Exploiting information from path dependency in Oaxaca–Blinder decomposition procedures

Abstract

This article addressed the issue of path dependency in Oaxaca–Blinder decomposition procedures. It shows that obtaining different results from decompositions computed on different base models and population structures should not be considered as a limitation but as valuable information about the underlying discrimination processes. Illustration is provided for the evaluation of racial discrimination in health in South Africa for 1999.

Acknowledgements

The author is indebted to Cécile Charrasse-Pouélé for her help on the illustrative case presented in the last section of the article.

Notes

Discussions presented here for the simplest case (linearity, no selection bias, etc.) generalize to any specification. See for example Sakellariou (2004) for recent examples of the generalizations of the Oaxaca–Blinder approach to the use of quantile regressions.

Both evaluations can be derived from the econometric estimation of Equation 1.

In what follows the term discrimination is used for simplicity but Oaxaca–Blinder decompositions may be used to explain any type of differences in mean between two populations. See for example Juhn et al. (1993), Bourguignon et al. (2001) or Bourguignon et al. (2004) for decompositions of time variations (in these cases the term ‘discrimination effect’ may be replaced by ‘price’ or ‘market effect’).

Equation 2 may in turn imply that

is believed to have some ‘natural’ property if one wishes to run a perfect decomposition.

Another alternative would be to use Hirschberg and Slottje (2002) values of β* which maximize/minimize discrimination. We believe that both approaches are complementary but that the use of observed models provide a better direct interpretation of counterfactuals (see illustration below), since the bounds defined by Hirschberg and Slottje (2002) have no reason to remain within the scope of economic reality.

Decomposition results are based on an ordered probit specification for health status. For further details see Charasse-Pouélé and Fournier (2004).