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Abstract:
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Economic choice models often contain parameters whose support is constrained to a subset of the real line. In hierarchical models, these support constraints are usually operationalized by pairing an exponential transformation on the constrained parameters with a multivariate normal distribution of heterogeneity. The induced log-normal prior can have undesirable properties, however, as large variability in the lower/upper tail of the data can lead to a long estimated upper/lower tail in the distribution of heterogeneity. In the context of demand models, the consequence is overstating the distribution of price sensitivity, preferences, or willingness-to-pay in the population. Rather than reparameterizing the model, we propose using a truncated multivariate normal distribution of heterogeneity and build on recent advances in MCMC methods for intractable distributions to address the computational issues that arise from the loss of conjugacy. The advantages of a truncated normal specification are illustrated in the context of measuring heterogeneity of willingness-to-pay in demand models.
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