An Oaxaca decomposition for nonlinear models

The widely used Oaxaca decomposition applies to linear models. Extending it to commonly used nonlinear models such as duration models is not straightforward. This paper shows that the original decomposition that uses a linear model can also be obtained by an application of the mean value theorem. By extension, this basis provides a means of obtaining a decomposition formula which applies to nonlinear models which are continuous functions. The detailed decomposition of the explained component is expressed in terms of what are usually referred to as marginal effects. Explicit formulae are provided for the decomposition of some nonlinear models commonly used in applied econometrics including binary choice, duration and Box-Cox models.