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 articlehttp://www.stata.com/support/faqs/st...luster-option/ 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.