st: ivreg2 weak-id statistic and quadratic terms

[Miros Lav <ranjit.rosof.b189@googlemail.com>]

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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