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Re: st: puzzling semi-elasticity from margins
From
Austin Nichols <[email protected]>
To
"[email protected]" <[email protected]>
Subject
Re: st: puzzling semi-elasticity from margins
Date
Thu, 16 Jan 2014 14:41:17 -0500
Dimitriy V. Masterov <[email protected]>:
You can't really assess dy/dx because your regression is not a model
of how y changes with x but how the conditional mean of y changes with
x. So you can assess
dE[y|x]/dx
assuming you have a good model of the conditional mean in your
regression. Then the semielasticity eydx would be
dE[y|x]/dx * (1/E[y|x]).
Make sense?
On Thu, Jan 16, 2014 at 2:01 PM, Dimitriy V. Masterov
<[email protected]> wrote:
> I was under the impression that eydx corresponds to (dy/dx)*(1/y).
> There's an example of on p. 1169 of the Stata 13 manual where for obs
> 5, dy/dx = 0.5, y = 15, and x = 30, so eydx is 0.0333333. My
> assumption was that margins with this option would calculate the
> average over all the observations. That does not seem to be the case
> in this simple example:
>
> sysuse auto
> reg price mpg
> margins, eydx(*)
> gen double me = _b[mpg]*(1/price)
> sum me
> predict phat, xb
> gen double me2 = _b[mpg]*(1/phat)
> sum me2
>
> margins, eydx gives -.0421593.
> sum me gives -.0451027
> sum me2 yields -.0421593
>
> The version where I divide by the predicted price rather than the
> actual price for each observation seems to match the margins output.
> What am I missing here?
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