hausman test for -xtivreg-

[Johnny YANG]

With xtivreg, we could combine fixed-effect and random-effect model with instrumental variable model.
For example, the fixed-effect and random effect models are as follows,
xtivreg y (x=z1 z2 z3) controls, fe
xtivreg y (x=z'1 z'2 z'3) controls, re

As we can see, Fixed-effect model and random effect model use different set of instrumental variables. In this case, are the hausman test results still acountable? If not accountable, what test should we do to compare fixed effect and random effect models?
The second question is what should we do if we can't find IVs for fixed effect model? In this case, should we just go for random effect?


Thank you in advance for help! I'd really appreciate it if you could provide references also.

[Carlo Lazzaro]

Johnny:
I'd consider the community-contributed module -xtoverid- (its null is: -re- is the way to go).

[Johnny YANG]

Johnny:
I'd consider the community-contributed module -xtoverid- (its null is: -re- is the way to go).

Hi Carlo, thanks for replying.
I searched in the forum, the xtoverid after xtivreg, fe should be testing the overidentification of the set of IVs, is that right?
Because in my case, what I want to do is to do comparison between xtivreg, fe with xtivreg, re, in order to get a better estimation.

[Carlo Lazzaro]

Johnny:
you could simply code -xtivreg, re- and then invoke -xtoverid-, like in the following tiy-example:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtset idcode year

Panel variable: idcode (unbalanced)
 Time variable: year, 68 to 88, but with gaps
         Delta: 1 unit

. xtivreg ln_wage age (tenure = union south), re i(idcode)

G2SLS random-effects IV regression              Number of obs     =     19,007
Group variable: idcode                          Number of groups  =      4,134

R-squared:                                      Obs per group:
     Within  = 0.0559                                         min =          1
     Between = 0.1401                                         avg =        4.6
     Overall = 0.0972                                         max =         12

                                                Wald chi2(2)      =     542.92
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      tenure |   .1962067   .0128332    15.29   0.000     .1710541    .2213594
         age |  -.0398788   .0036139   -11.03   0.000    -.0469618   -.0327957
       _cons |   2.287752   .0698797    32.74   0.000      2.15079    2.424713
-------------+----------------------------------------------------------------
     sigma_u |  .37862603
     sigma_e |  .64315554
         rho |  .25737152   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented: tenure
 Instruments: age union south

. xtoverid

Test of overidentifying restrictions:
Cross-section time-series model: xtivreg g2sls  
Sargan-Hansen statistic  97.874  Chi-sq(1)    P-value = 0.0000

.

See https://www.stata.com/statalist/arch.../msg00721.html

[Johnny YANG]

Johnny:
you could simply code -xtivreg, re- and then invoke -xtoverid-, like in the following tiy-example:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtset idcode year

Panel variable: idcode (unbalanced)
Time variable: year, 68 to 88, but with gaps
Delta: 1 unit

. xtivreg ln_wage age (tenure = union south), re i(idcode)

G2SLS random-effects IV regression Number of obs = 19,007
Group variable: idcode Number of groups = 4,134

R-squared: Obs per group:
Within = 0.0559 min = 1
Between = 0.1401 avg = 4.6
Overall = 0.0972 max = 12

Wald chi2(2) = 542.92
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ln_wage | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
tenure | .1962067 .0128332 15.29 0.000 .1710541 .2213594
age | -.0398788 .0036139 -11.03 0.000 -.0469618 -.0327957
_cons | 2.287752 .0698797 32.74 0.000 2.15079 2.424713
-------------+----------------------------------------------------------------
sigma_u | .37862603
sigma_e | .64315554
rho | .25737152 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented: tenure
Instruments: age union south

. xtoverid

Test of overidentifying restrictions:
Cross-section time-series model: xtivreg g2sls
Sargan-Hansen statistic 97.874 Chi-sq(1) P-value = 0.0000

.

See https://www.stata.com/statalist/arch.../msg00721.html

Thanks!
This might be a silly quesiton...
But do we need to also test for the overidentification of IVs in the random effect also, if the overidentification of IVs in the fixed-effect model is good?

[Carlo Lazzaro]

Johnny:
you can focus on the -fe- estimator as a second step of your analysis:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtset idcode year

Panel variable: idcode (unbalanced)
 Time variable: year, 68 to 88, but with gaps
         Delta: 1 unit

. xtivreg ln_wage age (tenure = union south), fe i(idcode)

Fixed-effects (within) IV regression            Number of obs     =     19,007
Group variable: idcode                          Number of groups  =      4,134

R-squared:                                      Obs per group:
     Within  =      .                                         min =          1
     Between = 0.1261                                         avg =        4.6
     Overall = 0.0869                                         max =         12

                                                Wald chi2(2)      =  142054.65
corr(u_i, Xb) = -0.6875                         Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      tenure |   .2450528   .0382041     6.41   0.000     .1701741    .3199314
         age |  -.0650873   .0126167    -5.16   0.000    -.0898156    -.040359
       _cons |   2.826672   .2451883    11.53   0.000     2.346112    3.307232
-------------+----------------------------------------------------------------
     sigma_u |  .71990151
     sigma_e |  .64315554
         rho |  .55612637   (fraction of variance due to u_i)
------------------------------------------------------------------------------
 F test that all u_i=0: F(4133,14871) =     1.53          Prob > F    = 0.0000
------------------------------------------------------------------------------
Instrumented: tenure
 Instruments: age union south

. xtoverid

Test of overidentifying restrictions: 
Cross-section time-series model: xtivreg fe   
Sargan-Hansen statistic   0.965  Chi-sq(1)    P-value = 0.3259

.

[Johnny YANG]

Johnny:
you can focus on the -fe- estimator as a second step of your analysis:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtset idcode year

Panel variable: idcode (unbalanced)
Time variable: year, 68 to 88, but with gaps
Delta: 1 unit

. xtivreg ln_wage age (tenure = union south), fe i(idcode)

Fixed-effects (within) IV regression Number of obs = 19,007
Group variable: idcode Number of groups = 4,134

R-squared: Obs per group:
Within = . min = 1
Between = 0.1261 avg = 4.6
Overall = 0.0869 max = 12

Wald chi2(2) = 142054.65
corr(u_i, Xb) = -0.6875 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ln_wage | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
tenure | .2450528 .0382041 6.41 0.000 .1701741 .3199314
age | -.0650873 .0126167 -5.16 0.000 -.0898156 -.040359
_cons | 2.826672 .2451883 11.53 0.000 2.346112 3.307232
-------------+----------------------------------------------------------------
sigma_u | .71990151
sigma_e | .64315554
rho | .55612637 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4133,14871) = 1.53 Prob > F = 0.0000
------------------------------------------------------------------------------
Instrumented: tenure
Instruments: age union south

. xtoverid

Test of overidentifying restrictions:
Cross-section time-series model: xtivreg fe
Sargan-Hansen statistic 0.965 Chi-sq(1) P-value = 0.3259

.

Thank you!