Modelling unobserved heterogeneity in contingent valuation of health risks

Abstract

Human preferences for alternative levels of health risks can be heterogeneous. In this paper a flexible distribution approach to model health values elicited with the dichotomous choice contingent valuation method is considered. Rigid parametric structures cannot model sample heterogeneity while imposing strong assumptions on the error distribution. A mixture of normal distributions is considered which can approximate arbitrary well any empirical distributions as the number of mixtures increases. The model is applied to data on willingness to pay for reducing the individual risk of an episode of respiratory illness. The mixture distribution model is compared with the rigid probit model using a Bayes factor test. The results show that the mixture modelling approach improves performance while allowing for the consideration of alternative groups of individuals with different preferences for health risks.

Notes

¹ The mean and the variance of the error terms are ; respectively, and where .

² See Geweke and Keane (1999) for specific details about the specification.

³ See Huber (1981) or Amemiya (1985) for a more detailed discussion of the asymptotic properties of ML estimators.

⁴ The explicit conditional posterior distributions are presented in Appendix 2.

⁵ Appendix 1 presents the development of the statistics in more detail.

⁶ See for instance, Martins (2001) for a demonstration.

⁷ This restriction guarantees the identificability of the model (Geweke and Keane, 1999)