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# Re: st: How to compare coefficients from ols and quantile regressions

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: How to compare coefficients from ols and quantile regressions Date Wed, 28 Nov 2012 10:55:18 +0100

```On Wed, Nov 28, 2012 at 10:03 AM, Buchs M. wrote:
> We are interested in comparing the coefficients (based on the question whether the association between household emissions and hh characteristics differs for mean and high emissions). Many coefficients do in fact differ but we'd like to test whether they are significantly different.

It seems to me you can just reframe your question in terms of
comparing the effect of variables on a measure of central tendency and
the effects on the 75th percentile. Than you can use the median (50th
percentile) instead of the mean as your measure of central tendency,
and you can use -sqreg- to simultaneously estimate both regression and
-test- to test whether the effects are equal. Not only is this easier
to implement, but the to regression are conceptually similar, so are
substantively much easier to compare.

--- Jay Verkuilen wrote:
> There's no particularly good reason that a QR for the third quartile
> would be directly comparable to the OLS coefficients that I know of,

As long as the errors are homoskedatic the effects of explanatory
variables on any quantile should be the same as the effect on the
mean. I'll agree that that is not a very substantively interesting
relationship, but it is a relationship none the less.

*--------------------- begin example ----------------------
set seed 123456
drop _all
set obs 10000
gen x = rnormal()

// homoscedastic errors
gen y = 1 + .5*x + .5*rnormal()

// see the effect in linear regression
reg y x

// the constant changes but the effect of x is the
// same for all quantiles as the effect in -regress-
sqreg y x , q(10 25 50 75 90)

// heteroskedastic errors
replace y = 1 + .5*x + (.5 + 1/8*x)*rnormal()

// estimate regression,
// point estimates are still consistent
reg y x

// see that errors are heteroskedastic
rvfplot

// see that the effects of x for the different
// quantiles is different from the effect in -regress-
sqreg y x , q(10 25 50 75 90)
*---------------------- end example -----------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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