st: RE: First stage of panel IV

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Filippos,

You need to tell us more - what versions of software you are using, what
the actual output is (or the relevant pieces of the output), etc.

More comments below.

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Filippos Petroulakis
> Sent: Sunday, June 10, 2012 11:59 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: First stage of panel IV
> 
> Hi all,
> 
> I am running a panel first differences (fixed effects) model. 
> My regression is of the sort
> 
> y_it=b_0+b_1 x_it + b_k demographic_covariates + e_it
> 
> x_it is endogenous so I have an instrument z_it.
> 
> I essentially have 3 issues and I list them in descending 
> order of importance.
> 
> 1) xtivreg2 is running the first stage of x_it on z_it and 
> the exogenous demographic covariates as OLS instead of fixed 
> effects or first differences.

I doubt it very much (having programmed -xtivreg2-, I think I'm well
placed to say this!).  -xtivreg2- follows the standard procedure of
transforming the full set of variables used in the same say, i.e., the
within or between transformation is applied to all variables.

> I honestly do not know whether 
> this is due to theory but it seems to be very odd, especially 
> given the fixed effects is definitely the correct 
> specification for the model as a whole, and so I would think 
> it has to be the case for the first stage as well. I can do 
> the 2 stages manually and correct the errors using the 
> process outlined here 
> (http://www.stata.com/support/faqs/stat/ivreg.html) and I 
> presume the fact that I have a panel doesn't change much, but 
> my issue is basically whether this is the correct thing to do.
> 
> 2) xtivreg and xtivreg2 give me pretty different results, 
> which is due to the fact that xtivreg drops about half of the 
> observations in the first stage. I checked and the variable 
> that is causing the dropping (for whatever reason) is the 
> dependent variable. I am thus positive that xtivreg is the 
> wrong one but am still worried. Anyone knows why this happens?

Again, I doubt the problem is the one you suspect.  My guess is that
Most likely you are using different estimators, e.g., fixed effects with
-xtivreg2- and random effects with -xtivreg-.  But you need to show us
the output.

> 3) Finally, at some point I will need to include a further 
> two variables, call them w_it and q_it, which are surely 
> endogenous. I don't care about instrumenting for them as I am 
> not interested in a causal interpretation, but the problem is 
> that they are also endogenous to x_it. So my first stage will 
> be regression x_it on variables that are endogenous to itself 
> and to y_it. Is that an issue I should be concerned about?

This is confusing.  Do you mean that w_it and q_it are correlated with
x_it?  That's not a problem.  The key requirement is that in

y_it=b_0+b_1 x_it + b_k demographic_covariates + w_it + q_it + e_it ,

w_it and q_it should be uncorrelated with e_it.  If they are correlated,
then you have two options: (1) Add w and q to your list of endogenous
variables.  But as you say, you will need instruments for them.  And if
you aren't interested in a causal interpretation, then maybe you
shouldn't bother.  (2)  Instead of using w and q as regressors and
instrumenting them, insert the instruments as (exogenous) regressors.

HTH,
Mark

> Thank you very much in advance - answers to any or all of 
> those issues will be immensely appreciated.
> 
> Best,
> 
> Filippos Petroulakis 
> 
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