The dangers of conditioning on the time of occurrence of one demographic process in the analysis of another

In studies of the fertility of migrants in which the data are confined to the migrants only, estimation bias will normally appear in comparisons of childbearing before and after migration. The same issue arises in studies of union formation before and after first birth, marriage formation before and after home purchase, and in any other comparison of behaviour before and after an index event if one confines the study only to those who have experienced the index event. It is normally better to avoid analysis of behaviour before the index event because such analysis actually conditions on the later arrival of the index event. In this paper, we provide graphical and mathematical representations of this problem and show how one can get a meaningful (unconditional) comparison of behaviour before and after the index event provided the data contain enough information for both sub-periods. Otherwise, the analyst should refrain from making a comparison of this nature.