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# Re: st: level of measurement for instrumental variable

 From Partho Sarkar <[email protected]> To [email protected] Subject Re: st: level of measurement for instrumental variable Date Sat, 10 Sep 2011 18:33:23 +0530

```I am not very familiar with mixed models as such, and am responding
from first principles of statistics/econometrics.  By definition an
"instrument" for Z would have to be correlated with Z, so I would
think it must vary at the same level as Z.  And as for part 2 of your
question, I can't think of any way in which you could meaningfully use
the same instrument for 2 variables, if indeed that was the import of
your question.  I will leave further elucidation of this issue to
those with more insight in this particular topic.

Best
Partha Sarkar

On Sat, Sep 10, 2011 at 4:21 PM, Akresh, Ilana Redstone
<[email protected]> wrote:
> I saw on the Statalist website that statistics are an appropriate topic of discussion (in addition to direct questions on Stata). Thus, my questions:
>
> I am specifying the following multi-level regression:
>
> yhat = x1i  + x2i + z1j
>
> where x1 and x2 vary at the individual level, i, (the unit of analysis in my regression) and z1 varies at the census tract level, j
>
> [1] Since where someone lives (and therefore their census tract) is a choice variable and isn't random, I believe I need to instrument for z1. In that case, does my ideal instrument vary at the level j (the level of measurement of z) or at the level i (the level of the analysis)?
>
> [2] If I add z2j to the analysis (where z2 also varies at the tract level), would I need a separate instrument for z2?
>
> Thank you for your patience with this (probably very elementary) question.
>
> ----------------------------
> Ilana Redstone Akresh
> Department of Sociology
> University of Illinois at Urbana-Champaign
> Website: https://netfiles.uiuc.edu/redstone/www
> Email: [email protected]
>
>
>
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```