RIF Oaxaca-Blinder Decomposition and Selection Bias

[Packard Otto]

Hello all.

am planning on using a RIF Oaxaca-Blinder model to evaluate for labor's impact on gendered wage dispersion for a paper. However, I preemptively ran the first step of the Heckman Model and the Inverse Mills Ratio suggests that there is selection bias for male and female workers in my data. Is it possible to account for selection bias in the final Oaxaca-Blinder model? My first thought was to include the Mills Ratio's in the model, but I doubt that is sound econometric implementation for this problem. Are there other alternatives that address the selection bias issue?

Thank you for your insight.

[FernandoRios]

Hi Packard
Unfortunately, there is no other approaches that I am aware off. There is one paper that suggests exactly what you describe, using a more flexible first stage (nonparemtric probit), and adding polynomials f the IMR. However this paper was more applied, without theoretical support for the implementation.
I know of another researcher (who I was in contact with) who was also planning a similar approach. After some back and forth, we agreed that empirically, such approach has some merits, but that it will be difficult to explain how is the IMR correcting for selection. And what is the impact of that selection in the model.
Before jumping into the application directly, I would suggest to start a conversation with other colleagues on the merits and problems of RIF regressions in this context. (you can email me as well for further discussion)
F