Can robust standard errors be less than those from normal OLS? I'm reading about Robust Standard Error Estimators for Panel Models from the developer of plm R package (Millo, 2017: 21). But my question is not about software.
In the example I see that some heteroscedasticity robust standard errors are in fact less than those in benchmark OLS. I thought that we normaly expected robust errors to be at least as large as their OLS counterparts.
Below you see the comparison of different HC procedures, for the same model with coefficients arranged by columns.

My question concerns this situation. Is it fine in general and how to interpret this fact if, i.e. in real model, such a change in s.e. changes the significance of a coefficient?

OLS gives every point equal weight in estimating the error of the estimates. The variance/error is estimated as
$$\widehat{\text{Var}(\beta) }= \hat{\sigma} (X^TX)^{-1} $$
A weighted least squares estimator might use an estimate like
$$\widehat{\text{Var}(\beta) }= \hat{\sigma} (X^TWX)^{-1} $$
The weights might make some points more and others less important. As a result the estimates of the standard error can improve for some coefficients.
In the example figure below an OLS estimator would assume that the variance is constant. As a result it would give the points near the origin the same weight as the points far from the origin. However, a robust regressor might give the points near the origin more weight because of the smaller variance. As a result that robust estimator will estimate a lower error for the intercept term. (And as we can see with our naked eye, the intercept is clearly around 0, but OLS will not see this because it assumes equal variance)

