What is the name for a regression undertaken with robust variance estimators for clustered data? Just wondering what you call a regression undertaken with robust variance estimators for clustered data. 
Is it ok to say you have used OLS regression with robust variance estimators for clustered data, or is this fundamentally not the case (i.e. once you are using robust variance estimators for clustered data you are no longer doing OLS)?.
Reference would be great.
 A: Yes, it is still OK to say that you are using OLS. You can run OLS either with the usual variance estimator, which assumes iid errors, or with a variance estimator that is robust to heteroskedasticity, or with a cluster-robust variance estimator which is robust to heteroskedasticity as well as within cluster correlation of the errors. In each case, you will get the same point estimates (i.e. the same estimated coefficients) and only the standard errors on the estimated coefficients will change.
Since you are interested in clustering in particular, this might be a useful reference:
Cameron, A. C., and D. L. Miller (2010): “Robust inference with clustered data,” in Handbook of empirical economics and finance, ed. by A. Ullah, and D. E. Giles, pp. 1–28. Chapman & Hall/CRC.
If you look at p. 5, they answer your question as follows: "The most common approach in applied econometrics is to continue with OLS, and then obtain correct standard errors that correct for within-cluster correlation." Pages 5-6 explain this quite nicely.
