USING BINARY CHOICE MODELS IN ESTIMATING WILLINGNESS TO PAY FOR IMPROVED WATER

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1 USING BINARY CHOICE MODELS IN ESTIMATING WILLINGNESS TO PAY FOR IMPROVED WATER FELIPE PEREZ-PINEDA INCAE Km 15.5 Carretera Sur, Montefresco Nicaragua address: Abstract: - A non-market evaluation technique the contingent valuation method- is used with a binary choice model to estimate the economic value that people in four semi-urban communities in El Salvador, place on improved water quality and sanitation. The findings suggest that the access to potable water and sanitation is a high priority for people living in these communities. In addition, the high willingness to pay for these improved services support the argument that medium-sized water supply projects in El Salvador are likely to be attractive for potential investors in that country. Key-Words: - Contingent valuation, water projects, El Salvador, willingness to pay, Binary Choice models, logit model 1 Introduction The ability to put a value on environmental resources has been a core problem in environmentally sustainable development in industrialized [1] and developing countries [2]. Contingent Valuation Methodology (CVM) requires that members of a given population are surveyed about their willingness to pay (WTP) for the provision of a non-market good, such as potable water. The initial applications of the contingent valuation method in developing countries were precisely in water supply and sanitation [3], [4], [5], [6], [7], [8]. Sustainable provision of water and sanitation depend on the extent to which consumer s preferences and willingness to pay are incorporated in the investment planning, and implementation process. In spite of the fact that CVM applications are growing in developing countries, there are none in El Salvador on addressing a today s very sensitive issue like valuing improved water supplies. Moreover, application of contingent valuation to a local environmental policy is internally valid by theoretically and empirically examining the economic determinants of responses to a hypothetical referendum [9]. In 1997, the population of El Salvador numbered more than 6 million inhabitants, 30% of which were concentrated in what is known as the Metropolitan Area or Grand San Salvador. A proportion of 45% of the population does not have access to safe water, [18] that makes El Salvador the country with the lowest coverage of potable water in Central America. The situation of sanitation looks even worse. A proportion of 31% of the population lack sanitation services. If latrines are not included in this count, the figure jumps to 70.6% [18]. From the institutional side, there is neither a public institution manager of the potable water sector in El Salvador nor there is a regulator of that resource. 2 An Empirical Model of Resource Values Natural resources and environmental attributes such as water quality are valuable assets in the sense that they yield flows of services to consumers. Public policies and the actions of individuals and firms can lead to changes in the flow of these services. Freeman [10] states that it is the failure of the market system to allocate and price resource and environmental services correctly that creates the need for economic measures of values to guide policy-making. Briscoe et al [5] propose a model that describes the probability that a particular family will choose to use a new water source. First, they

2 assumed that a family chooses between two sources (j = 1, 2) based in maximizing two conditional indirect utility functions. The first of these functions describes the utility gained from using the new water source (j = 1), and the second, describes the utility derived from the use of the current, old water source (j = 2). In each case, the utility, U, for a particular family, i, of a particular source depends on time and monetary costs of obtaining water from that source (C j ). Other variables that are defined in the model are the perceived quality of the water sources (V j ), household income, (Y i ), and a set of socioeconomic variables used as proxies for the families' preferences, (Z i ). Finally, and because the researcher does not observe all components of utility, an error term, (e ij ), is added to the utility function. The utility function for each household is thus: U ij = a o + a 1 C j + a 2 V j + a 3 Y i + a 4 Z i + eij (1) The probability that family i will decide to use the new rather than the old source is the probability that the conditional indirect utility function for the new source, U i1, is greater than the conditional indirect utility function for the old source, U i2. Now let's assume individuals have utility function u(x,q,z), where x is a vector of demands for different forms of water supply, q is a vector of water supply attributes like quality, reliability, accessibility, and other features, and Z is a composite of all market goods. The expenditure function, e(p,q,u), is found by solving the consumer problem: minimize Z + p'x subject to u = u(x,q,z) where p is a vector of access prices for different water supply alternatives and also assume the price of Z is equal to $1. The expenditure function measures the minimum amount of money a consumer must spend to achieve a fixed utility level and is increasing in p and u and decreasing in q. Willingness to pay is the maximum amount of money respondents would give up in order to enjoy an environmental quality change. In the random utility model an individual is assumed to compare his/her current utility level to the utility level that would be obtained after the improvement, and paying the specified monthly price. Consider the case of two different forms of water supply. Let's call q 1 water in its current supply form to the communities and q 2 water supplied through a potable water system, with all other resources suppressed. A formal definition of willingness to pay is: WTP 1 = e (p 1, p 2, q 1 o, q 2, u) - e (p 1, p 2, q 1 1, q 2, u) (2) Where q 1 o is the current (unsafe and expensive) level of water and q 1 ' represents an improvement in water supply. Expenditures to maintain the utility level decrease with an increase of the service quality q 1 o to q 1 ' so that WTP 1 0. In this framework, WTP 1 is a Hicksian measure of economic welfare. 2.1 Binary Choice Models and Dichotomous Dependent Variables CV researchers have developed dichotomous choice methods based on suggesting a possible cost of a change in the quality and/or quantity of an environmental good and observing the respondent's agreement or refusal to pay the offered amount to secure that change. The yes / no responses, the offered amounts and additional information about the respondents' characteristics are used to fit binary response models. The fitted models can then be used to trace out the distribution of the unobservable WTP variable and obtain estimates of welfare measures of interest (mean and medians WTP) that can change dramatically with the assumed distribution for WTP [11]. Often just two of the finite sets of alternatives are considered in a yes-no decision. In this class of models, the dependent variable, y, may take on only two values. Suppose that we model the probability of observing a value of one as: Pr(y i = 1 x i, β) = 1 - F(-x' i, β) Where F is continuos strictly increasing function that takes a real value and returns a value ranging from zero to one. It follows that: Pr(y i = 0 x i, β) = F(-x' i β)

3 We are typically interested in examining what factors affect the choice probability P i. It is thus assumed that the average utility derived from a choice by an individual is based on the attributes of the choice, which are specific to the individual, for example, the individual's socioeconomic characteristics. These individual characteristics do not vary across alternatives The Logit Model The Logit model lead to probabilities that are confined to the unit interval, unlike the linear probability model. The object of estimation in the model is the vector of unknown parameters β. We can estimate P i using the sample proportion of the occurrences that alternative one (connect to the system) was chosen and use this to facilitate the estimation of β. The logit model is based on the logistic c.d.f. given by: P i = F(x' i β) = 1/[1+exp (-x'iβ) ] Like the normal distribution, the logistic is also a symmetric distribution with zero mean (E{ε} = 0) and variance (var{ε} = σ 2 = π/3), but it has more probability on its tails [12]. The sample proportions are used to form the odd ratio p i /(1- p i ). ln(p i /1-p i ) ln(p i /1-p i ) + ε i /P i (1-P i ) = x' i β+ u i Once again, all T observations can be written as v = Xβ+ u, although v is now a vector of observed logits, that is, the natural logarithm of the observed odds ratio and the variance of u i is [1/(n i P i (1-P i ))]. 3 Research Design A three-stage stratified random sample procedure was used to select 500 households from the total population in four villages. The sample included two groups of households from two different sub-samples (N i, i = 1,2). The first and largest group was constituted by those households that owned or rented their houses on land which was not public property (N 1 = 2,665). The second group consisted of households that owned their home but did not have title of the land where their houses were built (N 2 = 400). To obtain 500 completed interviews, we assumed that 75% of the head of households of occupied dwellings would be successfully interviewed. Following this assumption, a random stratified sample of 667 dwellings was selected expecting to yield about 500 completed interviews. Only heads of family were eligible for the face to face interviews. Different questionnaires were designed for each of the two groups because the level of the service to be provided was different. The instruments also differed in the degree of detail of the general scenario as was to test for strategic bias [8]. 3.1 Data Collection and Empirical Results All the interviews were face-to-face in the respondent s homes and were done and closely supervised in the field during the first half of January Each interview lasted on average 45 minutes and all of them took place over the course of the same week. Respondents were asked if they were willing to join the project, paying a one-time connection fee prior to having access to potable water services and thereafter paying in monthly installments per barrel of water for the household private connection. Random prices were, as starting bid points, used in ascending or descending order depending upon the first response to the iterative bid format game. This format was used to minimize the possibility of starting point bias [14]. The bid points were selected based on values between the 20 th and the 85 th percentiles of the probability distributions obtained for the WTP bids in the pretest of the instrument. A total of five drafts of the questionnaires were revised before having the final version. A version of the questionnaire was pre-tested in December 1998 with a sample of 45 households (including those in focus groups). The total number of questionnaires returned as completed was 583 giving an overall response rate of 87.4%, 1 which is considered very high. 1 This response rate was higher than others reported in the literature. This was probably due to two factors: the presence of one member of the community with the enumerators who introduced them before starting an interview, and the nature of the

4 4 The Logistic Regression Analysis In the logistic regression equation, the probability for a household to connect to the new system can be written as: Where, Prob(connect) = 1/(1 + exp -z ) z = (BUYWMDS) (GENDER) (REMITT) (DEFMEAS) (INITBIDB) (WSADMCOM) (TLIVCOM) (NPHHWAGE) (PEOPLLHH) (STATE) (STORAGE) (WQUALMDS) (AWARENESS) Applying this equation to the mean values of the continuous variables, and values of 0 for the remaining indicator variables 2 : z = (5.63) (18.87) (1.47) (5.80) (1.71) z = For a household with the above characteristics, the probability of getting connected to the new system is then estimated to be: Prob(connect at INITBIDB) = 1/(1 + exp ) = = 79.1% Based in this estimate, our prediction would be that connection to the improved water system is very likely. 3 Likewise, the representative bid curve is obtained from setting the choice probability equal to one-half [15]. The Hicksian demand function can thus be recovered from the previous equation: problem we surveyed; a highly sensitive issue for the people in the four communities. 2 When these values are equal to 1, the probability of connecting to the new system decreases to In general, if the estimated probability of the event is less than 0.5, we predict that the event will not occur. If the probability is greater than 0.5, we predict that the event will occur. In the unlikely event that the probability is exactly 0.5, we can flip a coin for our prediction. E[WTP] = [ (BUYWMDS) (GENDER) (REMITT) (DEFMEAS) (WSADMCOM) (TLIVCOM) (NPHHWAGE) (PEOPLLHH) (STATE) (STORAGE) (WQUALMDS) (AWARENESS)]/0.509 Using this expression, the economic benefit of the new potable water system was calculated for each household in the sample, and these values were averaged to determine a mean household willingness to pay in colones per barrel [8]. Households living on railroad land (subsample RR) were willing to pay about 7.94 colones per barrel; households living in private land (subsample PCV) were willing to pay 8.06 colones per barrel. The mean WTP for the whole sample was 8.04 colones per barrel. 4.1 Testing Hypotheses about the Coefficients In our model, only the coefficient of INITBIDB appear to be significantly different from zero, using a significance level of NHHWAGE, and WSADMCOM appear to be significantly different from zero, using a significance level of The coefficients of REMITT, PEOPLLHH, and BUYWMDS appear to be significantly different from zero using a significance level of AWARENESS is not significant at any of these levels however it is close to the 15% level of significance (17.82%). Only INITBIDB had a great partial contribution to the model. All the other variables had medium and small partial contributions. As INITBIDB increases in value, so does not the likelihood of the event (hookup) occurring. 4.2 Accuracy of CVM Estimates In all of the models the intercept indicates a strong WTP independent of respondent, household, and traditional water source characteristics. The intercept in the logit model represented 57.16% of the mean WTP calculated as the mean final price to which the respondent answered ``yes'' [8]. Household characteristics generally considered significant determinants of WTP were also in this study. The sign of their coefficients also leaned in the expected direction. For example, higher household

5 income (REMITT) increases the probability of connection to the new water system, larger household number of member earning a wage (NPHHWAGE) improves the chances of hookup to the new project, and the positive sign of the coefficient may reflect higher earnings. In addition, traditional water source characteristics are counted among group of variables, which influence the probability of connection to the improved water system. Three variables were included to identify bias and randomness in the responses. AWARENESS to control for hypothetical bias, STATE to measure strategic behavior, 4 and INTQLTY to control for randomness. None of these variables were significant at the 1%, 5%, and 10% levels of significance. 4.3 Testing for Strategic, Starting Point, and Hypothetical Biases It was only found evidence of starting point bias. This finding only reinforced our decision of just using the first bid of the sequential bidding game in our WTP estimations. 5 In testing for starting point bias, we found a linear relation between starting bids and the final bids [16]. The coefficient on the starting bid was significantly different from zero at the 99% level of confidence, indicating the presence of starting point bias. This type of bias have subtle but significant effects on observed final bids. [17] Comparing average WTP in both subpopulations (PCV and RR) also tested the presence of strategic bias. There were no significant differences between them at the 99% level of confidence, therefore we could not reject the null hypothesis that both means were equal. This test [8] suggests that strategic bias was not present in our estimations. 4 In the version PCV of the questionnaire, in section B ``The New Potable Water System in the Community,'' the respondent was informed that the tariffs in the new system would be decided by a local water association elected by the community. This same section in version RR of the questionnaire did not contain this type of information transmitting the respondent a sense that the implementation of the project was still uncertain. 5 In addition we estimated the distributions of the first bid (Rayleigh) and the last bid (Weibull) meaning that in fact in our data exists a significant difference between the WTP distributions implied by initial and follow up question responses. Starting point bias might be an explanation for such a difference. Finally, for hypothetical bias we took the average WTP of those respondents who answered they were aware of the existence of other water systems in the country against those who said the opposite (AWARENESS). We could not find significant differences between both means at the 99% level of confidence. This suggests that hypothetical bias was not present in our estimations. 6 Conclusions The careful design and conduct of this survey needed to be emphasized. This meant several months working at the project site, observing current household practices for supplying water, interviewing individuals in the communities, working with focus groups, and pre-testing and adapting the survey instrument to the local circumstances. Of equal importance was the meticulous training and supervision of the interviewers, and the careful ``cleaning'' of the data. As a percentage of household income, the stated maximum household's WTP might be equivalent to monthly water expenditure for an average family, of about 20% and 34% of its mean monthly income. These figures look plausible if we compare them with what people are currently spending in water supplies. 6 Household income was a statistically significant determinant of household willingness to pay for potable water. 7 The econometric analysis shows that the major determinants of willingness to pay for improved water were household income, the cost to users, satisfaction with existing water supply options, and the desire for operating the improved system by the community itself. The findings also suggest that potable water supply is a high priority for residents of the four villages, the main concern of which is for water convenience, 6 People in the four villages are currently spending about 300 colones per month per household, or 21% of their HH income. Considering the payment to third parties for carrying water, the monthly expenditures was colones per household. Moreover, considering the opportunity cost of the time spent in carrying water, our estimate was approximately 900 colones per month or 65% of a family monthly income. These figures give us some idea of the order of magnitude of the current cost of water supplies in the site of study. 7 This was in fact the case, using a set of dummy variables as ``proxy'' for household income.

6 reliability, and quality. Even though the specificity of the conclusions of this study need to be recognized, we claim that these results could be applicable to other water projects in El Salvador, given the more or less homogeneous socioeconomic set of characteristics to be found in a very small country like this. References: [1] Carson, R & Mitchell, R. (1993). The value of clean water: The public s willingness to pay for boatable, fishable, and swimmable quality water. Water Resources Research, 29:7: [2] Seragelding, I. & Steer, A. EDITORS (1994). Valuing the environment. Technical report, The World Bank, Washington, DC. [3] Whittington, D. & Mu, X. (1990). Estimating the willingness to pay for water services in developing countries: A case study of the use of contingent valuation surveys in southern Haiti. Economic Development and Cultural Change, 38(2): [4] Whittington, D., Lauria, D., & Choe, K. (1996). Households willingness to pay for improved sanitation services in Davao, Philippines. Technical report, The World Bank. A Report to the World Bank. CVM, Inc. [5] Briscoe, J., Furtado de Castro, P., Griffin, C., North, J. & Olsen, O. (1990). Toward equitable and sustainable rural water supplies: A contingent valuation study in Brazil. The International Bank for Reconstruction and Development. The World Bank. [6] Singh, B., Ramasubban, R., Bhatia, R., Briscoe, J., Griffin, C., & Kim, C. (1993). Rural water supply in Kerala, India: How to emerge from a low-level equilibrium trap. Water Resources Research, 29: [7] McPhail, A. (1994). Why don t households connect to the piped water systems? Observations from Tunis, Tunisia. Land Economics, 70(2): [8] Choe, K., Whittington, D. & Lauria, D. (1996). The economic benefits of surface water quality improvements in developing countries: A case study of Davao, Philippines. Land Economics, 72:4: [9] Danielson, L., Hoban, T., Van Houtven, G. & Whitehead, J. (1995). Measuring the benefits of local public goods: Environmental quality in Gaston county, North Carolina. Applied Economics, 27:12: [10] Freeman.III, A. (1993). The measurement of environmental and resource values. Theory and methods. Resources for the future, Washington DC. [11] Alberini, Anna. Testing Willingness to Pay Models of Discrete Choice Contingent Valuation Survey Data. Land Economics, February, [12] Nelson, Wayne. Applied Life Data Analysis. John Wiley and Sons, [13] Kennedy, Peter. Elements of Econometrics. The MIT Press, Cambridge, Massachusetts, 3 rd edition, [14] Whittington, D., Smith, V., Okafor, A., Okore, A., Liu, J., & McPhail, A. (1998). Administering contingent valuation surveys in developing countries. Elsevier Science Ltd. [15] Loehman, E. & Hu De, V. (1982). Application of stochastic choice modeling to policy analysis of public goods: A case study of air quality improvements. The Review of Economics and Statistics. Pages [16] Boyle, K., Bishop, R. & Welsh, M. (1985). Starting point bias in contingent valuation bidding games. Land Economics, 61: [17] Samples, K. (1985). A note on the existence of starting point bias in iterative bidding games. Western Journal of Agricultural Economics, 10 (1): [18] Dirección General de Estadística y Censos, El Salvador. Anuario Estadístico Octubre 1966.