# Abstract

Climate change has been receiving wide attention from the international community. The

UK, like many other countries, has set its target to achieve a 12.5% reduction in levels of six

greenhouse gases (GHG) by 2010, relative to 1990 levels. In order to gain a complete

understanding of the costs and benefits of GHG reductions, the public’s willingness-to-

pay (WTP) must be considered. In this study the preference and WTP for GHG emissions

reductions involving one of the major UK water companies’ customers were investigated

using a Bayesian mixed logit analysis of survey-based choice experiment data. Advanced

econometric techniques were employed to accommodate indifference and multi-modality

in preferences and WTPs across various customer segments. Results show that average per

unit WTP to avoid increased GHG emissions is larger than that for efforts to reduce them. In

addition, customers are less likely to be indifferent to the former compared to the latter; this

is particularly true when GHG emission reductions are relatively small. In this case a

relatively large proportion of customers are found to be indifferent with a near-zero per

unit WTP. On the other hand, as reductions in GHG emissions increase more customers

become sensitized as reflected by the smaller proportion of customers with a near-zero per

unit WTP. The implications of these results as related to cost-effective investment planning

aimed at mitigating climate change risks are further discussed.

*2012 Elsevier Ltd. All rights reserved.*

# 1. Introduction

Climate change strategy drives the transition to a low carbon economy, creating opportunities and risks to which businesses must respond to succeed. International policies such as the Kyoto Protocol are major drivers behind the EU and UK emissions targets and behind legislations that shape thebusiness environment. The UK adopted the Climate Change Act (2008), which sets a target for the UK to reduce carbon emissions to 80% below 1990 levels by 2050 (Department of

Trade and Industry, 2003). It also sets an interim target of a 34% reduction by 2020 (with the potential to increase this to a 42% cut given an international agreement) and established the

concept of carbon budgets. It also targets to achieve a 12.5% reduction in levels of six greenhouse gases (GHG’s) by 2010, relative to 1990 levels (Tompkins et al., 2010). In the UK, the

water industry is made up of 12 water and sewage service providers and 14 water suppliers delivering more than 17 billion litres of water per day to domestic and commercial customers, the majority of which is then processed before being returned to the environment. As a result of these processes, the water industry produces about 4 million tonnes of CO2 (Carbon Trust, 2011). Out of the UK total GHG emissions, water and wastewater utility companies generate close to 0.8%. This contribution increases to 5.5% if GHG emissions from household water heating is included (Reffold et al., 2008). In this respect, the UK water industry faces difficult choices during investment planning as it needs to meet regulatory demands as well as its customers’ needs. An obvious interest for these water companies is thus to maximize benefits and revenues on their investments which may involve trade-offs between the various aspects of the service delivered, such as water quality, security of supply, and environmental steward-ship. In order to justify investment, it is important to acquire accurate information regarding attitude and associated benefits emerging from the mitigation of various risks linked to climate change ensuing from the operations of water companies and other related industries (e.g., emissions from water and sewage treatment plants, emissions from water heating systems, aging fleet). There is a wealth of literature examining public percep-tions of climate change. According to a UK survey, only 1% of the English public are not familiar with terms like ‘climate change’, ‘global warming’, or ‘greenhouse effect’; in fact, most people claim that they are familiar with the main causes of climate change and are concerned about it (DEFRA, 2002). In addition, the bulk of literature has focused on climate change mitigation and socio-technological transitions relating to energy policy (Foxon and Pearson, 2008; Jacobsson and Bergek, 2004; Smith et al., 2005). Evidence suggests that societal shifts occur as a result of a set of simultaneous changes in technology, practices, regulation, industrial networks, infra-structure and culture (Geels, 2002). However, many factors come to play when considering mitigating climate change through reduction in GHG emission levels. One of these factors is societal benefits, as often elicited in stated preference surveys by measures of willingness-to-pay (WTP), for improvements to existing services that may contribute to such mitigations. Several empirical studies, have demonstrated the public concern surrounding GHG emissions, and have shown a positive WTP for strategies aimed at reducing GHG emissions. Valuation studies conducted in a variety of countries and contexts (Brouwer et al., 2008; Carson et al., 2010; Lee and Cameron, 2008; MacKerron et al., 2009; Viscusi and Zeckhau- ser, 2006) all estimated a positive and often substantial WTP among the public for strategies aimed at reducing GHG emissions and attendant climate change risks. Stated preference studies of GHG emissions reduction have been important for demonstrating public support for mitigat-ing climate change, and for providing information on the effective design of policies to this end. Such studies reflect the uncertainties and misconceptions inherent in the debate on the role of GHG emissions in global warming, rainfall irregularities, and other symptoms of climate change (Viscusi and Zeckhauser, 2006). These uncertainties and misconcep-tions are demonstrated through the diversity of public opinion and support for GHG emissions reduction strategies. This has driven some studies to account for preference heterogeneity (i.e. the variation of preference intensities across members of the population) in the modelling of WTP for GHG mitigation (Carson et al., 2010; Fleischer and Sternberg, 2006; Layton and Brown, 2000). However, the assumption of joint normality adopted by such mixed logit (MXL) applications, whether applied to parameters governing GHG emissions or other service factors, could be unrealistic. A case in point is the price parameter and the need for it to be strictly negative, something which cannot be achieved with unbounded normal distributions. As a result, distributions of price parameters always end up with a share of the population counter-intuitively preferring higher prices. Moreover, since the normal distribution includes zero, the calculation of WTP becomes intractable with the price parameter being in the denominator. For these reasons, price parameters have been usually either fixed, or assigned alternative distributions such as lognormal (Revelt and Train, 1998), uniform and con-strained triangular distributions (Hensher and Greene, 2003; Revelt and Train, 1999). The problem is even more general than the need to impose sign constraints on the price parameters. Indeed as far as risk attitudes are concerned, levels of ‘dislike’ of higher risks of climate change are expected to be strictly positive when evaluated against a lower- or no-risk baseline level, which means that the distribution of attitudes would be bounded by zero at the lower end. Moreover, indifference towards risk of climate change might be prevalent among a large proportion of customers, especially where risk levels are low, while other customer groups may have a significant dislike of risk, in which case the distribution of risk parameters would be bimodal or diffuse. To the best of our knowledge, such distributional assumptions remain largely ignored by the stated preference literature dealing with climate change risks, if indeed preference heterogeneity is accounted for at all. This is rather surprising given the evidence on perceived individual and social barriers to taking action to address climate change, despite widespread agreement that people have a responsi-bility to do so (Lorenzoni et al., 2007). A recent exception to this pattern is Carson et al. (2010) who examined key determinants of public preferences toward climate change policy in Australia using a discrete choice experiment. Policy attributes included: (1) the starting date of an emissions trading program (2010 vs. 2012); (2) how to redistribute revenue generated by the policy option (reducing the Goods and Service Tax (GST) vs. give it to low to low-income households and seniors); (3) whether to invest some of the policy revenue in R&D (invest in R&D vs. lower taxes); (4) whether initially to exempt the transport sector (yes vs. no);

and (5) whether energy-intensive industries should receive special treatment (yes vs. no). Carson et al. (2010) employ an original orthogonal main effects design, combined with its mirror image or ‘‘fold-over’’ and subjected to some further modifications, resulted in a highly balanced design of 16 pairs of policy options. Respondents were then asked to choose the option they preferred most and their choices were recorded. The highly balanced nature of the design enabled the authors to employ a simple non-parametric alternative to the computationally intensive mixed logit model to analyze respondents’ stated choices. Attribute strengths of preference and their heterogeneity were recovered merely by counting the number of times particular levels were chosen and constructing their resultant frequency distributions. To this end, strengths of preference for attribute levels chosen as frequently as their opposites (i.e. eight times each) were normalized to 0, signifying actual indifference to it. Hence strengths of preference ranged from 8 (level never chosen) to 8 (level always chosen). Results indicated significant heterogeneity in the public’s preferences towards climate change policy attributes. Moreover, indifference and multi-modality was prevailed in more than one policy attribute. For example, a sizeable fraction of respondents were indifferent to the starting date of the emissions

trading scheme (with the largest mode at zero), with the number of respondents favouring a 2010 start outnumbering those preferring a 2015 start (with another mode at 8). Likewise with investing 20% of the revenue generated by the climate change policy to R&D, whereby a sizeable fraction was indifferent between it and lowering taxes, while another supported it. Moreover, tri-modality was observed with respect to the revenue redistribution attribute, where the largest fraction was indifferent between lowering GST and giving it to low-income households and the second and third roughly equally split between supporting the former and latter option, respectively. In this study, we investigate similar patterns of indifference and multi-modality in water customers’ preferences for reductions of greenhouse gas emissions associated with the operations of Veolia Water Central (VWC), a UK water company, and their WTP for such mitigations. Sources of GHG emissions associated with the water company include water treatment and distribution, wastewater collection and treatment, as well as other running operations related to transportation and administration. This study presents and discusses an application of Train and Sonnier’s (2005) bounded hierarchical Bayes (HB) mixed logit model to analyze data from a choice experiment (CE) on customers’ preferences for improvements in water service levels; reduced GHG emissions among others. In comparison to Carson et al. (2010), our data directly gauge attitudes to quantitative reductions of GHG emissions, rather than to policies implemented to achieve emission reduction targets. Hence it can be safely assumed

that such attitudes will be in the same positive direction for customers and will only differ in scale, where some would be indifferent with near-zero WTPs and others sensitive with positive and significant WTPs. In contrast, respondents may hold opposite views to given policies in Carson et al. (2010), varying between support and opposition to the proposed

policy.

In distributional terms, we can herein justify imposing bounds on preference parameter distribution, so as to restrict attitudes and WTP to be on one side of zero. Therefore, this study departs from the restrictive assumption of joint normality of preference parameters by using bounded and flexible distributions of tastes that are based on simple transformations of the normal distribution with zero at one end. This approach has been applied by Rigby and Burton

(2006) and Rigby et al. (2009) to model consumer perceptions and demand for genetically modified (GM) foods, showing that consumers are polarized into two segments: one strongly averse to purchasing GM food while another is indifferent. Balcombe et al. (2009) explored various bounded specifications to model consumers’ WTP for reduced and no-pesticide food.

As regards risk attitudes governing the safety of the water service, Chalak and Reid (2010) have also implemented this approach to modelling customers’ attitudes to risks of water

safety failure. They reported that indifference or nearindifference to risk is prevalent among a sizeable segment of the population, especially where risk levels are relatively low, and that recent experience of water safety events considerably reduces the extent of this indifference. Thus, they concluded that awareness campaigns realistically mimicking the trauma associated with such events would sensitize customers to such lower-risk events, much like TV ads warning against the dangers of drunk-driving by means of graphic representations of car accidents and their aftermaths. Similar evidence of indifference to risks of climate change

among a segment of water customers can be noted in this study.

# 2. The hierarchical Bayes mixed logit model

Since the development of simulation methods and their integration into relatively user-friendly software packages in the mid-1990s, the popularity of the mixed logit model was boosted and the number of applications of this computationally intensive model was dramatically increased (Hensher and Greene, 2003). The mixed logit model is one of many discrete choice models that aim to relax many of the constraining assumptions imposed by the standard conditional logit specification, most notably the independence from irrelevant alternatives (IIA) and taste homogeneity assumptions (Hensher and Greene, 2003; Train, 2009). This model assumes

a continuity of preferences over some range of values following a distribution that is commonly assumed to have a parametric form of known properties. Most commonly, the normal distribution is conveniently chosen to this end. In this model, a person n faces a choice among J alternatives in each of T time periods. The utility derived from alternative j and

period t (Unjt) would be:

where bn is a vector of k preference parameters to be estimated and Xnjt a vector of k attributes associated with alternative j and period t. The larger the absolute magnitude of the preference

parameter, the more (dis-)utility the increased provision of the corresponding attribute would confer to the customer and the more weight this attribute would carry in his/her

choices. Where the attribute is a ‘good’ (e.g. water savings), its increased provision will confer utility to the customer and its corresponding preference parameter would be expected to

be positive. Conversely, where the good is a bad (e.g. GHG emissions; the attribute of interest), its increased provision would confer dis-utility (i.e. negative utility) to the customer

and its preference parameter would be expected to be negative as a result. Typically, the error terms enjt are assumed to be independently and identically distributed (iid) with a Type I Extreme Value distribution. Preference parameters are taken to follow a multivariate normal distribution with a k 1 vector of means b, and a k k a variance-covariance matrix V (bn N(b,V)). The k diagonal terms of V denote the preference variances which summarize the spread of these preferences in the population. The larger the variances, the more spread out the preferences

across members of the population, and vice versa. The off-diagonal terms, when freely estimated, measure the extent of two-way correlations across all pairwise combinations of

preferences. Accounting for correlations would capture the tendency of some preference parameters to vary jointly with others across members of the population. For example,

preferences for both reduced GHG emissions and water savings preferences are expected to rise and fall jointly to some extent, giving rise to positive correlation, since they are both partly

animated by shared environmental concerns. Conversely, some preferences may be negatively correlated, such as would be the case with reduced GHG emissions and second-car purchasing,

as they would be partly animated by conflicting attitudes towards the environment. Accounting for preference correlation is a powerful tool to improve model fit, predictive ability

and accuracy of parameter and WTP estimates.

Conditional on the choice set of J options and time period t, the probability of choice per individual, if bn were known, would be a conditional logit function. Let ynt denote the option

chosen by respondent n on choice occasion t; the probability of this option being chosen would be:

The components of this equation can be understood in intuitive terms. The exponentiated utility of the chosen option in the numerator refers to the odds of choosing this option relative to a reference option in which the value of X is arbitrarily set to zero (the choice of this reference value is irrelevant as it drops out of the logit function). Likewise, the denominator sums up the odds of choosing each option in the choice set, including the chosen option, relative to the same

reference level.

Now let yn denote the whole sequence of choices over T time periods, and the set of yn over the N respondents by Y. The probability of the sequence of choices per respondent, conditional on bn, would be given by the product of the individual logit functions described above:

Given bn is unknown and is drawn from a multivariate normal distribution, the unconditional probability becomes the integral of L(ynjbn) over all possible values of bn weighted by

the density of bn – the multivariate normal distribution of mean b and variance-covariance V. The unconditional probability, denoted Pn, is called the mixed logit choice probability, as it is the product of conditional logit probabilities mixed over a density of preference parameters.

We estimate b, V and the individual-specific vector of parameters bn for each respondent n using a HB implementation of the MXL model. A full account of the Bayesian simulation procedures involved can be found in Train (2009,2005). HB methods are well-suited for the estimation of MXL

models with normally distributed parameters, and are much more flexible than Classical simulated maximum likelihood methods in accommodating bounded distributions of the type

employed in this study.

To ensure model convergence, a high number of ‘burn-in’ iterations (30,000 in this application) are initially implemented,followed by another high number of iterations (20,000) of which only one in ten are retained for inference in order to minimize correlation among draws. The mean of these retained draws is the simulated mean of the posterior distribution. Train (2005) explains that, under conditions observed in the below application, results could be interpreted in Classical terms. That is, mean and covariance of the posterior distribution could be taken to be asymptotically equivalent to the maximum likelihood estimator and its covariance. In this paper we interpret the results in classical terms (i.e. point estimates and associated standard errors).

To characterize more flexible distributions that could accommodate indifference, polarization and bounds in risk attitudes, HB procedures can easily accommodate certain

transformations of normals. For example:

Lognormal distribution: ln = exp (bn),

Normal censored from below at zero: cn = max (0, bn) and

Johnson’s SB distribution: jn = l + (u l)[exp(bn)/(1 + exp(bn))].

where bn for all values of n is normally distributed. The person’s utility and sequence of choice probabilities become the following:

where T is any of the transformations of normals proposed above.

According to Train and Sonnier (2005) and Rigby and Burton (2006), lognormal distributions have relatively thick tails which may yield unrealistically large WTP estimates. Moreover, log-normal distributions assign zero probability to null taste parameters and WTPs and hence do not accommodate indifference. In practice, a model with log-normal distributed parameters yielded unreasonably large parameter estimates and was consequently ignored. In the normal censored distribution, on the other hand, a mass of tastes is around zero with the density above zero being normally distributed, hence accommodating indifference in tastes. Finally, the SB distribution

allows a distribution of tastes between l and u. in this application, l was fixed at zero while u was determined in an iterative process to maximize model fit as measured by loglikelihood at convergence. This distribution is flexible enough to accommodate distributions that look like the lognormal albeit with a thinner tail, but also the possibility of flat plateaus between drop-offs on both sides, and even bi-modality. It is worth noting that the model parameters can be easily specified with full correlation under any combination of parameters distributions, since the correlation among the elements of b simply induces correlation among the elements of l, c or j.

# 3. Empirical study—customers’ preferences for greenhouse gas reductions

This study is based on a choice experiment (CE) survey undertaken for Veolia Water Central (VWC) – formerly known as Three Valleys Water – which serves 1.2 million households in Southeast England, as part of their periodic business plan submission to Ofwat, the England and Wales economic regulator of the water industry, for the price review cycle ending in 2009 (referred to as Price Review 2009, or PR09). Such submissions by water and sewerage companies in England and Wales help Ofwat’s to set limits on the prices water and sewerage companies can charge to their customers. In their submissions, water and sewerage companies need to demonstrate that their investments are consonant with their customers’ preferences and WTP’s for proposed improvements. Hence this study was commissioned by VWC with the

aim is to gauge customers’ priorities for investment in their water service. The approach of using customer preference surveys for investment planning in the water industry is not new, with surveys carried out by Thames Water in Price Review 1999 (PR99) and more recently by Yorkshire Water at Price Review 2004 (PR04) (Willis et al., 2005).

Respondents were presented with a series of ten choice scenarios consisting each of three options; a fixed status quo option characterizing the current situation and two generically constructed options. These options were described in terms ‘service attributes’. Extensive focus groups conducted with customers throughout the VWC region were used to help select the service attributes that were most relevant to the customers, as well as their most appropriate metrics and level ranges. The final list of attributes included:

River water levels (RIVER), with two levels: a status quo level

equivalent to ‘no change’ with generally low flow of rivers

throughout the summer months and drying up of some

smaller rivers, and an ‘enhanced service’ level where low

flows and some drying of small rivers will occur in at most 1-

2 summer months;

Water saved through further water efficiency measures

(SAVED), ranging from a status quo level of no further

efficiency measures to a maximum improvement level

equivalent to the water used by 300,000 household in a year,

or, 25% use reduction;

Number of tests of water quality failing to meet standards

(TESTS), ranging from a deterioration level of 100 in 100,000

to a maximum improvement of 5 in 100,000; and

Annual greenhouse gas emissions (EMISS), the attribute of

interest, ranging from a deterioration (1) level equivalent to

130,000 cars doing average yearly mileage to a maximum

improvement (+2) level equal to 15,000 cars doing average

yearly mileage.

A full account of the attributes and their levels is presented in Table 1. Levels of 0 characterize the current level or status quo; 1 deterioration relative to the status quo, and +1, +2 and +3 improvements relative to the status quo. It was ensured that for each attribute, the range of levels cover realistic situations, as advised by VWC. As to the associated changes in annual

bills that would accompany improvements/deteriorations in attribute levels, 8 rather than 4 levels were defined: 2 decreases in annual bill (decrease by £15 or £5), no change in annual bill (i.e., status quo), and 5 increases in annual bill (increase by £5, £10, £15, £20 or £35). An example choice card is presented in Table 2.

A Db—optimal design (Ferrini and Scarpa, 2007) was obtained for the CE in which parameter mean estimates and their standard errors from a preliminary pilot survey of 50 respondents were used to update the design for the main data collection phase. A total of 120 choice sets were thus designed and blocked into twelve groups of ten sets each. Each respondent was faced with a randomly assigned block of choice sets. The survey targeted a representative sample of 245 households served by VWC. This included the 50 interviews from the pilot phase since virtually no modifications were made to the pilot survey instrument before it went into the main data collection phase. Interviews were conducted face-to-face, in the home and using computer-aided personal interviewing (CAPI) scripts. Interviewing took place in October and November 2007. The sample was geographically representative down to the parish level (based on the UK’s 2001 population census). In addition, the sample was also representative of the company’s customer base in terms of age, gender and socio-economic grade, in addition to geography.

# 4. Results

Three HB mixed logit models with fully correlated parameters were estimated, differing with respect to the distributional speciﬁcation of parameters: (1) normal, (2) censored normal and (3) SB. Econometric estimation was implemented in MATLAB R2009a using code written by Kenneth Train and available on his home page (http://elsa.berkeley.edu/Software/abstracts/train1006mxlhb.html). Levels were dummy coded such that they measured attitudes towards each level relative to its status quo baseline level (i.e. events that were assigned levels of zero in Table 1). We accounted for full correlation among parameters since each of the RIVER, SAVED, TESTS and EMISS parameter sets pertained to quantitative levels of the same attribute and are hence governed by similar perceptions. We follow the terminology of Train and Sonnier (2005) by referring to underlying parameter estimates as bn and their censored normal or SB transforms as partworths. A partworth estimate indicates the marginal utility of a given attribute; that is, the utility derived from a unit increase in the provision of a good, or reduction in the emission of a ‘bad’, such as GHGs. A positive partworth indicates the actual preference for the good in question, and a negative partworth reﬂects the dislike of the bad in question.

As for yearly bill increase/decrease (BILL), it was treated as continuous such that its partworth represented a per-unit value. The BILL parameter was ﬁxed in order to avoid unreasonably high WTP values for customers with virtually null BILL parameters. The signs of BILL and deterioration (1) levels of the TESTS and EMISS were reversed since censored normal and SB distributed partworths can only be positive. This ensures that the partworth estimates are necessarily negative. An error component (s) to account for the correlation among the two generic options other than status quo was also estimated (with a normal distribution centered around zero). This error component is particularly useful where utilities associated with generic options are more prone to noise given the fact that they are ‘imagined’, as opposed to the ‘experi-enced’ status quo situation. Indeed all three models returned highly signiﬁcant estimates of the variance of s ( p-value < 0.01).

In the three models, means and variances of the bn’s were estimated by making 2000 draws of b and the diagonal elements of V. In terms of model ﬁt, the model with SB distribution of parameters yielded the best model ﬁt with a simulated log-likelihood function lower than that given by models with normal and censored-normal distributions ð2091:3; 2094:9 and 2105:3; respectivelyÞ thus supporting the decision to impose sign restrictions on partworth esti-mates. It further suggests that shares of respondents who ‘dislike’ improvements (i.e. negative parameters) or ‘prefer’ deterioration (i.e. positive parameters are) in the normal distribution model are an artefact of the speciﬁcation. To illustrate, such shares take implausibly high values such as 33% who ‘prefer’ to see an increase of GHG emission equivalent to 65,000 cars doing average yearly mileage (GHG = 1), or 43%who ‘dislike’ enhanced river water levels (RIVER = +1). Further, we interpret the fact that higher log-likelihood is attained by the model with SB distribution of parameters compared to censored normal as evidence in support of imposing upper bounds to parameter distributions. Henceforth discussions and comparisons will be limited to the SB model.

In terms of model outputs, results broadly conform to expectations (see Table 3). Mean estimates of bn were all highly signiﬁcant ( p-value < 0.01). Results also suggest that hetero-geneity is supported for most parameters, as evidenced by the signiﬁcant variances for all except the TESTS = 1, TESTS = +1 and EMISS = +2 attributes. As for the partworths, these were bounded by zero at the lower end, and an iteratively determined upper bound. Wide bounds were tried ﬁrst, and then models with incrementally lower bounds were estimated for as long as smaller log-likelihoods were attained at convergence. In the end, upper bounds of 5 were found to maximize the simulated log likelihood. Time-consuming as it is, this trial-and-error process is nevertheless necessary since parameter estimates are to a certain extent contingent upon it. We argue that, with minimum log-likelihood being the criterion for the choice of bounds, the resulting estimates are credible as they enhance the predictive ability of our model. Note that even for partworths which underlying variances were insigniﬁcant, their standard deviations turned out to be substantial relative to their values, indicating a high level of heterogeneity for them as well.

Mean estimates of partworths again conform to prior expectations. That is, customers desire to see enhanced river water levels (RIVER = +1), increased water savings through efﬁciency measures (SAVED = +1, +2 and +3), decreased numbers of failed water quality tests (TESTS = +1 and +2) and GHG emissions (EMISS = +1 and +2). Conversely, custo-mers negatively view increases in failed water quality tests and GHG emissions (TESTS = 1 and EMISS = 1; respectively).

Per unit WTP estimates associated with decreasing/increasing levels of GHG emissions and their breakdown by various sociodemographic groupings are presented in Table 4. These are evaluated against a baseline status quo level of emissions equivalent to that of 65,000 cars doing average yearly mileage. WTPs are expressed per 1000 cars per household per year so as to be able to compare them across various GHG emissions reduction/increase levels. Results show that on average, customers are willing to pay more to avoid increasing GHG emissions (EMISS = 1; £0.52 for an increase equivalent to 65,000 more cars) compared to decreasing in GHG emissions (EMISS = +1 and +2; £0.11 and£0.44 for decreases equivalent to 35,000 and 50,000 less cars; respectively). This conforms with the evidence from the literature on discrepancies between willingness to accept compensation (WTAC) and WTP, especially where the good valued is non-market in nature (Horowitz and McConnell, 2002). Gender, income and the presence of children in the household do not seem to play any signiﬁcant role in shaping WTP for GHG emissions reductions (none of the two-way t-test comparisons were signiﬁcant at p-value < 0.10), consistently with previous literature on the topic (MacKerron et al., 2009). On the other hand, 30–49 and 50 or more year-old customers had signiﬁcantly higher WTP magnitudes than the younger 18–29 year-old customers ( p-value < 0.05).

Fig. 1 presents histograms of the empirical population distribution of per unit WTP for GHG emissions reductions. The shapes of these distributions suggest that customers are less likely to be indifferent to avoiding climate change risks associated with GHG emission increases compared to mitigat-ing these risks through emissions reductions, especially when the latter is relatively small, as is the case with the ‘35,000 less cars’ scenario. This can be visualized through the smaller proportions of customers with null and near-null WTPs in the top histogram in Fig. 1 compared to the bottom two. Moreover, hints of a second mode in the £1.50–£2.00 range could be seen, suggesting the presence of an active ‘dislike’ segment when it comes to avoiding increasing GHG emissions as opposed to decreasing them.

In terms of the two GHG emissions reduction scenarios, Fig. 1 suggests that when the proposed reduction scenario is relatively small (equivalent to 35,000 less cars), a relatively large proportion of customers will be indifferent to the mitigated risks and hence will have zero or near-zero WTPs). With a larger GHG emissions reduction (equivalent to 50,000 cars—EMISS = +2), more customers will be sensitized as shown by the smaller proportion of customer with zero or near-zero WTP. In addition, rather than the distribution tailing off abruptly at around £1.00 as in the case of EMISS = +1, the distribution in EMISS = +2 is more diffuse and reaches £2.60.

In addition, the effects of importance accorded to GHG emissions reduction while making choices on the distribution of risk attitudes and WTP was examined. Results can be visualized in Fig. 2. Histograms of WTP distributions were compared across GHG emissions levels and customers’ self-assessed levels of priority they think should be accorded to the reduction of these emissions aggregated into two categories: ‘Not Important’ and ‘Very Important’. Results show that for avoiding GHG emission increases (EMISS = 1) and reducing relatively high GHG emissions (EMISS = +2), indifference is more pronounced among ‘Not Important’ than ‘Very Impor-tant/Vital’ customers. This is witnessed by the higher proportion of ‘Not Important’ customers that have zero or near-zero dislike levels. This observation does not seem to apply to relatively low GHG reductions (EMISS = +1), where the two sub-samples seem to converge to the same distribution.

We also veriﬁed whether these visual interpretations could be substantiated by means of mean comparison t-tests (Table 5). Indeed average WTP for EMISS = 1 and +2 were signiﬁcantly different at the 5 percent conﬁdence level, while they were not for EMISS = +1. This supports the observations made based on histograms. Moreover, the focus on mean levels of dislike adds a new angle from which to understand the mechanism through which climate change attitudes inﬂuence customers’ WTP for GHG emissions reductions. Where differences are signiﬁcant across ‘Not Important’ and ‘Very Important/Vital’ groups, this is at least partly attribut-able to the sensitizing effect of climate change concerns. That is, rather than trigger an increase in climate change risk dislike across the whole sub-sample of climate-change-concerned customers, such concerns operate by sensitizing a larger proportion to GHG reductions than would have been the case in the climate-change-indifferent sub-sample.

# 5. Conclusions

In this paper we show how the use of advanced econometric tools can be used better to characterize customers’ attitudes towards, and WTP for, mitigating risks of climate change as represented by GHG emissions reductions. A hierarchical Bayes implementation of the mixed logit model to analyze choice experiment data on customers’ attitudes towards GHG emissions reductions suggests that indifference is prevalent among a sizeable proportion of VWC customers. This is particularly the case when GHG emissions reductions are relatively low. In order to adequately capture this indifference, distributional assumptions departing from the restrictive normal distribution of risk dislike parameters need to be avoided. Indeed results show that the employment of the bounded SB distribution achieves a better model ﬁt than models where parameters’ are normally distributed.

The obtained results provide insights of the attitudinal shifts in response to varying levels of GHG emissions, whether increase or decrease. Treating GHG levels as qualitative dummies rather than quantitative measures on a common scale also highlights the limitations of the latter speciﬁcation. On another note, specifying a risk attribute as continuous would assume that the shape of the attitudes’ distribution would be replicated across increasing risk levels, and that the only change involved is a shift of the distribution’s mean. One may add that only the distribution’s spread is allowed to change, and only in proportion to the change in the mean value. The results clearly demonstrate that the change in distributional shape is as important as shifts in the mean value. Moreover, indifference substantially fades away with increased reduction of GHG emissions a process partly contributing to the shift in mean values.

If water companies are to account for customer priorities in their investment plans, then such ﬁndings can have substan-tial implications for implementing cost-effective interven-tions aimed at mitigating their GHG emissions and reducing climate change risks. On the one hand, water company interventions would need to be mapped carefully against levels of risks to be mitigated and the extent of their planned improvements. For example, investments aimed at reducing GHG emissions might need to achieve considerably high reductions to avoid high levels of customer indifference. Indeed such indifference could result in relatively low aggregate customer beneﬁt for the intervention and failure to justify the associated cost.

On the other hand, campaigns to raise awareness among customers by informing them about the perils of climate change caused by GHG emissions could prove instrumental in adding value to such interventions. This might shift the attitude of some customers from being indifferent to becom-ing more sensitive to climate change risks. As highlighted in Lorenzoni et al. (2007) with respect to achieving the UK Government’s GHG emissions reduction target, ensuring public engagement with climate change issues is instrumental in justifying climate change-mitigating investments on the part of water and wastewater companies. This becomes even more urgent in the current context of economic crisis, where the notion of paying additional expenses to mitigate could easily arouse feelings of indignation among many customers experiencing ﬁnancial difﬁculties. Therefore, a worthwhile avenue for future research would be to study how the information content of such campaigns would shape and reshape climate change attitudes, and through them add value to water company infrastructural investments.

Finally, some of the limitations of the econometric methods employed in this paper to capture climate change risk indifference and dislike need to be highlighted. Though bounded SB distributions add ﬂexibility to our MXL model and thus improve its ﬁt, they remain considerably restrictive. Though it allows bimodality, modes will only occur at the two extremities of the bounded distribution. In addition, the shape of the distribution is highly contingent upon the choice of bounds, which is an iterative and tedious task to perform. In particular, the extent of indifference is determined to a signiﬁcant extent by the choice of bounds. Moreover, though we argue that the simulated log-likelihood is a good criterion for choosing the bounds, it may not be without drawbacks. We observe that the iterative process to determine partworth bounds does not seem to be subject to maximizing a function that is globally concave. Rather, the function has numerous local maxima. Yet we think that resorting to such distribu-tional assumptions greatly improves the economic analysis and interpretation of choice experiment data. In terms of future research, we think that the further exploration of SB distributions where bounds are freely estimated would be an interesting avenue for research, and have already been explored by Hess et al. (2005). Also, future investigation of ﬂexible mixing distributions will likely greatly improve the performance of MXL models. Some promising models would be the use of semi-nonparametric distributions such the ones implemented in Scarpa et al. (2008), and the Generalized Multinomial Logit (GMNL) illustrated in Fiebig et al. (2010) and Greene and Hensher (2010).

# Acknowledgements

The authors would like to thank Veolia Water, in particular Mr. Christopher Offer, Economic Regulation Manager at Veolia Water Central, for his support and advice during this work.

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