Joint F test for fixed effects/Heteroskedasticity

[Vincent Barros]

Hello,
I have 2 quick questions.
Question 1:
I have panel data and I'm running xtreg, fe.
I'm trying to determine from the output if Stata did a joint F test of the fixed effects. At the very bottom is: F test that all u_i=0. Is this the significance of the fixed effects?

Question 2:
Regarding the same fixed effects regression, I ran the Modified Wald test (xttest3) for groupwise heteroskedasticity. For this test, when you can reject the null hypothesis... does that indicate that the model is heteroskedastic? If so, will xtreg, fe vce(robust) provide the constant variance?

Thank you!

[Carlo Lazzaro]

Vincent:
Q1) The F test at the bottom of the table test the joint statistical significance of u_i;
Q2) under the null hypothesis, -xttest3- assumes homoskedasticity (please see the related help file by typing -rnethelp "http://www.stata-journal.com/software/sj4-2/st0004_2/xttest3.hlp"-

[Vincent Barros]

Thanks Carlo. But what test can I run in Stata that conducts an F-test to test the joint statistical significance of the fixed effects in my regression?

[Carlo Lazzaro]

Vincent:
I might have overlooked something in your post, but taking a look at:
-xtreg- entry, Stata 13.1 .pdf manual, page 380: e(F_f) is reported as a joint F-test for ui=0 (where ui means fixed effect).

[Jeff Wooldridge]

You should not use the vce(robust) option with fixed effects unless you have many time periods and are willing to rule out serial correlation. With a small number of time periods, the heteroskedasticity-robust standard errors are not valid even without serial correlation (because the within transformation induces serial correlation). You should use the vce(cluster id) option, which is valid for any T and for any serial correlation pattern (including none). If your N is pretty large, I wouldn't even bother with the test for serial correlation.

As Carlo said, the test that Stata reports without the vce(robust) or vce(cluster id) options at the bottom of the xtreg output is the test for the absence of heterogeneity. But there is no robust form for it because it relies on large T (or the classical linear model assumptions so the test is exact). I doubt this is what you want to test. I suspect you want to compute a Hausman test comparing FE and RE, and fully robust forms are available.

[Sergio Correia]

Thank's for the insightful comment!

As a minor note, I just wanted to point out that recent versions of Stata already replace vce(robust) with vce(cluster id) due to the inconsistency you mentioned.

From "help whatsnew":

xtreg, fe now uses vce(cluster id) when vce(robust) is specified, in light of the new results in Stock and Watson, "Heteroskedasticity-robust standard errors for fixed-effects panel-data
regression," Econometrica 76 (2008): 155-174.

[Jeff Wooldridge]

Very good, Sergio. I think I once knew that, but the mind is starting to forget some details. :-) And above, I should have said "test for heteroskedasticity or serial correlation."

[Vincent Barros]

You should not use the vce(robust) option with fixed effects unless you have many time periods and are willing to rule out serial correlation. ... If your N is pretty large, I wouldn't even bother with the test for serial correlation.

I'm working with country-level macro data (GDP/capita, inflation rate, FDI, etc) for about 150 countries over 51 years. My N = 5000+ as a data set. In my regressions, my n = 549. At what level can I not bother testing for serial correlation?

[Vincent Barros]

Also, thank you for your posts. I appreciate all the help understanding the Stata output and the advice regarding my testing.

[Carlo Lazzaro]

Vincent:
- provided that you have not deliberately excluded most part of your dataset, you seemingly have some problems concerning missing values (as your regression includes about 1/10 of your original sample);
- that said, I would invoke vce(cluster id) for standard errors.

[Alexandra Mossenberg]

Very good, Sergio. I think I once knew that, but the mind is starting to forget some details. :-) And above, I should have said "test for heteroskedasticity or serial correlation."

Jeff, Im curious why whould you ignore heteroskedasticity? I always assumed that heteroskedasticity cant be ignored even with large N, since its one of the main assumptions of GM

[Jeff Wooldridge]

Alexandra: I ran across this post just now. Especially with large N, small T, there is no reason to model the heteroskedasticity. We can now use cluster-robust standard errors and test statistics to obtain valid inference for the usual FE estimator. The inference is robust to serial correlation and heteroskedasticity of unknown form. It's not as easy to model heteroskedasticity with fixed effects as you think, due to the within transformation, as you might think. In fact, getting it right is quite tricky.

In any case, I invite you to read either my introductory econometrics book or my MIT Press book. There I give a systematic treatment of the properties of OLS and fixed effects. You do not need the full GM assumptions to do most interesting things. Use robust inference. The one caveat is that these comments are geared toward the microeconometric case where N is large and, more to the point, T is not very large.

[Chiraz KARAMTI]

Mr Wooldridge
I'm so glad you are part of this forum. Please I have a precise questions.
For fixed effects models in all references the vce (cluster) is the best solution to deal with hetroscedasticity and within autocorrelation. However it doesn't deal with across correlation. For this it is adviced to use Discroll and Kraay estimates. In Stata journal, it is noted that the best command is xtscc.
My questions:
1) is this really the best solution for across and within hetroscedasticity and autocorrelation problems in fixed effects models???
2) what kind of hetroscedasticity is corrected? within or across?
3) is this what you called in your book the FEGLS?

Many thanks

[Jerry Roc]

Hello every one, I have the wage gap between immigrants and natives Born by census metropolitan area/regions(cma), level of education (education) and year (t). So I regressed this wage gap on an observable vector of characteristics and I also included the fixed effects of cma, e and t. I do it like this in Stata --> reg wagegap xb i.cma i.educ i.t, robust So I would like to perform a fixed effects stability test and also test if there are any interactions between the fixed effects (i.cma#i.educ i.cma#i.t i.educ#i.t). 1) Did you think that the stability test and Joint F test for fixed effects are different? 2) If no, Does this amount to performing an F test where the null hypothesis will be the absence of heterogeneity and the alternative will be the presence of heterogeneity to the stability test? 3) For the presence of interactions between fixed effects do I have to perform either a F test? Best! thank you