IV/2SLS models

Zi=11=0.57Zi=00=0.80

0=31861=3278

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

1o

iv= (1 - 0)/(1 - 0) = -487.8/0.159 = $3067.9

CPI78 = 65.2 CPI81=90.9 65.2/90.9 = .7173

.717*3067.92 = $2199

Chart1

31.8

32.3

33.3

34

34.1

33.9

34.2

35.4

36.4

36.5

36.9

37.1

37.6

38

37.8

38.3

38.9

39.4

40.1

41.1

41.6

42.7

43.3

43.3

43.7

44.4

45.3

46

47

48.1

49.6

50.6

51.3

52.1

52.7

53.1

53.7

54.7

55.5

56.2

56.8

57.7

58

57.9

58.5

58.5

59.3

59.4

59.9

60.5

60.4

60.7

60.6

60.6

60.5

60.6

60.3

Year

Percent in labor force

Female Labor Force Paticipation Rate

female_lfp

194831.8

194932.3

195033.3

195134

195234.1

195333.9

195434.2

195535.4

195636.4

195736.5

195836.9

195937.1

196037.6

196138

196237.8

196338.3

196438.9

196539.4

196640.1

196741.1

196841.6

196942.7

197043.3

197143.3

197243.7

197344.4

197445.3

197546

197647

197748.1

197849.6

197950.6

198051.3

198152.1

198252.7

198353.1

198453.7

198554.7

198655.5

198756.2

198856.8

198957.7

199058

199157.9

199258.5

199358.5

199459.3

199559.4

199659.9

199760.5

199860.4

199960.7

200060.6

200160.6

200260.5

200360.6

200460.3

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Correlation coefficient

0.0020246/0.0291243= 0.0695OLS of bivariate modelIV of bivariateModel (Wald Est)Ratio of std errors should equal corr coefFrom previous page

First stage regression with two instruments

IV estimate-0.0083481/0.0694= -0.12031Notice t-stat on Reduced formIs almost the same As t-stat in 2SLS

0.12/.028 = 4.285

STRUCTURAL MODELLIST OF EXOGENOUS VARIABLESALL VARIABLES NOT IN LISTARE CONSIDERED ENDOGENOUS

2SLS by IVREGRESS

2SLS Worked for Pay Model, 2 instruments

Can reject at 5.1 percent the null the coefficients areThe same

Output residuals from 2LSL modelRegress on all exo factorsR2 is useless because ofRounding must calculateyourselfGet test of overid by brute force

SSM = 1.467SST = 60444.5R2 = SSM/SST = 2.43E-5N = 254654NR2 = 6.18Dist as 2(1) P-value of 6.18 is 0.0129

ExampleSuppose a school district requires that a child turn 6 by October 31 in the 1st gradeHas compulsory education until age 18Consider two kidsOne born Oct 1, 1960Another born Nov 1,1960

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

Ratio of Std errors is 0.0003386/0.0239 = 0.0125Abs[Rho(qob1,educ)] =0.0142

The number you get

First-stageReduced-forms-0.0110989/-0.1088179=.101995

Wald Estimate

OLS, Table V, Column (1)