OLS回归是组间回归
fixed effect是组内回归
因为回归系数符号相反也是正常的，可使用如下code进行模拟，下图的回归结果一目了然。

clear
set obs 5
gen panel_id = _n
expand 2
set seed 1234
by panel_id , sort: gen y = 4*panel_id - _n + 3 + rnormal(0, 0.5)
by panel_id: gen x = panel_id + _n
xtset panel_id
xtreg y x, fe
regress y x

//    GRAPH THE DATA TO SHOW WHAT'S HAPPENING
separate y, by(panel_id)
graph twoway connect y? x || lfit y x

原贴见：https://www.statalist.org/forums/forum/general-stata-discussion/general/1385133-ols-and-fixed-effect-s-coefficient-is-exactly-the-opposite