Hi,
in help xt_vce_options I found the following recommendation:
When working with panel-data models, we strongly encourage you to use the vce(bootstrap) or vce(jackknife) options instead of the corresponding prefix command.
Of course, this called into my curiosity, and I was wondering if it was because of the clustering nature of the data to avoid any mistakes when using the prefix, or because there is something else to it. So I decided to try it out. When doing a fixed-effects estimation, I found no difference in using either method:
Fitting random effects, however, presents a different picture
The question, then, is why? It seems odd that with a fixed effects estimation there is no difference, but with a random effects estimation there is. It is unfortunate, because there may be applications where the statistic we want to bootstrap is some post-estimation, not simply the standard errors of the coefficients, but that it is based on those standard errors. In any case, can someone explain why the different results?
Thanks!!!
in help xt_vce_options I found the following recommendation:
When working with panel-data models, we strongly encourage you to use the vce(bootstrap) or vce(jackknife) options instead of the corresponding prefix command.
Of course, this called into my curiosity, and I was wondering if it was because of the clustering nature of the data to avoid any mistakes when using the prefix, or because there is something else to it. So I decided to try it out. When doing a fixed-effects estimation, I found no difference in using either method:
Code:
. clear all
. set more off
. webuse nlswork
(National Longitudinal Survey. Young Women 14-26 years of age in 1968)
. local xv "c.age##c.age c.ttl_exp##c.ttl_exp south"
. xtset idcode year
panel variable: idcode (unbalanced)
time variable: year, 68 to 88, but with gaps
delta: 1 unit
. xtreg ln_w `xv', fe vce(boot, reps(50) seed(1234))
(running xtreg on estimation sample)
Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
Fixed-effects (within) regression Number of obs = 28,502
Group variable: idcode Number of groups = 4,710
R-sq: Obs per group:
within = 0.1546 min = 1
between = 0.2856 avg = 6.1
overall = 0.2149 max = 15
Wald chi2(5) = 1521.76
corr(u_i, Xb) = 0.1348 Prob > chi2 = 0.0000
(Replications based on 4,710 clusters in idcode)
-------------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
age | .0291285 .0055949 5.21 0.000 .0181626 .0400943
|
c.age#c.age | -.0006749 .0000913 -7.39 0.000 -.0008539 -.000496
|
ttl_exp | .0617062 .0035824 17.22 0.000 .0546848 .0687275
|
c.ttl_exp#c.ttl_exp | -.000893 .0001529 -5.84 0.000 -.0011927 -.0005933
|
south | -.0684464 .0200641 -3.41 0.001 -.1077714 -.0291214
_cons | 1.126962 .0780397 14.44 0.000 .9740066 1.279917
--------------------+----------------------------------------------------------------
sigma_u | .36581516
sigma_e | .29463102
rho | .60654417 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
. bs, reps(50) cl(idcode) id(cid) group(year) seed(1234): xtreg ln_w `xv', fe
(running xtreg on estimation sample)
Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
Fixed-effects (within) regression Number of obs = 28,502
Group variable: idcode Number of groups = 4,710
R-sq: Obs per group:
within = 0.1546 min = 1
between = 0.2856 avg = 6.1
overall = 0.2149 max = 15
Wald chi2(5) = 1521.76
corr(u_i, Xb) = 0.1348 Prob > chi2 = 0.0000
(Replications based on 4,710 clusters in idcode)
-------------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
age | .0291285 .0055949 5.21 0.000 .0181626 .0400943
|
c.age#c.age | -.0006749 .0000913 -7.39 0.000 -.0008539 -.000496
|
ttl_exp | .0617062 .0035824 17.22 0.000 .0546848 .0687275
|
c.ttl_exp#c.ttl_exp | -.000893 .0001529 -5.84 0.000 -.0011927 -.0005933
|
south | -.0684464 .0200641 -3.41 0.001 -.1077714 -.0291214
_cons | 1.126962 .0780397 14.44 0.000 .9740066 1.279917
--------------------+----------------------------------------------------------------
sigma_u | .36581516
sigma_e | .29463102
rho | .60654417 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
Code:
. xtreg ln_w `xv', re vce(boot, reps(50) seed(1234))
(running xtreg on estimation sample)
Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
Random-effects GLS regression Number of obs = 28,502
Group variable: idcode Number of groups = 4,710
R-sq: Obs per group:
within = 0.1538 min = 1
between = 0.2971 avg = 6.1
overall = 0.2249 max = 15
Wald chi2(5) = 2034.78
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
(Replications based on 4,710 clusters in idcode)
-------------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
age | .0325329 .0050847 6.40 0.000 .0225671 .0424987
|
c.age#c.age | -.0007202 .0000839 -8.58 0.000 -.0008847 -.0005557
|
ttl_exp | .0639336 .0027724 23.06 0.000 .0584998 .0693674
|
c.ttl_exp#c.ttl_exp | -.000943 .0001341 -7.03 0.000 -.0012059 -.0006801
|
south | -.1253318 .0116613 -10.75 0.000 -.1481877 -.102476
_cons | 1.08762 .0695168 15.65 0.000 .9513691 1.22387
--------------------+----------------------------------------------------------------
sigma_u | .31293049
sigma_e | .29463102
rho | .53009223 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
. bs, reps(50) cl(idcode) id(cid) group(year) seed(1234): xtreg ln_w `xv', re
(running xtreg on estimation sample)
Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
Random-effects GLS regression Number of obs = 28,502
Group variable: idcode Number of groups = 4,710
R-sq: Obs per group:
within = 0.1538 min = 1
between = 0.2971 avg = 6.1
overall = 0.2249 max = 15
Wald chi2(5) = 1979.20
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
(Replications based on 4,710 clusters in idcode)
-------------------------------------------------------------------------------------
| Observed Bootstrap Normal-based
ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
age | .0325329 .0052315 6.22 0.000 .0222793 .0427865
|
c.age#c.age | -.0007202 .0000858 -8.39 0.000 -.0008884 -.000552
|
ttl_exp | .0639336 .002964 21.57 0.000 .0581244 .0697429
|
c.ttl_exp#c.ttl_exp | -.000943 .0001408 -6.70 0.000 -.001219 -.000667
|
south | -.1253318 .01277 -9.81 0.000 -.1503606 -.1003031
_cons | 1.08762 .0719991 15.11 0.000 .9465039 1.228735
--------------------+----------------------------------------------------------------
sigma_u | .31293049
sigma_e | .29463102
rho | .53009223 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
Thanks!!!
