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

Abstract

Studies investigating how the number of children in a family affects the parents or the children face problems because the variable of interest is endogenous in the model. The currently accepted solution to this problem is to use instrumental variables (IVs), for example, based on twin births. In this paper, I review and add to the critique of IVs based on twin births and show that that there are so many issues—major and minor—with these IVs that results based on them are not reliable or interpretable. I also review other IVs used in the literature, for example IVs based on the sexes of the firstborn children, and conclude that there are, as of yet, no credible IVs for the number of children. We need to disregard results from studies applying these IVs, reevaluate the current state of knowledge, and develop new, more credible methods.