-xtreg, fe vce(cluster clusterid)- citation help

[Anggi Surya]

hello everyone,

I did some fixed effect panel data regression for my model (N=34, T=4) since the chow and hausman test indicates the fixed effect as the best model. but unfortunately, my data suffer from autocorrelation (tested with xtserial command) and heteroscedasticity (test with xttest3) and I already read a lot (especially the post from Mr. Wooldridge and Clyde, attached below) about what kind of treatment I need to do and I came to the conclusion that -xtreg, fe vce(cluster clusterid)- will do the job to generate valid standard errors even with autocorrelation and heteroscedasticity.

Using robust standard errors does not eliminate the heteroscedasticity. What it does is assure that the standard errors of the regression output are valid in spite of the heteroscedasticity. This is generally all that people care about.

If you really want to eliminate the heteroscedasticity, you have to change the dependent variable. Sometimes a log transformation will accomplish this when the pattern looks like the one you show (error variance increases in a funnel-like shape as predicted value increases.) But, of course, this approach should only be used if a linear relationship between the log of your outcome variable and the predictors is a reasonable model of reality.

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.

what I want to ask is there any citation I can use to justify the use of -xtreg, fe vce(cluster clusterid)- will generate a valid standard error despite the problem Im talking before?

or this line from xtreg manuals is enough for my citation?

). vce(cluster clustvarlist) specifies that standard errors allow for intragroup correlation within groups defined by one or more variables in clustvarlist, relaxing the usual requirement that the observations be indepen

thank you for your responses and have a nice day!

[George Ford]

https://jhr.uwpress.org/content/50/2/317

[Jeff Wooldridge]

Anggi: Yes, cluster using vce(cluster id) where id is the cross sectional identifier. N = 34 is pretty small but you probably have no choice.

[Anggi Surya]

Thank you Mr. Wooldridge and George for your help!!