Causal Inference -- 9/23 -- Heckman Selection Model

[@arkantos143]

Thanks for your great lectures! Can we extend the Heckman's selection model for continuous treatments and outcomes? Assume a joint distribution of treatment and outcome unobserved terms and estimate the two regressions (treatment and outcome) using maximum likelihood estimation method?

[@ben_elsner]

This might be possible but already with a binary treatment and IV, and with a binary treatment and continuous IV (or the other way around: binary IV and continuous treatment) things are really difficult to estimate without severe parametric restrictions. So while this may be possible in theory, it is difficult in practice.

[@alibagheri411]

Thanks a lot for this great lecture.
If a variable is involved both in the selection process and in the outcome, for example, a bank is funding loans for those who have a job, and those who have a job are more likely to pay their debts, what type of model should be used to measure the effect of having a job on paying out the loan?

[@ben_elsner]

You will need an instrument in the selection equation, i.e. a variable that determines having a job but not whether someone repays their debt. That's tricky, as is any IV approach.