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

692 M. Beenstock, G. Rahav / Journal of Health Economics 21 (2002) 679–698
Table 4
Comparison between 2SP and 2SBP
Variable 2SP 2SBP
Cigarette prices −0.00553 (7.119) −0.00538 (7.133)
ρ 0 0.57 (27.1)
PPS 3.228 (13.058) 3.402 (14.300)
The t-values are shown in parentheses.
two reasons. First, because PPS is an estimate of its true value. Secondly, because in any
case IV estimation requires correction of the standard errors in the second stage. We use 200
i.i.d. resamplings to calculate the standard errors. Andrews and Buchinsky (1999) discuss
the number of resamplings required to attain a prescribed degree of accuracy for different
P-values. It turns out that the original (unbootstrapped) standard errors provide a reliable
guide to statistical significance. Also, the original parameter estimates reported in Table 3
turn out to be close to the means of their bootstrapped counterparts, suggesting that the
crude estimates are unbiased.
It is noteworthy that if the relative price of cigarettes is omitted from Table 2, PPS ceases
to be statistically significant in Table 3. This suggests that there is identifying information
in cigarette prices, and that the significance of PPS in Table 3 is not simply the result of
parametric identification.
We experimented with other instruments, including herd effects and exposure to cigarette
regulations. In the former case we used “personalized” cigarette consumption per capita
(based in Fig. 2) as an additional covariate in Table 2, but it was not statistically significant. 7
In the latter case, we defined exposure to be the number of adult years lived prior to the
introduction of mandatory health warnings on cigarette packets. We expected that more
exposed individuals are more likely to smoke, holding other variables constant. However,
this did not turn out to be the case. This was true when we used a variety of health warning
trigger dates (1983 Israel, 1971 UK, 1965 US) both individually and collectively. If anything,
we found that more exposed individuals, as defined, were less likely to smoke. However, this
may be the manifestation of some complex cohort effect; early birth cohorts are less likely
to smoke. In summary, the main instrument for smoking turned out to be the personalized
relative price of cigarettes.
Other results in Table 3 include a negative cohort effect; older birth cohorts are less likely
to use cannabis, Sabras (native Israelis) are more likely to use cannabis, the uneducated and
the highly educated are more likely to use cannabis. When controlling for other factors,
women and secular Jews are more likely to use cannabis.
As noted in Section 2.2, 2SL is consistent but not efficient, because it restricts ρ = 0.
Inefficiency may induce bias in non-linear estimators. To investigate this we re-estimated the
model using two-stage probit (2SP), solved for PPS, and then iterated PPS using two-stage
bivariate probit (2SBP). Coefficient estimates for the main variables of interest are shown
in Table 4.
7 It is possible that prevalence data would have produced different results. See Footnote 5.