Non-causality in Bivariate Binary Panel Data

selected range is reported in parentheses. Therefore the following variables have
been selected:

• Yl: the variable is set to 1 in t if the individual has had (at least) a child
during the year t, 0 otherwise;

• Y2: this variable is set to 1 in t if the individual was married during the
year t, 0 otherwise;

• AGE: this is equivalent to the PSID variable AGE OF THE INDIVIDUAL;

• INCOME: it is equivalent to MONEY INCOME (in the period 1968-1974) or
TAXABLE INCOME plus TRANSFER INCOME (in the period 1975-1990) or the
sum of TRANSFER INCOME, LABOR INCOME and ASSET INCOME (in the pe-
riod 1991-1993); this is due to the increased precision of the variables in
the PSID database;

• HOURS: it is the PSID HOURS WORKED variable;

• EDU: it is essentially the PSID YEARS OF SCHOOL COMPLETED variable:
however it has been checked for incongruences with HIGHEST GRADE COMPLETED
and COMPLETED EDUCATION.

To provide an application of causality testing for binary bivariate processes,
six models belonging to the class presented in Section 3 have been estimated on
PSID data.¹⁴ We are interested in performing a series of tests on these models:
in particular, we would like to choose a model that fits parsimoniously the data
and to test for поп-causality between the two processes. In order to select the
model that seems to fit the data better we have to consider separately the case
in which one of the two models is nested in the other one, and the non-nested
case. In the nested case, Likelihood Ratio tests can be used; on the other side, to
test among non-nested models, we consider two well-known information criteria,
the Akaike Information Criterion and Schwarz’ Bayesian Information Criterion.
Then we study through Wald tests the поп-causality relations between the two
processes {Tj¹} and {Tj²}.

In the following we will use the mnemonics for the estimated models reported
in Table 1. The full estimates of the proposed models are reported in Appendix
C; for our purposes, it is enough to consider the log-likelihoods of the estimated

¹⁴Estimation has been performed using GAUSS-386i. The covariance matrix of the esti-
mates have been calculated through the cross-product of first derivatives.

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