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# FE: st: Interaction effects

 From frone@ria.buffalo.edu To statalist@hsphsun2.harvard.edu Subject FE: st: Interaction effects Date Mon, 14 Jun 2010 15:17:56 -0400

```> --- On Mon, 14/6/10, Lorenzo Ciari wrote:
> > I am estimating a probit model and my dependent variable is
> > entry (0-1) in a given market. I estimate the model using
> > form level data, so for each firm I observe whether it
> > enters or not a market (I have multiple markets): I want to
> > test whether entry depends on a given variable (call it
> > COMP) and see whether the effect of COMP on entry is
> > particularly strong for firsm with certain characteristics
> > (suppose the characteristics SIZE).
> >
> > 1)  Question 1: if I want to test the hipothesis that
> > COMP has no effect for values of SIZE lower that X, can I
> > create a dummy = 1 for firms with size<X and then
> > estimate a model with COMP, SIZE (continuous variable) and
> > the interaction between (COMP) and the dummy?

No.  The variable used to represent SIZE in the cross-product needs to be
the same as that used for the lower order terms.  The cross-product is not
an interaction until the constituent variables are partialled out.  So the
lower order SIZE should be the same as that used to compute the
cross-product.
So you could estimate:

COMP, SIZE (continuous variable) and the interaction between COMP and SIZE
(continuous)

or

COMP, SIZE (dummy) and the interaction between COMP and SIZE (dummy)

But if you have a continuous measure of SIZE, the first approach is
preferable.

> >Can I
> > interpret the interaction coefficient as in OLS (I wouldn't
> > know how to use AI-Norton inteff command within this
> > framework, as I do not interact SIZE with COMP, but the new
> > created dummy....

Greene addresses the suggestion by Ai & Norton and, in contrast to Ai &
Norton, would suggest yes.  Greene argues that hypothesis tests (about
aspects of the model specifications. Partial effects are neither
coefficients nor elements of the specification of the model. They are
implications of the specified and estimated model."  Then the interaction
can be graphically portrayed in a variety of ways, including predicted
probabilities.  A problem I've had with the Ai & Norton approach is that
they fail to demonstrate how their plots have any useful substantive
interpretation regarding the "form" of an interaction between predictors.
Understanding the form (shape) of the interaction is much more important
than merely knowing whether or not it is significantly different from
zero.  This is also discussed by Greene--see:

http://w4.stern.nyu.edu/economics/docs/workingpapers/2009/Interaction-Terms-in-Nonlinear-Models.pdf

Also take a look at:

Mike Frone

****************************************************************
Michael R. Frone, Ph.D.
Senior Research Scientist
State University of New York at Buffalo
1021 Main Street
Buffalo, New York 14203

Office:    716-887-2519
Fax:        716-887-2477
E-mail:     frone@ria.buffalo.edu
Internet: http://www.ria.buffalo.edu/profiles/frone.html
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