Quantile regression and panel data

[Javier C]

Dear all!

I’m interested in the estimating the effect on an explanatory variable along the distribution (quantiles) of a dependent variable. I am aware that quantile regression will allow me to do so. However, the issue is that I have panel data and quantile regression is not suggested for panel data unless the number of years is large and tends to infinite (which is not my case).
Would you mind giving me suggestions how to look at the effect of an explanatory variable along the distribution of a dependent variable for panel data in Stata?
Thank you very much in advance,
j

[Joao Santos Silva]

Dear Javier,

Estimation of quantile regression with fixed effects is currently an area of intense research, and several new methods have been suggested recently. However, there is very little information on the performance of these estimators, and I would say that at the moment there is no established method to address this problem.

A standard thing that can always be done is to estimate pooled quantile regression and use clustered standard errors; this can be done with qreg2 (check the help file for the appropriate references). An alternative that is also popular is the use of the so called correlated random effects, as in Abrevaya and Dahl. Again, you should use clustered standard errors.

All the best,

Joao

[Isa Lina]

Dear Joao,
I have the same issue as Javier and I would ask you if I can compare quantile regression estimated with pooled ols (panel data) or I can't.
Thanks

[Blaise Melly]

In addition to the good comments of Joao, if you have enough time periods, you may want to consider the estimator suggested by Ivan Canay. It is very easy to implement in Stata: see here. One caveat is that the s.e. should take the first stage estimation into account. You could do that by bootstrapping the individuals and applying both stages together.
Note that this estimator is consistent only as T goes to infinity! I would not use it if you only have a few time periods.

[Joao Santos Silva]

Dear Isa,

You can indeed compare the results of pooled OLS with the results of pooled quantile regression.

As noted by Blaise Melly, if you have reasonably large T you can also use Canay's estimator, but that estimator imposes the restriction that the fixed effects are constant across quantiles. An alternative is the elegant method proposed in this recent paper by Galvão and Wang.

Best wishes,

Joao

[Isa Lina]

Thanks Mr Joao.
I would further know if I can implement pooled quantile regression in STATA or I shall instead use R. I am working on a set of panel data containing 100 listed companies over eleven years period to investigate the determinants of effective tax rates. My supervisor suggests me to estimate a fixed effect then a random effect model then to choose the appropriate model through a Hausman test. But i would to do more advanced analysis using advanced methods. So i want to know how can i test autocorrelation and heteroscedasticity problems and how can i correct them. Then, I propose in my robustness checks and additional tests to compare quantile regression estimators with OLS as the methodology of Armstrong et Al., (2015). Armstrong, Christopher S., et al. "Corporate governance, incentives, and tax avoidance." Journal of Accounting and Economics 60.1 (2015): 1-17..
I need your help.
Thanks.

[Joao Santos Silva]

Dear Isa,

You can do pooled quantile regression with Stata using the -qreg2- command. Anyway, I suggest that you follow the advice of your supervisor.

Best wishes,

Joao

[Isa Lina]

Thanks Mr Joao. The results are only reported with the median quantile, indeed i would to measure other quantile within the same regression. Would you give me the exact code to do this please.

[Joao Santos Silva]

Dear Isa,

Please see the help file, especially the examples.

Best wishes,

Joao

[saba kausar]

Dear Researchers,
I would like to know whether quantile regression with fixed effects and testing the fixed effect or random effect via the Hausman test is the same thing? As I am confused with fixed effect via hausman test and Quantile regression with fixed effect. Or might be there is some extension the Hausman test to the quantile regression in order to test for endogeneity at different quantiles of the outcome distribution. Waiting for valuable answer and suggestions.

Regards,

[Joao Santos Silva]

Dear saba kausar,

Generally, random effects are not used with quantile regression.

Best wishes,

Joao

[Jeff Wooldridge]

I agree with Joao that exploiting a random effects variance-covariance structure is not done with quantile regression. Unlike in the case of estimating mean effects, it's difficult to impose an RE structure. But there are other ways to implement correlated random effects approaches and use pooled estimation. In 2007 lecture notes with Imbens, "What's New in Econometrics?", I proposed using the Mundlak device -- add the time averages of the covariates -- and then use pooled quantile regression. Clearly this is an approximation, but it could be as good as anything. This suggestion also appears in Section 12.10 of the second edition of my MIT Press book, "Econometric Analysis of Cross Section and Panel Data," 2010.

Joao might also be interested to know that the 2007 lecture notes with Imbens and my 2010 book proposed what appears to be the same cluster-robust variance covariance matrix studied in Parente and Santos Silva (2016). I only considered the panel data case but, of course, the structure is the same.

Here's a link to the NBER lecture notes; I can't link my MIT Press book chapter ....

http://www.nber.org/WNE/lect_14_quantile.pdf

[Jeff Wooldridge]

Oh, and the nice thing about the Mundlak device -- where you should also include as many time-constant controls as you have, as well as time dummies -- is that you get a kind of robust Hausman test by jointly testing the time average. If they are significant, they should be included. If the model where estimated by OLS rather than quantile regression, the usual FE estimator would be obtained. That was my motivation for suggesting the Mundlak device in quantile regression.

[Joao Santos Silva]

Dear Jeff Wooldridge,

Thanks for pointing out your lecture notes. We were not aware of those, but we were aware that others had use that very intuitive estimator, and we provide some references. The thing is that we wanted to implement the estimator in Stata and could not find anywhere the proof of its consistency and thought that someone had to do that work; it is not glamorous but hopefully users will find it useful.

Best wishes and thanks again,

Joao

[Joao Santos Silva]

Dear All,

This is an old thread, so users finding it may be interested in the command xtqreg (available from SSC) which implements the FE quantile regression estimator suggested by

Machado, J.A.F. and Santos Silva, J.M.C. (2019), Quantiles via Moments, Journal of Econometrics, forthcoming.

Best wishes,

Joao