I am trying to measure wage differences between two types of firms. I am mostly interested in the way different individual characteristics are remunerated differently, which is the “return” or “unexplained” component of Oaxaca decomposition. I also tried to estimate it by regressing wages on all my independent variables, a dummy for the type of organization and interaction variables with the dummy for all my independent variables. I get different coefficients than the detailed “unexplained component” of Oaxaca but the level of significance seems to be the same.
So my question is: what is the difference between the 2 methods? And how do I interpret the Oaxaca detailed coefficients?
ISSUE: Oxaca-Blinder decomposition
DECOMPOSITION: Assume that we study tow groups: A group A and Group B. The data set of Group A is given by Ai: (a1, a2, ..., an) and Bi: (b1, b2, ..., bn). The difference of the means of the two groups is given by:
(1) ΔY* = Y*A - Y*B ... where * denotes mean value.
... which may be rewritten as:
(2) ΔY*= X*'AB^A - X*BB^B
In further decomposition, the term Δy* is rewritten as:
(4) ΔY* = D1 + D2 + D3
(4.1) D1 = (X*A - X*B)'B^B
(4.2) D2 = X*'B(B^A - B^B)
(4.3) D3 = (X*A - X*B)' (B^A - B^B)
WHAT IS THE DIFFERENCE BETWEEN THE TERMS IN THE DECOMPOSITION? The decomposition has separated the individual terms into D1, D2 and D3. Their meanings follow:
D1 is the endowment term. This is the contribution of differences in the explanatory variables across groups.
D2 is the coefficient. it answers the questions of how different are the groups? The coefficient tells us that the groups differs from one another by a factor of ...(the value of the coefficient).
D3 is the interaction. This measures the interaction across group differences among the explanatory variables and coefficients simultaneously.
REFERENCES: See attached articles.
Hi Nathalie
I think you should ignore Blinder-Oaxaca for the purposes of your research question. I would suggest that an endogenous switching model (movestay in STATA) would be more appropriate. In basic terms, the model estimates 2 separate equations for pay determination in firms of 2 types. You can then read the respective coefficients across the 2 types of firms to see what variables are important and the marginal effects of key variables in determining pay. But the really useful post-estimation test you can then do is take the characteristics of people in firm type 1 and impose them on firm type 2 (pretend they have moved job from a type 1 to type 2 firm). It then estimates their wages if they moved. You can do this also to make type 2 workers 'move' to a type 1 firm. This type of model is used widely to estimate union-non-union pay determination and the costs of not being in a union for un-unionised workers. Good luck.
Cheers, Marc
The Oaxaca decomposition is generally applied by running two separate regressions and using the results of one as a counterfactual for the outcome of the other. if instead of running two regressions you run a single regression with dummies everywhere (constants and interaction terms), this is equivalent to run the two regressions separately, and the results should be the same, provided that you apply the results for a value of the dummies (say all the coefficients corresponding to d=1) as counterfactuals for the other value (e.g. d=0).
Thank you very much for your help.
Paul, does this mean that D1 (which appears in Stata results as the "unexplained" part of the gap) is the same as an interaction term in a simple MCO regression?
Marc, thank you I will try "movestay"
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