1. 1 Angrist/Evans Angrist/Krueger

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10. 10 Correlation coefficient

11. 11 0.0020246/0.0291243 = 0.0695 OLS of bivariate model IV of bivariate Model (Wald Est) Ratio of std errors should equal corr coef From previous page

12. 12 First stage regression with two instruments

13. 13 F equals 715 --- no finite sample bias concerns here

14. 14 IV estimate -0.0083481/0.0694 = -0.1202 Notice t-stat on Reduced form Is almost the same As t-stat in 2SLS 0.12/.028 = 4.285

15. 15 1st stage

16. 16 STRUCTURAL MODEL LIST OF EXOGENOUS VARIABLES ALL VARIABLES NOT IN LIST ARE CONSIDERED ENDOGENOUS

17. 17 Can reject at 5.1 percent the null the coefficients are The same

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19. 19 Output residuals from 2LSL model Regress on all exo factors R2 is useless because of Rounding – must calculate yourself

20. 20 SSM = 1.467 SST = 60444.5 R2 = SSM/SST = 2.43E-5 N = 254654 NR 2 = 6.18 Dist as χ 2 (1) P-value of 6.18 is 0.0129

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22. 22 Example Suppose a school district requires that a child turn 6 by October 31 in the 1 st grade Has compulsory education until age 18 Consider two kids One born Oct 1, 1960 Another born Nov 1,1960

23. 23 Oct 1, 1960 –Starts school in 1966 (age 5) –Turns 6 a few months into school –Starts senior year in 1977 (age 16) –Does not turn 18 until after HS school is over Nov 1, 1960 –Start school in 1967 (age 6) –Turns 7 a few months into school –Starts senior year in 1978 (age 17) –Turns 18 midway through senior year

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27. 27 Ratio of Std errors (OLS)/(IV) is 0.0003386/0.0239489 = 0.014 Abs[Rho(qob1,educ)] =0.014

28. 28 1 st stage Reduced-form

29. 29 Correlation coefficient: z and x

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34. 34 Overidentified model 10 years of birth 3 quarters of birth 30 instruments

35. 35 The xi command i.m*i.n takes and generates dummies for i.m, i.n then all the unique interactions of m and n

36. 36 YOB effects QOB main effects and qob x yob interactions as instruments

37. 37. estat overid; Tests of overidentifying restrictions: Sargan (score) chi2(29)= 25.4394 (p = 0.6553) Basmann chi2(29) = 25.4383 (p = 0.6553)

38. 38 1 st stage F – lots of concerns about finite sample bias

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40. 40 Generate instruments by interacting 3 QOB x 10 YOB dummies (30) 3 QOB x 50 YOB dummies (147) 177 instruments, 176 DOF in NR 2 test

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