children’s later alcohol use are possibly correlated, the correlation purely operates
through children’s own smoking habits (and other observables) but does not capture
a direct effect. Fortunately, with respect to the validity of our identifying assumptions
we do not have to rely on intuition alone but we have the opportunity of testing
them. Consumption habits of both mothers and fathers serve as instruments. Thus,
the vectors zait and zcit consist of more than one element.12 Hence, the structural
coefficients γ are over-identified and one can apply tests of over-identifying restrictions.
3.2 Estimation
The consumption patterns of both alcohol and tobacco are characterized by large
shares of corner solutions as observed in the data used for this study. That is, many
consumers do not drink or smoke at all. To account for this, the linear equations (1)
and (2) are formulated in terms of latent consumption, rather than actual demand.
Latent consumption, i.e. the inclination to consume, might well fall below zero if an
individual dislikes tobacco or alcohol. In contrast, actual consumption is always non-
negative and zero consumption is observed regardless how strong the disgust at alcohol
or nicotine might ever be. Since negative latent consumption is observed as zero actual
consumption, the dependent variables are censored and if one accepts the assumption
of normally distributed errors, the Tobit model is the obvious estimation procedure
both for the reduced form and the structural model13, cf. Maddala (1983: 245) and
Nelson & Olsen (1978).
Employing a two-step estimation procedure requires some caution in calculating
valid standard errors. Either an appropriate correction procedure, cf. Murphy & Topel
(1985), is required or bootstrapping, which encompasses both stages of the estimation
procedure. We chose the latter strategy and report bootstrapped standard errors for
the structural model parameters. Because of censoring in the dependent variables,
one cannot calculate regression residuals on which to base tests for over-identifying
restrictions. We therefore use an alternative representation of the usual test procedure
that is not based on residuals but compares fitted values obtained from estimating
12 In addition, consumption habits of mothers and fathers (expressed in different consumption levels)
are parameterized as sets of dummy-variables not as two single variables.
13We do not account for correlated errors by estimating the equations of the systems simultane-
ously. Potential gains in efficiency that might be achieved by using a system estimator seem to be
rather limited since both equations share all/most of the explanatory variables and no cross-equation
restrictions are imposed.
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