Unconditional Quantile Regression with IV and fixed effects

[Johannes Carow]

Dear Stata Users,

I want to run an unconditional quantile regression in combination with IV and also include (e.g. firm) fixed effects.
First of all, large parts of the literature on quantile regression seem to refer only to conditional quantile regression which is mirrored by several Stata commands that are only available for conditional quantile regression. However, for many applications, I consider unconditional quantile regressions to be a more decent technique.

1. (Why) is it not possible to estimate this kind of regression by simply defining RIF (as given by Alexandra Killewald and Jonathan Bearak “Is the Motherhood Penalty Larger for Low-Wage Women? A Comment on QuantileRegression” (p. 353)) and then using the xtivreg – command to include the RIF as dependent variable in the instrumental variable estimation?
2. Which Stata command for the above regression (unconditional QReg with IV and FE) would you suggest? The following commands did not help me to solve the problem:
   • genqreg (installed with ssc install genqreg and ssc install moremata). As pointed out here: https://www.statalist.org/forums/for...-using-genqreg this command seems to have problems dealing with lots of dummies
   • qregpd. As noted above, I think that this command only offers conditional quantile regression, no unconditional quantile regressions.
   • ivqte would generally be a decent choice. However, the corresponding article in the Stata Journal (available here: https://journals.sagepub.com/doi/pdf...867X1001000309 ) underlines that this is only an appropriate command if the instrument is binary which does not apply to the instrument I use.

Thanks for your help!

[FernandoRios]

Hi Johannes,
welcome to the forum.
So let me make some comments on your post, in regards to what i know and what I have worked/been working on.
-. "large parts of the literature on quantile regression seem to refer only to conditional quantile regression"..."I consider unconditional quantile regressions to be a more decent technique."
While I am also inclined to use UQR more broadly, you shouldnt discard CQR for two reasons:
1. Many of the problems you describe have been analyzed in depth for quantile regressions.
2. It all depends on what your research question will be. Do you only care about changes in the whole distribution (UQR) or changes conditional on characteristics (CQR). Both can be useful, depending on the question.

- (Why) is it not possible to estimate this kind of regression by simply defining RIF (as given by Alexandra Killewald and Jonathan Bearak “Is the Motherhood Penalty Larger for Low-Wage Women? A Comment on QuantileRegression” (p. 353)) and then using the xtivreg – command to include the RIF as dependent variable in the instrumental variable estimation?

I think the better question is why no one has tried to see what happens with UQR when the assumption of exogeneity is lifted. If you read Firpo, Fortin and Lemieux (2009) "unconditional quantile regressions", they said that it was part of future research, to explore endogeneity and selection. I think the theory to justify solutions is harder that you may think, which is why is an open question.
Rhothe (2010) (https://doi.org/10.1016/j.econlet.2010.08.028) has written something about endogeneity, for a more generalized case. You may want to check that.
There is also the paper by Gosh(2016) https://papers.ssrn.com/sol3/papers....act_id=2765035 who explicitly addresses the issue for UQR.

My own sense of the problem, which i have verified only with limited simulations, is that if you treat endogeneity as a correlated but omitted variable problem, you can apply a control function (adding the residuals to the outcome model) approach to correct for endogeneity.

- Which Stata command for the above regression (unconditional QReg with IV and FE) would you suggest? :

If you apply a control function approach, you will have to estimate the whole system manually, in which case either xtrifreg or rifhdreg (install it with ssc install rif) will do what you need. I personally would suggest rifhdreg.

As an additional note: neither of the commands you mention, genqreg, qregpd or ivqte, estimate unconditional quantile regressions in the spirit of Firpo, Fortin and Lemieux (2009).

HTH
Fernando

[Johannes Carow]

Thank you, Fernando, for your very detailed reply! Your hint regarding the CF approach as well as the additional references you mentioned were quite helpful.

Best,
Johannes