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

[Jason Wichert <jasonw8907@gmail.com>]

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unpublished working paper on 2SLS as source for this comment, and I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?

Kind regards,
Jason

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