Disentangling the Causes of Informal Housing

Transcription

1 Disentangling the Causes of Informal Housing Daniel Da Mata Version: June 3, Preliminary draft. 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. I construct a structural model to explain the determinants of informal housing. The model supports the main empirical evidence regarding slums 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 I present several counterfactual experiments to assess the role of income, migration and land use regulation. The results show that these factors explain about half of the variation in slums growth between 1980 and I also perform ex-ante evaluation of the impacts of slum upgrading interventions and show how policies may have unintended adverse effects on slums formation. Keywords: Slums; rural-urban migration; city growth; land use regulations JEL Classification: O17, O15, R52 1 Introduction Informal housing represents a large portion of housing markets in developing countries 1. Although the definition of informal housing varies depending on the country, informal I am grateful to Tiago Cavalcanti for his guidance and comments. I have benefited from discussions with Toke Aidt, Klenio Barbosa, Thomas Crossley, Petra Geraats, Chryssi Giannitsarou, Pramila Krishnan, Danilo Igliori, Povilas Lastauskas, Hamish Low, Diana Motta, and Cezar Santos. All remaining errors are mine. University of Cambridge and Ipea. dd346@cam.ac.uk 1 Informal housing may be seen as a general notion when there is insecure land tenure, non-compliance with building regulations, and/or with inappropriate infrastructure. In this sense, informal housing is a general notion that entails slums and squatter settlements. Squatting means illegal dwelling on a land one does not own (Jimenez (1985)). By and large, slums are characterized by overcrowding, lack of access to basic urban services, and illegal occupation of land (UN-Habitat (2003)). In this paper, the informal 1

2 housing is always associated with some sort of deprivation such as insecurity of land tenure, low standards of urban services, and even non-durable housing structure. Why do informal housing markets exist? Are there any economic incentives concerning squatting or is it only a last resort? 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)). This paper has two goals: to quantify the contribution of three factors - urban poverty, urban-rural migration, and land use regulations - to the growth of informal housing and to perform ex-ante evaluation of the impacts of slum upgrading interventions. To achieve these goals, I construct a structural model to explain the determinants of informal housing formation. The model supports the main empirical evidence regarding slums formation and it 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 dataset 2. The model is calibrated and estimated to be consistent with several statistics related to the Brazilian urbanization process during the period from 1980 to I use the Brazilian case to motivate the analysis and to calibrate the model even though the model can be applied to other developing countries. After calibrating and estimating the model, I simulate several counterfactuals events in order to disentangle the impact of specific factors on informal housing growth. I then present policy simulations to verify the impact of policies that aim to make the formal housing market more accessible to the urban poor. The problem is motivated by data facts from Brazil that suggests 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 regulation to build. I also present reduced-form evidence (using panel data from Brazilian cities) connecting the data facts. Even though the reduced-form evidence shows strong correlations regarding the determinants of slums growth, the regression results do not show the mechanisms through which income, migration and regulation affect slums formation. The housing sector is characterized by low provision of public infrastructure, lack of property rights and noncompliance with existing construction regulations. Therefore, my concept of informal housing is closely related to the notion of a slum. I will use the words informal housing, slums, and squatter settlements interchangeably. 2 The Prefecture 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

3 channels are explained by using a simple general equilibrium model of slums formation. The model formalizes the household decision on the type of housing tenure: formal or informal housing. The agents are heterogeneous in respect to their ability (and income) 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. I 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. 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 so high that households are better off living in the formal housing sector. The model shows that there is an income cutoff (associated with the opportunity costs of protecting the informal plot) separating formal and informal housing agents 3. Protection costs and defensive expenditures play an important role in studies concerning urban squatting (for instance, Jimenez (1985), Field (2007), and Brueckner and Selod (2009)). Field (2007) provides evidences about the importance of the forgone labor income when agents lack property title. Field (2007) studied a titling program carried out by the Peruvian government and concluded that land titling has a substantial impact on the number of working hours. In order to protect the informal plot, the household 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 benevolent 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 difference from previous works is that my paper is the first to explain why heterogeneous households choose different types of housing tenure. My paper is also the first to study quantitatively the determinants of slums growth. The present model includes also zoning constraints that may interfere households decisions. Specifically, according to building regulations set (exogenously) by the local government, households that choose to live in formal housing units must occupy a minimum 3 Weak law enforcement is taken as given in the model and thus it is possible to dwell illegally. I discuss this issue later on section

4 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 the MLS affordable. I compare the two income cutoffs that 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 when enforced. 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, I 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. In this work, I 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, I will employ the words informal housing, squatter and slums as synonymies throughout the paper. 4 How do income, migration, and land use regulations impact informal housing formation? 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. My model states that 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 4 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

5 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. 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. 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 in the late 1970 s stipulated that developers should employ specific construction parameters. But 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. But, instead several municipalities in Brazil have enacted land use laws with stricter parameters (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. This article follows a trend of some papers that use calibration to explore quantitative implications of urban phenomena (for instance, Chatterjee and Carlino (2001), Baum-Snow (2007), Kopecky and Suen (2010), Brinkman, Coen-Pirani, and Sieg (2010), and Michaels, Rauch, and Redding (2012)). Due to the paucity of data about some urban phenomena mainly in developing countries, applications of calibration is necessary in several cases. Some of the parameters of my model have similar data counterparts so that their calibration is straightforward; others were obtained by minimizing a loss function. The estimated parameters of the structural model are obtained via a nested fixed point algorithm. I use a distance minimization procedure in order to fit the model to the data from the Brazilian urbanization process during 1980 and Analogous to moments conditions, I match three predictions of the model to their data counterparts. Thus I 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 5 Municipalities are the third level of administrative (autonomous government) division according to the Brazilian Constitution. 5

6 conducted by the IBGE, specially the Population Censuses of 1980, 1991, 2000, and I discuss the data in greater details in the following sections and in appendix A. Even though the model is very stylized, it 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 about half of the variation in slums growth during But these factors are not very important to explain the recent evolution of slums in Brazil. The four factors are not able to explain much of the variation of slums growth in the last decade ( ). The literature on slums has focus more on the (ex-post) evaluation of policies. Examples include the studies on how land title influences outcomes in slums 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. I aim at contributing to this literature by performing an ex-ante evaluation of key policies on slums. 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. I show how policies may have unintended adverse impacts on slums formation. The remainder of the paper is organized as follows. The data facts are presented in section 2. Section 3 presents the model. In section 4, I discuss the steps taken to calibrate the model and to estimate its parameters. Section 5 shows the quantitative analysis to measure the determinants of slums formation and to perform ex-ante policy simulations. Section 6 concludes. 2 Data Facts and Reduced-Form Evidence The main idea of the data facts is to argue that the access to (formal) urban land becomes difficult to low-income 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). I connect the data facts by presenting reduced-form evidence for 123 urban agglomerations in Brazil. Data sources and definitions are shown in appendix A. 6

7 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 Moreover, the urban share of population jumped from 36% to 84% in 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. Table 1: Population in Brazil: Year Urban Population Rural Population Total Population % 63.8% 51,944, % 55.3% 70,070, % 44.1% 93,139, % 32.4% 118,562, % 24.4% 149,094, % 18.8% 171,279, % 15.6% 190,755,799 Notes. IBGE, Population Censuses Fact 2: The surge in urban population has been accompanied by stagnant real incomes and persistent income inequality. Figure 1(a) shows the evolution of real labor income, while figure figure 1(b) shows the evolution of income inequality (measured by the Gini coefficient) from 1980 to I have used a nonparametric local linear smoother to obtain the trend path for the real income and income inequality time series. By 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 The 1980 s are known as the lost decade, when Brazil economic growth became slow, after a severe sovereign debt crisis. Brazilian National Accounts shows that Gross Domestic Product (GDP) growth was nearly 10% per year during , while the GDP grew only by 1.6% per year on average during when the economy lost its dynamism. Brazil has great regional disparities, but the country as a whole suffered from the economic recession during the 1980 s. Several economic reforms were implemented during 1990 s, but Brazil experienced only limited recovery not reaching the former two-digit growth figures again. Notice that Brazil presents a very high and persistent income inequality (but it has declined recently as shown by the trend path). 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) 7

8 Fig. 1: Evolution of Real Income and Income Inequality Real Income Income Inquality Gini Index Trend: Real Income Trend: Trend: Year (a) Real Income Year (b) Income Inequality Notes: Nonparametric local linear smoother used to obtain the trend paths. I computed two trends for real income (one between 1981 and 1993 and the other for ) and one trend for income inequality (for ). stipulated that developers in Brazil must follow federally-mandated construction parameters 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 m 2. 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 housing 6. 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 1482 municipalities that have established their own land use laws, 1183 established larger minimum lot sizes. 7 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 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 8. The case of Sao Paulo 6 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 stipulated parameters to building housing units in the country. 7 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. 8 The 2010 Census changed the methodology to improve the identification of the subnormal agglomerates, so the data from 2010 is not directly comparable with the other Censuses. 8

9 Table 2: Number of municipalities adopting local land use laws - from 1979 until and the the minimum lot size Years/Minimum lot size Up to 125 m 2 More than 125 m 2 Total Total Notes. The Federally-mandated minimum lot size is 125 m 2. The second column shows the number of municipalities that have lot sizes smaller or equal to 125 m 2. The third column the number of municipalities that have adopted stricter parameters. See appendix A for details. 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. I discuss data on slums in greater details in appendix A. Table 3: Population, Housing and Slums in Brazil: Urban Agglomerations Housing units(a) 14,012,484 20,564,931 27,126,584 34,188,992 Slum units(b) 476, ,667 1,488,779 2,732,576 Population(c) 62,390,783 80,885,091 96,951, ,287,840 Slum dwellers(d) 2,224,164 4,084,051 5,775,890 9,516,899 % Slums(b/a) 3.40% 4.59% 5.49% 7.99% % Slum dwellers (d/c) 3.56% 5.05% 5.96% 8.63% Notes. Data from Da Mata, Lall, and Wang (2008) and tabulations from the 2010 Population Census in Brazil. 2.2 Reduced-Form Evidence 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. I present now reduced-form evidence that aims at connecting the four stylized facts. I assume an empirical specification in additively separable form as y it = µ(x it ) + ϵ it. where y it is the share of slum dwellers in city i at year t, X it are the city-level determinants of slums growth (such as average income, income inequality, urban regulation measures and rural-urban migration), µ(x it ) is the mean function, and ϵ it represents the unobservable 9

10 determinants of slums growth. I impose a parametric and linear form for the mean function, i.e., µ(x it ) = α + βx it. Therefore, the empirical specification is linear-in-parameters: y it = α + βx it + ϵ it. Table 4 shows reduced-form evidence on the potential determinants of slums formation at city level: per capita income, income inequality (measured by the Gini coefficient), urban regulation, and population density. I use panel data for 123 urban agglomerations in Brazil covering the period The results are for Pooled OLS, but they are virtually the same when I 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 inefficiency to estimate the rarely changing variables (such as income inequality measured by the Gini coefficient). Therefore, I cannot estimate the reduced-form by conventional fixed effects. I also used the fixed effect vector decomposition proposed by Plümper and Troeger (2007) and the results are similar. Summary statistics for the variables in the Pooled OLS regressions are in table 10 in appendix C. The results in 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. But the results point out that, after controlling for the 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. I performed some robustness checks. I test each determinant separately and combinations of them (see columns (i) to (vii) in table 4). The results are also similar when I use urban population density instead of total population density. I employed two different dependent variables: % of slum dwellers and the (log) number of slum dwellers in the urban agglomeration. Besides, I used geographical controls, such as mean temperature and precipitation, and the results are basically 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. I 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 and it is able to quantitatively assess the role of each determinant of slums growth. The model is presented in the next section. 10

11 Table 4: Reduced-form Evidence: Pooled OLS VARIABLES % of Slum Dwellers ln # of Slum Dwellers (i) (ii) (iii) (iv) (v) (vi) (vii) (ln) per capita Income ** ** *** 2.337*** (0.0045) (0.0064) (0.0060) (0.841) (0.851) Income inequality (Gini index) 0.172*** 0.235*** 0.257*** 35.99*** 40.02*** (0.0482) (0.0526) (0.0507) (6.991) (6.435) Urban regulation *** *** ** 1.709** 1.444** (0.0029) (0.0041) (0.0039) (0.704) (0.702) (ln) Population Density *** 1.161*** (0.0018) (0.223) Constant * *** *** *** ** *** *** (0.025) (0.026) (0.002) (0.054) (0.051) (6.911) (6.690) Observations R-squared Notes. Robust standard errors in parentheses. All the regressions are for 123 urban agglomeration in Brazil. The pooled OLS is for 1980, 1991, and 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 3 The Model I 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. This simple model assumes that the decision on the type of housing tenure does not have inter-temporal linkages. As mentioned before, I motivate the model using the Brazilian case, even though the model is more general. The model presents the basic trade-off of slum dwellers: paying the cost associated with formal housing or losing time to protect the informal plot? I add minimum housing space consumption as a form of urban regulation. The model can be thought as a variant of (i) the Rosen-Roback model with heterogenous agents and different types of housing tenure (Rosen (1979) and Roback (1982)) or a variant of (ii) the static Melitz model (Melitz (2003)) with heterogenous households (instead of heterogenous firms), housing tenure cutoff (instead of firm exit and entrance cutoff), and housing production. 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. 11

12 3.1 The Environment Households There is a measure N of agents, each of whom with heterogeneous ability (λ). There are a minimum λ min and a maximum λ max ability levels. The ability distribution function is denoted by f(λ) with accumulative distribution F (λ), where F (λ min ) = 0 and F (λ max ) = N. Each agent is a worker and lives alone in a housing unit, so that the number of people equals both the number of households and houses. Agents 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 (s j ), where j equals F if formal housing and I if informal housing. The utility function is specified as U(c, s j ) = c 1 α s α j, where α (0, 1) and j = F, I. Utility derived from formal housing is higher compared to informal housing. Housing service flow (s j ) 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). I assume that housing service flow is a linear function, i.e., gh if Formal housing (j=f) s j = 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 high congestion costs in informal settlements: the main complain of Caju s slum dwellers is violence (circa 50% of the population stated that violence in the main problem in the community), while the lack of public services was the third major complain (14%) 9. The parameter θ is less than one to informal housing because for a given housing size, informal housing service is lower. If the agent decides do dwell legally, she can derive utility over the entire housing services, but if she decides to dwell illegally, she will face a utility discount. In a scenario of high land law enforcement, θ is very low, which means that the utility from occupying illegally a plot is very low. In other words, the model assumes that (i) formal housing is secure and provides the entire housing services and that (ii) the lower provision of public goods associated with informal housing influences negatively housing service utility. 9 The second main complain was high housing prices (17%). 12

13 An agent labor income is given by λw, where w is the average wage of the location and λ is her ability level. represented by λw(1 τ). Every agent pays an income tax (τ), so the net income is An agent allocates her labor income between non-housing consumption (c), housing services (s), and a property tax (η). To be precise, only formal housing agents pay a property tax η - a cost associated with being located in the formal housing sector. One could 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 formal 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. Each agent has 1 unit of time. If the household decides to live in the informal sector, she occurs in protection costs (Ψ). I 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. I 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 ability and housing space: Ψ(λ, h). The greater the ability, 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 a linear function of both factors: Ψ(λ, h) = ψwλh, where ψ is a constant. Therefore, Ψ(λ) = ψwλ represents the protection cost per unit of housing service 10. The parameter ψ reflects both the penalty costs and the probability of being caught by the government due to live in a informal settlement. Moreover, if the households chooses to live in the formal housing, she must comply with building regulations. In this paper, a formal housing unit must comply with a specific building-related requirement: the minimum lot size (MLS). In the model, the MLS is the parameter h exogenous set by the local government. 11 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 10 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 if the community leader spends his income outside the city boundaries. 11 The minimum lot size is exogenous in the model, i.e., I assume that the city and its households take the MLS parameter as given. There are cases where MLS is federally mandated, such as in the case of municipalities that followed the Brazilian national law stipulating the minimum lot size of 125m 2. 13

14 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 the 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, the 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 There are also extreme cases when the protection cost is huge: anecdotal 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 despair 13. 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 returnsto-scale production function f(n, K) = BN υ K 1 υ, where N represents units of (idiosyncratic) labor efficiency, K represents units of capital and B is an average productivity (total factor productivity) of the city. Labor is supplied by the households given wages w and K is an elastically supplied factor with rental price r determined outside the city in the national economy. The optimization problem for the consumption good firms is max N π = BN υ K 1 υ wn rk. The first order condition (F.O.C) for K is r = (1 υ)b( N K )υ, while the F.O.C. for L is given by w = υb( K L )1 υ. Combining both first order conditions generates the labor demand of the city: [ (1 υ)b w = υb r ] 1 υ υ. (1) Equation 1 shows that labor demand is perfect elastic because the rental of capital r is exogenous to the city point of view. As a result, wages w in the model are determined solely by the labor demand equation. Housing

15 Housing is produced in a competitive market environment as well. Housing space is produced using land (L) and capital (K): L is supplied inelastically, while K is an elastically supplied with price r. Housing space production function is h(l, K) = L γ K 1 γ, where γ (0, 1). Land price (p L ) is the same at every unit of land and is privately owned. Land belongs to a group of absentee landlords and this group spends the land rent outside the city. Total land cost is p L L, where p L is the land price and L is the quantity of land. Developers buy land at market prices and have the following optimization problem: max q Π = pl γ K 1 γ p L L rk, where p is the housing price. The first order condition (F.O.C.) is equal to the zero profit condition: r = p(1 γ)k γ L γ. Total housing supply is obtained by manipulating the F.O.C: H s = Lp 1 γ γ [ 1 γ r ] 1 γ γ. (2) 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 housing market equilibrium. Government and Land Law Enforcement Let e(g) represent the local government expenditure and assume that e(g) is linear: e(g) = g. The government finances its spending (g) through a property tax rate (η) paid only by formal housing residents and by a income tax (τ) paid by all residents. Define Γ(F ) as the set of abilities of the agents that resides in formal housing units, i.e., Γ(F ) {λ {λ min, λ max } : j = F }. Government runs a balanced budged and therefore g = ηr H h F (λ)f(λ)dλ + λmax Γ(F ) λ min τwλf(λ)dλ, where R H is the land rent and h F (λ) is the housing size chosen by each formal housing agent. Property tax η and income tax τ are parameters. The local government matches expenditure g so as to equalize it to the total revenue. Note that the local government spending g enters the utility function of all households (but there is a discount θ 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, I assume that government spending involves only the security of 15

16 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. I follow Brueckner and Selod (2009) by adding a no-eviction constraint in the model: I 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 evictions Decision Problems and Properties of the Model Formal housing problem Taking w and R F as given, formal households problem is V F (λ) = max c,s j U(c, s j ) = max c,h [c 1 α (gh) α ] subject to c + [R H (1 + η)]h = wλ(1 τ), h h > 0, (3) c 0, h 0. The parameter g is a utility-shifter and it stands for public-goods type of benefits from dwelling legally. The household must pay two different taxes: property tax η and labor 14 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 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. As I will show in the next sections, the model tells that there is a income cutoff that, from this point on, the households have clear incentives to enter the formal housing market in order to have their plot protected by the government and to be able to spend their entire time endowment working. 16

17 tax τ. The left hand side of the budget constraint shows the several types of expenditure (consumption and housing), while the right hand side shows the household income given her ability level (λ). Recall that in the formal housing case, s j = s F = h. Equation (3) means that there is a minimum housing space that stems from minimum lot size (MLS) regulations from a zoning constraint in the city. Equation (3) allows the use of a two-step maximization strategy. I solve for both when h > h (that is, when the MLS constraint is not binding) and when h = h (the constraint is now binding). The first order condition (F.O.C.) with respect to c and h shows that the marginal benefit of housing equals its marginal costs: αc α = (1 α)h (1 α) [R H (1 + η)]. When equation (3) is not binding, optimal consumption and housing choices for a formal household are respectively: c F (λ) = (1 α)wλ(1 τ). wλ(1 τ) h F (λ) = α R H (1 + η). (4) Recall that the term wλ corresponds to the household income given her ability λ. When equation (3) is binding choices are: c F (λ) = wλ(1 τ) R F (1 + η)h. h F (λ) = h. Given the utility function functional form, the household will choose a housing space consumption such that [ ] wλ(1 τ) h F = max α R H (1 + η), h. The following proposition states that not necessarily every agent will have enough income to afford a formal housing unit with the minimum lot size dimensions (h). This result appears in proposition 1. The proofs of the propositions are shown in Appendix B. Proposition 1 There is income level λ MLS such that for any λ λ MLS formal housing becomes affordable, i.e, there is an ability level λ < λ MLS that makes equation (3) binding. Informal housing problem 17

18 Taking w and R H as given, informal households problem is: subject to V I (λ) = max U(c, s j ) = max c,s j c,h [c1 α (θgh) α ] c + R H h = wλ(1 τ) Ψ(λ, h), Ψ(λ, h) = ψwλh, (5) c 0, h 0. I used the fact that s j = 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). Notice that equation (5) takes a linear form and acts like an additional housing cost: an opportunity costs associated with dwelling in the informal housing market. Informal households receive lower utility and incur protection costs due to living at an insecure place, but they do not incur any costs associated with being in the formal housing market. The F.O.C.s for c and h together yield: αc α = (1 α)h (1 α) [RI + ψwλ]. Optima choices are given by: c I (λ) = (1 α)wλ(1 τ). λw(1 τ) h I (λ) = α R H + ψλw. (6) I compare the income elasticities of formal and informal housing consumption in proposition 2. The result is that income elasticity for formal housing is greater than the one for informal housing. Precisely, formal housing has income elasticity of 1 (normal good), while informal housing has a income elasticity of less than 1 (inferior good). Proposition 2 Formal housing is a normal good and informal housing is a inferior good. The result of proposition 2 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. Choosing between formal and informal tenure 18

19 Agents will live in formal housing units if V F (λ) > V I (λ). Conversely, if the benefits of breaking the law surpass the costs of penalty and the probability of being caught, the agent will choose to live in an informal settlement. The housing type decision can be described by the function Ω(λ) where for λ [λ min, λ max ] if V F (λ) > V I (λ) Ω(λ) = 0 if V F (λ) V I (λ) In order to obtain the indirect utility functions given ability (V F (λ)) of the formal housing residents, I substitute optimal consumption and optimal housing choices into the utility function of formal housing residents yielding: Vnb F (λ) = αα (1 α) 1 α wλ[r H (1 + η)] α, where Vnb F (λ) stands for the indirect utility when housing space is non-binding. It is possible to prove that the utility when housing space non-binding (Vnb F (λ)) strictly dominates the utility when housing space is binding Vbind F (λ), except for the ability levels when equation (3) holds (see proposition 1). As a result, I will work from now on with V F (λ) = max {V F nb (λ), V F bind (λ)}. The indirect utility for informal households (V I (λ)) is given by: V I (λ) = α α (1 α) 1 α wλ[r H + ψwλ] α θ α. I will first analyze the household decision when the MLS is not binding 16. V F (λ) V I (λ) = 0 the household is indifferent between living formally or informally: (7) When V F ( ) V I ( ) = α α (1 α) 1 α wλ[r H (1 + η) θ 1 R H θ 1 ψwλ] α = 0. (8) The relevant parameters concerning the decision to live formally or informally are given by equation (8). Rearranging equation (8) generates λ = R H [θ(1 + η) 1]. (9) ψw Equation 9 shows that there is an ability cutoff ( λ) separating formal and informal housing agents. Figure 2(a) depicts the mechanics of housing tenure choice of the model. Consumption of non-housing goods are identical for formal and informal housing agents, so decision on whether to be formal or informal depends solely on the (i) housing cost differential (paying property tax η for formal tenure and the opportunity cost ψ of informal 15 Rural-urban migration driven by difference in rural and urban utility is associated with squatting and informal housing in developing countries (Turnbull (2008)). Therefore, the squatter participation constraint is fulfilled if max{v F (λ), V I (λ)} u, where u represents the utility of rural areas. 16 When housing space is binding the indirect utility becomes V F bind(λ) = [wλ R H (1 + η)h] 1 α h α. 19

20 housing) and on (ii) the disutility from informal housing (θ). The intuition of equation 9 and figure 2(a) is as follows. Each household takes R H as given. If the household chooses to live in the formal housing sector, she also has to pay property taxes (η). Then the housing costs per unit of housing service of the formal sector is given by R H (1 + η) and it is independent of the household ability. Conversely, if she decides to dwell illegally, she pays R H plus protection costs (ψwλ) per unit of housing service 17. Protection costs rise as income grows. As a consequence, the household with lower abilities must dwell in the informal housing market. In other words, R H and η act as a barrier the screens out from the formal housing market those with lower income. As ability (and income) grows, formal housing units become more affordable and, at the same time, informal housing becomes less desirable 18. As shown in figure 2(a), up to an ability threshold λ the household must dwell informally. Ability levels greater than the ability threshold λ are associated with formal tenure choice given the high opportunity costs linked to informal housing. Note that if θ(1 + η) 1 < 0 in equation 9, all households are formal. The model is capable of explaining when there is no incentives to be informal: it happens when disutility of being informal is so high (i.e., θ is very low) and/or the cost of formal housing (represented by η) is so low that nobody wants to be located in the informal housing sector 19. Now I add the minimum lot size (MLS) constraint to the analysis. How do man-made regulations interfere housing type decision? Proposition 1 shows that there is an ability level (λ MLS ) that for abilities greater than this cutoff the MLS is not binding anymore. The ability cutoff (λ MLS ) associated with the affordability of formal housing units (when the constraint h h is binding) is given by λ MLS = h R H (1 + η) α w(1 τ). (10) As a result, there is an ability level λ given by the opportunity cost related to the protection cost and another ability level λ MLS stipulated (exogenously in the model) by man-made regulations. Notice that λ MLS λ depending on the value of h (see figure 2). When λ MLS < λ the MLS regulations do not interfere the household decision on whether being in the informal housing market; it means that the household only consider the protection costs when taking the decision of what type of housing to live. When λ MLS > λ, MLS matters to decisions. In the latter 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 17 Notice that when ability in zero, informal housing costs in figure 2(a) is R H /θ. Once θ represents a utility discount, the informal housing cost given the preferences of the individual is greater then R H. 18 Recall that informal housing is less desirable when one takes into account only the utility functions because of the utility discount θ. 19 This is a partial equilibrium result. See proposition 7 in section 3.3 for a discussion on the size of the informal housing sector in general equilibrium. 20

21 Fig. 2: Income Cutoffs and MLS Regulations Housing cost per unit of housing space Informal Housing R H (1 + η) Formal Housing R H + ψwλ θ Informal λ Formal Ability Level (a) Income Cutoff: λ Housing cost per unit of housing space Informal Housing R H (1 + η) Formal Housing R H + ψwλ θ λ MLS λ λ MLS Ability Level (b) Income Cutoffs λ and λ MLS Notes. The graphs shows the two income cutoffs of the static model ( λ and λ MLS ). 21

22 formal housing sector given only their trade-off formal housing costs versus protection costs. When λ λ MLS, slums growth is explained by Incentives and Institutions (when ability is between 0 and λ) Man-made Regulations (when ability is between λ and λ MLS ) Note that there is a discontinuity around the λ MLS threshold (see 2(b)). Informal housing agents with less income than λ MLS pays a higher total price (and thus consume less housing space) than formal housing agents with income slighter superior than λ MLS. One implication of the model is that there are some people that live in informal settlements and pay more (i) than some formal housing agents and (ii) than they would in case there was no MLS regulations (the households with income between λ and λ MLS ). Figure 3 summarizes the implications of the model. The main result of the model is that heterogenous agents sort into different housing tenure modes: low-ability households will live in informal settlements due to incentives and institutions (the ones with ability between λ min and λ), other low-ability households will dwell illegally due to regulations (the ones with ability between λ and λ MLS when land regulations generate λ MLS > λ) and higher-ability households will choose to live formally. This sorting is similar in nature to one in the Melitz model (Melitz (2003)) where firms with different productivity sort into different modes (exit the market, production to domestic market or export). Fig. 3: Ability Distribution and Sorting into Tenure Modes Land Enforcement and Incentives Man-made regulations Compliance with regulations Informal Housing Informal Housing Formal Housing MLS Ability λ λ Level Notes: There are two ability cutoffs in the model ( λ and λ MLS ). The figure was construct for λ MLS > λ. There are 6 relevant parameters in the two ability cutoff equations (equations 9 and 10): disutility shifter (θ), property taxes (η), labor tax (τ), informal housing opportunity cost 22

23 (ψ), minimum housing consumption (h), and housing expenditure weight (α). Housing rents R H will be determined via housing market equilibrium, while wages w is stipulated by the labor market equilibrium. The following proposition summarizes the discussion on housing tenure choice: it shows that there is an unique ability cutoff that determines if a household will live in the formal or informal housing sector, i.e., the proposition characterizes housing tenure choice for a given household ability. Proposition 3 For a given minimum housing consumption (h), there is an unique ability level λ = max [ λ, λ MLS ] such that, for each λ > λ, V F > V I, i.e., all agents choose to live in the formal housing sector. One implication of proposition 3 is that if there is no λ such that λ > λ, all households will choose to dwell in the informal housing sector. 3.3 Competitive Equilibrium I now complete the analysis of the equilibrium of the model. In the equilibrium, markets clear and households and firms do not have incentives to modify their decisions as follows: Definition 4 Definition of Equilibrium: A competitive equilibrium consists of a set of allocation rules (consumption and housing services) for both formal and informal households, a housing-type decision rule (Ω(λ)), a no-eviction condition, a set of prices (R H, p and w), and a set a parameters (ψ, θ, η) such that, given a distribution of individual ability (F (λ)): (i) individuals solve both formal and informal maximization problems, (ii) goods firms and developers maximize profits, (iii) the government has a balanced budget and (iv) goods market, input markets, and housing market clear. Firms optimization decisions generate equilibrium wages. Equilibrium in the asset market with no uncertainty means that the housing price equals the discounted value of housing rents: p = R H /r, where R F represents the housing rent and r is the real interest rate (Saiz (2010)). For simplicity, I assume perfect mobility, so the rental price of capital is equal to the real interest rate (no arbitrage). Equilibrium housing rent is determined by the housing market equilibrium. Housing market equilibrium Total housing demands are λ λ H I = h I (λ)f(λ)dλ = λ min 23 λ min α λw(1 τ) R H + ψλw f(λ)dλ

24 for informal housing (using equation 6) and H F = λmax λ h F (λ)f(λ)dλ = λmax λ α λw(1 τ) f(λ)dλ (1 + η)r H for formal housing (using equation 4). I used the fact that λ = max [ λ, λ MLS ] divides formal and informal housing agents (see proposition 3). Recall that housing supply is given by equation 2. The housing market clearing condition can be stated as λ λ min α λw(1 τ) R H + ψλw f(λ)dλ + λmax λ α λw(1 τ) f(λ)dλ = LR (1 + η)r H 1 γ γ H [ 1 γ r 2 ] 1 γ γ (11) where the left hand side (LHS) shows the housing demands and the right hand side (RHS) shows the total housing supply of the city. I used the fact that p = R F /r in the RHS of equation 11. Housing prices adjustments generate the housing market equilibrium. Equation 11 says that all land within the economy will be used for residential purposes. The equilibrium of the model generates the same housing rent (per housing space or per square meter) for both formal and informal housing. Usually, the literature argues that formal housing units have higher prices because of their better infrastructure. But some author have emphasized that informal housing may be even more expensive because it has a premium associated with urban freedom 20 and future land regularization (Smolka and Biderman (2011)). Even though the housing rent is equal in the model, the effective cost of formal and informal housing units differs depending on the ability of the agent: informal housing is cheaper for low-income agents and formal housing is cheaper for higher income households. Final Equations and Comparative Statics There are two relevant equations that solve the model of slums formation and that jointly determined the two unknowns of the model (ability threshold λ and housing prices p). The relevant equations of the model are: and λ = max [ λ, λ MLS ] = max [ R H ψw [θ(1 + η) 1], (1 + η)h α R H w ] (12) λ λ min α λw(1 τ) R H + ψλw f(λ)dλ + λmax λ α λw(1 τ) f(λ)dλ = LR (1 + η)r H 1 γ γ H [ 1 γ r 2 ] 1 γ γ (13) 20 The freedom to choose exactly the construction specifications of one s housing unit. 24

25 Recall that wages w are determined by the city s labor demand (equation 1): w = [ ] 1 υ υb (1 υ)b υ. r Even this stylized model may lack closed-form solution for the stationary equilibrium of the housing market due to the ability heterogeneity assumption. The main problem is how ability distribution F (λ) is modeled. model may lack closed-form solution. as λ 1 ϵ Even with extreme assumptions, the Tractable cumulative distribution functions such (Chatterjee, Corbae, Nakajima, and Ríos-Rull (2007)) does not necessarily generate closed-form solution 21. Equations 12 and 13 are thus solved using numerical methods. I solve the model numerically using the following steps: 1. Guess λ; 2. Compute the correspondent housing price p using equation 12; 3. Check whether the new p clears the housing market (see equation 13); 4. If p does not clear the housing market, update it accordingly; 5. Based on the updated p, update λ using equation 12 and check whether or not the housing market clears; 6. Keep updating p (and consequently λ) until the housing market clears so as to obtain the final λ. Proposition 5 proves the existence and uniqueness of the equilibrium of the model. Proposition 5 Existence and Uniqueness. Given the structure of the model, an equilibrium exists and is unique. equations 12 and 13. The competitive equilibrium is characterized by equations The comparative statics of the model are shown by the next proposition. Proposition 6 shows the impact of several parameters on household tenure choice. Proposition 6 Comparative statics. Greater w has an ambiguous effect on slums formation, i.e., an increase in wages can be partly, or even fully, offset by an increase in housing prices. Greater ψ do not increase squatting, while larger σ, N, h, θ, η, r and τ do not decrease informal housing formation. The comparative statics entails the following parameters: average income w, income inequality σ, urban population N, land use regulation h, protection cost ψ, informality disutility θ, property taxation η, labor tax τ and real interest rate r. It is possible to 21 When ϵ equals 1, λ 1/ϵ represents a uniform distribution. In this simpler case with support [0, 1], it is possible to obtain a closed-form solution for housing rents (R H ). When ϵ is less than 1, as is the case of actual income distributions, the complexity of the rational integral involving h I increases and closed-form solutions are not longer necessarily obtained. 25

26 partition the parameters into two categories: determinants of slums formation and policyparameters, i.e.,. Local and National Policies {}}{ w, σ, N, h, ψ, θ, η, τ, r }{{} Determinants It is possible to analyze the impact of each determinants of slums formation (income level w, income inequality σ, urban population N, and land use regulation h). It is also possible to verify the impact of local policies regarding slums (land use regulations h, property taxation η, titling policies that affect ψ, and upgrading policies that affect θ) and national policies (labor tax τ and real interest rate r). Income has an ambiguous effect on slums formation. This result is consistent with Jimenez (1985). The results of the comparative statics exercise help to explain the directions of the correlations found previously by the reduced-form evidence (section 2). Income level, income inequality, regulation, and population size were positively correlated with slums growth. The comparative statics explain why the correlations are positive. In partial equilibrium, when one considers only housing tenure choice (and do not consider the effects on housing prices), the magnitudes of λ and λ MLS will dictate whether a policy is effective or not. When λ > λ MLS, the minimum lot size restriction is not important when it comes to housing tenure choice and reducing h is ineffective to reduce informality. In this case, to reduce informality, one can increase the opportunity cost ( ψ), decrease informality utility ( θ) or reduce the property tax rate η. These are all partial equilibrium results that translate into general equilibrium effects: if λ > λ MLS, h does not influence housing informality even in general equilibrium because h does not affect housing prices. In partial equilibrium, when λ < λ MLS, decreasing h reduces informality, but increasing ψ, decreasing θ or reducing η have no impact on informality at all. In general equilibrium, changes in ψ, θ or η have impacts on housing space consumption and housing rents. Therefore, ψ, θ or η impact λ MLS via housing rents R H. In other words, in general equilibrium ψ, θ or η affect housing affordability and thus they impact λ MLS and households choice on housing tenure. Note that the effect of the policies in general equilibrium depends on the elasticity of supply and on the size of the informal and formal sectors (demand shifters). The bigger the size of the informal sector, the greater the impacts of policies (that affect the informal sector) on housing prices and rents. An additional feature of the model relies on its capacity to explain when housing informality does not exist. For instance, informal housing may be too risky (then θ is near zero and ψ is almost one) that every agent chooses formal housing tenure type, given that 26

27 the agent fulfills the participation constraint max{v F (λ), V I (λ)} u, i.e., the household has a greater utility than the rural or reservation utility u. This is described in proposition 7. Proposition 7 There is a level of informal housing risk such that θ is too low and ψ is too high that no household in the city lives in informality, given that the household fulfills the participation constraint. The population size is determined exogenously in the model, but a simple modification suffices to endogenize the population size. Let the reservation utility be u. The endogenous population size ( N) would be determined by the following spatial indifference condition: max{v F (λ), V I (λ)} = u. The growth in urban population can be generated by a higher total factor productivity (TFP) in the production function of firms in urban sector vis-àvis firm in the rural economy (as in Hansen and Prescott (2002)). Higher TFP generates wage differential between urban and rural areas. Recall that the total factor productivity is given by B in the production function (see section 3.1). A higher TFP for urban firms would implicate that B u > B r, where B u is the TFP for firms in urban areas and B r the TFP for firms in rural places. Shocks in B u would generate that max{v F (λ), V I (λ)} > u to some agents (to induce migration to the city) and max{v F (λ), V I (λ)} = u to other agents to guarantee the spatial equilibrium. I can related my model to several models of the literature. First, the model is a general equilibrium model of city (small open economy), so it can be considered as an extension of the Rosen-Roback model with heterogenous agents and different types of housing tenure (Rosen (1979) and Roback (1982)). It can be also considered as a variant of the static Melitz model (Melitz (2003)) with heterogenous agents (instead of heterogenous firms), housing tenure cutoff (instead of firm exit and entrance cutoff), and housing production. Besides, it can be seen as a variant of the monocentric Alonso-Muth-Mills (AMM) model (Alonso (1964), Muth (1969), and Mills (1967)). The AMM model (Alonso (1964), Muth (1969), and Mills (1967)) has been successful in explaining the spatial patters of housing prices in cities (Brueckner and Rosenthal (2009)). For instance, in the standard AMM model, housing prices decline with distance to compensate households for increasing transportation costs. The present model works as if in the monocentric AMM model land price variance across the city space is zero or negligible because I abstract from transportation costs and within city location decisions. 4 Estimation The model formalized the mechanisms by which income, population size, and land use regulations affect housing type decisions. Now I want to determine the magnitude of 27

28 those factors on slums formation. The parameters of the model are set to match relevant features of the Brazilian economy in four baseline years (1980, 1991, 2000, and 2010). I verify the model s prediction for all four years and confront those prediction with the data. The contribution of each factor impacting slums growth is analyzed in section 5, once the model fit the data. Table 5 describes the parameters values for the numerical example. I need to calibrate 11 parameters generated by the structure of the model and represented by the following parameter vector ξ = {B, λ p80 λ p20, α, γ, η, τ, N, r, ψ, θ, h}. The values of the parameters of vector ξ were either selected from previous studies or from a existing dataset ( external calibration ) or determined by a distance minimization procedure ( internal calibration or estimation). Let a be the partition of vector ξ containing eight parameters to be (externally) calibrated and b 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 a = {B, λ p80 λ p20, α, γ, η, τ, N, r}. Due to the shortage of empirical literature on slums, in particular applied to Brazil, I had to select parameters directly from datasets to use in the calibration. I 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), income ratio of the 80% richer to the 20% poorer ( λ p80 λ p20 ), weight of housing consumption (α), weight of land input (γ - recall that housing supply price-elasticity comes from γ), property tax rate (η), income tax rate (τ), total urban population ( N), and real interest rate (r). One key aspect of the present numerical exercise is the distribution of ability (F (λ)). Since the model assume income heterogeneity among households, it is necessary to have a distribution of income. I use the fact that the lognormal distribution works as an approximation to the empirical income distribution (except from its tails). As such, the distribution ability F (λ) is set as a doubly-truncated lognormal distribution, i.e., I use the (doubly-truncated) lognormal distribution in order to fit empirical income distribution 22. I adjust the lognormal distributions two parameters to match moment of the income distribution of Brazil in the relevant years. I use two income data moments from PNAD (IBGE s household survey - see IBGE (2002) and appendix A) for this exercise: mean 22 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. 28

29 income (proxy for the average city-level productivity B) and ratio of the income of the household in the 80th percentile to the household in the 20th percentile ( λ p80 λ p20 ). The estimated lognormal distribution provides the income distribution for the calibration exercise. The artificial income data is set to match moments of the empirical income data. In other words, I adjust the two parameters of the lognormal distribution to match moment of the income distribution of Brazil in the relevant years. The weight of housing consumption in the utility function (α) is set at 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. This I set the weight of land input (γ) to be equal to The parameter γ can be rewritten as the share of land out of total output given the Cobb-Douglas production function of the developers. Production technology of developers in Brazil varies, but data from construction companies show that the target value for land price lies between 25% to 35% of the total output when it comes to residential units. Several factors influence the ratio land price to total sales, such as whether the land was bought directly or the company has offer residential units in exchange for the land. 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). The property tax rate (η) equals 1%. Carvalho Jr. (2008) studied the structure of property tax rates in a sample of 365 Brazilian municipalities (all of them with more than 50,000 inhabitants) for Although there is some variability among the property tax rates set by the municipalities (and even within a particular municipality boundary), the median rate for residential units was 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. Out of 365 Brazilian municipalities sampled, the 2/3 adopted a single rate. In Brazil, the rate of the property tax may vary according to the type of construction (for instance, commercial real state or residential unit). For residential units, it is equivalent to 1% of the housing prices (p) in many municipalities. In São Paulo, it varies between 0.8% and 1.6% of the market value of the housing unit, while in Rio de Janeiro it is 1.2%. Note that the parameter η multiplies housing rents (R H ) in the model, so it is necessary to calculate the effective property tax as of housing rents values. 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%. According to the Brazilian Revenue Service, the effective labor income tax is 12% 23. There is a social security contribution of 10% on 23 Precisely, it is between 0.3% and 12% because of the progressive structure of labor taxation. 29

30 top of labor income tax, so the parameter τ is set to The parameter N is set to be equal to the total urban population in the country. I also need to stipulate the interest rate r. On one hand, Brazil was characterized by high real interest rates during the 1990 s and 2000 s. On the other hand, annual real interest rates were very low, sometimes even negative, during the 1970 s and 1980 s 24. Based on a 30 years average for Brazil, the interest rate is set to be 4% per annum in real terms. Estimation: Internal Calibration Due to the paucity of data, the additional three parameters (from the partition b of vector ξ) were found by minimizing the distance between the model and the data moments. Therefore, I 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. The internal calibration consisted of estimating three parameters (protection costs ψ, informality disutility θ, and minimum housing space h) such that the model would match key statistics of the Brazilian urbanization process. Note that the estimation via distance minimization is influenced by the choice of moments. Precisely, I match three predictions of the model to their data counterparts: (i) fraction of population in slums, (ii) formal-informal housing space ratio, and (iii) housing space inequality (measured by a Gini housing space coefficient). To create the slums share I verify the decision rule (Ω(λ)) for each agent and then create the slums share value. After verifying the optimal choices of the each agents, it is also possible to retrieve information about the housing space consumption for each them and to compute the average housing space ratio (of formal and informal housing). All three information are used as moments in the minimization procedure. I use the Method of Moments or Minimum Distance to find the unknown parameters (i.e., the three parameters I want to estimate). 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 ˆb that minimizes the distance between the model s prediction and the data. By carrying out this procedure, I aim to obtain the parameter values that most closely reproduces 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 exactly identified, since the number of parameters in b equals the number of moments. Let L be the quadratic loss function to be minimized, M d be the vector of data moments, and M m be the correspondent vector of model moments. Formally, I want to find a ˆb such 24 According to data from Ipeadata, in the mean real interest rate was -4%, in the average real interest rate was 7%, and during the rate was 12%. 30

31 that 1 ˆb = arg min L(a, b) = arg min b b N [M m(a, b) M d ] 1 W N N [M m(a, b) M d ]. (14) where M m (a, b) M d is the orthogonality condition and W N is a positive semi-definite weighting matrix. The matrix W N converges in probability to W. It follows that ˆb is a consistent and asymptotically normal estimator of b. In the analysis, I use an optimal weight matrix W is given by the inverse of the variance-covariance matrix of the data moments (S) 25, i.e., W = S 1. I want also to determine the precision of the parameter vector ˆb. standard error I use the following equation: To calculate its V (ˆb) = (D W D) 1 D W SW D(D W D) 1, (15) N where S is variance-covariance matrix of the data moments, N is the sample size, and D is a gradient matrix equivalent to D = [M m(a, b) M d ] b Equation 15 simplifies to b=ˆb = M m(a, b) b = b=ˆb V (ˆb) = (D S 1 D) 1 N Mm 1 (a,b) ψ Mm(a,b) 2 ψ Mm 3 (a,b) ψ Mm 1 (a,b) θ Mm(a,b) 2 θ Mm 3 (a,b) θ when I use the optimal matrix W. I compute the standard error (SE) via Mm 1 (a,b) h Mm(a,b) 2 h Mm 3 (a,b) h. SE(ˆb) = (diagv (ˆb)) 1 2. (16) Given the structure of the model, I had to consider the following constraints in the estimation procedure: 0 < ψ < 1: protection costs must be a positive share of the labor income θ > 0: there must be a disutility on living at a informal housing unit θ(1+η) 1 > 0: to guarantee that income threshold (λ T HRE ) is positive (see equation 12) h > 0: enforcement of MLS regulations Table 5 shows the values for the three estimated parameters. The estimated parameters have the expected sign and are somewhat precise. It is useful to confront the estimated values with the ones found in the literature. For instance, I compare ψ with the estimated 25 All three data moments are calculated from Brazilian microdata. I computed data-moments variancecovariance matrix S directly from city level variance-covariance information. The off-diagonal elements of the matrix S also come from the city-level information. 31

32 forgone labor from the literature. Field (2007) estimates that no legal claim to property is associated to a reduction of 14% in total household working hours. My estimate for ψ is Table 5: Estimation of the Model: Parameters External Calibration Parameter Description Values Source α Preferences: Weight of housing service 0.14 POF survey γ Housing: Weight of land input 0.25 Construction Companies B Production: Productivity PNAD survey r Real interest rate 0.04 Central Bank of Brazil η Government: Property tax rate 0.01 Ministry of Finance τ Government: Income tax rate 0.22 Ministry of Finance λ p80 λ p20 Income ratio 80% to 20% 15 PNAD survey N Urban population size 139m 2000 Census Parameter Description Internal Calibration Point Estim. (Std. Error) Source ψ Protection costs 0.19 (0.05) Estimation θ Housing Informality Disutility 0.94 (0.32) Estimation h Minimum housing space 0.72 (0.15) Estimation Notes. Eight parameters were chosen via external calibration. Three parameters were estimated via a distance minimization procedure (internal calibration). Table 6 shows the baseline economy in The data moments stem from the 2000 Population Census. The Census has information about whether the housing units is considered informal ( aglomerado subnormal ), so the calculation of the slums share is direct. To compute the housing space moments, I had to use both the Census and PNAD. The Census provided information on the number of bedrooms, rooms (excluding bedrooms), and bathrooms. I used these information as a proxy for size. From PNAD, I obtained the correspondence between the number of rooms and the average size of the housing unit. According to the data and to the simulations, housing space inequality in 2000 (0.32) is lower compared to income inequality (more than 0.5) in the same year. In the model, a lower income agent that lives in the informal housing sector consumes more housing space then she would have consumed in case she was only 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 Both formal and informal housing sectors contribute to determine the magnitude of housing rents in the model - see equation 13. Nonetheless, because of the share of slums in the data, housing rents in the simulations are guided basically by formal housing 32

33 Table 6 also shows the comparison between the slums share generated by the model and the one from the data for 1980, 1991 and Recall that the estimate parameters are for I change three variables to generate the results for 1980, 1991, and 2010: income level, income inequality, and the size of population. All three factors explain the number of slum dwellers. Let s analyze the data for 1980 to grasp the mechanics of the model. In 1980, population is almost 30% smaller (and so housing rents and prices are smaller as well) and real income is 18% lower than in Less people and less income are associated with fewer people in informal housing. On the other hand, income inequality (measured by the Gini coefficient) is greater and it causes more informality. The enforcement of land law is considered to be the same every year, and this may explain the difference between the data result and the model result in Table 6: Moments: Data and Model Baseline Comparison Moments Data Model Data Model Data Model Data Model Slums share (%) Gini housing space h20/h Quantitative Analysis This section comprises two parts. In the counterfactual part I quantify how much of the growth in slums is accounted by poverty, regulation and migration. In the policy experiments I perform several ex-ante policy simulations. 5.1 Counterfactual Analysis I carried out several counterfactual experiments to evaluate the determinants of slums formation. A relevant factor has its 1980 value fixed in order to assess the role of this factor on the increase in slums share during the period from 1980 to The counterfactual experiments aim to answer questions such as: what is the impact of land use regulation changes (h)? What is the impact of low income growth (or income decline - w)? What is the impact of increasing income inequality and of rapid rural-urban migration? The 1980 s and 1990 s decades are specially important for counterfactual experiments in Brazil. For instance, Imparato and Ruster (2003) shows that in 1973 Sao Paulo had 1.2% of its 33

34 population living in slums, while by % of the population was living in slums (see also table 9 in appendix A). In the 1990 s the rate of propagation of slums was even more intense. I perform seven different counterfactual exercises. In four exercises, I shut down each determinant of slums growth separately. In other words, the four counterfactuals are (i) no change in income level during ; (ii) no change in income inequality; (iii) no change in land use regulations; and (iv) no rural-urban migration. Then I shut down a combination of the determinants to generate new scenarios: (v) no change in both income level and inequality, (vi) no change in income level, inequality, and MLS regulations, and (vii) no change in income level, inequality, MLS regulations, and migration. Table 7 show the results of the counterfactuals. First, the counterfactuals shows that land-use regulations seems to have the greatest impacts on slums formation vis-à-vis the other determinants of slums formation. Moreover, while income level was important to explain the variation of slums formation, inequality had a sizeable effect on slums growth. Rural-urban migration has also a important role in explaining slums formation, but its impact is not as important as the ones for income inequality and man-made regulations. Note that, when I shut down all four factor (see the last counterfactual in table 7), more than half of the variation in slums growth disappears. In other words, more than half of the variation of slums growth during is accounted for by the four relevant variables. Table 7: Counterfactual Experiments Counterfactuals Fraction of population in slums in 2000 Data Model Counter. 1. No real income change 5.96% 6.02% 6.79% 2. No change in income inequality 5.96% 6.02% 4.55% 3. No change of MLS regulations 5.96% 6.02% 3.72% 4. No Rural-Urban Migration 5.96% 6.02% 4.65% 5. No change in income and inequality 5.96% 6.02% 5.41% 6. No change in income, inequality and MLS regulations 5.96% 6.02% 3.26% 7. No change in income, inequality, 5.96% 6.02% 2.31% MLS regulations and migration 5.2 Policy Simulations I also perform different policy simulations. The simulations seeks to quantify the ex-ante impact of policies that makes formal housing market more accessible to the urban poor. It 34

35 is important to consider 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 policies. I analyze several policies 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. Recall the basic trade-off of the model: formal housing means payment of property taxes (η) and compliance with building regulations (h), while informal housing means lower provision of public services (θ) and incurring in defensive costs (ψ). I simulate changes in each of these four aspects (η, h, θ, and ψ) separately. I first simulate the impact of (i) a reduction in real estate taxation and of (ii) less-strict man-made regulations. Then I evaluate the impact of greater enforcement of formal housing (i.e., more government inspections and evictions). My last simulation is the effects of providing better basic infrastructure to informal settlements. Notice that all policies have general equilibrium impacts. Given the structure of the model, it is possible to measure general equilibrium response to policy changes such as slum upgrading interventions. I focus both on individual-level and aggregate-level outcomes. I separate the analysis into three parts: treatment effects, policy-relevant treatment effects and macro effects. Treatment Effects. I follow the treatment effect literature that have largely focused on average effects of the treatment (Imbens and Wooldridge (2009)), but the model is also able to show individual-specific treatment effects. I consider housing tenure formalization as the treatment. In the program evaluation literature, the individual-level treatment effect (ITE) is impossible to obtain because of the unobserved counterfactual outcome (Holland (1986), Heckman (2001)). The structural approach overcomes this issue. In the structural approach, it is possible to observe the counterfactual outcome and then to calculate the ITE. In the model, there is no compliance bias because of there is no deviations from the protocol: perfect compliance to the program means that everyone in treatment group receives treatment and nobody in the control group receives treatment. The ITE is given by (λ) = V F (λ) V I (λ). (17) The plot of the ITE shows how heterogeneous is the treatment effect: the benefits from being in the formal housing sector increases exponentially with ability. See graph??. There are several alternatives to calculate treatment effect estimands. To obtain each of them, I integrate and weight the ITE over the relevant group. The treatment-on-the- 35

36 treated (TOT) is given by T OT = 1{Ω = 1} (λ)f(λ)dλ 1{Ω = 1}f(λ)dλ = λmax λ λmax λ (λ)f(λ)dλ, f(λ)dλ where 1{} is an indicator function. Recall that Ω (equation 7) is the choice between being formal or informal and it can be thought as a dummy variable regarding housing tenure type. The second equality follows from the fact that I can partition the treated group according to their ability levels (see preposition 3). The treatment-on-the-untreated (TUT) is T UT = 1{Ω = 0} (λ)f(λ)dλ 1{Ω = 0}f(λ)dλ = λ λ min (λ)f(λ)dλ λ λ min f(λ)dλ. I classify the untreated group according to household s ability using again the results of proposition 3. The average treatment effect (ATE) is AT E = (λ)f(λ)dλ f(λ)dλ. Notice that, in the presence of heterogeneity in the treatment effect, the estimands (ATE, TOT and TUT) will be different from each other. Policy-Relevant Treatment Effects. Individual-level impacts are also analyzed by applying the concept of policy relevant treatment effect - PRTE (Heckman and Vytlacil (2001), Heckman and Vytlacil (2005)). Each agent faces two potential outcomes (Y 0, Y 1 ), where 0 refers to the no treatment state and 1 to the treated state. Given the structure of the model, the potential outcomes can be the indirect utility (V ( )) or housing space consumption (h( )). For instance, potential outcome in the no treatment state can be the housing space consumption under informal housing (h I ), while the treated state is housing space under formal housing (h F ). Let b represent a baseline policy and a represent the alternative policy being evaluated. Let Y a and Y b be the outcomes under policy a and b respectively. Each agent will have the potential outcomes for each policy scenario: (Y 0 a, Y 1 a ) and (Y 0 b, Y 1 b ). The potential outcomes under each policy regimes (policies a and b) are not invariant for each person (as assumed by unconfoundedness in the program evaluation literature) because of general equilibrium effects, i.e., Ya I Yb I and Ya F Yb F. Recall that Ω is the choice between being formal or informal. Extending the notation, let Ω a and Ω b be the choice under each policy regime. For example, if Ω b = 0 and Ω a = 1, it means that the household moved from informal to formal housing because of the policy. It is possible to write the observed outcomes under each policy (alternative a and baseline b) as a function 36

37 of their potential outcomes and the choice functions: Y a = Y F Ω a + Y I (1 Ω a ) and The PRTE is given by Y b = Y F Ω b + Y I (1 Ω b ). P RT E = E(Y a Y b ), (18) where E( ) is the population expectation. The PRTE is useful because it allows for policies to affect people s incentives to participate into the program, but do not force people to participate (Heckman and Vytlacil (2001)). A policy shifts the distribution of participants in the program being evaluated. Let s use one specific policy - land titling - to illustrate how the PRTE works in the present application. Land titling affects directly the parameter ψ. Let b be the scenario before the titling program and a the alternative scenario after the titling program. Each agent will choose between formal and informal housing that will constitute her Y b and Y a. The PRTE is the weighted average of Y a Y b for the agents in the city. Recall that I can use housing consumption or indirect utility as measures of potential outcome under the policy scenarios. The PRTE shows a weighted impact of the policy on mean utility of individuals or on housing space consumption. When I use indirect utility V ( ), it is a Bethamite-type of comparison of outcomes under different policies (Heckman and Vytlacil (2001)). I can calculate the PRTE for each relevant subpopulation. Recall that Ω b and Ω a are the dummies for housing tenure before and after the policy respectively. The subpopulation PRTE are given by E(Y a Y b ) Ω b = 0 & Ω a = 0 Informal in both scenarios E(Y a Y b ) Ω b = 1 & Ω a = 1 E(Y a Y b ) Ω b = 0 & Ω a = 1 P RT E subpopulation E(Y a Y b ) Ω b = 1 & Ω a = 0 E(Y a Y b ) Ω a = 1 E(Y a Y b ) Ω a = 0 Formal in both scenarios Switching tenure Switching tenure Formal in counterfactual Informal in counterfactual. I also ignore general equilibrium effects and calculate a partial equilibrium PRTE. The idea is to compare the results of the analysis with the ones from a standard exercise in the program evaluation literature. The partial equilibrium PRTE would verify the average impact when general equilibrium effects are not considered. In this case, policy would change individual decision but would not affect housing prices. It is interesting to 37

38 compare the results of the general equilibrium PRTE and of the partial equilibrium PRTE. One useful application of PRTE micro-effects is associated with an increase in income. One might suggest that such an increase will induce housing formalization, but what about the individual response to policies after considering general equilibrium aspects (such as changes in housing prices)? The size of the treatment influence the impact of the policy: an individual responde varies when only his or her income changes and when the average income of the economy changes. The results of the quantitative exercises suggest that slums are not a entrepôt to the urban poor. Frankenhoff (1967) pointed out that the slums of Latin American cities act as staging areas for rural immigrant search of a better life. The results suggested that the size of the treatment influence households decision on the tenure mode. Macro Effects. The macro outcome is the change in fraction of population in slums and is given by the following relation: SS = 1 N N 1{V F (λ, ξ(z )) V I (λ, ξ(z ))}, i=1 where SS stands for slums share, 1{} is an indicator function, ξ( ) represents the vector of all 11 parameters of the model and z the parameter subject to the policy variation. Calculating the macro effects (via slums share), I am able to identify the fraction of households induced to change from one state (formal housing) to the other (informal housing). Table 8: Policy Simulations: Macro Effects Policy Simulations Fraction of population in slums in 2000 Data Model Counter. 1. Property tax reduction by half 5.96% 6.02% 5.41% 2. MLS reduction by half 5.96% 6.02% 3.71% 3. Upgrading: Reduction of informal housing disutility 5.96% 6.02% 6.05% 4. Titling: Reduction of protection costs 5.96% 6.02% 6.13% The aggregate-level effects of the policy scenarios are shown in table 8. I first simulate a reduction of the property taxation. The comparative statics point out that this will decrease the amount of slums dweller. The quantitative exercise will show by how much. According to table 8, a reduction of property tax η by half would decrease the informal housing by 0.6 percentage points. Even though the costs of formal housing is a relevant 38

39 factor, this result suggest that the other barrier to formalization (land use regulations) play a greater role in slums formation. The second simulation is associated with the reduction of the minimum lot size of the location. 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. I therefore simulate the impact of an overall reduction of the minimum lot size, i.e., supposing that most municipalities enact less-severe urban parameters. Note that the effect of a reduction of the MLS by half is the same as having no MLS regulation at all, because either way I have that λ MLS < λ. The relaxation of the minimum lot size has great impact on slums. I also simulate the impact of two common policies towards slums: upgrading and titling. By upgrading, I mean better infrastructure and public services. Land titling means a reduction in the likelihood of expropriation by giving property rights to slum dwellers. Usually, upgrading policies aim to both provide infrastructure and titling, but I separate the policies to understand the different potential incentives. Let s consider the impact of providing infrastructure. In the model, it means a decrease in the informal housing disutility θ. A reduction in θ is associated with an increase in the number of slum dwellers. It means that slum upgrading interventions can have an unintended adverse impact. 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 show how land titling programs impact the welfare of the urban poor. The literature shows that giving property rights to the urban poor increases housing investments and housing prices. The results point out that more people will live in informal settlements, because giving property rights means reducing the cost of informal housing. It is parallel result to the one found for upgrading policies: now there is security, but no improvement of urban infrastructure (and the household still do not comply with regulation and do not pay taxes). In the simulations, better infrastructure or property rights increase slums share because they give incentive toward living in informal units. If each policy is accompanied to an implementation of property taxation, this will further increase the size of the informal sector. The main lesson from the analysis is that one must differentiate two groups of policies. By changing separately improving the infrastructure (θ) or giving property rights (ψ), the government is in practice changing the type of the informal housing. Improving the infrastructure by decreasing θ means the the informal housing is becoming better and 39

40 this explain why more people wants to live in informal settlements. The same reasoning applies to a decrease in defensive expenditures ψ. Only by reducing the cost of formal housing (decreasing the lot size (h) and the rate of property tax η), the government induce households to migrate from informal to formal housing units. 6 Conclusion Informal housing plays an important role in developing countries. In Brazil, the housing sector is also characterized by the presence of a large informal housing sector. This article aims to measure the main determinants of the informal housing expansion in the last decades and to evaluate the impact of slum upgrading interventions. I construct a simple model to explain the determinants of informal housing formation. The model is calibrated and estimated to be consistent with several statistics related to the Brazilian urbanization process. 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, I 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. The analysis has several policy implications. The model points out that regulation may induce more slums when enforced. Another important result of the analysis is that informal settlements may not be seen as an entrepôt to the urban poor. The housing ladder from informal to formal housing seems not to be the case. Housing formalization policies may decrease the opportunity cost of informal housing (protection costs) and so increase welfare. But the analysis shows also that public policies such as slum upgrading can have an unintended adverse impact: slum upgrading may modify location incentives and attract more people to live in slums. 40

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45 A Appendix: Data A.1 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 Domicílios) 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 Municípios Brasileiros, a survey conducted yearly by IBGE. I 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 The presence of special Pacifying Police Units (in Portuguese, Unidade de Polícia Pacificadora) started on March 3rd After being controlled for years by drug traffickers, the slums in Rio de Janeiro are undergoing a change to make slums safer Map?? 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 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

46 Fig. 4: 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 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. Cortic os 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). 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 Sa o Paulo shows the evolution of slums as well as the issues regarding the measurement of slums in Brazil. Table 9 shows the number of people in slums in Sa o 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 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 46