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Re: st: Quantile regression: determine to which quantile an individual belongs


From   Alex Olssen <alex.olssen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Quantile regression: determine to which quantile an individual belongs
Date   Thu, 18 Apr 2013 09:34:37 +1000

Dear Maria,

You should carefully consider whether or not you want to include sector and industry in your regression. In particular, I suggest you consult Section 3.2.3 Bad Controls in Angrist and Pishke's mostly harmless econometrics.

The problem is that job sector and industry may be endogenous to gender.

If you want your regression to tell you about the causal effect of being female on wages, then you are implicitly relying on a selection on observables story. A lot of people are going to find this hard to buy. However, including sector and industry does not make the selection on observables assumption more likely to hold. Furthermore, it complicates the interpretation of the coefficients; they probably don't mean what you want them to mean.

Best,
Alex

On 17/04/13 9:09 PM, Maria Juul Hansen wrote:
Dear list members

I am using –sqreg- in Stata 12.0.
I run a quantile regression on a cross-section data set containing
individuals from the Danish labor market aged 40-55.
My analysis should try to detect whether there is an unexplained gender wage
gap in my sample (a negative coefficient on my gender dummy). My
LHS-variable is log(wage).
I divide my control variables into 2 groups (see below) and start by
controlling for group 1. After having run my regression on the variables
from group 1, I add group 2.
Group 1: experience, tenure and education.
Group 2: sector, industry, geography and other variables specific to the
job.

After having controlled for group 2 variables, the gender wage gap seems to
increase at the median compared to the gap estimated in the model that only
includes group 1 variables.
Therefore I would like to find out why this is so by investigating whether
women (at the median) primarily work in that industry, geographic region
etc. that pays the highest wages.
In order to do this, I have considered obtaining the residuals for each
individual. Then I would find the quantiles of the residuals. By comparing
the residual of each individual with the quantiles just defined, I determine
which quantile each individual belongs to.
In that way I hope to be able to say what characterizes the women belonging
to the median.

Do any of you know whether the residuals can be used in this way for
defining the quantile each individual belongs to? References to work dealing
with this issue would be highly appreciated.

I thank you in advance!

Best regards,
Maria



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