AngristEvans AngristKrueger

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Angrist/EvansAngrist/Krueger
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Correlation coefficient
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OLS of bivariate model
IV of bivariate Model (Wald Est)
0.0020246/0.0291243 0.0695
Ratio of std errors should equal corr coef From
previous page
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First stage regression with two instruments
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F equals 715 --- no finite sample bias concerns
here
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Notice t-stat on Reduced form Is almost the same
As t-stat in 2SLS 0.12/.028 4.285
IV estimate -0.0083481/0.0694 -0.1202
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1st stage
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LIST OF EXOGENOUS VARIABLES ALL VARIABLES NOT IN
LIST ARE CONSIDERED ENDOGENOUS
STRUCTURAL MODEL
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Can reject at 5.1 percent the null the
coefficients are The same
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R2 is useless because of Rounding must
calculate yourself
Output residuals from 2LSL model
Regress on all exo factors
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• SSM 1.467
• SST 60444.5
• R2 SSM/SST 2.43E-5
• N 254654
• NR2 6.18
• Dist as ?2(1)
• P-value of 6.18 is 0.0129

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Example

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

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• 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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Ratio of Std errors (OLS)/(IV) is
0.0003386/0.0239489 0.014 AbsRho(qob1,educ)
0.014
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1st stage
Reduced-form
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Correlation coefficient z and x
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Overidentified model

• 10 years of birth
• 3 quarters of birth
• 30 instruments

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The xi command i.mi.n takes and generates
dummies for i.m, i.n then all the unique
interactions of m and n
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YOB effects
QOB main effects and qob x yob interactions
as instruments
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. estat overid Tests of overidentifying
restrictions Sargan (score) chi2(29) 25.4394
(p 0.6553) Basmann chi2(29) 25.4383
(p 0.6553)
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1st stage F lots of concerns about finite
sample bias
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Generate instruments by interacting 3 QOB x 10
YOB dummies (30) 3 QOB x 50 YOB dummies (147) 177
instruments, 176 DOF in NR2 test
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