Participation in marijuana, cocaine and heroin consumption in Australia: a multivariate probit approach

Abstract

This article investigates factors affecting the participation in marijuana, cocaine and heroin using micro-unit data from an Australian national survey on recreational drugs. Accounting for cross-drug correlation potentially induced by unobserved personal characteristics such as individual tastes and addictive personalities, we estimate a trivariate probit model, where the participation decisions are jointly modelled as a system with correlated error terms. The estimated correlation coefficients are significant across all three drugs. The study provides valuable empirical information on conditional and joint probabilities of drug participation. The multivariate approach is shown to provide better analysis relative to a univariate approach that does not address the endogeneity of all drug participation variables.

Acknowledgements

We thank Mark Harris and Don Poskitt, Department of Econometrics and Business Statistics, Monash University and Jenny Williams, Department of Economics, University of Melbourne, for helpful comments. We also wish to acknowledge financial support of the Australian Research Council.

Notes

¹ One DALY is a lost year of ‘healthy’ life and is calculated as a combination of years of life lost due to premature mortality and equivalent ‘healthy’ years of life lost due to disability (WHO, 2007).

² Alternatively, we can compute the average MEs over all individuals. Harris et al. (2006) estimated MEs for a different discrete choice model using both approaches and found that the difference between them was trivial.

³ Income and price variables have been transformed to logarithms assuming that it is the relative changes in these regressors that will have a constant effect on the latent dependent variable. The MEs of these variables represent the change in the probability of participation following a 1% change in income/price.

⁴ SEs for the predicted probabilities and MEs presented in the brackets in Tables5–9 are calculated using simulation and numerical gradients. As presented in the model section, conditional and joint probabilities are highly nonlinear in both parameters and X variables, which prevent tractable analytical solution of MEs and SEs. In particular, for the case of SEs for the MEs on various joint and conditional probabilities, we simulate 500 sets of parameters from an asymptotic multivariate normal distribution, each time calculate the numerical derivatives of the probability with respect to the relevant X variables evaluated at the means of all covariates, and thereby obtain 500 sets of MEs. Sample SEs are then calculated as estimates of the SEs for the MEs.