RE: st: Quantile Regression with FE

["Swanquist, Quinn Thomas" <qswanqui@utk.edu>]

Thank you Travis.

Some of you mentioned issues with FE in quantile regressions. Are the issues similar to the incidental parameters problem in logit/probit regressions with a small time series?

Quinn T. Swanquist
qswanqui@utk.edu


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Travis Smith
Sent: Tuesday, February 19, 2013 8:26 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Quantile Regression with FE

G.A.Hughes@ed.ac.uk wrote:
> By removing the fixed effects you would be estimating conditional median deviations from the mean/median values of the observed variables.

To clarify Gordon's point, which is the crux of the issue, when you demean, difference, or include an additive individual ``fixed'' effect in a quantile regression, the estimated coefficients will NOT have the same interpretation as the standard cross-sectional quantile regression.

This is not to say this approach is wrong, but many people interpret the estimation incorrectly.

See David Powell's recent work and references therein:
http://www.rand.org/pubs/working_papers/WR710-2.html

qswanqui@utk.edu wrote:
> Is there a more efficient way to estimate this similar to -xtreg-?

In the above article, you will see that Powell uses GMM. Under the Powell specification, ``fixed effects'' are never specified, which substantially reduces the number of parameters needed to identify the model (in his example, from 162 to 1).  There is no canned package for this approach and will require knowledge of GMM estimation using Stata's -gmm- command and possibly with use of the moment-evaluator program.  See Stata's reference manual for detailed examples.

Travis
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