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| From | Erkal Ersoy <erkal6@gmail.com> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | st: ivreg2 vs. Manual IV |
| Date | Mon, 7 Mar 2011 03:16:01 +0000 |
Hello Statalisters,
Apologies in advance if my question has already been answered
somewhere. It feels like the answer should be out there somewhere, but
I spent a lot of time looking for it and couldn't get to it.
The essence of my question is possibly about the inner-workings of the
command "ivreg2." As illustrated below, I keep getting different
estimates on some coefficients when I do a 2SLS estimation manually
rather than using ivreg2 directly.
I am trying to evaluate the effect of education on earnings, so please
pay attention only to the coefficients on educ (education), age and
agesq (age squared). YR* are the years of birth of individuals, and
QTR* are the interaction terms of their years of birth with quarters
of birth--as done in Angrist and Krueger (1991).
In the ivreg2 regression, the coefficients on educ, age, and agesq are
0.0775**, 0.0961, and -0.0011 respectively.
When I go ahead and do the first and second stage regressions by hand,
I get 0.0775** on educ, 0.0694** on age, and -0.0007 on agesq.
Note that I used ** to denote that the coefficient is statistically
significant at the 5% level.
The fact that the coefficient on education stays the same is
comforting, but the 3 percentage-point change in the coefficient of
age is not... It also seems to become statistically significant when
the manual approach is used. I have not been able to figure out why
this is happening. Am I overlooking something simple? or Is ivreg2
doing something inherently that I am not aware of?
Thank you in advance and I look forward to hearing from you!
Best,
Erkal
Here is the output:
. ivreg2 loghrearn age agesq YR* (educ=QTR*), robust
Warning - collinearities detected
Vars dropped: YR57 YR58
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
Number of obs = 1930
F( 30, 1899) = 10.25
Prob > F = 0.0000
Total (centered) SS = 442.0938306 Centered R2 = 0.2791
Total (uncentered) SS = 10400.84512 Uncentered R2 = 0.9694
Residual SS = 318.6885935 Root MSE = .4064
------------------------------------------------------------------------------
| Robust
loghrearn | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ | .0775441 .0160336 4.84 0.000 .0461187 .1089695
age | .0960978 .1423516 0.68 0.500 -.1829063 .3751018
agesq | -.0010697 .0017913 -0.60 0.550 -.0045807 .0024412
YR30 | .0729663 .1068284 0.68 0.495 -.1364134 .2823461
YR31 | .07704 .1309457 0.59 0.556 -.1796089 .3336889
YR32 | .0973292 .163443 0.60 0.552 -.2230131 .4176716
YR33 | .1417888 .1929499 0.73 0.462 -.2363861 .5199638
YR34 | -.1038325 .2259978 -0.46 0.646 -.54678 .339115
YR35 | -.0904907 .2650057 -0.34 0.733 -.6098924 .428911
YR36 | .0211021 .2889079 0.07 0.942 -.5451469 .5873512
YR37 | -.0095714 .3094713 -0.03 0.975 -.6161241 .5969812
YR38 | -.1243342 .3284837 -0.38 0.705 -.7681505 .519482
YR39 | .0318703 .33975 0.09 0.925 -.6340275 .6977681
YR40 | -.012432 .3502283 -0.04 0.972 -.6988668 .6740027
YR41 | -.0104493 .362811 -0.03 0.977 -.7215458 .7006471
YR42 | -.0702727 .3685554 -0.19 0.849 -.792628 .6520826
YR43 | .0575015 .3747713 0.15 0.878 -.6770368 .7920399
YR44 | .0096079 .370298 0.03 0.979 -.7161628 .7353786
YR45 | .002713 .3662465 0.01 0.994 -.715117 .720543
YR46 | -.0635162 .3581167 -0.18 0.859 -.765412 .6383797
YR47 | -.0433715 .343595 -0.13 0.900 -.7168054 .6300624
YR48 | .0054387 .3286098 0.02 0.987 -.6386247 .6495021
YR49 | -.099746 .3100412 -0.32 0.748 -.7074155 .5079235
YR50 | -.0773254 .2898625 -0.27 0.790 -.6454454 .4907946
YR51 | .0145518 .2642092 0.06 0.956 -.5032888 .5323923
YR52 | -.0292709 .2321661 -0.13 0.900 -.4843081 .4257663
YR53 | .0184112 .1987312 0.09 0.926 -.3710947 .4079172
YR54 | -.0401541 .1639762 -0.24 0.807 -.3615416 .2812333
YR55 | -.0174335 .1241698 -0.14 0.888 -.2608018 .2259348
YR56 | -.0569723 .0847047 -0.67 0.501 -.2229904 .1090458
_cons | -.7115404 2.495252 -0.29 0.776 -5.602144 4.179063
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 87.887
Chi-sq(87) P-val = 0.4532
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 1.147
(Kleibergen-Paap rk Wald F statistic): 1.139
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 21.12
10% maximal IV relative bias 10.91
20% maximal IV relative bias 5.69
30% maximal IV relative bias 3.92
10% maximal IV size 222.24
15% maximal IV size 113.33
20% maximal IV size 76.67
25% maximal IV size 58.36
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 82.395
Chi-sq(86) P-val = 0.5901
------------------------------------------------------------------------------
Instrumented: educ
Included instruments: age agesq YR30 YR31 YR32 YR33 YR34 YR35 YR36 YR37 YR38
YR39 YR40 YR41 YR42 YR43 YR44 YR45 YR46 YR47 YR48 YR49
YR50 YR51 YR52 YR53 YR54 YR55 YR56
Excluded instruments: QTR230 QTR231 QTR232 QTR233 QTR234 QTR235 QTR236 QTR237
QTR238 QTR239 QTR240 QTR241 QTR242 QTR243 QTR244 QTR245
QTR246 QTR247 QTR248 QTR249 QTR250 QTR251 QTR252 QTR253
QTR254 QTR255 QTR256 QTR257 QTR258 QTR330 QTR331 QTR332
QTR333 QTR334 QTR335 QTR336 QTR337 QTR338 QTR339 QTR340
QTR341 QTR342 QTR343 QTR344 QTR345 QTR346 QTR347 QTR348
QTR349 QTR350 QTR351 QTR352 QTR353 QTR354 QTR355 QTR356
QTR357 QTR358 QTR430 QTR431 QTR432 QTR433 QTR434 QTR435
QTR436 QTR437 QTR438 QTR439 QTR440 QTR441 QTR442 QTR443
QTR444 QTR445 QTR446 QTR447 QTR448 QTR449 QTR450 QTR451
QTR452 QTR453 QTR454 QTR455 QTR456 QTR457 QTR458
Dropped collinear: YR57 YR58
------------------------------------------------------------------------------
. reg educ age agesq YR* QTR*
note: YR42 omitted because of collinearity
note: YR58 omitted because of collinearity
Source | SS df MS Number of obs = 1930
-------------+------------------------------ F(116, 1813) = 1.72
Model | 1172.63491 116 10.1089217 Prob > F = 0.0000
Residual | 10684.3231 1813 5.89317326 R-squared = 0.0989
-------------+------------------------------ Adj R-squared = 0.0412
Total | 11856.958 1929 6.14668638 Root MSE = 2.4276
------------------------------------------------------------------------------
educ | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .4445861 .4307161 1.03 0.302 -.4001659 1.289338
agesq | -.0060692 .0054336 -1.12 0.264 -.0167259 .0045876
YR30 | -.8890242 .9932762 -0.90 0.371 -2.83711 1.059062
YR31 | .6960782 .9116261 0.76 0.445 -1.09187 2.484026
YR32 | .6377634 .9109859 0.70 0.484 -1.148929 2.424456
YR33 | 1.800134 .8846079 2.03 0.042 .0651759 3.535092
YR34 | .5381042 1.082161 0.50 0.619 -1.584309 2.660517
YR35 | -2.185563 1.041604 -2.10 0.036 -4.228433 -.1426933
YR36 | -.4344303 1.228448 -0.35 0.724 -2.843753 1.974892
YR37 | .6838194 1.199013 0.57 0.569 -1.667774 3.035413
YR38 | -1.465554 1.275869 -1.15 0.251 -3.967881 1.036773
YR39 | -.1861233 1.234434 -0.15 0.880 -2.607185 2.234938
YR40 | -1.394554 1.344123 -1.04 0.300 -4.030746 1.241638
YR41 | 1.02279 1.292272 0.79 0.429 -1.511709 3.55729
YR42 | (omitted)
YR43 | -.1970156 1.392313 -0.14 0.887 -2.927722 2.53369
YR44 | 1.018107 1.274471 0.80 0.424 -1.48148 3.517694
YR45 | -1.504632 1.385526 -1.09 0.278 -4.222028 1.212764
YR46 | .556196 1.250079 0.44 0.656 -1.89555 3.007942
YR47 | -.7041711 1.166875 -0.60 0.546 -2.992731 1.584389
YR48 | .2142667 1.132912 0.19 0.850 -2.007683 2.436216
YR49 | -.6242047 1.097718 -0.57 0.570 -2.777129 1.528719
YR50 | -.1981569 1.042875 -0.19 0.849 -2.24352 1.847206
YR51 | .9638388 .9958603 0.97 0.333 -.9893155 2.916993
YR52 | -.823932 .9013091 -0.91 0.361 -2.591645 .9437814
YR53 | -.2495645 .8451451 -0.30 0.768 -1.907125 1.407996
YR54 | .4278504 .8061783 0.53 0.596 -1.153286 2.008986
YR55 | .2133633 .7942078 0.27 0.788 -1.344295 1.771022
YR56 | .4657228 .6636603 0.70 0.483 -.8358964 1.767342
YR57 | -.360123 .6362917 -0.57 0.571 -1.608065 .8878189
YR58 | (omitted)
QTR230 | 1 1.13807 0.88 0.380 -1.232066 3.232066
QTR231 | -1.492063 1.223388 -1.22 0.223 -3.891462 .9073353
QTR232 | .6 1.2536 0.48 0.632 -1.858652 3.058652
QTR233 | -2.897436 1.19813 -2.42 0.016 -5.247297 -.5475746
QTR234 | -.6805556 1.179595 -0.58 0.564 -2.994063 1.632952
QTR235 | 2.121212 1.581181 1.34 0.180 -.9799165 5.222341
QTR236 | .8214286 1.256395 0.65 0.513 -1.642706 3.285563
QTR237 | .1666667 1.27945 0.13 0.896 -2.342685 2.676018
QTR238 | 2.375 1.128003 2.11 0.035 .1626788 4.587321
QTR239 | -.1666667 1.232046 -0.14 0.892 -2.583047 2.249713
QTR240 | -.2083333 1.108036 -0.19 0.851 -2.381495 1.964829
QTR241 | -2.763636 1.060689 -2.61 0.009 -4.843937 -.6833361
QTR242 | -.6941176 1.235027 -0.56 0.574 -3.116343 1.728108
QTR243 | -.05 1.062791 -0.05 0.962 -2.134424 2.034424
QTR244 | -1.3 1.005116 -1.29 0.196 -3.271307 .6713073
QTR245 | .4444444 1.179595 0.38 0.706 -1.869063 2.757952
QTR246 | -1.365546 .8761268 -1.56 0.119 -3.08387 .3527779
QTR247 | .8033794 .6860974 1.17 0.242 -.5422451 2.149004
QTR248 | -.2731092 .6737625 -0.41 0.685 -1.594542 1.048323
QTR249 | 1.271212 .6879242 1.85 0.065 -.0779952 2.620419
QTR250 | 1.114846 .792013 1.41 0.159 -.438508 2.6682
QTR251 | -1.213636 .7500201 -1.62 0.106 -2.684631 .2573581
QTR252 | .7857143 .6611588 1.19 0.235 -.5109989 2.082427
QTR253 | -2.58e-14 .6799908 -0.00 1.000 -1.333648 1.333648
QTR254 | -.8030303 .668171 -1.20 0.230 -2.113496 .5074357
QTR255 | -.5035842 .7193753 -0.70 0.484 -1.914476 .9073074
QTR256 | -.3017078 .6028524 -0.50 0.617 -1.484066 .8806505
QTR257 | .3812636 .625775 0.61 0.542 -.8460521 1.608579
QTR258 | -.2581522 .7902837 -0.33 0.744 -1.808114 1.29181
QTR330 | .75 1.154547 0.65 0.516 -1.514383 3.014383
QTR331 | -1.414141 1.091119 -1.30 0.195 -3.554123 .7258406
QTR332 | -.8 1.085649 -0.74 0.461 -2.929255 1.329255
QTR333 | -.8307692 1.021097 -0.81 0.416 -2.833419 1.17188
QTR334 | -.325 1.383937 -0.23 0.814 -3.039278 2.389278
QTR335 | .4545455 1.173723 0.39 0.699 -1.847446 2.756536
QTR336 | .0714286 1.350584 0.05 0.958 -2.577436 2.720293
QTR337 | -1.444444 1.144375 -1.26 0.207 -3.688877 .7999876
QTR338 | 7.06e-15 1.213793 0.00 1.000 -2.38058 2.38058
QTR339 | -.5714286 1.173723 -0.49 0.626 -2.87342 1.730562
QTR340 | 1.432692 1.090856 1.31 0.189 -.7067752 3.57216
QTR341 | -1.69697 1.232046 -1.38 0.169 -4.11335 .7194102
QTR342 | -.025 1.383937 -0.02 0.986 -2.739278 2.689278
QTR343 | -.35 1.151505 -0.30 0.761 -2.608416 1.908416
QTR344 | -1.5 .9175412 -1.63 0.102 -3.299549 .2995491
QTR345 | 1.25 1.051176 1.19 0.235 -.8116425 3.311643
QTR346 | .6558442 .9781022 0.67 0.503 -1.262482 2.57417
QTR347 | 1.238095 .7491693 1.65 0.099 -.2312305 2.707421
QTR348 | -.3928571 .7007837 -0.56 0.575 -1.767285 .9815712
QTR349 | .9431034 .7056001 1.34 0.182 -.4407712 2.326978
QTR350 | .1829574 .7686315 0.24 0.812 -1.324539 1.690454
QTR351 | -.5772727 .7500201 -0.77 0.442 -2.048267 .8937217
QTR352 | .5833333 .6871749 0.85 0.396 -.7644045 1.931071
QTR353 | -.1785714 .6679801 -0.27 0.789 -1.488663 1.13152
QTR354 | -.3909091 .6443608 -0.61 0.544 -1.654677 .8728586
QTR355 | -.8377778 .7504168 -1.12 0.264 -2.30955 .6339948
QTR356 | -.6129032 .6166074 -0.99 0.320 -1.822239 .5964325
QTR357 | .0946292 .6554033 0.14 0.885 -1.190796 1.380054
QTR358 | .5624123 .6680773 0.84 0.400 -.7478699 1.872695
QTR430 | 1.6 1.421449 1.13 0.260 -1.18785 4.38785
QTR431 | .0555556 1.27945 0.04 0.965 -2.453796 2.564907
QTR432 | .5444444 1.115399 0.49 0.626 -1.643157 2.732046
QTR433 | -3.321678 .994517 -3.34 0.001 -5.272198 -1.371159
QTR434 | -3.267857 1.256395 -2.60 0.009 -5.731991 -.803723
QTR435 | 1.025974 1.173723 0.87 0.382 -1.276017 3.327965
QTR436 | -1.678571 1.52157 -1.10 0.270 -4.662786 1.305643
QTR437 | -.8888889 1.144375 -0.78 0.437 -3.133321 1.355543
QTR438 | 1.041667 1.311046 0.79 0.427 -1.529653 3.612987
QTR439 | -1 1.232046 -0.81 0.417 -3.41638 1.41638
QTR440 | 1.375 1.486587 0.92 0.355 -1.540603 4.290603
QTR441 | -1.205742 .9197337 -1.31 0.190 -3.009591 .5981075
QTR442 | .3777778 1.354043 0.28 0.780 -2.27787 3.033426
QTR443 | -1.138889 1.179595 -0.97 0.334 -3.452397 1.174619
QTR444 | -1.3125 .8884055 -1.48 0.140 -3.054906 .4299059
QTR445 | 1.833333 1.031526 1.78 0.076 -.1897704 3.856437
QTR446 | .3035714 .8163883 0.37 0.710 -1.297589 1.904732
QTR447 | .8154762 .8055747 1.01 0.312 -.764476 2.395428
QTR448 | .4596273 .732702 0.63 0.531 -.9774016 1.896656
QTR449 | .51 .7282758 0.70 0.484 -.9183478 1.938348
QTR450 | .0662526 .732702 0.09 0.928 -1.370776 1.503281
QTR451 | -1.475 .8142371 -1.81 0.070 -3.071941 .1219414
QTR452 | 1.595238 .7122414 2.24 0.025 .198338 2.992138
QTR453 | -.2916667 .6937405 -0.42 0.674 -1.652281 1.068948
QTR454 | -.6909091 .6814034 -1.01 0.311 -2.027327 .6455093
QTR455 | -1.305556 .7007837 -1.86 0.063 -2.679984 .0688728
QTR456 | -.7050691 .6329082 -1.11 0.265 -1.946375 .5362369
QTR457 | .0455408 .6028524 0.08 0.940 -1.136817 1.227899
QTR458 | .5735786 .6948996 0.83 0.409 -.7893094 1.936467
_cons | 5.374223 7.5253 0.71 0.475 -9.384946 20.13339
------------------------------------------------------------------------------
. predict double yhat, xb
. reg loghrearn yhat age agesq YR*, robust
note: YR42 omitted because of collinearity
note: YR58 omitted because of collinearity
Linear regression Number of obs = 1930
F( 30, 1899) = 8.18
Prob > F = 0.0000
R-squared = 0.1052
Root MSE = .45641
------------------------------------------------------------------------------
| Robust
loghrearn | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yhat | .0775439 .0191366 4.05 0.000 .040013 .1150748
age | .0694072 .0339128 2.05 0.041 .0028969 .1359176
agesq | -.0007319 .0004448 -1.65 0.100 -.0016041 .0001404
YR30 | .0824261 .1079102 0.76 0.445 -.1292089 .2940611
YR31 | .0952839 .1039415 0.92 0.359 -.1085676 .2991354
YR32 | .1236817 .1023798 1.21 0.227 -.077107 .3244704
YR33 | .175574 .0965876 1.82 0.069 -.013855 .3650029
YR34 | -.0632905 .0979068 -0.65 0.518 -.2553067 .1287257
YR35 | -.0438676 .1320984 -0.33 0.740 -.3029407 .2152056
YR36 | .0731311 .119703 0.61 0.541 -.1616321 .3078943
YR37 | .0471875 .1099594 0.43 0.668 -.1684665 .2628415
YR38 | -.0635212 .119788 -0.53 0.596 -.298451 .1714086
YR39 | .0960618 .1044298 0.92 0.358 -.1087474 .300871
YR40 | .0544622 .1014802 0.54 0.592 -.1445622 .2534866
YR41 | .058472 .1090039 0.54 0.592 -.155308 .2722521
YR42 | (omitted)
YR43 | .1284498 .1235006 1.04 0.298 -.1137613 .370661
YR44 | .0805562 .1001809 0.80 0.421 -.1159199 .2770324
YR45 | .0729855 .1031693 0.71 0.479 -.1293516 .2753226
YR46 | .005405 .0995799 0.05 0.957 -.1898925 .2007024
YR47 | .0235223 .0874715 0.27 0.788 -.1480281 .1950727
YR48 | .0696297 .0827435 0.84 0.400 -.0926481 .2319075
YR49 | -.0389337 .0825409 -0.47 0.637 -.2008141 .1229468
YR50 | -.0205674 .0861564 -0.24 0.811 -.1895386 .1484038
YR51 | .0665797 .08236 0.81 0.419 -.0949458 .2281053
YR52 | .0173513 .0697737 0.25 0.804 -.1194899 .1541924
YR53 | .0589519 .0642448 0.92 0.359 -.0670459 .1849496
YR54 | -.0063706 .0611902 -0.10 0.917 -.1263777 .1136365
YR55 | .008917 .057011 0.16 0.876 -.1028937 .1207278
YR56 | -.0387302 .0522458 -0.74 0.459 -.1411954 .0637349
YR57 | .0094559 .0524493 0.18 0.857 -.0934085 .1123202
YR58 | (omitted)
_cons | -.255431 .5957228 -0.43 0.668 -1.423771 .9129089
------------------------------------------------------------------------------
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