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I am working with an endogenous independent survey variable, $x$, which has a value range from 0 - 10, where 0 is always and 10 is never. Because the question pertains to wrongdoing, the answer to the question is very skewed and has a large concentration at 10 (see histogram). I am trying to evaluate the effect of $x$ on $y$.

$$ y = B_1x + X +u$$

I found an Instrumental Variable (IV) for $x$, called $z$, so for stage 1 I do:

$$ x = B_1z + X +u$$

using a tobit regression to account for the skewdness and censoring. And I use the predicted values for $x$ in stage 2.

$$ y = B_1x_-hat + X +u$$

Now the problem is that, the predicted values fofr $x-hat$ are way higher than 10, and even the mean is above ten, so they fall outside the censored range.

Now my question is, is this normal, is this okay? And if not, is there anything I can do?

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  • $\begingroup$ What does "IV" mean in this context? $\endgroup$
    – Bernhard
    Commented Dec 27, 2020 at 18:35
  • $\begingroup$ Sorry, Instrumental Variable. Made an edit. $\endgroup$
    – Tom
    Commented Dec 27, 2020 at 18:36
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    $\begingroup$ Predicting $y$ via strictly linear regression will never respect boundaries. You could compress the $y$ values to a 0-to-1 intervall by dividing them by 10 and then try beta regression or logit or another tobit regression to predict those transformed values between 0 and 1. ( cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf ) $\endgroup$
    – Bernhard
    Commented Dec 27, 2020 at 18:41
  • $\begingroup$ @Bernhard Thank you for your comment. It's definitely something to consider as a robustness test, but I'm not sure it would theoretically really be a valid alternative. Would it be an option to manually censor the predictions? $\endgroup$
    – Tom
    Commented Dec 27, 2020 at 20:45

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