Expansion of piped water and sewer networks: The effects of regulation

dos Santos, Carolina Tojal Ramos; Guidetti, Bruna Morais Working Paper Expansion of piped water and sewer networks: The effects of regulation IDB Working Paper Series, No. IDB-WP-1734 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: dos Santos, Carolina Tojal Ramos; Guidetti, Bruna Morais (2025) : Expansion of piped water and sewer networks: The effects of regulation, IDB Working Paper Series, No. IDBWP-1734, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0013622 This Version is available at: https://hdl.handle.net/10419/324841 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/igo/ Expansion of Piped Water and Sewer Networks: The Effects of Regulation Carolina Tojal R. dos Santos Bruna Morais Guidetti WORKING PAPER No IDB-WP-1734 InterA merican Development Bank Department of Research and Chief Economist July 2025 * InterA merican Development Bank ** University of Michigan Expansion of Piped Water and Sewer Networks: The Effects of Regulation Carolina Tojal R. dos Santos* Bruna Morais Guidetti** InterA merican Development Bank Department of Research and Chief Economist July 2025 Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Tojal, Carolina. Expansion of piped water and sewer networks: the effects of regulation / Carolina Tojal R. dos Santos, Bruna Morais Guidetti. p. cm. — (IDB Working Paper Series ; 1734) Includes bibliographical references. 1. Water-supply-Law and legislation -Brazil. 2. Water utilities-Law and legislation-Brazil. 3. Sewer-pipe-Brazil. 4. Drinking water-Brazil. I. Morais Guidetti, Bruna. II. Inter-American Development Bank. Department of Research and Chief Economist. III. Title. IV. Series. IDB-WP-1734 http://www.iadb.org Copyright © 2025 Inter-American Development Bank ("IDB"). This work is subject to a Creative Commons license CC BY 3.0 IGO (https://creativecommons.org/licenses/by/3.0/igo/legalcode). The terms and conditions indicated in the URL link must be met and the respective recognition must be granted to the IDB. Further to section 8 of the above license, any mediation relating to disputes arising under such license shall be conducted in accordance with the WIPO Mediation Rules. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the United Nations Commission on International Trade Law (UNCITRAL) rules. The use of the IDB's name for any purpose other than for attribution, and the use of IDB's logo shall be subject to a separate written license agreement between the IDB and the user and is not authorized as part of this license. Note that the URL link includes terms and conditions that are an integral part of this license. The opinions expressed in this work are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. Abstract* This paper investigates strategies to expand piped water and sewer through private providers. Using billing data from a major provider in Brazil and a structural model of consumer sanitation demand and service expansion, we assess the viability of connection targets and the welfare effects of connection subsidies and price incentives. We find that universal connection targets are largely unfeasible due to low sewer take-up. Combining connection subsidies with higher sewer prices boosts expansion and adoption but requires government funding. Charging consumers upon sewer availability is self-sustaining and promotes adoption and expansion, but it shifts costs to households. JEL classifications: L95, Q25, L51 Keywords: Piped water, Sanitation, Regulation, Structural model ∗We are grateful to Ying Fan, Catherine Hausman, Zach Brown, and Francine Lafontaine for their guidance throughout this project. We also thank participants at seminars and conferences hosted by the University of Michigan, Berkeley Energy Camp, MSU & UM Energy and Environmental Economics Day, the Seminar on Water Economics (SWELL), the Annual Conference on Taxation (NTA), the University of South Carolina, the Inter-American Development Bank, Miami University (Ohio), PUC Chile, ITAM, University of Chicago Harris, Michigan State University, Insper, Oberlin College, LACEA-LAMES, the Encontro da Sociedade Brasileira de Econometria (SBE), and the WASH Conference for their feedback and suggestions. We are also thankful to Rene Alejandro Nieto for excellent research assistance. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank. 1 Introduction Access to clean water and sanitation remains a critical global challenge, with 2.2 billion people lacking safely managed drinking water and 3.4 billion without adequate sanitation as of 2022 (UNICEF and WHO, 2023). Expanding piped water and sewer systems is particularly difficult in developing countries, where governments often face financial constraints that limit infrastructure investment. A widely adopted strategy to address this issue is attracting private investment in infrastructure development and service provision, as seen in Brazil, Argentina, Chile, the Philippines, Indonesia, and South Africa (Marin, 2009). However, this approach presents a trade-off between financial viability and social inclusion, as under-served populations have a low willingness to pay for services and it is costly to reach them (Fay et al., 2021). While extensive research highlights the benefits of improved access to water services (Gamper-Rabindran et al., 2010; Devoto et al., 2012; Alsan and Goldin, 2019; Kresch et al., 2023), there is limited evidence on policy and regulation to promote infrastructure expansion while ensuring that households connect to available services. This paper addresses this gap by examining the case of Brazil, where a large share of the population is still not connected to piped water and sewer services, particularly in the Northern region.1To tackle this issue, the government introduced the New Sanitation Regulatory Framework in 20202, which encourages municipalities to contract with private providers and sets connection targets of 99% of households with piped water and 90% with piped sewer collection within each concession by 2033. These connection targets follow the United Nations Sustainable Development Goals (UN, 2022), but it is unclear if they are viable for private providers. Moreover, the regulation overlooks a crucial factor: while providers install the pipes up to the sidewalk, it is ultimately up to consumers to complete the connection to their homes. Thus, the feasibility of these connection targets hinges on both firms having incentives to expand the pipes and consumers taking up the service when it is available. 1In the Northern region, only 54% of the population had access to piped water, and just 14% were connected to piped sewer services in 2017, according to the National Sanitation Survey (Pesquisa Nacional de Saneamento B´asico - PNSB) from IBGE. Appendix Figure A1 provides connection rates for other regions of the country. 2Novo Marco Regulat´orio do Saneamento - Federal Law 14.026, Brazil, July 15, 2020. 2 In this paper, we investigate the feasibility of achieving universal access to services through private providers under current regulated prices. Specifically, we assess whether connection targets would be met if the firm expanded infrastructure across all concession areas. Our findings suggest that a substantial share of households would choose to remain unconnected to piped sewer services even if the infrastructure were available. We then explore policies to encourage take-up and expansion, evaluating the effectiveness of sewer connection subsidies, price adjustments, and charging consumers based on sewer availability regardless of connection status. Finally, we analyze the implications of these policies for welfare distribution between consumers and the provider. We answer these questions using novel billing data from a private provider in Brazil. Our dataset includes monthly billing records at the address level from consumers in various municipalities across the country under the firm’s concessions, covering three years before the new regulation. These data, combined with demographic information from the Census, provide detailed consumption information and show which postal codes3the firm expanded to and which services they installed (water or water and sewer) within its concessions. We first use the data to document key patterns in the firm’s expansion decisions, consumer connections, and water consumption choices. We show that postal codes that receive expansion of both services have, on average, higher incomes than postal codes that receive only water. Moreover, the firm is more likely to expand in postal codes close to the installed network. We also document that part of households do not connect when the services are available. Within postal codes where both water and sewer services are available, on average, approximately 71% of households take up both services, while roughly 20% opt for water-only connections. Furthermore, higher-income areas exhibit, on average, higher rates of service adoption. In our setting, connected consumers face non-linear pricing structures4for their water and sewer and respond to the average price. Two pieces of evidence suggest that consumers respond to the average price of their bill rather than the marginal price. First, we find no evidence of consumption bunching at price schedule kinks where marginal prices increase. 3In Brazil, postal codes are referred to as CEPs (C´odigos de Endere¸camento Postal), which function similarly to zip codes in the United States. 4Increasing block rates with a fixed fee. 3 Second, we observe consumption changes in response to price adjustments that affect the average price without altering the marginal rate. Accurately identifying which price consumers respond to is crucial for modeling demand and assessing the impact of price changes on provider revenues. We use a structural model to predict both demand in areas without services, based on prices and demographics, and to recover expansion costs, which allows us to simulate the effects of various policies. The demand side consists of two components: i) a discrete-choice model where households select which service to connect to among the available options in their postal code, and ii) a continuous-choice model where connected households decide on their water consumption. On the supply side, the firm faces a discrete-choice problem when deciding which services to install in each postal code based on profitability. We use cross-sectional variation in demographics and exogenous price changes to identify consumer preferences and their responsiveness to average prices. Using the estimated demand, we predict the potential revenue from expansion and estimate cost parameters from observed expansions. Using the estimated model, we first assess the feasibility of meeting the connection targets by simulating the firm expanding water and sewer services across all postal codes in its concessions. We find that household connections would not meet the targets due to limited consumer take-up, with only about 51% of households connecting to piped sewer once it is universally available. We then allow the firm to optimally select expansion areas and examine three policies aimed at increasing the share of connected households: i) offering a connection subsidy to cover the cost of installing the final segment between homes and the main sewer line, ii) combining this subsidy with an increase in monthly sewer bills, and iii) imposing a charge for sewer availability, irrespective of whether households connect.5 The connection subsidy increases sewer take-up in areas with existing infrastructure but does not incentivize firm expansion. In some regions, the price charged to consumers is insufficient to cover provision costs, making additional connections financially detrimental to the firm and deterring further expansion. To address this, we pair the subsidy with a 50% 5Under this policy, in every postal code with sewer pipes, consumers who receive a water bill will also be charged for sewer service, regardless of whether they are connected. 4 increase in the average sewer price paid by households on their monthly bills. This combination encourages firm expansion, resulting in approximately 82% of households connecting to the sewer network, primarily driven by adoptions in postal codes receiving the service. While this scenario benefits both consumers and providers, it requires government funding for subsidies, which could be politically and fiscally challenging. An alternative that does not require direct government intervention is the Sewer Availability Charge, a policy already permitted under existing regulations but rarely implemented by providers. Under this policy, consumers in postal codes with piped sewer infrastructure must pay for the service even if they do not connect. It effectively works as an externality tax that internalizes part of the social cost of remaining unconnected. This approach encourages firm expansion and consumer adoption, increasing sewer connections to approximately 55% of the households. However, unlike the subsidy-based approach, this policy shifts the financial burden entirely onto consumers, raising affordability concerns despite its effectiveness in boosting overall connection rates. The contributions of this paper are threefold. First, we endogenize firm expansion decisions and link them to consumer choices in the water and sanitation market, providing a framework to evaluate incentives to increase service coverage. This approach adds to existing work that focuses on the benefits of improved sanitation access (Coury et al., 2024; Kresch et al., 2023; Devoto et al., 2012; Alsan and Goldin, 2019; Gamper-Rabindran et al., 2010; Barreto et al., 2007) by addressing how expansions can be achieved. Considering both demand and supply allows us to identify trade-offs created by different policies. This perspective is essential for avoiding unintended consequences, such as those observed with energy subsidies in India and Colombia, where underpricing resulted in underinvestment in infrastructure (Mahadevan, 2024; Burgess et al., 2020; McRae, 2015). Second, we contribute to the growing literature on the adoption of sanitation technologies, which has largely focused on toilets and septic tanks (Deutschmann et al., 2024, 2023; Gautam, 2023). We extend this work by adapting empirical strategies from the energy demand literature (Resende et al., 2025; Barreca and Clay, 2016; Davis and Kilian, 2011; Dubin and McFadden, 1984) and leveraging detailed billing data to model household take-up and consumption of piped water and sewer services. Our findings reveal that low sewer take-up 5 for both water and sewer in subsequent years indicate that sewer services were expanded. For the cost estimation and the simulations, we focus on concessions in the North and Northeast, where there is still significant room for expansion within the firm’s boundaries. In contrast, concessions in the South and Southeast already have near-universal water and sewer coverage in our data. 4 Descriptive Evidence This section provides descriptive evidence of the service expansion, connections, and consumption from our data. First, the firm expands closer to the existing network and to wealthier postal codes, consistent with a profit-maximizing strategy. Second, once the pipes are installed, a significant share of consumers do not connect; demographics, such as income, are good predictors of take-up. Third, for connected households, we also find evidence that the water demand responds to average prices rather than marginal prices, which is key to computing consumers’ demand price elasticity. These patterns guide the model presented in Section 5. 4.1 Firm Expansion The firm builds pipes of only water, or water and sewer, in postal codes under its concessions. Table 2 shows that postal codes with both water and sewer pipes tend to have higher average incomes compared to postal codes with only water pipes or no service at all. This pattern holds for postal codes that originally had pipes installed (“old”) and for postal codes where the firm expanded the pipes (“new”). 12 Table 2 – Postal Code Characteristics by Pipe Network Availability Pipe network Number of Postal codes Avg. income Distance from Only water network (km) Distance from Water and sewer network (km) Old water and sewer 2188 4163 Old only water 2542 2543 8.41 Old only water/new sewer 67 3148 3.30 New water and sewer 36 4360 0.08 0.15 New only water 219 3252 0.12 20.63 Nothing 539 2827 3.75 22.00 Notes: This table summarizes demographic and infrastructure characteristics (columns) by type of service availability (rows). It includes only postal codes within the firm’s concession areas in the North and Northeast regions of the country. Postal codes with at least one bill for the service in 2017 are classified as “old.” Postal codes that first appeared in the water billing records in 2018 or 2019 are categorized as “new.” The remaining postal codes, with no billing records during the period, are considered to have no service. The firm expands closer to the installed network. The last two columns of Table 2 show that the postal codes where the firm expanded are on average closer to the network of the specific service installed. This pattern is unsurprising given the interconnected nature of water and sewer pipelines within a broader network. It is economically advantageous to install pipes near existing infrastructure; the costs related to infrastructure tend to increase as the distance from the installed network grows. Additional evidence that the firm expands service near its existing network is shown in Appendix Figure A3. 4.2 Incomplete Service Take-up We show that many households do not take up the services in postal codes with the pipes available. As depicted in Figure 2, on average approximately 24% of households choose not to connect to the water service when it is the only service available in their postal code. In areas where both water and sewer services are available, approximately 71% of households connect to both services, while 20% prefer to connect to water only. Connecting to the sewer system involves connecting the house to the main pipeline, a substantial increase in the bill, and users may not directly perceive benefits. These factors may help explain the incomplete take-up of water and sewer services. Demographic factors influence the connection to the main water and sewer pipelines. The regression analysis presented in Appendix Table A1 examines the relationship between demographic variables and the share of connected households in each postal code where services are available. Income is positively correlated with complete take-up and negatively 13 Figure 2. Average Service Take-up 0 .2 .4 .6 .8 1 Share of households connected Zips with only water pipes Zips with water and sewer pipes Take-up only water Take-up water and sewer Notes: This figure illustrates the average service take-up across postal codes. The blue bars represent the average share of households connected to only water, while the orange bars indicate the average share of households connected to both water and sewer. The left bar corresponds to postal codes with only water pipelines, whereas the right bar represents postal codes with both water and sewer infrastructure. correlated with incomplete take-up.17 Additionally, larger households are more likely to adopt the services fully, while those with alternative sewer collection methods are, on average, less likely to connect. 4.3 Consumption Responds to Average Price We investigate whether consumers facing non-linear price schedules respond to marginal or average prices, as this distinction is crucial for accurately estimating their price elasticity. We find suggestive evidence that consumers react to average price, consistent with other work in the water and energy markets (Ito and Zhang, 2020; Sears, 2023; Ito, 2014; Wichman, 2014; Ito, 2013; Borenstein, 2009). However, this result goes against other related papers on water markets that model consumers reacting to marginal prices as Szabo (2015), Olmstead (2009), and Hewitt and Hanemann (1995). The difference might be associated with how the prices are presented to consumers and other particularities of the context where the utility bills are charged. 17Complete take-up is defined as connecting to all the services available at the postal code, while connecting to only water when both water and sewer are available is considered incomplete. 14 1. No Bunching at the Kinks All the concessions included in our sample have non-linear price schedules characterized by increasing block rates. These price schedules result in budget sets that exhibit convex kinks at the points where the marginal price rises. If consumers were responsive to changes in marginal prices, we would expect to observe a bunching of consumption at these kinks, as shown by Hausman (1985) and Moffitt (1990). In our context, the marginal price for the initial consumption bracket is set at zero across all concessions. Consequently, if consumers were responsive to marginal prices, there would be an incentive for them to maximize their consumption without surpassing the threshold of the next bracket, where the marginal prices become strictly positive. To investigate whether such bunching behavior exists, we plot histograms depicting the residential water consumption patterns for the concessions in our sample. In Figure ??, we present the histograms for two municipalities: Municipality X (Figure 3a) and Municipality Y (Figure 3b), with the price discontinuities represented by the vertical lines. Here, we show the graphs separated by concession because they face different price schedules, although all have the same feature of increasing block rates with zero marginal price in the first block. The histograms reveal a smooth distribution of consumption around the kink points, indicating an absence of bunching. The absence of bunching can be interpreted in two ways: either consumers exhibit zero elasticity to prices or they respond to an alternative measure of price. To distinguish between these possibilities, we focus on households that consistently consume within the first consumption bracket, where the marginal price is zero, but the average price is strictly positive due to the fixed fee. Analyzing this specific group of households allows us to distinguish if demand responds to average price, given that our setting lacks price variation that would move average prices and marginal prices in different directions, as explored by Ito (2014). In our setting, when price changes occur, all the marginal prices above the first bracket and the fixed fee change at the same rate, while the marginal price of the first bracket remains constant at zero. Consequently, for consumers who consistently consume below the first threshold, an increase in the fixed fee leads to a variation in the average price but not 15 Figure 3. No bunching in residential water consumption (a) Municipality X 0 50000 100000 150000 Number of bills 0 10 20 30 40 50 60 70 80 90 100 Measured water consumption (m3) (b) Municipality Y 0 5000 10000 15000 20000 Number of bills 0 10 20 30 40 50 60 70 80 90 100 Measured water consumption (m3) Notes: This figure shows the histogram of measured water consumption for water bills from consumers in municipality X (Figure (a)) and municipality Y (Figure (b)). The vertical lines on the graphs represent the end of the brackets, where the marginal prices increase. The marginal price is zero in the first bracket, i.e., for volumes to the left of the dashed vertical line, and increases in the remaining brackets. The graphs include bills for consumers connected since the beginning of our sample and in single-unit residences with individual billing. in the marginal rate. To isolate the effect of changes in the fixed fee from weather shocks and other changes that may be happening at the concession level, we leverage the case of one concession that spans across two different states where consumers face different prices depending on which state they are located in. Given the proximity, they are exposed to similar weather events but are charged different prices. Moreover, we include other concessions in the same state to isolate the effect of price changes from other economic changes happening at the state level. Appendix Figure A4 illustrates this scenario. Using this subset of water bills, we employed a specification similar to the one used by Ito (2014) to test whether consumers react to the fixed fee: ∆ln(qiusjt) = α∆ln(feeusjt)+∆ln(Ict) + δst +γut +uiusjt (1) where qiusjt represents the metered water consumption of household (address) iin concession u, state s, and connected to service jduring billing month t.feeusjt denotes the minimum 16 payment required from any address connected to service jin that concession state. Ict represents the income at the census tract where household i is located. δst denotes statebilling month fixed effects, while γut represents concession-billing month fixed effects. We utilized the difference ∆ln(qiusjt) = ln(qiusjt)−ln(qiusj0) between the consumption charged at time tand the same billing month in the previous year t0, which eliminates household-month of the year fixed effects that account for household characteristics and seasonal components of water demand. ∆ln(feeusjt) = ln(feeusjt)−ln(feeusj0) and ∆ln(Ict) = ln(Ict)−ln(Ic0) represent the equivalent difference for the fixed fee and the income, respectively. If households responded to the marginal price, they would not reduce their consumption in response to increases in the fixed fee, as reducing consumption would not affect the total amount charged in their water bills. In particular, since our sample only includes price increases and no price decreases over the given time frame, we would expect the coefficient αto be zero. However, the results presented in Table 3 indicate that consumers reduce their consumption in response to increases in the fixed fee. The preferred specification described by equation 1 is reported in column (3), but we also report the results for specifications including only time-fixed effects in column (1) and concession-time fixed effects in column (2). This finding suggests that consumers do not differentiate between fixed and variable costs, which is consistent with evidence found in heating demand in China (Ito and Zhang, 2020). Although consumers do not directly respond to marginal prices, this behavior demonstrates that they react to prices. Considering consumers’ misconceptions regarding the non-linear price schedule, we treat them as responding to average prices in the demand model. 5 Model To explore the feasibility of service mandates and alternative policies, we use a structural model that incorporates the key patterns found in the data. The model encompasses the supply and demand for piped water and sewer collection within the geographic limits under the responsibility of a private firm. Having won the concession, the firm is the sole provider 17 Table 3 – Consumption Response to Changes in the Fixed fee ∆ln(quantity) (1) (2) (3) ∆ln(fee)−0.193** −0.211* −0.250* (0.083) (0.114) (0.145) ∆ln(income) 0.024* 0.027* 0.027* (0.014) (0.014) (0.014) Time FE yes no no Concession-time FE no yes yes State-time FE no no yes Observations 384,704 384,704 384,704 Notes: This table presents regression estimates for the coefficients in equation 1. The dependent variable is the change in the logarithm of water consumption in a given month relative to the same month in the previous year. The key independent variables are the corresponding change in the minimum water bill payment and the census tract’s income. The columns differ in fixed effects specifications: Column (1) includes month-by-year fixed effects, Column (2) adds concession-by-month-by-year fixed effects, and Column (3) further includes state-by-month-by-year fixed effects. The sample is restricted to addresses with continuous water billing throughout the period, no service type changes (water only vs. water and sewer), and consumption consistently within the first bracket. Only single-unit households billed individually are included. Standard errors are clustered at the address level. *** p<0.01, ** p<0.05, * p<0.1. of these services in the region and operates as a monopolist. The supply side of the model uses a discrete choice approach to represent the firm’s decision-making process regarding entry and service offerings at specific postal codes to recover the fixed cost of expansion and variable costs associated with service provision. On the demand side, the model consists of discrete-continuous consumer choice for service take-up and the amount of water consumed after connecting to the network to estimate their preferences regarding the services. The market outcomes depend on the interplay between the monopolist’s expansion decisions and the households’ demand decisions. In particular, the availability of services, the share of connected households, and the quantity of water consumed depend on the underlying preferences of households and the fixed costs faced by the monopolist. Overall, this model provides a framework for examining the economic incentives and outcomes of different policies related to the provision of water and sewer services in private monopoly settings with regulated prices. 18 5.1 Demand Households (addresses) in each postal code have preferences for piped water and sewer services, which affect their decision to connect to the network and their water demand. We represent the decision using a discrete and continuous model, where each household decides whether to connect to only water or water and sewer when the service network is available in their postal code and, conditional on being connected, households choose their water usage. 1. Take-up Households in a given postal code choose to connect to only water, j=w, both water and sewer services, j=s, or remain unconnected, j=o. More specifically, if the postal code has water and sewer pipes available, households can choose to connect to both services or only water, while if the postal code has only water pipes, the households can only choose to connect to water or remain unconnected. The indirect utility of household (address) i, located at postal code z(in concession unit uand census tract c), for service j∈(w, s, o) in year yis: Uijzy =Vjzy +εijzy (2) Vjzy =     α0jus +α1jcjcy +α2javgpjuy +α3jIcy +α0 4jDcy +ξjzy if j=w, s 0 if j=o (3) where cjcy represents the installation costs for connecting a household to the street pipe network for service j.avgpjuy denotes the average price faced by a representative consumer in concession ufor service j.Icy indicates average income, while Dcy is a vector of demographic characteristics influencing the decision to connect to the network. These characteristics include household size, urban location, the share of households on paved streets, the proportion of rental units in the census tract, the share of households with access to alternative water sources (such as truck delivery, cisterns, or pits), and the share with access to alternative sewage disposal methods (such as septic tanks, chemical toilets, or composting pits). Finally, 19 ξjzy captures an unobserved demand shock at the service-year-postal code level. The parameter α0jus is a product-concession-state fixed effect that incorporates preferences for specific services common for all consumers in a concession-state. The parameter α1jcaptures consumers’ sensitivity to the installation costs of each service. The parameter α2jcaptures the willingness to trade off the price per unit of water, with or without sewer, against other service features. Parameters α3jand α4jincorporate interactions between demographic and census tract characteristics, respectively, and service alternatives, while εijzy is an idiosyncratic preference shock. We assume that the idiosyncratic utility shocks have a nested structure with one nest (g) that includes the inside options, Jg={w, s}, which in our setting are the services of only water or water and sewer, respectively. The only option outside of the group is not connecting to any service. Specifically, εijzy =ζigzy +(1−σ)µijzy, where µijzy is i.i.d. extreme value and ζigzy is the same for all products in group g and has a distribution that depends on the nesting parameter σ∈[0,1) such that εizjy is distributed extreme value following Cardell (1997). As σapproaches 1, the utility within-group correlation goes to one, and only groups matter, meaning households care primarily about whether they are connected to any service rather than the specific type of service. As σapproaches 0, the within-group correlation goes to zero, reducing the model to a standard logit where choices are independent. This structure allows for more flexible substitution patterns. In particular, we expect that if one service option is unavailable, households are more likely to choose the remaining service rather than opt out of connection altogether. Under these assumptions, the probability of selecting service j, conditional on choosing to connect to any service (g), is given by Sjzy|g=exp(Vjzy/(1 −σ)) Pj∈Jgexp(Vjzy/(1 −σ)) (4) The probability of choosing to connect to any service is Sgzy =(Pj∈Jgexp(Vjzy/(1 −σ)))(1−σ) 1+(Pj∈Jgexp(Vjzy/(1 −σ)))(1−σ)(5) Finally, the choice probability of product j, which represents the take-up, when service 20 jis available at postal code zis given by the following multiplication. Sjzy =Sjzy|gSgzy (6) 2. Water Consumption The demand for water is represented by: ln(qijzt) = β0+β1ln(avgpijut) + β2ln(Icy) + β0 3Dcy +δj+δmτ +ηijzt (7) such that qijzt is the amount of water consumed by a household (address) iat postal code z(located in concession unit uand census tract c), connected to service jat a billing month t.avgpijut denotes the average price faced by household i.Icy is the average income at the census tract level, and Dcy is a vector that includes the number of people per household and an indicator of whether the census tract is in an urban area. δjis a service fixed effect and δmτ is a municipality-month-of-the-year fixed effect. ηijzt represents an idiosyncratic demand shock for water. We model households as responding to the average price, avgpijut, which is computed based on the increasing block schedule of each concession. Households that consume only within the first bracket pay a fixed fee. Households with consumption in higher brackets (b) pay the fixed fee plus the cost of the quantities that exceed each bracket’s limit, multiplied by the corresponding marginal prices, mpbjut. The average price faced by household is expressed below as a function of the fixed fee, feejut, the bracket limits, ¯qbu, and the marginal prices, mpbjut. avgpijut =feejut +PB b=2 max(min(qijzt −¯qub−1,¯qub −¯qub−1),0)mpbjut qijzt (8) 5.2 Supply There is a single monopolist firm that offers different services in the postal codes within its concessions. For each postal code, the firm decides which service to offer in order to 21 instrumental variable is the average price the household would pay under the price schedule of their own concession and time if they consumed the average consumption of households in the same group but located in other concessions. This instrument is convenient because it captures exogenous variation in the price schedule, but it is not affected by the quantity consumed by the household. Additionally, we assess the robustness of our average price instrument by comparing it to an alternative approach that uses observed marginal prices for each bracket as instruments, following Olmstead (2009). The advantage of using marginal price-based instruments in our setting is that consumers generally do not switch brackets, as shown in Appendix Figure A7. By holding consumption levels fixed, we can leverage variation in price schedules over time and across concession states to identify price elasticity. We follow Barreca and Clay (2016), Davis and Kilian (2011), and Dubin and McFadden (1984) to address the potential selection problem, allowing the discrete and continuous components of demand to be correlated. Specifically, the expected value of the continuous water demand shock, ηijzt, is assumed to be a linear function of the demand shock of the service choice, εjzy, to compute the selection controls based on the estimated take-up of the service, ˆ Sjzy. For households in postal codes with only water available, we include a single selection term accounting for the choice between connecting to water and the outside option of remaining unconnected. In postal codes where both water and sewer services are offered, we include two selection terms: one capturing the choice relative to the outside option and another reflecting the inside option not chosen (e.g., choosing water only vs. both water and sewer).24 The results are presented in Table 5. Column (1) reports estimates without an instrument or selection controls. Column (2) instruments for the average price using marginal prices for each bracket. Column (3) replaces this with the simulated average price instrument. Finally, Column (4) builds on Column (3) by accounting for potential selection, making it our preferred specification. Appendix Table A2 reports the first-stage results, while Appendix 24In our setting, for a household connected to any inside option j, the selection term for the outside option is given by ˆ Sozy ln(ˆ Sozy ) (1−ˆ Sozy )+ln(ˆ Sjzy ). If there is another inside option kavailable, which happens when there is both water and sewer, there is another selection term given by ˆ Skzy ln(ˆ Skzy ) (1−ˆ Skzy )+ln(ˆ Sjzy ). 28 Table A3 presents the reduced-form results. In summary, the results indicate that households reduce their water consumption in response to higher average prices, though the elasticity is small. Higher-income households consume more water, with a stable coefficient across IV specifications. Households with piped sewer connections use more water than those with only water connections. As expected, water consumption increases with household size. Additionally, households in urban areas tend to consume less water on average than those in rural areas. Note that the price elasticity remains similar regardless of the instrument used or the inclusion of the selection control. However, it differs significantly from the OLS estimates, suggesting that our instrument effectively corrects the downward bias. Our analysis focuses on selection bias arising from consumers’ decisions to connect to the pipe network. We assume the firm decides where to expand pipes based on observable demand factors and costs, with demand shocks occurring only after these decisions are made. This implicitly assumes that the firm does not have access to demand shocks that are unobserved by us as econometricians. However, if the firm did anticipate positive demand shocks, it might prioritize expansion in those areas, introducing an additional selection issue that could lead us to overestimate unconditional water demand. We believe this concern is minimal in our context. While the firm may receive additional input from technicians on the ground, we rely on the same administrative data they use. Given the scale of operations, it is unlikely this information is systematically incorporated. Therefore, any bias from unobserved demand shocks known to the firm but not to us is likely minimal. To predict the consumption of connected addresses, we use the reduced-form estimates presented in Appendix Table A3. Using the reduced form simplifies the problem by allowing us to rely on the simulated average price to determine a single price that households respond to, enabling straightforward consumption predictions. In contrast, using the 2SLS results for prediction would require jointly solving for consumption and the average price. Given the nonlinear shape of the average price function in our setting, this approach would generate two equilibrium consumption quantities –— one in the first bracket and another in the higher brackets —– forcing us to rely on an ad hoc rule to select between them. 29 Table 5 – Continuous Demand Model Estimates (1) (2) (3) (4) OLS Mg. prices IV Simulated IV Simulated IV with selection ln(Avg. price) −1.030*** −0.249*** −0.214*** −0.213*** (0.002) (0.006) (0.009) (0.009) ln(Income) 0.157*** 0.123*** 0.122*** 0.123*** (0.003) (0.003) (0.003) (0.003) Piped sewer 0.548*** 0.090*** 0.070*** 0.070*** (0.003) (0.004) (0.006) (0.006) Urban −0.112*** −0.158*** −0.160*** −0.154*** (0.020) (0.023) (0.023) (0.023) Household size 0.053*** 0.054*** 0.054*** 0.053*** (0.004) (0.005) (0.005) (0.005) Selection inside opt. −0.013*** (0.005) Selection outside opt. 0.014*** (0.005) Municipality-month FE yes yes yes yes F-statistic 13,545 32,034 32,241 Observations 8,643,951 8,643,951 8,643,951 8,643,951 Notes: This table presents the parameter estimates from the water consumption model. The dependent variable is the logarithm of water consumption, and the key independent variable is the logarithm of the average price. Column (1) reports OLS estimates. Column (2) uses the marginal price of water as an instrument. Column (3) instruments for price using a simulated average price, constructed by grouping households into 16 categories based on income quartile, service type (water only or water and sewer), and urban or rural location. For each group, the average consumption of households in different concessions is computed, then used to calculate the price each household would face under its own concession’s pricing schedule if it consumed the group’s average usage in other concessions. Column (4) builds on Column (3) by accounting for potential selection bias among households that opted to connect. The sample includes only addresses with water bills for all periods in the dataset that did not switch service type. The reported F-statistics correspond to the Kleibergen-Paap rk Wald F-statistic. Standard errors are clustered at the household level. *** p<0.01, ** p<0.05, * p<0.1. Using the estimated model, we compute ˆqjzt, which represents the predicted consumption of a representative consumer in a given billing month, located in postal code z, and connected to service j. This calculation assumes average income and household size within the postal code. We then aggregate this monthly consumption to obtain the yearly consumption, Qjzy, and calculate the corresponding revenue generated by the firm, denoted as Rjzy, based on the price schedule. 30 6.3 Cost To estimate the costs associated with providing a service in different postal codes, we consider the water consumption and revenue a firm would generate for the next five years if it installed only water or both water and sewer pipes in that postal code. We assume that the firm has perfect foresight of future interest rates, population growth, and income in the areas they have concession over the provision of piped water and sewer. The firm chooses where to install pipes considering their ex-ante profit, given by their expected take-up and water demand, the marginal cost of providing the services and the sunk cost of building the pipes. We consider that the fixed fees and marginal prices are updated annually based on inflation projections from 2017. The population of each postal code grows at the same rate as the municipal population projections. The income per capita also grows at the same rate as the municipal income projections reported by the Brazilian Institute of Geography and Statistics (IBGE). Using the demand estimates and random draws from the empirical distribution of ξand η, we compute the expected predicted take-ups ( ˆ Sjzy), the average monthly household water consumption (ˆqjzt) and the associated revenue (R(ˆqjzt)). We estimate the marginal cost associated with each service, mcj, and the fixed cost parameter, ωj, via maximum likelihood using the predicted choice probability of connecting postal code zwith service j(equation 13) and the observed expansion choices in 2018 and 2019. The key idea is to identify the cost parameter values that maximize the likelihood of observing the firm’s actual choices, given the model’s assumptions. The estimation results are available in Table 6. They indicate that the cost of supplying one cubic meter of water is roughly 6.13 Brazilian reais (R$). When including the collection of piped sewer with the same amount of water, the cost increases to about 12.71 Brazilian reais. These costs are based on the metered water consumption at each address and cover expenses associated with water treatment, delivery, and sewer collection, and account for potential water losses during distribution. The sunk cost for constructing one kilometer of water pipes is approximately R$10869.47, 31 R$12569.58 for a kilometer of combined piped water and sewer and R$2141.60 to extend sewer pipes to postal codes that had only water. These costs encompass not only the pipes but also all the materials and labor required for excavation and restoring the path after pipe installation. Appendix Tables A4 and A5 present alternative cost estimates, assuming the firm recovers sunk investment costs over 10 or 30 years. Table 6 – Cost Estimates Costs Mg. cost water (m3) 6.130*** (0.157) Mg. cost water and sewer (m3) 12.706*** (0.472) Cost per distance water (km) 10869.465*** (3982.539) Cost per distance water and sewer (km) 12569.585** (5350.286) Cost per distance sewer (km) 2141.603*** (376.737) Number of zip codes 3,279 Notes: This table presents cost estimate parameters under the assumption that firms consider projected profits over the next 5 years when making decisions. The estimation includes postal codes within the firm’s concessions in the North and Northeast regions of the country. From the total 3403 postal codes without service or with only water in 2017, we missed 124 where we could not predict the demand based on our estimated model. These postal codes are dropped either because when matched with the census, they are missing relevant demographics or because there was only one postal code in the municipality, so we could not estimate municipalitymoth fixed effects. All estimated costs are reported in Brazilian reais (R$). In 2017, the exchange rate was approximately 3.3R$ per 1U$. *** p<0.01, ** p<0.05, * p<0.1. Comparing our estimates with existing literature is challenging. Engineering studies, such as von Sperling and Salazar (2013), typically consider only accounting costs and focus on a limited number of projects. Additionally, studies based on survey data from different countries, such as Brichetti et al. (2021), often do not distinguish between the costs incurred by firms when installing the network and the costs consumers bear to connect their homes to street pipes. 32 7 Counterfactual Simulations For the simulations, we assume connection targets of 99% of households with piped water and 90% with sewer and use the estimated model to analyze incentives for achieving them. Reaching these targets depends on both the company’s expansion decisions and consumers’ choices to adopt services. To disentangle these factors, we first simulate a scenario where the firm expands services in all postal codes, such that the gap between connection rates and the targets depends solely on consumer decisions. Next, we allow the firm to endogenously select expansion areas and introduce different policies, focusing on sewer connection subsidies and sewer availability charges. These policies encourage consumer adoption and may incentivize the firm to extend services to uncovered postal codes.25 To predict the outcomes, we use demand estimates and the empirical distribution of ξ and ηto compute the predicted take-up rates, water consumption, and the resulting firm revenue under the different scenarios. By combining predictions with the cost estimates, we calculate the variable profit the firm would generate and the sunk costs involved in the expansion. We also measure the changes in consumer surplus and infant deaths that arise from these policy changes. Consumer surplus is computed using the discrete-choice component of the model, where consumers decide which service to connect to when it is available. While consumer surplus is a commonly used welfare measure, the interpretation requires caution in contexts with high inequality. The willingness to pay for the services may not fully capture the benefits consumers would experience upon connecting. Nevertheless, we present this measure to understand its impact on consumers who can afford the service and may not choose to connect under the different simulations. We compute the number of averted infant deaths in each simulation to capture consumer health benefits. We create a back-of-the-envelope measure using the estimated impact of piped water and sewer in Brazil from Gamper-Rabindran et al. (2010) and the number of live births from DATASUS. This measure incorporates both private benefits from water 25In the counterfactual scenarios, we assume that the firm cannot remove services from areas where pipes had already been installed by 2019. 33 connections and externalities from sewer connections. It is important to note that it does not encompass all dimensions of external benefits, as discussed by Kresch and Schneider (2020), but provides an extra dimension to compare the policies.26 7.1 Full Expansion of Piped Water and Sewer In the first exercise, we simulate a scenario where the company expands water and sewer services to all postal codes within its concessions in the northern region. In this setting, connection rates depend solely on consumer take-up, as all households could potentially connect to the services. Our results show that connection targets would not be met at current pricing levels even if the firm expanded to all postal codes, due to low take-up, especially for sewer. Despite universal availability in this scenario, 85.95% of the households would connect to water and only 51.09% would connect to the sewer network. Figure 4a illustrates the 99% piped water coverage target (red line), the pre-policy connection rate (gray bar), and the simulated expansion outcome (blue bar). Similarly, the right panel of Figure 4b depicts the 90% sewer coverage target (red line), with the baseline and full-expansion connection rates shown in gray and orange, respectively. Table 7 provides more details of the simulation results. Panel A displays information on the share of postal codes within each concession where each service is available, while Panel B presents welfare measures of each alternative policy relative to the baseline situation. We present variable profit and consumer surplus over a five-year period in line with our cost estimation framework. Column (1) presents the baseline scenario, while column (2) shows the outcomes under full expansion. By design, the latter ensures all postal codes have access to water and sewer services, as reflected in the first two rows. However, not all households adopt these services, as indicated in the third and fourth rows and the colored bars in Figure 4. 26The number of averted infant deaths represents a lower bound of the externalities generated by increasing connections to piped water and sewer. For instance, the services might also reduce the incidence of waterborne diseases, such as diarrhea, which do not always result in child death (Barreto et al., 2007). Social externalities could influence the decisions of neighbors to adopt alternative methods for water sanitation and wastewater disposal (Deutschmann et al., 2024). Additionally, externalities could manifest as increased housing prices in neighborhoods with the service (Coury et al., 2024). 34 Figure 4. Share of Household Connections (a) Piped water 0 10 20 30 40 50 60 70 80 90 100 % of households connected to piped water Baseline Full expansion (b) Piped sewer 0 10 20 30 40 50 60 70 80 90 100 % of households connected to piped sewer Baseline Full expansion Notes: This figure compares the baseline percentage of households connected to piped water (Figure (a)) and piped sewer (Figure (b)) to a scenario in which the firm expands service everywhere. The red lines indicate the connection targets set by the 2020 Sanitation Regulatory Framework. The connection share is calculated as the number of households connected to the service divided by the total number of households within the North and Northeast concession areas. Under the “Full Expansion” scenario, all postal codes have piped water and sewer, and the predicted take-up determines the share of connections for each service. Additionally, we show in column (2) of Table 7 that extending services to all postal codes is not viable for the company, as the substantial sunk costs outweigh the increased variable profit from new connections. However, the expansion increases consumer surplus, as more consumers have the services available and decide to connect. The full expansion also generates a reduction of 10.37% in infant mortality among children below 1-year-old, amounting to roughly 22 fewer deaths when contrasted with the baseline scenario without expansion. 7.2 Endogenous Expansion of Piped Water and Sewer In this set of simulations, we allow the firm to determine which postal codes to expand water and sewer services to while providing incentives for consumers to connect to sewer via subsidies and the sewer availability charge. We focus on sewer adoption and expansion as it presents the largest gap to the connection targets, while for water most people connect to it 35 Table 7 – Simulations (1) (2) (3) (4) (5) Baseline Full expansion End. expansion End. expansion End. expansion Connection subsidy Connection subsidy Price increase Availability charge Panel A: Service coverage and household connections % of zips with water and sewer 41.36 100.00 41.36 78.20 71.75 % of zips with only water 48.77 0.00 48.77 12.00 18.41 % of households connected to water 79.71 85.95 83.38 84.13 78.86 % of households connected to sewer 33.43 51.09 55.17 81.58 54.77 Panel B: Welfare impact relative to the baseline ∆ Variable profit (mi R$)−95.77 −127.15 188.62 282.81 Sunk cost (mi R$) 249.69 0.00 4.34 3.83 ∆ Consumer surplus (mi R$) 3.37 53.03 65.46 −4.40 Connection subsidy (mi R$) 0.00 127.16 281.94 0.00 ∆% Infant deaths −10.37 −2.60 −2.66 −0.02 Expansion: firm choice yes no yes yes yes Expansion: all zips with sewer no yes no no no Subsidy sewer connection no no yes yes no Sewer price increase no no no 50% no Sewer availability charge no no no no yes Notes: This table presents counterfactual results, with each column corresponding to a different counterfactual simulation. Column (1) shows the baseline. Column (2) considers full expansion. Column (3) allows the firm to expand endogenously while providing consumers with a subsidy to connect. Column (4) adds a price increase to the policy implemented in Column (3). Column (5) combines endogenous firm expansion with charging for sewer service based on availability rather than connection. Panel A reports service coverage outcomes, while Panel B presents welfare outcomes. Differences in variable profit, consumer surplus, and infant mortality are measured relative to the baseline. Variable profit and consumer surplus are calculated over five years, while the change in infant deaths is based on the estimated increase in household connections, following Gamper-Rabindran et al. (2010). The baseline scenario includes 216 infant deaths. All cost estimates are in Brazilian reais (R$). In 2017, the exchange rate was approximately 3.3 R$per 1 U$. when it is available. 1. Connection Subsidies The second simulation examines the impact of a one-time sewer connection subsidy, which covers the cost of connecting homes to street pipes. This subsidy applies only to households connecting to both water and sewer, excluding those opting solely for water. Once connected, consumers must continue paying their bills to remain in the system and cannot receive the subsidy again if they disconnect. The subsidy effectively increases household sewer connections but has no impact on firm expansion. As shown in Table 7, column (3), the share of connected households rises to approximately 55.17%, yet service coverage remains at 41.36%. This indicates that the new connections occur in areas where sewer infrastructure was already available. Furthermore, the subsidy reduces firm profits in locations where sewer pipes were previously installed, suggesting that the revenue from water and sewer bills is insufficient to cover the costs of service provision for newly connected households. The subsidy significantly increases consumer surplus, valued at 53.03 million Brazilian reais, by enabling more households to access services. However, the policy is costly, amount36 ing to 127.16 million Brazilian reais. We do not take a stand on how the government would finance this subsidy or whether it would compensate firms for incurred losses. Appendix Figure A8 shows that subsidies covering more than 50% of the cost do not further improve connection rates, which is mainly driven by consumer take-up. Appendix Figure A9 suggests that offering subsidies only to low-income households does not significantly boost connections because the firm does not substantially expand. 2. Connection Subsidies with Price Increases In our third simulation, we show that combining connection subsidies with an increase in sewer prices can effectively boost connection rates. In some concessions, the new sewer price is high enough to cover the costs of sewage collection, which encourages firms to expand their network. As shown in Table 7, column (4), pairing the subsidy with a 50% increase in the sewer price raises sewer connections to 81.58% of households. Appendix Figure A10 shows that further price increases beyond 50% yield only a marginal increase in connections, as the firm does not expand significantly beyond this threshold. On the consumer side, the increase in consumer surplus from the subsidy more than offsets the higher sewer price. However, the expansion makes the subsidy more expensive for the government, as more consumers use it to connect to newly available sewer infrastructure. Despite the significant rise in sewer connections, the reduction in infant mortality remains small. 3. Sewer Availability Charge In our fourth simulation, we introduce the “Sewer Availability Charge,” which requires consumers to pay for sewer in their monthly bills once pipes are available in their postal code, even if they are only connected to water. Although established under the 2007 Sanitation Regulatory Framework, this policy has been rarely implemented, with only a few municipalities adopting it. In our dataset, just one municipality employs this pricing strategy.27 This charge works as a tax, incentivizing consumers to internalize the externality created when 27The availability charge was introduced in this municipality midway through the study period, so it is excluded from demand and cost estimations. 37 Wichman, C. J. (2014). Perceived price in residential water demand: Evidence from a natural experiment. Journal of Economic Behavior & Organization 107, 308–323. Wollmann, T. G. (2018). Trucks without bailouts: Equilibrium product characteristics for commercial vehicles. American Economic Review 108 (6), 1364–1406. 44 A1 Appendix Figures Figure A1. Share of the Population Connected by Region in Brazil (a) Piped water 54% 76% 90% 85% 82% (b) Piped sewer 14% 34% 81% 46% 38% Notes: This figure illustrates the share of people connected to piped water (Figure (a)) and sewer collection (Figure (b)) across the country’s regions in 2017. Data source: National Sanitation Survey (Pesquisa Nacional de Saneamento B´asico - PNSB) from IBGE. 45 Figure A2. Share of Households with Sanitation Services by Income percentile (a) Water 0 .2 .4 .6 .8 1 Share of households with piped water 0 20 40 60 80 100 Income percentile Other providers Company (b) Sewer 0 .2 .4 .6 .8 1 Share of households with piped sewer 0 20 40 60 80 100 Income percentile Other providers Company Notes: This figure illustrates connections to piped water (Figure (a)) and sewer services (Figure (b)). Each observation represents the average share of households connected across census tracts within income percentiles. In the left graph, areas within our firm’s concession are highlighted in blue, while others are shown in gray. The right-hand graph marks our firm’s concession areas in orange, with all other areas in gray. The data come from the 2010 Census. Figure A3. Distances to the Installed Network (a) Only water 0 .2 .4 .6 .8 1 Share of zip codes without service in 2017 [0,200] (200,400] (400,600] (600,800] (800,1000] above 1000 Distance to the only water network (m) Expansion only water Expansion water and sewer No Expansion (b) Water and sewer 0 .2 .4 .6 .8 1 Share of zip codes with no sewer in 2017 [0,200] (200,400] (400,600] (600,800] (800,1000] above 1000 Distance to the water and sewer network (m) Expansion sewer Expansion only water No expansion Notes: This figure depicts the distance from new expansions to the existing network. Figure (a) shows the distance to the installed water network, while Figure (b) includes both water and sewer networks. These graphs cover all postal codes within the firm’s concession areas in the North and Northeastern regions of the country that lacked service in 2017. 46 Figure A4. Differences in the Price Schedule across Concessions and States Notes: This figure illustrates the variation in the price schedule across concessions and states. Concession u1is entirely within State A, where consumers face price pu1. Concession u2spans State A and State B, leading to different prices (p0 u2and p00 u2) for consumers in the same concession but in different states. This setup generates both within-concession and within-state price variation, which helps identify consumer responses to fixed fee changes. Figure A5. Distance of New Postal Codes per Month (a) Only water 0 .1 .2 .3 .4 .5 .6 Avg. distance to the water network (km) Jan 18 May 18 Sep 18 Jan 19 May 19 Sep 19 Month of expansion (b) Water and sewer 0 .1 .2 .3 .4 .5 .6 Avg. distance to the sewer network (km) Jan 18 May 18 Sep 18 Jan 19 May 19 Sep 19 Month of expansion Notes: This figure depicts the distance of network expansions from the existing infrastructure in 2018 and 2019. Figure (a) includes postal codes where only water pipes were expanded, while Figure (b) on the right highlights postal codes that received expansions of both water and sewer pipes in the North and Northeast regions. 47 Figure A6. Predicted vs. Observed Service Take-up (a) Water take-up in postal codes with only water pipes 0.00 0.20 0.40 0.60 0.80 Fraction of zip codes -1 -.5 0 .5 1 Predicted - observed take-up only water (b) Water take-up in postal codes with water and sewer pipes 0.00 0.20 0.40 0.60 Fraction of zip codes -1 -.5 0 .5 1 Predicted - observed take-up only water (c) Water and sewer take-up in postal codes with water and sewer pipes 0.00 0.10 0.20 0.30 0.40 0.50 Fraction of zip codes -1 -.5 0 .5 1 Predicted - observed take-up water and sewer Notes: These figures show the difference between the observed and estimated take-up rates. Figure (a) shows this difference for only water take-up in postal codes where only water pipes were available. Figure (b) presents this difference for only water take-up in postal codes with both water and sewer pipes. Figure (c) presents this difference for water and sewer take-up in postal codes where both water and sewer pipes are available. 48 Figure A7. Bracket Change 0 .2 .4 .6 .8 Share of households Jan #days . measured Feb . Mar 29 Apr 30 May 30 Jun 30 Jul 29 Ago 31 Sep 30 Out 30 Nov 31 Dec 28 2018 0 .2 .4 .6 .8 Share of households Jan 32 Feb 29 Mar 31 Apr 29 May 31 Jun 29 Jul 31 Ago 29 Sep 30 Out 30 Nov 32 Dec 30 2019 Block increase Same block Block decrease Notes: This figure illustrates the share of households that switch brackets from one month to the next. The data only includes households already connected in 2017 and had water bills for all months of 2017 and 2018. The graphs also include the number of days in the billing cycle from March 2018 to December 2019, which where not available for previous months. 49 Figure A8. Varying levels of subsidy (a) Share of households connected to sewer 0 10 20 30 40 50 60 70 80 90 100 % of Households with sewer 0 10 20 30 40 50 60 70 80 90 100 Sewer connection subsidy (% of the cost) (b) Share of postal codes with sewer 0 10 20 30 40 50 60 70 80 90 100 % of Zip codes with sewer 0 10 20 30 40 50 60 70 80 90 100 Sewer connection subsidy (% of the cost) (c) Firm Profits -150 -100 -50 0 Firm profits (mi R$) 0 10 20 30 40 50 60 70 80 90 100 Sewer connection subsidy (% of the cost) Notes: These figures present outcomes from counterfactual simulations under varying subsidy levels, ranging from 0% to 100% of the connection costs for the sewer network. Figure (a) illustrates the impact on the percentage of households with sewer access. Figure (b) shows the effects on the share of postal codes with sewer pipes. Figure (c) depicts changes in the firm’s profit. 50 Figure A9. Subsidies to Different Income Levels (a) Share of households connected to sewer 0 10 20 30 40 50 60 70 80 90 100 % of Households with sewer 12345678910 Sewer connection subsidy (up to x-th income decile) (b) Share of postal codes with sewer 0 10 20 30 40 50 60 70 80 90 100 % of Zip codes with sewer 12345678910 Sewer connection subsidy (up to x-th income decile) (c) Firm Profits -150 -100 -50 0 Firm profits (mi R$) 12345678910 Sewer connection subsidy (up to x-th income decile) Notes: These figures present outcomes from counterfactual simulations where subsidies are targeted to different income deciles. Figure (a) illustrates the impact on the percentage of households with sewer access, Figure (b) shows the effects on the share of postal codes with sewer pipes, and Figure (c) depicts changes in the firm’s profit. The subsidy is allocated to households up to the x-th income decile, meaning that for the 10th decile, all households receive the subsidy. 51 Figure A10. Subsidies with Price Increases (a) Share of households connected to sewer 0 10 20 30 40 50 60 70 80 90 100 % of Households with sewer 0 10 20 30 40 50 60 70 80 90 100 Sewer price increase(%) (b) Share of postal codes with sewer 0 10 20 30 40 50 60 70 80 90 100 % of Zip codes with sewer 0 10 20 30 40 50 60 70 80 90 100 Sewer price increase(%) (c) Firm Profits -200 0 200 400 600 Firm profits (mi R$) 0 10 20 30 40 50 60 70 80 90 100 Sewer price increase(%) Notes: These figures present outcomes from counterfactual simulations with a 100% subsidy on connection costs, combined with varying increases in sewer prices. Figure (a) illustrates the impact on the percentage of households with sewer access. Figure (b) shows the effects on the share of postal codes with sewer pipes. Figure (c) depicts changes in the firm’s profit. 52 A2 Appendix Tables Table A1 – Take-up Regression (1) (2) (3) Take-up only water (Zips with only water) Take-up water and sewer (Zips with water and sewer) Take-up only water (Zips with water and sewer) ln(Connection cost) −0.073*** −0.080*** −0.073*** (0.014) (0.020) (0.005) ln(Income) 0.121*** 0.126*** −0.039*** (0.010) (0.005) (0.003) Urban −0.215*** 0.113*** −0.051*** (0.049) (0.034) (0.019) Household size 0.199*** 0.174*** −0.043*** (0.018) (0.008) (0.004) Share rented 0.347*** 0.443*** −0.052*** (0.042) (0.022) (0.013) Share other water −0.024 0.319*** −0.181*** (0.033) (0.029) (0.017) Share other sewer 0.147*** −0.092*** 0.070*** (0.014) (0.009) (0.005) Municipality-year FE yes yes yes Observations 7,068 24,335 24,335 R-squared 0.614 0.2 0.371 Notes: This table reports the relationship between demographic variables and the share of connected households in each postal code where services are available. In column (1), the dependent variable is the probability of a household being connected to only water in postal codes that have only water pipes. In column (2), the dependent variable is the probability of a household being connected to both water and sewer in postal codes that have water and sewer pipes. In column (3), the dependent variable is the probability of a household being connected to only water in postal codes that have both water and sewer pipes. *** p<0.01, ** p<0.05, * p<0.1. 53 A3.2 Estimation 1. Empirical Bayes estimator take-up One challenge in the service take-up estimation is that in some postal codes, all the addresses connect to the available pipes, generating market shares that are equal to 1 for the inside option and 0 for the outside option. In these cases, we would not be able to use the standard demand estimation methods Berry (1994); Berry et al. (1995) because the inversion step requires strictly positive market shares for each good in the market, in our case, for each service in the postal code. One common alternative is to aggregate markets, but in this setting, aggregating postal codes would not capture the relevant take-up faced by the firm when making expansion decisions. Another simple alternative, such as dropping the zeros/ones, would underestimate the service take-up. We follow Li (2019) and use a parametric empirical Bayes or shrinkage estimator to generate strictly positive posterior take-up probabilities using information from similar postal codes. The number of addresses connected to service jin postal code z, given by Kjz, is modeled as a draw from a binomial distribution with Nztrials, representing the total number of addresses in the postal code. Here we omit the year subscripts to facilitate the notation. The take-up probabilities S0 jz for each service in each postal code are drawn from a Beta prior distribution with parameters λ1jz and λ2jz. Such that Kjz ∼Binomial(Nz, S0 jz) and S0 jz ∼Beta(λ1jz, λ2jz). The posterior distribution of the take-up is also a Beta distribution Sjz ∼Beta(λ1jz +Kjz, λ2jz +Nz−Kjz) with posterior mean ˆ SP jz =λ1zj +Kjz Nz+λ1jz +λ2jz For each postal code zand service jthe Beta prior is formed using the 100 closest in income per capita that also have pipes for j,l∈ζz, where lis a postal code from the set of similar postal codes ζz. The parameters of the beta prior distribution λ1jz and λ2jz are 60 estimated from maximizing the log-likelihood over the take-up of similar markets f(Kjz, l ∈ζz|λ1jz, λ2jz) = Y l∈ζzKlj NlΓ(λ1jz +λ2jz)Γ(λ1jz +Klj)Γ(Nl−Klj +λ2jz) Γ(λ1jz)Γ(λ2jz)Γ(λ1jz +Nlλ2jz) With the estimated parameters, we construct the posterior mean of the take-up probabilities for each postal code and service ˆ SP jz =ˆ λ1jz +Kjz Nz+ˆ λ1jz +ˆ λ2jz , which are strictly between 0 and 1. The figures below show the empirical Bayes posterior mean take-ups and the observed take-ups for only water and water and sewer. Figure OD.1. Take-up Only water: Empirical Bayes Posterior vs. Observed (a) All take-ups 0 .2 .4 .6 .8 1 Empirical bayes posterior mean take-up 0 .2 .4 .6 .8 1 Observed take-up only water (b) Zooming in on observed take-ups below 0.1 0 .01 .02 .03 .04 .05 Empirical bayes posterior mean take-up 0 .002 .004 .006 .008 .01 Observed take-up only water Notes: These graphs show the empirical Bayes Posterior Mean for each observed take-up of only water services. 61 Figure OD.2. Take-up Water and Sewer: Empirical Bayes Posterior vs. Observed (a) All take-ups 0 .2 .4 .6 .8 1 Empirical bayes posterior mean take-up 0 .2 .4 .6 .8 1 Observed take-up water and sewer (b) Zooming in on observed take-ups above 0.9 .92 .94 .96 .98 1 Empirical bayes posterior mean take-up .99 .992 .994 .996 .998 1 Observed take-up water and sewer Notes: These graphs show the empirical Bayes Posterior Mean for each observed take-up of water and sewer services. 62