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st: how to deal with two variables mutually determined variables with self-selectivity


From   "natalie chan" <natalie.channew@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: how to deal with two variables mutually determined variables with self-selectivity
Date   Sat, 26 Jul 2008 18:01:46 +0100

Dear Statalisters,

I wonder if any of you could help me on this.

I want to examine the impacts of two variables, say, variable A and
variable B, on variable C. Variable A and B are both subject to
self-selection problem. My proposed solution is this:

First step:
Estimate Probit model with A as the dependent variable, B and other
control variables as independent variable. obtain reversed mills ratio
1;
Similarly, Estimate Probit model with B as the dependent variable, A
and other control variables as independent variable. obtain reversed
mills ratio 2.

Second step:
estimate two equations separately, both with C as the dependent
variable, but one with B, reversed mills ratio 1 and other control
variables as indepdent variables, and another one with C, reversed
mills ratio 2 and other control variables as indepdent variables.

But I am not sure if this is right as someone could argue that A and B
should enter the equation of C simultaneously, rather than separately.
On the other hand, if I have both A and B in the equation of C, how
can I deal with the self-selection problem?

Or probably you have other suggestions?

Many thanks.

Natalie.
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