Non-causality in Bivariate Binary Panel Data



absorbing state 3. When this happens, no additional information is obtained
by increasing
T further. Notice however that, up to this point, the estimates
become more efficient and, loosely speaking, closer to normality, as
T increases.

6 An Illustrative Example for Panel Data

Notwithstanding the interest in timing fertility and in working choices, the joint
study of marital duration and fertility has not been a deeply studied topic in
Sociometrics: Waite and Lillard (1991), Lillard and Waite (1993) and Lillard
(1993) are almost the only contributions to its study.

However, the picture they draw is quite clear. Married couples with children
appear to be less likely to end their marriages than childless couples. This
seems to suggest that children affect the chances that they parents divorce;
however, the process may not be so simple, since the chances that the marriage
will last may affect couples’ willingness to have children. The economic model
used by the authors is quite sophisticated and able to capture a wide variety of
situations: the problem with Lillard’s and Waite’s approach is that the method
of estimation they use is not able to yield consistent estimators and therefore
the inferences they draw from the model are fallacious.13

Our analysis will be based on data from the PSID database and therefore a
brief description appears to be necessary. The Panel Study of Income Dynam-
ics (PSID), begun in 1968, is a longitudinal study of a representative sample of
U.S. individuals (men, women, and children) and the family units in which they
reside. It emphasizes the dynamic aspects of economic and demographic behav-
ior, but its content is broad, including sociological and psychological measures.
Starting with a national sample of 5,000 U.S. households in 1968, the PSID
has reinterviewed individuals from those households every year since that time,
whether or not they are living in the same dwelling or with the same people.
Adults have been followed as they have grown older, and children have been
observed as they have advanced through childhood and into adulthood, forming
family units of their own. The study is conducted at the Survey Research Cen-
ter, Institute for Social Research, University of Michigan. Information about
the original 1968 sample individuals and their current со-residents (spouses,
co-habitors, children, and anyone else living with them) is collected each year.
This has allowed us to select 266 women appearing in the database from 1968 to
1993: subjects with missing covariates have been eliminated and the variables
has been elaborated in order to yield a certain uniformity over time.

More information about the variables can be found in Section B: each column
represents a variable and for each year and variable the code is reported; the
13The Lillard and Waite approach suffers from a problem of endogeneity since they use
a model with unobserved heterogeneity that is valid only under the hypothesis of strong
exogeneity of the regressors. However, since they use as explicative variables some lagged
dependent variables, this condition seems to be violated.

The methods of Arellano and Carrasco (1996) and Honoré and Kiriazidou (1997) could be
of interest here.

17



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