Real Estate Market in Developing Countries: Slums and Housing
Supply
*Ricardo Guedes†, Felipe Iachan†, and Marcelo Sant’Anna†
†FGV EPGE
June, 2020
Abstract
We study real estate markets where squatting is tolerated by authorities and a dual (formal
and informal) housing market emerge. We develop a housing supply model in which geographical
constraints and squatting play distinct roles on the housing supply curve. We estimate supply curves
for more than 90 metropolitan areas using satellite data that maps steep-sloped terrain and bodies of
water, a comprehensive slum survey, and census data of more than 600 municipalities. We find that
illegal settlements are more important to explain the cross-sectional variation in supply elasticities
than geographical constraints. As an illustrative application, estimated supply elasticities are used
to forecast future housing prices increase due to natural population growth.
Keywords: Urban Economics, Housing Supply, Real Estate Markets, Squatting and Slums
*We are grateful to Fernando Ferreira, Daniel da Mata, Cecilia Machado and Ciro Biderman for helpful comments. Financial support is gratefully acknowledged from Rede de Pesquisa Aplicada FGV and from Coordena¸c˜ao de Aper-fei¸coamento de Pessoal de N´ıvel Superior - Brasil (CAPES) - Finance Code 001.
1
Introduction
Housing expenses represent a mean share of more than 15% of households total consumption among Brazilian households, and exceeds 20% for poor families (IBGE, 2019). It is the main investment in the lifetime of many families. They enjoy most of their leisure time at home, and it serves as a safe, clean and healthy shelter. Housing location impacts access to labor market, schooling and health services. Therefore housing will be an important topic in many fields, including finance, public policy, economic development, and urban economics. These markets are exclusively local, once real estate is perfectly non-tradable.1 Local specific geographical restrictions manifest in different supply price sensitivities across cities. This means that cities will experience different movements in housing prices as they react to similar demand shocks. This is the original framework developed by Saiz (2010) to estimate housing supply curves for US cities.
The presence of illegal housing settlements is common in developing countries. These settlements develop without land use regulations, which evokes additional concerns as many households suffer with the more general absence of the rule of law in these communities. The extension of Saiz (2010) to such environment is a challenge considering the distinct features of their fast and disordered urban expansion and large informal housing markets. The interplay between formal and informal markets, and their distinct responses to shocks is of crucial importance to understand the price volatility that urban dwellers face in developing countries.
This article contributes to the literature with an empirical housing supply model that includes infor-mal house market and physical features. This model is estimated with a dataset that includes the most
1
In fact, several studies have showed the importance of allowing for heterogeneity across locations when modeling housing markets (Ferreira and Gyourko, 2012; Green et al., 2005; Malpezzia and Maclennan, 2001).
populated 180 commuting zones2 in all Brazilian regions. We build this dataset complementing census information with satellite data on geographical features and an extensive slums survey. Simulating the results of the theoretical framework with Brazilian data, illegal settlements could increase the supply elasticity, so cities with slums will accommodate demand shocks with less steep price variations. In other words, the prevalence of slums might alleviate the previously documented effect of geographic restrictions on housing supply. Our empirical results not only confirm that to be true but also imply that this effect is more important than geographical constraints in shaping the supply elasticity. This has important implications as policies targeting slum formalization may have significant consequences to how prices will respond to demand shocks.
Our model considers two types of land to populate the city: formal and informal. Homogeneous agents trade off illegal housing for better locations. The inhabitants prefer to live near the center to spend less time and money commuting, while dwellers are willing to accept a lower quality housing to live closer to the workplace. Squatters do not compete with formal residents for land, they take public or private abandoned lands and form large illegal settlements. Due to community size, legal procedures and political costs, the government is not able to enforce the law and evict them. Our model nests naturally the model in Saiz (2010) as a particular case when squatting is not possible.
Brazil is a good place to investigate the relationship of slums and housing supply given the large number of cities, with significant cross section variation in illegal settlements and geographical con-straints. Housing and utilities expenses represent a mean share of 20% of households total expenses in Brazil, which can be higher in large cities (IBGE, 2011). Affordability is then one of the reasons for proliferation of illegal houses in urban areas where building is prohibited. There are more than 11 million people living in urban slums, most of them in large metropolitan areas, adding up more
than 3 millions houses.3 Slum expansion supplies a part of the demand for well-located homes, and is encouraged by the lack of available land, the amount of public urban property, the labor market and resident’s financial situation.
These are the first estimates for housing supply elasticities for metropolitan areas considering ge-ographical constraints and incorporating informal housing markets. A typical challenge in any supply curve estimation is demand simultaneity. We address this issue with a standard instrumental variables approach. We calculate the rate of natural increase of population using demographic data from each city and use this growth measure as an instrument to disentangle the endogeneity of population growth caused by migration and city attractiveness. Another potential source of endogeneity in our supply equation is slum prevalence. Here we propose the use of an original instrument. The area occupied by federal public property in these cities is correlated with illegal available land in metropolitan area, but most of these properties have historical origins before the spread of slums. Since federal government makes centralized decisions and does not engage in urban policy, we consider this exogenous variable as a reasonable instrument for slum ratio within the cities.
As an illustrative example on the use of those supply elasticities, we consider the predicted price increase that would be implied in the next ten years from demographic population growth. Our estimates project housing price growths in a range between 5% and 86%, while population would expand between 16% and 72%. Most of this variation is due to the inclusion of informal housing in the model.
The elasticities estimated in this paper take into account not only geographic constraints, but also include the informal house market ratio in urban agglomerations. These two features have opposite effects that could cancel each other out if not estimated separately. Squatting is common practice in
3
In Brazil, there is a common perception that slums occupy hills, but our database shows this is not a predominant feature of informal settlements and most of them are located on flat lands, i.e., under 15% slope. Slum dwellers construct their houses at lower costs in denser settlements near the urban center. For more information on the determinants of slum formation and its relation to demographic and geographical characteristics, see Guedes (2020b).
many developing countries and this method can be useful to calculate housing supply elasticities in all these cases. By considering the impacts of public properties, unavailable land, and commuting costs on illegal housing and regular real estate market, policy makers can mitigate the externalities of illegal settlements and prevent the formation of new ones.
The housing supply elasticity was previously estimated for developed countries (Malpezzia and Maclennan, 2001), for a developing country (Wang et al., 2012), and using physical constraints (Oikari-nena et al., 2015), but never for developing countries and using geographical constraints simultaneously. Other models discussed the competition for land between formal households and squatters (Brueckner and Selod, 2009) and rent-seeking squatters organizers (Brueckner, 2013). Housing supply and demand in Brazil was discussed (Da Mata et al., 2007), as well as other research that found correlation between illegal settlements and steep lands and riversides (Nadalin and Mation, 2018), however they did not connect these two topics. Other slums studies highlight the importance of rural-urban migration, labor market and land policy (Marx et al., 2013; Cavalcanti et al., 2019; Ferreira et al., 2016; Smolka and Biderman, 2012). Da Mata et al. (2008) found that lowering minimum lot size regulations increases housing supply, but is also accompanied by higher population growth, and supply elasticities in Brazil are lower than countries like Malaysia and South Korea.
In the next section we extend the housing model to include an informal housing market and discuss the implications of these added features in the housing supply curve. The third section describes the set of linked databases we build, which includes satellite-based geographic data of steep lands and bodies of water, a slum survey of all illegal settlements in Brazil detailed by houses, location and public services, Census data of the 185 large metropolitan areas with information about population, houses, rents, income and labor. Section 4 discusses the identification strategy, showing how the instrumental variables were used in the estimation. We present the supply curve in Section 5, including elasticities
estimates for metropolitan areas, an analysis of the results and a simulation of rate of natural increase for 2030. Finally we conclude the article with a summary of contributions and final remarks.
2
Housing Extended Model
This monocentric city model is based on Alonso–Muth–Mills articles (Alonso, 1964; Muth, 1969; Mills, 1967), unified by Brueckner (1987), and extends this framework to include geographical constraints and illegal lands occupied by slums dwellers. Individuals are homogeneous, have the same preferences, and inhabit legal and illegal housing, but unlike other models (Brueckner and Selod, 2009), these two types of housing do not compete with each other for land. These invaded lands are private properties without residential use or public terrains, usually with legal restrictions to build houses that exclude the legal market from land competition. We can also interpret these settlements as regions with lack of man-made regulatory constraints, without zoning and other land use policies, which allow a high density urbanization. The state is not willing to pay the political cost of evicting a large number of illegal residents. The canonical Rosen-Roback model (Rosen, 1979; Roback, 1982) estimates also wages along with rents, but we will simplify this mechanism and consider wages and amenities as exogenous. Households derive utility from amenities (Ak) and wages (ωk) in each city k and disutility Skfrom living
in an illegal land and commuting cost (t) to travel a distance d to central business district (CBD):
U (Ck) = Ak− Sk1f + ωk− γr0− td, (2.1)
where t is commuting cost per distance, constant across the cities, ωk is the wage in the city k and
the rent per land is r = γr0, in which γ is units of land per housing-space and r0 is the rent per unit of housing-space. When land is illegal and 1f = 1, households pay a fixed cost (Sk) related with
Figure 1: Formal and Informal Housing Market
S
kCC
rent
distance
r
0S
k/t
φ
kprecariousness of essential public services, legal uncertainty and higher density. All city homogeneous inhabitants attain the same utility level Uk via competition in the land markets. The demand for land
depends on distance from Central Business District (CBD) and the legality of land, which generates two demands for each type k of terrain:
r(d) = r0− td − Sk1f. (2.2)
In Figure 1, the equilibrium in formal market is depicted by the curve with higher rents, which varies from the construction cost (CC), in the border of city, up to r0 in the center. Informal market
faces disutility Sk and has lower rents to compensate this downside.
Cities are circular with radius φk and their areas are divided in physical constraints (Θk), which in
Figure 2: City Shape
Informal Ocupation
Geographic Constraints
Formal Ocuppation
Vacant Available Land
S
k/t
φ
kφ
k- S
k/t
(Ωk) occupation, that add up to 1 (Λk+ Ωk+ Θk= 1). A portion of the available area (1 - Θk), without
geographical constraints, is occupied by formal households (Λk). Another portion of available land is
not allowed to build formal residences but can be occupied by informal dwellers (Ωk). There are slums
in the city k when φk> Sk/t and Ωk> 0, it means that reducing financial and time costs of commuting
by living near the center offsets the fixed cost (Sk) of living on illegal land. In Figure 2, households
established in the orange area are close enough to the CBD to reduce transport costs compared to the more peripheral areas (green). The condition −∆d · t ≥ Sk must be satisfied in order for the agent to
keep the same utility level, despite living in illegal settlements. Due to the absence of urban regulation, unplanned urbanization, and narrow streets, this informal area has a higher density, or lower units of land are necessary to build a housing space. The inverse density γ in this space has a lower value of γI = γρ where ρ ∈ (0, 1). The total households can be divided in formal area (Λkπφ2k), fraction of
Multiplying these two areas by the inverse density of housing land (γ and γI ), we can find the share of each type of housing considering city size φk endogenous:
Hk= Λkπφ2k γ | {z } Formal Households +Ωkπ(φk− Sk/t) 2 γρ | {z } Informal Households . (2.3)
An important metric we will use in our analysis is the Informal Household Ratio (IHR), that measures the relative presence of informal households:
IHRk= Informal Households Total Households = Ωk(φk− Sk/t)2 ρΛkφ2k+ Ωk(φk− Sk/t)2 , for φk− Sk/t ≥ 0. (2.4)
When the city radius φk is smaller or equal than Sk/t, IHRk is zero. That is, Sk/t is the minimum
city size for a city to accommodate a slum. It is easy to show that for larger populations (Hk), and
consequently larger radii φk, we have higher IHRk for Λk, Ωk, ρ and Sk/t constant. In one particular
case, when there is no land occupied by informal dwellers (Ωk = 0 in Equation 2.3) and available land
is equal to formal occupation (Λk = 1 − Θk), this framework becomes the same model of Saiz (2010).
In this case, φk =
q
γHk
Λkπ, equal to the equilibrium found in his article.
2.1 Housing Supply
The model has two different types of occupied areas, illegal and legal, with different land cost (LCj(d))
for each type of land j ∈ {formal, informal}. Illegal area are not occupied by the formal housing due to government that acts occupying or regulating these lands (environment protection, safety regulations, judicial imbroglios, barriers to housing formalization4). The construction cost (CCj) is constant within
all houses of the same type j. There is no uncertainty, prices (P ) equal the discounted values of rents
4
(r) with an interest rate i: Pj(d) = rj/i = CCj+ LCj(d). We normalize land cost at the edge of city to
zero, LCf ormal(φk) = 0, therefore rf ormal(φk) = iCCf ormal. As discussed in the last subsection (Figure
1), the demand for housing implies that rental rates in each type of land are given by
rj(d) = r0− td − 1fSk.
We can then use the normalization on land costs at the edge of the city (rf ormal(φk) = iCCf ormal)
to find rf ormal(0) = iCCf ormal+ tφk. Therefore, rents in type j are
rkj(d) = iCCf ormal+ t(φk− d) − 1j=inf ormalSk. (2.5)
Note that this normalization also implies that informal land costs at the edge of the informal region will not be zero. First, note that informal rents (2.5) evaluated at the edge of the informal region is given by:
rk,inf ormal(φk− Sk/t) = iCCf ormal.
However, the competitive hypothesis in the development industry of the informal sector implies that
rk,inf ormal(d) = iCCinf ormal+ iLCinf ormal(d).
Therefore, when CCf ormal > CCinf ormal the rents and quantities of informal sector do not change
and informal land cost compensates this difference:
Although the difference between rents in a distance d depends exclusively on Sk, we will consider
CCf ormal = CCinf ormal in order to simplify the distance between edges of formal and informal market
as Sk/t. Following the derivation of mean rent as a function of the radius (see appendix A), the average
rent of type j in city k is given by
˜ rkj = rkj 2 3(φk− 1j=inf ormalSk/t) .
So for the formal sector:
˜ rk,f ormal = rk,f ormal 2 3φk = iCCf ormal+ t 3φk,
and for the informal sector:
˜
rk,inf ormal= rk,inf ormal
2 3(φk− Sk/t) = iCCf ormal+ t 3φk− Sk/3.
That generates an interesting implication about the difference between average formal and informal rents, which is independent of φk, Λk and Ωk:
˜
rk,f ormal− ˜rk,inf ormal = Sk/3. (2.6)
The difference between mean rents of formal and informal market are not correlated with commuting costs (t), but only with disutility from living in an illegal land (Sk). If φk−Sk> 0, a portion of households
˜ rk=
Λkφ2kr˜k,f ormal+Ωρk(φk− Sk)2r˜k,inf ormal
Λkφ2k+Ωρk(φk− Sk)2
Replacing the equations of ˜rk,f ormal and ˜rk,inf ormal, we find an rent equation analogous to Saiz
Model, however it also depends on Informal Households Ratio:
˜ rk= iCCf ormal+ t 3φk− Ωk(φk− Sk/t)2 ρΛkφ2k+ Ωk(φk− Sk/t)2 | {z }
Informal Households Ratio
Sk
3 (2.7)
Taking the derivative of equation 2.7 on IHR, we will find that rent and price are negatively correlated with informal households.
˜ Pk= CCf ormal+ LC(Hk) z }| { t 3iφk− Ωk(φk− Sk/t)2 ρΛkφ2k+ Ωk(φk− Sk/t)2 | {z } IHRk Sk 3i or ˜ Pk = CCf ormal+ t 3iφk− Ωk(φk− Sk/t)2 ργHk πSk 3i (2.8)
The city-specific inverse elasticity of supply is
βkS = ∂(fPk) ∂(Hk) Hk f Pk = t 3i Hk f Pk ∂(φk) ∂(Hk) −2Ωk ∂(φk) ∂(Hk)(φk− Sk/t)Hk− Ωk(φk− Sk/t) 2 ργHk2 πSk t t 3i Hk f Pk (2.9)
We also can observe the behavior of the derivative:
∂(βSk) ∂(Ωk) = ∂ 2( e rk) ∂(Hk)∂(Ωk) Hk e rk − ∂(rek) ∂(Hk) Hk e rk2 ∂(rek) ∂(Ωk) (2.10)
The results of equation 2.10 have a wide dispersion due to the input values. In the model, slum ratio of households depends on unobservable values of Ωk and Sk. Using values in 2010 for number of
Figure 3: βk and Ωk dynamics in the model
𝛽
𝑘
𝜕𝛽
𝜕Ω
𝑘 𝑘𝑆
𝑘(𝑅$)
Ω
𝑘
𝑆
𝑘(𝑅$)
Ω
𝑘
𝑆
𝑘(𝑅$)
Ω
𝑘
𝑆
𝑘(𝑅$)
Ω
𝑘
𝑆𝑢𝑝𝑝𝑙𝑦
𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦
𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑙 𝐻𝑜𝑢𝑠𝑒ℎ𝑜𝑙𝑑
𝑅𝑎𝑡𝑖𝑜 (𝐼𝐻𝑅)
households (Hk), urbanized area per household in the city (γ) and the factor for density in illegal area
(ρ)5, plus a share of unavailable land (1 − Ωk− Λk) of 0.2 and transportation cost t = 100 reais6, the βk
assumes inverse elasticities values close to the results found in Data Section. Since it is not possible to ensure the correct value, we use a range of values of Ωk (from 0, no slums, to 0.4) and Sk/t (from 1 to 5
kilometers closer to CBD to compensate informality, i.e. from 100 to 500 reais monthly of disutility Sk).
These input values are equivalent to informal household ratios between 0 and 54% (forth quadrant of Figure 3). The derivative of βk on Ωk is negative for the range of values of Ωk and Sk (second quadrant
of Figure 3).
We will analyze the supply elasticities starting from the price equation and totally differentiating the log of fPk = CC + LC(Hk), where LC(Hk) is the price component not related with construction
cost in 2.8, and multiplying the last term by Hk Hk dHk dHk: dlnfPk= dfPk f Pk = dCC f Pk +dLC(Hk) f Pk = dCC f Pk + βS k z }| { dLC(Hk) dHk Hk f Pk dln(Hk) z }| { dHk Hk
Defining σk= CC/fPkas the initial share of construction costs on housing prices, and assuming that
dfPk/dHk= dLC(Hk)/dHk: dlnfPk= dCC f Pk ·CC CC + β S k · dln(Hk) = σk· dCC CC + β S k · dln(Hk)
The empirical specification can include region fixed effects (Rjk, for j country region) and an error
5
Using the data described in Section 5, the median size of cities with slums is 118,000 households, the median density of 1500 households per square kilometer and the double in informal area (ρ = 0.5).
6This cost is consistent with the opportunity cost of a household income of 1600 reais (3 minimum wages in 2010) or 10 reais per hour and the transportation cost of 3 people who travel frequently by public transport to the center (ANTP and Sistema de Informacao da Mobilidade Publica, 2010).
term (εk), estimating the supply equation in differences. We will also consider constant construction
cost (CC) over time. In the next section, the following housing supply equation will be estimated with a decomposed inverse of supply elasticity (βS
k) in two other components that will take into account: the
physical constraints measured by the ratio of undevelopable land in circle around MSAs‘ CBDs (βLAN D· (1 − Ωk− Λk)) and the absence of regulatory constraints in informal households areas (βSLU M · IHR):
∆lnfPk= βS· ∆lnHk+ βLAN D· (1 − Ωk− Λk) · ∆lnHk+ βSLU M· IHRk· ∆lnHk+
X
Rjk+ k
(2.11) f
Pk is a measure of median housing prices and βkS has 3 components: βS equal for all cities, βLAN D
depending on unavailable land in a city k (1 − Ωk− Λk) and βSLU M that estimate the impact of Informal
Household Ratio (IHR) on prices. We know that βS
k should be positive as well as βS and βLAN D, but
βSLU M should be negative, once it was estimated by a proxy of informal unavailable land (Ωk), in this
case, the ratio of public land in the city.
3
Data
Real estate markets are local and we defined each market considering geographical proximity and flow of citizens between cities. The Brazilian Institute of Geography and Statistics (IBGE) grouped cities in the “Arranjos Populacionais e Concentra¸c˜oes Urbanas” (Brazilian Metropolitan Statistical Areas) with at least one of these relations: (a) flow of workers and students above 10,000 people or above 17% of one city’s population; or (b) its urbanized areas located not more than 3 kilometers away. We used in our sample the most populated MSAs with more than 100,000 residents in 2010 Population Census. Demographic data and household quantity were collected in 1991 and 2010 Census, i.e., only occupied
Figure 4: Unavailable Land
(a) Unavailable Land with 15% Slope and 50 Km radius
0 5 10 15 Frequency 0 .2 .4 .6 .8 1 Unavailable 15% 50km
(b) Unavailable Land with 30% Slope and 10 Km radius
0 20 40 60 80 Frequency 0 .2 .4 .6 .8 Unavailable 30% 10km
Figure 5: Number of Rooms
(a) Mean Rent by Number of Rooms
93 86 78 78 77 87 94 102 112 119 126 124 92 81 76 79 86 93 102 109113 125 0 50 100 150 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 1991 2010
Mean rent by room (2010 prices)
Graphs by year
(b) Distribution by Number of Rooms
8 16 23 23 12 8 5 3 2 1 0 6 16 22 26 13 8 4 2 1 1 0 0 5 10 15 20 25 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 1991 2010
Percentages of Observations by Room
houses are considered in this data set. Housing rents are also collected in the extended questionnaire applied to 25% sample of Census households. The country has a legislation concentrated in federal level, so all these cities are under a similar jurisprudence. In this paper, we will always work with rental data and will assume that the prices are based on the present value of rents. Since area variable is not available in the data, we are calculating the rent divided by the numbers of room, excluding houses with just one room, as proxy of rent per area. In Figure 5 we observe that this metric is relatively stable for different number of rooms in 1991 and 2010, excluding rents for houses with only 2 rooms. Since we will use the median rent of each MSA and the 2 rooms share is not high, this fluctuation will not significantly impact our metric.
Table 1: Descriptive Statistics of MSAs
mean sd mean (slums) sd (slums) 1,000 Households (1991) 111.1 364.0 193.2 507.0 1,000 Households (2010) 190.4 561.1 329.3 777.3 % Slum Households 4.0% 7.2% 8.2% 8.5% Rent per Room (reais - median) 64.1 16.4 68.8 16.7 Income (reais - median) 1567 415 1585 404
Rented 17.4% 5.1% 17.1% 4.8% Sanitation 74.38% 22.8% 74.41% 21.3% Unavailable 15% 50km 39.5% 27.3% 47.9% 27.1% Unavailable 30% 10km 17.1% 21.2% 25.0% 24.0% Water 50km 10.8% 18.2% 18.0% 22.1% Slope 15% 50km 28.6% 25.0% 29.9% 25.8% Observations 185 91
Due to illegality and precarious housing conditions, data on slums are often rare and inaccurate. IBGE provides a standard slum definition using some characteristics of informality, public utilities and urbanization for all cities. A subnormal agglomeration (slum technical name) is formed by housing units occupying, or having occupied until recent years, land owned by other public or private agents. Most of them do not have access to essential public services, and generally arranged in a disorderly and dense
manner. The identification of slums is based on the following criteria: (1) illegal occupation of land, that is, construction on lands owned by others (public or private) at the moment or in a recent period (obtaining the property title in the last ten years or less); and (2) have at least one of the following characteristics: (a) urbanization outside current standards - narrow and irregularly aligned roadways, plots of unequal sizes and shapes and constructions not regularized by public authorities; or (b) pre-cariousness of essential public services. IBGE used Census Data to map all subnormal agglomerations in the country. They further refined the initial mapping through Municipal Commissions of Geography and Statistics in 350 cities to add, remove and define slums areas. Field technicians had also to evaluate and verify the slums characteristics defined above. A subnormal agglomeration had to contain at least 51 housing units, but only 0.3% of more than 3 million slum houses in the country were removed because of this criterion (IBGE, 2011).
We developed a new dataset for this article using geographic information system (GIS) available for the regions around Brazilian metropolitan areas. The steep lands were calculated by the Instituto Nacional de Pesquisas Espaciais (INPE) satellite-base data of DEM (Digital Elevation Model) that provides slope maps at 30-meters resolution. The United States Geological Survey (USGS) satellite-base geographic data was used to calculate bodies of water at 0.5-kilometer resolution. Unavailable land is calculated inside a circle of 50 and 10 kilometers radius and considering bodies of water plus lands with 15% or 30% of slope. The amount of land unavailable varies greatly between cities, reaching more than 80% in some circles with slopes above 15% plus bodies of water (Figure 4a). Less than 40% of MSAs have roughly no undevelopable land when we consider 30% of slope and bodies of water (Figure 4b), despite some 10 kilometers circles have more than 60% of 30% steep land.
In some cities like Rio de Janeiro, the hilly landscape is covered by brick houses piled on the slopes and the native inhabitants use the word morro (hill) as a synonym of slums. However, this is not a
Table 2: Share of Flat Census Blocks (%)
Brazil Northeast and North South Southeast Slopes Non-slums Slums Non-slums Slums Non-slums Slums Non-slums Slums
< 15% 83 70 92 82 88 75 77 61
< 20% 92 82 98 93 93 84 89 74
< 30% 98 94 99 99 98 94 97 89
N 132,361 15,539 26,405 5,703 18,518 854 76,591 8,709 Type Share 89% 11% 82% 18% 96% 4% 90% 10%
Note: Percentages in the middle of table are the share of census blocks with slopes below 15%, 20% and 30%. Type Share is the ratio of non-slums (or slums) blocks in the sample. Only census blocks of MSAs with slums.
predominant feature of informal settlements in the country and most of them are located in flat lands. Only 6% of informal Census blocks have over 30% of inclination. Northeast and North have the highest ratio of subnormal blocks (slums) in Brazil (18%), but we observe in Table 2 that less than 1% of formal and informal houses were built on very steep lands (above 30%). Less than 20% of the favelas in Rio de Janeiro are on lands with slopes greater than 30%. Besides this evidence, there is a law7 that prohibits buildings and urbanization infrastructure in terrains over 30% of slope.
4
Identification Strategy
The identification of housing supply is naturally challenged by price endogeneity that emerges as a result of classical demand and supply simultaneity. In our setting we have an additional arguably endogenous variable besides prices: the Informal Household Ratio (IHR). Supply shocks may also have shifted the IHR in different cities. Housing supply curves will be estimated using demographic instrumental variables and area of public properties in the cities, that are only correlated with demand changes in the house market and urban slums ratios, respectively, being orthogonal with unobservable component
7
of the supply.
Brazil has a low migration rate: less than 5% of population moved across states between 2005-2010, or approximately 1% annually, and one-fifth of these people were returning to their state of birth), 65% live in the city of birth and 86% of total population live in the state of birth. According with US Census Bureau, 2.5% of Americans migrated to a different state annually, during 2005 and 2009, which is more than double the rate of Brazilians. In addition, most of the population has low income and transportation services are expensive, which increases the moving cost. Considering these characteristics, we use an exogenous estimate of the rate of natural increase (RNI) of each MSA, excluding in-migration and out-migration. This demographic instrument was calculated just subtracting the crude urban death rate by cohort of each MSA’s state from the 1991 population of each metropolitan area. Birth rates after 1991 were not used in this projection because it was taken into account only the population above 20 years old as housing demand. Suppose a MSA k in one state S with a set MS of
mortality rates by cohort in urban areas. We subtracted of each 1991 cohort the corresponding mortality rate of MSto estimate the population above 20 years old in 2010. Since death rates is exogenous because
affects the demand of housing markets without impact on supply, it is a good candidate for instrumental variable in this model. We are also supposing that median rent in a city k does not affect mortality rates in its states S.
Slums (favelas) have been appearing in all major cities of the country in the last decades. The first appeared in the late 19th century, in the center of Rio de Janeiro, then these settlements began to spread in large cities in the 1940s along with industrialization. However, most modern favelas emerged in the 1970s due to rural exodus. At this time, the government tried to solve this issue building public housing projects in the suburbs to settle favela’s inhabitants, meanwhile other favelas were still arising and growing faster in different urban zones inside the city. The neighborhood Cidade de Deus (City of
Figure 6: Slums
(a) Number of Households and Slums
0.0000 0.2000 0.4000 0.6000 % Slums/Total Households 0 2 4 6 8 10 1,000,000 Households
% Slum Households Fitted values
(b) Public Land and Slums
0.0000 0.2000 0.4000 0.6000 % Slums/Total Households 0 2 4 6 8 % Public Lands
God) in Rio de Janeiro is a remarkable example of this inefficient policy that was almost abandoned in the end of 20th century. Nowadays local governments focus more on infrastructure and essential services improvements in slums. During all these decades, authorities did not succeed in avoiding these illegal settlements. These occupations are also a proxy of effective regulation in metropolitan areas and an intense presence of slums can be interpreted as a tolerant state without authority to impose urban order. According to Flood (2006), “49 percent of land invasions in Sub-Saharan Africa, 60 percent in North Africa, East Asia, and West Asia and 90 percent in South Asia occur on public land” (Shah, 2014) and only 40 percent share of “land invasions” in Latin America and the Caribbean occurring on private land (Brueckner and Selod, 2009). Federal public lands were defined in previous Constitutions of 1831 and 1946, and reaffirmed in the Constitution of 1988.8 Regularization of low-income occupations on public properties was one of the goals of the federal government, which initiated processes of ownership transfer to approximately 500 thousand households during 2003 and 2010 (Secretaria do Patrimˆonio da Uni˜ao, 2010). For this reason, the area of federal public properties, most vulnerable areas to these invasions, was used as an instrument for informal housing ratio in metropolitan areas (Figure 6b). Since housing public policies of municipalities would be correlated with government real estate assets, the use of federal data also avoids the issue of this variable being affected by urban policies or real estate markets.9 Large MSAs are dynamic labor markets and the number of informal houses is positively correlated with the MSA’s size (Figure 6a). Therefore, the demographic instrument (number of households in 2010) was also used to estimate slum share in cities. The first stage of supply equation estimates α coefficients of
8See decree-law number 9,760, of 1946, and article 20 in the 1988 Constitution.
9Article 185 in the Constitution of 1988 states that urban policy will be approved and implemented by municipal authorities.
following equation:
Ykj = αj0+ αj1· ∆91−10P Dk+ αj2· P D10k · ∆91−10P Dk+ αj3· P Pk· ∆91−10P Dk+ αjRCR+ jk (4.12)
where ∆91−10P Dkis the demographic growth projection, P D10k is the demographic projected population
for 2010, P Pk is the the ratio of public property area in the MSA k, and CR is regional control dummy.
The dependent variable (Ykj) is one of three components (j ∈ [1, 2, 3]) of household quantity change (∆91−10lnH) in supply equation: ∆91−10lnHk, U Lk· ∆91−10lnHk or IHRk· ∆91−10lnHk, where U Lkis
unavailable land and IHRk is the informal house ratio in city k.
5
Results
As discussed in the last section, we will start analyzing the housing demand and slums instruments used in the two-stage least squares. Table 3 presents the first stage of housing supply, i.e., the variation of logarithms of households between 1991 and 2010 regressed against the demographic instrument for demand. In the first row of regressors, the coefficients are similar using regional controls or a subsample of cities with slums (columns 3 and 4). In order to show the correlation between public properties and slums, the analysis was made using two variables. The first one is the quantity of urban public properties divided by the number of households. In Table 4, the percentage of informal households in cities are correlated with number of public properties for all regressions, even if it is controlled by unavailable land, density and regional controls. Table 5 is showing public area without buildings10 divided by urban area and the results also indicate a correlation between slums and public lands. We also used the amount of houses in MSAs in 2010 as another slum instrument, which was estimated using number of
10
Table 3: 1st Stage - Household Growth
(1) (2) (3) (4)
% ∆91−10 Households Slums Slums
∆91−10 Demog. Instr. 0.768*** 0.659*** (0.248) (0.234) South -0.100** -0.071** -0.102** -0.056 (0.039) (0.035) (0.047) (0.045) Northeast -0.044 -0.125** -0.044 -0.069 (0.048) (0.058) (0.045) (0.048) Constant 0.621*** 0.290*** 0.627*** 0.325*** (0.026) (0.091) (0.029) (0.102) N 186 186 91 91 R2 0.024 0.113 0.043 0.166 F-stats 3.29 3.89 2.33 3.75
Note: A */**/*** next to coefficient indicates significance at the 10%/5%/1% level. Standard errors in parentheses. % ∆91−10Households is the natural growth projection between 1991 and 2010 considering regional mortality rates and population age distribution of each MSA in 1991.
households in 1991 multiplied by demographic growth between 1991 and 2010, following demography instrument methodology.
Working with the data presented in Section 3, the supply curve was estimated as described in equa-tion 2.11. The inverse elasticities including the ratio of unavailable land (U nav.15%50km∗∆2010−1991Log(H)
and U nav.30%10km ∗ ∆2010−1991Log(H)) and slums ratio in 2010 (%Slums2010∗ ∆2010−1991Log(H))
are estimated in Table 6. The increase of supply constraints make inverse supply elasticities higher, i.e., larger geographical constraint areas and lower illegal household ratio. The base supply curve (∆91−10Log(H)) is positively sloped. The coefficients are aligned with the theoretical results,
metropoli-tan areas with more unavailable land have higher supply inverse elasticity (βLAN D) and cities with higher
informal housing ratio have lower supply inverse elasticity (βSLU M), but only the slum factor shows a significance at the 5% level. Focusing on our target cities, i.e. cities with slums, which include all major metropolitan areas and 26 of 27 state capitals of the country, the same models were regressed with this
Table 4: Slums and Public Properties (1) (2) (3) (4) (5) (6) % Slums/Households % Public Properties† 1.008*** 0.837*** 0.891*** 0.501** 0.530** 0.559*** (0.217) (0.239) (0.225) (0.223) (0.208) (0.207) # Households 2010 0.018** 0.017** 0.010 0.016*** 0.016*** 0.013** (0.008) (0.007) (0.007) (0.006) (0.006) (0.006) Unav. Land 15% 50Km 0.048*** 0.033 (0.018) (0.023) Unav. Land 30% 10Km 0.146*** 0.145*** 0.133*** (0.033) (0.033) (0.031) South -0.020** -0.024*** -0.021** (0.008) (0.008) (0.008) Northeast -0.019 0.002 -0.006 (0.019) (0.010) (0.015) Density 0.000 0.000 (0.000) (0.000) Constant 0.025*** 0.008 -0.027 0.005 0.010** -0.007 (0.004) (0.006) (0.021) (0.004) (0.005) (0.020) N 186 186 185 186 186 185 R2 0.229 0.257 0.308 0.369 0.387 0.390
Note: A */**/*** next to coefficient indicates significance at the 10%/5%/1% level. Standard errors in parentheses. † Number of federal public properties divided by quantity of households in the MSA.
Table 5: 1st Stage - Slums
(1) (2) (3) (4) (5) (6)
% Slums/Households Slums Slums
% Public Land† 0.031*** 0.028*** 0.021*** 0.015** (0.010) (0.008) (0.006) (0.006) Household 2010 (Demog.) 0.016** 0.014** 0.014*** 0.008** (0.007) (0.007) (0.005) (0.003) Unav. Land 15% 50Km 0.077*** (0.017) Unav. Land 30% 10Km 0.162*** 0.164*** (0.030) (0.036) South -0.021** -0.016* -0.019** -0.017** -0.044*** -0.039*** (0.009) (0.008) (0.008) (0.008) (0.014) (0.015) Northeast 0.005 0.002 0.006 0.004 0.025 0.016 (0.015) (0.013) (0.012) (0.010) (0.025) (0.019) Constant 0.043*** 0.030*** 0.001 0.006 0.087*** 0.036*** (0.007) (0.007) (0.008) (0.005) (0.013) (0.009) N 186 185 185 185 91 91 R2 0.016 0.190 0.270 0.399 0.068 0.371 F-stats 3.85 5.54 10.63 15.36 8.08 11.69
Note: A */**/*** next to coefficient indicates significance at the 10%/5%/1% level. Standard errors in parentheses. † Area of federal public properties without building divided by the MSA urban area. Household 2010 (Demog.) is the projection for 2010 population considering only regional mortality rates and population age distribution of each MSA in 1991.
sample. The results were even more clear in Table 7 and unavailable lands (water bodies included) in the 10km circles using slopes over 30% are strong geographical restriction on housing supply. These results indicate that regulatory constraints play a stronger role in supply elasticities than physical constraints. Using the parameters of the sixth column in Table 7, housing supply inverse elasticities are presented in Table 8. All inverse elasticities are positive, between 0 and 1.6, with the exception of Belem, the only metropolitan area with over 50% of slum houses. These supply elasticities vary between 0.6 and 6.4 with lower mean and variance than distribution found by Saiz, but not as lower as the elasticity found by Da Mata et al. (2008). One possible explanation is the mitigating effect of squatting in physical constraints reducing the variance of elasticity. In Figure 7 we can observe that slums ratio in horizontal axis is positively correlated with supply elasticities, but has a slightly negative correlation with geographical constraints in Figure 8. These two figures make clear the importance of regulatory restriction in estimating the supply curve.
In order to measure an impact on prices generated by a change in demand, we simulate an increase in population between 2010 and 2030 based on RNI (Rate of Natural Increase), excluding long run migration effects. We are considering an infinitely inelastic demand and excluding the effects of the birth rate on the intensive margin (Guedes, 2020a). Table 9 presents the population (houses) growth and correspondent price change. Teresina would face an increase in prices of more than 200%, despite the average population growth. Other eight cities would have their prices more than doubled, but more than half would grow below 40%. The variance in price changes is even greater than the supply growth.
Table 6: Supply Curve 1991-2010 (All MSAs)
(1) (2) (3) (4) (5) (6)
Rent per Room (median) OLS IV IV IV IV IV
∆91−10Log(H) -0.228*** 0.536 0.833* 0.680 0.657* 0.711* (0.059) (0.363) (0.497) (0.422) (0.399) (0.412) Unav. 15% 50Km*∆91−10Log(H) 0.122 -0.008 0.300 (0.091) (0.122) (0.209) Unav. 30% 10Km*∆91−10Log(H) 0.465 0.477 0.440 (0.343) (0.353) (0.367) % Slums*∆91−10Log(H) -0.051 -3.140** -3.273** -3.296** -3.159** (0.297) (1.334) (1.339) (1.348) (1.390) Northeast 0.017 0.042 (0.061) (0.064) South 0.096** (0.049) Constant 0.302*** -0.121 -0.291 -0.175 -0.165 -0.221 (0.033) (0.199) (0.274) (0.227) (0.214) (0.224) N 186 186 185 185 185 185
Note: A */**/*** next to coefficient indicates significance at the 10%/5%/1% level. Standard errors in parentheses.
Table 7: Supply Curve 1991-2010 (Only MSAs with Slums)
(1) (2) (3) (4) (5) (6)
Rent per Room (median) OLS IV IV IV IV IV
∆91−10Log(H) -0.124 0.368 1.249* 0.851** 0.906** 0.910** (0.160) (0.412) (0.702) (0.423) (0.440) (0.448) Unav. 15% 50Km*∆91−10Log(H) 0.178 0.092 0.558* (0.136) (0.131) (0.308) Unav. 30% 10Km*∆91−10Log(H) 1.089*** 1.076*** 1.137*** (0.338) (0.372) (0.411) % Slums*∆91−10Log(H) 0.047 -4.368** -4.634*** -4.520*** -4.827** (0.312) (2.107) (1.499) (1.652) (1.876) Northeast -0.086 -0.090 (0.073) (0.076) South -0.035 (0.093) Constant 0.192** -0.075 -0.505 -0.258 -0.280 -0.267 (0.076) (0.236) (0.373) (0.212) (0.222) (0.227) N 91 91 91 91 91 91
Note: A */**/*** next to coefficient indicates significance at the 10%/5%/1% level. Standard errors in parentheses.
Figure 7: Elasticities and Slums -2 0 2 4 6 Elasticities 0.0000 0.2000 0.4000 0.6000 % Slums 2010
Supply Elasticity Fitted values
6
Conclusion
This article presents a housing market model with formal and informal sectors, a very common situation in many developing countries. Residents can choose to live in an informal house (absence of title deed and lack of essential services) to be closer to center and reduce commuting cost; or to live in a formal house (legal property security with essential services) away from their workplaces. Public or private uninhabited lands close to the center are occupied against the law, but government has no political power to enforce evictions or apply an urban regulation in these regions. There will be more high density slums in large metropolitan areas due to long distances and higher transportation costs. This effect counterbalances geographic constraints reducing pressure on prices, since there are cheaper options
Table 8: Supply Elasticities
MSAs Elasticities SE MSAs Elasticities SE
Nova Friburgo*/RJ 0.61 0.22 Juazeiro do Norte/CE 1.19 0.61
Florianopolis/SC 0.68 0.25 Tubarao - Laguna/SC 1.19 0.59
Petropolis/RJ 0.71 0.26 Vitoria/ES 1.20 0.58
Rio Grande*/RS 0.71 0.27 Cachoeiro de Itapemirim*/ES 1.21 0.57
Itajai - Balneario Camboriu/SC 0.72 0.28 Jundiai/SP 1.21 0.61
Juiz de Fora/MG 0.77 0.30 Guarapari*/ES 1.21 0.57
Colatina*/ES 0.83 0.33 Sorocaba/SP 1.21 0.63
Parintins*/AM 0.84 0.33 Ribeirao Preto/SP 1.22 0.63
Pelotas/RS 0.85 0.35 Mossoro*/RN 1.24 0.66
Itabira*/MG 0.87 0.36 Montes Claros*/MG 1.27 0.67
Cameta*/PA 0.87 0.36 Cabo Frio/RJ 1.29 0.64
Governador Valadares*/MG 0.89 0.37 Londrina/PR 1.30 0.70
Tramandai - Osorio/RS 0.89 0.36 Campos dos Goytacazes/RJ 1.31 0.71
Maceio/AL 0.92 0.37 Ipatinga/MG 1.32 0.68
Corumba/MS 0.93 0.39 Caruaru*/PE 1.33 0.73
Atibaia/SP 0.95 0.42 Piracicaba/SP 1.33 0.74
Porto Alegre/RS 0.96 0.41 N. Hamburgo - S. Leopoldo/RS 1.35 0.74
Joinville/SC 0.98 0.44 Ponta Grossa/PR 1.37 0.76
Natal/RN 1.01 0.43 Brasilia/DF 1.38 0.78
Marilia/SP 1.02 0.47 Aracaju/SE 1.41 0.77
Taubate - Pindamonhangaba/SP 1.04 0.49 Macapa/AP 1.43 0.76
Blumenau/SC 1.04 0.46 Araguaina*/TO 1.47 0.87
Bento Goncalves/RS 1.05 0.47 Baixada Santista/SP 1.49 0.81
Itabuna*/BA 1.05 0.50 Parauapebas*/PA 1.51 0.88
Boa Vista*/RR 1.06 0.50 Ilheus*/BA 1.55 0.87
Americana - Sta B. dOeste/SP 1.08 0.52 Teresopolis*/RJ 1.62 0.95
Santarem*/PA 1.09 0.48 Campina Grande/PB 1.72 1.14
Sao Jose dos Campos/SP 1.09 0.52 Curitiba/PR 1.72 1.14
Rio de Janeiro/RJ 1.09 0.48 Cuiaba/MT 1.73 1.15
Itu - Salto/SP 1.10 0.54 Campinas/SP 1.96 1.45
Caxias do Sul/RS 1.10 0.52 Linhares*/ES 2.08 1.57
Campo Grande*/MS 1.11 0.54 Maraba*/PA 2.09 1.58
Passos/SP 1.11 0.54 Belo Horizonte/MG 2.11 1.64
Arapiraca*/AL 1.11 0.55 Porto Velho/RO 2.12 1.65
Goiania/GO 1.11 0.55 Manaus*/AM 2.20 1.71
Paranagua*/PR 1.11 0.51 Salvador/BA 2.22 1.76
Umuarama/PR 1.11 0.55 Rio Branco*/AC 2.29 1.94
Foz do Iguacu/PR 1.12 0.54 Sao Paulo/SP 2.42 2.14
Anapolis*/GO 1.12 0.56 Araruama/RJ 2.64 2.45
Volta Redonda - Barra Mansa/RJ 1.15 0.54 Recife/PE 3.70 4.77
Macae - Rio das Ostras/RJ 1.15 0.53 Resende/RJ 4.18 6.12
Passo Fundo*/RS 1.16 0.59 Angra dos Reis*/RJ 4.25 6.77
Fortaleza/CE 1.16 0.54 Sao Mateus*/ES 4.63 7.71
Bauru/SP 1.17 0.60 Sao Luis/MA 5.20 9.50
Joao Pessoa/PB 1.18 0.56 Teresina/PI 6.39 14.76
Note: *Isolated municipalities. Elasticities were estimated by the model in Table 7 and column 6. SE are Standard Errors.
Table 9: RNI and Prices Growth between 2010 and 2030†
MSAs ∆Supply ∆Price MSAs ∆Supply ∆Price
Parintins*/AM 72% 86% Caruaru*/PE 32% 24%
Cameta*/PA 60% 69% Itu - Salto/SP 26% 24%
Boa Vista*/RR 54% 51% Pelotas/RS 20% 24%
Corumba/MS 47% 51% Ipatinga/MG 31% 24%
Santarem*/PA 54% 49% Cabo Frio/RJ 30% 23%
Itajai - Balneario Camboriu/SC 31% 43% Passos/SP 25% 23%
Macapa/AP 60% 42% Rio Branco*/AC 52% 23%
Maceio/AL 37% 40% Manaus*/AM 50% 23%
Parauapebas*/PA 60% 40% Cachoeiro de Itapemirim*/ES 27% 23%
Florianopolis/SC 25% 37% Passo Fundo*/RS 26% 22%
Paranagua*/PR 41% 37% Caxias do Sul/RS 24% 22%
Foz do Iguacu/PR 41% 37% Ilheus*/BA 34% 22%
Arapiraca*/AL 41% 37% Sorocaba/SP 26% 22%
Governador Valadares*/MG 31% 34% Porto Velho/RO 46% 21%
Itabira*/MG 28% 33% Campos dos Goytacazes/RJ 28% 21%
Rio Grande*/RS 23% 32% Novo Hamburgo - Sao Leopoldo/RS 28% 21%
Joinville/SC 31% 32% Cuiaba/MT 36% 21%
Juazeiro do Norte/CE 37% 31% Umuarama/PR 23% 20%
Araguaina*/TO 46% 31% Jundiai/SP 25% 20%
Natal/RN 30% 30% Rio de Janeiro/RJ 21% 19%
Goiania/GO 32% 29% Londrina/PR 24% 19%
Anapolis*/GO 32% 29% Volta Redonda - Barra Mansa/RJ 22% 19%
Colatina*/ES 24% 29% Tubarao - Laguna/SC 22% 19%
Fortaleza/CE 33% 28% Americana - Santa Barbara dOeste/SP 20% 18%
Brasilia/DF 39% 28% Marilia/SP 19% 18%
Tramandai - Osorio/RS 25% 28% Linhares*/ES 38% 18%
Maraba*/PA 58% 28% Ribeirao Preto/SP 22% 18%
Itabuna*/BA 29% 28% Campina Grande/PB 31% 18%
Montes Claros*/MG 35% 28% Curitiba/PR 30% 18%
Campo Grande*/MS 31% 28% Bauru/SP 20% 17%
Macae - Rio das Ostras/RJ 32% 27% Bento Goncalves/RS 18% 17%
Nova Friburgo*/RJ 16% 27% Piracicaba/SP 22% 17%
Petropolis/RJ 19% 27% Baixada Santista/SP 23% 16%
Ponta Grossa/PR 36% 26% Teresopolis*/RJ 23% 14%
Blumenau/SC 27% 26% Salvador/BA 29% 13%
Guarapari*/ES 32% 26% Belo Horizonte/MG 27% 13%
Juiz de Fora/MG 20% 26% Campinas/SP 24% 12%
Taubate - Pindamonhangaba/SP 27% 26% Sao Paulo/SP 26% 11%
Aracaju/SE 36% 26% Araruama/RJ 24% 9%
Joao Pessoa/PB 30% 26% Sao Mateus*/ES 39% 8%
Sao Jose dos Campos/SP 28% 25% Angra dos Reis*/RJ 35% 8%
Mossoro*/RN 31% 25% Recife/PE 27% 7%
Vitoria/ES 30% 25% Sao Luis/MA 34% 7%
Atibaia/SP 24% 25% Resende/RJ 27% 6%
Porto Alegre/RS 23% 24% Teresina/PI 34% 5%
Note: †Rate of Natural Increase considers only the mortality rate to predict the population growth of citizens over 20 years old. *Isolated municipalities.
Figure 8: Elasticities and Unavailable Land -2 0 2 4 6 Elasticities 0 .2 .4 .6 .8 % Unavailable Land 30% 10km Supply Elasticity Fitted values
of house to be chosen by the households.
The data set makes the empirical study of slums possible in a large number of cities. Using Census data of more than 90 metropolitan areas we were able to estimate for the first time the supply curve of a developing country including physical constraints and informal house market with no man-made regulatory constraints. This geographic measure of unavailable land can be used in future work exploring topics as diverse as housing and mortgage markets, labor mobility, urban density, transportation, and urban environmental issues. The public properties are good predictors of informal housing markets and might be the main opportunity for dwellers to squat urban areas. The results show that slums increase supply elasticities, which makes hard to assess the impact of geographic constraints without considering the dual housing markets. The distribution of elasticities in Brazil has lower mean and variance than in US, but the rate of natural increase simulation shows a widespread dispersion of price growths for 2030.
The study of informal housing market may open new paths to improve urban policy design, including infrastructure, public essential services, transportation, and real estate market regulation. Today, large slum settlements have disappeared in most advanced economies, but it is far from clear how compara-ble these historical examples are to the situations faced in the developing world. Understanding this issue nowadays in these developing countries is determining to reduce one of the greatest difficulties in improving the quality of life and curb slums growth.
References
Alonso, W. (1964). Location and land use.
Brueckner, J. K. (1987). The Structure of Urban Equilibria: A Unified Treatment of the Muth-Mills Model. Handbook of Regional and Urban Economics 2, 821–845.
Brueckner, J. K. (2013). Urban squatting with rent-seeking organizers. Regional Science and Urban Economics 43, 561–569.
Brueckner, J. K. and H. Selod (2009, February). A Theory of Urban Squatting and Land-Tenure Formalization in Developing Countries. American Economic Journal: Economic Policy 1 (1), 28–51.
Cavalcanti, T., D. Da Mata, and M. Santos (2019, January). On the Determinants of Slum Formation. The Economic Journal , 47–64.
Da Mata, D., U. Deichmann, J. V. Henderson, S. V. Lall, and H. G. Wang (2007). Determinants of city growth in Brazil. Journal of Urban Economics 62 (2), 252–272.
Da Mata, D., S. V. Lall, and H. G. Wang (2008). Do Urban Land Regulations Influence Slum Formation? Evidence from Brazilian Cities. Ensaios de Economia Regional e Urbana, 47–64.
Ferreira, F. and J. Gyourko (2012, May). Heterogeneity in Neighborhood-Level Price Growth in the United States, 1993–2009. American Economic Review 102 (3), 134–140.
Ferreira, P. C., A. Monge-Naranjo, and L. T. d. M. Pereira (2016). Of Cities and Slums. Working Papers (22).
Flood, J. (2006). Secure Tenure Survey Final Report. Urban Growth Management Initiative.
Green, R. K., S. Malpezzia, and S. K. Mayo (2005, May). Metropolitan-Specific Estimates of the Price Elasticity of Supply of Housing, and Their Sources. Papers and Proceedings of the One Hundred Seventeenth Annual Meeting of the American Economic Association 95 (2), 334–339.
Guedes, R. (2020a). Real Estate Markets and Household Behavior. Working Paper .
Guedes, R. (2020b). Slum Shape: The Role of Space and Location. Working Paper .
IBGE (2011). Censo Demografico 2010 - Aglomerado Subnormais.
IBGE (2019). Pesquisa de Or¸camentos Familiares 2017-2018.
Malpezzia, S. and D. Maclennan (2001, September). The Long-Run Price Elasticity of Supply of New Residential Construction in the United States and the United Kingdom. Journal of Housing Economics 10, 278–306.
Marx, B., T. Stoker, and T. Suri (2013). The Economics of Slums in the Developing World. Journal of Economic Perspectives 27 (4), 187–210.
Mills, E. (1967). An aggregative model of resource allocation in a metropolitan area. American Economic Review 57 (2), 197–210.
Muth, R. (1969). Cities and housing.
Nadalin, V. G. and L. Mation (2018). Localiza¸c˜ao interurbana das Favelas Brasileiras: o papel dos fatores Geogr´aficos. Texto para Discuss˜ao.
Oikarinena, E., R. Peltolab, and E. Valtonen (2015, January). Regional variation in the elasticity of supply of housing, and its determinants: The case of a small sparsely populated country. Regional Science and Urban Economics 50, 18–30.
Roback, J. (1982, December). Wages, Rents, and the Quality of Life. Journal of Political Econ-omy 90 (4), 1257–78.
Saiz, A. (2010). The Geographic Determinants of Housing Supply. Quarterly Journal of Eco-nomics 125 (3), 1253–1296.
Secretaria do Patrimˆonio da Uni˜ao (2010). Balan¸co de Gest˜ao 2003-2010.
Shah, N. (2014). Squatting on Government Land. Journal of Regional Science 54 (1), 144–136.
Smolka, M. and C. Biderman (2012). Housing Informality: An Economist’s Perspective on Urban Planning. In: Nancy Brooks; Kieran Donaghy; Gerrit-Jan Knaap. (Org.). The Oxford Handbook on Urban Economic and Planning., 814–833.
Wang, S., S. H. Chan, and B. Xu (2012, September). The Estimation and Determinants of the Price Elasticity of Housing Supply: Evidence from China. Journal of Real Estate Research 33 (3).
A
Appendix
A share of 2πdΛkj
γHkj households live in the sector j, and at the circumference with radius d and center in
CBD. The total number of households living in the sector j of city k is Hkj. We simplify this notation
considering that Λkj is Λkfor the legal sector, and Ωk/ρ for illegal sector. Average housing rents in the
city for both sectors, conditional on population, can thus be obtained as frkj =
Rφkj 0
2πxΛkj
γHkj · r(x) · dx ,
which implies thatrfkj = 2πΛkj γHkj · Rφkj 0 (r0x − tx 2)dx. Using φ2 kj = γHkj
Λkjπ, where φkj is φk for legal sector,
and φk− Sk/t for illegal sector:
f rkj = 2πΛkj γHkj ·" r0φ 2 kj 2 − tφ3 kj 3 # = 2πΛkj γHkj ·γHkj Λkjπ · r0 2 − tφkj 3 = r0− 2tφkj 3 = r( 2φkj 3 )
way between the CBD and the city’s fringe (r(2φkj 3 )): f rkj = rkj 2 3(φk− 1j=inf ormalSk/t) = i · CCf ormal+ t · 1 3 s γHkj πΛkj (A.13) g PS kj = CCf ormal+ 1 3it s γHkj πΛkj (A.14)
