Study area

The study area is the city of Puno, capital of the department (district) of Puno, located in southeastern Peru, between geographic coordinates 15° 50” 15’ SL and 70° 01” 18’ WL. The city is located at a height of 3,827 m on the shore of Lake Titicaca (^{Municipalidad Provincial de Puno [MPP], 2008}).

Puno has diversified tourist offerings, making it the third most visited Peruvian city after Lima and Cusco. The main tourist attraction is Lake Titicaca, recognized as a Ramsar site. The lake covers a total area of 8,562 km² (the Peruvian side has an area of 4,772 km² and the Bolivian side 3,790 km²), measures 204 km long by 65 km wide, has a maximum depth of 283 m and is estimated to contain 883 million m³ of water (^{MPP, 2008}). A population increase has generated greater consumption of drinking water and, consequently, the generation of a greater volume of domestic wastewater. According to projections by the National Institute of Statistics and Information Technology (^{INEI, 2009}), the city was expected to have a population of 141,064 by 2015. The "El Espinar" wastewater treatment plant (built in 1972) has now completely collapsed, resulting in much of the wastewater discharge pouring directly into Lake Titicaca’s Inland Bay (LTIB).

Contingent valuation method

The CVM is based on a simulation of a hypothetical market for the service to be valued; that is, it consists of asking direct questions to the users (households) involved about their WTP for a change in the provision of the public service, in this case, for improvements in the wastewater treatment system. Evidence shows that contingent valuation surveys for access to public services, such as basic sanitation, can be successfully carried out in developing countries (^{Lauria, Whittington, Choe, Turingan, & Abiad, 1999}).

WTP was estimated through data obtained in a survey of 393 heads-of-household. Due to the type of survey it was only applied to households with water and drainage connections. To this end, the city of Puno was divided into three sectors: southern, central and northern. Systematic random sampling was performed in each sector, the advantage of which is that the sample is distributed proportionally (in strata) throughout the city. The selected households were visited to apply the surveys to the head-of-household or the person in charge of it. All surveys were conducted in December 2014.

Willingness to pay referendum model

^{Bishop and Heberlein (1979)} introduced a variant of the contingent valuation method, called the referendum format. Basically, this format consists of presenting two response alternatives to the interviewee: YES/NO. The individual is asked if he would be willing to pay a certain amount of money to access the proposed environmental improvement, in which case the respondent should issue a binary (YES or NO) response.

According to ^{Hanemann (1984)}, the structure of the referendum-type WTP model assumes that a representative individual has a utility function U. This utility function depends on income Y, on the state of the wastewater treatment plant Q, and on the socioeconomic characteristics S. The initial state is defined as Q = 0 and the final state as Q = 1. Puno city residents have to pay an amount of money B if they want to gain access to the environmental benefits implied by improvements to the wastewater treatment system. The utility function Ui(Q,Y;S for each of these situations (with and without the project) has a deterministic component Vi(Q,Y;S , estimated from information collected in the survey, and an unobservable stochastic component, εi . The utility function of the representative individual can be expressed as:

Ui(Q,Y;S)=Vi(Q,Y;S)+εi

where the subscript i with value 1 or 0 denotes the state with and without the project, respectively. The term εi is assumed to have a zero mean and constant variance. When the person interviewed agrees to pay an amount of money B to obtain the proposed scenario, it must be fulfilled that:

Vi(Q=1,Y-B;S)+ε1>Vi(Q=0,Y;S)+ε0

Vi(Q=1,Y-B;S)-V0(Q=0,Y;S)>ε0-ε1

Errors ε0 y ε1 are assumed to be random, independent, and identically distributed. The utility change defined as the difference between the levels of final and initial utility, ΔV , can be represented as:

ΔV=V1(Q=1,Y-B;S)-V0(Q=0,Y;S

η=ε0-ε1

Consequently, the probability of having an affirmative response (YES) to the willingness to pay question is given by:

Prob(Si)=Prob(ΔV>η)=FΔV

Regression analysis is done using a logit or probit model since, in the referendum model, the dependent variable is discrete. In this research the former was used. A typical formulation of the logit model is proposed as follows:

Prob(Si)=Fβ'xi=11+exp-β'xi

The estimation problem is solved through the maximum likelihood method with the joint density function given by:

L=∏i=1n1-Fβ'xi1-yiFβ'xiyi

where y _i is the binary dependent variable that takes the value of 1 and 0 if the answer to the willingness to pay question is YES or NO, respectively. The maximum likelihood estimator is obtained by maximizing this function with the parameters as decision variables.

Willingness to pay double-bounded model

The use of the referendum-type CVM has been subject to criticism regarding its ability to make reliable and accurate WTP estimates. As a way to reduce this inefficiency, ^{Hanemann, Loomis, and Kanninen (1991)} suggest using a double dichotomous format, known as double-bounded. This format consists of adding a second question about willingness to pay, also of a dichotomous nature.

According to ^{Hanemann et al. (1991)}, in the context of a double question on willingness to pay, the initial question proposed to the individual i (B _i ) is reasked on the basis of the first response ( Bid or Biu ), where Biu is the second price proposed after a positive response to the first and Bid is the second price proposed after a negative response to the first. Figure 1 illustrates the choice procedure in the double-bounded format.

Figure 1 .Double-bounded dichotomous choice process. 

According to ^{Hanemann et al. (1991)} and ^{Habb and McConell (2002)}, the responses in terms of probability for the double-question case can be expressed as follows:

Probyes,yes=1-Fβ'xiu

Probyes,no=Fβ'xiu-Fβ'xi

Probno,yes=Fβ'xi-Fβ'xid

Probno,no=Fβ'xid

The econometric estimation problem is solved through the maximum likelihood method with the joint density function given by:

L=∏i=in1-Fβ'xiudissFβ'xiu-Fβ'xidisnFβ'xi-Fβ'xiddinsFβ'xiddinn

where diss,disn,dins y dinn are binary variables derived from the responses: yes-yes, yes-no, no-yes and no-no respectively. When the interviewee's response is in any of the alternatives, the variables take the value of 1; otherwise, the value is 0. The maximum likelihood estimator is obtained by maximizing this function with the parameters as decision variables. The parameters of the referendum and double-bounded models were estimated using NLOGIT software version 4.0 (^{Econometric Software, Inc., 2007}).

According to ^{Hanemann et al. (1991)}, the double dichotomous model provides a gain in precision in the variance-covariance matrix of the estimated coefficients, yielding smaller confidence intervals with respect to the simple dichotomous model; in addition, they found that the point estimate for the median WTP of the double dichotomous models is generally lower.

^{Calia and Strazzera (2000)} demonstrated that the double-bounded format is more efficient than the simple one and that it yields more efficient and precise WTP estimates. For their part, ^{Bateman, Langford, Jones, and Kerr (2001)} point out that dichotomous choice (referendum type) contingent valuation questions are relatively inefficient for large samples.

Willingness to pay

Before formulating the willingness to pay question in the contingent valuation survey, the interviewees were informed that the MPP had developed a project to control pollution from wastewater dumping and thus prevent further pollution of the LTIB. It was emphasized that the viability of such projects depends to a large extent on the monetary contribution of the population, which consists of an additional monthly contribution to the one currently paid for drinking water and sewage.

Consequently, in the contingent valuation survey, the analysis of the WTP for improvements to the wastewater treatment system revealed that 39.2 % of the interviewees are not willing to pay for such a project, compared to 60.8 % who stated otherwise. Table 1 shows the WTP results; it can be seen that 77.5 % of 40 interviewees responded affirmatively to a rate of 1 PEN, against 29.7 % who answered affirmatively in the case of a rate of 7.50 PEN. In general, what was expected a priori was confirmed; that is, lower rates had more positive responses compared to higher rates, where there are more negative responses.

On the other hand, Table 2 contains the responses that were formulated with the referendum format and the iterative questions with double-bounded format. As can be seen, 53.7 % of those surveyed responded affirmatively to the bids offered (YES/YES and NO/YES), while 46.3 % answered that they were not willing to pay (YES/NO and NO/NO). These results differ from those obtained in the simple format, where there is a greater percentage of affirmative answers to the willingness to pay question.

Econometric analysis of the referendum and double-bounded models

The results of the regressions of the referendum and double-bounded (linear and logarithmic) models are shown in Table 3. Of the four models presented, the linear double-bounded model, comprised by the variables hypothetical price to pay, income, education and distance, was selected. The results of the double-bounded model show that the signs of the coefficients accompanying the variables are as expected; the individual parameters are highly significant (P = 0.01) in all cases. The joint significance is very high in terms of the likelihood ratio statistic (LR = 996.27) and the critical value of χ² = 15.08 (P = 0.01, gl = 5), so the joint hypothesis that the coefficients of all explanatory variables are zero is rejected.

The coefficient of the price variable, as expected, is negative. This indicates that the higher the rate increase or bid offered for the project’s development the lower the probability of obtaining a positive response from the respondent. The income variable, on the other hand, has a positive sign indicating that the probability of obtaining a positive response is greater when the interviewee’s income level is high.

The fact of having a higher educational level increases the probability of responding positively to the willingness to pay question for improvements to the wastewater treatment system. This corroborates what was expected a priori; that is, when heads-of-household have a higher educational level they are more aware of environmental problems and are therefore willing to sacrifice part of their income for a project that seeks to control pollution caused by the dumping of wastewater into the LTIB.

On the other hand, the distance variable has a negative sign, indicating that the probability of a positive response decreases as the distance from the water treatment plant to the interviewee's home increases. The most conscious households are those located closest to the current plant, since they see the consequences of the environmental problem on a daily basis.

When comparing the WTP results obtained by the referendum model to those estimated by the double-bounded model (Table 3), it can be seen that, in all cases, the absolute value of the Z statistic of the estimated parameters increases. This reflects the fact that the double-bounded model coefficients have lower variance, are more significant and, therefore, as a whole have a better approximation to the true WTP of the respondents; as a result, the monthly WTP changes. In this case, the WTP is reduced from 5.43 PEN to 4.38 PEN (1.81 USD to 1.46 USD), reflecting an overestimation with the referendum model. The above validates the claims of ^{Hanemann et al. (1991)}, ^{Calia and Strazzera (2000)} and ^{Bateman et al. (2001)}, who demonstrate the superiority of the double-bounded model over the referendum model.

When analyzing the results of the logarithmic model in its two versions, it can be seen that the Z statistics of the double-bounded model were significant (P = 0.01) for all coefficients. Comparing these results with those of the referendum model, the supremacy of the double-bounded model is evident. For this reason, the WTP measure decreases from 6.82 PEN to 4.43 PEN (2.27 USD to 1.48 USD), again observing an overestimation of WTP with the classic referendum model.

Analysis of willingness to pay at zone level in the city

With respect to the estimated models, the best models, in terms of individual significance and the likelihood ratio statistic, are those that use the double-bounded format. Within this classification there are two versions: linear and logarithmic (in both cases the functional form is for the change in utility). Between these versions, the linear double-bounded model was selected because it had the highest likelihood ratio statistic value. Taking into account the econometric results of the linear double-bounded model (Table 3), the mean WTP was estimated for each interviewee, according to their area of origin (Table 4).

Table 4 shows that the WTP of residents living in the southern zone, the main area affected by the wastewater pollution, stated a greater willingness to pay than those in the city’s central and northern zones (4.90 PEN> 4.33 PEN> 3.96 PEN or 1.63 USD> 1.44 USD> 1.32 USD). This shows that the residents of this area highly value the proposed improvements to the wastewater treatment system.

The results of the linear double-bounded model yield an average total WTP of approximately 4.38 PEN per household (1.46 USD). This amount would be reflected in an increased rate for potable water and sewerage service, once the wastewater treatment system in the city of Puno is improved. This result differs from that obtained by ^{Tudela (2008)}, who using the referendum format obtained a WTP of 4.21 PEN per household (1.40 USD), a value that could be considered overestimated for that year.