Local Instruments, Global Extrapolation : External Validity of the Labor Supply-Fertility Local Average Treatment Effect

We investigate whether local average treatment effects (LATE's) can be extrapolated to new settings. We extend the analysis and framework of Dehejia, Pop-Eleches, and Samii (2015), which examines the external validity of the Angrist-Evans (1998) reduced-form natural experiment of having two first children of the same sex on the probability of an incremental child and on mother's labor supply. We estimate Angrist and Evans's (1998) same-sex instrumental variable strategy in 139 country-year censuses using data from the Integrated Public Use Micro Sample International. We compare each country-year's LATE, as a hypothetical target, to the LATE extrapolated from other country-years (using the approach suggested by Angrist and Fernandez-Val 2010). Paralleling our findings in Dehejia, Pop-Eleches, and Samii (2015), we find that with a sufficiently large reference sample, we extrapolate the treatment effect reasonably well, but the degree of accuracy depends on the extent of covariate similarity between the target and reference settings. Our results suggest that - at least for our application - there is hope for external validity