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

Demographers and others often study the interaction between two types of individual-level behaviour, such as migration and childbearing. Unfortunately, one can get estimation bias if one compares childbearing before and after migration from data confined to migrants, say, as is sometimes done to see whether international migration disrupts fertility. Similar issues can arise in comparisons of union formation before and after first birth, marriage formation before and after home purchase, as well as in other comparisons of behaviour before and after an index event if one confines the study only to those who have experienced the index event. We point out that if one does this, then the study of behaviour before the index event actually conditions on the later arrival of the index event. This amounts to anticipatory analysis, which normally produces an estimation bias. In this paper we discuss this issue, provide a mathematical and graphical representation of it, and show how one can avoid estimation bias and get a meaningful (unconditional) comparison of behaviour before and after the index event provided the data contain enough information for both sub-periods.