How to repeat sampling randomly and run GLS regressions with fixed effects?

[Elaine Lin Shi]

Dear all,

My regression results report less than 200 observations. Thus, I hope to repeat sampling randomly for the GLS regressions with fixed effects.
I have tried bsample and bootstrap but cannot work.

My GLS codes are xtgls y x1 x2 i.year i.firm

Does any one know how to solve this problem?

Thanks in advance!

Best,
Elaine

[Carlo Lazzaro]

Elaine:
if you use default standard errors, thinghs are pretty manageable, as in the following toy-example:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age i.c_city, re

Random-effects GLS regression                   Number of obs     =     28,502
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1087                                         min =          1
     Between = 0.1077                                         avg =        6.1
     Overall = 0.0910                                         max =         15

                                                Wald chi2(3)      =    3417.32
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0594298   .0027187    21.86   0.000     .0541013    .0647583
             |
 c.age#c.age |  -.0006789   .0000451   -15.07   0.000    -.0007672   -.0005906
             |
    1.c_city |   .0330141   .0064045     5.15   0.000     .0204615    .0455666
       _cons |   .5271331    .039939    13.20   0.000      .448854    .6054121
-------------+----------------------------------------------------------------
     sigma_u |  .36328408
     sigma_e |  .30245358
         rho |  .59061651   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
 bootstrap, reps(200): xtreg ln_wage c.age##c.age i.c_city, re
(running xtreg on estimation sample)

Bootstrap replications (200): .........10.........20.........30.........40.........50.........60.........70.........80.........90.........100.........110.........120.........1
> 30.........140.........150.........160.........170.........180.........190.........200 done

Random-effects GLS regression                   Number of obs     =     28,502
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1087                                         min =          1
     Between = 0.1077                                         avg =        6.1
     Overall = 0.0910                                         max =         15

                                                Wald chi2(3)      =    2940.14
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                  (Replications based on clustering on idcode)
------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
     ln_wage | coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0594298    .003096    19.20   0.000     .0533617    .0654979
             |
 c.age#c.age |  -.0006789   .0000513   -13.23   0.000    -.0007795   -.0005783
             |
    1.c_city |   .0330141   .0066888     4.94   0.000     .0199043    .0461239
       _cons |   .5271331   .0452976    11.64   0.000     .4383513    .6159148
-------------+----------------------------------------------------------------
     sigma_u |  .36328408
     sigma_e |  .30245358
         rho |  .59061651   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

[Elaine Lin Shi]

Elaine:
if you use default standard errors, thinghs are pretty manageable, as in the following toy-example:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age i.c_city, re

Random-effects GLS regression Number of obs = 28,502
Group variable: idcode Number of groups = 4,710

R-squared: Obs per group:
Within = 0.1087 min = 1
Between = 0.1077 avg = 6.1
Overall = 0.0910 max = 15

Wald chi2(3) = 3417.32
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ln_wage | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
age | .0594298 .0027187 21.86 0.000 .0541013 .0647583
|
c.age#c.age | -.0006789 .0000451 -15.07 0.000 -.0007672 -.0005906
|
1.c_city | .0330141 .0064045 5.15 0.000 .0204615 .0455666
_cons | .5271331 .039939 13.20 0.000 .448854 .6054121
-------------+----------------------------------------------------------------
sigma_u | .36328408
sigma_e | .30245358
rho | .59061651 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.
bootstrap, reps(200): xtreg ln_wage c.age##c.age i.c_city, re
(running xtreg on estimation sample)

Bootstrap replications (200): .........10.........20.........30.........40.........50.........60.........70.........80.........90.........100.........110.........120.........1
> 30.........140.........150.........160.........170.........180.........190.........200 done

Random-effects GLS regression Number of obs = 28,502
Group variable: idcode Number of groups = 4,710

R-squared: Obs per group:
Within = 0.1087 min = 1
Between = 0.1077 avg = 6.1
Overall = 0.0910 max = 15

Wald chi2(3) = 2940.14
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

(Replications based on clustering on idcode)
------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
ln_wage | coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
age | .0594298 .003096 19.20 0.000 .0533617 .0654979
|
c.age#c.age | -.0006789 .0000513 -13.23 0.000 -.0007795 -.0005783
|
1.c_city | .0330141 .0066888 4.94 0.000 .0199043 .0461239
_cons | .5271331 .0452976 11.64 0.000 .4383513 .6159148
-------------+----------------------------------------------------------------
sigma_u | .36328408
sigma_e | .30245358
rho | .59061651 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

Hi Carlo,

Thank you for sharing the codes and the example!

I have tried your codes (but reps 300 and 500) and been informed that ''insufficient observations to compute bootstrap standard errors no results will be saved''.

My GLS regressions showed that only 180 observations of my unbalanced panel dataset were involved in the regressions.

Are there any methods to deal with the problem?

Thank you!

Best regards,
Elaine

[Carlo Lazzaro]

Elaine:
according to one of the bootstrap holy writings (An Introduction to the Bootstrap | Bradley Efron, R.J. Tibshirani | Ta (taylorfrancis.com)) 25 up to 200 (the upper limit is what would seem acceptable to nasty reviewers) bootstrap replications for standard errors are usually enough.

[Elaine Lin Shi]

Elaine:
according to one of the bootstrap holy writings (An Introduction to the Bootstrap | Bradley Efron, R.J. Tibshirani | Ta (taylorfrancis.com)) 25 up to 200 (the upper limit is what would seem acceptable to nasty reviewers) bootstrap replications for standard errors are usually enough.

Thank you for your reply and guidance, Carlo!

I have used bsample to do the additional regression analyses. But I will try bootstrap again according to your suggestion.

Thanks again!

Best,
Elaine