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



Table 3: Results for non-linear model extensions

Model

Drinking

Smoking

Parameter

Estimate

St. Error

Estimate

St. Error

γa1

0.546

0.394

-

-

γa2

-0.461

0.395

-

-

(i)

γc1

-

0.770**

0.247

γc2

-

-0.167**

0.045

ovi-test

0.000

0.000

γa1

0.589

0.308

-

-

(ii)

γa2
γc1

-0.507

0.310
-

0.079

0.156

γc2

-

-

-0.004

0.003

ovi-test

0.000

0.000

γa1

0.452

0.289

-

-

(iii)

γa2
γc1

-0.365

0.258

-0.197

0.170

γc2

-

-

-0.001

0.028

ovi-test

0.116

0.000

Note:

“ovi-test” indicates p-values for testing over-identifying restrictions.

additional instruments; see Table 3 for the estimation results concerning γa1 , γa2 , γc1 ,
and
γc2 .

These results indicate that the additional insights gained from estimating non-linear
extensions to the basic model are rather limited. Tests for over-identifying restrictions
always reject the assumptions which are necessary to identify the non-linear model or,
at least, do not allow for accepting them. Moreover, the coefficients
γa2 and γc2 often
turn out to be insignificant. Therefore, we stick to the original linear model.

6.2 Separate Models for Males and Females

Our analysis reveals pronounced gender-effects on the consumption of tobacco as well
as the consumption of alcohol, see Tables 1 and 2. In order to analyze whether gender
does matter not just for the level of consumption but also for the interdependence
in consumption, the model is separately estimated for males and females. Table 4
displays estimates for the structural coefficients
γ ; see Tables 9 to 12 in Appendix B
for a comprehensive list of estimation results.

Though the LR-statistic22 strongly argues in favor of separate models for males

22The comprehensive χ2(58)-statistic for the reduced form takes a value as high as 2978. If smoking

20



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