st: RE: ivreg2 weak-id statistic and quadratic terms

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

Hi Miroslav, hi all.

I've checked this with the toy auto dataset.  I can replicate this
behaviour.

Miroslav - either before or after rescaling your covariates, do the
estimated coefficients vary hugely in scale?

In my toy auto dataset example, I am pretty sure that it is driven by
scaling problems.  For example, after

sysuse auto, clear
gen double weight2=weight^2
ivreg2 price (mpg=turn) weight weight2

gives a large weak ID stat of 11.5.  But there are big scaling problems
in the first-stage and main estimations, with coeffs that are something
like a factor of 10^8 different in magnitude.

If I estimate and just partial out the constant,

ivreg2 price (mpg=turn) weight weight2, partial(_cons)

the ill-conditioning is less pronounced and I get a weak ID stat of
0.73.

If I partial out all the exogenous covariates,

ivreg2 price (mpg=turn) weight weight2, partial(weight weight2)

the ill-conditioning is gone and I again get a weak ID stat of 0.73.

I will investigate further and will report back to the list if I find
anything more.  It may be that -ivreg2- could handle these cases more
robustly.

--Mark (ivreg2 coauthor)

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Miros Lav
> Sent: 20 February 2012 21:25
> To: statalist@hsphsun2.harvard.edu
> Subject: st: ivreg2 weak-id statistic and quadratic terms
> 
> Dear all,
> 
> I am using ivreg2 to estimate a model where a control 
> variable enters with a quadratic term. A simplified version 
> of the command is as follows
> 
> ivreg2 y   (a=instrument)  x x^2, r cluster(id).
> 
> Estimating this model results in a very large 
> Kleinbergen-Paap weak-id F statistic.
> 
> However, generating z=x/1000 and z^2=z*z and estimating the model
> 
> ivreg2 y   (a=instrument)  z z^2, r cluster(id)
> 
> results in a very low Kleinbergen-Paap weak-id F statistic.
> 
> (The z-statistics and significance levels in the first and 
> second stage regressions are the same as in the previous model.)
> 
> Does anyone have an idea why these two equivalent models 
> result in very different Kleinbergen-Paap weak-id F statistic?
> 
> Thanks for your help!
> 
> Miroslav
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