Non-causality in Bivariate Binary Panel Data



Models

L

P

AIC

BIC

Uj1

-2998.7815

18

-2980.7815

-3078.21022

U12nl,

-2985.8111

24

-2961.8111

-3091.71605

ClJWJ
ɔl_____

-2914.4933

48

-2866.4933

-3126.30321

Ui

-2980.7935

22

-2958.7935

-3077.87304

U2

-2962.6891

31

-2931.6891

-3099.48300

Si

-2894.4002

52

-2842.4002

-3123.86094

Table 2: Information criteria for the estimated models

Restrictions

χ2 Test

DoF

Signif.

Uι→U≡ ^

35.9760

4

2.92678E-07

25.9408

6

2.28367E-04

-spψπ-→upvτi-

168.5764

30

3.10543E-21

Si →U'a"'j

208.7626

34

5.20616E-27

U2 →U≡

72.1848

10

1.67555E-11

U2 →U^≡

46.2440

4

2.19107E-09

Si →S≡

40.1862

4

3.96112E-08

Si →Uι

172.7866

30

5.31910E-22

U2 →Uι

36.2088

6

2.51064E-06

Table 3: Restrictions on the estimated models

following ones:

AIC = Lm —p,

BIC = Lm - 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.

20



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