RE: st: Interaction Variables as Instruments

[Jessie C <jessiecoh@gmail.com>]

I am sorry but my notation was not fully explained.  The letters a, b,
and c are coefficients as are k, l, and m.

I hope the following explanation clarifies:

We can think of y as wages and x as schooling for ease of exposition.
Schooling is not exogenous as we know.  To instrument for schooling,
there is a policy that affected female schooling relative to male
schooling.  And it affected some women more than other women depending
on age and geography.  Let us call the gender, z_1.  Let us call the
policy measure, z_2.

So the first stage would be:
x = a*z_1 + b*z_2 + c*z_1*z_2 + e

where x is schooling, z_1 is a binary for gender, z_2 is the extent to
which your schooling is affected by the policy, and c is the parameter
that capture how much female schooling would be affected relative to
male schooling as a result of the policy.

The goal is then to estimate wages as a function of schooling, taking
advantage of this policy that affects female schooling relatively more
than male schooling for some women.
y = k*x + u is a minimum that I need.

z_1 should be a regressor and not an instrument, right?

Are both z_2 and z_1*z_2 the instruments?  Do they instrument for only
x?  Do I need to include x*z_1 as an regressor too?
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