Oaxaca vs. mvdcmp commands for non-linear Blinder Oaxaca decomposition analyses with dummy variables

[Tiffany Kim]

Hi all,

In the mvdcmp Stata documentation, after normalization, the contributions of each category of a categorical variable (i.e., medu) is presented separately. In this case: 1) How should the individual contributions of each of the categories (e.g., medu1, medu2, medu3) be interpreted; 2) If I wanted to know the contribution of all categories of the categorical variable (i.e., contribution of education as a whole), would it be valid to sum the contributions from each of the categories (i.e., medu1 + medu2 + medu3); and 3) If I were to do 2, how would I interpret this?

In the oaxaca Stata documentation, after normalization, the contributions of a categorical variable (i.e., isco) are presented as one. In this case: 4) How are the contributions of the entire categorical variable being calculated? Is this the sum of contributions from each of the levels of the categorical variable?

Any help would be greatly appreciated. Thank you!

[Andrew Musau]

oaxaca and mvdcmp are from SSC (FAQ Advice #12). I do not use mvdcmp, but your questions can be answered by experimentation.

In the oaxaca Stata documentation, after normalization, the contributions of a categorical variable (i.e., isco) are presented as one. In this case: 4) How are the contributions of the entire categorical variable being calculated? Is this the sum of contributions from each of the levels of the categorical variable?

Consider this:

use http://fmwww.bc.edu/RePEc/bocode/h/homecomp.dta, clear

oaxaca homecomp female age (educ:hsgrad somecol college) ///
             (marstat:married prevmar) if white==1|black==1, by(black) ///
             logit pooled


oaxaca homecomp female age hsgrad somecol college ///
             (marstat:married prevmar) if white==1|black==1, by(black) ///
             logit pooled

lincom _b[explained:hsgrad]+ _b[explained:somecol] + _b[explained:college]   

Res.:

. oaxaca homecomp female age (educ:hsgrad somecol college) ///
>              (marstat:married prevmar) if white==1|black==1, by(black) ///
>              logit pooled

Blinder-Oaxaca decomposition                    Number of obs     =      1,969
                                                Model             =      logit
Group 1: black = 0                              N of obs 1        =      1,737
Group 2: black = 1                              N of obs 2        =        232

    explained: (X1 - X2) * b
  unexplained: X1 * (b1 - b) + X2 * (b - b2)
               with b from pooled model (including group dummy)

------------------------------------------------------------------------------
             |               Robust
    homecomp | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
overall      |
     group_1 |   .7322971   .0105765    69.24   0.000     .7115675    .7530267
     group_2 |   .4310345   .0324628    13.28   0.000     .3674086    .4946604
  difference |   .3012626   .0341423     8.82   0.000     .2343449    .3681802
   explained |   .0776741   .0125458     6.19   0.000     .0530848    .1022634
 unexplained |   .2235885   .0343375     6.51   0.000     .1562883    .2908887
-------------+----------------------------------------------------------------
explained    |
      female |  -.0026198   .0020091    -1.30   0.192    -.0065576    .0013179
         age |    .000233   .0018939     0.12   0.902    -.0034789    .0039449
        educ |   .0211536   .0066281     3.19   0.001     .0081627    .0341445
     marstat |   .0589074    .009818     6.00   0.000     .0396645    .0781502
-------------+----------------------------------------------------------------
unexplained  |
      female |   .0184261   .0389236     0.47   0.636    -.0578627    .0947149
         age |   .3196448   .1585697     2.02   0.044     .0088538    .6304357
        educ |  -.0390517   .0682921    -0.57   0.567    -.1729018    .0947983
     marstat |    .018174    .055918     0.33   0.745    -.0914232    .1277712
       _cons |  -.0936047   .1783961    -0.52   0.600    -.4432545    .2560452
------------------------------------------------------------------------------
educ: hsgrad somecol college
marstat: married prevmar

.
.
. oaxaca homecomp female age hsgrad somecol college ///
>              (marstat:married prevmar) if white==1|black==1, by(black) ///
>              logit pooled

Blinder-Oaxaca decomposition                    Number of obs     =      1,969
                                                Model             =      logit
Group 1: black = 0                              N of obs 1        =      1,737
Group 2: black = 1                              N of obs 2        =        232

    explained: (X1 - X2) * b
  unexplained: X1 * (b1 - b) + X2 * (b - b2)
               with b from pooled model (including group dummy)

------------------------------------------------------------------------------
             |               Robust
    homecomp | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
overall      |
     group_1 |   .7322971   .0105765    69.24   0.000     .7115675    .7530267
     group_2 |   .4310345   .0324628    13.28   0.000     .3674086    .4946604
  difference |   .3012626   .0341423     8.82   0.000     .2343449    .3681802
   explained |   .0776741   .0125458     6.19   0.000     .0530848    .1022634
 unexplained |   .2235885   .0343375     6.51   0.000     .1562883    .2908887
-------------+----------------------------------------------------------------
explained    |
      female |  -.0026198   .0020091    -1.30   0.192    -.0065576    .0013179
         age |    .000233   .0018939     0.12   0.902    -.0034789    .0039449
      hsgrad |   .0048713   .0033115     1.47   0.141    -.0016192    .0113617
     somecol |    .000355   .0014399     0.25   0.805    -.0024671    .0031771
     college |   .0159274   .0054179     2.94   0.003     .0053086    .0265462
     marstat |   .0589074    .009818     6.00   0.000     .0396645    .0781502
-------------+----------------------------------------------------------------
unexplained  |
      female |   .0184261   .0389236     0.47   0.636    -.0578627    .0947149
         age |   .3196448   .1585697     2.02   0.044     .0088538    .6304357
      hsgrad |  -.0410456   .0348716    -1.18   0.239    -.1093926    .0273015
     somecol |   .0185114   .0286759     0.65   0.519    -.0376924    .0747153
     college |  -.0165176   .0180242    -0.92   0.359    -.0518445    .0188093
     marstat |    .018174    .055918     0.33   0.745    -.0914232    .1277712
       _cons |  -.0936047   .1783961    -0.52   0.600    -.4432545    .2560452
------------------------------------------------------------------------------
marstat: married prevmar


. lincom _b[explained:hsgrad]+ _b[explained:somecol] + _b[explained:college]  

( 1)  [explained]hsgrad + [explained]somecol + [explained]college = 0

------------------------------------------------------------------------------
    homecomp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   .0211536   .0066281     3.19   0.001     .0081627    .0341445
------------------------------------------------------------------------------