Empirical Example: Instrumental Variable Estimation

So on average, a woman with more than two kids works 6 weeks fewer than her counterpart with fewer than 2 kids. The result changes a little after we include age as the regressor. The question is, does this correlation imply causality? So the key regressor is morekids. The main concern is that morekids may be endogenous, i.e., correlated with the error term, due to simultaneity or omitted variable. After controlling for age, the coefficient of morekids is -6.6 and significant at 5% level. The negative sign is expected. The number -6.6 means having more than 2 kids on average causes a woman to work 6.6 weeks (one and half month) fewer in a year than a woman with same age, but with fewer than 2 kids. Given that one year has only 48 weeks, this is a big effect. Some people may argue that the true effect may not be that big. For instance, there is an unobserved factor u of preferring staying home over working. Women with that preference tend to have more kids (so E(u · morekids) > 0), and that preference reduces labor supply (so the coefficient of u in the true model could be negative). This omitted variable results