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As Fernando said, xtqreg estimates quantile regressions for panel data and it, indeed, includes fixed effects. (See also mmqr, which implements the same estimator and allows fixed effects.) In contrast, qregpd estimates a very different model that does not include fixed effects.
If you want to estimate quantiles with fixed effects, I recommend you try xtqreg or mmqr, they should give you the same results, but have different functionalities.
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