Exploring natural experiments: gender of offspring and the challenges of the stopping rules

The sex of children has frequently been used in the field of social sciences to conduct natural experiments. The key hypothesis behind this methodology is that the sex of the firstborn (or the first k births) is an exogenous variable, meaning it is not influenced by family characteristics observed before the birth of the children. Recent analyses have questioned the supposed exogeneity of the sex of children, proposing that stress experienced during pregnancy results in higher male embryo mortality, thereby leading to a higher probability of female births. This hypothesis casts doubt on the results reached by studies that have used the sex of children to conduct natural experiments. However, the analyses supporting this hypothesis have not properly considered the problems arising from stopping rules, specifically the tendency of some families to continue having children until a child of the desired sex is born. In this work, we show, using an indirect approach, that if stopping rules are properly taken into account, the sex of offspring is not associated to parental stress.