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st: Marginal effects of probit model with an interaction term only

From   Richard Lo <[email protected]>
To   "[email protected]" <[email protected]>
Subject   st: Marginal effects of probit model with an interaction term only
Date   Thu, 27 Apr 2006 23:48:10 +0100 (BST)

Dear Statalist members,

I am estimating a probit model with interaction terms.
For simplicity, assume the probit model takes the
following formulation.
E(y|x1, x2)=�(b0+b1*x1+b2*x2+b3*x1x2)
The FAQ in Stata website provides guidance and example
to calculate the marginal effects at the means of
x1,x2 and the interaction term x1x2. Due to the high
correlations among these regressors, I want to
consider a specification with only the interaction
term. Under this specification, the marginal effects
of x1 and x2 on the conditional mean function at the
means or at each observation can still be computed
following the same procedure, though b1 and b2 are set
to zeros ex ante. (See Norton, Wang and Ai (2004)).
Although the computed marginal effect and the standard
error varied for each observation, the z-statistics of
the marginal effects of x1 and x2 show no variation
and are equal to the value computed at the mean. I am
not sure whether there is any problem in calculating
the standard errors of these marginal effects, as x1
and x2 do not enter into the estimation. Could anyone
kindly advise whether predictnl or nlcom command will
produce the correct results using the delta method
under this setting.

Thank you in advance.

Richard Lo

Norton, E. C., Hua Wang and Chunrong Ai, 2004,
Computing Interaction Effects and Standard Errors in
Logit and Probit Models, The Stata Journal 4(2),

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