No difference between robust and clustered standard errors

[Ele Kol]

Hi!

I have a panel data set with fixed effect on products.
I use robust standard errors and as a robustness check I would like to see how much the standard errors/significance change when I use cluster(product) instead.
However, the standard errors are exactly the same (using 5 decimals) with robust and with cluster. Have I done something wrong, or is there a decent explanation for this? For instance that there is no autocorrelation in my data set?
I have used week and year controls.

Thank you very much in advance!

[Fei Wang]

If you look into the help file of -xtreg-, you would see

Specifying vce(robust) is equivalent to specifying vce(cluster panelvar)

[Joao Santos Silva]

Dear Ele Kol,

Further to the helpful information above, I would like to add that this is because if you have fixed effects, the traditional robust standard errors that only account for heteroskedasticity are not valid, and therefore if you want to account for it you have to cluster.

Best wishes,

Joao

[Ele Kol]

Thank you very much for the answer. That explains my results. However, I then wonder if it is possible to estimate the robust standard errors?

[Andrew Musau]

You can do it, but as Joao states, they are not valid for panel data fixed effects models. See the PDF manual entry of xtreg and the Econometrica article by Stock and Watson. For your question, White standard errors are equivalent to clustering at the observation level.

gen obs=_n
xtreg y x1...xn, fe cluster(obs) nonest

Reference:
Stock, J. H., and M. W. Watson. 2008. Heteroskedasticity-robust standard errors for fixed effects panel data regression. Econometrica 76: 155–174. https://doi.org/10.1111/j.0012-9682.2008.00821.x.

[Fei Wang]

Technically, you may use -reghdfe- (from SSC) to estimate robust SE, and it's different from specifying vce(cluster id). But as Joao pointed out, -reghdfe- also sends a warning message in its help file as below

Warning: in a FE panel regression, using robust will lead to
inconsistent standard errors if for every fixed effect, the other
dimension is fixed. For instance, in an standard panel with individual
and time fixed effects, we require both the number of individuals and
time periods to grow asymptotically. If that is not the case, an
alternative may be to use clustered errors, which as discussed below
will still have their own asymptotic requirements.

[Eric de Souza]

From my lecture notes from a couple of years ago (I no longer teach, having retired):
Stock and Watson (Econometrica 2008) have shown that in fixed effect models, correcting only for heteroscedasticity results in inconsistent standard errors. This is avoided by correcting for both heteroscedasticity and serial correlation simultaneously. For this reason, recent versions of Stata substitute cluster for robust when the latter is specified for fixed effects models and produce heteroscedasticity and serial correlation consistent standard errors automatically.
Stock and Watson also propose a correction for the bias in the covariance matrix of the coefficients when only heteroscedasticity is present. Mark Schaffer has programmed this bias correction in -xtivreg2‒. On Statalist, he stated that “‒xtivreg2‒ has an undocumented option ‘sw’ that implements the Stock-Watson bias-corrected heteroskedastic-robust SEs. It's undocumented because at the time I programmed it, I wanted to replicate a published example but couldn’t find one. Feel free to use this option, but caveat emptor.”