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 Right hand term is (1/F) for the null hypothesis That the coefficients in the 1 st stage are all zero

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

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21 Correlation coefficient

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

23 First stage regression with two instruments

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

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

27 2SLS by IVREGRESS

28 2SLS Worked for Pay Model, 2 instruments

29 Can reject at 5.1 percent the null the coefficients are The same

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31 Output residuals from 2LSL model Regress on all exo factors R2 is useless because of Rounding – must calculate yourself Get test of overid by brute force

32 SSM = SST = R2 = SSM/SST = 2.43E-5 N = NR 2 = 6.18 Dist as χ 2 (1) P-value of 6.18 is

33 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

34 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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38 Ratio of Std errors is / = Abs[Rho(qob1,educ)] =0.0142

39 The number you get

40 First-stage Reduced-forms / =

41 Wald Estimate

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44 OLS, Table V, Column (1)

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