Testing Gateway Theory: do cigarette prices affect illicit drug use?

684 M. Beenstock, G. Rahav / Journal of Health Economics 21 (2002) 679–698
to Eq. (6) is used to replace A c in Eq. (4) in the second stage. The parameter standard errors in
the second stage are bootstrapped. Having thus estimated Eq. (4), we may use it to calculate
E(A s ) and to replace A s in a CPHM for hard drugs.
In the bio-statistical literature this class of dependent hazard model is known as a “frailty”
model (Hougaard, 1995; Klein and Moeschberger, 1997). Frailty models usually consist of
two hazards functions that happen to be stochastically related. If u denotes the stochastic
component of the empirical hazard function for cigarette initiation, and v denotes its counterpart
for cannabis initiation, then frailty models estimate the parameter ρ = cov(u, v).
However, they do not usually specify A c in the hazard function for cannabis. Here, we
specify the dependence between the two hazard functions directly via β in Eq. (1), as in the
two-stage procedure that we have described. A more general specification would estimate
both ρ as well as β in Eq. (4), i.e. frailty may be transmitted directly via β and indirectly
via ρ. 3
3. The data
3.1. The surveys
The data to be used in the present analysis are from three epidemiological surveys carried
out in Israel by the Israel Anti-Drug Authority in 1989 (N = 5280), 1992 (N = 1816) and
1995 (N = 5044), providing a total of some 12,700 observations. While sample size varied
between surveys, the sampling procedure remained the same. The sample is intended to
represent the Jewish population in Israel aged 18–40 years. It was based on a geographic
sample of points in each of the larger Jewish cities and towns (i.e. with population of
30,000 or more) and a sample of the smaller localities. Starting at each of these geographic
points a cluster of 10 residential apartments was sampled. Experienced interviewers first
checked if there were individuals in the designated age bracket in the household. One
individual was selected from each household by one of two, predetermined methods: either
the first available eligible person was interviewed, or the interviewee was selected by the
Troldahl–Carter method (for more details see Barnea et al. (1990)).
Interviewers were instructed to make at least three attempts to obtain a sampled household,
or person within the household. If there was no response from an apartment there was no
way of determining whether it is residential, commercial, or an unoccupied apartment. Most
probably there is some under-representation of new immigrants, and others who are either
away from home much of their time, or do not speak Hebrew. Otherwise, the sample seems
to be representative of Israeli Jews in this age bracket who live at home. It does not cover
at all institutionalized persons, including those in military service away from home and
prisoners, nor members of Kibbutzim (collective farms) who make up about 2% of the
population.
3 In the classic frailty model the survival hazards of parents and children are assumed to be related via ρ. This
has a genetic interpretation; strong parents breed strong children. Additionally, or independently, there may be a
behavioral effect in that the early death of the parent may adversely affect the survival of the child. This direct
frailty effect is captured by β. We are unaware of empirical examples where direct and indirect frailty effects are
estimated.