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This question is somewhat related to my previous question, see here: https://stats.stackexchange.com/questions/463221/why-when-do-attitudinal-scales-introduce-endogeneity

I wonder why a scale as an explanatory variable will always make a binary-dependent model endogenous?

This is what an editor told me along with rejecting my paper, and as long as I don't change it/acknowledge the possible endogeneity I cannot resubmit the paper.

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    $\begingroup$ Would it be possible to share the exact wording of the concern? $\endgroup$ – 1muflon1 May 15 at 18:28
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    $\begingroup$ Absolutely. It was: including a self-reported scale will induce endogeneity. $\endgroup$ – canIchangethis May 19 at 9:14
  • $\begingroup$ Oh okay now it makes sense. $\endgroup$ – 1muflon1 May 19 at 9:34
  • $\begingroup$ Really,why? I cannot see the sense yet. All variables (except spatial ones) are self reported even age and sex is... $\endgroup$ – canIchangethis May 19 at 9:35
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Based on the clarification in your comment this is not because you use scale variables but because the scale variable that you use is self-reported.

It is well known in literature that self-reporting leads to endogeneity. See for example: Lindeboom, M., & Kerkhofs, M. (2004). Subjective health measures, reporting errors and endogeneity in the relationship between health and work.

The reason why that is when people self-report some outcomes those are often affected by other unobservables that you do not include in your model which is a form of endogeneity. For example, studies that measure happiness show that the self reported happiness can vary depending on which time of the day/week/season you make the measurement.

Moreover, you can have also endogeneity in more narrow sense unemployed people can self-report that they cannot work as a rationalization of their unemployment status and hence you would get reversed causality where the unemployment actually causes the self-reported inability to work even though the person actually would be able to work as measured by objective measurable criteria (in a model where employment is regressed on self-reported ability).

So it’s not that there is any problem with having scale variables. For example, having some 1-10 index but rather the problem is that in your case the scale was made from self reported data.

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    $\begingroup$ great answer! Please could you give the full reference of Lindeboom, M., & Kerkhofs, M. (2004)? There seems to be a typo in the first sentence. $\endgroup$ – emeryville May 19 at 9:59
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    $\begingroup$ @emeryville I added hyperlink to ungated version of the paper $\endgroup$ – 1muflon1 May 19 at 10:03
  • $\begingroup$ the link doesn't work for me. I would like to comment in detail, but I would like to read the paper beforehand. Thank you. $\endgroup$ – canIchangethis May 19 at 12:09
  • $\begingroup$ @canIchangethis I updated the link it should work now - sorry I was logged into SSRN when I copied the link so it probably affected the URL hope that now it works $\endgroup$ – 1muflon1 May 19 at 12:16
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    $\begingroup$ I just found it, too here poseidon01.ssrn.com/… $\endgroup$ – canIchangethis May 19 at 12:17

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