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

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: How to compare coefficients from ols and quantile regressions Date Tue, 27 Nov 2012 17:38:19 +0100

```JVerkuilen (Gmail) <jvverkuilen@gmail.com> and Buchs M. <M.Buechs@soton.ac.uk>:

I think the poster is interested in comparing
dE(Y|X)/dX from OLS
to
dF_{.75}(Y|X)/dX from QR,
i.e. coefs, not individual predictions.

The trouble is the discontinuous nature of QR, and the lack of scores
and cluster-robust inference, which precludes use of -suest- and
related models.

I don't know about consistency of the bootstrap for comparisons across
effect on conditional means and conditional quantiles (calling
Stas...) but it is at least straightforward to implement:

sysuse auto, clear
g gpm=1/mpg
cap prog drop both
prog both, rclass
reg gpm weight
ret scalar ols=_b[weight]
qreg gpm weight, q(75)
ret scalar qr=_b[weight]
su gpm if e(sample), mean
assert r(N)==_N
eret clear
end
bs ols=r(ols) qr=r(qr):both
test _b[ols]=_b[qr]

On Tue, Nov 27, 2012 at 5:21 PM, JVerkuilen (Gmail)
<jvverkuilen@gmail.com> wrote:
> On Tue, Nov 27, 2012 at 9:54 AM, Buchs M. <M.Buechs@soton.ac.uk> wrote:
>> Hi all,
>>
>> I've run two regressions, one OLS and one quantile on the 75th percentile, using the same sample, dependent and independent variables (the dependent variable being household emissions). Now I'd like to test whether the coefficients for individual IVs from these two regressions are significantly different - is this possible and do you know how I could do this in STATA?>
>
> 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,
> but perhaps I'm wrong. Medians often are, as long as the error
> distribution is symmetric and doesn't have heavy tails. What you might
> want to try doing is generate meaningful comparison cases and compute
> the predicted 75th percentile from both regressions.

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