In my model, I regress wages by country-occupation on explanatory variables and country-occupation fixed effects, clustering standard errors at the country level. To automatically drop singletons and reduce computation time, I considered using the user-written program "reghdfe" by Sergio Correia instead of "xreg, fe" (although there is just a single fixed effect, namely the country-occupation identifier). As it should be, point estimates are identical when using both commands. However, standard errors are identical only if I do not cluster standard errors at the country level. With clustering, they are quite a bit smaller when using "reghdfe". Has anybody encountered this issue/ has an idea where the difference comes from?

In the "reghdfe" help-file and online discussions, I only found that xtreg, fe and reghdfe use the same degrees-of-freedom adjustment to account for the fact that my panel variable (country-occupation) is nested in my cluster variable (country)- hence this should not explain the difference.