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st: Power Computations with IV Regression

From   "Scott Winship" <>
To   <>
Subject   st: Power Computations with IV Regression
Date   Tue, 15 Feb 2005 09:55:46 -0500

I have a small dataset that I'd like to use to conduct a power analysis for
an IV regression analysis on a much larger dataset that I hope to obtain.
The Y I have in my current dataset isn't on the same scale as the Y I hope
to have data on, but I have all the relevant right-hand-side variables in my
current dataset.

My plan has been to use the IV variance formula, var(b-hat) =
var(e)*var(Z)/(n*cov(X,Z)^2), with my covariates partialled out of the
variance and covariance terms.  I can obtain the estimates of var(Z) and the
covariance term from my data (though part of my question regards the easiest
way to do so in Stata).  Am I correct that if my (future) Y will have mean 0
and SD 1, I can try out different values for R-squared -- translating them
into values of var(e) -- and then examine what n is needed to detect an
effect of b standard deviations or what b I can detect with an n of a given

If yes (and even if no), then I'm hoping for some help understanding the
mechanics of how Stata computes SEs in iv regression so I can conduct the
power analyses.  My equations are essentially:


If no (or maybe even if yes), any suggestions on how to conduct the power
analysis would be greatly appreciated.  I don't do much matrix algebra on my
own, but I can usually figure out what I need to from examples.  Thanks.

Scott Winship                        
Ph.D. Candidate in
Sociology & Social Policy
Harvard University

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