The casual effect of fertility: Reviewing the multiple problems with instrumental variables for the number of children in families

For years, instrumental variables (IVs) based on parity-specific twin births have been considered the “gold standard” method for estimating the causal effect of how the number of children in the family affects parents and children. However, recent research questions the validity of these IVs. This paper argues that the issues with twin birth IVs are more profound than previously recognized. The empirical literature has overlooked the need for a definition of causality. The definition used when applying IVs is the potential outcomes framework. This framework requires clear definitions of the active and control treatments because the causal effect is defined as the difference in outcome between the groups undergoing these two treatments. Previous research using twin birth IVs has failed to provide clear and accurate definitions of the treatments, making it impossible to accurately interpret the estimated effects or assess the validity of the study design and IVs.