Hi Users
I am trying to compute a threefold decomposition manually. I am using the non-discriminatory beta star coefficient using the Cotton and Nuemark method. As STATA's "oaxaca" command doesn't allow threefold with these weighting methods, I have to do it interactively. However, to ensure that I am doing it correctly, I tried "nldecompose," which produces decomposition in terms of Advantage and Disadvantage factors and does not match the coefficient and interactive factor that I have computed. Please check the steps. (Dummy data "zodel.dta" attached)
*Threefold OB with nuemark** (PART-A)
***********************
clear
use zodel
qui {
count if group == 0
local n0 = r(N)
count if group == 1
local n1 = r(N)
local ntotal = `n0' + `n1'
local w0 = `n0' / `ntotal'
local w1 = `n1' / `ntotal'
qui reg y x1 x2 x3 if group==0
matrix b_A = e(b)
qui reg y x1 x2 x3 if group==1
matrix b_B = e(b)
matrix b_star = 0.5*b_A+0.5*b_B
qui tabstat x1 x2 x3 cons if group==0, stat(mean) save
matrix X_A = r(StatTotal)'
qui tabstat x1 x2 x3 cons if group==1, stat(mean) save
matrix X_B = r(StatTotal)'
* Total difference
matrix total_diff = (b_A*X_A) - (b_B*X_B)
* Calculate the endowment effect (Explained part)
matrix endowment = b_star*(X_A-X_B)
* Calculate the coefficient effect (Unexplained part)-Disadv
matrix coefficient = (b_A- b_star)*X_A
* Calculate the interaction effect-Adv
matrix interaction = (b_star-b_B)*X_B
mat Z = total_diff\endowment\coefficient\interaction
noi mat list Z
}
However
nldecompose, by(group) threefold omega(neumark) : reg y x1 x2 x3
above produces the same results as the following syntax(s) (PART-B)
clear
use zodel
qui {
count if group == 0
local n0 = r(N)
count if group == 1
local n1 = r(N)
local ntotal = `n0' + `n1'
local w0 = `n0' / `ntotal'
local w1 = `n1' / `ntotal'
qui reg y x1 x2 x3 if group==0
matrix b_A = e(b)
qui reg y x1 x2 x3 if group==1
matrix b_B = e(b)
qui reg y x1 x2 x3
matrix b_star = e(b)
qui tabstat x1 x2 x3 cons if group==0, stat(mean) save
matrix X_A = r(StatTotal)'
qui tabstat x1 x2 x3 cons if group==1, stat(mean) save
matrix X_B = r(StatTotal)'
* Total difference
matrix total_diff = (b_A*X_A) - (b_B*X_B)
* Calculate the endowment effect (Explained part)
matrix endowment = b_star*(X_A-X_B)
* Calculate the coefficient effect (Unexplained part)-Disadv
matrix coefficient = (b_A- b_star)*X_A
* Calculate the interaction effect-Adv
matrix interaction = (b_star-b_B)*X_B
mat Z = total_diff\endowment\coefficient\interaction
noi mat list Z
}
H0: I guess the "nldecompose" doesn't split in terms of coefficient and interaction factor (or my formulation (part A) is correct)
I am trying to compute a threefold decomposition manually. I am using the non-discriminatory beta star coefficient using the Cotton and Nuemark method. As STATA's "oaxaca" command doesn't allow threefold with these weighting methods, I have to do it interactively. However, to ensure that I am doing it correctly, I tried "nldecompose," which produces decomposition in terms of Advantage and Disadvantage factors and does not match the coefficient and interactive factor that I have computed. Please check the steps. (Dummy data "zodel.dta" attached)
*Threefold OB with nuemark** (PART-A)
***********************
clear
use zodel
qui {
count if group == 0
local n0 = r(N)
count if group == 1
local n1 = r(N)
local ntotal = `n0' + `n1'
local w0 = `n0' / `ntotal'
local w1 = `n1' / `ntotal'
qui reg y x1 x2 x3 if group==0
matrix b_A = e(b)
qui reg y x1 x2 x3 if group==1
matrix b_B = e(b)
matrix b_star = 0.5*b_A+0.5*b_B
qui tabstat x1 x2 x3 cons if group==0, stat(mean) save
matrix X_A = r(StatTotal)'
qui tabstat x1 x2 x3 cons if group==1, stat(mean) save
matrix X_B = r(StatTotal)'
* Total difference
matrix total_diff = (b_A*X_A) - (b_B*X_B)
* Calculate the endowment effect (Explained part)
matrix endowment = b_star*(X_A-X_B)
* Calculate the coefficient effect (Unexplained part)-Disadv
matrix coefficient = (b_A- b_star)*X_A
* Calculate the interaction effect-Adv
matrix interaction = (b_star-b_B)*X_B
mat Z = total_diff\endowment\coefficient\interaction
noi mat list Z
}
However
nldecompose, by(group) threefold omega(neumark) : reg y x1 x2 x3
above produces the same results as the following syntax(s) (PART-B)
clear
use zodel
qui {
count if group == 0
local n0 = r(N)
count if group == 1
local n1 = r(N)
local ntotal = `n0' + `n1'
local w0 = `n0' / `ntotal'
local w1 = `n1' / `ntotal'
qui reg y x1 x2 x3 if group==0
matrix b_A = e(b)
qui reg y x1 x2 x3 if group==1
matrix b_B = e(b)
qui reg y x1 x2 x3
matrix b_star = e(b)
qui tabstat x1 x2 x3 cons if group==0, stat(mean) save
matrix X_A = r(StatTotal)'
qui tabstat x1 x2 x3 cons if group==1, stat(mean) save
matrix X_B = r(StatTotal)'
* Total difference
matrix total_diff = (b_A*X_A) - (b_B*X_B)
* Calculate the endowment effect (Explained part)
matrix endowment = b_star*(X_A-X_B)
* Calculate the coefficient effect (Unexplained part)-Disadv
matrix coefficient = (b_A- b_star)*X_A
* Calculate the interaction effect-Adv
matrix interaction = (b_star-b_B)*X_B
mat Z = total_diff\endowment\coefficient\interaction
noi mat list Z
}
H0: I guess the "nldecompose" doesn't split in terms of coefficient and interaction factor (or my formulation (part A) is correct)
