threefolder decomposition
R = {E(XA) − E(XB)}×βB + E(XB)×(βA − βB) + {E(XA) − E(XB)}×(βA − βB)
twofolder decomposition
R = {E(XA) − E(XB)}×β∗+ {E(XA)×(βA − β∗) + E(XB)×(β∗− βB)}
actually, you may use stata package, oaxaca
here is the article written by oaxaca developer,
The Blinder–Oaxaca decomposition for linear regression models
http://www.stata-journal.com/sjpdf.html?articlenum=st0151
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