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Angrist/Evans Angrist/Krueger

Dec 31, 2015

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carlos-barlow

Angrist/Evans Angrist/Krueger. Correlation coefficient. 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. First stage regression with two instruments. - PowerPoint PPT Presentation
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Angrist/EvansAngrist/Krueger

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Female Labor Force Paticipation Rate

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Year

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t in

lab

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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 ------------------------------------------------------------------------------

. * wald estimate; . reg worked morekids (samesex); Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 1,254652) = 22.33 Model | 766.561812 1 766.561812 Prob > F = 0.0000 Residual | 62694.1587254652 .24619543 R-squared = 0.0121 -------------+------------------------------ Adj R-squared = 0.0121 Total | 63460.7206254653 .249204685 Root MSE = .49618 ------------------------------------------------------------------------------ workedm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.1376139 .0291243 -4.73 0.000 -.1946967 -.080531 _cons | .5805895 .0111272 52.18 0.000 .5587805 .6023984 ------------------------------------------------------------------------------

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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. * column (6);

. * test twoboys=twogirls, the two coefficients are the same;

. * test twoboys=twogirls=0, the two coefficients equal zero;

. reg morekids twoboys twogirls boy1st 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] -------------+---------------------------------------------------------------- twoboys | .0598382 .0025731 23.26 0.000 .0547951 .0648813 twogirls | .0789326 .0026467 29.82 0.000 .0737452 .08412

First stage regression with two instruments

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. test twoboys twogirls; ( 1) twoboys = 0 ( 2) twogirls = 0 F( 2,254645) = 715.13 Prob > F = 0.0000

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

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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= -0.1202

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

0.12/.028 = 4.285

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. * 1st stage estimates;

. * married women sample;

. * these numbers are in Table 6, columns 4-6;

. *column (4);

. reg morekids samesex agem1 agefstm black hispan othrace; Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 6,254647) = 3756.08 Model | 4880.82564 6 813.47094 Prob > F = 0.0000 Residual | 55150.0111254647 .21657436 R-squared = 0.0813 -------------+------------------------------ Adj R-squared = 0.0813 Total | 60030.8368254653 .235735832 Root MSE = .46538 ------------------------------------------------------------------------------ morekids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | .0688381 .0018446 37.32 0.000 .0652228 .0724533 agem1 | .0304158 .0002981 102.05 0.000 .0298316 .031 agefstm | -.0435664 .0003462 -125.83 0.000 -.044245 -.0428878 black | .0680954 .0041858 16.27 0.000 .0598913 .0762995 hispan | .1261094 .0038979 32.35 0.000 .1184697 .1337491 othrace | .0478738 .0044214 10.83 0.000 .039208 .0565397 _cons | .3133116 .0091753 34.15 0.000 .2953282 .331295 ------------------------------------------------------------------------------

1st stage

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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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. * Run Hausmans test of endogeneity, one instrument case;

. * add residual from 1st stage regression to OLS of structural model;

. reg workedm morekids boy1st agem1 agefstm black hispan othrace res_1st_2zs; Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 8,254645) = 1677.06 Model | 3176.20362 8 397.025453 Prob > F = 0.0000 Residual | 60284.5169254645 .236739449 R-squared = 0.0500 -------------+------------------------------ Adj R-squared = 0.0500 Total | 63460.7206254653 .249204685 Root MSE = .48656 ------------------------------------------------------------------------------ workedm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.1127816 .0276489 -4.08 0.000 -.1669726 -.0585906 boy1st | .0009424 .001947 0.48 0.628 -.0028736 .0047585 agem1 | .0217057 .0008957 24.23 0.000 .0199501 .0234612 agefstm | -.0261649 .0012566 -20.82 0.000 -.0286279 -.0237019 black | .1895035 .004759 39.82 0.000 .180176 .1988311 hispan | -.014818 .0053636 -2.76 0.006 -.0253305 -.0043054 othrace | .0439784 .0048067 9.15 0.000 .0345574 .0533994 res_1st_2zs | -.0541136 .0277264 -1.95 0.051 -.1084566 .0002294 _cons | .4448388 .013693 32.49 0.000 .4180009 .4716768 ------------------------------------------------------------------------------

Can reject at 5.1 percent the null the coefficients areThe same

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. * 2sls worked for pay model;

. * 2boys 2girls as instruments;

. reg workedm morekids boy1st agem1 agefstm black hispan othrace > (twoboys twogirls boy1st agem1 agefstm black hispan othrace); Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 7,254646) = 987.26 Model | 3014.74939 7 430.678484 Prob > F = 0.0000 Residual | 60445.9712254646 .237372553 R-squared = 0.0475 -------------+------------------------------ Adj R-squared = 0.0475 Total | 63460.7206254653 .249204685 Root MSE = .48721 ------------------------------------------------------------------------------ workedm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.1127816 .0276858 -4.07 0.000 -.1670451 -.0585182 boy1st | .0009424 .0019496 0.48 0.629 -.0028787 .0047636 agem1 | .0217057 .0008969 24.20 0.000 .0199477 .0234636 agefstm | -.0261649 .0012583 -20.79 0.000 -.0286312 -.0236987 black | .1895035 .0047654 39.77 0.000 .1801636 .1988435 hispan | -.014818 .0053708 -2.76 0.006 -.0253446 -.0042914 othrace | .0439784 .0048131 9.14 0.000 .0345448 .053412 _cons | .4448388 .0137113 32.44 0.000 .417965 .4717126 ------------------------------------------------------------------------------

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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

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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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. * Run Hausmans test of endogeneity, one instrument case;

. * add residual from 1st stage regression to OLS of structural model;

. reg workedm morekids boy1st agem1 agefstm black hispan othrace res_1st_2zs; Source | SS df MS Number of obs = 254654 -------------+------------------------------ F( 8,254645) = 1677.06 Model | 3176.20362 8 397.025453 Prob > F = 0.0000 Residual | 60284.5169254645 .236739449 R-squared = 0.0500 -------------+------------------------------ Adj R-squared = 0.0500 Total | 63460.7206254653 .249204685 Root MSE = .48656 ------------------------------------------------------------------------------ workedm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.1127816 .0276489 -4.08 0.000 -.1669726 -.0585906 boy1st | .0009424 .001947 0.48 0.628 -.0028736 .0047585 agem1 | .0217057 .0008957 24.23 0.000 .0199501 .0234612 agefstm | -.0261649 .0012566 -20.82 0.000 -.0286279 -.0237019 black | .1895035 .004759 39.82 0.000 .180176 .1988311 hispan | -.014818 .0053636 -2.76 0.006 -.0253305 -.0043054 othrace | .0439784 .0048067 9.15 0.000 .0345574 .0533994 res_1st_2zs | -.0541136 .0277264 -1.95 0.051 -.1084566 .0002294 _cons | .4448388 .013693 32.49 0.000 .4180009 .4716768 ------------------------------------------------------------------------------

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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 = 0.014Abs[Rho(qob1,educ)] =0.014

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. * get reduced-forms for wald estimate;

. * compare to table III, panel B;

. reg educ qob1; Source | SS df MS Number of obs = 329509 -------------+------------------------------ F( 1,329507) = 67.57 Model | 727.393312 1 727.393312 Prob > F = 0.0000 Residual | 3546940.27329507 10.7643852 R-squared = 0.0002 -------------+------------------------------ Adj R-squared = 0.0002 Total | 3547667.66329508 10.76656 Root MSE = 3.2809 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- qob1 | -.1088179 .0132376 -8.22 0.000 -.1347633 -.0828725 _cons | 12.79688 .0065904 1941.75 0.000 12.78397 12.8098 ------------------------------------------------------------------------------ . reg earnwkl qob1; Source | SS df MS Number of obs = 329509 -------------+------------------------------ F( 1,329507) = 16.42 Model | 7.56705582 1 7.56705582 Prob > F = 0.0001 Residual | 151830.3329507 .460780197 R-squared = 0.0000 -------------+------------------------------ Adj R-squared = 0.0000 Total | 151837.867329508 .460801763 Root MSE = .67881 ------------------------------------------------------------------------------ earnwkl | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- qob1 | -.0110989 .0027388 -4.05 0.000 -.0164669 -.0057309 _cons | 5.902694 .0013635 4329.00 0.000 5.900022 5.905367 ------------------------------------------------------------------------------

1st stage

Reduced-form

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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

Correlation coefficient: z and x

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% of Mothers that Smoked During Pregnancy by Birth Month of their Child

11.0%

11.5%

12.0%

12.5%

13.0%

13.5%

14.0%

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Month

% S

mo

ked

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Average Birth weight by Birth Month

3280

3290

3300

3310

3320

3330

3340

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Month

Bir

th w

eig

ht

in g

ram

s

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Overidentified model

• 10 years of birth

• 3 quarters of birth

• 30 instruments

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. * get dummies needed for the models;

. xi i.yob*i.qob; i.yob _Iyob_30-39 (naturally coded; _Iyob_30 omitted) i.qob _Iqob_1-4 (naturally coded; _Iqob_1 omitted) i.yob*i.qob _IyobXqob_#_# (coded as above)

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

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. * run 2sls, qob times yob interactions as instruments; . * compare to column (2), table V; . ivregress 2sls earnwkl _Iyob_* (educ=_Iqob* _IyobX*); Instrumental variables (2SLS) regression Number of obs = 329509 Wald chi2(10) = 41.67 Prob > chi2 = 0.0000 R-squared = 0.1102 Root MSE = .64034 ------------------------------------------------------------------------------ earnwkl | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0891154 .0161098 5.53 0.000 .0575408 .1206901 _Iyob_31 | -.0088813 .0055293 -1.61 0.108 -.0197185 .0019558 DELETE SOME RESULTS _Iyob_39 | -.0585271 .0104573 -5.60 0.000 -.0790231 -.0380311 _cons | 4.792727 .2006807 23.88 0.000 4.3994 5.186054 ------------------------------------------------------------------------------ Instrumented: educ Instruments: _Iyob_31 _Iyob_32 _Iyob_33 _Iyob_34 _Iyob_35 _Iyob_36 _Iyob_37 _Iyob_38 _Iyob_39 _Iqob_2 _Iqob_3 _Iqob_4 _IyobXqob_31_2 _IyobXqob_31_3 _IyobXqob_31_4 _IyobXqob_32_2 _IyobXqob_32_3 _IyobXqob_32_4 _IyobXqob_33_2 _IyobXqob_33_3 _IyobXqob_33_4 _IyobXqob_34_2 _IyobXqob_34_3 _IyobXqob_34_4 _IyobXqob_35_2 _IyobXqob_35_3 _IyobXqob_35_4 _IyobXqob_36_2 _IyobXqob_36_3 _IyobXqob_36_4 _IyobXqob_37_2 _IyobXqob_37_3 _IyobXqob_37_4 _IyobXqob_38_2 _IyobXqob_38_3 _IyobXqob_38_4 _IyobXqob_39_2 _IyobXqob_39_3 _IyobXqob_39_4

YOB effects

QOB main effects and qob x yob interactions asinstruments

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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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. estat firststage; First-stage regression summary statistics -------------------------------------------------------------------------- | Adjusted Partial Variable | R-sq. R-sq. R-sq. F(30,329469) Prob > F -------------+------------------------------------------------------------ educ | 0.0033 0.0032 0.0004 4.90707 0.0000 --------------------------------------------------------------------------

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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