samlet årgang - Økonomisk Institut - Københavns Universitet

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NATIONALØKONOMISK TIDSSKRIFT 2005. NR. 3
age, between 3 and 6 years of age, between 7 and 9 years of age, between 10 and 17
years of age, an indicator variable for the presence of stepchildren, and finally an indicator
variable that takes the value 1 if the couple had a child together before marriage.
I also include variables measuring the age of the couple and the age difference. The variable,
sickness, is an indicator variable taking the value 1 if the individual receives
sickness benefits during the year. As a general rule sickness benefits are received if a
person has a spell of illness for more than 13 weeks. I distinguish between individuals
living in the Copenhagen metropolitan area and individulas living in the provinces by
the indicator variable province. Each individual's degree of unemployment during the
year is defined as the number of hours of unemployment divided by the number of potential
supplied working hours.
4. Econometric specification
Our empirical model closely follows Lillard et al. (1995). That is, I specify a model
of the risk of divorce which explicitly incorporates both the direct effect of premarital
cohabitation and a potential self-selection of more divorce-prone individuals into premarital
cohabitation. Our model differs slightly from Lillard et al.’s as our data are
observed on a yearly basis. Hence, I model the transition out of marriage as a grouped
duration model. In addition, I impose a different distributional assumption on the
unobserved heterogeneity components. The correlation structure between the two processes;
the transition out of marriage and the decision to cohabit before marriage, determines
the endogeneity of cohabitation, i.e. the self-selection effect. Therefore,
if unobserved factors both influence the individual risk of divorce and the decision to
cohabit, then they are correlated and cohabitation is endogenous. Below I briefly sketch
the empirical model employed in this study.
4.1. Empirical model
The hazard function is specified as a mixed proportional hazard. That is, it is a product
of a function of time spent being married (the baseline hazard), a function of observed
time-varying characteristics, x d , and a function of unobserved characteristics,
v d ;
h(t|x d t ,vd )= (t) · (x d t ,vd ) , (4.1)
where (t) is the baseline hazard and (x d t ,vd ) is the scaling function specified as
exp(x d t d + v d ). I follow Lillard et al. (1995) and assume that the unobserved component,
v d , is individual-specific to the unit of observation. The unit of observation is the
person in our sample that is followed throughout the period from 1980 to 1995.