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st: marginal effect after cmp - combining results from two equations


From   Guy Grossman <guygrossman1@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: marginal effect after cmp - combining results from two equations
Date   Mon, 13 Sep 2010 08:59:17 -0400

Dear Stata list members -

I am using Mac and Stata 10.1 to estimate a model that has a binary
outcome and a binary endogenous treatment indicator:

prob(Yij=1) =  bo + b1*Tj  + B*xlist1 + Q*xlist2 + eij + ej.  note
that Tj = v0 + v1 * Zj + epsilon j


Yij = the dependent variable is binary, for person i from group j
(takes values 0/1).

Zj = encouragement to take up one of two types of treatment - applied
at the group level j . Zj is binary: groups are either encouraged to
take up Zj=0 or Zj=1.

Tj = treatment take up - takes place at the group level j. Tj is
binary (Tj=0 or Tj =1). Take up rates are about 75% for both
treatments.

xlist1 = set of control variables at the individual level i

xlist1 = set of control variables at the group level j

The idea is to apply an encouragement research design, using Zj as an
instrumental variable for t.  I fitted the model with the user-written
-cmp- command:
cmp (y = t $xlist1 $xlist2) (t=z), ind($cmp_probit $cmp_probit) cluster (group)

My questions is how to calculate the partial (marginal) effect and
confidence intervals of t on the probability that Yij=1, given changes
in z (holding control variables at their means or medians)?

Your response would be highly appreciated!
Thanks!
Guy

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