Testing the validity of the sibling sex ratio instrument

We test the validity of the sibling sex ratio instrument in Angrist and Evans (1998) using the methods proposed by Kitagawa (2008) and Huber and Mellace (2011). The sex ratio of the first two siblings is arguably randomly assigned and influences the probability of having a third child, which makes it a candidate instrument for fertility when estimating the effect of fertility on female labor supply. However, identification hinges on the random assignment of the instrument, an instrumental exclusion restriction, and the monotonicity of fertility in the instrument, see Imbens and Angrist (1994). We find that the instrumental variable tests of Kitagawa (2008) and Huber and Mellace (2011) do not point to a violation of these assumptions in the Angrist and Evans (1998) data (which can, however, not be ruled out even asymptotically as the tests cannot detect all possible violations).