International Choice Modelling Conference, International Choice Modelling Conference 2015

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Eliciting Preference Heterogeneity in Willingness to Pay Space with Post Estimation Clustering
Laura-Lucia Richter, Melvyn Weeks

Last modified: 18 May 2015


We present an alternative approach to explore heterogeneity of willingness to pay (WTP) for product attributes to inform more precise policy evaluations and targeted marketing. We combine the flexibility of the general multinomial logit (GMNL) model with post estimation clustering to improve model specification and inference in WTP space. The approach is applied to elicit the heterogeneity of customers' WTP for attributes of grid reliability in the UK.

When exploring consumer preferences and making inference on the WTP for product attributes, the concepts of preference and scale heterogeneity have long been acknowledged. Preference heterogeneity implies that consumers derive different (marginal) utility from product characteristics, while scale heterogeneity reflects the degree of uncertainty in the decision maker's choice process. In traditional discrete choice models such as multinomial logit (MNL) and mixed logit (MXL) models, preference heterogeneity due to observable characteristics is accounted for by including interactions of attribute and individual characteristics into the utility function. One major challenge, though, is how to determine which demographics matter for which attributes and in which combination. It is likely that heterogeneity is a complex function of demographics and unobservable factors and that this varies by attributes. It is often infeasible to consider all possible interactions. Moreover, even if all relevant interaction terms were included, this would imply a loss of a large number of degrees of freedom and hence convergence. To address these drawbacks our approach does not include customer characteristics in the initial model specification, but uses information on individuals' choices in posterior cluster analysis to explore the respondents' preference heterogeneity as suggested by Train (2003).

A common model that considers customer segmentation in the population is the latent class (LC) model in which preferences are assumed to vary discretely across a predefined number of classes, but to be homogeneous within each class. Class membership and preference parameters for each class are usually estimated simultaneously. Our approach on the other hand assumes a continuous distribution of preference parameters and explores customer segmentation post estimation. Moreover, while the LC approach is predicated on class sorting being determined by individual characteristics, our approach is agnostic about the role of customer characteristics, segmentation and type of heterogeneity within the population. We estimate a number of models that exclude demographics, but differ in the manner in which unobserved heterogeneity is accommodated. We then derive the posterior individual parameter distributions and explore them performing standard k-means as well as Expectation-Maximisation (EM) clustering algorithms. With clustering conditional on the stated choices, the sorting into classes can then be based on factors such as individual preferences WTP and degree of randomness in choice.

To avoid confoundedness of our WTP estimates with scale heterogeneity, we estimate the models in WTP space rather than in preference space as suggested by Train and Weeks (2004). This allows us to impose distributional assumptions directly on the individual WTPs and has been proven to result in more plausible estimates of the full WTP distributions than when deriving the WTP from the utility parameters in preference space (Hensher and Greene, 2011). On the other hand, there has been evidence that models in preference space fit the data better than models in WTP space (see e.g. Train and Weeks, 2004 and Sonnier et al., 2007). Highlighting this trade-off in preference space, Hensher and Greene (2011) find that the gap between plausibility of WTP distributions is smaller when scale heterogeneity is taken into account, while Hess (2007) addresses the problem of unrealistic WTP estimates in preference space exploiting individual-specific posterior distributions.

The GMNL model as proposed by Fiebig et al. (2010) and Keane and Wasi (2013) nests models with and without scale heterogeneity, can accommodate correlated coefficients, permits estimation in preference and WTP space and allows the derivation of individual-specific posterior distributions. We follow the interpretation of Rose et al. (2012), who see GMNL as a MXL model with more flexible, but still restrictive, mixtures of distributions that do not necessarily imply an ability to separately identify preference and scale heterogeneity. We acknowledge and combine the considerations above, estimate the flexible GMNL model in WTP space and perform posterior cluster analysis to inform respecification of the model towards different or greater segmentation as proposed by Hess (2010). We aim to improve inference in WTP space and examine how existing models perform in comparison to ours.

We illustrate our approach using the example of preference heterogeneity for grid reliability, an application that is relevant for at least two reasons. Firstly, as there is no real market for reliability, its valuation via stated choice experiments and precise willingness to pay estimates can inform cost benefit analyses and hence policy making. An example could be the valuation of infrastructure investments such as the undergrounding of overhead transmission lines. Summing up the individual-specific WTPs across the population yields more precise estimates of the total value of a product or service than under the assumption of an average WTP. Secondly, the exploration of different customer segments can inform targeted marketing and contracting. As Akcura and Weeks (2014) point out, a precondition for the supply of differentiated services is an understanding how preferences vary. Instead of estimating an average value of lost load (VoLL) for example, individual specific preferences for service reliability can feed into customer specific electricity service contracts.

In fact, eliciting customer preferences and estimation of WTP via choice experiments has become an important part of price review processes of regulators such as Ofgem in the UK. Data from such experiments can be exploited to identify customer groups with similar tastes and design products to match those customer specific preferences (Akcura and Weeks, 2014). In our application we use data from a stated choice experiment performed by Accent and Ofgem in 2008 and focus on customer willingness to pay for attributes of grid reliability. A questionnaire accompanying the experiment includes further information on the customer such as demographics or previous experience with grid reliability and resilience.



Akcura, E. and M.Weeks (2014):  Valuing Reliability in the Electricity Market," Working Paper, Faculty of Economics, University of Cambridge, UK.

Fiebig, D. G.; Keane, M. P.; Louviere, J. and N. Wasi. (2010), 'The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity.', Marketing Science 29 (3) , 393-421.

David A. Hensher and William H. Greene (2011): Valuation of Travel Time Savings in WTP and Preference Space in the Presence of Taste and Scale Heterogeneity," Journal of Transport Economics and Policy, vol. 45(3), pages 505-525.

Hess, S. (2007): Posterior analysis of random taste coefficients in air travel behaviour modelling," Journal of Air Transport Management, 13, 203-212.

Hess, S. (2010): Conditional parameter estimates from Mixed Logit models: distributional assumptions and a free software tool," Journal of Choice Modelling, 3, 134-152.

Keane, M. and N. Wasi (2013): Comparing Alternative Models Of Heterogeneity In Consumer Choice Behavior," Journal of Applied Econometrics, 28, 1018-1045.

Rose, J., S. Hess, W. Greene, and D. Hensher (2012): The Generalised Multinomial Logit model: Misinterpreting scale and preference heterogeneity in discrete choice models or untangling the un-untanglable?".

Sonnier, G., A. Ainslie, and T. Otter (2007): Heterogeneity distributions of willingness-to-pay in choice models," Quantitative Marketing and Economics, 5, 313-331.

Train, K. (2003): Discrete Choice Methods with Simulation, no. emetr2 in Online economics textbooks, SUNY-Oswego, Department of Economics.

Train, K. and M. Weeks (2004): Discrete Choice Models in Preference Space and Willingness-to Pay Space," Cambridge Working Papers in Economics 0443, Faculty of Economics, University of Cambridge.

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