I have a question about the first stage regression in xtivreg, re. I assume it should possible to replicate it using xtreg, re, but I could not get the same results if I add the option first in xtivreg, re. For instance, using Stata's example:
Code:
. use https://www.stata-press.com/data/r16/nlswork
(National Longitudinal Survey. Young Women 14-26 years of age in 1968)
. xtivreg ln_w age c.age#c.age not_smsa 2.race (tenure = union birth south), re first
First-stage G2SLS regression
Number of obs = 19,007
Wald chi(7) = 5185
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
tenure | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0859978 .0348599 2.47 0.014 .0176737 .1543219
|
c.age#c.age | .0032321 .0005594 5.78 0.000 .0021356 .0043285
|
not_smsa | -.0141086 .0736087 -0.19 0.848 -.1583791 .1301618
|
race |
black | .316991 .0831899 3.81 0.000 .1539419 .4800402
union | .9664885 .0645912 14.96 0.000 .8398921 1.093085
birth_yr | .1426261 .0122313 11.66 0.000 .1186531 .166599
south | -.2031909 .0712932 -2.85 0.004 -.3429231 -.0634587
_cons | -9.546047 .7705592 -12.39 0.000 -11.05632 -8.035779
------------------------------------------------------------------------------
G2SLS random-effects IV regression Number of obs = 19,007
Group variable: idcode Number of groups = 4,134
R-sq: Obs per group:
within = 0.0664 min = 1
between = 0.2098 avg = 4.6
overall = 0.1463 max = 12
Wald chi2(5) = 1446.37
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
tenure | .1391798 .0078756 17.67 0.000 .123744 .1546157
age | .0279649 .0054182 5.16 0.000 .0173454 .0385843
|
c.age#c.age | -.0008357 .0000871 -9.60 0.000 -.0010063 -.000665
|
not_smsa | -.2235103 .0111371 -20.07 0.000 -.2453386 -.2016821
|
race |
black | -.2078613 .0125803 -16.52 0.000 -.2325183 -.1832044
_cons | 1.337684 .0844988 15.83 0.000 1.172069 1.503299
-------------+----------------------------------------------------------------
sigma_u | .36582493
sigma_e | .63031479
rho | .25197078 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented: tenure
Instruments: age c.age#c.age not_smsa 2.race union birth_yr south
------------------------------------------------------------------------------Code:
. xtreg tenure age c.age#c.age not_smsa 2.race union birth south, re
Random-effects GLS regression Number of obs = 19,007
Group variable: idcode Number of groups = 4,134
R-sq: Obs per group:
within = 0.3001 min = 1
between = 0.0677 avg = 4.6
overall = 0.1409 max = 12
Wald chi2(7) = 6261.51
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
tenure | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0798705 .0327708 2.44 0.015 .0156408 .1441001
|
c.age#c.age | .0035999 .0005253 6.85 0.000 .0025704 .0046295
|
not_smsa | -.1027399 .0828931 -1.24 0.215 -.2652074 .0597276
|
race |
black | .3394806 .1040601 3.26 0.001 .1355266 .5434347
union | .7374317 .063774 11.56 0.000 .612437 .8624265
birth_yr | .1611627 .0150945 10.68 0.000 .1315781 .1907473
south | -.23614 .081409 -2.90 0.004 -.3956987 -.0765813
_cons | -10.66948 .8674532 -12.30 0.000 -12.36966 -8.969308
-------------+----------------------------------------------------------------
sigma_u | 2.4434475
sigma_e | 2.5869529
rho | .47149556 (fraction of variance due to u_i)
------------------------------------------------------------------------------Code:
. xtivreg ln_w age c.age#c.age not_smsa 2.race (tenure = union birth south), fe first
First-stage within regression
Fixed-effects (within) regression Number of obs = 19,007
Group variable: idcode Number of groups = 4,134
R-sq: Obs per group:
within = 0.3019 min = 1
between = 0.0578 avg = 4.6
overall = 0.1289 max = 12
F(5,14868) = 1285.83
corr(u_i, Xb) = -0.1871 Prob > F = 0.0000
------------------------------------------------------------------------------
tenure | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0863031 .0343238 2.51 0.012 .0190241 .1535821
|
c.age#c.age | .0039115 .000549 7.12 0.000 .0028353 .0049876
|
not_smsa | -.3552488 .1269318 -2.80 0.005 -.6040507 -.1064468
|
race |
black | 0 (omitted)
union | .3896861 .0706568 5.52 0.000 .2511901 .5281821
birth_yr | 0 (omitted)
south | -.4296172 .1349122 -3.18 0.001 -.6940618 -.1651726
_cons | -2.554764 .5293374 -4.83 0.000 -3.59233 -1.517197
-------------+----------------------------------------------------------------
sigma_u | 3.1334845
sigma_e | 2.5869529
rho | .59467598 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4133, 14868) = 6.40 Prob > F = 0.0000
Fixed-effects (within) IV regression Number of obs = 19,007
Group variable: idcode Number of groups = 4,134
R-sq: Obs per group:
within = . min = 1
between = 0.1304 avg = 4.6
overall = 0.0897 max = 12
Wald chi2(4) = 147926.58
corr(u_i, Xb) = -0.6843 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
tenure | .2403531 .0373419 6.44 0.000 .1671643 .3135419
age | .0118437 .0090032 1.32 0.188 -.0058023 .0294897
|
c.age#c.age | -.0012145 .0001968 -6.17 0.000 -.0016003 -.0008286
|
not_smsa | -.0167178 .0339236 -0.49 0.622 -.0832069 .0497713
|
race |
black | 0 (omitted)
_cons | 1.678287 .1626657 10.32 0.000 1.359468 1.997106
-------------+----------------------------------------------------------------
sigma_u | .70661941
sigma_e | .63029359
rho | .55690561 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4133,14869) = 1.36 Prob > F = 0.0000
------------------------------------------------------------------------------
Instrumented: tenure
Instruments: age c.age#c.age not_smsa 2.race union birth_yr south
------------------------------------------------------------------------------
. xtreg tenure age c.age#c.age not_smsa 2.race union birth south, fe
note: 2.race omitted because of collinearity
note: birth_yr omitted because of collinearity
Fixed-effects (within) regression Number of obs = 19,007
Group variable: idcode Number of groups = 4,134
R-sq: Obs per group:
within = 0.3019 min = 1
between = 0.0578 avg = 4.6
overall = 0.1289 max = 12
F(5,14868) = 1285.83
corr(u_i, Xb) = -0.1871 Prob > F = 0.0000
------------------------------------------------------------------------------
tenure | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0863031 .0343238 2.51 0.012 .0190241 .1535821
|
c.age#c.age | .0039115 .000549 7.12 0.000 .0028353 .0049876
|
not_smsa | -.3552488 .1269318 -2.80 0.005 -.6040507 -.1064468
|
race |
black | 0 (omitted)
union | .3896861 .0706568 5.52 0.000 .2511901 .5281821
birth_yr | 0 (omitted)
south | -.4296172 .1349122 -3.18 0.001 -.6940618 -.1651726
_cons | -2.554764 .5293374 -4.83 0.000 -3.59233 -1.517197
-------------+----------------------------------------------------------------
sigma_u | 3.1334845
sigma_e | 2.5869529
rho | .59467598 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4133, 14868) = 6.40 Prob > F = 0.0000
0 Response to xtivreg, re first
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