World War II veterans earn more than nonveterans in their cohort. We test whether the World War II veteran premium reflects nonrandom selection into the military of men with higher earnings potential. The estimation is based on the fact that from 1942 to 1947 priority for conscription was determined by date of birth. Information on individuals' dates of birth may therefore be used to construct instrumental variables for veteran status. Empirical results from the 1960, 1970, and 1980 censuses, along with two other microdata sets, support a conclusion that World War II veterans earn no more than comparable nonveterans and may well earn less.

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.