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st: alternative specification for Oaxaca decomposition?


From   "Akresh, Ilana Redstone" <redstone@illinois.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: alternative specification for Oaxaca decomposition?
Date   Sun, 31 May 2009 18:46:02 -0500

Hello,

I have a paper where I carried out a Oaxaca decomposition using the following code:

reg y x if group == 1
predict yhat
sum yhat if group == 2
scalar a = r(mean)

sum y if group == 1 
scalar meany1 = r(mean)
sum y if group == 2
scalar meany2 = r(mean)
scalar fractionduetodiscrim = (a - meany2) / (meany1 - meany2)
scalar list fractionduetodiscrim

This should then correspond to the equation:

ybarDIS - ybarADV = [(xbarDIS - xbarADV)BetaDIS] + [xbarADV(BetaDIS - BetaADV)]

Where DIS indicates the disadvantaged group and ADV indicates the advantaged group. 

-----------------------------

**However, I would like to know how to calculate the decomposition as:

Yadv - Ydadv = <beta>*(Xadv - Xdadv) + Xadv(<beta>dadv - <beta>*) + Xdadv (<beta>* - <beta>adv) 

In the case directly above, <beta>* should be a vector containing the weighted averages of the 'adv' and 'dadv' regression coefficients, with the proportion of 'adv' and 'dadv' in the sample as the relevant weights. The first component on the right-hand side is the productivity advantage of the 'adv' group over the 'dadv' group in the absence of discrimination. The second term is the 'adv advantage' or the amount by which 'adv' are overcompensated relative to a discrimination-free setting, and the last term is the 'dadv disadvantage' or the amount by which 'dadv' is paid less than the wage that would prevail in the absence of discrimination. 

However, I am totally unclear on how to do this in Stata - in other words, what would be the code to get me there?  Advice, please?

------------------------
Ilana Redstone Akresh 
Assistant Professor 
Department of Sociology 
University of Illinois at Urbana-Champaign 
Email: redstone@illinois.edu 
Web: https://netfiles.uiuc.edu/redstone/www




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