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st: Interpreting Oaxaca with Heckman


From   Carlos Eduardo Hernandez Castillo <cehc84@hotmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Interpreting Oaxaca with Heckman
Date   Fri, 13 Jun 2008 11:16:19 -0500

Hello everyone. "Oaxaca" by Ben Jann (ssc install oaxaca; http://repec.ethz.ch/rsc/ets/wpaper/jann_oaxaca.pdf) computes the the Blinder (1973)-Oaxaca (1973) decomposition and  allows the use of Heckit models. If both equations are estimated using "heckman", it deducts "the selection effects from the overall differential and then apply the standard decomposition formulas to this adjusted differential" (Jann, 2008; http://repec.ethz.ch/rsc/ets/wpaper/jann_oaxaca.pdf). As far as I understand, this is equivalent to equation (7) in Neuman & Oaxaca (2004; http://www.springerlink.com/content/x0403312676k0042/).


I am not sure if I am interpreting my results in a proper way. I am estimating a wage decomposition. Could you please tell me if I am interpreting my (partly unexpected) results properly?


If I do not take selection into account, I get:

. oaxaca ln_saltotal_hora escolaridad experpotencial experpotencial2 mujer, by(dummy_inm_lejos) svy weight(0)


Blinder-Oaxaca decomposition


Number of strata   =         1                  Number of obs      =      3258
Number of PSUs     =      3227                  Population size    =   2408211
                                                Design df          =      3226


           1: dummy_inm_lejos = 0
           2: dummy_inm_lejos = 1


------------------------------------------------------------------------------
             |             Linearized
             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Differential |
Prediction_1 |   8.157024   .0332043   245.66   0.000      8.09192    8.222128
Prediction_2 |   8.384579   .0794506   105.53   0.000       8.2288    8.540358
  Difference |  -.2275553     .08611    -2.64   0.008     -.396391   -.0587195
-------------+----------------------------------------------------------------
Decomposit~n |
   Explained |  -.0631618   .0686883    -0.92   0.358     -.197839    .0715153
 Unexplained |  -.1643935    .069404    -2.37   0.018    -.3004739    -.028313
------------------------------------------------------------------------------


If I take selection into account, I get:

. oaxaca ln_saltotal_hora escolaridad experpotencial experpotencial2 mujer, by(dummy_inm_lejos) svy weight(0) model1(heckman, select(unionli
> breocasado nummen6 mujconmen6)) model2(heckman, select(unionlibreocasado nummen6 mujconmen6))


Blinder-Oaxaca decomposition


Number of strata   =         1                  Number of obs      =      3258
Number of PSUs     =      3227                  Population size    =   2408211
                                                Design df          =      3226


           1: dummy_inm_lejos = 0
           2: dummy_inm_lejos = 1


------------------------------------------------------------------------------
             |             Linearized
             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Differential |
Prediction_1 |   7.343391   .1449762    50.65   0.000     7.059137    7.627646
Prediction_2 |   9.085916   .3827884    23.74   0.000     8.335383    9.836449
  Difference |  -1.742525   .4093227    -4.26   0.000    -2.545083   -.9399657
-------------+----------------------------------------------------------------
Decomposit~n |
   Explained |  -.0600035   .0693592    -0.87   0.387     -.195996     .075989
 Unexplained |  -1.682521   .4012326    -4.19   0.000    -2.469218   -.8958244
------------------------------------------------------------------------------


As can be seen, the differential grows from  -.2275553 to -1.742525 (which is huge, given that wage is measured in logs). Notice also that prediction_1 decreases, while prediction_2 increases. This is mostly explained by growth in the unexplained part, which grows from -.1643935 to -1.682521.


My interpretation is the following:


Group 1 estimated wage was biased upwards, while group 2 wage was biased downwards. Bias in group 1 can be explained in the "traditional" way: People who would receive lower wages are unlikely to work, because those wages are lower than their reservation wages. Bias in group 2 could be explained via reservation wages: reservation wages are higher (more than proportionally) for people with high wages: It's like if the income effect of wages were more important than the substitution effect for group 2, assuming everyone in that group has the same preferences.


Am I understanding the output properly?
What do you think about my interpretation?


Thanks in advance for your help.


Carlos Eduardo Hernandez
Colombia
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