Recentered influence function, Oaxaca-blinder decomposition and Heckman selection approach

[Aleksandra Anic]

Dear all,

First of all, Happy New Year.

I use the Firpo, Fortin and Lemieux methodology for decomposing the gender pay gap using recentered influence function. The methodology is presented in paper Firpo, S., Fortin, N., & Lemieux, T. (2018). Decomposing Wage Distributions Using Recentered Influence Function Regressions. Econometrics, 6(2), 28. https://doi.org/10.3390/econometrics6020028

The problem is that the method assumes that there is no selection effect, i.e. that the distribution of unobservables is the same across groups, i.e. males and females. Is it possible somehow to use that methodology when there is selection into employment which differs between genders? I would like to combine the FFL methodology with Heckman selection procedure. May I just put Inverse Mills Ratio as the explanatory variable? Is that a "legitimite" computation?

Thank you for your help.

Best wishes,
Aleksandra

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. You've posted 36 times previously, so you have probably heard this before.

I'm afraid an answer to your question would require an econometric extension to the Firpo et al paper. Indeed, what you are proposing would merit a full paper to improve the Firpo et al methodology. But, it is unlikely that anyone here can solve that problem sufficiently easily to answer your question.

[Valentina San Martino]

Aleksandra, I am working with the same approach and I have the same question. I am wondering how did you end up solving the issue. I've found this (quite recent ) paper: https://women.govt.nz/documents/empi...ap-new-zealand, apparently it is ok to just include the inverse mills ratio in the Oaxaca Blinder decomposition when using Recentered Influence Functions, but I am quite dubious because it is a new approach and I don't fully understand why this is correct or whether they are doing a different thing and I'm not quite getting it. I would appreciate any update in your research in this topic.

[FernandoRios]

Hi Valentina
I have been working quite extensively with RIFregressions and RIF decomposition methods over the last few months. I had the intention to add an extension to the package RIF with that feature, unfortunately there is no formal solution to the problem, at least not using RIF regressions.
Empirically, there is another paper that also suggests, like the one you describe, to simply add the IMR to the outcome equation (see https://pdfs.semanticscholar.org/ed5...4bab6f7af9.pdf). Specifically, this paper suggests adding the IMR and its square, where the IMR comes from a nonparametric model. Unfortunately this is not quite correct, specially when working with OB type of decompositions.
In contrast with the standard Heckman selection model, where its possible to recover the latent conditional mean of the outcome, you cannot recover "latent" unconditional quantiles, unless you impose some assumptions about the distribution function of the overall wage distribution, and how it is affected due to sample selection.

One option that you could use is to use conditional quantile regressions including sample selection, following, for example, this paper :https://www.cemfi.es/~arellano/selec...-ecma-2017.pdf
And use that to make assessments about unconditional quantiles. As far as I know, except for the user written command -mmsel- (which i think you already tried), there is no implementation in Stata.
HTH
Fernando