A researcher is interested in the effect of military service on human capital in the United States. He collects the data from a random sample of 4000 workers aged 40 and runs the OLS regression = + + , where is a worker's annual earnings and 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. (Hint: The United States doesn't have a conscription system(). Which variables are omitted from the regression? Are they correlated with military service?) (b) During the Vietnam War there was a draft in which priority for the draft was determined by a national lottery. (The days of the year were randomly reordered 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.)