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In OLS you can reason to the direction of omitted variable bias by using the following formula:

OVB = [Omitted in long] x [Relationship between omitted and variable of interest]

My question: is there a similar method in 2sls? If I know that my instrument is not randomly assigned, how would I go about working out whether my uncontrolled 2sls coefficient is positively or negatively biased?

Hamza
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  • this may be of interest: http://stats.stackexchange.com/questions/187271/what-is-the-result-of-violated-exclusion-restrictions/187290#187290 – Christoph Hanck Jan 02 '17 at 16:03
  • I'm interested in the case where exclusion restriction is satisfied but random assignment is not i.e. where there is a confounder between the instrument and outcome. My understanding is that we can fix this by controlling for the confounder is the regression. If we are unable to do so, say due to lack of data, how would we go about reasoning the direction of bias in the uncontrolled 2sls regression. – Hamza Jan 02 '17 at 16:09

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