θ(1 + η) − 1].
ψw(1 − τ )
F
Function VbF (λ; o) is defined at λ ∈ (λ(o), ∞). Moreover, VbF (λ; o) ≤ Vnb
(λ; o) and equalM LS
M LS
ity holds if and only if λ = λ
(o) > λ(o). Therefore, if λ
(o) < λ̄nb (o), then MLS
regulations do not affect housing choice and
λ̄(o) = λ̄nb (o) =
RH
[θ(1 + η) − 1],
ψw(1 − τ )
such that for any λ ∈ (0, λ̄(o)), then λ ∈ (E F )c (o); and for any λ ∈ (λ̄(o), ∞), then
λ ∈ E F (o). We can easily observe that items (i) and (ii) of Lemma 4 are also satisfied.
When λM LS (o) < λ̄nb (o), then for λ ∈ (λ(o), λM LS (o)) V F (λ; o) = VbF (λ; o). Notice that
F
F
for λ > λ̄nb (o) V I (λ; o) is uniformly lower than Vnb
(λ; o). Since VbF (λ; o) = Vnb
(λ; o) at
λM LS (o), we have have that VbF (λ; o) has to cross V I (λ; o) from below at λ̄b (o) = λ̄(o) ∈
(λ(o), λM LS (o)). Therefore,
VbF (λ̄(o); o) − V I (λ̄(o); o) ≡ 0.
Using the implicit function theorem, it can be shown that for instance
∂ λ̄(o)
−[w(1 − τ )λ − RH (1 + η)h]−α hα−1 [RH (1 + η)h − αw(1 − τ )λ]
=−
.
I
∂VbF (λ̄(o);o)
∂h
− ∂V (λ̄(o);o)
∂λ
∂λ
The denominator of this above equation is positive, since VbF (λ; o) crosses V I (λ; o) from
H (1+η)h
below at λ̄(o) ∈ (λ(o), λM LS (o)). Notice that λ̄(o) < λM LS (o) = Rαw(1−τ
, which implies
)
that ∂ λ̄(o)
> 0. Using similar arguments, it can be shown that items (i) and (ii) of Lemma
∂h
4 are satisfied.
Proposition 5. Define the housing excess demand function by HED(RH ; o, P, L)
HED = P
&
λ̄(o)
0
λw(1 − τ )
α
dΥ(λ) + P
RH + ψwλ(1 − τ )
&
∞
max
λ̄(o)
'
(
1−γ
1−γ $
wλ(1 − τ )
1−γ% γ
α
, h dΥ(λ) − LRHγ
.
RH (1 + η)
r2
Functions V F (λ; o) and V I (λ; o) '
are continuous
( in RH .
)
α RH λw(1−τ
and hF (λ; o) = max
+ψwλ(1−τ )
Notice also that hI (λ; o) =
)
α Rwλ(1−τ
, h are continuous in RH Therefore, measure
H (1+η)
λ̄(o) varies smoothly with RH and HED(RH ; o, P, L) is also continuous in RH . As RH → 0,
then limRH →0 HED(RH ; o, P, L) = ∞. Moreover, limRH →∞ HED(RH ; o, P, L) = −∞.
54
Therefore, an equilibrium exists. Notice also that
&
λ̄(o)
λw(1 − τ )
∂ λ̄(o)
λ̄(o)w(1 − τ )
)dΥ(λ) + P
α
υ(λ̄(o))
2
(R
+
ψwλ(1
−
τ
))
∂R
R
+ ψwλ̄(o)(1 − τ )
H
H
H
0
'
(
& ∞
wλ(1 − τ )
∂ λ̄(o)
wλ̄(o)(1 − τ )
+P
(−α 2
)Imax≥h dΥ(λ) − P
max α
, h υ(λ̄(o))
RH (1 + η)
∂RH
RH (1 + η)
λ̄(o)
∂HED
=P
∂RH
(−α
−
1−γ
1−2γ $
(1 − γ)
1−γ% γ
LRH γ
,
γ
r2
where υ(λ̄(o)) is the probability function evaluated at λ̄(o) and Imax≥h is an indicator
)
λ̄(o)
function which takes value 1 when α Rwλ(1−τ
≥ h and zero otherwise. Recall that ∂∂R
> 0,
H (1+η)
H
then the only positive term in the above equation is the second one. A sufficient condition
for ∂HED
to be negative is that
∂λ
'
(
∂ λ̄(o)
λ̄(o)w(1 − τ )
wλ̄(o)(1 − τ )
D=P
υ(λ̄(o))[α
− max α
, h ] ≤ 0.
∂RH
RH (1 + η)
RH + ψwλ̄(o)(1 − τ )
When λM LS (o) < λ̄nb (o), then
λ̄(o) = λ̄nb (o) =
RH
[θ(1 + η) − 1].
ψw(1 − τ )
In this case, we have that when θ → 1, then D → 0 and
then when h ≥ 1+ ψ1+η
, then D ≤ 0 and ∂HED
< 0.
∂RH
(1+η)
∂HED
∂RH
< 0. When λM LS (o) > λ̄(o),
α
Proposition 6. For the comparative statics we have the following two equations:
P
&
λ̄(o)
0
λw(1 − τ )
α
dΥ(λ) + P
RH + ψwλ(1 − τ )
&
∞
λ̄(o)
max
'
(
1−γ
1−γ $
wλ(1 − τ )
1−γ% γ
α
, h dΥ(λ) − LRHγ
= 0,
RH (1 + η)
r2
V F (λ̄(o); o) − V I (λ̄(o); o) = 0.
These two equations define λ̄(o) and RF . The last equation has two cases. The first
in which the MLS regulation does not bind, i.e., V F (λ̄nb (o); o) − V I (λ̄(o); o) = 0 and
RH
λ̄(o) = ψw(1−τ
[θ(1+η)−1], and the case when the MLS regulation does bind V F (λ̄b (o); o)−
)
V I (λ̄(o); o) = 0. Define the 2x2 matrix J(RH , λ̄(o)), such that
J11 = P
&
λ̄(o)
0
λw(1 − τ )
−α
dΥ(λ) + P
(RH + ψwλ(1 − τ ))2
J12 = α
&
λ̄(o)w(1 − τ )
υ(λ̄(o)) − max
RH + ψwλ̄(o)(1 − τ )
∞
(−α
λ̄(o)
'
α
wλ(1 − τ )
)Imax≥h dΥ(λ) < 0,
2
RH
(1 + η)
(
wλ̄(o)(1 − τ )
, h υ(λ̄(o)).
RH (1 + η)
When the MLS regulation is not binding and θ → 1, then J12 = 0. When the MLS
η α
regulation is binding and h ≥ (1+η)
, then J12 < 0. In addition, we have that:
ψ
J21 = −
1
[θ(1 + η) − 1] < 0,
ψw(1 − τ )
55
if the MLS regulation is not binding and if this constraint is binding we have that
J21 = −[w(1 − τ )λ̄(o) − RH (1 + η)h]−α hα [
RH (1 + η)h − αw(1 − τ )λ̄(o) + (1 − α)(1 + η)ψw(1 − τ )λ̄(o)
].
RH + ψw(1 − τ )λ̄(o)
The term in brackets is positive, since when the MLS regulation is binding we have that
H (1+η)h
λM LS (o) = Rαw(1−τ
> λ̄(o). Therefore, J21 < 0. Finally,
)
J22 = V1F (λ̄(o); o) − V1I (λ̄(o); o) > 0,
since V I (λ̄(o); o) crosses V F (λ̄(o); o) from below. Therefore, we can easily show that
det(J) < 0. Define J P,1 as a 2x2 matrix, such that we substitute the first column of matrix
P,1
J by the derivative of P of the equilibrium system of equations. Therefore, J12
= J12 ,
P,1
J22
= J22 ,
'
(
& λ̄(o)
& ∞
λw(1 − τ )
wλ(1 − τ )
P,1
J11 =
α
dΥ(λ) +
max α
, h dΥ(λ) > 0
RH + ψwλ(1 − τ )
RH (1 + η)
0
λ̄(o)
and
P,1
J21
= 0.
In this case, det(J P,1 ) < 0. Similarly, define J P,2 as a 2x2 matrix in which we substitute the
second column of matrix J by the derivative of P of the equilibrium system of equations,
P,2
P,2
P,2
P,1
P,2
where J11
= J11 , J21
= J21 , J12
= J11
, and J22
= 0. Consequently, det(J P,2 ) < 0.
Using Cramer’s rule, we can show that
∂RH
det(J P,1 )
(−)
∂ λ̄(o)
det(J P,2 )
(−)
=
=
> 0;
=
=
> 0.
∂P
det(J)
(−)
∂P
det(J)
(−)
Similarly and using analogous notation we can show that
∂RH
det(J L,1 )
(+)
∂ λ̄(o)
det(J L,2 )
(+)
=
=
< 0;
=
=
< 0;
∂L
det(J)
(−)
∂L
det(J)
(−)
∂RH
det(J r,1 )
(+)
∂ λ̄(o)
det(J r,2 )
(+)
=
=
> 0;
=
=
> 0;
∂r
det(J)
(−)
∂r
det(J)
(−)
∂RH
det(J θ,1 )
(+)
∂ λ̄(o)
det(J θ,2 )
(−)
=
=
< 0;
=
=
> 0;
∂θ
det(J)
(−)
∂θ
det(J)
(−)
∂RH
det(J w(1−τ ),1 )
(−)
∂ λ̄(o)
det(J w(1−τ ),2 )
(+) − (+)
=
=
> 0;
=
=
! 0;
∂w(1 − τ )
det(J)
(−)
∂w(1 − τ )
det(J)
(−)
∂RH
det(J h,1 )
(−) − (−)
∂ λ̄(o)
det(J h,2 )
(−)
=
=
! 0;
=
=
≥ 0;
∂h
det(J)
(−)
∂h
det(J)
(−)
∂RH
det(J ψ,1 )
(+) − (+)
∂ λ̄(o)
det(J ψ,2 )
(+)
=
=
! 0;
=
=
< 0;
∂ψ
det(J)
(−)
∂ψ
det(J)
(−)
∂RH
det(J η,1 )
(+)
∂ λ̄(o)
det(J η,2 )
(−)
=
=
< 0;
=
=
> 0;
∂η
det(J)
(−)
∂η
det(J)
(−)
∂RH
det(J µ,1 )
(+)
∂ λ̄(o)
det(J µ,1 )
(+)
=
=
> 0;
=
=
> 0.
∂µ
det(J)
(−)
∂µ
det(J)
(−)
56
F
Proposition 7. When h = 0, then V F (λ; o) = Vnb
(λ; o) = VbF (λ; o). Moreover, when
(1 + η)θ < 1, then V F (λ; o) ≥ V I (λ; o) for all λ > 0.
57
C
Extra Tables
Table 11: Summary statistics - Variables in OLS and RE regressions
Variable
Mean
% of Slum Dwellers
0.016
# of Slum Dwellers
32,748.25
(ln) per capita Income
5.571
Income inequality (Gini index)
0.563
Urban regulation
0.854
Population Density
199.526
Std. Dev.
0.033
146,599.09
0.345
0.042
0.354
285.953
Min.
Max.
0
0.241
0
1,666,033
4.597
6.255
0.427
0.664
0
1
1.297 2,248.611
N
369
369
369
246
369
369
Notes. Data for 123 urban agglomeration in Brazil. The variable “urban regulation” is a
dummy variable that takes value 1 if the majority of people in the urban agglomeration lives
in municipalities with own land use law. The Gini index is measured only in two year (1991
and 2000).
Table 12: Reduced-form Evidence: Random Effects
VARIABLES
ln # of Slum Dwellers
(i)
(ln) per capita Income
(ii)
(iii)
(iv)
(v)
2.252**
(1.0340)
0.906
(0.8109)
17.927**
(6.9960)
2.178**
(1.1100)
-0.011
(0.8295)
21.525***
(6.8185)
1.844*
(1.0444)
1.167***
(0.2794)
-14.487**
(5.9009)
2.097***
(0.8014)
Income inequality (Gini index)
16.501**
(7.0111)
Urban regulation
(ln) Population Density
Constant
Observations
Number of Agglomerations
-7.613*
(4.4789)
-4.679
(3.9651)
369
123
246
123
2.147** -12.398**
(0.9553) (5.9698)
369
123
246
123
246
123
Notes. Standard errors in parentheses. All the regressions are for 123 urban agglomeration in Brazil.
The Random Effects (RE) regressions are for 1980, 1991, and 2000. Therefore, there 369 observations
in each regression. The dependent variable is log number of slum dwellers (columns (vi) and (vii)).
Each urban agglomeration is formed by more than one municipality - the lowest autonomous administrative entity in the Brazilian federation. The explanatory variable “urban regulation” is a dummy
variable that takes value 1 if the majority of people in the urban agglomeration lives in municipalities
with own land use law. The Gini index is measured only in two year (1991 and 2000), and this explains
the 246 observations in regressions (ii), (iv), and (v).
*** p<0.01, ** p<0.05, * p<0.1
58