Using GLS or OLS for country data with heteroskedasticity

[Jannik Skak]

Hello.
I am performing an analysis of a country and time specific variable for about 60 different countries over ar 21 year time period.
Thus I have a panel-data set of T=21 and N=60.
As my variable by every logic reason should depend on other state-specific traits, I am running my regression with fixed effects.
Running a Wald-test for groupwise heteroskedasticity I find, chi2 (59) = 9588.82 Prob>chi2 = 0.0000. Thus I clearly have heteroskedasticity.
My question is then, should I still use XTREG with robust standard errors?
I have a notion, that this should be run as an OLS-regression, as I have significantly more panel variables than time variables, but I am not certain it is the case.

[Jannik Skak]

All help is greatly appreciated.
Thank you very much in advance!

[Joao Santos Silva]

What is your dependent variable?

[Jannik Skak]

My dependent variable is a measure I've constructed of the equating effects of state redistribution

[Carlo Lazzaro]

Jannik:
I'd go -xtreg,fe vce(cluster panelid)-

[Jannik Skak]

Hello Carlo.
Thank you very much for your answer and in general to your contribution to this forum, I've had much use of many answers of yours!
Just to be clear, when running an OLS with fixed effects in Stata it interprets robust variables as vce(cluster) automatically right?
Furthermore to be sure, that my results are not driven by outliers, running a quantile regression for fixed effects should be feasible right?

[Carlo Lazzaro]

Jannik:
not quite.
Unlike -xtreg,fe- -regress- adjust the standard errors for heteroskedasticty (see the option -robust-) and autocorrelation (see the option -vce(cluster clusterid) separately.
Both options should be imposed by the researcher, though.
As far as outliers are concerned (I'm a bit queasy about the correctness of the definition of ouliers. Set aside blatand data entry errors, many data generating processes allow "extreme" observation. A case in point is the Gamma distribution, with its long right tail), I would start with a visual inspection but I would not omit them if part of the data generating process under investigation.

[Jannik Skak]

Carlo:
In that case these results kind of riddle me? (see below results of baseline regression)
It seems the specification is identical whether I cluster standard errors by country or run the regression with robust standard error. Am I overlooking something crucial here?




xtreg deltaG vdem, fe vce(cluster countrycode)

Fixed-effects (within) regression Number of obs = 1,297
Group variable: countrycode Number of groups = 59

R-squared: Obs per group:
Within = 0.0154 min = 21
Between = 0.2512 avg = 22.0
Overall = 0.1797 max = 22

F(1,58) = 2.84
corr(u_i, Xb) = -0.5960 Prob > F = 0.0972

(Std. err. adjusted for 59 clusters in countrycode)
------------------------------------------------------------------------------
| Robust
deltaG | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
vdem | -.0347145 .0205893 -1.69 0.097 -.0759285 .0064994
_cons | .1028449 .015274 6.73 0.000 .0722706 .1334192
-------------+----------------------------------------------------------------
sigma_u | .03547219
sigma_e | .0144267
rho | .85806819 (fraction of variance due to u_i)
------------------------------------------------------------------------------








. xtreg deltaG vdem, fe r

Fixed-effects (within) regression Number of obs = 1,297
Group variable: countrycode Number of groups = 59

R-squared: Obs per group:
Within = 0.0154 min = 21
Between = 0.2512 avg = 22.0
Overall = 0.1797 max = 22

F(1,58) = 2.84
corr(u_i, Xb) = -0.5960 Prob > F = 0.0972

(Std. err. adjusted for 59 clusters in countrycode)
------------------------------------------------------------------------------
| Robust
deltaG | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
vdem | -.0347145 .0205893 -1.69 0.097 -.0759285 .0064994
_cons | .1028449 .015274 6.73 0.000 .0722706 .1334192
-------------+----------------------------------------------------------------
sigma_u | .03547219
sigma_e | .0144267
rho | .85806819 (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Jannik:
no, it makes sense.
The difference I highlighted in my previous reply is about -regress-, whereas both the options do the very same job (and, as a consequence, your codes give back the very same coefficients) with -xtreg-.
That said, please note that your -xtreg,fe- outputs show a very low within R-sq, that calls for more predictors, as a first step.