2. Data and method of analysis 
Our study is based on the Austrian Fertility and Family Survey (FFS) which contains information on individuals concerning partnerships, fertility, employment, education, and habitation [Doblhammer et al. 1997]. The retrospective histories of partnerships and fertility for each respondent allow us to determine the timing of all births in the current and any previous union [Note 4]. Additionally, each respondent was asked whether the partner already had children at the time of union formation and if this was the case, the respondent was asked for the number and residence (living in the current household or not) of the partner's children at this time. Similarly, we can determine whether or not the respondent's children live in the current household or not, since for each child of the respondent we know if and when the child has left the household. Since we wish to analyse the influence of preunion children on a couple's shared fertility, we restrict our analysis to the second union [Note 5]. In second unions there are more preunion children than in first unions; 59.6 per cent of all second unions but only 17.5 per cent of all first unions in the Austrian FFS data set record the existence of one or more preunion children of at least one partner [Table 1.b]. Furthermore, 81.5 per cent of all higherorder unions in the Austrian FFS data set are of order two [Note 6]. Only 14.5 per cent are of order three and 4 per cent are of an order greater than three. Among all second unions, the majority recorded at least one preunion child. In 43.8 per cent of the cases one partner had at least one child while the other partner was still childless, and in 15.8 per cent of second unions both partners had preunion children. In 38.8 per cent of second unions neither partner had a child [Table 1.b]. Among all third unions the situation is comparable to second unions. These numbers show that in a considerable percentage of higherorder unions at least one partner had one or more preunion children. Within the second union, which can, of course, be the current union at the time of the interview, we study the intensity of the conception of a first shared child [Note 7]. By choosing conception instead of birth as the event under consideration we take care of any reverse causality between the event and various covariates, e.g. marriage. If we had taken birth as the event, we would not have been able to verify the causal relationship between marriage and fertility, for instance [Note 8]. Moreover, this setup of our data allows us to include children conceived within the union but born after the end of the union. Table 2 summarises the number of eligible respondents included in the analysis and the number of censored cases by cause. Of 6,120 respondents, 824 indicated a secondorder union. We restricted the analysis to native Austrians, to respondents who had not experienced a death or adoption of a child before the second union, and to records with no missing answers with respect to (a) information regarding the respondent's and (b) the partner's preunion children, as well as (c) the beginning and end of the second union. As was done in [Griffith et al. 1985], those records where the woman was 40 years or older at the start of the second union [Note 9] were excluded. Comparing the birthdate of a child with the union biographies allows us to assign a child to a given union if it was born within that union. But what about a child born after the end of the first union and before the formation of the second union or a child born after the interview date? It is questionable whether a child born shortly before two partners moved in together should be defined as their shared biological child, since the data include no further information. To focus on the determinants of childbearing within the second union, we exclude records where a child was born 11 months prior to union formation [Note 10]. On the other hand, we keep those records where the woman was pregnant with the first child of the second union at the time of the interview. For those records where the woman was pregnant at the time of the interview, the event (i.e. the conception of the first child) is set as the expected date of birth  which is coded in our data set  minus nine months. In the Austrian FFS data set the beginning of a union is coded as the date when the couple moved into a joint household. We start the observation nine months before the time of the formation of the second union, assuming that the couple is already exposed to the risk of the conception of a shared child before they set up a household together. This assumption allows us to include all births that occurred in the second union but were conceived prior to moving in together. The validity of this assumption is strengthened by the fact that about 68 out of a total of 339 children born in second unions were conceived before a common household was established. If the difference between the end of the first and the beginning of the second union is less than nine months, we distinguish between two cases. On the one hand, we determine the start of the observation to be the end of the first union if the latter ended in divorce. But if, on the other hand, the first union ended because the partner died, we set the starting time to be the time of formation of the second union, i.e., the date when the respondent forms a joint household with his/her second partner. Behind this latter assumption lies the fact that the death of a partner is not predictable, in contrast to an upcoming divorce. Our setup is arranged such that that we exclude those unions where the conception of the first child of the second union falls within the first union. In the following analysis "start of the second union" is always to be understood as the time point when the respondent is assumed to be exposed to the risk of conceiving a first shared child. We set the start of the time of exposure nine months prior to union formation at the earliest, and at the date of union formation at the latest. Altogether we are left with 695 respondents, 199 of them men and 496 of them women. Among these 695 respondents, 339 recorded at least one common child in their second union. Censoring for the remaining 356 records is performed as follows: two records are censored at the date of adoption of the first common child, four records are censored at the date of the death of a child who was born before the union, 151 records are censored at the date of disruption of the union and 199 records are censored at the date of the interview because no child was born. Since we do not have any clear knowledge about the time dependence of the process, we model the intensity of the conception of a first common child within the second union using a piecewise constant exponential model (see [Blossfeld and Rohwer 1995]):
Here l(t) is the number of the interval of constancy that contains time t, and _{k} is a constant associated with the kth time interval. A(t) denotes a row vector of categorical covariates (including also timevarying covariates, which may change their value over the process time), and represents the associated column vector of coefficients assumed not to vary across time intervals. We split the duration variable into eight time intervals: 1^{st}  5^{th} month, 6^{th}  9^{th} month, 10^{th}  15^{th} month, 16^{th}  21^{st} month, 22^{nd}  33^{rd} month, 34^{th}  45^{th} month, 46^{th}  69^{th} month, and 70^{th} month and later. Keeping in mind that for 71.3 per cent of all respondents the start of observation begins nine months prior to moving in together, these intervals can, for the majority of respondents, be described as following: nine to five months before moving in together, four to one month before moving in together, "formal" start of union (i.e. the time when the couple moved into a common household), up to five months after moving in together, six to eleven months after moving in together, second year, third year, fourth to fifth year after moving in together and finally sixth year onward. Within each of these eight time intervals transition rates are assumed to be constant, but we allow transition rates to vary across the intervals. In a first step we postulate that only the baseline transition rate  as given by the intervalspecific constant transition rates _{k}  can vary across time intervals and that each covariate has the same proportional effect in each time interval. In a second step we test for interactions between covariates and interactions between covariates and the duration parameter. The latter extension allows us to test whether the proportionality assumption of the regression model is justified for each of the covariates under investigation. We apply the program ROCANOVA [Martinelle 1993], which implements the maximum likelihood estimation of the coefficients of the transition rate model. For a comprehensive review of event history analysis as connected to indirect and direct standardisation in demography see [Hoem 1987].


Fertility in second unions in Austria: Findings from the Austrian FFS Isabella Buber, Alexia Prskawetz © 2000 MaxPlanckGesellschaft ISSN 14359871 http://www.demographicresearch.org/Volumes/Vol3/2 