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 at individual or private benefits only, the analysis may
growing cities in developing countries is how to raise underestimate the overall social welfare from investing in
fiscal revenues to finance basic services in a fair and service supply especially among the poorest residents. The
efficient manner. This paper applies hedonic analysis that paper further demonstrates how policy simulations based
explicitly accounts for spatial spillovers to derive the value on these estimates help prioritize spatial targeting of
of improved access to water in the Indian cities of Bhopal interventions according to efficiency and equity criteria.
and Bangalore. The findings suggest that by looking
This paper--a product of the Sustainable Rural and Urban DevelopmentTeam, 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*
Luc Anselin1, Nancy Lozano-Gracia2, Uwe Deichmann3 and Somik Lall4
*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.
1School of Geographical Analysis and GeoDa Center for Geospatial Analysis and Computation, Arizona
State University.
2GeoDa Center for Geospatial Analysis and Computation, Arizona State University.
3Development Research Group, World Bank.
4Finance, 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=(z1,...,zn) 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:
p = Wp + X + u
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, is a k ×1vector of regression
coefficients, 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).5 It should be noted that since the house locations constitute a sample, the
5For 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
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 a One if neighborhood feels safe for women, zero otherwise
Crime decr. b One for crime decrease in last five years
Open Dump a No open dump near house
Access to Water
Water - DPW Days per week water is available through direct connection
Other sources of Water: Indicator Variables
Else's Someone else's 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 Indicator variable for every 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), or 6
MWTPg = p = ^p, (1)
g
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.7 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:
MWTPg = p 1
(2)
g = ^p1 - ^,
with , 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.
6We use the mean house rent in the sample to calculate the MWTP
7In 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 and 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 kernel8. 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.
8Results were consistent when using bisquare and triangle kernels.
Table 4 Bhopal: Estimated MWTP and confidence intervals (INR)
BHOPAL
OLS 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)
BANGALORE
OLS 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
of marginal willingness to pay. Given a vector of coefficient estimates , the conditional
^
expectation E[p | Z] is obtained as
E[p | Z] = p^ = Z^ (3)
since E[ | 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 = [- k ]. The predicted value can then be decomposed into a part that does not
k
change with the value of zk and a part that does:
p^ = Z-k-k + zkk = p^-k + zkk. (4)
Consider the prediction p^0 using the observed values for Z-k and zk. Now, consider a new vector
of attributes z1k , reflecting a policy change, such as a given percentage increase in access to
water. The new vector of predicted values follows as:
p^1 = p^-k + z1kk , (5)
with the change in valuation as p^0 - p^ , or (z1k - zk )k . Since this is a vector of observation-
specific 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
approach slightly. Instead of the simple difference, (z1k - zk )k , the total effect is obtained as
(I - ^W )-1(z1k - zk )k , where ^ is the estimated spatial autoregressive coefficient and
(I - ^W )-1 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] eE[ln p|Z] , 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
form E[ p | Z] = e(I -W )-1 X + (2 /2), where 2 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).9 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
9All simulations consider the constraint that access to water must be less than or equal to seven days.
shows the differences in the average changes in house prices if we ignore the multiplier effect.
Numbers in parenthesis give the lower and upper bounds for a confidence interval created using
two standard deviations from the estimated coefficients.
Table 6: Policy Simulations: Mean Change in House Rents (INR)
Bangalore Bhopal
Policy Intervention Simulated
Direct With Multiplier Direct With Multiplier
Uniform Increase of 33% 20.98 196.36 13.20 97.64
(7.1337.57) (25.42-1202.7) (3.04-26.29) (10.97-504.1)
Increase of 33% for <3 DPW 2.50 22.23 0.76 5.89
(0.89 4.28) (3.09 125.75) (0.2-1.34) (0.70-27.41)
Increase of 10% for <3 DPW 0.75 6.68 0.23 1.78
(0.27 1.28) (0.93 37.59) (0.06-0.40) (0.21-8.25)
Increase to 3 all with <3 DPW 5.28 47.61 6.01 46.40
(1.92 5.28) (6.72 264.5) (1.54-10.72) (5.45-219.22)
Increase to 1 all with <1 DPW 1.67 15.12 1.94 15.01
(0.62 2.74) (2.17 82.71) (0.51-3.40) (1.79-69.71)
Figure 1: Bangalore: Direct vs. Total (With Multiplier) effects for an increase of 10% in water
availability (days per week, DPW) for all households with less than 3 days per week 10
10C10%_3 shows for the total effect while the dotted line labeled C10%_3d shows the direct effect that
ignores the multiplier from the spatial model.
Figure 2: Bangalore: Direct vs. Total (With Multiplier) effects for increasing water availability (days
per week) to one day for all households with less or no access. 11
Figure 3: Bangalore: Direct effects from three alternative policy changes (see text).
We also consider the average changes for different levels of water accessibility. Figure 1 shows
the average change in house prices by levels of water availability for a non-uniform change. This
11C1_1 shows for the total effect while the dotted line labeled C1_1d shows the direct effect that ignores
the multiplier from the spatial model.
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 non-
uniform 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.
Figure 4: Bhopal: Direct vs. Total (With Multiplier) effects for an Increase of 10% in water
availability (days per week) for all households with less than 3 days per week. 12
Figure 5: Bhopal: Direct vs. Total (With Multiplier) effects for increasing water availability (days per
week) to one day for all households with no access. 13
12C10%_3 shows the total (with multiplier) effect while the dotted line labeled C10%_3d shows the direct
effect that ignores the multiplier from the spatial model.
13C1_1 shows the total effect while the dotted line labeled C1_1d shows the direct effect that ignores the
multiplier from the spatial model.
Figure 6: Bhopal: Direct Effects from three alternative policy changes. 33% and 10% increases for
households with less than 3 days per week and bringing availability to at least 3 days per week.
Finally, we consider the spatial distribution of the impacts by computing an estimate for the
average change by ward. This is obtained by taking the average change in value for all the houses
in the sample that are located in a given ward. This allows for an assessment of the spatial
distribution of the impact of the policy change. Figures 7 through 10 summarize this for the cities
of Bhopal and Bangalore. The spatial distribution of the average changes is very different from
one policy to the other in both cities.
To illustrate this point, we illustrate the case of Bangalore. For a 10% increase in water access for
those households below the mean level, in Bangalore the highest average changes (dark red) are
observed for the ward of Kodandaramapura in the North and Hanumanthanagara in the South-
West of the city. For the policy to increase the availability to one day per week for the same
households, the highest change in average house rents (dark red) are observed in five Eastern
wards: Kaval Bairasandra, Banasavadi, Benniganahalli, Lingarajapura and Sir C.V.
Ramannagara.
Figure 7: Bangalore: Average Change in Water Availability by Ward (10% Increase for all
households with less than 3 DPW)
Figure 8: Bangalore: Average Change in Water Availability by Ward (all households with less 1
DPW are guaranteed 1DPW)
Figure 9: Bhopal: Average Change in Water Availability by Ward (10% Increase for all households
with less than 3 DPW)
Figure 10: Bhopal: Average Change in Water Availability by Ward (all households with less 1 DPW
are guaranteed 1DPW)
VIII. Conclusions
This paper presents a spatially explicit approach to estimating willingness to pay for water supply
in two Indian cities. By incorporating neighborhood effects in spatial hedonic estimates of the
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.
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APPENDIX
Table AA 1: Estimates hedonic price (rent) equation, Bhopal
BHOPAL
OLS LAG
VARIABLES
WATER DPW 0.0257 0.0242
Classic (0.0083) * (0.0082) *
White (0.0083) * (0.0082) *
HAC-ep (0.0092) * (0.0089) *
W_RENT ---- 0.2421
Classic ---- (0.0390) *
White ---- (0.0366) *
HAC-ep ---- (0.0380) *
SIZE 0.0002 0.0002
Classic (0.0000) * (0.0000) *
White (0.0000) * (0.0000) *
HAC-ep (0.0000) * (0.0000) *
ROOMS 0.0529 0.0542
Classic (0.0069) * (0.0068) *
White (0.0088) * (0.0088) *
HAC-ep (0.0090) * (0.0088) *
BATHROOMS 0.2786 0.2637
Classic (0.0301) * (0.0299) *
White (0.0336) * (0.0329) *
HAC-ep (0.0354) * (0.0336) *
FLOOR 0.2488 0.2339
Classic (0.0538) * (0.0533) *
White (0.0451) * (0.0445) *
HAC-ep (0.0480) * (0.0461) *
WALLS 0.1377 0.1197
Classic (0.0507) * (0.0503) **
White (0.0455) * (0.0446) **
HAC-ep (0.0486) * (0.0478) **
ROOF 0.4517 0.4145
Classic (0.0415) * (0.0415) *
White (0.0425) * (0.0423) *
HAC-ep (0.0455) * (0.0439) *
KITCHEN 0.1366 0.1656
Classic (0.1523) (0.1509)
White (0.1272) (0.1199)
HAC-ep (0.1288) (0.1201)
WOMEN SAFE -0.0049 -0.0164
Classic (0.0449) * (0.0445)
White (0.0415) * (0.0418)
HAC-ep (0.0465) * (0.0461)
ELECTRICITY 0.1772 0.1649
Classic (0.0433) * (0.0429) *
White (0.0415) * (0.0408) *
HAC-ep (0.0446) * (0.0425) *
NO DUMP 0.0366 0.0282
Classic (0.0339) * (0.0336)
White (0.0330) * (0.0330)
HAC-ep (0.0322) * (0.0318)
TOILET-SEWER 0.1417 0.0963
Classic (0.0472) * (0.0473) **
White (0.0459) * (0.0462) **
HAC-ep (0.0555) ** (0.0534)
ELSE 0.0574 0.0295
Classic (0.0866) (0.0859)
White (0.0946) (0.0941)
HAC-ep (0.0926) (0.0918)
HAND PUMP 0.1034 0.0662
Classic (0.1283) (0.1272)
White (0.1191) (0.1221)
HAC-ep (0.1233) (0.1284)
TUBE WELL 0.1764 0.1801
Classic (0.0688) ** (0.0681)
White (0.0694) ** (0.0693) **
HAC-ep (0.0719) ** (0.0721) **
COMMON TUBE WELL 0.0117 -0.0034
Classic (0.0733) (0.0726)
White (0.0724) (0.0722)
HAC-ep (0.0848) (0.0832)
COMMON TAP -0.0760 -0.0549
Classic (0.0536) (0.0532)
White (0.0543) (0.0539)
HAC-ep (0.0592) (0.0585)
COMMON HAND PUMP -0.1266 -0.0968
Classic (0.0598) ** (0.0594)
White (0.0565) ** (0.0562)
HAC-ep (0.0615) ** (0.0592)
TANKER -0.0414 -0.0408
Classic (0.0988) (0.0979)
White (0.1096) (0.1074)
HAC-ep (0.1141) (0.1060)
OTHER -0.1409 -0.2070
Classic (0.4654) (0.4611)
White (0.4054) (0.4347)
HAC-ep (0.4507) (0.4715)
RAIN 0.8814 1.1967
Classic (0.6558) (0.6514)
White (0.1598) (0.1649)
HAC-ep (0.1579) (0.1682)
SURFACE -0.2928 -0.4021
Classic (0.3315) (0.3287)
White (0.1201) (0.1649)
HAC-ep (0.1401) (0.1831)
BOTTLED -0.1118 -0.0144
Classic (0.3257) (0.3229)
White (0.2065) (0.2142)
HAC-ep (0.1998) (0.2063)
CONSTANT 5.2237 3.6260
Classic (0.1917) * (0.3199) *
White (0.1671) * (0.2913) *
HAC-ep (0.1872) * (0.2927) *
R-squared (var ratio) 0.6438 0.6517
STATISTIC p-value
LM-Err 6.818 0.009
LM-Lag 31.56 0.000
Robust LM-Err 4.52 0.033
Robust LM-Lag 29.27 0.000
Anselin Keleijian 7.37 0.006
* Significant only at 1% ** Significant only at 5%
Table AA2: Estimates hedonic price (rent) equation, Bangalore
BANGALORE
OLS LAG
VARIABLES
WATER DPW 0.0326 0.0287
Classic (0.0084)* (0.0083)*
White (0.0088)* (0.0086)*
HAC-ep (0.0096)* (0.0090)*
W_RENT --- 0.2429
Classic --- (0.0368)*
White --- (0.0396)*
HAC-ep --- (0.0439)*
SIZE 0.000 0.0001
Classic (0.0000)* (0.0000)*
White (0.0000)* (0.0000)*
HAC-ep (0.0000)* (0.0000)*
ROOMS 0.0438 0.0444
Classic (0.0054)* (0.0053)
White (0.0070)* (0.0068)*
HAC-ep (0.0079)* (0.0076)*
BATHROOMS 0.1782 0.1667
Classic (0.0180) (0.0178)
White (0.0806) ** (0.0770) **
HAC-ep (0.0830) ** (0.0792) **
FLOOR -0.1462 -0.1544
Classic (0.1166) (0.1150)
White (0.1607) (0.1544)
HAC-ep (0.1568) (0.1501)
WALLS 0.3217 0.2964
Classic (0.0731) (0.0722)
White (0.0772) (0.0759)
HAC-ep (0.0846) (0.0826)
ROOF 0.5638 0.5371
Classic (0.0375) (0.0372)
White (0.0424) (0.0416)
HAC-ep (0.0446) (0.0421)
KITCHEN -0.0304 0.0489
Classic (0.1587) (0.1569)
White (0.1771) (0.1779)
HAC-ep (0.1814) (0.1825)
CRIME DECR. -0.0359 -0.0421
Classic (0.0304) (0.0300)
White (0.0300) (0.0293)
HAC-ep (0.0332) (0.0316)
ELECTRICITY 0.6420 0.6357
Classic (0.1197)* (0.1180)*
White (0.1286)* (0.1253)*
HAC-ep (0.1496)* (0.1391)*
TOILET-SEWER 0.2516 0.2293
Classic (0.0297)* (0.0294)*
White (0.0316)* (0.0308)*
HAC-ep (0.0357)* (0.0342)*
TUBE WELL 0.0784 0.0737
Classic (0.0403) ** (0.0397) **
White (0.0407) ** (0.0396) **
HAC-ep (0.0426) ** (0.0409) **
TANKER 0.1876 0.2120
Classic (0.1944) (0.1917)
White (0.1126) (0.1285)
HAC-ep (0.1151) (0.1338)
OTHER -0.1360 -0.0365
Classic (0.1299) (0.1290)
White (0.1502) (0.1533)
HAC-ep (0.2007) (0.1867)
SURFACE 0.3951 0.4147
Classic (0.2398) (0.2364)
White (0.1431) (0.1342) **
HAC-ep (0.1416) (0.1295)
FOUNTAIN -0.2775 -0.2638
Classic (0.0448)* (0.0442)*
White (0.0471)* (0.0465)*
HAC-ep (0.0505)* (0.0487)*
COMMON TUBE -0.3279 -0.3182
Classic (0.0557)* (0.0549)*
White (0.0664)* (0.0661)*
HAC-ep (0.0757)* (0.0740)*
CONSTANT 6.0573 4.1224
Classic (0.2515)* (0.3842)*
White (0.2813)* (0.4069)*
HAC-ep (0.2998)* (0.4586)*
R-squared (var ratio) 0.5620 0.5687
STATISTIC p-value
LM-Err 37.94 0.000
LM-Lag 82.02 0.000
Robust LM-Err 2.32 0.127
Robust LM-Lag 46.40 0.000
Anselin Keleijian 3.84 0.05
* Significant only at 1% ** Significant only at 5%