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?

Yes they can be smaller than the standard variance estimates. The reason is that even in the case of linear models, robust standard errors are biased but consistent. Their variance estimates might be (severely) biased downwards due to this small-sample bias, see Imbens & Kolesar (2016, The Review of Economics and Statistics; ungated working paper version here):

Second, and this has been pointed out in the theoretical literature before [e.g. Chesher and Jewitt, 1987], without having been appreciated in the empirical literature, problems with the standard robust EHW and LZ variances and confidence intervals can be substantial even with moderately large samples (such as 50 units / clusters) if the distribution of the regressors is skewed.

Imbens, G. W., & Kolesar, M. (2016). Robust standard errors in small samples: Some practical advice. Review of Economics and Statistics, 98(4), 701-712.
