CHAPTER 2 LITERATURE REVIEW: METHODOLOGIES FOR ESTIMATING THE WTP FOR
2.4 Stated Preference Approach 45
2.4.2 Choice Modelling 58
2.4.2.2 Theoretical Framework for CE 59
Louviere et al. (2000) discuss the theory of stated choice methods using a modified Lancaster (1966) and Rosen (1974) approach. In Lancaster’s analysis an individual’s utility is a function of commodity characteristics, and Rosen extends this for discrete goods. In Louviere and others’ modified
approach, individuals are assumed to derive utility from the consumption of services delivered by commodities they choose to purchase. These commodities have certain attributes and together produce the desired level of service. However, the actual level of service that can be provided by a
60
commodity is not known to the individual, therefore the consumption of that commodity depends on the expected level of service that will be provided by the commodity instead. In other words, an individual’s utility is a function of the expected level of service they will attain when certain attributes of a commodity are grouped together.
The analyst does not observe the consumer’s true utility function. Therefore the utility function observed by the analyst is a function of observed as well as unobserved components of the expected levels of services. The utility function observed by the analyst is:
) ) ( ,..., ) ((seo seuo 1 seo seuo K U U
where (seo + seuo )k is the expected amount of kth service for k=1,..,K; seo is the observed component and seuo is the unobserved component.
The commodities are consumed in the quantities that will produce the utility maximizing levels of services. In a random utility model (RUM) the utility function has a systematic component (from attributes observed by the analyst) and a random component (from attributes unobserved by the analyst). Therefore the utility of the ith alternative for the qth individual can be expressed as:
iq iq iq V
U
where the first term on the right hand side is the systematic and the second term is the random component. Viq depends on the attributes of alternative i and the attributes of individual q. It is often assumed that Viq’s are homogenous across the entire population and εiq’s are independent and
61
identically distributed (IID). The choice model selected for the particular study depends on the assumptions made on the distribution of the random error term.
When faced with a set of possible alternatives, A, a utility maximizing individual q will choose alternative i over alternative j if and only if:
A i j U Uiq jq ) ( ) (Viq iq Vjqjq ) ( ) (Viq Vjq jqiq
The right hand side of the inequality is not observed by the analyst, therefore statements about choice outcomes can only be made up to a probability of occurrence, i.e. the probability that (Viq- Vjq)>(εjq – εiq).
Let q be a randomly drawn individual with attributes s (e.g. socio-economic background), facing a set of alternatives A, and a vector of attributes x. Then the RUM states that the probability that an individual q will select alternative xi, given his socio-economic background s and the alternative set A
is: i j x s V x s V x s x s P P A s x P( iq | q, ) iq [{( , j)( , i)}{ ( , i) ( , j)}]
62
Assuming ε is distributed extreme value type I (EVI), the standard multinomial logit (MNL) model is obtained, where the probability of individual q choosing alternative i is given by:
J j V V iq jq iq e e P 1 and λ is a scalar factor given by
6
When the random error terms are IID, the variance of the random error σ is constant across individuals, therefore so is λ. Because λ cannot be estimated separately from the parameters of explanatory variables of Vjq, it is often normalized to one.
Assuming Vjq to be a linear and additive function of attributes X,
jq jq X
V
where Xjq is the vector of attributes of choice j as viewed by individual q, and β is the parameter vector to be estimated. Maximum likelihood techniques are used in estimating the parameters of the utility function.
63
If X consists of K attributes, p is the price attribute and the alternative is chosen with certainty, then the marginal WTP for a change in the level of a single attribute k, and the WTP for the entire good for changes in levels of all attributes are given by (Lancsar, 2004):
p k k k p V X V MWTP / / ) ( 1 k K k p k X WTP
The MNL model is limited by the Independence from Irrelevant Alternatives Axiom (IIA), which states that the ratio of the probabilities of choosing one alternative over another (given that both alternatives have a non-zero probability of choice) is unaffected by the presence or absence of any additional alternatives in the choice set. Another limitation of the MNL model is the IID assumption of the error terms. This implies that cross-substitutions between pairs of alternatives are equal and unaffected by the presence/absence of other alternatives.
In Chapter 6 of Louviere et al. (2000), alternative models to the MNL that relax the IID assumption are discussed. The authors describe the generalized extreme value (GEV) model and its special case the nested logit (NL) model. The main assumptions of the models of the logit family are that the individuals have homogenous preferences, they act rationally and use all the information to choose the utility maximizing option subject to a budget constraint.
The heteroscedastic extreme value (HEV) models relax the assumption of identically distributed random errors, and the mixed logit (ML) models or the random parameters logit (RPL) models
64
accommodate different covariances of the random errors, as well as the individual-specific effects. Latent class heteroscedastic MNL models include heterogeneity and heteroscedasticity. Multinomial probit (MNP) models totally relax the IID assumption but at the expense of complex estimation requirements. Finally, the authors discuss the multiperiod multinomial probit models as the most general models of all, capable of accommodating assumptions on autoregressivity, correlation between alternatives and time periods, unobserved heterogeneity across individuals, and different variances across alternatives. As the analyst moves from the simple MNL to more complex models mentioned above, there is a trade off between the benefits of adding behavioural realism to the model and the cost of higher sophistication in the statistical techniques required.
Choice models can be parameterized in two different ways (Louviere et al., 2005): either in terms of utility coefficients or in terms of WTP. In the first case, the marginal WTP estimates are obtained by dividing the coefficients of the non-price attributes with the coefficient of the price attribute. In the second case the coefficients are the product of WTP for each attribute and the negative of the price coefficient. In models with fixed coefficients the second approach enables easier calculation of the standard errors, however in models with variable coefficients the choice of parameterization approach is more complex (Louviere et al., 2005)
Being a generalization of the discrete choice CVM, the CE method share the same potential errors/biases, such as the hypothetical bias (Carlsson and Martinsson, 2001; Lusk and Schroeder 2004; Carlsson et al., 2005), scope effects, elicitation effects (Scheufele and Bennett, 2010), order effects (McNair et al., 2010), strategic bias (Louviere et al., 2005; McNair et al., 2010), and framing
65
issues (Rolfe et al., 2002), and whether the CE performs better on any of these problems is being debated (Hanley et al. 2001). Carlsson and Martinsson (2001) tested for hypothetical bias in CE using a cheap talk script, and found that out of the 10 attributes seven had lower marginal WTP estimates on the version with the script. They concluded that, just like the CVM, the CE may also suffer from hypothetical bias.
However, the CE does offer some advantages over the CVM (Boxall et al., 1996; Hanley et al., 2001; Rolfe et al., 2002; Shen, 2005; Mogas et al., 2006). The CE method is able to measure the tradeoffs between the different attributes of the good, and when one of these attributes is price, it estimates the marginal value of changes in each attribute as well. This type of multidimensional analysis is possible in the CVM as well, however it is more costly. In the CVM, respondents are given a
hypothetical scenario and their stated WTP relies on the accuracy of the information provided in this scenario. On the other hand, the CE method offers the respondents different choice sets and
different alternatives in each choice set, so instead of being questioned in detail on one single scenario, the respondents are given the opportunity to select among different events. The fact that reminders about substitutes and complements improve the accuracy of the WTP measure is
explained in the discussion about the potential biases of the CVM above. Since the CE has different choice sets and in each choice set different alternatives, it incorporates the substitutes and
complements.
In addition to the common criticisms on potential biases in stated preference methods in general, there are some potential problems with CE methods that need to be considered before it is put into
66
practice (Hanley et al. 2001). Because CE methods measures the marginal value of each attribute, it assumes that the value of the whole good is equal to the sum of the values of its parts, and the validity of this is questioned. Some studies find estimates from the CE method to be significantly higher than those from the CVM (Maynard 1996).
Sensitivity to design, for example, the choice of alternatives, levels, choice sets, is claimed to have an impact on WTP estimates (Hensher et al. 2005a). There is a limit to the amount of information that can be processed by an individual, and when they are presented with different alternatives, with changing levels, learning and fatigue effects may lead to irrational choices. There is also the statistical problem of correlation between the responses given by the same respondent when faced with repeated choice sets (Louviere et al. 2000). These potential problems of the CE method and suggestions to minimize or eliminate them will be discussed in more detail in the next chapter.