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st: Modeling proportion with endogenous treatment indicator


From   Guy Grossman <guygrossman1@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Modeling proportion with endogenous treatment indicator
Date   Fri, 10 Sep 2010 17:25:34 -0400

Dear Stata list -

I am using Stata 10.1 on Mac and am seeking advice about the best way
to fit the following model:

Yij = bo + b1 * Tj  + b2 * Ci + b3 * Cj + eij + ej

Tj = v0 + v1 * Zj + epsilon j, where...


Yij = the dependent variable is a proportion (0<Yij <1), for person i
from group j.

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 80% for both
treatments.

Ci = control variables at the individual level i

Cj = control variables at the group level j

The idea is to apply an encouragement research design, using Zj as an
instrumental variable for Tj.

Given the nature of the dependent variable (proportion), my question
is how is it best to fit the model in Stata. In the past I have used
the glm command with link(logic) and family (bin) to fit a model with
a dependent variable that was a proportion, but the independent
variables were all exogenous. Is there a way to fit a glm with an
endogenous independent variable? Is it possible to use treatreg with
DV which is a proportion?

I look forward for your astute recommendations.
Thanks!
Guy
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