"Random Effect model and FGLS" "Fixed effect model and FGLS"

[Haj Noor]

Hi Experts
Hope you are doing well!


Details of my dataset:

Unbalanced Panel Dataset
Data were taken from only 1 country; and there are 25 institutes
Total Observations:425
Time Period: 2003-2019


My question is:
Can we use FGLS both for Random Effect Model and Fixed Effect Model?

Many Thanks!

[Haj Noor]

Carlo Lazzaro

my three variables coefficients value 0.000 thats why i am moving to FGLS models. FGLS giving accurate results.

Many Thanks!

[Carlo Lazzaro]

Haj:
set aside FGLS models for a while (and, by the way, I do not know what command you ran about FGLS), are you sure to have a panel-wise effect?

[Haj Noor]

Hi again Carlo Lazzaro

First, I ran the below command: (my dataset is an unbalanced panel so it hadn't work)
xtgls par30 dlr lev sizelog plia pm fb gdp inf, igls panel
option panel not allowed
r(198);



Then I ran this command.
xtgls par30 dlr lev sizelog plia pm fb gdp inf, igls
Iteration 1: tolerance = 0


Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: homoskedastic
Correlation: no autocorrelation

Estimated covariances = 1 Number of obs = 231
Estimated autocorrelations = 0 Number of groups = 25
Estimated coefficients = 9 Obs per group:
min = 4
avg = 9.24
max = 15
Wald chi2(8) = 136.26
Log likelihood = -861.0214 Prob > chi2 = 0.0000


par30 Coef. Std. Err. z P>z [95% Conf. Interval]

dlr .0113138 .0028984 3.90 0.000 .005633 .0169946
lev 4.894468 2.699998 1.81 0.070 -.3974305 10.18637
sizelog -2.049918 .497024 -4.12 0.000 -3.024067 -1.075769
plia .8106217 .2566308 3.16 0.002 .3076345 1.313609
pm -.0240679 .0063953 -3.76 0.000 -.0366025 -.0115334
fb -.0649979 .0230164 -2.82 0.005 -.1101092 -.0198865
gdp 1.489972 .6367946 2.34 0.019 .241878 2.738067
inf .2609757 .260585 1.00 0.317 -.2497616 .7717129
_cons 28.83517 10.83372 2.66 0.008 7.601465 50.06887


. estimates store hetero

. xtgls par30 dlr lev sizelog plia pm fb gdp inf

Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: homoskedastic
Correlation: no autocorrelation

Estimated covariances = 1 Number of obs = 231
Estimated autocorrelations = 0 Number of groups = 25
Estimated coefficients = 9 Obs per group:
min = 4
avg = 9.24
max = 15
Wald chi2(8) = 136.26
Log likelihood = -861.0214 Prob > chi2 = 0.0000


par30 Coef. Std. Err. z P>z [95% Conf. Interval]

dlr .0113138 .0028984 3.90 0.000 .005633 .0169946
lev 4.894468 2.699998 1.81 0.070 -.3974305 10.18637
sizelog -2.049918 .497024 -4.12 0.000 -3.024067 -1.075769
plia .8106217 .2566308 3.16 0.002 .3076345 1.313609
pm -.0240679 .0063953 -3.76 0.000 -.0366025 -.0115334
fb -.0649979 .0230164 -2.82 0.005 -.1101092 -.0198865
gdp 1.489972 .6367946 2.34 0.019 .241878 2.738067
inf .2609757 .260585 1.00 0.317 -.2497616 .7717129
_cons 28.83517 10.83372 2.66 0.008 7.601465 50.06887


. local df=e(N_g)-1

. display e(N_g)-1
24

. lrtest hetero ., df(24)

Likelihood-ratio test LR chi2(24) = 0.00
(Assumption: . nested in hetero) Prob > chi2 = 1.0000

. est replay hetero


Model hetero


Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: homoskedastic
Correlation: no autocorrelation

Estimated covariances = 1 Number of obs = 231
Estimated autocorrelations = 0 Number of groups = 25
Estimated coefficients = 9 Obs per group:
min = 4
avg = 9.24
max = 15
Wald chi2(8) = 136.26
Log likelihood = -861.0214 Prob > chi2 = 0.0000


par30 Coef. Std. Err. z P>z [95% Conf. Interval]

dlr .0113138 .0028984 3.90 0.000 .005633 .0169946
lev 4.894468 2.699998 1.81 0.070 -.3974305 10.18637
sizelog -2.049918 .497024 -4.12 0.000 -3.024067 -1.075769
plia .8106217 .2566308 3.16 0.002 .3076345 1.313609
pm -.0240679 .0063953 -3.76 0.000 -.0366025 -.0115334
fb -.0649979 .0230164 -2.82 0.005 -.1101092 -.0198865
gdp 1.489972 .6367946 2.34 0.019 .241878 2.738067
inf .2609757 .260585 1.00 0.317 -.2497616 .7717129
_cons 28.83517 10.83372 2.66 0.008 7.601465 50.06887

[Carlo Lazzaro]

Haj:
-xtgls- is for T>N panel dataset (whereas you have an N>T one; hence -xtreg-);
moreover, you were interesetd in -fe- specification, as per https://www.stata.com/statalist/arch.../msg00484.html, -xtgls- is not a -fe- estimator by default.
At the top of that, if you go -re- when you should go -fe- (provided that you actually have a panel-wise effect in your dataset) you are playing with an inefficient estimator that produces misleading standard errors (and statistical significance soaked with snake oil).
As an aside, please note that, despite what most of us are/were taught at the university, non-statstical significant results are as informative as their significant counterparts.

[Haj Noor]

Carlo Lazzaro

I have tried each and every method but I am not sure which is best.

here is the detail:
(There were no autocorrelation problems but hetero issue)
First I ran the Hausman test, gave the results "Fixed effect is best"
then I applied the Robust test gave only one significant variable

(there were no hetero issues but the problem of autocorrelation)
then I had taken the log of the dependent variable then robust gave 3 variables significant but now the issue is there are three variables coefficient's value is 0.000. (below are the results) what should I do know?

[Carlo Lazzaro]

Haj:
provided that you have a panel-wise effect:
go -xtreg,fe- and -xtreg,re- with the robust option and then compare them with the community-contributed module-xtoverid-. If the null is rejected go - fe- and live qith your results.

[Rui Zha]

Haj:
-xtgls- is for T>N panel dataset (whereas you have an N>T one; hence -xtreg-);
moreover, you were interesetd in -fe- specification, as per https://www.stata.com/statalist/arch.../msg00484.html, -xtgls- is not a -fe- estimator by default.
At the top of that, if you go -re- when you should go -fe- (provided that you actually have a panel-wise effect in your dataset) you are playing with an inefficient estimator that produces misleading standard errors (and statistical significance soaked with snake oil).
As an aside, please note that, despite what most of us are/were taught at the university, non-statstical significant results are as informative as their significant counterparts.

xtgls is not a fixed-effect estimator, in that it does not allow any coefficient to vary over the panel, including the intercept (unless you put in dummies, of course). So, it means if you add Year or ID dummies, you can use it with FE