The Price of Illicit Drugs: 1981 through the - The White House

From the viewpoint of the model, the Rest of U.S. is just another “city”, and at times we use the
shorthand “30 cities” for “the 29 large U.S. cities and the Rest of U.S.”.
The distribution level has no precise definition, but the intention was to distinguish purchases that
were predominantly retail (Level 1) from those involving dealers (Level 2 and above). The levels,
inclusive of the upper limit, were as follows: cocaine (0-1, 1-10, 10-100, >100 pure grams); heroin
(0-0.1, 0.1-1, 1-10, >10 pure grams); methamphetamine (0-10, 10-100, >100 pure grams);
marijuana (0-10, 10-100, 100-1,000, >1,000 bulk grams).
3. A Model for Price
For each drug and each level of distribution, we regressed standardized price against standardized
amount, purity, time and city. For the reason just outlined, purity was not included in the model
for marijuana. Because price changes over short periods of time are of interest, both time and city
were treated as factors (with 78 and 30 levels respectively). Had time been treated continuously,
means estimated by the model would not have exhibited short-term fluctuations in price.
The regression model took the form of a generalized linear model with log link function,
logarithmic predictors, and constant coefficient of variation (McCullagh and Nelder, 1989, ch. 8).
This model implies the following mean and variance specifications:
E(price itj ) = exp( + city i + time t + log(amount itj ) + log(purity itj )) (1)
V(price itj ) = E 2 (price itj ) (2)
In these expressions, price itj represents the jth observation from the ith city at the tth time period,
with covariate values amount itj and purity itj . E(price itj ) is the mean value of price itj , and V(price itj )
is its variance. is a dispersion parameter analogous to 2 in a linear model based on least
squares.
Estimation and inference for the above model was carried out via the method of quasi-maximum
likelihood. Under distributional assumptions involving only the first two moments (those
embodied in (1) and (2)), quasi-maximum likelihood estimates are consistent and asymptotically
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