Help with standard deviations of oaxaca command

[Felipe Salce]

Dear all,

I'm trying to replicate the results of the oaxaca9 command manually, but I have problems calculating the standard deviations since in no case do they give me the same as the direct command. All this prior to the classic Heckman corrections. I think my mistake is that the way he calculates the variances oaxaca9 is not the same as the one I do, but if that's the problem I do not know how to calculate the variances oaxaca.

My command of oaxaca9 is:

oaxaca9 lwage_h $controles2 if lwage_h>0, by(female) svy

On the other hand, the way in which I estimate the standard deviations of salary differences and the coefficients of Oaxaca is

mat K = (X1' * B1_var * X1) + (B1' * var1 * B1) + trace(var1 * B1_var)   + (X2' * B2_var * X2) + (B2' * var2 * B2) + trace(var2 * B2_var)
matrix oax[2,1] = sqrt(K[1,1]) matrix oax[3,1] = oax[1,1]/oax[2,1]  matrix L =  (X1-X2)' * B1_var * (X1-X2)+ B1' * (var1+var2) * B1
matrix oax[2,2] = sqrt(L[1,1]) matrix oax[3,2] = oax[1,2]/oax[2,2]  matrix M = X2' * (B1_var+B2_var)*X2  +  (B1-B2)'*var2*(B1-B2)
matrix oax[2,3] = sqrt(M[1,1]) matrix oax[3,3] = oax[1,3]/oax[2,3]  
matlist oax

where, B and B_var were obtained from:

global malelist "0 1"
 foreach sexo in $malelist {
svy: reg lwage_h $controles2 if female==`sexo' & lwage_h>0              
  if `sexo'==0 {      
        gen used = e(sample)==1      
          matrix B1 = e(b)                
matrix B1_var = e(V)  //matriz de varianzas y covarianzas      
          predict yhat1 if used==1 & female==0, xb        
        }          
      if `sexo'==1 {              
  replace used=1 if e(sample)==1        
        matrix B2 = e(b)            
    matrix B2_var = e(V) //matriz de varianzas y covarianzas      
          predict yhat2 if used==1 & female==1, xb          
      }
}
drop if used==0  
mat B1=B1'
mat B2=B2'
mat B1_v=B1_v'
mat B2_v=B2_v'

So, X and X_var (var1 and var2):

 global controles3 "educ exper exper2 rural publico used" // used at the end for the vector of 1 of the variables matrix
local nvar = 6 matrix X=J(`nvar',4,0)  
qui forval i=0/1 {
local a=1
foreach v in $controles3 {
local j=`i'+1
svy: mean `v' if female==`i'        
mat x_`a'_`j'=e(b)      
mat X[`a',`j']= x_`a'_`j'[1,1]  
mat v_`a'_`j'=e(V)    
mat X[`a',`j'+2]= v_`a'_`j'[1,1]        
local ++a      
  }    
  }      
mat X = X'        
matrix rownames X = hombre mujer hombre_var mujer_var      
matrix colnames X = $controles3 //
matrix X1 = J(`nvar',1,0)
matrix X2 = J(`nvar',1,0)
matrix X1_v = J(`nvar',1,0)
matrix X2_v = J(`nvar',1,0)
qui forval i=1/6 {  
mat X1[`i',1] = X[1,`i']
mat X2[`i',1] = X[2,`i']
mat X1_v[`i',1] = X[3,`i'] mat X2_v[`i',1] = X[4,`i'] }
 svy: mean $controles2 if female==0 &  lwage_h>0
mat var1=e(V)
svy: mean $controles2 if female==1 lwage_h>0
mat var2=e(V)

thank you very much in advance for your help dear community