Two-stage least squares 1

D1 S1 2

P Q D1 D2D2 S1 S2 Increase in income Increase in costs 3

D1 S2 D2 D3 S3 S1 4

Births in 1997 Variable Smoked during pregnancyDid not smoke Birthweight of child (grams) Mom Unmarried51.2%29.7% Mom a teen16.2%12.7% Received inadequate prenatal care 17.2%11.5% Black12.6%17.6% Mom is hispanic4.2%15.5% Mom < HS degree*47.9%30.1% Mom HS degree *24.1%10.6% 5

6 Z i =1 1 =0.57 Z i =0 0 =0.80

7  0 =3186  1 =3278 Sample Sizes

8 Data set used in previous 2 slides bweight.dta Three variables –treat (1=yes, 0=no) –smoke (1=yes, 0=no) –bweight (birth weight in grams)

9. * how many people are treated. tab treat dummy | variable, | =1 if | treated, =0 | otherwise | Freq. Percent Cum | | Total |

10 Two-sample t test with equal variances Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] | | combined | diff | diff = mean(0) - mean(1) t = Ho: diff = 0 degrees of freedom = 865

11. ttest bweight, by(treat) Two-sample t test with equal variances Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] | | combined | diff | diff = mean(0) - mean(1) t = Ho: diff = 0 degrees of freedom = 865

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13 * 1st stage. reg smoke treat Source | SS df MS Number of obs = F( 1, 865) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = smoke | Coef. Std. Err. t P>|t| [95% Conf. Interval] treat | _cons |

14. * reduced form. reg bweight treat Source | SS df MS Number of obs = F( 1, 865) = 7.37 Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval] treat | _cons |

15. reg bweight smoke (treat) Instrumental variables (2SLS) regression Source | SS df MS Number of obs = F( 1, 865) = 6.65 Model | Prob > F = Residual | R-squared = Adj R-squared =. Total | Root MSE = bweight | Coef. Std. Err. t P>|t| [95% Conf. Interval] smoke | _cons |

Angrist: Vietnam Draft Lottery 16

17 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

1980 Men, Cohorts VariableNon-veteransVeterans In labor force93.2%95.9% Unemployed5.0%4.7% Labor earnings$15,155$15,875 Nonwhite16.8%12.3% < HS degree21.5%8.8% HS degree49.4%67.8% College degree28.9%23.3% Married72.1%75.5% 18

OLS Estimates Impact of Viet Vet Status Independent Variable Labor EarningsUnemployed Age510 (6.5) (0.0001) Non-white-3446 (67)0.029 (0.0014) < high school-9449 (74)0.078 (0.0015) High school-4800 (57) (0.0011) Viet vet523 (53) (0.0010) Mean of outcome $15,3724.9% R2R

20 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

21 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

22 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

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

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25 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)

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

27 1 st stage Because Z is dichotomous (1 and 0), this makes it easy = θ 1 (change in military service from having a low DLN)

28 Reduced form y i = π o + z i π 1 + v i π 1 = dy/dz=(dy/dx)(dx/dz)

29 Intention to treat y i = γ o + z i γ 1 + v i  1 -  0 = π 1 (difference in earnings for those drafted and those not)

30 Divide reduced form by 1 st stage π 1 /θ 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 π 1 /θ 1 is an estimate of β 1

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

32 1 o

33 Graph of  1 -  0

34  1 -  0 in numbers

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

36 Although DLN is random, what are some ways that a low DLN could DIRECTLY change wages

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39 Angrist and Evans: The impact of children on labor supply

40 Introduction 2 key labor market trends in the past 40 years –Rising labor force participation of women –Falling fertility These two fact are intimately linked, but how? –Are women working more because they are having less children –Are women having less children because they are working more

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44 Note that between 1970 and 1990 –Mean children ever born has fallen by 33%, from 1.78 to 1.18 –% worked last year increased by 32%, from 60 to 79% Hundreds have studies have attempted to address these questions Lots of persistent relationships, but what have we measured?

45 Women with children are not randomly assigned Who is most likely to have large families? –Lower educated –Those with lower wages –Certain minority groups –Certain religious groups –Those who want more children

46 Problem is, many of these same groups are also those most likely to be out of the labor force Of the lower labor supply women among women with young children, how much is due to the kids, how much is attributable to some of these other factors?

47 Preferences for sex mix Among married couples who desire 2+ kids –66% wives and 75% of husbands prefer mix Of women with 2 boys and desiring a 3 rd, 85% would prefer a girl Of women with 2 girls and desiring a 3 rd, 84% would prefer a boy

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51 “The desire for a son is the father of many daughters”

52 The sex composition is only impacting 6 percent of women So the change in labor supply should be for this group only, So, if we divide by 0.06, we get /0.06 = Having a 3 rd child will reduce labor supply by 13.3 percentage points

53 Exactly identified model With 1 instrument Over-identified Model with 2 instruments

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58 Exactly Identified Model

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61 Over-identified Model

62 Test the coefficients on twoboys and twogirls are the same test the coefficient on twobots and twogirls are both equal to zero

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