st: Interpretation of Oaxaca decomposition results after re-transformation of log scale

[Vaidyanathan Ganapathy <vaidyang@usc.edu>]

Dear Statalisters,

I am performing an Oaxaca type decomposition to understand the
healthcare cost differences between two groups -  controls and
premature infants. Here is my specification:

. oaxaca lnallhccx2 tpcat2-tpcat6 bpdx2 chdx2 asthbrdx2 resinfxdx2
cnsdx2 motordx2 physdevdx2 nddx2 chrnic1 period, by(premie_cat) pooled
vce(cluster pcn) eform

The dependent variable is ln(healthcare costs) and the other variables
are covariates including poverty levels (tpcat2-tpcat6) and certain
medical diagnoses. Since the dependent variable is in log scale I used
the -eform option to exponentiate and report the predicted costs and
the decomposed cost differentials. While I am able to interpret the
predicted values for the two groups, I have some trouble in
interpreting the overall, explained and unexplained differences. Here
is the output -



Blinder-Oaxaca decomposition                      Number of obs   =     137972

        1: premie_cat = 0  (controls)
        2: premie_cat = 1   (premature infants)

                              (Std. Err. adjusted for 68994 clusters in pcn)
-------------------------------------------------------------------------------
           |               Robust
lnallhccx2 |     exp(b)   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
Differential  |
Prediction_1 |   348.9868   1.737476  1176.03   0.000      345.598    352.4089
Prediction_2 |    956.743   75.23525    87.28   0.000     820.0862    1116.172
Difference |   .3647655   .0287414   -12.80   0.000     .3125676    .4256803
--------------+----------------------------------------------------------------
Decomposition |
 Explained |   .5206098    .035001    -9.71   0.000     .4563368    .5939355
Unexplained |   .7006504   .0489067    -5.10   0.000     .6110629    .8033722
-------------------------------------------------------------------------------

Using simple math, it could be seen from the results in panel 1
(Differential) that healthcare costs among controls is only 36.47% of
that of healthcare costs among premature infants. This led me to the
following interpretation about the overall cost differential between
premature and control infants:  The healthcare cost among premature
infants increases by 174% of that of the costs among controls as
predicted by the group models. Is it correct to make this
interpretation?

The interpretation of the decomposition results (panel 2 above) - the
explained and unexplained components, doesn't seem to be that straight
forward.

Any help in understanding these difference estimates will be very helpful.

Thanks!
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