What are the necessary assumptions to use lag of an ordinal variable as instrument in 2SLS to deal with mesurement error?

16 June 2020 0 4K Report

I want to analyze the effect of an ordinal regressor (with 4 categories, such as self-reported health status or self-reported risk aversion) on a dependent variable.

Since these self-reported measures are prone to measurement error, I want to use lag of them as an instrument in 2SLS. But since they are ordinal (discrete) there need some assumptions. I already know one assumption which is "the measurement errors of these variables should be time-invariant".

Do I need other assumptions? Any reference or paper doing similar thing?

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