Introduction

In the field of public policies assessment, the contingent valuation model (CVM) is a useful tool to estimate changes in the welfare of people. When these changes involve improvements, it is possible to estimate the potential economic benefits, in order to justify the costs associated with the implementation of the said policies (^{Uribe et al., 2003}). The quantitative evidence of the potential benefits of public policies enables a cost-benefit analysis which, in turn, justifies the viability of the said policies. In developing countries, domestic, regional, and local government must prioritize policies or projects according to their typology. In the sanitation sector, evaluating the viability of comprehensive projects is relevant; those projects cover basic services (water, sewers, and wastewater treatment). Currently, the management of basic sanitation services is a high-priority public policy in Peru; therefore, the public investment committed for this purpose is high: approximately US$1.018 billion (^{CVMS, 2017}).

The City of Puno, located in southwestern Peru, is not unaffected by this problem and 61.63 % of its population has less than 12 continuous hours of drinking water supply; the daily average is 7.03 h and, in some areas of the city (particularly in the high areas), it barely lasts 1 h. Additionally, the harvesting system network and “El espinar” treatment plant have problems, mainly due to their old infrastructure, which has completely collapsed and a great amount of wastewater is dumped into the inner bay of Lake Titicaca, a natural area with high diversity and international relevance.

In order to find a solution for this situation, the Provincial Municipality of Puno, the Basic Sanitation Company of the Municipality (EMSAPUNO), and the Ministry of Housing, Construction, and Sanitation of Peru have worked together to materialize investments and to improve basic services. The concept of benefit is interpreted in a very particular way: the basic idea is that “what people want” (what individuals prefer) must be the basis of the benefits measure. Through direct surveys, the CVM determines the mean value of the willingness to pay (WTP), as an approximate measure of the compensating variation of a specific population; this matches an approximation of the benefits generated by public policies or projects (^{Pearce and Turner, 1995}; ^{Just et al., 2004}; ^{Tudela-Mamani, 2007}; ^{Freeman et al., 2014}).

Two types of formats are used to estimate the WTP for the improvement of the access to public services: referendum and double-bounded. The referendum format points out the usefulness of the CVM in the estimation of the WTP for the improvement of public services; the main variables for the calculation are socioeconomic: education and income (^{Del Saz et al., 2009}; ^{Valdivia et al., 2011}; ^{Arias et al., 2011}; ^{Awad, 2012}; ^{Awanyo et al., 2013}; ^{Pérez and Quintanilla, 2013}; ^{Lu et al., 2015}). The double-bounded format has higher statistical efficiency than the referendum model: the parameters of the former have a higher individual and joint significance (^{Bogale and Urgessa, 2012}; ^{Dupont, 2013}; ^{Guzmán, 2015}; ^{Tudela, 2017}). The said studies specifically posed the problem of accessing improved public services. However, in our research, the basic sanitation problem is dealt in a comprehensive manner.

The objective of this research was to estimate the economic benefits of the WTP, through a referendum and double-bounded formats, with regard to the improvement of basic sanitation services (water, sewer, and wastewater treatment) in the city of Puno. The estimation of the economic benefits that could be gained from the implementation of the improvements requires the inclusion of the users’ socioeconomic variables (such as income, education level, children in the household, age, and the degree of individual awareness of the problems in the basic sanitation services).

Materials and Methods

For a population of 30 945 households connected to the water and sewer systems, a 400-household sample size was determined -based on the simple random sampling method. However, after a verification and cross-checking process was carried out, 8 surveys were rejected due to their inconsistent information. The final sample was made of 392 households randomly chosen from three areas of the city: center (24 %), south (37 %), and north (39 %). The surveys were applied to the heads of the households (who have the spending power). All the surveys were carried out during two weekends, in January, 2017, by students of the Facultad de Ingeniería Económica of the Universidad Nacional del Altiplano-Perú, in the city of Puno. In order to verify the efficiency and the relevance, and to validate the survey format, a pilot survey was carried out with 30 randomly selected heads of households. As a result of this test, the minimum and maximum rates were identified and some questions were dismissed. The final survey format had 17 questions.

Double-bounded model for willingness to pay

The capacity of the referendum-style CVM to deliver reliable and precise WTP estimates is questioned. In order to diminish this inefficiency, ^{Hanemann et al. (1991)} suggested using a double dichotomous format (double-bounded), which adds a second question about the willingness to pay which also has a dichotomous nature (^{Tudela-Mamani, 2017}).

According to ^{Hanemann et al. (1991}; quoted by ^{Tudela-Mamani, 2017}), within the context of a double question about the willingness to pay, interviewees are asked the initial question (BI) again based on their first answer (BU: the second price proposed after a positive answer; BD: the second price proposed after a negative answer). Figure 1 illustrates how choices are made when the double-bounded format is used.

Source: ^{Tudela-Mamani, 2017}.

Figure 1 Dichotomous choice process in a double-bounded format. 

According to ^{Hanemann et al. (1991)} and ^{Habb and McConnell (2002)}, probability-wise answers can be set forth as follows:

Pryes,yes=1-Fβ'xiu

Pryes,no=Fβ'xiu-Fβ'xi

Prno,yes=Fβ'xi-Fβ'xid

Prno,no=Fβ'xid

For the double-bounded case, the function of the likelihood logarithm (log-likelihood) is given by:

LL=∑i=1ndissln⁡1-11+exp-(β'xiu+disnln⁡11+exp-β'xiu-11+exp-β'xi+dinsln⁡11+exp-β'xi-11+exp-β'xid+dinnln⁡11+exp-β'xid

where diss, disn, dins and dinn are binary variables derived from the YES-YES, YES-NO, NO-YES, and NO-NO answers, respectively. They have a value of 1 when the interviewee’s answer is found in this position and 0, otherwise. This function is maximized -using the parameters as decision variables- in order to find out the maximum likelihood estimator.

According to ^{Hanemann et al. (1991}; quoted by ^{Cerda et al., 2007)}, the double dichotomous model increases the accuracy of the variance-covariance matrix of the estimated coefficient, creating narrower confidence intervals with regard to the simple dichotomous model. Additionally, they found out that the accurate estimator of the WTP median of the dichotomous model is lower.

^{Tudela (2017)} proved that the double-bounded format has greater theoretical consistency, as a result of the greater individual and joint significance of the parameters. According to ^{Bateman et al. (2001)}, the contingent valuation questions (referendum type) with dichotomous choices are relatively inefficient for big samples.

Once the parameters estimates were obtained, the monetary measure of welfare was calculated; the formula to estimate the WTP will depend on the functional form of the utility change (Δv), which can be linear or a logarithm. The detail and identification of the variables that enabled the estimation of the logit econometric model for the referendum and double-bounded model is shown in Table 1.

Table 1 Description of the variables used for the analysis. 

Variable	Descripción	Opciones de respuesta
PSI	Probabilidad de responder SI a la pregunta de disponibilidad a pagar	1=Si la respuesta en la primera ronda es SI; 0=Si responde negativamente.
BI	Precio hipotético inicial	2, 4, 6, 8, 10.
BD	Precio hipotético menor	1, 2, 4, 6, 8.
BU	Precio hipotético mayor	4, 6, 8, 10, 12.
DSS	Variable dummy para SI-SI	Si la respuesta en la primera ronda fue SI: 1=si la respuesta en la segunda ronda es SI; 0=en otro caso
DSN	Variable dummy para SI-NO	Si la respuesta en la primera ronda fue SI: 1=si la respuesta en la segunda ronda es NO; 0=en otro caso
DNS	Variable dummy para NO-SI	Si la respuesta en la primera ronda fue NO: 1=si la respuesta en la segunda ronda es SI; 0=en otro caso
DNN	Variable dummy para NO-NO	Si la respuesta en la primera ronda fue NO: 1=si la respuesta en la segunda ronda es NO; 0=en otro caso
GEN	Género del encuestado	Hombre=1; Mujer=0
EDA	Edad del encuestado	Número entero
HIJO	Presencia de menores edad	Número entero
EDU	Nivel de educación	1=Sin educación formal, 2=Primaria incompleta, 3= Primaria completa, 4=Secundaria incompleta, 5=Secundaria completa, 6=Superior técnica, 7=Superior pedagógica, 8=Universitaria incompleta, 9=Universitaria completa, 10=Posgrado.
ING	Nivel de Ingreso	1=Menos de 400 soles, 2=Entre 400 y 600 soles, 3=Entre 600 y 800 soles, 4=Entre 800 y 1000 soles, 5=Entre 1000 y 1500 soles, 6=Entre 1500 y 2500, 7=entre 2500 y 3500, 8=3500 y 4500, 9=Entre 4500 y 5000, 10=Entre 5000 y 6500, 11=Entre 6500 y 7500, 12=Más de 7,500 soles.
INGR	Ingreso monetario	Número entero (Promedio aritmético de cada categoría de la variable ING).
CON	Conocimiento sobre problemática	1=Nada, 2=Poco, 3=Medio; 4=Mucho.

The survey format designed for this research had three parts: questions about the problems related to basic sanitation services; questions regarding the willingness to pay for improvements to basic sanitation services; and questions about certain socio-economical characteristics of the individuals. The second part of the survey referred to the willingness to pay for the proposed change; with that purpose in mind, the proposal for the improvement of basic sanitation services in the city of Puno was summarized as a package or set of projects aimed at improving the quality of life of the city’s inhabitants. Those changes consisted of improvements to the supply of drinking water, the sewer system, and the treatment of wastewater. The following valuation scenario was proposed for the survey:

Currently, groundwork is being laid to materialize a group of projects aimed at improving basic sanitation services in the city of Puno. The goal of the first comprehensive project is to improve the drinking water and sewer systems. The drinking water system will basically include the expansion of the services (increased range), their improvement (increasing the continuity of the service, i.e., increasing the drinking water service continuity up to an average of 24 h), and service quality. Regarding the sewer system, the proposal is to expand and improve the system, by increasing the coverage and optimizing the collection of wastewater, without jamming the pipe network. The second project comprises the improvement of the wastewater treatment system. For this purpose, a treatment plant will be built. As a result, the pollution problem that affects the inner bay of Lake Titicaca will be controlled.

Based on the valuation scenario, the core question about the WTP for improvements was posed as follows:

Taking into account [the valuation scenario], would you be willing to make a monthly contribution for the amount of _____ additional soles in your water bill, in order to fund the operation and maintenance activities connected with the improvement of the basic sanitation services I have explained before?

During the first round, the pollster asked about the initial stance (BI), which included five price types: 2, 4, 6, 8, and 10. Once the interviewee had answered the initial question (“YES” or “NO”), the pollster modified the question, depending on the first answer. If the interviewee answered “YES” in the first round, the high stance price vector (BU) was used (it included the following prices: 4, 6, 8, 10, and 12). If the interviewee answered “NO” in the first round, the low stance price vector was used in the second round (it included the following prices: 1, 2, 4, 6, and 8). In every case, only one type of price was included in the BI, BU, and BD cases. Additionally, the second round question was also dichotomous.

Results and Discussion

The first round of the contingent valuation survey (referendum type) about the improvement to the basic sanitation services revealed that, out of 392 polls, 44 % of the interviewees were not willing to pay for this kind of project, while 56 % stated that they were willing to pay. The most accepted rate was $2 soles. Additionally, part of the population would accept a $10 soles rate (Table 2) which would enable price discrimination. The interviewees showed a rational behavior, i.e., higher rates receive less positive responses, while positive responses prevail when lower rates are involved.

The answers to the WTP questions during the second round (when the double-bounded format was used) show that 50.3 % of the participants have a positive stance (YES/YES and NO/YES) (Table 3). A greater ratio for positive WTP answers was obtained with the referendum format.

A contingent valuation study has the aim of estimating the WTP as an approximation of the compensating variation. Several econometric regressions were analyzed using binomial logit models. The parameters for various econometric models were estimated during this research (Table 4).

Once the econometric models was estimated, the next step was to select the best binomial econometric model, based on the following economic and econometric criteria (^{Greene, 2003}):

The logarithmic model was chosen based on the criteria mentioned for the group of models that used the referendum format. ^{Hensher et al. (2005)} carried out simulations that proved that the values of Pseudo R² (comprised in the 0.30-0.40 interval) were equivalent to R² (0.60-0.80) in the conventional case. The model made an accurate prediction (78.061 %), according to the prediction percentage. The joint significance was high, because the P-value of the statistic for the likelihood ratio was low. All explanatory variables were individually significant (1-5 %).

Among the groups of models that used the double-bounded format, the linear double-bounded model was chosen, because its likelihood logarithm had the highest value. Therefore, it had the highest statistical value for the likelihood ratio.

The results revealed that, in most of the cases, the absolute value of the “Z” statistics for the estimated parameters was greater than for the double-bounded models; the coefficients for this model showed less variance and were more significative. Therefore, they were closer to the interviewee’s true WTP. This result matches those of ^{Hanemann et al. (1991)}, ^{Calia and Strazzera (2000)}, and ^{Tudela (2017)}. Consequently, the linear double-bounded model was used to estimate and analyze WTP.

The results of the linear double-bounded model showed that the signs of the coefficients that go along with the explanatory variables were as expected: the BI coefficient was negative, i.e., the higher the price or stance offered to carry out the improvements to the sanitation services, the lower the likelihood of obtaining a positive answer from the interviewee. The income variable (INGR) had a positive sign: interviewees with higher incomes were more likely to provide a positive answer. The coefficient of the variable that represents the presence of children in the household (HIJO) had a positive sign: as more children were presents in a house, the likelihood of paying for an improvement to basic sanitation services (water, sewers, and treatment) will increase.

Likewise, according to the positive sign of the EDU coefficient, a higher education level will increase the likelihood that the interviewee gives a positive answer when asked if he or she is willing to pay for improved sanitation services. The expected results were therefore corroborated: heads of households with higher education levels were more aware of the urban sanitation service problem and were willing to use part of their income to improve that service.

EDA had a negative relation with the dependent variable, because older people are less likely to enjoy the benefits of the improvements to basic sanitation services. Meanwhile, the variable that summarizes the degree of awareness about the problems of basic sanitation services (CON) has a positive sign. This also confirmed that people who are more aware of the problems are more likely to give a positive answer when asked about their willingness to pay for improved services.

Based on the recommendations of ^{Jianjun et al. (2006)}, when the double-bounded CVM is used to estimate WTP, the average WTP results must be taken into account, excluding negative answers; the results of the linear double-bounded model generate an approximate WTP of $8.538 soles per month per each house (Table 5). This amount reflects the increased rate of the drinking water and sewer systems, after the basic sanitation services in the city of Puno have been improved.

^{Tudela (2017)} used the double-bounded CVM to estimate WTP regarding improvements to the wastewater treatment system in the city of Puno and found an average WTP of $4.38 soles per month per house. As a point of contrast, the average WTP estimated in this research includes the WTP for a comprehensive improvement of the basic sanitation services. Therefore, 51.3 % of the overall WTP ($4.38 soles) estimated in the current research matches the improvement to the wastewater treatment, while the remaining 48.7 % is related to the water and sewer systems ($4.16 soles).

Figures 2 and 3 include the histograms for the WTP estimated using the linear double-bounded model, including all the answers and excluding negative answers.

Source: Developed by the authors, based on the double-bounded model estimate.

Figure 2 WTP double-bounded histogram, including all answers. 

Source: Developed by the authors, based on the double-bounded model estimate.

Figure 3 WTP double-bounded histogram, excluding negative answers. 

The histogram for the double-bounded WTP that excludes negative answers (Figure 3) -unlike the double-bounded WTP that includes all the answers (Figure 2)- shows a typical behavior of contingent valuation studies, i.e., WTP distribution approaches a normal distribution, where most of the results concentrate near the average. This aspect reinforced the selection of the WTP average for this kind of model.

Conclusions

The double-bounded contingent valuation model showed a greater theoretical consistency, as a result of the greater individual and joint significance of the parameters. The average WTP estimate was $8.53 soles per month per house (US$2.84). Taking into consideration the overall number of benefited houses, this represented a measurement of the economic benefit that the improvements set forth in the valuation scenario have in the cost-benefit evaluation.

The variables involved -cash income, educational level, presence of children in the household, the age of the respondents, and the degree of awareness of the problems in the basic sanitation services- determined the estimation of the WTP, as a result of changes in the said services in the city of Puno.

The main contribution of this research was the empirical use of the (linear, restricted, and logarithm) referendum model and the (linear and logarithm) double-bounded model in a contingent valuation study. This proves the usefulness of comparing different functional forms of econometric models and their implications for WTP estimation.