Confusing Decomposition output for the explained component using oaxaca and mvdcmp

[Sunga Kalemba]

Good day,

I am using decomposing analysis to run the following command on individual level data in Stata version 15.1.

oaxaca move normalize(b.age1624 age2534 age3544 age4554 age55over) normalize(b.male female) normalize(b.ausborn migrant ) normalize(b.married divorced nvmarried widowsep) normalize(b.degree nodegree ) normalize(b.ownerbuyer renters ) normalize(b.notinLF inLF ) normalize(b.noduoinc duoinc), by( svyear) pooled logit

I have created dummies for all my variables. The summary statistics are OK and as excepted. So are the odds ratios. But the coefficient for the explained component are a bit confusing as you can see. It seems the effects are duplicates for each of the vars that are paired eg, male and female ausborn and foreign, degree and no degree, inLf and noiinLF, and duoinc noduoinc. But not for the variables that are more than 2 categories such as age categories and married, divorced, nvmaried an widowsep.

explained	Coef.	Std. Err	z	P>z	[95% Conf.	Interval]
age1624	-0.00011	1.55E-05	-7.14	0	-0.00014	-8E-05
age2534	-0.00011	1.67E-05	-6.67	0	-0.00014	-7.9E-05
age3544	-1.3E-05	1.31E-05	-1	0.317	-3.9E-05	1.26E-05
age4554	-3.21E-07	5.38E-06	-0.06	0.952	-1.1E-05	1.02E-05
age55over	-0.00043	7.22E-05	-5.93	0	-0.00057	-0.00029
male	-4.49E-07	7.25E-07	-0.62	0.536	-1.87E-06	9.73E-07
female	-4.49E-07	7.25E-07	-0.62	0.536	-1.87E-06	9.73E-07
ausborn	-3.2E-05	9.34E-06	-3.44	0.001	-5E-05	-1.4E-05
migrant	-3.2E-05	9.34E-06	-3.44	0.001	-5E-05	-1.4E-05
married	-3.8E-05	2.21E-05	-1.69	0.091	-8.1E-05	5.92E-06
divorced	1.27E-05	1.26E-05	1.01	0.314	-1.2E-05	3.74E-05
nvmarried	-4E-05	1.74E-05	-2.31	0.021	-7.5E-05	-6.15E-06
widowsep	3.75E-06	6.95E-06	0.54	0.59	-9.88E-06	1.74E-05
degree	0.000385	6.17E-05	6.23	0	0.000264	0.000506
nodegree	0.000385	6.17E-05	6.23	0	0.000264	0.000506
ownerbuyer	0.000175	0.000026	6.75	0	0.000124	0.000226
renters	0.000175	0.000026	6.75	0	0.000124	0.000226
notinLF	1.64E-05	5.91E-06	2.78	0.005	4.86E-06	0.000028
inLF	1.64E-05	5.91E-06	2.78	0.005	4.86E-06	0.000028
noduoinc	-5.7E-05	9.51E-06	-5.98	0	-7.6E-05	-3.8E-05
duoinc	-5.7E-05	9.51E-06	-5.98	0	-7.6E-05	-3.8E-05

This doesn't repeat in the unexplained component as you can see

unexplained	Coef.	Std. Err	z	P>z	[95% Conf.	Interval]
age1624	-0.00052	0.000567	-0.92	0.356	-0.00164	0.000588
age2534	-2.7E-05	0.000438	-0.06	0.952	-0.00088	0.000831
age3544	-0.00016	0.000514	-0.31	0.76	-0.00116	0.00085
age4554	-0.00075	0.000647	-1.16	0.248	-0.00202	0.00052
age55over	0.002367	0.001627	1.46	0.146	-0.00082	0.005555
male	-0.00057	0.000667	-0.86	0.389	-0.00188	0.000734
female	0.000609	0.000707	0.86	0.389	-0.00078	0.001995
ausborn	6.73E-05	0.001059	0.06	0.949	-0.00201	0.002143
migrant	-1.9E-05	0.000422	-0.04	0.964	-0.00085	0.000808
married	-0.00069	0.001442	-0.48	0.633	-0.00351	0.002137
divorced	-1.42E-06	0.000283	-0.01	0.996	-0.00056	0.000553
nvmarried	-0.00031	0.000854	-0.36	0.72	-0.00198	0.001368
widowsep	0.000175	0.000335	0.52	0.601	-0.00048	0.000832
degree	0.000247	0.000263	0.94	0.348	-0.00027	0.000761
nodegree	-0.00143	0.001386	-1.03	0.304	-0.00414	0.001291
ownerbuyer	0.00335	0.002312	1.45	0.147	-0.00118	0.007881
renters	-0.00131	0.000906	-1.45	0.147	-0.00309	0.000461
notinLF	0.000959	0.000727	1.32	0.187	-0.00047	0.002383
inLF	-0.00184	0.00139	-1.33	0.185	-0.00457	0.000883
noduoinc	-0.00111	0.001449	-0.76	0.445	-0.00395	0.001733
duoinc	0.000456	0.000595	0.77	0.443	-0.00071	0.001622

I have tried using an alternative command

mvdcmp svyear, reverse normal(age1624 age2534 age3544 age4554 age55over| male female| ausborn migrant| divorced married nvmarried widowsep | non_student students| degree nodegree| ownerbuyer renters| inLF notinLF| noduoinc duoinc ): logit move age2534 age3544 age4554 age55over female migrant divorced nvmarried widowsep students degree renters inLF duoinc

and as you can see, i get similar results.

inters	Coef.	Std.err	z	P>z	[95% Conf.	Interval]	Pct.
age1624	-0.00011	2.08E-05	-5.48	0	-0.00015	-7.3316E-05	4.279
age2534	-0.00011	2.25E-05	-4.83	0	-0.00015	-6.4537E-05	4.07
age3544	-9.52E-06	1.71E-05	-0.56	0.577	-4.3E-05	0.000023915	0.35701
age4554	-3.64E-07	7.43E-08	-4.9	0	-5.10E-07	-2.19E-07	0.013652
age55over	-0.00038	8.75E-05	-4.33	0	-0.00055	-0.00020723	14.2
male	3.08E-07	9.05E-07	0.34	0.733	-1.47E-06	2.08E-06	-0.01156
female	3.08E-07	9.05E-07	0.34	0.733	-1.47E-06	2.08E-06	-0.01156
ausborn	-2.5E-05	1.18E-05	-2.14	0.032	-4.9E-05	-2.15E-06	0.95013
migrant	-2.5E-05	1.18E-05	-2.14	0.032	-4.9E-05	-2.15E-06	0.95013
divorced	9.71E-06	1.63E-05	0.6	0.551	-2.2E-05	0.000041621	-0.36401
married	-2.3E-05	2.73E-05	-0.83	0.405	-7.6E-05	0.000030706	0.85185
nvmarried	-3.9E-05	2.26E-05	-1.71	0.086	-8.3E-05	5.55E-06	1.4551
widowsep	-4.74E-07	9.15E-06	-0.05	0.959	-1.8E-05	0.000017458	0.01776
non_student	-9.14E-06	2.69E-06	-3.4	0.001	-1.4E-05	-3.88E-06	0.3428
students	-9.14E-06	2.69E-06	-3.4	0.001	-1.4E-05	-3.88E-06	0.3428
degree	0.000385	9.4E-05	4.09	0	0.0002	0.00056893	-14.423
nodegree	0.000385	9.4E-05	4.09	0	0.0002	0.00056893	-14.423
ownerbuyer	0.000152	2.9E-05	5.25	0	9.54E-05	0.00020929	-5.7122
renters	0.000152	2.9E-05	5.25	0	9.54E-05	0.00020929	-5.7122
inLF	1.62E-06	7.81E-06	0.21	0.835	-1.4E-05	0.000016934	-0.06089
notinLF	1.62E-06	7.81E-06	0.21	0.835	-1.4E-05	0.000016934	-0.06089
noduoinc	-5E-05	1.08E-05	-4.6	0	-7.1E-05	-2.8506E-05	1.8609
duoinc	-5E-05	1.08E-05	-4.6	0	-7.1E-05	-2.8506E-05	1.8609

I have tried separating out the variables to including more categories but then the model becomes insignificant.

What could i possibly be doing wrong?

Please help.

[FernandoRios]

Hi Sunganani,
I think there is nothing you are doing wrong perse. I replicated the issue you are having even with the simplest of the examples:

 use http://fmwww.bc.edu/RePEc/bocode/o/oaxaca.dta, clear
gen notmarried=1-married

.  oaxaca lnwage educ exper tenure normalize(married notmarried), by(female) w(0) first relax
(normalized: married notmarried)

Blinder-Oaxaca decomposition                    Number of obs     =      1,434
                                                  Model           =     linear
Group 1: female = 0                               N of obs 1      =        751
Group 2: female = 1                               N of obs 2      =        683

------------------------------------------------------------------------------
      lnwage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
overall      |
     group_1 |   3.440222   .0174934   196.66   0.000     3.405936    3.474508
     group_2 |   3.266761   .0218655   149.40   0.000     3.223906    3.309617
  difference |   .1734607   .0280021     6.19   0.000     .1185776    .2283439
   explained |   .0771106   .0160709     4.80   0.000     .0456122    .1086089
 unexplained |   .0963502    .027173     3.55   0.000     .0430921    .1496083
-------------+----------------------------------------------------------------
explained    |
        educ |   .0514117   .0122975     4.18   0.000     .0273092    .0755143
       exper |   .0257804   .0088749     2.90   0.004     .0083859    .0431749
      tenure |   .0098732   .0086464     1.14   0.254    -.0070735    .0268198
     married |  -.0049773   .0025346    -1.96   0.050     -.009945   -9.70e-06
  notmarried |  -.0049773   .0025346    -1.96   0.050     -.009945   -9.70e-06
-------------+----------------------------------------------------------------
unexplained  |
        educ |  -.1471334   .1242443    -1.18   0.236    -.3906478    .0963811
       exper |  -.0775717   .0467549    -1.66   0.097    -.1692096    .0140661
      tenure |   .0305542   .0365443     0.84   0.403    -.0410712    .1021797
     married |   .0844044   .0136654     6.18   0.000     .0576208    .1111881
  notmarried |   -.077299   .0125709    -6.15   0.000    -.1019375   -.0526604
       _cons |   .2833955   .1334567     2.12   0.034     .0218253    .5449658
------------------------------------------------------------------------------

I think the reason for the results is related to how exactly the normalization is being done.
Just to back up a bit. What you are facing here is a problem of dummy trap. In order to identify the detailed effect of all covariates in the analysis, one needs some assumptions (constraints) on the estimated coefficients. Knowing these coefficient constrains will give you the clue of why the results are puzzling.
That simply means that you may need to go back to Ben Jann's oaxaca paper, and the reference there in, to figure out how exactly the normalization is being done, if you want to explain why the results are as they are.
If knowing the blackbox of the methodology is beyond of what you want do do, then simply provide the aggregate values for the explained component. after all, you cannot explain how the outcome will change when (in the example above) the proportion of married increases keeping unmarried as constant, because both variables depend on each other.

Hope this helps.
Fernando

[Sunga Kalemba]

Thank you Fernando for the very important insight.