Modelling Illegal Drug Participation in Australia

We contribute to the small, but important, literature exploring the incidence and implications of mis-reporting in survey data. Specifically, when modelling ?social bads such as illegal drug consumption, researchers are often faced with exceptionally low reported participation rates. We propose a modelling framework where firstly an individual decides whether to participate or not and, secondly for participants there is a subsequent decision to mis-report or not. We explore misreporting in the context of the consumption of a system of drugs and specify a multivariate inflated probit model. Compared to observed participation rates of 12, 3 and 1.3% (for marijuana, speed and cocaine, respectively) true participation rates are estimated to be some 5 percentage points higher for marijuana, and nearly double for cocaine. There was an estimated 36% (18%) percent chance that a cocaine (marijuana) user would mis-report their participation. Less evidence of mis-reporting was found for speed users.