Robust vs. Clustered Errors

A constant problem is the homoscedasticity of error terms assumption is required to validate the Gauss-Markov Theorem (making straight foward OLS the BLUE). As the assumption can often be violated leading to funky standard error estimates, and therefore inference, the two most common corrections are estimating error variances and covariances (VCs) as a function of observables.  So now instead of estimating the error VCs unconditionally as in the basic OLS formulation an additional step is taken whereby the VCs are estimated with an additional preceding auxilliary regression whereby error components are a function of individual terms or cluster terms.  For example,the equation { error = individual (or group) effect + random component }. So while the error term was originally not homoscedastic the assumption here is that the random component is since the heterocedasticity was derived from the individual or group effects and these are controlled for.  Modeling the error structure as having an individual or group effect is what makes the error estimator as either robust (former) and clustered (the latter).  This method was introduced by White (1980), hence the name White estimator (among others), and is within the family of GLS methods.

Here are some helpful links:
http://www.stata.com/support/faqs/stat/cluster.html
http://sekhon.berkeley.edu/causalinf/sp2010/section/week7.pdf