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st: To: Statalist <statalist@hsphsun2.harvard.edu>

 From "Dimitriy V. Masterov" To undisclosed-recipients:; Subject st: To: Statalist Date Tue, 13 Nov 2012 17:55:43 -0800

```I am trying to make sense of the results of a Oxaca-Blinder
decomposition produced by Ben Jann's oaxaca command (version 4.0.5
from ssc). I have a binary outcome y, a single continuous explanatory
variable x (0-100), and a binary group indicator d:

oaxaca y x, by(d) probit nodetail

Blinder-Oaxaca decomposition                      Number of obs   =    2178524
Model           =     probit
Group 1: DElectronics_1 = 0                       N of obs 1      =    1612480
Group 2: DElectronics_1 = 1                       N of obs 2      =     566044

------------------------------------------------------------------------------
bbe_flag1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
overall      |
group_1 |   .0617275   .0001892   326.25   0.000     .0613567    .0620983
group_2 |   .0698966   .0003379   206.85   0.000     .0692343    .0705589
difference |  -.0081692   .0003873   -21.09   0.000    -.0089282   -.0074101
endowments |  -.0135059   .0001323  -102.10   0.000    -.0137651   -.0132466
coefficients |   .0024407   .0004099     5.95   0.000     .0016374     .003244
interaction |    .002896   .0001549    18.69   0.000     .0025924    .0031996
------------------------------------------------------------------------------

The rate for Group 2 is about 0.8 of a percent point higher. That can
be broken out as the sum:
(1) the difference due to different characteristics x (-1.35)
(2) the difference in the effect of x on y (+0.24)
(3) interaction (+0.3)

In the draft version of Yun's 2004 paper (link below), I only see two
terms that correspond to (1) and (2) above in the probit example. The
interaction seems to be a sort of residual. Where does it come from?

Finally, using the SJ version of Yun's mvdcmp command, also produces
only two terms. His difference due to coefficients seems to be the sum
of (2) and (3) from above.

DVM

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```