GLS vs robust

[Jo Smith]

My results under robust regression is somwhat different from the results of main estimation method (GLS or random effect). what should I do in this case. should I rely on GLS results when I discuss the my findings and ignore robsut results?
And what are reasons behind this difference?
Thanks in advance.

[Richard Williams]

Robust regression can mean many different things. I think you need to show us your code and output for us to advice you. See pt 12 in the FAQ.

[Jo Smith]

Thanks Richard,
I mean Robust Standard Error. in panel data, If some variables turn to be not significant under robust standard error while they were significant under GLS approach. should my discussion of findings mainly based on GLS?
MAny thank

[Jo Smith]

the code for GLS is Y=B+BX1+BX2........, re
the code for robust is Y=B+BX1+BX2........, robust

[Jeff Wooldridge]

What kind of GLS did you use? To be comparable, you should report the robust standard errors for GLS, too, as you GLS assumptions might not be entirely correct.

[Nick Cox]

This is just to underscore that for many tribes in statistical science "robust regression" does not mean "regressions with robust standard error". The point is brought out very well in

Stigler, S.M. 2010. The changing history of robustness. American Statistician 64: 277–281.

[Jo Smith]

Thanks for all of you,
The Hausman test indicates that random effect is more appropriate (this random effect regression what I meant by GLS). I am not sure if this precise.

[Jeff Wooldridge]

Obtaining the proper RE inference is the first step. You should be using

xtreg y x1 x2 ... xK, re cluster(id)

where "id" is the cross sectional identifier. If you don't use the cluster option then your inference may be very misleading. There is often neglected serial correlation in the time-varying errors, and possibly heteroskedasticity, and RE assumes there is none. This isn't a problem for consistency of the estimators, but it does affect standard errors and inference.

Then, the Hausman test should be computed by

xtoverid

This provides the same level of robust as cluster(id) for the RE standard errors.

Incidentally, if you really did

reg y x1 x2 ... xK, robust

then all you did was make your standard errors robust to heteroskedasticity, and this is insufficient with pooled OLS and panel data. You need to use

reg y x1 x2 ... xK, cluster(id)

But, even with this, there are problems with what you did, because the Hausman test does not compare RE and pooled OLS. It compares RE and fixed effects. That's what the xtoverid command does. So you should do this:

xtreg y x1 x2 ... xK, re cluster(id)
xtreg y x1 x2 ... xK, fe cluster(id)
xtoverid

and be sure to determine if the differences in the RE and FE estimates are practically important. If the differences are important and the statistic rejects, then RE is rejected.

In the future, please show actual Stata commands. What you did above is a cross between an equation and a Stata command.

[Jo Smith]

Thanks very much Jeff
I tried what you advised but I found the results all the same for coefficent and t value using both code
xtreg y x1 x2 ... xK, robust and
xt reg y x1 x2 ... xK, cluster(id)
Also I tried xtreg y x1 x2 ... xK, fe cluster(id) I found something odd which is : F(22,114) = . Prob > F = .

[Jeff Wooldridge]

The default for xtreg is RE; that's why you got the same result. You were supposed to use reg, not xtreg, in the second case.

[daniel klein]

Specifying robust, or equivalent, vce(robust) with panel data that is xtset, usually is the same as vce(cluster clustervar), that is why results are the same.

The missing F-statistic should be "clickable" and links to an explanation, which has probably to do with the the ratio between the number of clusters and the number of parameters to be estimated. If your standard error are non-missing and look reasonable, then you are probably fine anyway.

Best
Daniel

[Jo Smith]

Thanks for you,
I am studying effect of board characteristics (board independence, board size, board meetings, board expertise) on audit fees.
By using GLS as well as cluster(id) approaches all variables are significant except board size.
however, when I used robust standard error
xtreg y x1 x2 ... xK, robust
I found all variables are significant except board meeting and board independence turned to be insignificant. I am struggling what are the reasons behind this difference, and when I write final conclusion which result should I consider? many thanks in advance for your help