1 IV/2SLS models

2 Z i =1 1 =0.57 Z i =0 0 =0.80

3  0 =3186  1 =3278

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7 Vietnam era service Defined as Estimated 8.7 million served during era 3.4 million were in SE Asia 2.6 million served in Vietnam 1.6 million saw combat 203K wounded in action, 153K hospitalized 58,000 deaths n%20war%20casualty.htm#t7

8 Vietnam Era Draft 1 st part of war, operated liked WWII and Korean War At age 18 men report to local draft boards Could receive deferment for variety of reasons (kids, attending school) If available for service, pre-induction physical and tests Military needs determined those drafted

9 Everyone drafted went to the Army Local draft boards filled army. Priorities –Delinquents, volunteers, non-vol –For non-vol., determined by age College enrollment powerful way to avoid service –Men w. college degree 1/3 less likely to serve

10 Draft Lottery Proposed by Nixon Passed in Nov 1969, 1 st lottery Dec 1, st lottery for men age on 1/1/70 –Men born Randomly assigned number 1-365, Draft Lottery number (DLN) Military estimates needs, sets threshold T If DLN<=T, drafted

11 Questions? What are the research questions? What can we NOT obtain estimates from observational data?

12 If volunteer, could get better assignment Thresholds for service DraftYear of BirthThreshold Draft suspended in 1973

13 Model Sample, men from birth cohorts Y i = earnings X i = Vietnam military service (1=yes, 0=no) Z i = draft eligible, that is DLN <=T (1=yes, 0=no)

14 Put this all together Model of interest Y i = β 0 + x i β 1 + ε i First stage x i = α 0 + z i α 1 + μ i α 1 =(dx/dz)

15 1 st stage Because Z is dichotomous (1 and 0), this males it easy 1 = mean of X when treated (z i =1) =α 0 + z i α 1 = α 0 + α 1 0 = mean of X when not treated (z i =0) =α 0 + z i α 1 = α = α 1 (change in military service from having a low DLN)

16 Intention to treat y i = γ o + z i γ 1 + v i γ 1 = dy/dz=(dy/dx)(dx/dz)

17 Intention to treat y i = γ o + z i γ 1 + v i  1 = mean of y when treated (z=1) γ o + z i γ 1 = γ o + γ 1  0 = mean of y when not treated (z=0) γ o + z i γ 1 = γ o  1 -  0 = γ 1 (difference in earnings for those drafted and those not)

18 Divide ITT by 1 st stage γ 1 /α 1 = (dy/dx)(dx/dz)/(dx/dz) = dy/dx Recall the equation of interest y i = β 0 + x i β 1 + ε i The units of measure are β 1 = dy/dx So the ratio γ 1 /α 1 is an estimate of β 1

19 β 1 = dy/dx β 1 = [  1 -  0 ]/[ ]

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21 1 o

22 Graph of  1 -  0

23  1 -  0 in numbers

24 Β iv = (  1 -  0 )/( ) = /0.159 = $ CPI 78 = 65.2 CPI 81 = /90.9 = * = $2199

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