Detailed decompositions in nonlinear models

Abstract

We propose a new approach for performing detailed decompositions of average outcome differentials when outcome models are nonlinear. The method can be flexibly applied to all generalized linear models, which are widely used in empirical research. The advantage over other approaches in the literature is that the effects of group-specific differences in covariate distributions are taken into account. At the same time, desirable features such as path independence are still satisfied. A simulation exercise demonstrates that our decomposition method produces more convincing results than existing methods.

Keywords:

• Oaxaca–Blinder
• detailed decomposition
• decomposition analysis
• generalized linear models

JEL Classification:

• C10
• C29
• C51

Acknowledgements

I am grateful to an anonymous referee, Michael Gerfin, Blaise Melly, Stefan Boes, Kaspar Wüthrich, Steven Stillman and various seminar participants for their helpful comments.

Notes

¹ Note that our decomposition approach does not depend on the choice of counterfactual.

² If all covariates are discrete, we define the contribution of covariate k as

(4)

³ The decomposition method is implemented in the STATA package glmdeco available on the author’s homepage.

⁴ Note that adding an error term does not affect the simulation results in a meaningful way because it only adds noise to the outcome model.