A comparison of Bayesian and sampling theory inferences in a multivariate probit model for tobacco, alcohol, and marijuana participations

Knott, Rachel. (2007). A comparison of Bayesian and sampling theory inferences in a multivariate probit model for tobacco, alcohol, and marijuana participations Honours Thesis, School of Economics, The University of Queensland.

       
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Author Knott, Rachel.
Thesis Title A comparison of Bayesian and sampling theory inferences in a multivariate probit model for tobacco, alcohol, and marijuana participations
School, Centre or Institute School of Economics
Institution The University of Queensland
Publication date 2007
Thesis type Honours Thesis
Total pages 89
Language eng
Subjects 14 Economics
Formatted abstract Each year in Australia national and regional governments spend large amounts of money on policies and interventions aimed at reducing tobacco, alcohol, and marijuana consumption in the community. Policymakers often rely on estimated quantities such as marginal effects and elasticities, which describe the responsiveness of consumption patterns to changes in various factors that affect demand. These factors may include prices, as well as the demographic and socio-economic characteristics of potential consumers. Zhao and Harris (2004) estimated participation demands for tobacco, alcohol and marijuana in a joint setting by estimating a multivariate probit (MVP) model. The MVP model, which allows for nonzero correlations between the error terms in the participation equations, was estimated by Zhao and Harris using maximum likelihood (ML) techniques. The purpose of this thesis was to investigate whether inferences concerning coefficients, elasticities, and marginal effects from the MVP model of Zhao and Harris were sensitive to estimation using ML or Bayesian techniques. The Bayesian results were consistent with those of Zhao and Harris in several important respects. In particular, complementary relationships were found to exist across the participation decisions that individuals make regarding the consumption of the three drugs.

The parameters of MVP models are usually identified by assuming the error variances are unity. Bayesian estimation of MVP models is then complicated by the fact that exploring the identified parameter space requires sampling from a correlation matrix, which is a difficult process. There is no general consensus in the economic or statistical literature as to the best or most effective way in which to conduct Bayesian estimation for this type of model. This thesis adopted the intuition of Edwards and Allenby (2003), who used a Gibbs sampler with data augmentation to explore the unidentified parameter space. The draws obtained using the Gibbs sampler were then post-processed to resolve the identification problem. The algorithm did not prove as reliable as anticipated, and the estimated coefficients in the participation equations appeared to be sensitive to over- or underestimation of the (unidentified) error variances. For this reason, the estimated coefficients were arbitrarily rescaled before inferences were drawn concerning the determinants of tobacco, alcohol, and marijuana participations.

Finally, the shortcomings of the Edwards-Allenby approach, and a possible solution to the scaling problem were identified.


 
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