Improvements in publically provided goods and services, like community drinking water treatment, have values to people arising from their self-interest, but may as well have value from their altruistic concerns. The extent to which the value is altruistic versus self-interested is an important empirical issue for policy analysis because the benefits to improving drinking water quality may be larger than previously thought. We conducted an internet survey across Canada to identify both self-interested willingness-to-pay and altruistic willingness-to-pay obtained through hypothetical responses to a series of stated choice tasks and actual self-protection data against health risks from tap water. We use the information on self-protection to identify altruistic WTP. We find significant differences between self-interested and altruistic WTP: the latter can be three times greater than the former. Whether benefits of water protection are actually larger, however, depends on whether the altruism is paternalistic or nonpaternalistic.
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 In Canada, governments are ultimately responsible for the provision of safe drinking water. Research indicates that chlorine, the dominant disinfection method used to reduce risks of microbial illnesses in water, can potentially produce carcinogenic disinfection by-products [Mills et al., 1998]. Alternative disinfection methods may create fewer carcinogenic disinfection by-products but are generally more expensive and may also be less effective at killing microbes. It is thus important for government agencies to identify public preferences for risk reductions in cancer and microbial illness from municipal drinking water quality improvement programs.
 Municipal water quality improvement programs are publically provided goods and have public goods characteristics. Once a preferred disinfection method is chosen and provided, every resident in the community will be able to access drinking water of a given quality. Many studies have shown that the demand for public goods is driven by both self-interest and altruistic motives [Holmes, 1990; Andreoni, 1990; Popp, 2001; Jones-Lee, 1992; Johansson, 1994]. Flores  indicates that a “selfish” benefit-cost test, which ignores altruism in the demand for public goods could potentially lead to a rejection of welfare-improving changes in public goods. McConnell  suggests that the role of altruism in benefit-cost analysis is sufficiently troubling to warrant empirical research on motives for nonuse values. Johansson  suggests that a willingness-to-pay approach to valuing health risk reductions is problematic in general if altruistic motives are ignored. Yet, current research on the extent of altruism in the valuation of public goods has largely remained at the theoretical level with a few exceptions [Jones-Lee, 1992; Lee and Chung, 2012; Whitehead et al., 2012]. Despite strong evidence of a willingness-to-pay by some people to obtain reductions in the risks of an unidentified death, many public policies that involve health benefits are still being evaluated with the benefits associated with private risk reductions only [Brady, 2008]. This paper provides an empirical investigation of the extent of altruism in the value of a public good that reduces health risks from municipal drinking water.
 The literature has typically differentiated two types of altruism: nonpaternalistic and paternalistic [Jones-Lee, 1992; Lazo et al., 1997; Flores, 2002; Jacobsson et al., 2007]. Nonpaternalistic altruism means that an altruist derives utility from his or her beneficiaries' general well-being and respects their preferences. Paternalistic altruism means that an altruist derives utility from his or her beneficiaries' consumption of a particular good [McConnell, 1997; Lazo et al., 1997; Flores, 2002], such as safety-focused altruism [Jones-Lee, 1991]. The literature is clear that individuals' willingness-to-pay for nonpaternalistic altruistic reasons should not be included in benefit-cost analysis since benefits received by the altruist and the beneficiaries imply double counting. In contrast, the presence of paternalistic altruism is considered to be less troubling for benefit-cost analysis. This type of altruism is self-motivated and should be counted as a part of the altruist's self-interested value.
 While in general it is difficult to differentiate between the two types of altruism since motivations are not often observable, there is a general consensus that individuals do exhibit paternalistic concern for other people's safety, access to natural resources like water and clear air, or access to health care services [Jones-Lee, 1991, 1992; McConnell, 1997; Jacobsson et al., 2007; Rodriguez and Leon, 2004; Loomis et al., 2009]. Results from a few studies, in which the presence of paternalistic altruism seems to be more plausible, suggest that, in theory, public-good WTP should be greater than the private-good counterpart [Jones-Lee, 1992; McConnell, 1997; Andersson, 2007; Brady, 2008]. A few other studies conducted in a road safety context, however, report the opposite [Johansson, 1994; Andersson, 2007; de Blaeij et al., 2003]. Svensson and Johansson  explain that one of the reasons for the difference between the two types of WTP estimates is that they are perceived as two different goods. For example, one such study asked respondents to state their willingness-to-pay for a private safety device (an airbag safety device that reduces a driver's and his or her passengers' risk of injury in a car accident) versus the same size of risk reduction associated with public safety programs (improved road quality) [Johannesson et al., 1996]. Despite the researchers' best efforts, the private risk reduction might have been perceived as more effective than an equivalent amount of public risk reduction, possibly because one is more in control of one's own actions, as opposed to other people's.
 In this study, rather than describing two types of goods through different questionnaires, we examine altruism and self-interest using a combination of stated preference data and actual self-protection data in a single public-good valuation context, in which respondents derive both private benefits and benefits for others through the consumption of the public good. Assuming the existence of altruism in Canadians' choices for alternative water treatment programs, we propose that an individual's total WTP for a public risk reduction program consists of two components: one is motivated by self-interest and the other is out of concern for others. To test this hypothesis, we need to identify both the self-interested and altruistic components of a respondent's total WTP for a public good. We conduct an internet survey to collect both hypothetical responses to a series of stated choice tasks and actual self-protection data against health risks from tap water across Canada. Expenditure data on self-protection against health risks from drinking water are used to distinguish the demand for the public good by individuals who are driven solely by altruistic motives from those who might have both self-interest and altruistic motives. We test the hypothesis that self-protection against the health risks decreases one's willingness-to-pay for a public program that aims to reduce these risks. We also examine the data for evidence that individuals who did not take any self-protection measures are willing to pay higher amounts for risk reduction from drinking water than those who did. We do not, however, explicitly test for or identify two types of altruism: paternalistic or nonpaternalistic.
 We adopt two different approaches to test the hypothesis that total WTP for a publicly provided good is greater than the self-interested WTP from the good [Jones-Lee, 1992; Strand, 2004; Brady, 2008]. Results from each approach, in general, support our hypothesis. We find that individuals are willing to pay for a program to reduce the risks to other people in the community regardless of whether they are self-protected from the risks or not. However, self-protection decreases individuals' willingness-to-pay for the municipal water treatment program that reduces health risks. Based on our approach that differentiates motives for health risk reductions from a municipal drinking water program, we derive two types of public-good values of statistical life (VSL), one arising from paternalistic altruism and one from nonpaternalistic altruism.
 The paper is organized as follows. Section 2 introduces a theoretical model incorporating altruism into a utilitarian framework and describes two approaches for implementing the model. Section 3 describes the survey, data, and model specifications. Section 4 reports model estimation results, WTP estimates, and values of statistical life and values of statistical illness estimates. The last section concludes the paper.
2. Accounting for Altruism in the Value of Risk Reductions
2.1 Public-Good Valuation of Risk Reductions
 We define individual i's utility to be a function of his or her private access to a municipally provided public good gi of quality level qi, gi(qi), the provision of a public good of G of quality q to individual i, Gi(q) and to other people, G-i(q), and a Hicksian composite good Z. Hence, where , , and [Andreoni, 1990]. Then, the indirect utility function can be specified as Vi = V(qi, Gi, G-i, M), where qi is individual i's private access to the water quality of the municipally provided public good, Gi is the public good that is provided to individual i, G-i is the public good that is provided to other people, M is individual i's income, and the price for Z is normalized to 1. Let V0i = V( , Gi0, G-i0, M) be the utility level before a quality improvement in the provision of G and let the utility level after the change be V1i = V( , Gi1, G-i1, M). Then, the compensating variation (CV) or total WTP for an improvement in the quality of the public good is the solution to equation (1).
 Alternatively, total WTP can be expressed explicitly as a change in expenditure functions:
 where Ui0 denotes individual i's utility level at the status quo. Adding and subtracting the term e( ,Gi0, G-i0, Ui0) on the right-hand side of the equation, we get:
 Altruistic WTP is defined as the difference between the last two terms:
 Equation (4) defines the amount that an individual is willing to pay for an improvement in the quality of the public good G when the individual does not derive any private benefits from such a change because she already experiences a higher quality private access to the public good—presumably through defensive spending. This is the WTP for other people to benefit from improvements in the quality of the public good.
 The self-interested WTP, WTPSelf, is the difference between the first two terms of equation (3):
 WTPSelf is the amount an individual would be willing to pay for private benefits from a quality change of a public good holding constant the quality level of the public good for other people. Therefore, total WTP can be decomposed into two components: altruistic WTP and self-interested WTP:
 Equation (6) illustrates that an individual can be purely selfish (WTPTotal = WTPSelf; WTPAltrm = 0), purely altruistic (WTPTotal = WTPAltrm; WTPSelf = 0), or in-between (WTPAltrm > 0; WTPSelf >0). Our approach thus allows for heterogeneity in the level of altruism in the population.
 Unlike Flores , in which a utility function has to be defined differently for the altruist and for his or her beneficiaries, our model does not differentiate the utility function of an altruist from that of his or her beneficiaries. Each individual's utility function is hypothesized to be motivated by both self-interest and altruism. This conceptual framework facilitates empirical investigation of the extent of altruism that is likely to be heterogeneous and unobservable. One does not have to identify the form of altruism before actually estimating it. If altruism is paternalistic, WTPTotal is an individual's self-motivated WTP. If altruism is nonpaternalistic, WTPSelf is an individual's self-motivated WTP, and WTPAltrm has to be excluded to avoid double counting. At the aggregate level, to conform to Samuelson's rule for optimal public good provision, if altruism is paternalistic, the total benefit (TB) of a public good is,
 Given nonpaternalistic altruism, however, TB is
 For our specific case of municipal drinking water, we make several assumptions about the nature of self-protection and the benefits of the public good. These assumptions are discussed in section 2.2.
2.2 Self-Interested WTP and Altruistic WTP
 A key to successful empirical decomposition of total WTP is to identify the types of benefits one receives from the public good. In the survey conducted, we collected data on self-protection measures against health risks from drinking water. We use these self-protection data to distinguish the demand for the public good by individuals who are driven solely by altruistic motives from those who might have both self-interested and altruistic motives. However, we also have to make several assumptions about the nature of self-protection and the benefits of the public good. First, for respondents who do not engage in self-protection against drinking water health risks, we assume the proposed water treatment program could provide both private benefits as well as benefits for others, since our valuation scenarios clearly described the health risk reductions from drinking water as potentially benefiting a community with a population of 100,000. Second, for respondents who do engage in self-protection against drinking water health risks, we assume they know that the proposed water treatment program would benefit other people through improved drinking water quality. However, they do not derive private benefits because they already undertake self-protection actions. Their WTP for the quality improvement of the public good, if greater than zero, is considered to be altruistic. This is a strong assumption in that it rules out any private benefits obtained from the provision of better quality water consumed outside the house, such as in a park, or in a public library. Respondents who employ water filter systems at home might be willing to pay for the public good for private reasons, such as saving future costs of installing and/or maintaining their water filter systems. Our analysis assumes that such private benefits are zero. Therefore, the altruistic values estimated in this study serve as an upper-bound estimate of WTP for other peoples' benefits.
 We adopt two empirical approaches to identify these two different demands within the sample of respondents. The first is a sample segmentation (SS) approach, while the second is an econometric interaction approach. The SS approach divides the entire sample into two groups, according to whether a respondent engaged in self-protection behavior. Separate models are estimated for each group. A shortcoming of this approach is that it does not account for the intensity of a respondent's self-protection efforts. In our sample, annual household expenditures on water filtration systems varied significantly among households, from $10 to $1050. The lower end values represent expenditures pertaining to the operation of container style filtration devices, while the higher end values are for in-tap home filtration systems. The perceived level of self-protection may differ significantly among households with different levels of expenditures on water filtration systems. Our second approach assumes that a respondent's total willingness-to-pay for public risk reductions decreases as more is spent on self-protection. This approach uses the entire sample and estimates an augmented utility function that includes interactions between attributes of the public good and expenditures on self-protection to control for different degrees of altruism and is referred to as the averting expenditure (AE) interaction approach hereafter. We expect that results from both approaches will be qualitatively similar: total WTP driven by both self-interest and concern for other people is greater than WTP driven by concern for other people only. However, we also expect slight differences in the quantitative results derived from the two different approaches due to differences in sample sizes, assumptions about the relationship between self-protection behavior and perceived risk reductions, and in handling the endogeneity between self-protection behaviour and risk preferences. By comparing results from the two approaches, we can undertake a sensitivity analysis on the relative magnitudes of altruistic and self-interested values in the demand for municipal water treatment programs.
 In the summer of 2004, an internet survey was conducted to identify preferences for risk reductions in drinking water across Canada. The survey employed nonmarket valuation methods to obtain information about consumer preferences and tradeoffs relating to household water bill increases and the morbidity and mortality health risks associated with the consumption of drinking water [Adamowicz et al., 2011]. About 35% of the respondents state that they have minor to moderate health concerns about drinking tap water in Canada. About 43% of the sample employs water filter systems or water container systems at home. It appears that many Canadians are concerned about their drinking water quality.
 In order to investigate self-interested and altruistic WTP, for this paper, we use a subset of choice experiment data collected from this survey: a two-alternative design that describes both a status quo and single option and a three-alternative design that describes the status quo plus two new options (Figure 1). These two designs are the two most popular designs used in choice experiments for eliciting preferences since they balance statistical efficiency with cognitive burden [Rolfe and Bennett, 2009; Zhang and Adamowicz, 2011]. We first generated 32 profiles that are combinations of different health risk levels and levels of annual increase in the current water bill. Then, two sets of 32 choice sets were generated by either grouping one profile with the status quo option for the two-alternative design, or grouping two profiles with the status quo option using a D-optimal design with restrictions on combinations of attribute levels (e.g., to exclude profiles that are dominating or dominated by the status quo option). The status quo option is presented with current levels of four different health risks associated with current water treatment programs in Canada [Adamowicz et al., 2011]. Due to sample size constraints, we adopted a main-effects choice experiment design (see detail in Adamowicz et al. ). According to Louviere et al. , this type of “main effect (design) typically account(s) for 70–90% of explained variance.” Our analysis is conducted on the pooled data set yielding an initial sample size of 406 respondents which was reduced to 366 in order to remove “yea-saying” responses [Adamowicz et al., 2011]. These individuals stated that they were willing to pay any amount to reduce the health risks posed in the survey. It is possible that these individuals were unwilling to make tradeoffs between attributes of a good or between attributes and money, and therefore, inclusion of their responses in the analysis might lead to erroneous inference. Since each respondent faced four choice tasks, we have a total of 1464 choice experiment observations. Since this paper is based on a subset of the data set that is used in Adamowicz et al. , please refer to Adamowicz et al.  for further details on survey administration, response rate, and representativeness of the sample. In summary, the overall response rate for the survey was 46%. Given the manner of respondent recruitment (initial email to Ipsos-Reid's panel of internet-enabled Canadians that numbered around 100,000 persons in 2004, followed by random recruitment into one of eight different question formats once a respondent followed up on the email), it is not possible to determine response rates for each separate subsample of data. In terms of sample representativeness, most of the characteristics of our sample are very similar to the Canadian population using 2001 Census statistics. For example, Census mean income is $58,360 compare to our pooled sample of $59,030. The proportion of males in our sample (53%) is slightly higher than the census data (50%) and the proportion of households living in urban areas (71%, defined as a city/town with more than 100,000 people) is slight lower than that found in the census data (80%, defined as a city/town that has a population greater than 1000). While Ipsos-Reid maintains its database in such a way as to provide representative samples of the Canadian population, respondents are drawn from a panel of internet-enabled Canadians and, therefore, our results are not necessarily generalizable to Canada, as a whole.
 In our study, each option is characterized as a bundle of health risk attributes associated with different water treatment programs and the costs that such a program would add to the annual household water bill. The survey identifies four types of drinking-water-related health risks: microbial illnesses (MICI), microbial deaths (MICD), cancer illnesses (CANI), and cancer deaths (CAND). The level of risk is defined as the number of morbidity and mortality cases related to drinking water quality in a community of 100,000 people over a 35 year period. A status quo option is included as a baseline program that does not involve any increase in the water bill. The alternatives are characterized with a reduction in at least one type of health risk, as well as increases in the water bill. According to random utility theory, individual i's utility associated with alternative j has two components: deterministic utility (Vij) and stochastic utility (ɛij). The deterministic utility Vij in this study is specified as a linear function of four risk attributes (MICI, MICD, CANI, and CAND) and increases in annual water bill (Bill) that describe alternative water treatment programs. The status quo levels for the MICI, MICD, CANI, and CAND are 23,000, 15, 100, and 20, respectively, and there is no increase in the current water bill. Regardless of the number of alternatives included in a choice set, a choice task always contains the status quo option that is featured with the status quo levels of health risks and zero increase in water bill. Since the status quo option is fixed across all choice tasks and across all individuals, a status quo alternative specific constant (SQ) is included to capture unobserved utility associated with staying at the status quo [Adamowicz et al., 1998; Scarpa et al., 2005]. An interaction term, CE3 * SQ, where CE3 is a version dummy variable for the three-alternative data set and the status quo alternative specific constant SQ, is included to account for a possible choice format effect on preferences for the status quo. Inclusion of this interaction term allows us to pool the data set while recognizing that choice format (number of alternatives in a choice set) might affect the preference for the status quo option. Statistical tests show that we cannot reject the null hypothesis that marginal WTP estimates for health risk reductions are the same for both choice formats. (We conducted this test controlling for scale heterogeneity. However, we did not find any statistically significant scale difference in the two data sets. Therefore, we continued our analysis with pooled data sets that do not include a scale parameter to control for scale heterogeneity between the two data sets.) See Zhang and Adamowicz  for an explanation of the impact of choice format on the preference for the status quo option based on the same data set. One way to incorporate additional sociodemographic information into the utility function is to add interaction terms between demographic variables and alternative-specific attributes to capture preference heterogeneity. These variables are defined in Table 1, along with attribute and expenditure variables on self-protection against drinking-water-related health risks.
Table 1. Definition of Variables
Pooled Data Set
Dummy variable, equals 1 if an alternative is the status quo option and 0 otherwise
Number of microbial illness cases over a 35 year period from drinking tap water in the community
Number of deaths due to microbial illnesses over a 35 year period from drinking tap water in the community
Number of cancer cases over a 35 year period from drinking tap water in the community
Number of cancer deaths over a 35 year period from drinking tap water in the community
The increase in the current water bill ($Cdn per year)
1 if an individual is faced with a choice set of three alternatives, and 0 if faced with a choice set of two alternatives
Dummy variable, equals 1 if an individual is equal to or over 65 years old and 0 otherwise
1 if an individual reports ever being ill due to drinking tap water, 0 otherwise
1 if an individual is married and 0 otherwise
1 if male, and 0 otherwise
Annual before-tax income of a household ($Cdn)
Squared annual household income
1 if a household has children under 6, and 0 otherwise
1 if a household has children between 6 and 12, and 0 otherwise
1 if a household has children between 13 and 17, and 0 otherwise
Categorical variables from 1 to 6, ranging from 1 denoting population of 1499 and under and 6 denoting 1,000,000 and over
1 if English is the primary language for a respondent and 0 otherwise
Index of the total number of health problems an individual has experienced, such as food allergies, cancer diseases, heart diseases, and so forth
Index of the total number of health problems other household members have experienced
1 if a household uses a water filter system at home, and 0 otherwise
Annual household expenditure on installing and maintaining water filter system at home ($Cdn)
Annual expenditure on purchasing bottled water consumed at home ($Cdn)
3.1. The SS Approach
 To identify self-interested and altruistic values, the SS approach splits the data into two samples according to whether a respondent engaged in self-protection behavior against health risks from drinking tap water. This behavior takes the form of expenditures on water filtration system purchases and maintenance [Adamowicz et al., 2011]. We hypothesize that individuals who employ water filtration systems (i.e., Filter = 1) believe themselves to be protected against tap-water-related health risks and do not obtain private benefits from the health risk reductions proposed in the improvement program(s). For individuals who do not employ water filter systems (i.e., Filter = 0), we assume that they will obtain both private benefits and altruistic benefits from the adoption of the improvement program. In looking at the respondents in the Filter = 0 sample, we note that a large number (46%) purchase bottled water to drink at home. Since purchased bottled water is considered to be free from drinking-water-related health risks, it is reasonable to assume that these individuals are also able to avoid tap-water-related health risks and might not necessarily derive private benefits from the public program of water quality improvements. Therefore, a “cleaner” sample of non-self-protecting individuals includes only those who do not use water filtration systems at home and do not purchase bottled water to drink at home (i.e., Filter = 0 and the expenditure on purchasing bottled water is also zero, BottleExp=0). Thus, WTP obtained from the individuals in the No-self-protection sample is considered to be driven by both self-interest and altruistic reasons. However, WTP obtained from individuals in the Self-protection sample is assumed to reflect only altruistic benefits from a proposed drinking water program.
 Separate models are estimated based on the stated choices of individuals in each sample: the No-self-protection model and the Self-protection model. Based on our assumptions, the WTP estimates derived from the No-self-protection model are total WTP estimates (WTPTotal), while the WTP estimates derived from the Self-protection sample are altruistic WTP (WTPAltrm) estimates. We are interested in examining whether WTPTotal is greater than (or equal to) WTPAltrm, on average.
3.2. The AE Interaction Approach
 The AE interaction approach accounts for differences in motives for risk reductions through interactions between deterministic utility Vij and an expenditure variable on self-protection against health risks from drinking water (FilterExp). This allows us to capture the intensity with which respondents take actions believed to provide self-protection against drinking water health risks. We explore two issues. The first is an investigation of the need to control for potential endogeneity between one's choice decisions to reduce health risks and one's risk preferences [Louviere et al., 2005]. The second is an examination of whether there is a relationship between the willingness-to-pay for risk reductions and levels of self-protection.
 We begin by assuming a linear additive indirect utility function to represent individual i's utility associated with an alternative water treatment program j:
 In this equation, MAINk is a vector of the six attributes previously described for the SS approach: SQ, MICI, MICD, CANI, CAND, and Bill. We also include the same interaction term as previously, CE3*SQ, to account for the elicitation format differences. We recognize that a risk-averse individual may not only take more self-protection measures than a risk-neutral individual but may also be willing to pay higher amounts for a program to reduce the risks. Thus, it is possible that FilterExp might be endogenous and correlated with the error term ɛ. One way to handle this issue is to create an instrumental variable that is correlated with FilterExp but uncorrelated with the error term ɛ [Greene, 2003; Louviere et al., 2005]. A predicted value for FilterExp is a good candidate. Since FilterExp is nonnegative, a Tobit model that handles censored data are used to derive predicted filter expenditures [Greene, 2003]. In the Tobit model, the dependent variable is a latent variable for FilterExp, denoted as Z*.
 where Z* can be negative, zero or positive, and x is a vector of sociodemographic variables.
 Using the results from the Tobit regression, we obtain the predicted latent expenditure, , for each respondent in the sample and use this to replace FilterExp in equation (9). When calculating total WTP (WTPTotal) for each type of reduced health risk using this approach, we use estimated WTP given FilterExp = 0 and, similarly, altruistic WTP (WTPAltrm) is the estimated WTP given FilterExp > 0. Since predicted expenditures ( ) may differ from actual expenditures, mean WTPTotal is estimated at the mean of for the sample satisfying FilterExp = 0 and mean WTPAltrm is estimated at the mean of for the sample satisfying FilterExp > 0. As with the SS approach, we are interested in testing whether WTPTotal is greater than WTPAltrm. Comparing to the results from the SS approach, the difference between WTPTotal and WTPAltrm is expected to be smaller using the AE interaction approach because, holding risk preferences constant, households with higher self-protection expenditures should be willing to pay less for the municipal drinking water program that reduces the health risks faced by them at home, and hence the larger proportion of their total WTP would be driven by altruism.
4. Results and Discussions
4.1. Model Estimation
 For each approach, we estimate a conditional logit (CL) model. (We also estimate random parameters logit (RPL) models using each approach in order to capture the panel structure of our data set and unobserved preference heterogeneity with respect to individuals' WTP for health risk reductions. Due to space limitation, the RPL results are included in supporting information.) Table 2 reports the estimated CL models for the No-self-protection model and the Self-protection model using the SS approach. Since “no-covariates models” are nested within their corresponding “with-covariates models,” likelihood ratio (LR) tests were conducted to determine a preferred specification. The test results indicate that adding covariates significantly improves model fit. A total of 13 covariates are included: Income, Income2, English, Age65, Married, Male, Kid0_6, Kid6_12, Kid13_17, Citysize, HealthSelf, HealthFamily, and IllfromWater. (They are defined in Table 1.) Estimated coefficients on all risk attributes (MICI, MICD, CANI, and CAND) are negative and significant at the 5% level in both models and are similar between both models. The estimated coefficients for SQ are positive and significant which implies that, on average, people derive utility from staying at the status quo. This could be due to an endowment effect or for other reasons that have been documented in the literature [Adamowicz et al., 1998; Dhar, 1997]. The estimated coefficients of the interaction term CE3*SQ are both significant and negative. The framing effect could arise from differences in the level of task complexity and preference matching caused by a different number of alternatives in a choice set [Zhang and Adamowicz, 2011]. The coefficients on Bill are significant in both models, albeit the absolute value of the coefficient on Bill in the Self-protection model is larger than that in the No-self-protection model. Given that we found no scale difference in the data sets, this result suggests that people are more price-sensitive when their willingness-to-pay for the public program is driven mainly by altruistic concerns.
Table 2. Estimated Conditional Logit Models to Explain WTP for Public Water Quality Improvement Program: Sample Segmentation Approacha
 In each model, sociodemographic variables enter as interaction terms with the SQ alternative-specific constant; therefore, demographic effects explain how people with different characteristics differ in choosing the status quo option. (Our preliminary analysis of pooling the two-alternative and three-alternative data sets indicated that most of the differences come from the preferences for staying at the status quo option [Zhang and Adamowicz, 2011], and we cannot reject equal preferences for risk attributes and cost attributes between the data sets. We also estimated models that incorporated interactions between demographic variables with health risk attributes and price attributes (for example, interacting male with each health risk attribute and the price attribute). Wald test results indicate that we cannot reject the null hypothesis that the model specification which excludes those interactions is the true model.) Most variables are found to be significant in one model but not in the other. Wald tests for equal means of each demographic variable between both groups cannot be rejected, so there is no statistically significant difference in the sociodemographic characteristics of respondents in the two groups. It is found that in the No-self-protection model, respondents are statistically more likely to choose the status quo at low levels of income, but as one's income goes beyond a certain level, a respondent is more likely to choose a water quality improvement program. Such income effects are insignificant in the Self-protection model, suggesting that income level is not an important factor in the decision to pay for other people's benefits. This is consistent with the findings of Ronsvalle and Ronsvalle . They find that the percentages of total cash donations of after-tax income for higher income groups are not higher than those for low income groups in the United States in 2005. Older people (greater or equal to 65) are more likely to choose the program when they do not use a water filter system at home. Households in smaller cities or communities are more likely to pay for a proposed water treatment program that offers health risk reductions. Individuals who experienced health problems from drinking water in the past were more likely to pay for the proposed program in the No-self-protection model. Married individuals, as well as male respondents, are less likely to pay for a proposed program in the Self-protection model. However, health problems experienced by either a respondent himself or his family members are found to have no significant effect on choosing the status quo option in that model. Other demographic variables, such as the presence of kids in different age brackets, primary language of communication (English or French) are not statistically significant in either model.
 The AE interaction approach is estimated using the entire data set in a two-step approach that allows for interaction effects between levels of expenditure on self-protection and each of the six risk reduction attributes. Results from Step 1—the Tobit model that regresses FilterExp on a vector of exogenous variables—are shown in Table 3. Since the marginal effects of Tobit models differ from the estimated coefficients by a factor that accounts for the proportion of data falling short of the lower bound of the dependent variable (zero in this case), estimated marginal effects are also reported. Most variables are found to have coefficients that are insignificantly different from zero with two exceptions. Respondents whose primary language is English spend, on average, $40 more on installing and maintaining water filtration systems at home. This may explain why the coefficients on the interaction term (English*SQ) in the SS models is not significant. In addition, households with children between 6 and 12 years old spend, on average, $33.50 more on filter expenditures than other households. An interesting finding is that BottleExp is found to be negatively related to FilterExp, suggesting that bottled water may be seen as a substitute for filtered water, regardless of the stated primary motivation for purchasing bottled water of convenience and taste.
Table 3. Results of Tobit Regressions on the Filter Expenditure Variablea
Filter expenditures are the sum of installing and maintaining water filter systems at home. Standard deviations are in parentheses.
 Results from the second step of the AE interaction approach are presented in Table 4. The first set of results shows estimates obtained when we interact predicted filter expenditures, Z*, with the six main attributes while the second uses actual filter expenditures, FilterExp in the interaction terms. Although it is difficult to compare the fit of the two models, their log-likelihood values are similar. The estimated coefficients for the health risk attributes and Bill are significant with expected signs in both models. The estimated sociodemographic effects on the likelihood of choosing the status quo option are also similar between the two models. However, the two models produce several estimated coefficients for the interaction terms that differ both in sign and degree of significance. One example is the interaction term between filter expenditure and microbial deaths (FilterExp*MICD). It is positive and significant for the model using the predicted filter expenditures but negative and significant for the model using the actual FilterExp. A second example is that the coefficient on the interaction term between filter expenditure and Bill (FilterExp* Bill) is more negative in the model using predicted filter expenditures, indicating a greater price sensitivity for a new municipal water treatment program when one uses in-home water filtration systems. These differences imply that a municipal water treatment program and household water filtration systems are substitutes in the model using predicted expenditures and complements when actual expenditures are used. Shogren and Stamland  discuss the presence of significant heterogeneity among people who choose to self-protect due to different skill levels and risk tolerance. If endogeneity is a serious concern, then ignoring endogeneity might generate biased estimates. Results from the model using predicted expenditures are preferred because this model controls for the correlation between individuals' risk preferences and their decisions to engage in self-protection against health risks from drinking water. The results from this model are consistent with our assumption that an individual's self-protection against drinking water health risks decreases his or her demand for municipal water treatment improvements.
Table 4. Estimated Conditional Logit Model to Explain WTP for Public Water Quality Improvement Program: Averting Expenditure Interaction Approacha
Interactions with Latent Filter Expenditures
Interactions with Actual Filter Expenditures
The latent filter expenditure variable is an instrumental variable for FilterExp, a predicted FilterExp variables based on the Tobit regression results (Table 4): Annual house expenditures on water filter systems. Standard deviations are in parentheses.
 Marginal WTP estimates for reductions in four different types of risk: microbial illnesses (MICI); microbial deaths (MICD); cancer illnesses (CANI); and cancer deaths (CAND) derived from both the estimated CL Models are reported in Table 5 (see supporting information for the results based on a random parameters logit specification.) Standard deviations of the WTP estimates are based on the Krinsky-Robb simulation approach [Krinsky and Robb, 1986]. The WTP estimates are all positive and significant at the 5% level and they differ by health risk outcomes (mortality versus morbidity) and cause (microbial versus cancer). The WTP for one fewer death is much higher than that for one fewer illness case. The WTP to avoid a cancer illness is significantly higher than the WTP to avoid a microbial illness. While we did not find the estimated WTP for mortality risk reductions significantly different between risk types (microbial risk versus cancer risk) here, we found WTP for cancer mortality risk reduction is greater than microbial risk reduction when we assume there is a 25 year cancer latency with a 5% discount rate [Adamowicz et al., 2011].
Table 5. Marginal Willingness to Pay Estimates for Health Risk Reductions From Drinking Watera
Sample Segmentation Approach
Averting Expenditure Interaction Approach
WTPtotal (From No-Self-Protection Model)
WTPAltrm (From Self-Protection Model)
Altruistic WTP as % of WTPtotal (95% CI)
WTPtotal (From No-Self-Protection Model)
WTPAltrm (From Self-Protection Model)
Altruistic WTP as % of WTPtotal (95% CI)
Standard deviations or confidence intervals (CI) are in parentheses.
 Turning to the main hypothesis being tested in this paper, we compare total WTP estimates with altruistic WTP estimates (Table 5), where we use WTP derived from the Self-protection model to measure altruistic WTP and WTP from the No-self-protection model to measure total WTP. We find WTPTotal > WTPAltrm using both the SS approach and the AE interaction approach. This ordering holds across all types of health risk reductions. Given the consistency of our findings across two different approaches, our data support the assumption that willingness-to-pay for public good valuation of health risk reduction may be driven by both self-interested and altruistic concerns. While tests of the differences between total WTP and altruistic WTP show these differences to be statistically insignificant when we use estimates from the SS approach, probably due to small sample size, results using estimates from the AE Interaction approach provide strong evidence in support of our hypothesis. Using this preferred method (because it deals with endogeneity), we have strong results suggesting that a large proportion of individuals' total WTP for a public good that leads to improvements in municipal drinking water may be motivated by altruistic concerns. The differences between total WTP and altruistic WTP are significant for both microbial illness risk reductions (p = 0.04) and for microbial death risk reductions (p = 0.01). Several factors may contribute to this finding. First, the AE interaction approach takes potential endogeneity into account. Second, it allows for intensity of self-protection. Third, the particular risk reductions are associated with microbial contamination, an issue that has concerned Canadians ever since the over 4000 illnesses and seven deaths from E. coli contamination in Walkerton, Ontario in 2000 [Livernois, 2001].
 The differences between total WTP and altruistic WTP for both cancer illness risk reductions and cancer death risk reductions are, however, insignificant. Heterogeneous latency effects in the cancer risk reductions may be one of the reasons for the insignificance [Adamowicz et al., 2011]. The finding that total WTP and altruistic WTP for cancer risk reductions are not statistically different implies that people are willing to pay for cancer risk reductions from municipal drinking water treatment mostly out of concern for other people's safety, not their own. Caution should be used in interpreting this finding because we may have overestimated the altruistic WTP in this study since we assume away the existence of private benefits on cost savings from a reduced need for self-protection in the future or when away from home.
 In order to get a sense of the relative magnitudes of altruistic WTP when compared to total WTP, we calculate the percentages of altruistic WTP relative to their corresponding total WTP using estimates from the interaction model. As Table 5 shows, altruistic WTP estimates account for between 75% and 89% of total WTP, which means that self-interested WTP accounts for about only 11%–25% of total WTP for the public good. Based on this result, we conclude that a large proportion of total WTP for a public good is motivated by concern for others in this drinking water context.
4.3. Public-Good Values of Statistical Life and Values of Statistical Illness
 WTP estimates for health risk reductions are widely used to derive VSL or values of statistical illness (VSI). Our VSL/VSI calculations are based on the results from the AE interaction approach. In addition, we distinguish between paternalistic and nonpaternalistic altruism, as noted in equations (7) and (8). The public-good VSL/VSI arising from an assumption of paternalistic altruism is derived from estimates of total WTP, since it is assumed to be motivated by both self-interest and concern for others. The public-good VSL/VSI arising from an assumption of nonpaternalistic altruism is obtained from estimates of self-interested WTP, calculated as the difference between total WTP and altruistic WTP and is, in this way, equivalent to a private-good VSL/VSI. In each case, since our estimated WTP is a household WTP, we first convert it into an individual WTP before further calculations in order to facilitate comparisons with other estimates in the literature. Since the average number of people in a household in Canada is 2.6 [Statistics Canada, 2005] and the risk level presented in the survey is based on a 35 year period within a community of 100,000 people, then using CL estimates from the AE interaction approach (Table 5), the public-good VSL for a microbial death is CAN$19.1 million (14.157 × 100,000 × 35/2.6). This and subsequent values reported in Table 6 are in $2004 constant Canadian dollars.
Table 6. Comparison of Public-Good Values of Statistical Life and Values of Statistical Illness Based on the Averting Expenditure Interaction Approach (2004 Constant $CAN)a
VSL or VSI Paternalistic Altruism
VSL or VSI Non-Paternalistic Altruism
Altruistic VSL or VSI
VSL and VSI denote values of statistical life and values of statistical illness cases. They are calculated using WTP estimates reported (from AE Interaction Approach) in Table 5. Confidence intervals (CI) are in parentheses.
The VSI associated with microbial illnesses is in dollars; however, the VSI/VSL values for all other health outcomes are in millions of dollars.
Denotes the 1% level.
Denotes the 5% level.
Indicates the difference between the public good value and altruistic values is significant based on 1000 Krinsky-Robb simulations.
 In Table 6, we report public-good VSL/VSI values for the two types of altruism (paternalistic and nonpaternalistic) obtained from our survey. We also report the magnitude of the altruistic component of these public-good VSL/VSI values. All values in Table 6 use estimates from our preferred model (the AE interaction approach). We find the paternalistic public-good VSL for a microbial disease death is $19.1 million and about $23,000 for a microbial illness, while the VSL for a cancer death is $14.4 million and the VSI for a cancer illness is $3.6 million. These public-good values assuming paternalistic altruism appear high when compared to most published VSL estimates that are based upon private risk reductions. We, therefore, provide estimates obtained by assuming nonpaternalistic altruism since these are closer to self-interested values. Since the difference in WTPTotal and WTPAltrm for cancer risk reductions are not significantly different from zero, probably due to small sample size, we focus on discussing the microbial disease and death estimates for the nonpaternalistic altruism public-good VSL/VSI only. The nonpaternalistic public-good VSL for a microbial death is estimated to be $4.7 million and is well within conventional expectations about the VSL. These values are approximately 25% of the corresponding paternalistic public-good VSL estimates. The nonpaternalistic public-good VSI of a microbial illness is estimated to be $3,122, or about 15% of the corresponding paternalistic public-good VSI estimates.
 In the health risk literature, extensive efforts have been undertaken to estimate VSLs [Viscusi and Aldy, 2003]. Despite the public-good nature of some VSLs, most empirical VSL estimates have been derived from private good contexts [Strand, 2004; Viscusi and Aldy, 2003; Mrozek and Taylors, 2002; Kochi et al., 2006]. The reason might be that the optimal provision of a public good, according to Samuelson's rule, should be found by aggregating over individuals' self-interested WTP for the good. Our “good” or risk change certainly has public good characteristics. Compared to these studies, our paternalistic public-good VSL estimates seem to be in the upper bound of these published estimates. Costa and Kahn  suggest that it is likely that the value of risk reductions has increased over time as per capita income increases. Our estimates may reflect that increase. On the other hand, our estimated VSL for microbial death is $4.7 million which is lower than the mean value of $6.3 million derived in a private risk reduction context [Chestnut and de Civita, 2009]. Therefore, our public-good VSL estimates that incorporate altruism encompass the published private-good VSL estimates. Depending on the extent of altruism, our estimated public-good VSL values may provide both a lower and upper bound of private-good VSL estimates. One caveat of our public-good VSL/VSI estimate is that we do not attempt to distinguish the form of altruism in each individual's willingness-to-pay for the public good.
 This paper is an empirical study to investigate the extent of altruism in individuals' WTP for a public good that reduces health risks from municipally provided tap water, meaning that our good provides both private and public benefits. We hypothesize that an individual's total WTP may be greater than his/her self-interested WTP if individuals are willing to pay for their own health risk reductions, as well as for other people's risk reductions.
 Two different approaches (SS and AE interaction) are adopted to test the hypothesis that total WTP is greater than its altruistic component. The results from both methods, in general, support this hypothesis. In addition, we find that self-protection against health risk decreases one's willingness-to-pay for a public program to reduce health risks to the general tap water using public. The differences in the WTP values for microbial risk reductions estimated using the AE interaction approach are significant. It is likely that microbial risks from drinking water are better understood than cancer risks in our sample. This is our preferred method since it controls for potential endogeneity between risk-averse beliefs and responses to stated preference questions. Taking endogeneity into account, it is found that, the more money spent on water filter systems, the less one is willing to pay for health-related risk reductions—presumably because the respondent feels that he/she is less susceptible to these risks.
 Using our estimated WTP values, we are able to construct both paternalistic and nonpaternalistic public-good VSL estimates and we find the former to be significantly greater (by about four times) than the latter. However, we note that our altruistic WTP might be overestimated because we did not take into account future cost savings of filter maintenance expenditures and private benefits of consuming better drinking water outside the home after an improved water treatment program becomes available. Also, there may be joint benefits associated with consuming purchased water, such as the taste, convenience, and the lack of odor. Further analysis is needed to account for such jointness. If this is the case, then our nonpaternalistic public-good VSL might be underestimated. Interestingly, Jones-Lee  argues that the VSL for a “caring” society will be some 10–40% larger than the value that would be appropriate for a society of purely self-interested individuals. Our results suggest that a society of individuals who are paternalistically altruistic value other people's lives about four times more than a society of individuals who are nonpaternalistically altruistic. Given the substantial differences in these nonpaternalistic and paternalistic VSLs, use of one or the other in public policy decisions could give rise to very different prescriptions about the desirability of public programs. Clearly, further research on understanding and testing for the type of altruism is needed [Cropper and Krupnick, 2009].
 Last but not least, similar to the results of many published stated preference studies, despite our best efforts in following best practices in conducting a stated choice study, our results are potentially subject to hypothetical bias and social desirability bias. Although it remains a challenge to identify the magnitude of hypothetical bias and the potential for social desirability bias in this study where revealed preference data on risk reduction values are not available, our analysis focuses on the difference between stated preference estimates from altruistic and nonaltruistic groups. If hypothetical bias affects these groups similarly, the value of this difference should not be much affected. Furthermore, several steps were taken to minimize these biases. This study used data from a survey that was designed to allow us to examine the validity of nonmarket valuation estimates based on different question formats [Adamowicz et al., 2011]. Results of these validity tests indicate our estimates are robust across formats. In addition, we removed responses that appeared to be yea-sayers to the valuation questions. Also, it is likely that results from online surveys are less prone to social desirability bias than in-person interviews [Leggett et al., 2003]. Comparisons of our WTP estimates with other published WTP estimates in similar contexts reveal that our WTP estimates are not unrealistic and thus we hope that the extent of hypothetical bias and social desirability bias is small.