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IV/2SLS models

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Zi=1

1=0.57

Zi=0

0=0.80

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0=3186 1=3278

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

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Βiv= (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

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Female Labor Force Paticipation Rate

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. * get correlation coefficient between;

. * instrument and endogenous RHS variable;

. corr morekids samesex; (obs=254654) | morekids samesex -------------+------------------ morekids | 1.0000 samesex | 0.0695 1.0000

Correlation coefficient

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. * correlation coefficient is 0.0695;

. * OLS of bivariate regression;

. reg worked morekids; Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 1,254652) = 3237.65 Model | 796.712284 1 796.712284 Prob > F = 0.0000 Residual | 62664.0083254652 .246077032 R-squared = 0.0126 -------------+------------------------------ Adj R-squared = 0.0126 Total | 63460.7206254653 .249204685 Root MSE = .49606 ------------------------------------------------------------------------------ workedm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.1152029 .0020246 -56.90 0.000 -.1191712 -.1112347 _cons | .5720607 .001249 458.02 0.000 .5696127 .5745087 ------------------------------------------------------------------------------

0.0020246/0.0291243= 0.0695

OLS of bivariate model

IV of bivariateModel (Wald Est)

Ratio of std errors should equal corr coefFrom previous page

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First stage regression with two instruments

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. * demonstrate 1st stage and reduced form results for;

. * exactly identified model;

. * 1st stage;

. reg morekids samesex boy1st boy2nd agem1 agefstm black hispan othrace; Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 8,254645) = 2825.70 Model | 4894.61525 8 611.826907 Prob > F = 0.0000 Residual | 55136.2215254645 .216521909 R-squared = 0.0815 -------------+------------------------------ Adj R-squared = 0.0815 Total | 60030.8368254653 .235735832 Root MSE = .46532 ------------------------------------------------------------------------------ morekids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | .0693854 .0018456 37.59 0.000 .065768 .0730028 boy1st | -.0111225 .0018456 -6.03 0.000 -.0147398 -.0075051 boy2nd | -.0095472 .0018456 -5.17 0.000 -.0131646 -.0059298

. * reduced form;

. reg worked samesex boy1st boy2nd agem1 agefstm black hispan othrace; Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 8,254645) = 845.42 Model | 1641.9059 8 205.238237 Prob > F = 0.0000 Residual | 61818.8147254645 .242764691 R-squared = 0.0259 -------------+------------------------------ Adj R-squared = 0.0258 Total | 63460.7206254653 .249204685 Root MSE = .49271 ------------------------------------------------------------------------------ workedm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | -.0083481 .0019543 -4.27 0.000 -.0121785 -.0045178 boy1st | .0022593 .0019543 1.16 0.248 -.001571 .0060897 boy2nd | -.0036827 .0019543 -1.88 0.060 -.0075131 .0001477

IV estimate-0.0083481/0.0694= -0.12031

Notice t-stat on Reduced formIs almost the same As t-stat in 2SLS

0.12/.028 = 4.285

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. * 2sls worked for pay model;

. * same sex as instrument;

. reg workedm morekids boy1st boy2nd agem1 agefstm black hispan othrace > (samesex boy1st boy2nd agem1 agefstm black hispan othrace); Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 8,254645) = 865.24 Model | 3058.04132 8 382.255165 Prob > F = 0.0000 Residual | 60402.6792254645 .237203476 R-squared = 0.0482 -------------+------------------------------ Adj R-squared = 0.0482 Total | 63460.7206254653 .249204685 Root MSE = .48704 ------------------------------------------------------------------------------ workedm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.1203151 .0278412 -4.32 0.000 -.1748831 -.0657471 boy1st | .0009211 .0019489 0.47 0.636 -.0028987 .0047409 boy2nd | -.0048314 .0019425 -2.49 0.013 -.0086387 -.001024 agem1 | .0219352 .0009013 24.34 0.000 .0201686 .0237018 agefstm | -.0264911 .0012647 -20.95 0.000 -.0289699 -.0240123 black | .1899764 .0047675 39.85 0.000 .1806323 .1993205 hispan | -.0139081 .0053813 -2.58 0.010 -.0244554 -.0033609 othrace | .0443545 .0048138 9.21 0.000 .0349196 .0537893 _cons | .4498966 .0138565 32.47 0.000 .4227383 .4770549 ------------------------------------------------------------------------------

STRUCTURAL MODELLIST OF EXOGENOUS VARIABLESALL VARIABLES NOT IN LISTARE CONSIDERED ENDOGENOUS

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2SLS by IVREGRESS

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2SLS Worked for Pay Model, 2 instruments

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Can reject at 5.1 percent the null the coefficients areThe same

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. * get test of overid;

. predict res_2sls_worked, res; . reg res_2sls_worked twoboys twogirls boy1st agem1 agefstm black hispan othra > ce; Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 8,254645) = 0.77 Model | 1.46731442 8 .183414303 Prob > F = 0.6269 Residual | 60444.5039254645 .237367723 R-squared = 0.0000 -------------+------------------------------ Adj R-squared = -0.0000 Total | 60445.9712254653 .237366028 Root MSE = .4872 ------------------------------------------------------------------------------ res_2sls_w~d | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- twoboys | -.0052822 .0026941 -1.96 0.050 -.0105625 -1.83e-06 twogirls | .0042367 .0027711 1.53 0.126 -.0011946 .0096681 boy1st | .004822 .0027461 1.76 0.079 -.0005603 .0102043

Output residuals from 2LSL model

Regress on all exo factors

R2 is useless because ofRounding – must calculateyourself

Get test of overid by brute force

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• SSM = 1.467

• SST = 60444.5

• R2 = SSM/SST = 2.43E-5

• N = 254654

• NR2 = 6.18

• Dist as χ2(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 is 0.0003386/0.0239 = 0.0125Abs[Rho(qob1,educ)] =0.0142

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. * get correlation coefficient for;

. * educ and qob1;

. corr educ qob1; (obs=329509) | educ qob1 -------------+------------------ educ | 1.0000 qob1 | -0.0143 1.0000

The number you get

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First-stage

Reduced-forms-0.0110989/-0.1088179=.101995

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Wald Estimate

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OLS, Table V, Column (1)

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