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st: Another method of squaring an instrumental variable

From   Nir Regev <>
Subject   st: Another method of squaring an instrumental variable
Date   Sat, 5 Jun 2010 15:47:18 +0300

I am trying to estimate an equation of     y = x + x^2+u
x is endogenous (which makes x^2 endogenous too) and I have only one
instrumental variable z, which is a dummy.

On a regular case, I would square z and let z and z^2 be the
instrumentals, however, since z is a dummy this is irrelevant.

I believe it is possible to run the first stage of 2SLS where:
predict x_hat,
square x_hat
and run the second stage both on x_hat and x_hat^2.

I think this is a consistent estimate but my standard errors and
hypothesis tests will no doubt be miscalculated.

Has anyone ever heard of such a method and knows how to fix the standart errors?

Nir Regev
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