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How does standardized mean decomposition differ from the simpler dummy variable regression? How does the average in mean outcomes or interpretation of results attributable to a particular treatment or dummy differ when standard decomposition is used, as opposed to dummy variable regression?

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In the Blinder Oaxaca decomposition, which is an econometric technique normally used to compare logged income, the interest is not just in the difference in the means, but also whether the difference is more due to:

  1. returns on human capital (so the coefficient values differ between the male and female equations), or
  2. human capital levels and other person-based attributes such as occupation (the X's), so there is some objective difference to income differentials.

The equation has been used historically to look at the gender pay gap. If the main reason for the difference is due to higher returns to one group (from the coefficients) then there is an argument that bias exists in the labour market. If the main reason for the difference is due to human capital, then there is less evidence for bias, but lower human capital levels for one group (e.g. lower education) may be suggestive of inequality of access to pathways that increase human capital.

If you run one regression for both groups, clearly you will have one overall average for the X values across the groups.

I published an article on this about 10 years ago, seems to be available here if you're interested.

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  • $\begingroup$ +1, nice, didn't know about this. So, am I correct to interpret this as Blinder Ozxaca vs. dummy variables is just apples and oranges? $\endgroup$ Feb 19, 2012 at 20:57
  • $\begingroup$ @gung yes, because they answer different hypotheses. $\endgroup$
    – Michelle
    Feb 19, 2012 at 21:43
  • $\begingroup$ I have a clarification, as I am trying to understand the model and how to interpret it, how do you interpret the results when the explained portion (due to endowments or endowments+ (coefficient x endowments)) comes out negative? This seems to happen depending on which 'variant' of the OB decomposition is used. The unexplained portion of the model seems clear enough. $\endgroup$
    – Victor
    Feb 20, 2012 at 15:35
  • $\begingroup$ When the explained portion is negative, your group has lower endowments (e.g. lower levels of education). It is called "explained" because you would expect lower returns for lower education, younger age, etc. It depends on which group you choose as the base, if you reverse your groups, you will get positive endowments. $\endgroup$
    – Michelle
    Feb 20, 2012 at 17:11
  • $\begingroup$ Oh, I see. Now I understand. Thank you, that made perfect sense. Thanks again for your help. :) $\endgroup$
    – Victor
    Feb 21, 2012 at 10:21

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