Tobacco and Alcohol: Complements or Substitutes? - A Statistical Guinea Pig Approach

characterized by three categories: (i) smoker, (ii) ex- or (iii) never-smoker whereas the
last one serves as reference group. With regard to parents’ drinking habits instruments
are parameterized as three dummy variables for each parent: parent drinks (i) (almost)
daily, (ii) several times a week, (iii) several times a month. Parent (almost) never drinks
is chosen as reference group. We interacted parental consumption habits with having
grown up with this parent in order to make sure that only parental habits enter the
analysis that could have influenced children’s consumption behavior. See Tables 5 and
6 in Appendix B for descriptive statistics of all variables.

5 Estimation Results

Naively estimating equations (1) and (2) by a Tobit procedure, ignoring the endogene-
ity of the right hand side variables consumption of tobacco or alcohol respectively,
indicates a strong correlation between the consumption of both substances. The es-
timates of γ_a as well as γ_c are highly significant and take values of 0.37 and 0.28 re-
spectively. However, these results are certainly biased and do not tell anything about
the interdependence of alcohol and tobacco consumption. For this, the instrumental
variables approach is required.

5.1 Reduced Form Results

The corresponding results for the reduced form equations (3) and (4) are presented
in Table 1. In qualitative terms, the main result is that the chosen instruments are
highly correlated with the endogenous variables c*_t and a*_t. Thus, the parents’ smoking
habits have a significant effect on the smoking behavior of the children and this holds
for drinking behavior as well. The inclination to smoke increases with the intensity of
parental tobacco consumption and the propensity to drink increases with the frequency
a parent drinks. The findings of relevant instruments are confirmed by LR-tests, see
Davis & Kim (2002),²⁰ and by tests of joint significance of instruments as well. For
smoking the corresponding F-statistics is as high as 272.6, for drinking it takes a
value of 104.9. Furthermore, results also exhibit “cross-correlations” between parental
drinking habits to individual’s smoking habits and vice versa. Surprisingly, while

²⁰The χ²(1)-statistic takes a value of 2484.9 concerning parents’ smoking habits and 716.6 con-
cerning parents’ drinking habits. Because of the absence of OLS-residuals Shea-Partial-R-Squares
are calculated using Tobit pseudo residuals instead.

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