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I'm currently working on some experimental data. The experimental design consists of two treatments. In each treatment, 20 subjects are randomly matched in pairs and participate to a simple game. The game is repeated for 20 periods. In each period, the pairs are randomly re-matched and a single decision is made.

I estimate the effect of the treatment with a model that includes individual random effects, session dummies and some lagged variables (to control for dynamic session effects). When I estimate the cluster-robust covariance matrix, with the xtreg_re option vce(cluster Session), the standard errors are smaller than the unclustered ones; when I exclude the session dummies, the cluster-robust standard errors become larger than the unclustered ones.

I read the article on the comparison of the standard errors for robust, cluster, and standard estimators. I understand that there must be a cancellation of variation when the residuals are summed over clusters, but it's not clear to me why this happen when I include fixed effects for the clusters?

Little Update: I think I tracked down the source of the problem. Indeed, what I observe with the standard errors is not specific to my data nor to the FGLS. I actually could replicate the problem with a fake panel and with standard OLS. I think that the source of the problem is my main independent variable, which is a dummy which takes a 1 if the observation is in the main treatment and 0 if it is in the control group. The session dummies that I want to plug into my model, to control for possible static session effects, are actually very correlated with the treatment dummy: each session belongs either to the main treatment or to the control treatment. Nevertheless, I still am not sure how exactly the inclusion of the session dummies reduce my standard errors from the cluster robust covariance matrix and why I don't observe anything odd in the estimates of the parameters.

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  • $\begingroup$ Cross-posted at statalist.org/forums/forum/general-stata-discussion/general/… General etiquette and Meta discussions imply that you should tell us (e.g. meta.stackexchange.com/questions/141823/…) $\endgroup$
    – Nick Cox
    Commented Oct 17, 2014 at 21:51
  • $\begingroup$ Thanks for this comment. I read the link you sent and now I understand the problem with posting on more forums. I will leave a comment on statalist. $\endgroup$
    – sciacallojo
    Commented Oct 17, 2014 at 22:03
  • $\begingroup$ Is the dependent variable binary as well? $\endgroup$
    – Andy
    Commented Oct 20, 2014 at 9:02
  • $\begingroup$ Nope, the dependent variable takes values between 0 and 100. $\endgroup$
    – sciacallojo
    Commented Oct 20, 2014 at 9:29

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Robust clustered standard errors can change your standard errors in both directions. That is, clustered standard errors can be larger or smaller than conventional standard errors. The direction in which standard errors will change depends on the sign of the intra-class correlation. This post explains robust standard errors in greater detail.

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