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

in terms of micro-economic theory - is fully equivalent to estimating Hicksian cross-
price effects.

However, the survey data used for this study are not gathered from an experiment.
Therefore, results from naively estimating (1) and (2) are severely biased because of
c*_it and a*_t being endogenous regressors. Nonetheless, the coefficients θ of the corre-
sponding reduced form representation

^ait = ^θ'a 1 xit ^{+ θ}a 2 zait ^{+ θ}a 3 zcit ^{+ υ}ait
^ci_t = θ ₁ xit ⁺ θ ₃ zait ^{+ θ}c 2 zcit ^{+ υ}cit

θc1 , θc2 , θc3, and υcit analogously

can be estimated consistently. If z_ait and z_cit were empty, that is, if we had no instru-
ments for alcohol and tobacco consumption respectively, estimates for θ would be of no
value to our research question. However, with valid instruments zait and zcit in hand
one can calculate any structural coefficients including y, since γ_a = θak and γ_c = θa3k
hold.¹¹ As a more efficient alternative, one can employ the classical two stage instru-
mental variables estimator. That is, fitted values obtained from estimating the reduced
form equations serve as regressors in the structural equations and the parameters Y
are directly estimated as regression coefficients. Evidently, this two-step approach still
relies on valid instruments. Our reported results are based on the two-step approach.

Fortunately, the data comprises variables which can be expected to be well suited
instruments both for the consumption of alcohol and tobacco. Drinking as well as
smoking habits at parental home are likely to have a strong effect on children’s later
consumption habits. For instance, Bantle & Haisken-DeNew (2002) find significant
correlations between parental smoking behavior and children’s tobacco consumption
for Germany. In order to use parental consumption habits as instruments, we argue
that parents’ smoking habits do influence children’s later tobacco consumption, but
conditional on children’s later smoking behavior, they will not have an effect on their
drinking habits, vice versa. That is, even though parents’ tobacco consumption and

¹¹ The subscript k indicates the kth element of the corresponding vector. I.e. if the vectors z_a
and z_c consist of more than one element, several different estimates for γ_a and γ_c can be calculated.
However, because of the two-step approach estimated in this paper, there is just one estimator of γ_a
and γ_c.

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