Non-causality in Bivariate Binary Panel Data

Table 2: Information criteria for the estimated models

Table 3: Restrictions on the estimated models

following ones:

AIC = L_m —p,

BIC = L_m - I ∙ InAf,

where Af is a shortcut for the number of observation, be it N, T or mixed (in
our case, Af = N-T = 6,805). It is important to remark that Akaike’s criterion
is not in general consistent, that is the probability of choosing the correct model
does not go to 1 as long as the number of observations go to infinity: moreover,
AIC has the unpleasant tendency to select overparameterized models; on the
other side, the BIC is consistent. From Table 2, we see that AIC selects model
Si, while BIC selects Ui-Even more interesting and more directly linked to the
topic of this Section would be to test for the presence of causality relations
between marriage decisions and fertility timing. To do so, we have performed a
Wald test as described in the previous Sections, whose results are displayed in
Table 4. The results of all of these tests are univocal:

• the hypothesis Hι<^₂, concerning the поп-causality of Y² towards Y¹ is
strongly rejected at any conventional significance level: therefore, we can-
not accept the hypothesis that Y² does not cause У¹. Therefore, a marital
relation seems to increase significantly the probability of having a child,
as common sense suggests.

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