Regression Discontinuity with Integer Running Variables: Effect of Education on Fertility

In regression discontinuity (RD), the treatment depends on whether a continuous running variable crosses a cutoff or not, and RD analysis is done only with some local observations around the cutoff. In reality, however, most running variables are discrete. If the degree of discreteness is low relative to the size of the chosen local neighborhood, the discreteness may be ignored; otherwise, discreteness hinders the RD localization. This paper deals with RD with a running variable on not many integers locally around the cutoff. We review the literature and propose new estimators that refine the intuitive approach of parametric fitting and interpolation toward the cutoff. We then apply the existing and new estimators to a Taiwanese census to find the effect of education on fertility, where an education reform of increasing compulsory education was implemented to affect children of age 12 or younger on September 2, 1968, to renders a RD with a running variable (age) observed only in years. In contrast to negative effects found by many previous studies, we find no education effect on fertility.