I believe these papers made some attempts to avoid seeing the effects of draft-dodging. For example one of them goes only by draft numbers, without looking at w

I believe these papers made some attempts to avoid seeing the effects of draft-dodging. For example one of them goes only by draft numbers, without looking at who actually fought, and finds worse outcomes among the children of the group with bad numbers (fighters and dodgers) compared to good numbers. But I don't know enough details to say whether some biases remain. Indeed "McNamara's Morons" is a pretty crazy story. Turns out the army had rules for who to recruit for a good reason.