The data identify the fraction of the population who self-report use, P[wt =1]. The data cannot identify the fraction who falsely claim to have consumed drugs, P[wt=1, yt=0], or who falsely claim to have abstained, P[wt=0, yt=1]. The data identify prevalence rates if the fraction of false negatives is exactly offset by the fraction of false positive reports, that is, if P[wt=0, zt=0]=P[wt=1, zt=0]. Otherwise, the fraction of users is not identified.
There is a large literature that provides direct evidence on the magnitude of misreporting in some self-reported drug use surveys. Validation studies have been conducted on arrestees (see, for example, Harrison 1992 and 1997; Mieczkowski, 1990), addicts in treatment programs (see, for example, Darke, 1998; Magura et al., 1987, 1992; Morral et al., 2000; Kilpatrick et al., 2000), employees (Cook et al., 1997), people living in high-risk neighborhoods (Fendrich et al., 1999), and other settings. See Harrison and Hughes (1997) for a review of the literature.
The most consistent information is collected as part of the Arrestee Drug Abuse Monitoring/Drug Use Forecasting (ADAM/DUF) survey of arrestees. To enable inferences on the extent of inaccurate reporting among arrestees, this survey elicits information on drug use from self-reports and urinalysis.11 Harrison (1992, 1997), for example, compares self-reports of marijuana and cocaine use during the past three days to urinalysis test results for the same period. In general, between 20 and 30 percent of respondents appear to give inaccurate responses. In the 1988 survey, for example, 27.9 percent of respondents falsely deny using cocaine and 1.4 percent falsely claim to have used cocaine. For marijuana, the false negative rates are lower (18.1 percent) and the false positive rates are higher (6.4 percent), but the same basic picture emerges. About half of those testing positive report use, while a substantially higher fraction testing negative report truthfully.
Despite this literature, very little is known about misreporting in the national probability samples. The existing validation studies have largely been conducted on samples of people who have much higher rates of drug use than the general population. Response rates in the validation studies are often quite low and, moreover, respondents are usually not randomly sampled from some known population.