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Re: st: test difference in marginal effects for the same dummy variable, computed first as difference and then as derivative


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: test difference in marginal effects for the same dummy variable, computed first as difference and then as derivative
Date   Tue, 5 Mar 2013 10:18:57 +0100

> On Mon, Mar 4, 2013 at 3:21 PM, Luca Fumarco wrote:
>> I would like to test whether the difference between the marginal effects of a dummy varaible, obtained first by computing the difference
>> and then by taking the derivative, is statistically significant. I want to implement this test in order to justify the utilization of the derivative. The model I am suing is the probit model

Statistical testing involves a very specific logic: there is
uncertainty in a estimate because, and only because, you have drawn a
random sample from a population and have not looked at the entire
population. The test tries to quantify this uncertainty by imagining a
population in which a null hypothesis is true, and than compute the
probability of drawing a sample from that hypothetical population
which deviates from the null hypothesis at least as much as the
observed data.

What you want to do is compare two models (marginal effects as either
difference or derivatives) of your model (probit). Both are wrong as
they are models, so by definition simplifications of "reality"(*), and
a simplification is just another word for "wrong in some useful way".
So the real question is how to compare the usefulness of both models.
Statistical testing cannot help you with that; its logic is just not
relevant for what you intend to do.

Instead you should just look at both marginal effects and see if they
are different in a meaningful way.

Hope this helps,
Maarten

(*) "reality" is a bit weird in this context as marginal effects are
models of models. So in this case "reality" is the probit model, which
in turn is a model of your data.

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

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