Oaxaca Binder decomposition query

[Sherine Maui]

Hi all,

I am using the blinder Oaxaca decomposition method to study spousal decision making outcomes by different groups (wives with children versus wives with no children). My dataset is a repeated cross section with two survey rounds. I ran a threefold decomposition using the below code (My outcome variable is a decision making score, independent variables are various demographic predictors and the groups I’m comparing are women who have children with women who have no children):

oaxaca M1 deduc2 deduc3 deduc4 dreleduc2 dreleduc3 dses1 dses2 dses3 dses4 dsondum1, by (birthstat) detail

Which returned the below output:

Blinder-Oaxaca decomposition                    Number of obs     =      4,560

           1: birthstat = 0
           2: birthstat = 1

------------------------------------------------------------------------------
          M1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Differential |
Prediction_1 |  -.2463795   .0761519    -3.24   0.001    -.3956345   -.0971245
Prediction_2 |   .0185322   .0219223     0.85   0.398    -.0244347    .0614991
  Difference |  -.2649117   .0792446    -3.34   0.001    -.4202281   -.1095952
-------------+----------------------------------------------------------------
Endowments   |
      deduc2 |   .0002665    .005405     0.05   0.961    -.0103271    .0108602
      deduc3 |   .0004218   .0014309     0.29   0.768    -.0023828    .0032263
      deduc4 |   .0011656   .0084264     0.14   0.890    -.0153499     .017681
   dreleduc2 |   .0015314   .0021107     0.73   0.468    -.0026055    .0056683
   dreleduc3 |   .0047169   .0035385     1.33   0.183    -.0022185    .0116522
       dses1 |   .0070985   .0068327     1.04   0.299    -.0062932    .0204903
       dses2 |   .0101704   .0062187     1.64   0.102    -.0020181    .0223589
       dses3 |  -.0097885   .0058672    -1.67   0.095    -.0212881     .001711
       dses4 |   -.001965   .0026364    -0.75   0.456    -.0071323    .0032022
    dsondum1 |  -.1796086   .0486933    -3.69   0.000    -.2750457   -.0841715
       Total |  -.1659911   .0495968    -3.35   0.001    -.2631991   -.0687831
-------------+----------------------------------------------------------------
Coefficients |
      deduc2 |  -.1537282   .1858926    -0.83   0.408    -.5180711    .2106147
      deduc3 |  -.0243597   .0096307    -2.53   0.011    -.0432357   -.0054838
      deduc4 |   .0247731   .0669242     0.37   0.711    -.1063959    .1559421
   dreleduc2 |     .08938   .0493094     1.81   0.070    -.0072647    .1860247
   dreleduc3 |    .072015   .0559359     1.29   0.198    -.0376173    .1816474
       dses1 |  -.0126002   .0334791    -0.38   0.707    -.0782179    .0530176
       dses2 |   .0858618   .0497683     1.73   0.084    -.0116823    .1834059
       dses3 |   .0455632   .0556434     0.82   0.413    -.0634959    .1546222
       dses4 |   .0754199   .0555338     1.36   0.174    -.0334242    .1842641
    dsondum1 |  -.1796086   .0486933    -3.69   0.000    -.2750457   -.0841715
       _cons |  -.3289041   .3380435    -0.97   0.331    -.9914571     .333649
       Total |  -.3061878    .080242    -3.82   0.000    -.4634593   -.1489163
-------------+----------------------------------------------------------------
Interaction  |
      deduc2 |    .016801   .0213559     0.79   0.431    -.0250558    .0586578
      deduc3 |  -.0040486   .0131121    -0.31   0.757    -.0297478    .0216507
      deduc4 |   .0108323   .0294287     0.37   0.713    -.0468469    .0685115
   dreleduc2 |   .0081574   .0099035     0.82   0.410    -.0112531    .0275678
   dreleduc3 |  -.0117695   .0111562    -1.05   0.291    -.0336352    .0100963
       dses1 |   .0021806    .006144     0.35   0.723    -.0098614    .0142225
       dses2 |  -.0179886   .0143918    -1.25   0.211     -.046196    .0102189
       dses3 |   .0128592   .0165353     0.78   0.437    -.0195494    .0452677
       dses4 |   .0106348   .0112055     0.95   0.343    -.0113276    .0325973
    dsondum1 |   .1796086   .0486933     3.69   0.000     .0841715    .2750457
       Total |   .2072672   .0580637     3.57   0.000     .0934645    .3210699
------------------------------------------------------------------------------

.

From my understanding I have interpreted as:

The mean of the decisions score is -0.24 for women with no children and 0.02 for women with children, yielding a gap in women’s contribution to decisions of -0.26. The decrease of -0.16 indicates that differences in endowments account for just over half of the gap. The total for endowments is the total explained portion by my predictors and the total for coefficients is total unexplained portion.

My question is threefold:

1. If the unexplained portion (-0.30) is smaller than the difference (-0.26) does that mean that the unexplained portion is explaining less than the total observed gap (in spousal decision making)?
2. What does it mean if the unexplained portion is larger than the explained portion?
3. How would one interpret the results below “endowments” and “coefficients”, for instance how are the results for deduc4 (having a university degree where reference group is no education at all) under endowments different from the results under coefficients?

I have used the following literature to help aid my understanding of Oaxaca:

Jann, B., 2008. The Blinder-Oaxaca decomposition for linear regression models. The Stata Journal, 8(4), pp.453-479.

O’Donnell, O., Van Doorslaer, E., Wagstaff, A. and Lindelow, M., 2008. Explaining differences between groups: Oaxaca decomposition. Analysing health equity using household survey data. Inst Learn Resourc Ser, pp.147-157.

Thank you.

[Weiwen Ng]

Sherine,

I am familiar with the 2-way Oaxaca decomposition (the pooled option in this command). I'm not as familiar with the 3-way decomposition, and thus I'm not 100% sure that there is an unexplained portion in the 3-way decomposition.

That said, the answer to #3 is in page 469 of Jann (2008). For Endowments, this is the predicted change in the disparity if you gave the disadvantaged group (I am assuming this is childless mothers) the same levels of all the variables as the other group. Coefficients is the predicted change if you kept both groups' endowments identical, but you give the disadvantaged group the same effects of each coefficient as the other group. The interaction represents the interaction between the two (i.e. both groups have different endowments AND different coefficients). If you add the totals under endowments, coefficients, and interaction, you come up with the total disparity. (Whereas in the 2-way decomp, explained + unexplained = total disparity).

If the unexplained portion is larger than the explained portion this basically means what it says. I'm not sure how to further decompose that explanation. It is what it is. If you had theoretical reasons to expect most of the disparity to be explained by endowments, then I think that goes in the discussion section of your paper.

Last, it seems like you may have manually created and included dummy variables for some categorical variables, but in at least one case, there isn't an obvious reference category. My main collaborator (who is an economist, unlike me) used the -xi- prefix in his work, e.g.

oaxaca M1 i.deduc i.dreleduc i.dses i.dsondum1, by (birthstat) detail

Stata will handle all the dummy variable creation automatically and omit the first category (I believe you can specify an alternate base category if desired). Alternatively, I see that Jann included the -categorical- option in the -oaxaca- command to handle categorical variables. I'm not sure if the results would be equivalent. But I would urge you to use one of the two options.

[Sherine Maui]

Thank you Weiwen for taking the time to respond, you've thoroughly answered my questions.

Sherine