He used the Wald estimator, _ = [E(Yi|Zi = 1) ) E(Yi|Zi = 0)]/[E(Xi|Zi = 1) ) E(Xi|Zi = 0)], to estimate the causal effffect of military service on earnings using the draft lottery as an instrument for military service. The draft lottery was used to determine priority in conscription: In each year 1970-1972, every 19-year-old man in the U.S. was randomly assigned a lottery number. Men with numbers below a cutoffff value were eligible for the draft (i.e. they could be forced to serve in the army). In practice, many draft-eligible men were still exempted from service, while many men who were draft-exempt nevertheless volunteered. This table presents some statistics from the data on white men born in 1951 used by the study: Percent Average taxable Lottery number. . . veterans earnings in 1980 (in $) . . . below cutoffff value 30% 15200 . . . above cutoffff value 10% 15600 Reference JD Angrist (1990), Lifetime earnings and the Vietnam era draft lottery: evidence from social security administrative records, American Economic Review, 80(3), 313336. 10. Replace Yi , Xi , Zi by appropriate variable names for this study and write down the equation for (i) the causal model, (ii) the fifirst stage model, (iii) the reduced form model. 11. Why is OLS estimation of the causal model problematic? Give a specifific example. 12. Calculate the reduced form effffect from the table and interpret it. 13. What is the exogeneity assumption for the instrument here? Do you think the instrument satisfifies it? 14. Calculate the fifirst stage effffect and interpret it. 15. Calculate the causal effffect and interpret it.
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