Preference heterogeneity for renewable energy ...

Energy Economics 42 (2014) 101–114

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Energy Economics journal homepage: www.elsevier.com/locate/eneco

Preference heterogeneity for renewable energy technology James Yoo a,⁎, Richard C. Ready b,1 a b

Department of Economics & Business, Bethany College, Bethany, WV 26032, USA Department of Agricultural Economics, Sociology and Education, Pennsylvania State University, University Park, PA 16802, USA

a r t i c l e

i n f o

Article history: Received 25 November 2012 Received in revised form 26 October 2013 Accepted 10 December 2013 Available online 17 December 2013 JEL Classification: Q2 Q4 Q28 Q42 Q48 Q51

a b s t r a c t This study explores heterogeneity in individual willingness to pay (WTP) for a public good using several different variants of the multinomial logit (MNL) model for stated choice data. These include a simple MNL model with interaction terms between respondent characteristics and attribute levels, a latent class model, a random parameter (mixed) logit model, and a hybrid random parameter-latent class model. The public good valued was an increase in renewable electricity generation. The models consistently show that preferences over renewable technologies are heterogeneous among respondents, but that the degree of heterogeneity differs for different renewable technologies. Specifically, preferences over solar power appear to be more heterogeneous across respondents than preferences for other renewable technologies. Comparing across models, the random parameter logit model and the hybrid random parameter-latent class model fit the choice data best and did the best job capturing preference heterogeneity. © 2013 Elsevier B.V. All rights reserved.

Keywords: Renewable energy Individual-specific willingness-to-pay Random parameter model Latent class model Hybrid random parameter-latent class model

1. Introduction Random utility models (McFadden, 1974) have a wide range of application in the analysis of choice data including recreational demand choice (Boxall and Adamovicz, 2002; Scarpa and Thiene, 2005; Train, 1998), stated choice valuation (Borchers et al., 2007; Revelt and Train, 2000; Scarpa and Willis, 2010), transportation choice (Greene and Hensher, 2003; Shen, 2010), and marketing (Swait and Adamowicz, 2001). Analyzing choice data with random utility models is often done by estimating a simple Multinomial Logit Model (MNL), which assumes that preferences are homogeneous across the population. The assumption of homogeneous preferences, however, is problematic since each person is unique in terms of habit, education background, characteristics, and income level, which might be correlated with preferences over non-market goods. Failure to incorporate the unique nature of each consumer in estimating discrete choice models would mask heterogeneity in preferences and could lead to biased estimates of average preferences over the population. Several different extensions of the MNL discrete choice model have been developed that can accommodate consumer preference ⁎ Corresponding author. Tel.: +1 602 705 7311. E-mail addresses: [email protected] (J. Yoo), [email protected] (R.C. Ready). 1 Tel.: +1 814 863 5575; fax: +1 814 865 3746. 0140-9883/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.eneco.2013.12.007

heterogeneity for non-market goods. Some of these also relax the IIA (Independence of Irrelevant Alternatives) assumption. The simplest and most commonly used approach is to interact attribute levels with measured individual characteristics to see whether people with different characteristics exhibit different preferences within the MNL model. This approach retains the unrealistic assumptions of the MNL model such as IIA and uncorrelated unobserved error over time. The IIA property assumes that the choice of alternatives A and B is not influenced by the addition or exclusion of the third choice, C. In general, this may not be a realistic assumption and create a problem of leading a model to erroneously predict the probability of choosing one alternative over the other. Also, assumption of uncorrelated errors might be problematic when using a panel data because a person's choice might be correlated across repeated choice through learning or fatigue effects. Two models that allow for preference heterogeneity and that relax the IIA assumption and/or uncorrelated error terms are the random parameter logit (RPL) model (Greene and Hensher, 2003; McFadden and Train, 2000; Train, 1998), also known as the mixed logit model, and latent class models (LCM) (Boxall and Adamovicz, 2002; Milon and Scrogin, 2006; Scarpa and Thiene, 2005; Swait and Adamowicz, 2001), also known as finite mixture models. Each model has strengths and weaknesses. LCM models are less flexible than RPL models, but have an advantage when it comes to computational simplicity. The continuous representation of preference variation in the RPL might be

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inappropriate when the sample consists of discrete groups with different group-specific tastes. The discrete representation of preference variation in the LCM cannot capture within-class heterogeneity. Using either of these models could oversimplify the taste variation of the sampled respondents (Allenby and Rossi, 1998; Bujosa et al., 2010; Wedel et al., 1999). A hybrid model that combines both continuous and discrete representation of taste variation was first proposed by Bujosa et al. (2010). They find that this hybrid model fits best in terms of statistical goodness-of-fit. In this research, we estimate several different discrete choice models that accommodate preference heterogeneity. These models include the MNL model with interactions between choice attributes and respondent characteristics, a LCM, a RPL model, and a hybrid RPL–LCM. These models are compared in terms of how well they fit the data and their ability to identify heterogeneity in WTP. This research includes two advances over previous studies that have explored preference heterogeneity in discrete choice data. First, the LCM developed here places specific restrictions on parameter values for certain latent classes. These restrictions are motivated by previous research that shows that some respondents, when faced with a complex choice task, focus their attention on a restricted set of attributes, and ignore other attributes that are less salient to them (Blamey et al., 2001). We extend Scarpa et al. (2009) model of attribute non-attendance in our LCM. Second, following Greene and Hensher (2010), our hybrid RPL–LCM is estimated in a way that accounts for the panel nature of stated choice data, but extends their hybrid model by incorporating the same types of restrictions on the preference parameters for certain latent classes. Finally, this is the first study to compare all of the above mentioned models based on their ability to capture heterogeneity in individual WTP, and therefore represents an extension of what Beharry-Borg and Scarpa (2010) did. This study, specifically, estimates Pennsylvania residents' preference over different renewable electricity production technologies and their willingness to pay (WTP) for an increase in renewable electricity production. Our results build on previous studies that have estimated WTP for increased renewable energy production (Borchers et al., 2007; Farha, 1999). We explore both the mean WTP for each of several different generation technologies and the degree of heterogeneity among respondents' individual for each technology. Information on mean WTP for individual renewable technologies is important from a policy perspective. Currently, Pennsylvania has in force an Alternative Energy Portfolio Standard (AEPS) to promote renewable energy production. The current AEPS policy specifies a minimum for the amount of electricity that must come from renewable and alternative sources, setting minimum standards for renewable content. The AEPS includes a carve-out (technology-specific minimum) for solar, but does not set individual requirements for other renewable technologies such as wind, hydroelectric power and biomass. If Pennsylvania residents prefer some renewable technologies over others, that preference could be reflected in differential requirements in the AEPS. If Pennsylvania residents have negative views toward some renewable energy technologies, the current AEPS could force them to pay for technologies that they do not want. It is equally important to know how WTP varies across the population, which is the main focus of this research. We find that mean WTP for some renewable technologies is positive, but that WTP exhibits heterogeneity such that an important proportion of the population has negative WTP for the technology. This result suggests that, while the average resident would support a policy that increases renewable energy production, an important proportion of residents could oppose such a policy. Policy makers in Pennsylvania should consider the entire distribution of preferences, rather than focusing only on the mean preference. The paper is organized as follows. Section 2 reviews previous literature on two topics: comparisons of LCM and RPL models and attribute non-attendance behavior. Section 3 presents the models that will be estimated in this study, followed by descriptions of the goods being valued

and of the survey methodology. Section 4 discusses the results and Section 5 presents a summary and discusses implications of the research.

2. Literature review 2.1. Previous studies on the RPL, LCM, and RPL–LCM models Both the RPL and LCM models relax some of the restrictions of the MNL model, but they do so in different ways. Since MNL is nested within both of these two models,2 comparisons between MNL and RPL and between MNL and LCM are feasible using likelihood ratio tests. Many recent studies (Beharry-Borg and Scarpa, 2010; Greene and Hensher, 2003; Kosenius, 2010; Shen, 2010) conclude that the LCM and the RPL both improve statistical fit relative to MNL. One exception is Provencher and Bishop (2004). However, a direct comparison between RPL and LCM cannot be made based on a likelihood ratio test, because one model is not nested within the other. In order to compare these two models, different approaches have been developed. Greene and Hensher (2003) compare LCM and RPL models by looking at choice elasticities for a change in travel times, mean willingness-topay estimates, and choice probability plots,3 and find that respondents' behavioral sensitivity to an attribute (changes in travel time) is reduced in the LCM relative to the RPL, although other measures such as choice probability plots and willingness to pay valuations yield similar patterns for both models. Shen (2010) adds a non-nested test4 and prediction success indices to investigation of the choice probabilities, WTP valuations, and choice probability plots to test which model is better. She finds that the LCM is superior to the RPL in terms of these two measures. Shen (2010) and Greene and Hensher (2003) show that LCM fits better than RPL based on statistical goodness-of-fit. Kosenius (2010) investigated consumer's preference heterogeneity for water quality attributes using RPL and LCM. In order to compare the two models, the author presents WTPs for 3 potential future nutrient reduction scenarios. Rather than focusing on statistical measures, Kosenius focused on the heterogeneity of WTP of a representative respondent. They conclude that a LCM was indisputably superior in terms of capturing the relative importance order of each attribute within different classes. However, the sample in that study was not representative of the population. They conclude that the RPL is better than the LCM when the sample is weighted to correct for sampling bias. Although their study was the first attempt to explore aspects of RPL and LCM other than statistical goodness-of-fit, the heterogeneity of individual WTP was not considered in their study. Beharry-Borg and Scarpa (2010) were the first study to compare LCM and RPL based on individual WTP. They use 2 sub-samples, snorkelers and non-snorkelers, in a study valuing quality change in Caribbean coastal waters. They found that an LCM outperformed a RPL model for the snorkeler sample, but that the LCM did not behave well for the non-snorkeler sample. They did not directly compare RPL and LCM based on individual WTP within each subsample. 2 In RPL, if a distribution of random coefficient is degenerate, then the integral term will vanish leaving a simple logit form behind. In LCM, if coefficients across different classes are the same, then the latent class model is reduced to the MNL. In that sense, MNL is a special form of both LCM and RPL (MNL is nested within LCM and RPL). 3 Greene and Hensher (2003) plotted choice probabilities under LCM and RPL for each alternative and investigated the relationship between choice probabilities for RPL and those for LCM via OLS. They found that there is a weak relation between two models. 4 Shen's non-nested test is based on an AIC proposed by Ben-Akiva and Swait (1986). The test procedure is as follows: Suppose there are 2 models (model 1 and model 2) and K1 and K2 represent the number of parameters in model 1 and model 2, respectively. Also define L0, L1 and L2 represent the likelihood value for constant-only model, the likelihood value at convergence for model 1, and likelihood value at convergence for model 2,

respectively. Then, fitness measure for model j is expressed as: ρ2j ¼ 1−

L j −K j L0

: An upper

bound for probability that model 1 is chosen as the true model despite model 2 being true h i
 1 is then given by Pr ρ22 −ρ21 Nz ≤ Φ −ð−2zL0 þ ðK 1 þ K 2 ÞÞ2 ; where z represents the difference between ρ22 and ρ22.

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Greene and Hensher (2010) and Bujosa et al. (2010) compare RPL, LCM, and a hybrid RPL–LCM based on statistical goodness-of-fit and individual-specific parameters using transportation choices and recreational trip data, respectively. One difference between the two studies is that the latter does not account for the panel nature of choice data, while the former incorporates it in the model. Both studies estimated hybrid RPL–LCM models with two latent classes. Both studies find that the hybrid RPL–LCM fits better than MNL, LCM, and RPL models.

attributes and the number of levels of attributes can make choice decisions more complicated, affecting choice consistency. There is also evidence (Rosenberger et al., 2003) that the strength of a person's disposition, attitude, and belief can explain discontinuous choice behavior. Non-attribute attendance behavior is investigated in this study through estimating a latent class model that includes latent classes with restrictions on parameters consistent with attribute non-attendance.

2.2. Previous studies on attribute non-attendance

3. Methodology

In a stated choice experiment, respondents are asked to answer a sequence of questions that consist of multiple alternatives, in which each alternative is described by attributes and their levels. The experiment assumes that each respondent makes trade-offs among the levels of each attribute across all alternatives, and he or she is expected to select the most preferred alternative. In other words, all respondents are assumed to pay attention to the level of all attributes. The ability of respondents to make trade-offs among attributes is represented by the property of substitutability or continuity (Freeman, 1993), which is the central to the economic concept of value (McIntosh and Ryan, 2002). When this property is violated, discrete choice valuation is confronted with some serious problems. First, respondents that violate the property of continuity cannot be represented by a conventional utility function (Campbell, 2008; Lancsar and Louviere, 2006). Second, without continuity, there will be no trade-off between two different attributes, and WTP cannot be computed (Campbell, 2008). Several studies (DeShazo and Fermo, 2002; Hensher and Rose, 2009; Rosenberger et al., 2003; Sælensminde, 2006) have found that the continuity assumption sometimes fails in discrete choice experiments. This implies that some respondents behave as if they do not care about the level of some attributes, resulting in zero marginal utility for those attributes. Scarpa et al. (2009) investigate the possible existence of non-attendance to attributes using four different latent class models. They classify respondents into groups using special notation: TA (total attendance—all attributes are simultaneously considered), TNA (total non-attendance—respondent does not consider any of the attribute levels), PNA1 (partial nonattendance ignoring one attribute), PNA2 (partial non-attendance ignoring the cost attribute and one non-monetary attribute), and PNA3 (partial non-attendance ignoring the cost attribute and 2 non-monetary attributes). They compare different models that incorporate different combinations of latent classes following each of these behaviors. They find that less than 0.1% of the sample cares about all attributes (TA), while most respondents seem to ignore at least 2 out of their 5 attributes. In their study, 80 to 90% of respondents ignore the cost attribute, raising doubt about the validity of choice experiments in terms of calculating WTP. What might cause discontinuous preference or attribute nonattendance in a choice experiment? By the nature of choice experiments, choice tasks are complicated, so that respondents might not understand how to make trade-offs between certain attributes of environmental goods. Due to this complexity, respondents might decide to simplify choice tasks by constantly choosing alternatives with attributes they consider to be important and favorable (Blamey et al., 2001; Caussade et al., 2005; Luce et al., 2000). Sælensminde (2006) investigates lexicographic choice behavior of respondents in a choice experiment, defined as situations where a respondent consistently chooses the alternative that is best with respect to one attribute, e.g. lowest price. He discovers that respondents exhibit lexicographic preferences as a consequence of simplification of the choice task when there is a high number of attributes and respondents have no prior information about the attributes. DeShazo and Fermo (2002) examine the relationship between choice complexity and respondents' choice consistency, and find that choice complexity significantly affects choice consistency. Other studies (Jacoby et al., 1974; Keller and Staelin, 1987) find that the number of

3.1. Models In this section, 5 different econometric models are presented. The MNL is the most basic and commonly used choice model. Its theoretical foundation is the random utility model (Manski, 1977; McFadden, 1974). According to random utility theory, the utility of consumer i choosing alternative j is expressed as: U ij ¼ V ij þ eij

ð1Þ

where Vij is a deterministic component and eij is a stochastic component. This model is called a random utility model because the utility a person receives depends to some degree on random factors. Assuming that Vij is a linear function of observed characteristics of alternative j and that the stochastic component follows a type 1 extreme value, the probability that individual i chooses alternative j over k from a set of J options is expressed as:     exp βX ij Prob U ij NU ik ; ∀k ¼ X J expðβX il Þ; l¼1

ð2Þ

where Xij is a vector of choice attributes, and β is a vector of preference parameters (marginal utilities) to be estimated. Individual characteristics of the consumer variables cannot enter into choice utility alone because individual characteristics are invariant across choice alternatives, and therefore do not affect choice probabilities. They can only enter through interactions with choice attributes (Champ et al., 2003). This generates the new relationship, where the marginal utility of a choice attribute is a function of the individual characteristics. Incorporating respondent characteristics/attribute level interactions can help identify systematic heterogeneity in preferences that is tied to respondent characteristics. An MNL model with interactions between choice attributes and respondent characteristics will be called here the MNL-INT model. A latent class model, also called a finite/mixture model, assumes that there are C segments in the population. Preferences differ among the segments, but are homogeneous within each segment. The latent class model probabilistically assigns each respondent to a segment according to covariates (individual characteristics) and choice behavior. Suppose individual i, who belongs to class c, chooses alternative j in a choice occasion k. The utility of this respondent is expressed as: U ijkjc ¼ X ijk βc þ eijkjc :

ð3Þ

Xijk is a vector of choice attributes, eijk|c is an unobserved component within a class, and βc is a class-specific vector of parameters to be estimated. Assuming IIA holds within a class, the probability of respondent i choosing alternative l in a choice occasion, k, is: expðX ilk βc Þ   P ilkjc ¼ X J exp X ijk βc : j¼1

ð4Þ

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In a LCM, it is necessary to specify a function that defines the probability of class membership in each class for each respondent. The class membership probability of individual i being classified to class C can also be modeled as a multinomial logit: expðθc Z i Þ P ic ¼ XC expðθc Z i ÞÞ c¼1

ð5Þ

where θc is a class specific parameter vector and Zi includes individual characteristics (income, age, etc.) of respondent, i. This class-specific parameter shows the influence of individual characteristics on the probability of being in a class c. By combining the conditional choice probability, Pijk|c with membership probability, Pic and taking the expectation over all classes, the joint unconditional probability for the choices made by individual i could be constructed as follows: 1

0 Pi ¼

i X XC h expðθc Z i Þ C X P ic P ijkjc ¼ c¼1 c¼1 expðθc Z i Þ c¼1

!

B expðX β Þ C K B ilk c C  ∏k¼1 BX C @ exp X ijk βc A j¼i

ð6Þ where k = 1,…K are the choices faced by respondent i. Eq. (6) then is individual is contribution to the likelihood function. Vectors of parameters θ and β for all classes are obtained by maximizing the log-likelihood function with respect to those parameters. In order to select the appropriate number of classes, the Bayesian information criterion (Roeder et al., 1999) and Akaike information criterion could be used. With   ^ obtained, the posterior estimate of vectors of parameters ^ θ and β the class membership probabilities, Hci, can be calculated as follows:     1 0 e X exp ^θc Z i exp β c ilk K @   ∏k¼1 X  A ðX ^ ^ X exp θ Z exp β c i c ijk c¼1 j¼1     13 H ci ¼ 2 0 ^ X exp ^θc Z i exp β XC c ilk K 4ðX   ∏k¼1 @X  A5: c¼1 ^ X exp ^θc Z i exp β c ijk c¼1 j¼1

ð7Þ

Hci is called an individual-specific estimate of the class probability (Greene and Hensher, 2003), conditional on estimated choice probability. The posterior individual-specific WTP is given by: EðWTP i Þ ¼

1 β d c;attribute A: H @− c¼1 ci βd

XC

0

(LWTP) and high WTP class (HWTP). Hence, the log-likelihood function for R4LCM is expressed as follows lnL ¼ XN

0 1  NC 1 exp ð Z θ Þ i ANA @X A lnP ¼ ln½ 4 i¼1 i¼1 3 ðZ i θc Þ c¼1   0 10 1 exp X ilcost βprice ðZ i θZWTP ÞA NC A@ exp þ∏i¼1 @ X3 X4 X β ðZ θ Þ j¼1 ijcost price c¼1 i c 0 1 expðX β Þ 1 NC þ∏i¼1 @X3 ilk LWTP A X4 X β ðZ θ Þ j¼1 ijk LWTP 1 c¼1 i c 0 exp ð X β Þ exp ð Z θ Þ NC þ∏i¼1 @X3 ilk HWTP A X4 i ZWTP ðZ θ Þ X β j¼1 ijk HWTP c¼1 i c XN

ð9Þ

where NC represents the number of choice questions that individual i faced. For the purpose of ease of interpretability, membership parameters for LWTP are constrained to zeros (i.e., the LWTP class is the baseline class). As with the LCM, the random parameter logit (RPL) model allows for parameters of attributes to vary across respondents. It overcomes three limitations of the standard MNL by allowing for random taste variation, unrestricted substitution patterns, and correlation in unobserved factors (Train, 1998). Each parameter for each attribute is assumed to be random, following a specific distribution. The log-likelihood function for the random parameter model does not have a closed form, so a simulation method is used. The utility associated with individual is choosing alternative j in choice occasion k is denoted by U ijk ¼ βi X ijk þ eijk

ð10Þ

where Xijk is a vector of choice attributes and eijk is a stochastic component unobserved (iid) by the econometrician. The vector Xijk can include interaction terms between choice attributes and the characteristics of the person making the choice, in which case we designate the model as a RPL with interactions (RPL-INT). In order to incorporate the correlation across alternative and across choice occasion and taste variation across respondents, the individual-specific parameter vector βi is partitioned into two parts, b, representing the average of taste in the population, and, ηi representing the deviation of individual taste from average taste in the population. Utility can then be re-written as: U ijk ¼ bX ijk þ ηi X ijk þ eijk :

ð11Þ

ð8Þ

c;cost

The latent class model introduced above is the generalized latent class model, in which people conventionally estimate LCMs with different classes (2 class, 3class, 4class, etc.), and select the model that is considered the best in terms of AIC, BIC, and AIC-3 criteria. As usually estimated, no restrictions are placed on βc vectors. In this study, however, a restricted 4 class latent class model (R4LCM) is proposed. Parameter restrictions are imposed on the marginal utilities in some classes consistent with a priori conjectures regarding attribute non-attendance. The four classes in the model are as follows. In the attribute non-attendance class (ANA), all the utility parameters are restricted to zeros. A respondent in the ANA class will choose randomly from the options without regard to attribute level. In the zero WTP (ZWTP) class, parameters are restricted such that all parameters except the cost parameter are set equal to zero. Members of this class will always choose the cheapest option available, and will have zero WTP for all attributes. The third and fourth classes have no restrictions imposed, but have different parameter values. We find that one class tends to have low WTP for all attributes, while the other has higher WTP, and call the two classes the low WTP class

Hence, the actual conditional probability of individual i choosing alternative j is: Z P ij ðΩÞ ¼

2

3 Þ 5 ilk 4∏Kk¼1 XexpðβX   f ðβjΩÞdβ: exp βX ijk j

ð12Þ

The goal is to estimate the population parameter Ω, representing the population parameters that explains the distribution of individual parameters. The integral term cannot be handled by the conventional maximum likelihood procedure. Instead, choice probabilities are approximated through simulation. The simulated log-likelihood function is,   XN 1X rijΩ SLLðΩÞ n¼1 ln : L β R r¼1 i¼1……R

ð13Þ

where R is a number of draws from the distribution and βri|Ω is a vector of βs obtained from r-th draw from the distribution, f(β|Ω) for individual i. The parameters are estimated by choosing Ω that maximizes SLL(Ω).

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Once the population parameters are obtained, one can generate Bayesian estimates of individual-specific preferences by deriving the conditional distribution based on the observed choices and the parameters obtained from the previous steps (Hensher and Green, 2003; Revelt and Train, 2000). The prior information is the set of parameters obtained. Given that prior information, an individual-specific WTP can be derived by calculating: 2 3 1 XR βi;attribute 4 K expðβX ilk Þ 5   ∏k¼1 X r¼1 β R i;cost exp βX ijk j 2 3 EðWTP i Þ ¼ 1 XR 4 K expðβX ilk Þ 5   : ∏k¼1 X r¼1 R exp βX

ð14Þ

ijk

j

Both the LCM and the RPL model allow for variation in the β victor among individuals. The LCM assumes that respondents fall into classes and that every member of a given class has the same β victor. The RPL model assumes that each respondent has a unique β victor, and that the distribution of β is the same for all respondents. A hybrid LCM–RPL model assumes that respondents fall into discrete classes, as in the LCM, but allows for variation in β within each class. The model simultaneously classifies respondents into a number of segments depending on individual characteristics or attitudinal tendency, and estimates utility parameters based on random parameter model procedure within each class. The log-likelihood function for RPL–LCM is expressed as:

lnL ¼

XN i¼1

lnPi ¼

20 XC ln c¼1 4@X i¼1

XN

c¼1

3

expðθc Z i Þ

 5: K expðθc Z i ÞÞ  ∏k¼1 Πikjc ð15Þ

Eq. (15) is exactly same as Eq. (6) except that the conditional choice probability Πik|c now takes an open form as, Z Πikjc ¼

X

expðX ilk βc Þ   : exp X ijk βc f ðβc Þdβc j¼1

ð16Þ

3.2. Policy context and good valued: renewable energy in Pennsylvania Pennsylvania relies largely on coal (48% of total electricity generated) and nuclear power (35%) for its electricity needs. In 2009, renewable sources accounted for 2.7% of total electricity generation in Pennsylvania, up from 2.3% in the early 1990s (US EIA, 2011a), though still far below the national average of 10.6% (US EIA, 2010). The dominant renewable electricity sources are hydropower (1.2% of total generation), municipal solid waste and landfill gas (0.7%), wind (0.5%) and biomass (0.3%) (US EIA, 2011b). Like many states, Pennsylvania has adopted a renewable energy portfolio standard that requires electricity supplies to source a specific percentage of their electricity from renewable energy sources. Pennsylvania's standard, adopted in 2004, differs from most portfolio standards in that it allows for production of unconventional, nonrenewable sources. The Pennsylvania program is called the Alternative Energy Portfolio Standard (AEPS), and requires that electric distribution companies and electric generation suppliers source 18% of their using electricity from renewable and alternative energy sources by the year 2020. Under this law, there are two types of energy sources, called, “Tiers”. The AEPS requires that utility companies generate 8% of their electricity from “Tier I” energy sources, which include most renewable technologies such as wind, solar and hydropower, and 10% from “Tier II” sources by 2020 (U.S. Energy Information

105

Agency, EIA, 2010).5 Electricity distribution companies or generation suppliers who do not themselves generate enough alternative energy to meet the AEPS requirements can buy alternative energy credits from other suppliers who generate more than their required amount. Within Tier I, there is a special carve out for solar power, whereby 0.5% of total electricity generated must come from solar by 2020. So far, AEPS requirements have been met with relative ease. AEPS targets are being exceeded, and are expected to continue to be exceeded for the next few years (PUC, 2011). There have been proposals to increase the renewable energy targets of the AEPS and/or to speed up the schedule for reaching those targets (for example, Pennsylvania House Bill 1580). In this study, respondents are presented with choices among different AEPS policies that result in different combinations of renewable energy production, allowing estimation of WTP for increases in different types of renewable energy. Knowledge of the preferences of residents for different types of electricity generation, and their WTP to increase renewable electricity generation, would be useful when considering such proposed changes to the AEPS.

3.3. Survey data The survey instrument (questionnaire) used in this survey was designed based on a review of instruments used in previous studies and based on insights gained from two focus groups, one conducted in a rural community, the other conducted in an urban community. The survey was administered as a mail questionnaire, and included four sections. The first section asks respondents a series of agree/disagree statements measuring respondents' attitudes toward issues related to renewable energy production in Pennsylvania. The second section asked respondents to rate different electricity generation technologies according to their impacts on scenery and land, local air quality, jobs in Pennsylvania, global climate, and the overall impact of each generation technology. In total, 10 electricity generation technologies were rated by respondents. The third section included the choice experiment (CE) questions, described in more detail below. Section 4 asks agree/disagree questions related to renewable energy policy, and elicits individual characteristics of the respondents such as age, income, and education. In Section 3, a brief, general description of the Tier I requirements of the AEPS was provided to respondents. Respondents were then told that the Tier I requirements of the AEPS could be changed. Respondents were asked five CE questions. In each CE question, respondents were given a choice from among three options, called scenarios. In each CE question, one of the scenarios was the baseline scenario, which involved no change to the current AEPS, and requires 8% of Pennsylvania electricity to come from renewable (Tier I) sources by the year 2020. The other two scenarios involved a change in the AEPS that would increase the amount of renewable energy produced in Pennsylvania in the year 2020. Each scenario in the CE questions was described in terms of how much electricity would be generated from wind, solar, biomass, and other renewable sources, the impact (positive or negative) on jobs in Pennsylvania, and the impact on the respondent's household costs. An example CE question is shown in Fig. 1. The scenarios differed in terms of the levels of six attributes listed in Table 1. The attributes and their ranges were selected based on a review of previous studies and on the results of the focus groups. Respondents may have had preconceptions about whether an increase in renewable energy production would have a positive or negative impact on jobs in Pennsylvania. In order to prevent respondents including concerns they

5 Tier I source: photovoltaic energy, solar-thermal energy, wind, low-impact hydro, geothermal, biomass, biologically derived methane gas, coal-mine methane and fuel cells. Tier II source: waste coal, distributed generation (DG) systems, demand-side management, large-scale hydro, municipal solid waste, wood pulping and manufacturing byproducts, and integrated gasification combined cycle (IGCC) coal technology.

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Fig. 1. Sample choice experiment question.

have over job impacts in their WTP for renewable energy, impact on jobs was included as a separate attribute. The level of the attributes in each scenario in each CE question was chosen to generate an experimental design that would provide the maximum possible information about respondent preferences over the attributes. The experimental design was performed using the modified Fedorov algorithm (Cook and Nachtsheim, 1980; Fedorov, 1972; Zwerina et al., 1996) via SAS macro (% Choiceff). Four different versions of the survey were ultimately constructed. The versions differed in the levels of the attributes in each CE question, so that a total of 20 different CE questions were presented to respondents. The survey was pretested in the field in November 2010 with a small sample (50 urban and 50 rural residents), using two survey versions. The response rate was 50%, and item non-response rates were acceptably low. Data from the pretest was used to estimate a preliminary MNL model. Based on this model, two more survey versions were constructed to provide a richer experimental design. Full survey implementation used the same method as the pretest, and began in January 2011. The Penn State Survey Research Center (SRC) purchased a mailing list of randomly chosen PA residents. Surveys were mailed to an additional 1500 PA residents (900 rural, and 600 urban). In order to improve the response rate, a $2 cash incentive was included in the survey. Seven

to ten days after the initial mailing, a postcard reminder was sent. A second survey was sent to non-respondents after another seven to fourteen days. Returns were accepted until March, 21st. Responses returned after that date were not included to avoid responses made after the incident at the Fukushima nuclear plant in Japan. By that cutoff date, across both the pretest and the main survey, 783 completed surveys were returned (271 from urban areas, and 512 from rural areas). An additional 47 surveys were returned as deceased or as bad addresses, yielding a 50.4% response rate. Item response varied from question to question. In the analysis below, sample sizes are adjusted in each analysis to include all respondents who answered the relevant questions. Nine respondents did not answer any CE questions, and 34 respondents answered some but not all of the CE questions. These item nonresponses, coupled with missing responses to attitudinal questions and individual characteristics, produced a final sample of 654 respondents with 3412 CE choices for estimation of preference models. 3.4. Principle component analysis of preferences In Sections 2 and 4 of the survey, respondents were asked 23 agree/disagree questions to measure their attitudes toward

Table 1 Description of attributes used in choice experiment. Attribute

Description

Range of values

Baseline value

Solar Wind Biomass Other renewables Job impact Cost

Percentage of electricity generated from solar power in Pennsylvania by 2020 Percentage of electricity generated from wind power in Pennsylvania by 2020 Percentage of electricity generated from biomass combustion in Pennsylvania by 2020 Percentage of electricity generated from other renewable sources in Pennsylvania by 2020 Impact on jobs in Pennsylvania Additional cost to household through higher electricity bills and/or taxes, per month

0.5%–1.4% 2.8%–4.6% 1.5%–2.8% 3.2%–4.7% −3000–+3000 $0–$25

0.5% 2.8% 1.5% 3.2% 0 $0

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Table 2 Principle component analysis coefficients. Item (1 = strongly disagree, 5 = strongly agree, except as noted)

Principle component Pro-Environment

As a society, we should be using less oil, coal, and natural gas in order to reduce environmental impacts on land, water, and air quality. Carbon dioxide from burning coal, oil, and natural gas is causing global warming. If global warming does occur, it would be bad for people and/or the environment. How would you describe yourself politically? (1 = Liberal, 5-Conservative) I want more of Pennsylvania's electricity supply to come from renewable sources. Overall, I think that the AEPS is a good policy for Pennsylvania. The AEPS should be made stronger, with a higher required amount of renewable energy than current law. I cannot afford to pay any more for my electricity than I do now. I would be opposed to any change to the AEPS that would increase how much I pay for electricity and taxes, even if the increase was small.

renewable energy and renewable energy policy. It is desirable to explore how WTP for renewable energy relates to differences in attitudes, as this is a potentially important source of preference heterogeneity, but it is not practical to include 23 different attitude measures, particularly because there is duplication and overlap among questions. A principal component analysis was conducted on 8 attitudinal questions and 1 political tendency variable to identify a limited set of dimensions along which attitudes vary. Three components were identified. Each component is calculated as a linear combination of the 9 measures. Component weights are assigned such that the three components are not correlated across respondents. The estimated weights for each measure are shown in Table 2. Weights with absolute value greater than 0.5, shown in bold in Table 2, indicate that there is a strong relationship between the measure and the component. Based on the measures that are strongly related to each component, it is possible to interpret each component. The first Table 3 Parameter estimates from MNL and MNL_INT model. Coefficient(MNL) Intercept parameters Solar Wind Biomass Other renewable Job gain Avoiding job loss Cost Interaction parameters Solar_Pro-Environment Wind_Pro-Environment Biomass_Pro-Environment Other_Renewable_Pro-Environment Job_Gain_Pro-Environment Avoiding_Job_Loss_Pro-Environment Solar_Pro-AEPS Wind_Pro-AEPS Biomass_Pro-AEPS Other_Renewable_Pro-AEPS Job_Gain_Pro-AEPS Avoiding_Job_Loss_Pro-AEPS Solar_Cost-Concern Wind_Cost-Concern Biomass_Cost-Concern Other_Renewable_Cost-Concern Job_Gain_Cost-Concern Avoiding_Job_Loss_Cost-Concern Log-likelihood AIC BIC N ⁎ Significance at 5% level. ⁎⁎ Significance at 1% level. ⁎⁎⁎ Significance at 0.1% level.

Coefficient(MNL_INT)

0.163(0.084)⁎ 0.368(0.052)⁎⁎⁎

0.299(0.096)⁎⁎⁎ 0.409(0.066)⁎⁎⁎

0.034(0.062) 0.359(0.047)⁎⁎⁎ 0.413(0.034)⁎⁎⁎ 0.648(0.039)⁎⁎⁎ −0.075(0.006)⁎⁎⁎

−0.029(0.073) 0.399(0.053)⁎⁎⁎ 0.462(0.039)⁎⁎⁎ 0.565(0.042)⁎⁎⁎ −0.085(0.007)⁎⁎⁎

– – –

0.451(0.089)⁎⁎⁎ 0.32(0.059)⁎⁎⁎ 0.253(0.063)⁎⁎⁎ 0.235(0.05)⁎⁎⁎ 0.104(0.038)⁎⁎

– – – – – – – – – – – – – −2983.234 8970.702 3011.527 3241

0.063(0.042) 0.625(0.099)⁎⁎⁎ 0.482(0.067)⁎⁎⁎ 0.289(0.07)⁎⁎⁎ 0.339(0.055)⁎⁎⁎ 0.145(0.042)⁎⁎⁎ 0.008(0.046) −0.553(0.088)⁎⁎⁎ −0.503(0.06)⁎⁎⁎ −0.427(0.064)⁎⁎⁎ −0.314(0.05)⁎⁎⁎ −0.175(0.039)⁎⁎⁎ −0.143(0.041)⁎⁎⁎ −2375.393 7201.2 2476.4 3241

Pro-AEPS

Cost Concern

0.68

0.37

−0.14

0.82 0.81 −0.60 0.49 0.07 0.33 −0.07 −0.23

0.15 0.17 −0.10 0.56 0.86 0.75 −0.05 −0.28

−0.15 −0.06 0.10 0.01 −0.17 −0.02 0.93 0.83

component is positively related to three attitudinal questions measuring concern over environmental quality, and negatively related to conservative political ideology. We label this component “Pro-Environment”. The second component is positively related to three attitudinal questions measuring desire to increase renewable energy production. We label this component “Pro-AEPS.” The third component is related to two attitudinal questions about concerns over electricity costs. We label this component “Cost-Concern.” For each respondent, values of each of three components were calculated. 4. Results and discussion 4.1. MNL and MNL_INT estimation results The first models estimated were the MNL model and the MNL model with interactions (MNL_INT) model. The MNL_INT model is often estimated as an alternative to a simple MNL to capture systematic preference heterogeneity. In this study, the individual characteristics interacted with the attribute levels were the three principle components scores. Table 3 presents the estimated coefficients from the MNL and the MNL_INT estimation. Consistent across both models, the results show that all coefficients are significant except the intercept coefficient for biomass energy. The results from MNL_INT estimation show that all interaction terms are statistically significant except the interactions between avoiding job loss and the Pro-Environment and Pro-AEPS components. The MNL_INT model has the capability of deriving individual WTP estimators for each respondent in the sample conditional on the calculated levels of the principle components. Fig. 2 describes the WTP distribution for renewable energy through kernel density plots. The kernel density plot is a useful tool for describing the distribution of WTP for each attribute non-parametrically without any assumption of the underlying distribution (Greene and Hensher, 2003). Table 7 represents the summary statistics and the proportion of positive values of individual WTP. Fig. 2 reveals that individual WTP for all renewable energy exhibits unimodal distributions with both positive and negative values. It is of interest to compare the means of the WTP distributions shown in Fig. 2. Because WTP for each individual is calculated as a ratio of estimated parameters, its sampling distribution is difficult to derive. Instead, empirical distributions of mean WTP were generated using a Monte Carlo approach described by Krinsky and Robb (1986). The Krinsky and Robb approach is frequently used because it is computationally less intensive than bootstrap and jackknife methods. The procedure requires drawing a large number (in our case, N = 5000) of parameter vectors from the multivariate normal distribution with a mean and covariance matrix equal to those of the estimated parameter vector β from the MNL model, and calculating WTP for each individual for each simulated β vector. The simulated sampling distribution of WTP was used in two ways. First, 95% confidence intervals of mean WTP for

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Fig. 2. Kernel density plot for renewable energy technologies (MNL_INT).

each technology were obtained by dropping 2.5% of the simulated observations on both tails. Second, a convolution method (Poe, Severence-Lossin and Welsh 1994) was used to test whether mean WTP estimates are significantly different among different technologies. Wind power has the highest mean WTP among renewable energy technologies, followed closely by “other renewable,” then solar. Biomass has the lowest mean WTP. Mean WTP for wind energy is not significantly different from mean WTP for “other renewable” energy, but mean WTP for both wind and “other renewable” is significantly larger than mean WTP for either solar or biomass. The mean WTP for solar is significantly higher than the mean WTP for biomass. Mean WTP to avoid job losses is higher than mean WTP for job gains. Heterogeneity in preferences is evidenced by the dispersion (standard deviation) of WTP among individuals. Differences among technologies in the standard deviation of MWTP can also be tested using a convolution test. The standard deviation of MWTP across households is significantly larger (p b 0.05) for solar than for any of the other three technologies,

and significantly larger for wind power than for biomass combustion or “other renewable” sources. The degree of heterogeneity is also significantly different between biomass combustion and “other renewable” sources. With heterogeneous preferences, some respondents have negative estimated WTP for each renewable energy technology. Table 7 shows that the positive portion of individual WTP is highest for “other renewable,” followed by wind, solar, and biomass among renewable energy technologies. The proportion of respondents with positive WTP for job gains is less than that for avoiding job loss. 4.2. R4LCM estimation results Estimated parameters for the R4LCM model are presented in Table 4. The LWTP class was set as the baseline class. For the other three classes, positive (negative) membership parameters imply that respondents with higher values of that characteristic are more (less) likely to fall

Table 4 Parameter estimates from Restricted 4-Latent-Class Model (reference class: LWTP). ANA class Marginal utilities Solar Wind Biomass Other Positive Negative Cost Class membership parameters Constant Age Certainty Pro-Environment Pro-AEPS Cost-Concern Log-likelihood AIC BIC N Posterior membership probability ⁎ Significance at 5% level. ⁎⁎ Significance at 1% level. ⁎⁎⁎ Significance at 0.1% level.

ZWTP class

−0.681(0.062)⁎⁎⁎ −2.546(0.843)⁎⁎ 0.033(0.01)⁎⁎ 0.117(0.062) 0.479(0.165)⁎⁎ 0.692(0.214)⁎⁎ −0.506(0.177)⁎⁎ −2013.949 6140.8 2147.3 3241 23.26%

LWTP class

HWTP class

−0.272(0.525) 2.074(0.341)⁎⁎⁎ −0.607(0.0.486) 1.624(0.298)⁎⁎⁎ 0.387(0.18)⁎⁎

2.466(0.44)⁎⁎⁎ 2.344(0.346)⁎⁎⁎ 0.104(0.374) 2.046(0.276)⁎⁎⁎ 0.53(0.18)⁎⁎ 4.457(0.491)⁎⁎⁎ −0.073(0.025)⁎⁎

6.829(4.862) −0.265(0.034)⁎⁎⁎

−2.579(0.939)⁎⁎ 0.021(0.013) 0.076(0.067) −0.807(0.209)⁎⁎⁎ −0.919(0.219)⁎⁎⁎ 1.104(0.264)⁎⁎⁎

23.20%

0.021(0.01) ⁎ 0.157(0.073)⁎ 0.793(1.174)⁎⁎⁎ 1.144(0.224)⁎⁎⁎ −1.156(0.185)⁎⁎⁎

18.80%

34.73%

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Fig. 3. Kernel density plot for renewable energy technologies (R4LCM).

into that non-reference class relative to reference class. Five respondent characteristics were included as determinants of class membership: age, the three principle component scores, and a measure of respondent certainty. Each respondent was asked to express the certainty level of

Table 5 Parameter estimates from RPL and RPL_INT models. Variable Mean parameter Solar Wind Biomass Other Positive Negative Cost

Coefficient (RPL) 0.518(0.326) 1.621(0.219)⁎⁎⁎ 0.448(0.218) 1.379(0.144)⁎⁎⁎ 0.656(0.124)⁎⁎⁎ 2.997(0.303)⁎⁎⁎ −0.214(0.02)⁎⁎⁎

Interaction parameters Solar_Pro-Environment Wind_Pro-Environment Biomass_Pro-Environment Other_Pro-Environment Job Gain Pro-Environment Avoiding Job Loss Pro-Environment Solar_Pro-AEPS Wind_Pro-AEPS Biomass_Pro-AEPS Other_Pro-AEPS Job Gain Pro-AEPS Avoiding Job Loss Pro-AEPS Solar_Cost-Concern Wind_Cost-Concern Biomass_Cost-Concern Other_Cost-Concern Job Gain Cost-Concern Avoiding Job Loss Cost-Concern Standard deviation parameters Solar_std Wind_std Biomass_std Other_std Positive_std Negative_std Log-likelihood AIC BIC N ⁎⁎ Significance at 5% level. ⁎⁎⁎ Significance at 1% level.

Coefficient (RPL_INT) 0.973(0.259)⁎⁎⁎ 1.138(0.183)⁎⁎⁎ 0.055(0.195) 1.161(0.116)⁎⁎⁎ 0.537(0.096)⁎⁎⁎ 2.974(0.319)⁎⁎⁎ −0.169(0.017)⁎⁎⁎ 0.818(0.233)⁎⁎⁎ 0.791(0.161)⁎⁎⁎ 0.567(0.162)⁎⁎⁎ 0.374(0.09)⁎⁎⁎ 0.23(0.093)⁎⁎ 0.132(0.151) 1.263(0.265)⁎⁎⁎ 1.245(0.197)⁎⁎⁎ 0.628(0.168)⁎⁎⁎ 0.526(0.103)⁎⁎⁎ 0.329(0.108)⁎⁎ −0.239(0.172) −1.164(.246)⁎⁎⁎ −1.282(0.179)⁎⁎⁎ −0.902(0.155)⁎⁎⁎ −0.456(0.09)⁎⁎⁎ −0.398(0.099)⁎⁎⁎ −0.025(0.159)

4.582(0.471)⁎⁎⁎ 3.005(0.274)⁎⁎⁎ 1.636(0.223)⁎⁎⁎ 0.994(0.171)⁎⁎ 2.164(0.199)⁎⁎⁎ 2.666(0.278)⁎⁎⁎

2.908(0.317)⁎⁎⁎ 2.109(0.221)⁎⁎⁎ 1.341(0.232)⁎⁎⁎ 0.546(0.182)⁎⁎⁎ 1.255(0.132)⁎⁎⁎ 2.507(0.281)⁎⁎⁎

−2300.515 6940.5 2353.1 3241

−1995.843 6080.5 2120.8 3241

his or her choice on a scale of 1 to 10 after each choice question. The certainty measure is created by averaging all certainty levels for each respondent. Other demographic variables such as rural/urban, gender, education, and income were found not to significantly predict class membership. The coefficient on the cost attribute is negative and significant across all classes, which is consistent with economic theory. The coefficients on wind power, other renewable energy, and job gains are all positive and significant in both LWTP and HWTP classes. The coefficients on solar and biomass are negative, but insignificant in LWTP class, while the coefficient on solar energy is positive and significant in HWTP class. In general, respondents with higher “Pro-AEPS” and “Pro-Environment” scores are more likely to belong to the HWTP and ANA class, and less likely to belong to the ZWTP class. Respondents with higher level of certainty about their choices are slightly more likely to belong to the HWTP class relative to the LWTP class. Respondents with higher “Cost-Concern” scores are more likely to belong to the ZWTP class, and less likely to belong to the HWTP class or the ANA class. The membership probabilities summarized in Table 4 are the average posterior membership probabilities, calculated based on both the observed choices and values of the five individual characteristics. The estimated share of respondents in the ANA class (23.26%) is larger than that (5.1%) from Scarpa et al. (2009). Scarpa et al. (2009) included additional classes that exhibited partial non-attendance, so smaller share of respondents in the ANA class in their study is not surprising. People in the LWTP class exhibit positive and significant WTP for wind, “other renewable,” and job gains, but not for solar, biomass or avoided job losses. People in the HWTP class exhibit positive and significant preference for all attributes except biomass. The difference in preferences over solar energy between the HWTP and the LWTP class is consistent with the finding from the MNL_INT model that preferences over solar power are more heterogeneous than for the other three technologies. People in both the HWTP and LWTP classes have low WTP for biomass, a result that is also consistent with the MNL_INT results. However, the location of the three peaks for biomass energy is not significantly different from each other, so that it is not possible to say that preferences for biomass energy show heterogeneity across classes. Fig. 3 shows the distribution of individual WTP for renewable energy attributes derived from the R4LCM. Preferences for the ANA class are excluded, and the probabilities of the other three classes are rescaled to equal 1. Fig. 3 shows that the distribution of WTP for each renewable energy technology is tri-modal, with one peak at WTP = 0 for the ZWTP, one for the LWTP class, and one for the HWTP class. Fig. 3 shows that the LWTP and HWTP peaks are both located at positive WTP values, while

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Fig. 4. Kernel density plot for renewable energy technologies (RPL_INT).

the peaks for biomass are both close to zero. The HWTP peak for solar is higher than for the other three technologies, but the LWTP peak is negative, consistent with the result from the MNL_INT model that solar exhibits the most heterogeneity in preferences. The distribution for biomass shows the least heterogeneity, with all three peaks near zero. A convolution test shows that the differences in dispersion among solar, wind, and “other renewable” are statistically significant. Table 7 shows mean and standard deviation of WTP across all classes except the ANA class, and the proportion of respondents with positive WTP. All respondents have positive individual WTP for wind power and “other renewable” energy. However, a large proportion of the sample appears to have negative individual WTP for solar (39.3%).

4.3. RPL and RPL_INT estimation results The first issue for estimating a RPL model is to determine how many draws to use for simulation. Hensher and Green (2003) found that 500 draws were more than necessary. A sensitivity test here showed that 400 Halton draws are enough to obtain stable estimates. The second issue is to determine which variables are random. Conventional practice is to estimate an RPL model in which all attributes except cost are random, and see if the standard deviation parameter of each variable is statistically significant. The results in this study show that standard deviation parameters of all attributes are statistically significant at least the 5% confidence level, hence random. Third, an appropriate

Table 6 Parameter estimates from 3-Class RPL–LCM (reference class: ZWTP). ANA class

ZWTP class

PWTP class

Mean parameters Solar Wind Biomass Other renewable Job gains Avoiding job loss cost

– – – – – – –

– – – – – – 1.172(0.039)⁎⁎⁎

2.148(0.497)⁎⁎⁎ 3.914(0.569)⁎⁎⁎ 0.889(0.336)⁎⁎ 2.236(0.284)⁎⁎⁎ 0.773(0.165)⁎⁎⁎ 5.77(0.95)⁎⁎⁎ −0.477(0.042)⁎⁎⁎

Standard deviation parameters Solar_std Wind_std Biomass_std Other renewable_std Job gains_std Avoiding job loss_std

– – – – – –

– – – – – –

4.511(0.658)⁎⁎⁎ 2.062(0.417)⁎⁎⁎ 1.203(0.411)⁎⁎⁎

0.397(0.11) 0.005(0.0144) 0.97(0.222)⁎⁎⁎ 1.062(0.226)⁎⁎⁎ −1.142(0.233)⁎⁎⁎

– – – – – –

1.023(0.767)⁎⁎ −0.004(0.009) 1.17(0.159)⁎⁎⁎ 1.529(0.172)⁎⁎⁎ −1.722(0.179)⁎⁎⁎ 0.073(0.058)

30%

59.4%

Class membership Constant Age Pro-Environment Pro-AEPS Cost-Concern Certainty Log-likelihood AIC BIC N Posterior membership probability ⁎⁎ Significance at 5% level. ⁎⁎⁎ Significance at 1% level.

0.021(0.078) −2010.38 6109.1 2115.5 3241 10.6%

0.408(0.414) 0.997(0.226)⁎⁎⁎ 4.828(0.794)⁎⁎⁎

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Fig. 5. Kernel density plot for renewable energy technologies (RPL_LCM).

distribution for each attribute must be specified. The normal distribution is the most frequently used in the literature (Beharry-Borg and Scarpa, 2010; Hensher and Green, 2003; Kosenius, 2010; Shen, 2010), and was used here. The normal distribution allows individual WTP for each technology to be either positive or negative, which is plausible for these goods. Table 5 shows the estimated coefficients from both the RPL and RPL_INT models. Mean coefficients for all attributes are statistically significant except solar and biomass energy in the RPL model, and biomass Table 7 Summary statistics of individual WTP derived from all models (654 respondents). Attribute

Mean

Standard deviation

Positive

MNL_INT Solar Wind Biomass Other Positive job impact Negative job impact

3.580 4.909 −0.323 4.751 5.481 6.719

11.242 9.092 6.794 6.146 2.957 1.844

66.3% 72.2% 49.3% 79.9% 95.2% 100%

R4LCM Solar Wind Biomass Other Positive job impact Negative job impact

16.631 17.674 −0.295 15.279 3.931 35.916

16.478 14.188 0.502 12.483 3.252 25.742

39.3% 100% 53.8% 100% 100% 100%

RPL_INT Solar Wind Biomass Other Positive job impact Negative job impact

5.827 6.977 0.397 6.874 3.126 17.697

14.999 13.791 8.060 4.803 5.871 9.846

61.2% 66% 50.8% 90.5% 60.3% 91.4%

RPL_LCM Solar Wind Biomass Other Positive job impact Negative job impact

5.181 7.274 2.093 3.908 1.887 11.504

7.682 4.127 1.555 1.675 1.845 6.844

67.3% 99.6% 96.9% 100% 80.9% 91.5%

in the RPL_INT model. Standard deviation parameters of solar and biomass energy are both significant in both models, showing there exists heterogeneity of respondents' preference for these energy technologies. The statistical evidence that there exists heterogeneity of respondents' preference for biomass energy is important because this information could not be unambiguously demonstrated in the R4LCM. In this sense, the RPL model provides more information than the R4LCM model about heterogeneity in preferences for biomass energy. One notable difference between the RPL and RPL_INT models is that the mean coefficient on solar is positive and significant in the RPL_INT model, while it is not in RPL model. The coefficient on biomass is not significant in either model. The standard deviation parameters are all significant in both models, showing that there exists preference heterogeneity of all attributes. Standard deviation parameters for the RPL_INT are smaller than for RPL, because some heterogeneity is captured by the interaction terms. A log-likelihood ratio test rejects the null hypothesis that all interaction terms in the RPL_INT model equal zero, supporting the RPL_INT model. Hence, the focus is placed on the RPL_INT model in this section. Parameter estimates derived from RPL_INT were used to obtain individual-specific posterior WTP estimates, conditional on observed choices, as shown in Eq. (14). Kernel density plots of individualspecific WTP are shown in Fig. 4 for the RPL_INT model. Consistent with the MNL_INT and R4LCM models, the heterogeneity of individual WTP estimates is largest for solar, followed by wind, biomass, and “other renewable” technology. A convolution test shows that the differences in standard deviation of individual MWTP among solar, wind, biomass, and “other renewable” were statistically significant.

Table 8 Comparison of models based on statistical goodness-of-fit. Model

Log-likelihood

AIC

BIC

MNL_INT R4LCM RPL RPL_INT RPL_LCM

−2375.393 2013.949 −2300.515 −1995.843 −2010.38

7201.2 6140.8 6940.5 6080.5 6109.1

2476.4 2147.3 2353.1 2120.8 2115.5

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Table 7 summarizes the proportion of respondents who have positive WTP for each attribute for the RPL_INT model. Almost half of respondents have negative WTP for biomass technology, explaining why the population mean coefficient for biomass is insignificant. However, the proportion of respondents who have positive WTP for solar energy is higher than the proportion of respondents with negative WTP. A Ztest for proportion shows that this difference is statistically significant, explaining the reason why the coefficient on solar energy is positive and significant for RPL_INT. 4.4. Hybrid RPL–LCM estimation results Bujosa et al. (2010) estimated a hybrid RPL–LCM model with 2 classes. Within each class, they allowed variation of each parameter. However, the model they estimated does not account for the panel nature of the data. Greene and Hensher (2010) incorporated the panel nature of choice data and estimated a 2-class RPL–LCM. In this study, a 3-class RPL–LCM model is estimated, but with restrictions on the parameters of two of the classes (the ANA and ZWTP class). In contrast to the LCM, the high and low WTP classes are now collapsed into one class, named the positive WTP (PWTP) class, which is modeled with random parameters. Table 6 shows the estimated coefficients from RPL–LCM, with the ZWTP class as the reference class. The class membership predictions show a similar pattern as in the R4LCM, though the RPL–LCM model predicts fewer members in the ANA class than did the R4LCM. For the PWTP class, the class membership parameters for all three principle components are significant and have expected signs. For the ANA class, the parameters for the three principle components are all significant with the same sign as found in the R4LCM. In contrast to the R4LCM results, the certainty measure and age turn out to be insignificant for both classes. The mean marginal utility parameter estimates from this hybrid model differ from the R4LCM, RPL, and RPL_INT in a few ways. First, in contrast to the other models, mean marginal utilities for biomass are now significantly positive, though small relative to the other technologies. Second, the standard deviation parameter for “other renewables” is not statistically significant, suggesting that preferences over that technology do not show heterogeneity within the PWTP class, although there is heterogeneity overall because of the existence of ZWTP class. Fig. 5 presents WTP distributions for the RPL_LCM model. Since “other renewables” have an insignificant standard deviation parameter, it was excluded from kernel density plots. The distributions in Fig. 5 show two peaks, one for the ZWTP class and the other for the PWTP class. The heterogeneity of individual WTP is again largest for solar energy, followed by wind and then by biomass technology, consistent with the findings from other models. The differences in standard deviation of individual WTP among the renewable technologies were all statistically significant (P-value b 0.001). Table 7 summarizes the proportion of respondents who have positive preference for each attribute for the RPL_LCM. In contrast to other models, the proportion of positive WTP is higher than the proportion of negative WTP for all attributes, including biomass. 4.5. Comparison of the models Table 8 summarizes goodness-of-fit measures for each model. The MNL_INT and the RPL models fit the data worst. They have the highest values of AIC and BIC, and highest absolute value of log-likelihood at convergence relative to other models. The two models that fit the data best were the RPL_LCM and the RPL_INT models. A ranking between the RPL_LCM and the RPL_INT model could not be made unambiguously based on the goodness-of-fit measures. The RPL_INT has slightly lower values of AIC and log-likelihood value at convergence relative to RPL–LCM, while RPL–LCM has a slightly lower value of BIC. The similarity in goodness of fit between the RPL–LCM and the RPL-INT is in contrast to the findings of Greene and Hensher

(2010) and Bujosa et al (2010), who found that the RPL–LCM fits much better than RPL. Their RPL models did not include interactions terms, suggesting that those terms in our RPL_INT model capture important heterogeneity that was not captured by the RPL model alone. Indeed, our RPL model performed much worse than the RPL–LCM or the RPL_INT. This suggests that estimating an RPL model without either interactions or latent classes is not sufficient to fully capture heterogeneity in preferences. It is not possible to choose between the RPL–LCM and the RPL_INT models based on goodness of fit. The two models provide different pictures of how WTP varies across the population. The R4LCM suggests a possible segmentation of the population. This model reveals that the number of respondents that exhibit high WTP for most renewable technologies is almost as twice the number of respondents that have low WTP for renewable technologies. In contrast, the RPL_INT model, by its construction, tends to suggest that preferences are distributed unimodally. The RPL_LCM model also provides richer insights on nonattribute attendance behavior of respondents (ANA and ZWTP class), which accounted for an important portion of total respondents. All models show that the heterogeneity of respondents' WTP is largest for solar technology. In fact, all models suggest that solar technology is the technology that has the largest proportion of respondents who have very high WTP and the largest proportion of respondents who have large, negative WTP (i.e. distribution of solar has the fattest right hand and left hand tails). Our analysis reveals that there is something about solar technology that elicits both the strongest positive and strongest negative preferences. The MNL_INT and RPL_INT models produced both positive and negative WTP for wind and “other renewable” technologies while the R4LCM produced only positive WTP for those. In the RPL–LCM, almost all respondents (99.6%) appeared to have positive WTP for wind technology. The true nature of respondents' preference for wind power is unknown, though previous studies find that wind power provides for both amenity and disamenity impact. The results from the MNL_INT and the RPL_INT models are more consistent with those from previous literature (Ek, 2005; Ladenburg and Dubgaard, 2007). As mentioned earlier, all models provide valuable information about the relative ranking of the degrees of heterogeneity toward renewable technologies. Consistent across all models, solar technology turns out to exhibit the largest heterogeneity, followed by wind, biomass, and “other renewables.” The RPL–LCM, the most flexible specification, conveys unique information about the heterogeneity of respondents' WTP, and suggests that there does not exist heterogeneity in respondents' WTP for “other renewables” within the class where respondents are willing to pay for renewable energy production. 5. Summary and implications The primary goal of this study is to compare the ability of several commonly used discrete choice models to capture the heterogeneity of respondents' WTP for renewable energy technologies. It should be noted that all of the models considered here are parametric, that is they impose a parametric structure on the systematic utility or assumptions about the distribution about the unobserved components of utility. Another body of studies has developed discrete choice methods in which utility functions and/or the distribution of the unobserved component utility are non-parametric (Bajari et al., 2007; Hall et al., 2004). Several discrete choice models are estimated and compared. All models show that heterogeneity in preferences is largest for solar energy while it is relatively smaller for biomass and “other renewables.” However, each model has its own strengths and weaknesses in terms of their capability of revealing individual WTP and their statistical performance. The MNL_INT model only captures heterogeneity in individual WTP that is tied to differences in measurable respondent attributes. In this

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study, those attributes included principle component scores based on agree–disagree questions, and thus capture some of the differences in attitudes across the respondent population. However, the MNL_INT model cannot capture heterogeneity that is not tied to those measurable respondent attributes, and it fit worst in terms of statistical goodnessof-fit. The R4LCM also relies on respondent attributes to motivate heterogeneity in WTP, but introduces the idea that respondents could belong to different groups with different preferences and/or choice behavior. The R4LCM combines classes with different preferences and classes that ignore some of the attributes when answering the choice questions. A unique discovery from this model is that there exists a class of respondents that has positive and significant WTP for solar energy. The R4LCM fits better than the MNL_INT. However, the R4LCM has three problems. First, the R4LCM does not capture possible negative WTP for technologies, such as wind power, that can have both amenity and disamenity impacts. This does not necessarily mean that respondents in our sample should have both positive and negative WTP for wind, because the true nature of WTP heterogeneity for wind power in Pennsylvania is unknown. It should be kept in mind that individual WTP for R4LCM was calculated by weighting membership probability by corresponding WTP of each attribute in each class, and summing over classes. Each person is both probabilistically in the high WTP and low WTP class. It is not possible to determine whether any individual respondent is truly in the HWTP or LWTP class. The RPL and RPL_INT models allow for random taste variation across respondents. The model results suggest some improvements over the R4LCM. Specifically, the RPL and RPL_INT produce both positive and negative values of respondents' preference for wind power, solar energy and biomass energy, consistent with expectations. In terms of statistical goodness-of-fit, the RPL–LCM and RPL-INT models fit better than other models. Both models provide for rich information on the heterogeneity of individual preference for renewable energy. However, they differ in terms of how they motivate and model heterogeneity.The RPL-INT model motivates heterogeneity through two sources: measurable differences in respondent characteristics and random variation in marginal utilities. The RPL–LCM motivates heterogeneity through a combination of class membership and random variation in preferences. It is difficult to unambiguously conclude which model is better for our data. The RPL–LCM might better capture our intuition about respondents' preference by incorporating within-class heterogeneity into a latent class model. RPL-INT might better identify the source of respondents' heterogeneity through interactions and better capture the variation of degree of heterogeneity by energy types. Regardless of which model is chosen, our results consistently show that there is important heterogeneity in WTP for increased renewable energy production. Heterogeneity in WTP has implications for building political support for policies to increase renewable energy production. It is important to remember that even if average WTP to increase renewable energy production exceeds average costs, not all residents will view a policy to increase renewable energy production positively. The observed heterogeneity in WTP is particularly interesting for solar power and for biomass combustion. Heterogeneity in WTP is greatest for solar power. WTP for solar power is more strongly correlated with Pro-Environment and Pro-AEPS attitudes than is WTP for wind, biomass combustion, or other types of renewable energy. The MNL-INT model reveals that residents who care about the environment and who support renewable energy policies prefer solar power over all other renewable technologies, while residents who care less about the environment and who do not support renewable energy policies view solar power as their least-preferred renewable technology. There seem to be unique aspects about solar power that make residents with strong Pro-Environment attitudes like it best and make residents with the least Pro-Environment attitudes like it least. In contrast, WTP for increased biomass combustion is consistently close to zero, with a

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small degree of heterogeneity. Apparently, attitudes toward biomass combustion are not favorable, and are fairly consistent across the population. From a policy perspective, this result suggests that revisions to the AEPS might consider whether biomass combustion should continue to be treated the same as wind power or hydropower. If the AEPS requirements are met through increased combustion of biomass, the net benefit to Pennsylvania residents could be negative.

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