As it is shown that γa and γc need to bear the opposite sign than Hicksian cross-
price derivatives do, which are well known to be symmetric, this asymmetry seems to
contradict theory, immediately raising the question whether we can trust this result. In
econometric terms, this means that we have to test if our identifying assumptions hold
that parental smoking habits do influence children’s later tobacco consumption but
do not affect their drinking behavior conditional on their smoking habits, vice versa.
Actually, the over-identification test as presented in Table 2 rejects the null hypothe-
sis for the smoking equation. In contrast, the test statistics for the drinking equation
indicate that parental smoking habits are valid instruments for smoking. These re-
sults are confirmed by “quasi-over-identification-tests”. With respect to smoking the
hypothesis is rejected that all different estimates for γ, which can be calculated from
the reduced form, coincide. Yet, the opposite holds for drinking.
These dissymmetric test results might be explained as follows. Apparently, our
empirical analysis supports the hypothesis that parental smoking habits do not have
effects on children’s future alcohol consumption that operate through unobserved chan-
nels. In contrast, the reverse does hold for parental drinking habits. Drinking at
parental home, therefore, seems to affect children’s future lives in a more general way
than parental smoking habits do. This result is quite plausible in the case of exces-
sive consumption. Severe alcohol abuse is likely to damage family live in general and,
therefore, might affect children through various channels, while excessive smoking -
though harmful to health - is not likely to have comparable effects. Yet, even beyond
this extreme case, drinking, which unlike smoking often is a collaborative activity,
might serve as an indicator for unobserved parental attributes like sociableness or
fun-lovingness. Such parental attributes potentially are of general importance to chil-
dren’s character building and therefore might be reflected in children’s future general
consumption behavior.
In consequence, we can trust the estimate for γa and, therefore, we can conclude that
alcohol and tobacco are consumed as complements rather than substitutes. This result
is in line with the main body of previous literature that comes to the same conclusion,
though applying approaches different to ours. In contrast, the estimate for γc is of
no value for any economic interpretation. Its negative sign that seemingly indicates
substitutability just represents a statistical artefact resting on invalid instruments.
At this point one may wonder why we have allowed ^a and γc to exhibit opposite
signs rather than imposing the restriction sign(γa) = sign(γc) on the estimates. The
reason for this is the lack of valid instruments for the identification of γc . Since we
18