Are users’ most recent drug purchases representative?☆
Introduction
The harms associated with illicit drugs include those created by their distribution and sale (UNODC, 2013), so understanding the size and character of illegal markets is important (Kilmer and Pacula, 2009).
Illicit drug markets have been studied in various ways, including analyses of court documents (e.g., Mason and Bjerk, 2011, Bright et al., 2012), ethnography (e.g., Fuentes and Kelly, 1999, Johnson, 2003), analysis of seizures and undercover buys (e.g., Reuter and Caulkins, 2004, Coomber, 2006, Burgdorf et al., 2011), analysis of surveillance videos (e.g., Moeller, 2012), and surveys of drug users. Surveys can ask users how much they spent; what they bought, from whom, when, and where; how easy it was to locate a dealer and whether law enforcement complicated that search, among other topics. Market-oriented questions have been analyzed in surveys of users in the household population (e.g., Caulkins and Pacula, 2006), street users (e.g., Hando et al., 1998), arrestees (e.g., ONDCP, 2012), web-survey respondents (e.g., van Laar et al., 2013), and high-school students (e.g., Johnston et al., 2012).
Estimating the markets’ size, in terms of revenue, is of particular interest since users’ spending drives economic-compulsive crime, systemic crime, impoverishment of some users, and incentives for corruption. Kilmer et al. (2011) describe four strategies for estimating markets’ size; the most direct multiplies prevalence of use by population and average spending per user, meaning that accurate estimates of average spending are needed.
Some analyses (e.g., ONDCP, 2012) estimate monthly spending by multiplying the size of most recent purchase by the number of purchases made in the past-month. This raises the question of whether the most recent purchase is representative and so whether extrapolating from descriptions of most recent purchases gives an accurate understanding of purchases overall and, hence, of markets. After all, even when surveys sample users at random, they do not sample purchases randomly. If because of the vagaries of sampling the most recent purchases tended to be larger than average, then the multiplication just described would over-estimate user’ spending and, hence, the size of the markets. This possibility is illustrated by the following hypothetical example from ONDCP (2014):
Suppose there were a population of users who consume one gram of cannabis each day (so 30 grams per month). Suppose further that they buy an ounce once each month, and also make two additional purchases of one gram each, perhaps because they shop around before making their main purchase. An ounce is roughly 28 grams, so these three purchases add up to 1 + 1 + 28 = 30 grams per month. If this population were surveyed about their most recent purchase and each respondent's survey date was random there would be one chance in thirty that the survey would be administered in the 24 hours following the first one-gram purchase, one chance in thirty it would be administered after the second one-gram purchase, and 28 chances in 30 that it would be administered after the one-ounce purchase and before those 28 grams run out, occasioning a new purchase. At the population level, 2 out of every 30 survey respondents would report their most recent purchase as one gram, and 28 out of 30 would report their most recent purchase as 28 grams. So the average size of the most recent purchase reported would be (2/30) * 1 + (28/30) * 28 = 26.2 grams. Since all respondents report making 3 purchases per month, the naïve estimate of 26.2 * 3 = 78.6 grams purchased per person per month would be two-and-a-half times the true value of 30 grams per person per month. This phenomenon of most recent purchases being larger than typical purchases if big purchases are followed by long inter-purchase times is known as random incidence (Larson and Odoni, 1981).
There are other potential sources of bias when using only most-recent purchase data. For example, if weekend purchases tend to be larger and survey staff work Monday to Friday, then the survey may under-estimate the average purchase size. Likewise if data are collected around mid-day and drug users purchase both small “wake-up” doses and larger amounts in the evening, then most recent purchases may be smaller than average purchases. There might even be Hawthorne effects if payments made to compensate respondents for participating in the survey are large enough to influence purchasing decisions (Landsberger, 1958).
In short, assuming that the most recent purchase is representative amounts to making a strong untested assumption, yet this is a feature of some studies of drug markets. We investigate the assumption by asking respondents in two different surveys to describe a larger number of past purchases, and then comparing the most recent purchases nominated to that larger set with respect to price paid, location, and time between purchases. If biases of the sort just described are commonplace, then we would expect to observe significant differences.
Estimates of market size combine estimates of purchase size with estimates of purchase frequency. We also investigate whether the intervals between the two most recent purchases are similar to gaps between the 2nd and 3rd most recent purchase and, more generally, whether asking about multiple recent purchases offers greater insight into purchase frequency than does simply asking directly how many purchases were made within a specified period of time.
Section snippets
Methods
Data were drawn from two surveys of drug consumers in two countries.
Comparison of purchase sizes
Table 1 presents the mean and standard error of the mean of the size of the most recent purchase and the average of the 3, 6, and 12 most recent purchases, omitting respondents who described one of the purchase sizes as zero or left that item missing.
The average size of the most recent purchase approximates well the average of the most recent 3 purchases for all substances. For all four measures of cannabis purchase size, the most recent purchase generates a slightly lower estimate of typical
Discussion
Survey designers struggle with constraining the length of the instrument and interview (Bogen, 1996), so it is important to understand whether one can assess characteristics of drug buyers’ behavior, including amount spent, by asking only about the most recent purchase or whether surveys should ask a larger battery of questions, e.g., asking about each of the last three purchases, or about all purchases made within a certain time window.
Before undertaking this work, we thought it would be
Role of funding source
The Melbourne Injecting Drug User Cohort Study is funded by the National Health and Medical Research Council (grant number 545891). Research reported in this paper has been funded by the National Drug Law Enforcement Research Fund (grant number 2012/13-13). Paul Dietze is the recipient of an ARC Future Fellowship. The authors gratefully acknowledge the contribution to this work of the Victorian Operational Infrastructure Support Program. The Washington Cannabis Consumption Survey was funded by
Contributors
Authors Dietze and Kilmer organized and designed the data collection for the MIX and WCCS studies, respectively. Authors Scott and Bond analyzed the data from the MIX and WCCS studies, respectively. Author Caulkins conceived of the research question and guided the overall analysis and wrote the first draft of the manuscript. All authors contributed to and have approved the final manuscript. None of the statements contained represent the views of the Carnegie Mellon University, RAND, or the U.S.
Conflicts of interest
Authors Caulkins and Kilmer consulted for the Washington State Liquor Control Board vis a vis its establishment of regulations governing the Washington State legal cannabis industry. Paul Dietze has received untied educational grants from Reckitt Benckiser. All other authors declare that they have no conflicts of interest.
References (22)
- et al.
Heterogeneity in the composition of marijuana seized in California
Drug Alcohol Depend.
(2011) The effect of questionnaire length on response rates: a review of the literature
- et al.
Illuminating dark networks: a social network analysis of an Australian drug trafficking syndicate
Crime Law Soc. Change
(2012) - et al.
Marijuana markets: inferences from reports by the household population
J. Drug Issues
(2006) - et al.
Drug supply and demand: the dynamics of the American drug market and some aspects of Colombian and Mexican drug trafficking
J. Contemp. Crim. Justice
(1999) Pusher Myths: Re-Situating the Drug Dealer
(2006)- et al.
The Development of an early warning system to detect trends in illicit drug use in Australia – the illicit drug reporting system
Addict. Res.
(1998) - et al.
Establishing the Melbourne Injecting Drug User Cohort Study (MIX): rationale, methods, and baseline and twelve-month follow-up results
Harm Reduct. J.
(2013) Patterns of drug distribution: implications and issues
Subst. Use Misuse
(2003)- et al.
Monitoring The Future National Results On Adolescent Drug Use: Overview Of Key Findings, 2011
(2012)
Bringing perspective to markets: estimating the size of the U.S. marijuana market
Drug Alcohol Depend.
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Supplementary material can be found by accessing the online version of this paper. Please see Appendix A for more information.