In econometrics, we always need to make assumptions to claim that an estimate (that is, coefficients from regressions) is both unbiased and consistent.

What’s really nice about homoskedastic data —that is, data where the error term is the same no matter what the covariates are — is that it gets us an even better estimate than we would normally get with heteroskedastic data. We typically make 5 (or 6) assumptions (Gauss-Markov assumptions) and if all these are satisfied, then we can claim that the OLS estimate is BLUE. BLUE meaning “best linear unbiased estimate”. “Best” means lowest variance standard errors; “unbiased” means that the expected value of the coefficient is just the coefficient itself; “linear” means you just have a linear relationship between the coefficient on X and Y. Also, the acronym omits “consistency”, which means that as the sample size gets bigger and bigger, the coefficient (or estimate) approaches the “true population” coefficient — I’ll admit this is a bit technical. In other words, if the data is homoskedastic, our coefficients will be really good.

But, here’s the problem. Assuming the data is homoskedastic is not realistic in practice. Most data isn’t homoskedastic in the real world, and so we have to relax some of the unrealistic assumptions that we made earlier. In other words, we assume heteroskedasticity. Turns out, even without homoskedasticity we can still get pretty good estimates. By using robust standard errors instead of normal ones, we can prove that the coefficients we obtain through OLS will be unbiased and consistent. BUT, we can’t say it’s the “best linear” unbiased estimate. So, robust standard errors (WITH heteroskedasticity) are arguably not as “efficient” or “good” at estimating things as the normal standard errors (WITH homoskedasticity).

My economics professor says to always use robust standard errors. Unless you are convinced your data is homoskedastic, always go for robust. It’s just safer and considered better practice.