RE: st: RE: Testing for instrument relevance and overidentification when the endogeneous variable is used in interaction terms

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

Jason,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Jason Wichert
> Sent: 10 June 2013 19:29
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: Testing for instrument relevance and overidentification
> when the endogeneous variable is used in interaction terms
> 
> Mark,
> 
> Again, thanks much. Admittedly, I feel like I’m losing track of what is what
> myself, especially after finding two papers of prolific authors in my field
> dealing with a similar problem of endogenous interaction terms. Both papers
> seem to choose close relatives of the approaches we discussed, but with minor
> tweaks I’m still trying to make sense of. However, which is rather comforting to
> me, while one doesn’t report weak- or underidentification F-stats for the
> extended case with multiple endogenous interaction as well, the other paper
> also shows a sharp decline in F-stats from a “base case” that includes only one
> endogenous variable, to an extended case in which the endogenous variable is
> also included in interaction terms.
> 
> I’m currently working on summarizing everything discussed so far with what I
> believe to be potential pitfalls or issues of concern, so I’ll be back with a longer
> post maybe tomorrow or so.
> 
> On a different note, in an empirically unrelated paper I found a comment
> mentioning the OLS bias to be reduced when the endogenous variable is
> included in an interaction term with a continuous exogenous variable (as in my
> case). Unfortunately, the author cited an unpublished working paper on 2SLS as
> source for this comment, and I haven’t been able to get a hold of the working
> paper or its author, yet. Would you – or anybody else following this discussion
> and willing to chime in – by any chance know of any proof/literature regarding
> this statement or provide some intuition or anecdotal evidence?

Doesn't ring any bells for me (and seems implausible but that's just a first impression).

--Mark

> 
> Kind regards,
> Jason
> 
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