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I am quite confused about the forbidden regression problem, and unsure if I have one in this case.

Stage 1:

Probit Model: Prob(Distress) = Set of regressors that predict vulnerability.

The predicted value "Predicted Vulnerability" is a variable of interest in stage 2.

Stage 2:

Seemingly Unrelated Regression: DV = Predicted Vulnerability + Controls

Does having a probit first stage model with a SUR in the second stage a case of a forbidden regression? If so, what is the best solution for this?

It seems the discussion around forbidden regressions is centered around instrumental variable approaches. In my setting, the first stage model is mostly useful for just condensing multiple determinants of vulnerability into one predicted measure.

Kevin Smith
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  • I wonder if it's time for a *forbidden-regression* tag. – Glen_b Sep 28 '21 at 23:34
  • I checked for one! – Kevin Smith Sep 29 '21 at 00:02
  • Given your use of relevant tags, I expected you had. My comment was directed elsewhere (not least as a reminder to myself that if I found some spare time to consider whether I could contribute something to helping make one, such as posting about it to meta, or looking at how many old posts it should be added to; I'm definitely not someone who should write the tag info though). – Glen_b Sep 29 '21 at 00:17

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