You have now been hired by the Department of Veterans Affairs to study the relation- ship between military service and earnings. You collect a random sample of adults and run the OLS regression earn; = Bo + Bimilitaryi + Ei where earn; is the annual earnings for person i and military; is a dummy variable equal to one if person i served in the military. (a) (5 points) Explain why the OLS estimate might be biased. (b) During the Vietnam war the US instituted a draft where the order in which peo- ple were drafted was randomly determined by birthdate with the first birthdate selected given a value of 1 and the last birthdate a value of 365. People with the lowest numbers were called into service first until the quota for the year was filled. Explain how the lottery might be used as an instrument to estimate the effect of military service on earnings. (This method was used by Angrist 1990.) In particular, (i) (5 points) Discuss what needs to be true for this instrument (lottery number) to be valid. (ii) (5 points) Discuss whether you think this instrument satisfies exogeneity re- striction (iii) (5 points) Provide all the steps you would take to estimate the effect of military service on earnings using lottery as an instrument, if you actually had the data to do it.