metadata: authors: 0: author: Anselin, Luc
1: author: Lozano-Gracia, Nancy
2: author: Deichmann, Uwe
3: author: Lall, Somik
count: India
docna: 0: docna: Valuing access to water - a spatial hedonic
            approach applied to Indian cities
docty: Policy Research Working Paper
subtopic: Urban Housing and Land Settlements,Sanitation and Sewerage,Engineering,Urban Governance and Management,Urban Housing,Energy Policies & Economics,Water and Human Health,Hydrology,Water Supply and Sanitation Economics,Sanitary Environmental Engineering,Small Private Water Supply Providers,Environmental Engineering,Municipal Management and Reform,Town Water Supply and Sanitation
teratopic: Water Supply and Sanitation,Communities and Human Settlements,Water Resources
abstracts: cdata!: An important infrastructure policy issue
            for rapidly growing cities in developing countries is how to
            raise fiscal revenues to finance basic services in a fair
            and efficient manner. This paper applies hedonic analysis
            that explicitly accounts for spatial spillovers to derive
            the value of improved access to water in the Indian cities
            of Bhopal and Bangalore. The findings suggest that by
            looking at individual or private benefits only, the analysis
            may underestimate the overall social welfare from investing
            in service supply especially among the poorest residents.
            The paper further demonstrates how policy simulations based
            on these estimates help prioritize spatial targeting of
            interventions according to efficiency and equity criteria.
geo_reg_key: 80475,80451,80470
repnme: repnme: Valuing access to water - a spatial hedonic
            approach applied to Indian cities
display_title: Valuing access to water - a spatial
            hedonic approach applied to Indian cities
listing_relative_url: /research/2008/02/9034859/valuing-access-water-spatial-hedonic-approach-applied-indian-cities
topicv3: Water m1326522 137,Power and Electricity Sector m1327094 515,Housing Markets m1327413 904,Wastewater Collection m1327591 148,Land and Housing m1327648 817
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Water Supply and Sanitation,Communities and Human Settlements,Water Resources
no_of_pages: 31
author_keys: 0: author_key: NA
1: author_key: NA
2: author_key: NA
3: author_key: NA
model_extractions: WPS4533 Policy ReseaRch WoRking PaPeR 4533 Valuing Access to Water – A Spatial Hedonic Approach Applied to Indian Cities _Luc Anselin Nancy Lozano-Gracia Uwe Deichmann Somik Lall_ The World Bank Development Research Group Sustainable Rural and Urban Development Team February 2008
Policy ReseaRch WoRking PaPeR 4533

# **Abstract**

An important infrastructure policy issue for rapidly growing cities in developing countries is how to raise fiscal revenues to finance basic services in a fair and efficient manner. This paper applies hedonic analysis that explicitly accounts for spatial spillovers to derive the value of improved access to water in the Indian cities of Bhopal and Bangalore. The findings suggest that by looking at individual or private benefits only, the analysis may underestimate the overall social welfare from investing in service supply especially among the poorest residents. The paper further demonstrates how policy simulations based on these estimates help prioritize spatial targeting of interventions according to efficiency and equity criteria.

This paper—a product of the Sustainable Rural and Urban Development Team, Development Research Group—is part of a larger effort in the department to understand the contribution of urban public services to household welfare and overall quality of life. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at udeichmann@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Valuing Access to Water –**

# **A Spatial Hedonic Approach Applied to Indian Cities**<sup>*****</sup>

Luc Anselin<sup>1</sup> , Nancy Lozano-Gracia<sup>2</sup> , Uwe Deichmann<sup>3</sup> and Somik Lall<sup>4</sup>

* This paper is part of a larger program to find ways to improve urban management through the collection, use, and public disclosure of spatially detailed information and analytic methods, which has been funded by the UK DFID’s Urban Knowledge Generation and Toolkits program and the World Bank Development Research Support Budget. We thank Mark Roberts for helpful comments. The findings reported in this paper are those of the authors alone, and should not be attributed to the World Bank, its executive directors, or the countries they represent.

> 1 School of Geographical Analysis and GeoDa Center for Geospatial Analysis and Computation, Arizona State University.

> 2 GeoDa Center for Geospatial Analysis and Computation, Arizona State University.

> 3 Development Research Group, World Bank.

> 4 Finance, Economics and Urban Unit, Sustainable Development Network, World Bank.
# **I. Introduction**

The population of Indian cities is currently growing at a rate of 3 to 4 percent per year, in line with the urban growth rates of cities in developing countries as a whole. This implies that their population will double within the next 17 to 23 years. Even if growth rates continue to decrease from their highs of more than 5 percent in the 1960s and 1970s, this means that local policy makers need to deal with a significant increase in the demand for public services while, at the same time, addressing the backlog of investments in under-serviced areas.

Municipal managers face these challenges in an environment in which they have been given significant new responsibilities. As in many other developing countries, urban policy in India had historically been formulated centrally by the national government with relatively little concern for local needs and interests. City officials simply implemented policies using funds allocated by state and national government. This changed with the passing of the 74th Amendment of the Indian Constitution in 1993. Since then, more and more administrative and fiscal authority has been devolved to local governments. Greater local control should lead to more appropriate local policy making. But it will also require cities to become financially more independent by expanding local revenue generation.

Cities are therefore exploring options to generate funds locally, either through user charges and fees or through property taxes (Lall and Deichmann 2006a). Successful introduction of such revenue schemes in an environment where residents are used to heavily subsidized or free service access depends on demonstrating that the charges realistically represent the benefits obtained by households in return. At the same time, policy makers need reliable estimates of potential revenue generation to relate benefits to the actual costs of service provision which in turn influence financing strategies. Furthermore, equity concerns guide many policy decisions. Urban managers require tools that enable prioritization of investments according to chosen equity-efficiency considerations, for instance, by targeting the poorest areas first or those areas where returns are highest.

This paper contributes to this debate by proposing an improved strategy for estimating benefits from infrastructure investments in urban neighborhoods. We assume that public services are
capitalized in the value of a dwelling unit. Hedonic analysis of house prices or rents conditional on service access will therefore yield estimates of the contribution of individual housing unit characteristics and thus the willingness-to-pay (WTP) of residents for those characteristics. In contrast to the standard hedonics and WTP literature, we use a spatial framework that allows us to measure both direct effects and externality spillovers from upgrading by neighbors. We illustrate this approach in a valuation of water services in two Indian cities, Bangalore and Bhopal, and compare the results with those obtained from a standard WTP questionnaire. The results suggest that standard hedonic analysis considerably underestimates the benefits from service upgrading. The higher spatial econometric estimates are surprisingly consistent with households’ expressed WTP. Finally, we present a policy analysis based on simulation of different upgrade scenarios that is based on predicted values for individual observations in our household survey rather than on marginal willingness-to-pay.

The remainder of the paper is structured as follows. The next section discusses the use of hedonic models for valuation purposes. Section III describes the estimation strategy. The data used in this analysis and estimation results are described in Sections IV and V. We derive the marginal willingness to pay for improved water availability in Section VI and present a policy analysis using a simulation exercise in Section VII. Section VIII concludes.

# **II. Hedonic Analysis of Housing Characteristics and Public Services**

Valuation of public services and other housing attributes has been addressed through methods such as contingent valuation (Whittington 2002), conjoint and discrete choice analysis (Earnhart 2002) and hedonic specifications (Malpezzi 2002). In hedonic models, dwelling unit prices represent the sum of expenditures on a bundle of characteristics that can be priced separately. If _z_ =( _z_ 1,..., _z_ n) is a set of characteristics of the home, the price of the home is determined by some hedonic function, _p_ ( _z_ ), according to prevailing market clearing conditions. The set of characteristics that determine home values consists of structural attributes of the home itself, such as the floor area, lot size, and construction material, as well as the availability of public services such as clean water supply or electricity. Such models have been used in developing countries to determine the optimum housing characteristics for low income groups (Follain and Jimenez, 1985) and for valuation of access to specific services (North and Griffin, 1993; Crane et al., 1997; Oliveira and De Morais, 2000, and Knight et al. 2004 among others).
Estimating the hedonic price function using a set of observed housing values and dwelling unit characteristics yields a set of implicit prices for housing characteristics that are essentially willingness-to-pay estimates. These can then be used in a second stage analysis, where the WTP estimates are used as the dependent variable in an inverse demand function. Estimates of income elasticities of demand can then be derived for various parts of a city or subgroups of the population. This allows analysis of various upgrading scenarios, for instance, in low-income neighborhoods.

Recent empirical econometric work has addressed the potential bias and loss of efficiency that can result when spatial effects are ignored in the estimation of hedonic models (e.g., Pace and LeSage 2004). Spatial patterns in the housing markets arise from a combination of spatial heterogeneity and spatial dependence (Anselin, 1998). Spatial heterogeneity—essentially the existence of discrete submarkets—can originate from characteristics of the demand, supply factors, institutional barriers or racial discrimination that cause house price differentials across neighborhoods. Spatial autocorrelation or spatial dependence, on the other hand, means that prices or characteristics of houses that are nearby are more similar than those of houses that are farther apart—that is, housing prices vary more continuously due, for instance, to spatial spillovers. In practice, spatial autocorrelation may be observationally equivalent to spatial heterogeneity and (Anselin, 2001) or it may result from spatial heterogeneity that is not correctly modeled (Baumont, 2004).

Besides being the result of some substantive underlying process such as spatial spillover or some form of contagion, spatial dependence may also arise from measurement problems in explanatory variables, omitted variables, and other forms of model misspecification. The presence of spatial autocorrelation has significant bearing on parameter estimation. If it is ignored, OLS may lead to inconsistent estimates and incorrect statistical test results. If the residuals are spatially correlated, OLS estimation would underestimate the residual variance and the t-statistics would be upwards biased. This may lead to erroneously concluding significance of some parameters. Some examples of the use of spatial hedonic models in the context of valuation of environmental amenities are Kim et al. 2003, Beron et al. 2004, Brasington and Hite 2005, Anselin and Le Gallo 2006, and Anselin and Lozano-Gracia 2007a. The present paper extends spatial hedonic
approaches to the analysis of service access in developing country cities.

# **III. Estimation Strategy**

We estimate a log-linear hedonic function for house rents in Bhopal and Bangalore and take an explicit spatial econometric approach by testing for spatial autocorrelation and controlling for its presence in the final specification estimated. The spatial econometric literature (see Anselin 1988) differentiates between two types of spatial dependence that result in two main spatial models: the spatial lag and spatial error models. The spatial lag model accounts for spatial dependence by introducing a spatially lagged dependent variable into the model, while the spatial error specification includes a spatially correlated error term.

Following Anselin (1988), we carry out a so-called forward specification analysis (see also Florax et al. 2003), and first obtain ordinary least squares (OLS) estimates for the hedonic model. Next, we test the residuals for the presence of spatial autocorrelation using Lagrange Multiplier test statistics for error and lag dependence, as well as their robust forms, and proceed with the alternative spatial regression model thus selected (Anselin et al. 1996). The estimation results consistently show very strong evidence of positive residual spatial autocorrelation favoring the spatial lag alternative (see Appendix 1, Tables AA1 and AA2).

In a hedonic model, a spatial lag model can be specified as follows: where _p_ is an _n_ × 1 vector of observations on the dependent variable, _X_ is an _n_ × _k_ matrix of explanatory variables, _u_ is an _n_ × 1 vector of i.i.d. error terms, β is a _k_ × 1 vector of regression coefficients, ρ is the spatial autoregressive parameter, and _W_ is a _n_ × _n_ spatial weights matrix. A spatial weights matrix incorporates the neighborhood relations between observations and is a standard tool employed in spatial econometric analysis (see Anselin 2006 for extensive discussion).<sup>5</sup> It should be noted that since the house locations constitute a sample, the

> 5 For this application we used a queen contiguity criterion to define neighbors. This is obtained by first taking the point coordinates of the house locations and creating a Thiessen polygon tessellation centered on each house. Polygons with common sides and vertices designate house locations as queen neighbors. On average, the weights matrix contains 7 neighbors for each location. In addition, we also used two weights
neighborhood relations in the spatial weights are only proxies for the true neighbors. The underlying assumption is that the spatial variation among sampled “neighbors” is representative of that among the true neighbors, an assumption commonly taken in spatial hedonic models. We are comfortable that the sample design employed in these surveys supports the conclusions we draw from this analysis. However, ideally it would be desirable to employ sampling designs that consider neighborhood structure explicitly, for instance by sampling households randomly and then including a number of direct neighbors for each households. Very few surveys have employed such as design, the US American Housing Survey being an exception (Ioannides 2002).

# **IV. Data and Variables**

Detailed household data for developing country cities are scarce. Most such data are collected at the national level through Living Standards Measurement Surveys or Demographic and Health Surveys. These tend to distinguish urban and rural areas, but the number of observations in each urban area is too small for city-specific analysis. In this paper we use comprehensive and geographically referenced information from urban household surveys for 2905 households in Bangalore and 2508 households in Bhopal (for further details on this data see Deichmann et al. 2003, Lall et al. 2004, Lall and Deichmann 2006b). These surveys were conducted in 2001 and 2003 respectively. The available variables differ slightly across the two cities since the original surveys were not totally identical. The key indicator in hedonic housing market analysis is the price or rent of the dwelling unit. Due to high official transaction costs, most recorded sales in Indian real estate markets do not reflect actual transaction amounts. Rents are also often artificially low due to rent control and therefore do not always match actual market rents. The surveys therefore asked households to report what they believe would be the market rent for a similar house in their neighborhood. Therefore this variable represents an estimated value reported by the surveyed individual. The survey team compared these values selectively to transactions revealed by real estate agents in the survey cities. This confirmed that, overall, residents have a fairly good idea of market rents. In our regression analyses, we apply a log matrices based on a nearest neighbor relation among the locations, for respectively 7 and 14 neighbors. The three weights matrices are used in row-standardized form. Although the remaining analysis refers only to the results using a queen weights matrix, the results are consistent for the alternative weights matrices based on a nearest neighbor relation.
transformation to correct for the high degree of skewness. House characteristics such as size, number of rooms, number of bathrooms, material of walls, roof, and floor, and alternative sources of water and electricity are also contained in the survey. Table 1 describes the variables included in the hedonic regressions and indicates when they are not available for both cities.

**Table 1: Description of Variables Used in Hedonic Models**

||_Dependent Variable_<br>|
|---|---|
|Lnrent|Log of estimated house rent|
||_House Characteristics_|
|Size|Size of house plot in sq. ft.|
|Number of Rooms|Number of rooms|
|Number of Bathrooms|Number of bathrooms|
|Floors|Indicator variable for floors of stone of better material|
|Walls|Indicator variable for walls of brick of better material|
|Roof|Indicator variable for Roof of Brick of better material|
|Kitchen|Kitchen inside the house|
|Electricity|Indicator for access to metered electricity|
|Toilet-Sewer|Indicator for toilet connected to sewer system|
||_Neighborhood Characteristics_|
|Women safe<sup>a</sup><br>|One if neighborhood feels safe for women, zero otherwise|
|Crime decr.<sup>b</sup>|One for crime decrease in last five years|
|Open Dump<sup>a</sup>|No open dump near house|
||<br>_Access to Water_|
|Water - DPW|Days per week water is available through direct connection|
|_Othe_<br>’|_r sources of Water: Indicator Variables_<br>’|
|Elses|Someone elses connection|
|Hand Pump|Individual Hand Pump Well|
|Tube Well|Individual Tube Well|
|Fountain|Public Fountain|
|Community Tube|Community Tube Well|
|Community Tap|Community Tap|
|Community Hand Pump|Community well/hand pump|
|Tanker|Tanker|
|Other|Other vendor|
|Rain|Rainwater harvesting|
|Surface|Surface water|
||_Ward Dummies_|
|Ward|Indicatorvariableforevery ward|
|Notes: (a) Bhopal only; (b)|Bangalore only.|
**Table 2  Bangalore: Descriptive Statistics**

|_Variable Name_|_Mean_|_Std. Dev_|_Min._|_Max._|
|---|---|---|---|---|
|House Rent|3085.398|3254.841|99|45000|
|Size|1100.871|873.5702|100|18000|
|Number of Rooms|4.554208|2.75|1|25|
|Number of Bathrooms|1.2565|0.7743|0|25|
|Floors|.98787|0.1094|0|1|
|Walls|0.9629|0.1863|0|1|
|Roof|0.8144|0.3888|0|1|
|Kitchen|0.9941|0.0764|0|1|
|Electricity|0.9889|0.1044|0|1|
|Toilet-Sewer|0.3605|0.4802|0|1|
|Crime decr.|0.2179|0.4129|0|1|
|Water - DPW|3.3399|2.1079|0|7|
|Hand Pump|0.0077|0.0875|0|1|
|Tube Well|0.1345|0.3412|0|1|
|Fountain|0.1907|0.3929|0|1|
|Community Tube|0.0606|0.2387|0|1|
|Tanker|0.0040|0.0634|0|1|
|Other|0.0102|0.1009|0|1|
|Surface|0.0025|0.0506|0|1|

**Table 3  Bhopal: Descriptive Statistics**

|_Variable Name_|_Mean_|_Std. Dev_|_Min._|_Max._|
|---|---|---|---|---|
|House Rent|1704.315|2706.4|50|50000|
|Size|760.2766|772.0118|70|8000|
|Number of Rooms|3.5526|2.7912|1|35|
|Number of Bathrooms|1.1343|0.5522|0|5|
|Floors|0.8703|0.3360|0|1|
|Walls|0.8114|0.3912|0|1|
|Roof|0.5354|0.4988|0|1|
|Kitchen|0.9901|0.0990|0|1|
|Electricity|0.7505|0.4328|0|1|
|Toilet-Sewer|0.1750|0.3800|0|1|
|Women safe|0.8713|0.3348|0|1|
|Open Dump|0.4859|0.4999|0|1|
|Water - DPW|3.1593|3.4391|0|7|
|Else’s|0.0375|0.1900|0|1|
|Hand Pump|0.0151|0.1219|0|1|
|Tube Well|0.0666|0.2495|0|1|
|Community Tube|0.0552|0.2284|0|1|
|Community Tap|0.3234|0.4679|0|1|
|Community Hand Pump|0.1093|0.3121|0|1|
|Tanker|0.0270|0.1623|0|1|
|Other|0.0010|0.0322|0|1|
|Rain|0.0005|0.0228|0|1|
|Surface|0.0020|0.0456|0|1|
# **V. Regression Results**

In both cities, we use the log of house rent as the dependent variable. For the main policy variable of interest, water availability, we use the number of days per week water is available in the house through a direct connection. The estimation results show the expected patterns in terms of signs and significance. For Bhopal, positive and very significant coefficients are observed for Size, Baths, Rooms, Floor, Walls, Roof, and Electricity (see Table AA1). Water availability measured through DPW is positive and significant. Among additional water sources different from an individual water connection, only the presence of a tube well has a negative and significant effect while the coefficient for Rain is positive and significant. Indicator variables are included for every Ward to account for neighborhood characteristics for which data are not available. Some of these variables remain significant even after introducing the spatial lag into the model. The coefficient estimated for the spatial lag is above 0.24 and very significant in all cases. The LM statistic for remaining spatial autocorrelation in the LAG model suggests the presence of remaining spatial autocorrelation of unspecified form. Therefore, following the approach suggested in Anselin and Lozano-Gracia (2007a), it is appropriate to use the Kelejian-Prucha Heteroskedasiticity and Autocorrelation Consistent estimator (HAC) (Kelejian and Prucha 2007). We employ three alternative kernels (epanechnikov, bisquare, and triangular) to further assess the robustness of our findings. We also compare the results to estimated standard errors that only correct for unspecified heteroskedasticity (White 1980). For the standard errors and confidence intervals using two standard deviations shown in Table AA1 we find that the largest changes in standard errors are seen when we go from classical to the White correction, with a much smaller effect for the spatial adjustment.

Estimates for Bangalore are shown in Table AA2. We observe a positive and very significant coefficient estimate for water availability measured through DPW. House characteristics have positive and significant effects as expected; the coefficient of number of bathrooms, however, loses its significance when going from the Classical to the HAC standard errors. The bathroom variable is significant at the 1% level when looking at the classical standard errors but only significant at 5% when moving to the more appropriate HAC standard errors. Other sources of water availability that show negative and significant results are fountain and community tube well. The coefficient for the spatial lag is also above 0.24 and very significant as is the case for Bhopal. The LM statistic for the lag model confirms the presence of remaining spatial
autocorrelation and heteroskedasticity suggesting the need to use the HAC estimator. The more realistic measure of standard errors provided by the HAC estimator is particularly important in assessing the precision of the derived welfare measures discussed in the following section.

# **VI. Marginal Willingness to Pay for Changes in Water Availability**

In this section we look at the valuation of water accessibility computed from the parameter estimates discussed in the previous sections. In a hedonic framework the MWTP is defined as the derivative of the hedonic price equilibrium equation with respect to the characteristic of interest, in this case access to water. In a non-spatial log-linear model, the MWTP equals the estimated coefficient for the water variable (DPW) times the price (P),<sup>6</sup> or where _g_ is DPW.

For the spatial lag model, the total effect consists of the direct effect and a spatial multiplier which is due to the fact that benefits from a household’s improved water access spill over to neighbors which, in turn, benefit the household.<sup>7</sup> This spatial multiplier effect needs to be accounted for to accurately compute the MWTP, as shown in Kim et al. (2003). For a uniform change across all observations, the multiplier effect is: with ρ<sup>ˆ</sup> , as the estimate of the spatial autoregressive coefficient. Small and Steimetz (2006) stress the need to separately estimate the direct effect in (1) and the multiplier effect included in (2). In their view, the multiplier effect should only be considered as part of the welfare calculation in the case of a technological externality associated with a change in amenities. In the case of a purely pecuniary externality, the direct effect is the only correct measure of welfare change.

> 6 We use the mean house rent in the sample to calculate the MWTP

> 7 In other words, each location is its neighbor’s neighbor, similar to the reflection problem in Manski (1993). This is a main difference to dependence in time series models which is uni-directional.
A strong argument in favor of using a spatial lag specification (where warranted by the data) is that it allows the two effects to be considered explicitly which clarifies the tradeoffs between spatial and non-spatial effects in a policy context. In Tables 4 and 5 we report the calculated MWTP for changes in DPW of water availability for the cities of Bangalore and Bhopal respectively. For the lag models, we include both the direct effect as well as the total effect. In addition to point estimates, we list a confidence band of +/ − two standard errors around the point estimate. In the non-spatial models and for the direct effect computation, the standard errors are those reported for the regression coefficients. In the spatial multiplier estimation, the standard error of β ˆ and ρ ˆ need to be accounted for jointly, which we implement by means of the delta method (see, e.g., Greene 2003, for further computational details).

We report the results for a queen spatial weights matrix and with standard errors based on the classic form, the White and the HAC formulation using an epanechnikov kernel<sup>8</sup> . MWTP are estimated for a change of one day per week. For both cities we see some difference between the OLS estimate and the result from the LAG model, with, in general, the LAG estimate being larger. For Bhopal, the OLS estimate would suggest a point estimate of INR 44 (Table 4). The LAG estimate on the other hand, gives an estimated MWTP of INR 54. For the case of Bangalore, MWTP values are reported in Table 5. The OLS estimated MWTP is INR 101 while the LAG model gives an estimate of INR 117. On average, households have access to water around 3 days per week in both cities. However, the distribution of water availability is quite different for Bhopal and Bangalore. While for Bhopal more than 80% of the households are concentrated on the tails of the distribution of water access, having either zero or seven days of water availability, in Bangalore 50% of the households have water available for 4 days in a week. From Tables 4 and 5 we see that for a similar change in water availability, on average, households in Bangalore are willing to pay almost twice as much as households in Bhopal. This is not surprising given that house rents are almost twice as much in Bangalore compared to Bhopal.

8 Results were consistent when using bisquare and triangle kernels.
**Table 4  Bhopal: Estimated MWTP and confidence intervals (INR)**

||_OLS_|_BHOPAL_<br>_LAG- Direct_|_LAG – With Multiplier_|
|---|---|---|---|
|MWTP – water (dpw)|44|41|54|
|Confidence Intervals||||
|Classic|13 - 69|14 - 69|19 - 90|
|White|13 - 70|14 - 70|19 - 90|
|HAC-epanechnikov|11 -72|12 -71|16-93|

**Table 5  Bangalore: Estimated MWTP and confidence intervals (INR)**

||_OLS_|_BANGALORE_<br>_LAG- Direct_|_LAG – With Multiplier_|
|---|---|---|---|
|MWTP – water (dpw)|101|89|117|
|Confidence Intervals||||
|Classic|48- 153|37 - 140|49 – 185|
|White|46 - 155|35 - 142|46 - 188|
|HAC-epanechnikov|41 - 160|33- 144|43- 191|

Since local public service provision was one of the main concerns in the two household surveys, the survey instrument also included a standard WTP questionnaire. Households were asked how much they would be willing to pay for improved water access using a stochastic payment card (e.g., Wang and Whittington 2005). Rather than presenting households with only one charge, this design starts with a very high charge which is then gradually reduced. At each step, the household is asked whether they would be willing to pay this charge with answers precoded as _definitely not_ , _probably not_ , _not sure_ , _probably yes_ , and _definitely yes_ . For Bangalore, the resulting point estimate of WTP for “definitely yes” is INR 119.62, while for Bhopal it is INR 45.14. For “probably yes” they are INR 170.12 and INR 119.34 respectively. This suggests a surprising degree of consistency between our estimated WTP and the survey responses. Although evidence from only two surveys is insufficient to draw general conclusions, the similarity of the two estimates lends credence to the hedonic estimation approach and also suggests that residents are able to quite accurately judge the value of water supply services.

# **VII. Simulations and Policy Analysis**

As an alternative to the traditional analytical derivation of marginal willingness to pay (MWTP) presented in the previous section, we also implement a simulation approach following a methodology similar to the one outlined in Anselin and Le Gallo (2006). The essence of the approach is that valuation is based on the computation of predicted values for individual observations given their actual household characteristics. Average valuation of a given policy
change is then obtained by adding the change in the predicted value relative to a benchmark and dividing by the total number of observations. A major advantage of the simulation approach is that it allows greater flexibility, both in the specification of the type of policy experiment (e.g., differential changes in water access) as well as in the valuation. Since the valuation is computed for individual house observations, the results can be obtained for any desired level of spatial aggregation, such as by ward. In essence this boils down to a discrete approximation to the notion ˆ of marginal willingness to pay. Given a vector of coefficient estimates β , the conditional expectation _E_ [ _p_ | _Z_ ] is obtained as

> since _E_ [ μ | _Z_ ] = 0 by assumption.

For the sake of simplicity, assume that interest is focused on attribute Zk and separate the matrix of observations and corresponding coefficient vector into Zk and the other variables, as Z = [ Z-k zk] and β = [β−k βk ]. The predicted value can then be decomposed into a part that does not change with the value of zk and a part that does:

> Consider the prediction _p_ ˆ 0 using the observed values for Z-k and zk. Now, consider a new vector of attributes z<sup>1</sup> k<sup>, reflecting a policy change, such as a given percentage increase in access to</sup> water. The new vector of predicted values follows as:

with the change in valuation as _p_ ˆ 0 − _p_ ˆ , or ( _z_ 1 _k_ − _zk_ ) β _k_ . Since this is a vector of observationspecific changes, it can be averaged over all observations or over any relevant spatial subset of observations.

The presence of a spatially lagged dependent variable in the hedonic equation complicates this 1 approach slightly. Instead of the simple difference, ( _zk_ − _zk_ ) β _k_ , the total effect is obtained as ( _I_ − ρ<sup>ˆ</sup> _W_ )<sup>−1</sup> ( _z_ 1 _k_ − _zk_ ) β _k_ , where ρ ˆ is the estimated spatial autoregressive coefficient and ( _I_ − ρ<sup>ˆ</sup> _W_ )<sup>−1</sup> is the inverse of a n × n matrix, of the same dimension as the data set. In large samples, a power approximation is used to avoid numerical problems. These procedures are implemented in the PySAL library of routines for spatial analysis (Rey and Anselin 2007). A
slight complication pertains to the application of this idea to a log-linear hedonic equation. As is well known, _E_ [ _p_ | _Z_ ] ≠ _e_<sup>_E_[ln</sup><sup>_p_|</sup><sup>_Z_]</sup> , but a bias correction needs to be applied to the exponentiated predicted value. As shown in Aitchinson and Brown (1957), the conditional expectation is a function of the variance. In our particular case, the conditional expectation would take the<sup>+(σ2 /2)</sup> form _E_ [ _p_ | _Z_ ] = _e_<sup>(</sup><sup>_I_−ρ</sup><sup>_W_)−1</sup><sup>_X_β</sup> , where σ<sup>2</sup> is approximated using its mean squared error estimate.

Approximate confidence intervals can be computed for the point estimates of the changed valuation in a number of ways. In the current application, we limit our attention to point estimates and use upper and lower bounds for the estimated coefficients to recompute the predicted value. Specifically, this is based on the estimate plus or minus two standard errors. As a starting point, we simulate a uniform change in water availability in the two cities, increasing it by one day for all households. The valuation from this simulation is comparable to the MWTP value obtained from the estimation of the hedonic model.

When considered relative to the mean DPW in each city, one day may constitute a non-marginal change, given that the average availability is around 3 days per week. Therefore, we refine the analysis by focusing on those households that do not attain the mean (DPW < 3). We assess both a uniform as well as a non-uniform change. First, we assess the impact of a 33% change (1 day on average) and a 10% change (around 7 additional hours on average) for those households. More interestingly, we consider non-uniform targeted policy interventions as well. Specifically, we assess a scenario where those same households are “moved up to” 3 DPW of water availability and a scenario where they are guaranteed one day a week of water through a direct connection.

The average valuation from simulating a uniform increase of 33% (one day on average) for the city of Bangalore is INR 196 which is somewhat higher than the MWTP obtained from the lag specification of the hedonic model (INR 117).<sup>9</sup> Similar changes in water availability are simulated for the city of Bhopal. A uniform increase of 33% (one DPW on average) in water access through a direct connection would lead to an average change on house rents of INR 98. For both cities, the total difference in value is divided by the number of observations to obtain the average changes in house rents reported in Table 6. Both Direct and Total (With Multiplier) changes are reported as it was done in the previous section for the MWTP estimates. Table 6 9 All simulations consider the constraint that access to water must be less than or equal to seven days.
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figure pertains to the simulation exercise where water availability is increased by 10% only for those households that currently have less than the mean water availability (3 DPW). Focusing only on the direct price effect, only those households with less than 3 days of water per week will face a change in their house prices (rents). More interestingly, if we also take into account the spatial spill-over effect and consider the multiplier changes in house prices as well, we observe not only that the change in house prices is much larger for all households below the mean water availability but also that all households (even those whose water access levels did not change) experience changes in their house values. Figure 2 shows similar results when comparing direct and total (with multiplier) effects of increasing to one DPW the availability of all households that currently have no water access through a direct connection in Bangalore. Figure 3 summarizes the changes in prices resulting from the three scenarios in water access change. It is interesting to note that in all cases we see that all households experience increased house values. The use of a spatial lag model allows us to observe the spill-over effects on house prices of a localized change in water availability that would otherwise be ignored in a traditional non-spatial specification.

For Bhopal the picture is very similar. Direct changes pertain only to the houses directly affected by the policy scenarios and therefore underestimate the effect on house prices over the entire city, as shown in Figures 4 and 5. Figure 6 shows the average changes for the three simulations for different levels of accessibility. For the city of Bhopal, it is interesting to see that for a nonuniform increase, households with higher levels of availability that are not directly facing the changes in water also experience higher house prices. Interestingly, the spillover effects seem to be higher for a policy that guarantees that everyone has at least one day a week of water. This may be a result of a general improvement of the conditions in the city by guaranteeing access.
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capitalization of improved water supply, we show that total benefits that include direct effects and neighborhood multipliers are considerably higher than estimates from non-spatial estimation. For Bangalore and Bhopal, the spatial estimates exceed standard MWTP estimates by 23 percent and 16 percent, respectively. Although we cannot isolate the specific underlying process by which neighbors’ quality of access affects each other, there are a number of possibilities. Generally, real estate markets tend to factor in neighborhood quality, so upgrading of a dwelling unit or maintenance of yards on a block has an effect on the value of all houses on the block. High quality water supply and sanitation also has considerable health benefits. One could thus interpret these neighborhood effects as specific health externalities as neighbors’ improved living conditions reduce the risk of communicable diseases. Beyond these more speculative conclusions, the policy implications of these results are clear. By looking at individual or private benefits only, we may underestimate the overall social welfare from investing in service supply especially among the poorest residents in developing country cities. In decision making under strict efficiency rules, this may lead to an underinvestment in critical infrastructure.

Besides presenting estimates of MWTP, we also report on a number of policy simulations that show how benefit estimates can be derived for each household on the basis of its actual (rather than mean) characteristics. The resulting information can be mapped geographically which informs prioritization and sequencing of investment decisions. This approach results in a flexible framework in which urban investment options can be evaluated. Using efficiency criteria, investments could be prioritized in areas where returns in the form of housing value increases (and thus user fee or tax increases) are highest. Introducing equity concerns would possibly alter the investment schedule to first target the poorest households where returns may be lower, but welfare benefits and positive health spillovers may be highest.

# **IX. References**

Aitchinson, J., and Brown, A.A. (1957). _The Lognormal Distribution_ . Cambridge: Cambridge University Press.

Anselin, L. (1988). _Spatial Econometrics: Methods and Models_ . Kluwer Academic Publishers, Dordrecht, The Netherlands.

Anselin, L. (2001). Rao’s score test in spatial econometrics. _Journal of Statistical Planning and_
_Inference_ , 97:113–139.

Anselin, L., Bera, A., Florax, R., and Yoon, M. (1996). Simple diagnostic tests for spatial dependence. _Regional Science and Urban Economics_ , 26:77 104.

- Anselin, L. and Le Gallo, J. (2006). Interpolation of air quality measures in hedonic house price models: spatial aspects. _Spatial Economic Analysis_ , 1:31– 52.

Anselin, L. and Lozano-Gracia, N. (2007a). Errors in variables and spatial effects in hedonic house price models of ambient air quality. _Empirical Economics_ (forthcoming).

Anselin, L. and Lozano-Gracia, N. (2007b). Exploratory spatial data analysis of the housing markets in Bhopal and Bangalore. mimeo. World Bank.

Baumont, C. (2004). Spatial effects in housing price models. Do housing prices capitalize urban development policies in the agglomeration of Dijon (1999)? Pole d’Economie et de Gestion, Université de Bourgogne Working Paper.

Beron, K.J., Hanson, Y., Murdoch, J.C. and Thayer, M.A. (2004). Hedonic price functions and spatial dependence: Implications for the demand for urban air quality. In Anselin, L., Florax, R.J., and Rey, S.J., editors, _Advances in Spatial Econometrics: Methodology, Tools and Applications,_ pages 267—281. Springer-Verlag, Berlin.

Crane, R., Daniere, A., and Harwood, S. (1997). The contribution of environmental amenities to low-income housing: a comparative study of Bangkok and Jakarta. Urban Studies, 34(9):1495–1512.

Deichmann, U., Lall, S.V., Suri, A., and Rajoria, P. (2003). Information-based instruments for improved urban management. In Policy Research Working Paper 3002. World Bank: Washington, D.C.

Earnhart, D. (2002), Combining Revealed and Stated Data to Examine Housing Decisions Using Discrete Choice Analysis, _Journal of Urban Economics_ , 51(1), 143-169.

- Florax, R.J.G.M, H. Folmer and S. Rey (2003). Specification Searches in Spatial Econometrics: The Relevance of Hendry’s Methodology. _Regional Science and Urban Economics_ 33, 557579.

- Follain, J.R. and Jimenez, E. (1985). The Demand for Housing Characteristics in Developing Countries. _Urban Studies_ , 15, 77-107

Greene, W. H. (2003). _Econometric Analysis_ , Fifth Edition. Prentice Hall, Upper Saddle River, NJ.

Ioannides, Y.M. (2002), Residential Neighborhood Effects, _Regional Science and Urban Economics_ . , 32(2):145--165.

- Kelejian, H. H. and Prucha, I. R. (2007). HAC estimation in a spatial framework. _Journal of Econometrics_ . 140(1), 131-154

- Kim, C. W., Phipps, T., and Anselin, L. (2003). Measuring the benefits of air quality improvement: a spatial hedonic approach. _Journal of Environmental Economics and Management_ , 45, 24–39.

- Knight, J. R., Herrin, W. E., and Balihuta, A. M. (2004). Housing prices and maturing real estate markets: Evidence from Uganda. _Journal of Real Estate Finance and Economics_ , 28(1), 5– 18.

- Lall, S. V. and Deichmann, U. (2006a), Fiscal and Distributional Implications of Property Tax Reforms in Indian Cities, _Economic and Political Weekly_ , July 22, 3209-3220.
- Lall, S. V. and Deichmann, U. (2006b). Household savings and residential mobility in informal settlements in Bhopal, India. _Urban Studies_ , 43(7):1025–1039.

- Lall, S. V., Deichmann, U., Lundberg, M. K., and Chaudhury, N. (2004). Tenure, diversity and commitment: Community participation for urban service provision. _The Journal of Development Studies_ , 40(3):1–26.

- Malpezzi, S. (2002). Hedonic pricing models: a selective and applied review. In Gibb, K. and O’Sullivan, A., editors, _Housing Economics: Essays in Honour of Duncan Maclennan_ .

- Manski, C. F.  (1993). Identification of Endogenous Social Effects: The Reflection Problem. _Review of Economic Studies_ . 60. (3): 531-542.

- North, J. and Griffin, C. (1993). Water source as a housing characteristic: Hedonic property valuation and willingness to pay for water. _Water Resources Research_ , 29(7):1923–1929.

- Oliveira, B. and De Morais, M. D. P. (2000) Demand for housing and urban services in Brazil: a hedonic approach. Paper Presented at the ENRH 2000 Conference in Gavle, Sweden.

- Pace, R. K. and J. LeSage (2004). Spatial econometrics and real estate. _Journal of Real Estate Finance and Economics_ 29, 147-148.

- Rey, S. and Anselin, L. (2007). Pysal, a Python library of spatial analytical methods. _The Review of Regional Studies_ , 37(1): 5–27.

- Small, K. A. and Steimetz, S. (2006). Spatial hedonics and the willingness to pay for residential amenities. Economics working paper no. 05–06–31, University of California, Irvine, CA.

- Wang H. and D. Whittington (2005), Measuring individuals' valuation distributions using a stochastic payment card approach, _Ecological Economics_ , 55, 143-154

- White, H. (1980). A heteroskedastic-consistent covariance matrix estimator and a direct test for heteroskedasticity. _Econometrica_ 48, 817-838.

- Whittington, D. (2002), Improving the performance of contingent valuation studies in developing countries, _Environmental and Resource Economics_ , 22:323-367.