A researcher is interested in the effect of military service on human capital. He collects data from a random sample of 4000 workers aged 40 and runs the OLS regression Yi = β0 + β1Xi + ui, where Yi is the worker's annual earnings and Xi is a binary variable that is equal to 1 if the person served in the military and is equal to 0 otherwise.
a. Explain why the OLS estimates are likely to be unreliable.
b. During the Vietnam War there was a draft, where priority for the draft was determined by a national lottery. (Birthdates were randomly selected and ordered 1 through 365. Those with birthdates ordered first were drafted before those with birthdates ordered second, and so forth.) Explain how the lottery might be used as an instrument to estimate the effect of military service on earnings.