Modelling illegal drug participation

We contribute to the small, but important, literature exploring the incidence and implications of misreporting 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 misreport or not. We explore misreporting in the context of the consumption of a system of drugs and specify a multivariate inflated probit model. Compared with observed participation rates of 12.2%, 3.2% and 1.3% (for use of marijuana, speed and cocaine respectively) the true participation rates are estimated to be almost double for marijuana (23%), and more than double for speed (8%) and cocaine (5%). The estimated chances that a user would misreport their participation is a staggering 65% for a hard drug like cocaine, and still about 31% and 17%, for the softer drugs of marijuana and speed