CHAPTER 15 - Instrumental Variables Estimation and Two Stage Least Squares#
import stata_setup
stata_setup.config("C:/Program Files/Stata18/", "se" ,splash=False)
Example 15.1 Estimating the Return to Education for Married Women#
%%stata
u mroz, clear
reg lwage educ
reg educ fathedu
ivreg lwage (educ=fathedu)
. u mroz, clear
. reg lwage educ
Source | SS df MS Number of obs = 428
-------------+---------------------------------- F(1, 426) = 56.93
Model | 26.3264193 1 26.3264193 Prob > F = 0.0000
Residual | 197.001022 426 .462443713 R-squared = 0.1179
-------------+---------------------------------- Adj R-squared = 0.1158
Total | 223.327441 427 .523015084 Root MSE = .68003
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ |
.1086487 .0143998 7.55 0.000 .0803451 .1369523
_cons | -.1851968 .1852259 -1.00 0.318 -.5492673 .1788736
------------------------------------------------------------------------------
. reg educ fathedu
Source | SS df MS Number of obs = 753
-------------+---------------------------------- F(1, 751) = 182.81
Model | 765.465719 1 765.465719 Prob > F = 0.0000
Residual | 3144.57412 751 4.18718259 R-squared = 0.1958
-------------+---------------------------------- Adj R-squared = 0.1947
Total | 3910.03984 752 5.19952106 Root MSE = 2.0463
------------------------------------------------------------------------------
educ | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
fatheduc | .2824277 .0208884 13.52 0.000 .2414211 .3234343
_cons | 9.799013 .1985373 49.36 0.000 9.409259 10.18877
------------------------------------------------------------------------------
. ivreg lwage (educ=fathedu)
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 428
-------------+---------------------------------- F(1, 426) = 2.84
Model | 20.8673606 1 20.8673606 Prob > F = 0.0929
Residual | 202.46008 426 .475258404 R-squared = 0.0934
-------------+---------------------------------- Adj R-squared = 0.0913
Total | 223.327441 427 .523015084 Root MSE = .68939
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .0591735 .0351418 1.68 0.093 -.0098994 .1282463
_cons | .4411034 .4461018 0.99 0.323 -.4357312 1.317938
------------------------------------------------------------------------------
Endogenous: educ
Exogenous: fatheduc
.
Example 15.2 Estimating the Return to Education for Men#
%%stata
u wage2, clear
reg educ sibs
ivreg lwage (educ=sibs)
reg lwage edu, nohead
. u wage2, clear
. reg educ sibs
Source | SS df MS Number of obs = 935
-------------+---------------------------------- F(1, 933) = 56.67
Model | 258.055048 1 258.055048 Prob > F = 0.0000
Residual | 4248.7642 933 4.55387374 R-squared = 0.0573
-------------+---------------------------------- Adj R-squared = 0.0562
Total | 4506.81925 934 4.82528828 Root MSE = 2.134
------------------------------------------------------------------------------
educ | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
sibs | -.2279164 .0302768 -7.53 0.000 -.287335 -.1684979
_cons | 14.13879 .1131382 124.97 0.000 13.91676 14.36083
------------------------------------------------------------------------------
. ivreg lwage (educ=sibs)
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 935
-------------+---------------------------------- F(1, 933) = 21.59
Model | -1.51973315 1 -1.51973315 Prob > F = 0.0000
Residual | 167.176016 933 .179181154 R-squared = .
-------------+---------------------------------- Adj R-squared = .
Total | 165.656283 934 .177362188 Root MSE = .4233
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .1224326 .0263506 4.65 0.000 .0707194 .1741459
_cons | 5.130026 .3551712 14.44 0.000 4.432999 5.827053
------------------------------------------------------------------------------
Endogenous: educ
Exogenous: sibs
. reg lwage edu, nohead
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .0598392 .0059631 10.03 0.000 .0481366 .0715418
_cons | 5.973063 .0813737 73.40 0.000 5.813366 6.132759
------------------------------------------------------------------------------
.
Example 15.3 Estimating the Effect of Smoking on Birth Weight#
%%stata
u bwght, clear
reg packs cigprice
ivreg lbwght (packs=cigprice)
. u bwght, clear
. reg packs cigprice
Source | SS df MS Number of obs = 1,388
-------------+---------------------------------- F(1, 1386) = 0.13
Model | .011648626 1 .011648626 Prob > F = 0.7179
Residual | 123.684481 1,386 .089238442 R-squared = 0.0001
-------------+---------------------------------- Adj R-squared = -0.0006
Total | 123.696129 1,387 .089182501 Root MSE = .29873
------------------------------------------------------------------------------
packs | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
cigprice | .0002829 .000783 0.36 0.718 -.0012531 .0018188
_cons | .0674257 .1025384 0.66 0.511 -.1337215 .2685728
------------------------------------------------------------------------------
. ivreg lbwght (packs=cigprice)
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 1,388
-------------+---------------------------------- F(1, 1386) = 0.12
Model | -1171.28207 1 -1171.28207 Prob > F = 0.7312
Residual | 1221.70241 1,386 .881459168 R-squared = .
-------------+---------------------------------- Adj R-squared = .
Total | 50.4203336 1,387 .036352079 Root MSE = .93886
------------------------------------------------------------------------------
lbwght | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
packs | 2.988676 8.698888 0.34 0.731 -14.07573 20.05309
_cons | 4.448136 .9081552 4.90 0.000 2.666629 6.229644
------------------------------------------------------------------------------
Endogenous: packs
Exogenous: cigprice
.
Example 15.4 Using College Proximity as an IV for Education#
%%stata
u card, clear
qui reg educ nearc4 exper* black smsa south smsa66 reg6*
display "Constant = " _[_cons] ", b1 = " _b[nearc4] ", b2 = " _b[exper]
eststo OLS: qui reg lwage educ exper* black smsa south smsa66 reg6*
eststo IV: qui ivreg lwage (educ=nearc4) exper* black smsa south smsa66 reg6*
estout, cells(b(nostar fmt(3)) se(par fmt(3))) stats(r2 N, fmt(%9.3f %9.0g) labels(R-squared Observations)) varlabels(_cons constant) varwidth(20) ti("Table 15.1 Dependent Variable: (lwage)")
est clear
. u card, clear
. qui reg educ nearc4 exper* black smsa south smsa66 reg6*
. display "Constant = " _[_cons] ", b1 = " _b[nearc4] ", b2 = " _b[exper]
Constant = 1, b1 = .31989894, b2 = -.41253338
. eststo OLS: qui reg lwage educ exper* black smsa south smsa66 reg6*
. eststo IV: qui ivreg lwage (educ=nearc4) exper* black smsa south smsa66 reg6*
>
. estout, cells(b(nostar fmt(3)) se(par fmt(3))) stats(r2 N, fmt(%9.3f %9.0g) l
> abels(R-squared Observations)) varlabels(_cons constant) varwidth(20) ti("Tab
> le 15.1 Dependent Variable: (lwage)")
Table 15.1 Dependent Variable: (lwage)
----------------------------------------------
OLS IV
b/se b/se
----------------------------------------------
educ 0.075 0.132
(0.003) (0.055)
exper 0.085 0.108
(0.007) (0.024)
expersq -0.002 -0.002
(0.000) (0.000)
black -0.199 -0.147
(0.018) (0.054)
smsa 0.136 0.112
(0.020) (0.032)
south -0.148 -0.145
(0.026) (0.027)
smsa66 0.026 0.019
(0.019) (0.022)
reg661 -0.141 0.083
(0.045) (0.059)
reg662 -0.044 0.184
(0.037) (0.055)
reg663 0.004 0.231
(0.035) (0.054)
reg664 -0.085 0.133
(0.042) (0.055)
reg665 -0.012 0.229
(0.027) (0.067)
reg666 0.000 0.246
(.) (0.072)
reg667 -0.023 0.218
(0.031) (0.068)
reg668 -0.197 0.000
(0.052) (.)
reg669 -0.022 0.191
(0.040) (0.051)
constant 4.761 3.583
(0.073) (0.951)
----------------------------------------------
R-squared 0.300 0.238
Observations 3010 3010
----------------------------------------------
. est clear
.
Example 15.5 Return to Education for Working Women#
%%stata
u mroz, clear
qui reg educ exper* fatheduc motheduc
test fatheduc motheduc
ivreg lwage (educ=fatheduc motheduc) exper*
qui reg lwage educ exper*
display "b1 = " _b[educ]
. u mroz, clear
. qui reg educ exper* fatheduc motheduc
. test fatheduc motheduc
( 1) fatheduc = 0
( 2) motheduc = 0
F( 2, 748) = 124.76
Prob > F = 0.0000
. ivreg lwage (educ=fatheduc motheduc) exper*
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 428
-------------+---------------------------------- F(3, 424) = 8.14
Model | 30.3074256 3 10.1024752 Prob > F = 0.0000
Residual | 193.020015 424 .455235885 R-squared = 0.1357
-------------+---------------------------------- Adj R-squared = 0.1296
Total | 223.327441 427 .523015084 Root MSE = .67471
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .0613966 .0314367 1.95 0.051 -.0003945 .1231878
exper | .0441704 .0134325 3.29 0.001 .0177679 .0705729
expersq | -.000899 .0004017 -2.24 0.026 -.0016885 -.0001094
_cons | .0481003 .4003281 0.12 0.904 -.7387744 .834975
------------------------------------------------------------------------------
Endogenous: educ
Exogenous: exper expersq fatheduc motheduc
. qui reg lwage educ exper*
. display "b1 = " _b[educ]
b1 = .10748964
.
Example 15.6 Using Two Test Scores as Indicators of Ability#
%%stata
u wage2, clear
ivreg lwage educ exper tenure married south urban black (IQ=KWW)
. u wage2, clear
. ivreg lwage educ exper tenure married south urban black (IQ=KWW)
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 935
-------------+---------------------------------- F(8, 926) = 36.96
Model | 31.4665121 8 3.93331401 Prob > F = 0.0000
Residual | 134.189771 926 .14491336 R-squared = 0.1900
-------------+---------------------------------- Adj R-squared = 0.1830
Total | 165.656283 934 .177362188 Root MSE = .38067
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
IQ | .0130473 .0049341 2.64 0.008 .0033641 .0227305
educ | .0250321 .0166068 1.51 0.132 -.0075591 .0576234
exper | .01442 .0033208 4.34 0.000 .0079029 .0209371
tenure | .0104562 .0026012 4.02 0.000 .0053512 .0155612
married | .2006903 .0406775 4.93 0.000 .1208595 .2805211
south | -.0515532 .0311279 -1.66 0.098 -.1126426 .0095361
urban | .1767058 .0282117 6.26 0.000 .1213394 .2320722
black | -.0225612 .0739597 -0.31 0.760 -.1677093 .1225869
_cons | 4.592453 .3257807 14.10 0.000 3.953099 5.231807
------------------------------------------------------------------------------
Endogenous: IQ
Exogenous: educ exper tenure married south urban black KWW
.
Example 15.7 Return to Education for Working Women#
%%stata
u mroz, clear
qui reg educ exper* fatheduc motheduc if inlf==1
predict v2, res
ivreg lwage (educ=fatheduc motheduc) exper* v2
qui reg lwage educ exper*
display "The OLS estimate is " _b[educ] " (" _se[educ] ")"
. u mroz, clear
. qui reg educ exper* fatheduc motheduc if inlf==1
. predict v2, res
. ivreg lwage (educ=fatheduc motheduc) exper* v2
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 428
-------------+---------------------------------- F(4, 423) = 20.50
Model | 36.2573098 4 9.06432745 Prob > F = 0.0000
Residual | 187.070131 423 .442246173 R-squared = 0.1624
-------------+---------------------------------- Adj R-squared = 0.1544
Total | 223.327441 427 .523015084 Root MSE = .66502
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .0613966 .0309849 1.98 0.048 .000493 .1223003
exper | .0441704 .0132394 3.34 0.001 .0181471 .0701937
expersq | -.000899 .0003959 -2.27 0.024 -.0016772 -.0001208
v2 | .0581666 .0348073 1.67 0.095 -.0102502 .1265834
_cons | .0481003 .3945753 0.12 0.903 -.7274721 .8236727
------------------------------------------------------------------------------
Endogenous: educ
Exogenous: exper expersq v2 fatheduc motheduc
. qui reg lwage educ exper*
. display "The OLS estimate is " _b[educ] " (" _se[educ] ")"
The OLS estimate is .10748964 (.01414648)
.
Example 15.8 Return to Education for Working Women#
%%stata
u mroz, clear
qui ivreg lwage (educ=fatheduc motheduc) exper*
predict u1, res
reg u1 exper* fatheduc motheduc
display "N*Rsquared =" e(r2)*e(N)
. u mroz, clear
. qui ivreg lwage (educ=fatheduc motheduc) exper*
. predict u1, res
(325 missing values generated)
. reg u1 exper* fatheduc motheduc
Source | SS df MS Number of obs = 428
-------------+---------------------------------- F(4, 423) = 0.09
Model | .170503136 4 .042625784 Prob > F = 0.9845
Residual | 192.84951 423 .455909007 R-squared = 0.0009
-------------+---------------------------------- Adj R-squared = -0.0086
Total | 193.020013 427 .452037502 Root MSE = .67521
------------------------------------------------------------------------------
u1 | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
exper | -.0000183 .0133291 -0.00 0.999 -.0262179 .0261813
expersq | 7.34e-07 .0003985 0.00 0.999 -.0007825 .000784
fatheduc | .0057823 .0111786 0.52 0.605 -.0161902 .0277547
motheduc | -.0066065 .0118864 -0.56 0.579 -.0299704 .0167573
_cons | .0109641 .1412571 0.08 0.938 -.2666892 .2886173
------------------------------------------------------------------------------
. display "N*Rsquared =" e(r2)*e(N)
N*Rsquared =.37807138
.
%%stata
qui ivreg lwage (educ=fatheduc motheduc huseduc) exper*
predict u1_h, res
qui reg u1_h exper* fatheduc motheduc huseduc
display "N*Rsquared =" e(r2)*e(N)
. qui ivreg lwage (educ=fatheduc motheduc huseduc) exper*
. predict u1_h, res
(325 missing values generated)
. qui reg u1_h exper* fatheduc motheduc huseduc
. display "N*Rsquared =" e(r2)*e(N)
N*Rsquared =1.115043
.
%%stata
qui ivreg lwage (educ=fatheduc motheduc huseduc) exper*
display "The IV estimate using all three instruments is " _b[educ] " (" _se[educ] ")"
qui ivreg lwage (educ=fatheduc motheduc) exper*
display "The IV estimate using two instruments is " _b[educ] " (" _se[educ] ")"
. qui ivreg lwage (educ=fatheduc motheduc huseduc) exper*
. display "The IV estimate using all three instruments is " _b[educ] " (" _se[e
> duc] ")"
The IV estimate using all three instruments is .08039176 (.02177397)
. qui ivreg lwage (educ=fatheduc motheduc) exper*
. display "The IV estimate using two instruments is " _b[educ] " (" _se[educ] "
> )"
The IV estimate using two instruments is .06139663 (.0314367)
.
Example 15.9 Effect of Education on Fertility#
%%stata
u fertil1, clear
ivreg kids (educ=meduc feduc) age agesq black-y84
qui reg kids educ age agesq black-y84
display "The OLS estimate is " _b[educ] " (" _se[educ] ")"
. u fertil1, clear
. ivreg kids (educ=meduc feduc) age agesq black-y84
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 1,129
-------------+---------------------------------- F(17, 1111) = 7.72
Model | 395.36632 17 23.2568424 Prob > F = 0.0000
Residual | 2690.14298 1,111 2.42137082 R-squared = 0.1281
-------------+---------------------------------- Adj R-squared = 0.1148
Total | 3085.5093 1,128 2.73538059 Root MSE = 1.5561
------------------------------------------------------------------------------
kids | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | -.1527395 .0392232 -3.89 0.000 -.2296993 -.0757796
age | .5235536 .1390348 3.77 0.000 .2507532 .796354
agesq | -.005716 .0015705 -3.64 0.000 -.0087976 -.0026345
black | 1.072952 .1737155 6.18 0.000 .732105 1.4138
east | .2285554 .1338537 1.71 0.088 -.0340792 .4911901
northcen | .3744188 .122061 3.07 0.002 .1349228 .6139148
west | .2076398 .1676568 1.24 0.216 -.1213199 .5365995
farm | -.0770015 .1513718 -0.51 0.611 -.3740083 .2200053
othrural | -.1952451 .181551 -1.08 0.282 -.5514666 .1609764
town | .08181 .1246821 0.66 0.512 -.162829 .3264489
smcity | .2124996 .160425 1.32 0.186 -.1022706 .5272698
y74 | .2721292 .172944 1.57 0.116 -.0672045 .6114629
y76 | -.0945483 .1792324 -0.53 0.598 -.4462205 .2571239
y78 | -.0572543 .1825536 -0.31 0.754 -.415443 .3009343
y80 | -.053248 .1847175 -0.29 0.773 -.4156825 .3091865
y82 | -.4962149 .1765888 -2.81 0.005 -.8427 -.1497297
y84 | -.5213604 .1779205 -2.93 0.003 -.8704586 -.1722623
_cons | -7.241244 3.136642 -2.31 0.021 -13.39565 -1.086834
------------------------------------------------------------------------------
Endogenous: educ
Exogenous: age agesq black east northcen west farm othrural town smcity y74
y76 y78 y80 y82 y84 meduc feduc
. qui reg kids educ age agesq black-y84
. display "The OLS estimate is " _b[educ] " (" _se[educ] ")"
The OLS estimate is -.12842683 (.0183486)
.
%%stata
//Endogeneity
reg educ meduc feduc
predict v2, res
ivreg kids (educ=meduc feduc) age agesq black-y84 v2
. //Endogeneity
. reg educ meduc feduc
Source | SS df MS Number of obs = 1,129
-------------+---------------------------------- F(2, 1126) = 207.06
Model | 2114.27432 2 1057.13716 Prob > F = 0.0000
Residual | 5748.84171 1,126 5.10554326 R-squared = 0.2689
-------------+---------------------------------- Adj R-squared = 0.2676
Total | 7863.11603 1,128 6.97084755 Root MSE = 2.2595
------------------------------------------------------------------------------
educ | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
meduc | .1844065 .021749 8.48 0.000 .1417333 .2270796
feduc | .2208784 .024996 8.84 0.000 .1718344 .2699225
_cons | 8.860898 .2034806 43.55 0.000 8.461654 9.260142
------------------------------------------------------------------------------
. predict v2, res
. ivreg kids (educ=meduc feduc) age agesq black-y84 v2
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 1,129
-------------+---------------------------------- F(18, 1110) = 9.21
Model | 400.801638 18 22.2667576 Prob > F = 0.0000
Residual | 2684.70766 1,110 2.41865555 R-squared = 0.1299
-------------+---------------------------------- Adj R-squared = 0.1158
Total | 3085.5093 1,128 2.73538059 Root MSE = 1.5552
------------------------------------------------------------------------------
kids | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | -.1507639 .0367462 -4.10 0.000 -.2228636 -.0786641
age | .5305436 .1384365 3.83 0.000 .2589168 .8021704
agesq | -.005796 .0015647 -3.70 0.000 -.0088661 -.0027259
black | 1.061535 .1747383 6.07 0.000 .7186803 1.40439
east | .2208112 .1329111 1.66 0.097 -.0399742 .4815965
northcen | .3715649 .1215229 3.06 0.002 .1331244 .6100054
west | .2044791 .1672389 1.22 0.222 -.1236609 .532619
farm | -.0651969 .1483216 -0.44 0.660 -.3562192 .2258255
othrural | -.1777856 .1767678 -1.01 0.315 -.5246223 .1690511
town | .0798824 .1247224 0.64 0.522 -.1648358 .3246006
smcity | .2099867 .1603553 1.31 0.191 -.104647 .5246204
y74 | .2719416 .1728386 1.57 0.116 -.0671855 .6110688
y76 | -.0984073 .1790925 -0.55 0.583 -.4498053 .2529906
y78 | -.0637286 .1818614 -0.35 0.726 -.4205596 .2931023
y80 | -.0651716 .1830214 -0.36 0.722 -.4242785 .2939352
y82 | -.5143435 .1728653 -2.98 0.003 -.8535231 -.1751638
y84 | -.534601 .1752043 -3.05 0.002 -.87837 -.190832
v2 | .0291597 .0415585 0.70 0.483 -.0523823 .1107017
_cons | -7.407479 3.089573 -2.40 0.017 -13.46954 -1.345417
------------------------------------------------------------------------------
Endogenous: educ
Exogenous: age agesq black east northcen west farm othrural town smcity y74
y76 y78 y80 y82 y84 v2 meduc feduc
.
Example 15.10 Job Training and Worker Productivity#
%%stata
u jtrain, clear
reg chrsemp cgrant if year==1988
ivreg clscrap (chrsemp = cgrant) if year==1988
ivreg clscrap chrsemp if year==1988
. u jtrain, clear
. reg chrsemp cgrant if year==1988
Source | SS df MS Number of obs = 125
-------------+---------------------------------- F(1, 123) = 79.37
Model | 18117.5987 1 18117.5987 Prob > F = 0.0000
Residual | 28077.3319 123 228.270991 R-squared = 0.3922
-------------+---------------------------------- Adj R-squared = 0.3873
Total | 46194.9306 124 372.539763 Root MSE = 15.109
------------------------------------------------------------------------------
chrsemp | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
cgrant | 27.87793 3.129216 8.91 0.000 21.68384 34.07202
_cons | .5093234 1.558337 0.33 0.744 -2.57531 3.593956
------------------------------------------------------------------------------
. ivreg clscrap (chrsemp = cgrant) if year==1988
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 45
-------------+---------------------------------- F(1, 43) = 3.20
Model | .274951237 1 .274951237 Prob > F = 0.0808
Residual | 17.0148885 43 .395695081 R-squared = 0.0159
-------------+---------------------------------- Adj R-squared = -0.0070
Total | 17.2898397 44 .392950903 Root MSE = .62904
------------------------------------------------------------------------------
clscrap | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
chrsemp | -.0141532 .0079147 -1.79 0.081 -.0301148 .0018084
_cons | -.0326684 .1269512 -0.26 0.798 -.2886898 .223353
------------------------------------------------------------------------------
Endogenous: chrsemp
Exogenous: cgrant
. ivreg clscrap chrsemp if year==1988
Instrumental variables 2SLS regression
Source | SS df MS Number of obs = 45
-------------+---------------------------------- F(1, 43) = 2.84
Model | 1.07071245 1 1.07071245 Prob > F = 0.0993
Residual | 16.2191273 43 .377189007 R-squared = 0.0619
-------------+---------------------------------- Adj R-squared = 0.0401
Total | 17.2898397 44 .392950903 Root MSE = .61416
------------------------------------------------------------------------------
clscrap | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
chrsemp | -.0076007 .0045112 -1.68 0.099 -.0166984 .0014971
_cons | -.1035161 .103736 -1.00 0.324 -.3127197 .1056875
------------------------------------------------------------------------------
(no endogenous regressors)
.