1 iv/2sls models. 2 3 4 vietnam era service defined as 1964-1975 estimated 8.7 million served during...

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IV/2SLS models

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0 0.80x 1 0.57x

0iz 1iz

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0 3186y 1 3278y

1 01

1 0

3278 3186ˆ 4000.57 0.80

y y

x x

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Vietnam era service

• Defined as 1964-1975• Estimated 8.7 million served during era• 3.4 million were in SE Asia• 2.6 million served in Vietnam• 1.6 million saw combat• 203K wounded in action, 153K hospitalized• 58,000 deaths• http://www.history.navy.mil/library/online/

american%20war%20casualty.htm#t7

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Vietnam Era Draft

• 1st part of war, operated liked WWII and Korean War

• At age 18 men report to local draft boards

• Could receive deferment for variety of reasons (kids, attending school)

• If available for service, pre-induction physical and tests

• Military needs determined those drafted

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• Everyone drafted went to the Army

• Local draft boards filled army.

• Priorities– Delinquents, volunteers, non-vol. 19-25– For non-vol., determined by age

• College enrollment powerful way to avoid service– Men w. college degree 1/3 less likely to serve

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Draft Lottery

• Proposed by Nixon• Passed in Nov 1969, 1st lottery Dec 1, 1969• 1st lottery for men age 19-26 on 1/1/70

– Men born 1944-1950.

• Randomly assigned number 1-365, Draft Lottery number (DLN)

• Military estimates needs, sets threshold T• If DLN<=T, drafted

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Questions?

• What are the research questions?

• Why can we NOT obtain estimates from observational data?

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• If volunteer, could get better assignment• Thresholds for service

• Draft Year of Birth Threshold• 1970 1946-50 195• 1971 1951 125• 1972 1952 95

• Draft suspended in 1973

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Angrist/Evans

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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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Ratio of variances = (0.0020246/0.0291242)^2 = 0.004832484

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R2 = 290.247937/60030.836855 = 0.004832

βiv = -0.0092924/0.0675253= -0.137631

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Reduced form, just identified model

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First stage, just identified model

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2SLS, just identified model

Βiv= -0.0083481/0.0693854 = -0.120315

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1st stage over identified model

ivreg2

• Download from www

• Within stata, type

ssc install ivreg2, replace

• and hit return

• Does all the tests seemlessly

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* the syntax is ivreg2 y w (x=z), first endog(x);* the first command asks stata to report the 1st stage, and;* endog(x) asks stata to do the hausman-wu test of endogeneity; ivreg2 workedm boy1st boy2nd agem1 agefstm black hispan othrace(morekids=samesex), first endog(morekids);

Endogenous variableAnd instruments

Ask for 1st stage

Test for endogeneityof morekids in model

Outcome of interestW’s (exogenous covariates)

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IV (2SLS) estimation--------------------

Estimates efficient for homoskedasticity onlyStatistics consistent for homoskedasticity only

Number of obs = 254654 F( 8,254645) = 865.24 Prob > F = 0.0000Total (centered) SS = 63460.72056 Centered R2 = 0.0482Total (uncentered) SS = 134513 Uncentered R2 = 0.5510Residual SS = 60402.67924 Root MSE = .487

------------------------------------------------------------------------------ workedm | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- morekids | -.1203151 .0278407 -4.32 0.000 -.1748818 -.0657483 boy1st | .0009211 .0019489 0.47 0.636 -.0028986 .0047409 boy2nd | -.0048314 .0019425 -2.49 0.013 -.0086386 -.0010241 agem1 | .0219352 .0009013 24.34 0.000 .0201687 .0237018 agefstm | -.0264911 .0012647 -20.95 0.000 -.0289698 -.0240124 black | .1899764 .0047674 39.85 0.000 .1806325 .1993203 hispan | -.0139081 .0053812 -2.58 0.010 -.0244551 -.0033611 othrace | .0443545 .0048137 9.21 0.000 .0349198 .0537891 _cons | .4498966 .0138562 32.47 0.000 .4227389 .4770543------------------------------------------------------------------------------Underidentification test (Anderson canon. corr. LM statistic): 1405.578 Chi-sq(1) P-val = 0.0000------------------------------------------------------------------------------Weak identification test (Cragg-Donald Wald F statistic): 1413.330Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53Source: Stock-Yogo (2005). Reproduced by permission.------------------------------------------------------------------------------Sargan statistic (overidentification test of all instruments): 0.000

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OLS estimation--------------Estimates efficient for homoskedasticity onlyStatistics consistent for homoskedasticity only Number of obs = 254654 F( 8,254645) = 2825.70 Prob > F = 0.0000Total (centered) SS = 60030.83676 Centered R2 = 0.0815Total (uncentered) SS = 96912 Uncentered R2 = 0.4311Residual SS = 55136.2215 Root MSE = .4653------------------------------------------------------------------------------ morekids | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- boy1st | -.0015753 .0026228 -0.60 0.548 -.0067158 .0035653 agem1 | .0304246 .000298 102.09 0.000 .0298405 .0310087 agefstm | -.0435676 .0003462 -125.85 0.000 -.0442461 -.0428891 black | .0679715 .0041853 16.24 0.000 .0597684 .0761747 hispan | .125998 .0038974 32.33 0.000 .1183591 .1336369 othrace | .0479479 .0044209 10.85 0.000 .039283 .0566127 twoboys | .0598382 .0025731 23.26 0.000 .0547951 .0648813 twogirls | .0789326 .0026467 29.82 0.000 .0737452 .08412 _cons | .3138696 .0092684 33.86 0.000 .2957038 .3320353------------------------------------------------------------------------------Included instruments: boy1st agem1 agefstm black hispan othrace twoboys twogirl> s------------------------------------------------------------------------------F test of excluded instruments: F( 2,254645) = 715.13 Prob > F = 0.0000Angrist-Pischke multivariate F test of excluded instruments: F( 2,254645) = 715.13

Prob > F = 0.0000

1st stage F

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Summary results for first-stage regressions------------------------------------------- (Underid) (Weak id)Variable | F( 2,254645) P-val | AP Chi-sq( 2) P-val | AP F( 2,254645)morekids | 715.13 0.0000 | 1430.31 0.0000 | 715.13

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IV (2SLS) estimation--------------------Estimates efficient for homoskedasticity onlyStatistics consistent for homoskedasticity only Number of obs = 254654 F( 7,254646) = 987.26 Prob > F = 0.0000Total (centered) SS = 63460.72056 Centered R2 = 0.0475Total (uncentered) SS = 134513 Uncentered R2 = 0.5506Residual SS = 60445.97117 Root MSE = .4872------------------------------------------------------------------------------ workedm | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- morekids | -.1127816 .0276854 -4.07 0.000 -.167044 -.0585193 boy1st | .0009424 .0019496 0.48 0.629 -.0028786 .0047635 agem1 | .0217057 .0008969 24.20 0.000 .0199478 .0234635 agefstm | -.0261649 .0012583 -20.79 0.000 -.0286312 -.0236987 black | .1895035 .0047653 39.77 0.000 .1801637 .1988433 hispan | -.014818 .0053707 -2.76 0.006 -.0253444 -.0042916 othrace | .0439784 .004813 9.14 0.000 .034545 .0534118 _cons | .4448388 .0137111 32.44 0.000 .4179656 .4717121------------------------------------------------------------------------------Underidentification test (Anderson canon. corr. LM statistic): 1422.320 Chi-sq(2) P-val = 0.0000------------------------------------------------------------------------------Weak identification test (Cragg-Donald Wald F statistic): 715.129Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25Source: Stock-Yogo (2005). Reproduced by permission.------------------------------------------------------------------------------Sargan statistic (overidentification test of all instruments): 6.182 Chi-sq(1) P-val = 0.0129

-endog- option:Endogeneity test of endogenous regressors: 3.809 Chi-sq(1) P-val = 0.0510Regressors tested: morekids------------------------------------------------------------------------------Instrumented: morekidsIncluded instruments: boy1st agem1 agefstm black hispan othraceExcluded instruments: twoboys twogirls------------------------------------------------------------------------------

Test of over id.

Hausman endo test

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. * output residuals and do the tests of overid;

. * and hausman test by brute force;

. predict res_2sls_worked, res;

. * test of overid;

. reg res_2sls_worked twoboys twogirls boy1st agem1 agefstm black hispan othr> ace; Source | SS df MS Number of obs = 254654-------------+------------------------------ F( 8,254645) = 0.77 Model | 1.46731447 8 .183414308 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 agem1 | 3.72e-07 .000312 0.00 0.999 -.0006112 .000612 agefstm | 2.07e-06 .0003625 0.01 0.995 -.0007084 .0007125 black | -.0000392 .0043822 -0.01 0.993 -.0086282 .0085498 hispan | -.0000393 .0040807 -0.01 0.992 -.0080375 .0079588 othrace | .0000149 .0046288 0.00 0.997 -.0090575 .0090872 _cons | -.0021381 .0097043 -0.22 0.826 -.0211583 .016882------------------------------------------------------------------------------

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• SSM = 1.467

• SST = 600444.50

• 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, two 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------------------------------------------------------------------------------. * notice that OLS of this model generates 2SLS estimates of the other;. * variables in the model (morekids, boy1st, etc.);. test res_1st_2zs; ( 1) res_1st_2zs = 0 F( 1,254645) = 3.81 Prob > F = 0.0510

Do Hausman test brute force

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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

Angrist/Krueger

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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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. * 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

βiv==-0.0110989/-0.1088179=-0.10199

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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

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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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In columns (4) and (8), age and agesq reduce information containedin instrument. 1st stage F falls to 1.6. Compare 2sls to IV in these cases.In this instance, low F – poor 1st stage fit – results collapse to OLS

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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

Notice how close the 2SLS and OLS are

1 iv/2sls models. 2 3 4 vietnam era service defined as 1964-1975 estimated 8.7 million served during...

Documents

drafted slide

total centered ss

total uncentered ss

t7 slide

maximal iv size

uncentered r2

residual ss

vietnam era draft