xtqreg and reghdfe

Hello,

My question can be summarized as... why does xtqreg and reghdfe produce similar results when my data set has large outliers on both ends?

When I just use 'reghdfe' with firm and year fixed effects, due to large outliers, the estimated coefficients do not make sense at all; they are way too big. Thus, I decided to estimate with a quantile regression with fixed effects so that the estimates are less sensitive to large outliers.

I understand that qregpd and xtqreg estimate very different models, thus, they should produce different estimates. When I use qregpd, the scale of estimates is sensible. However, when I use xtqreg, the scale of estimates looks very similar to ones produced by reghdfe. I am little bit confused because median and mean of my data set are very different, so I expected xtqreg to produce different results from reghdfe. Could anyone help me understand why this might be happening?

Thank you so much in advance!

Sincerely,
Soyoung