Is it fair to say that robust estimation should be used when the iid assumption doesn't hold? My understanding is that the sample has to be random/independent/uncorrelated but it can follow non-identical distributions - and that's when robust estimation is useful. In other words, robust estimation should be used in cases where X's and the error term are correlated but not identically distributed (could follow two normal distributions with different mean and variance). Robust estimation should produce the same consistent parameters as OLS but with different standard errors that allow for valid statistical inference.
However, if the data is clustered (panel data), then robust estimation is not necessarily the only/right tool. GLS will produce different estimates and standard errors. Is that right?
Empirical examples would be great.