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st: ITT and TOT pvalues

From   Allyson Barnett <>
Subject   st: ITT and TOT pvalues
Date   Thu, 31 Jan 2013 15:20:15 -0500

I'm working on data from an RCT where a
lottery serves as an instrument for a program, and am thus running OLS
regressions to estimate the impact of the lottery, and IV regressions
to estimate the impact of the program.  There is a reasonably large sample
size- 12161 total of whom 6387 are selected for the lottery and 3803
get the program (2718 of whom won the lottery), and all are clustered
by hh and weighted with a sample weight variable.

One would expect that pvalues would be the same for
the IV and the OLS, as

"The TOT impact can be calculated as the ITT effect divided by the
treatment take-up rate (Bloom 1984, Angrist, Imbens and Rubin, 1996).
The standard error for the TOT effect is calculated the same way, by
dividing the ITT standard error by the treatment take-up rate, so that
the p-value for the ITT and TOT estimates will be the same under this

In most cases, they are the same up through the digits we are
concerned about (two sig figs after decimal), but in 2/18 vars they
are off by .001, and we can't figure out why.  Any ideas?  Could it
have something to do with the way Stata is calculating the pvalues
and/or some cutoff for estimating/approximating using t vs normal
distribution?  Is there an econometric reason?

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