Most recent, modal, or median heroin purchase: Does it matter when estimating market size?

Assessing the size of illicit drug markets is an important activity of many government agencies; however, the expenditure-based method for estimating market size relies on the relatively untested assumption that the cash value of the most recent purchase is representative of the average purchase amount. Using panel data, we test the representativeness of the most recent, modal and median purchase compared to the average purchase amount.

Data were drawn from a prior study that collected daily transaction-level purchase data from a sample of 120 people who were using heroin regularly. The same study participants completed two distinct two-week waves of data collection, separated by six months. T-tests and bootstrapping were used to detect differences within each wave between the average cash value of participant heroin purchases and the cash value of their most recent, modal and median heroin purchases.

In both waves, we found (a) no evidence that the expected value of the most recent purchase differs from the expected value of the average purchase, and (b) the expected values of the modal and median purchases are smaller than the expected value of the average purchase. These results imply that estimates of total market size based on the modal or median purchase will suffer from a significant downward bias, but that estimates based on the most recent purchase will be unbiased.

We provide evidence in support of using the most recent (but not the modal or the median) purchase to estimate market size for heroin.