A Simple Question about Instrumental Variables

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Article #744

#744

From: Priyabroto
Date: Wed, 16 Dec 1992 01:30

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Hi,

I had a small question:

Let Y = Xb + u   (in matrix notation)

such that Cov(X,u) is not equal to zero.

Now, we use Z as an instrumental variable where:

Cov(X,Z) is not equal to zero but,
Cov(Z,u) is equal to zero.

Then, WHY is it that b hat(instr. var) = (Z'X)inverse * Z'y?

As we know b hat = (X'X)inverse * X'y.

Would really appreciate any help.

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From: bubai@matt.ksu.ksu.edu (Priyabroto)
Newsgroups: sci.math.stat
Subject: A Simple Question about Instrumental Variables
Date: 15 Dec 1992 19:30:38 -0600
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