Is it possible to apply Heckman correction for the probability to pass an exam to compute students performance?

[Chiara Tasselli]

Good evening to everyone,
I have more cohorts of university students and I want to compute the effect of a policy on them (I have factual and counterfactual groups).

The dependent variable is a continuous numeric variable that correspond to exams mark. My question is how to treat students who fail their exams?

Is it possible to utilize data of students that didn't passed to apply the Heckman correction for the probability to pass the exam and then compute my model exclusively on those who have passed?
If not, how should I deal with inefficiencies?

Many thanks in advance.

[Jeff Wooldridge]

I’m not quite clear about the setup. Is the problem that for students who fail you don’t observe future performance at the university?

[Chiara Tasselli]

Dear Jeff,
many thank for your interest in my question.

I can observe future performance: but the crucial point is that I have no idea how to deal with students who fail the exam.
In Italy the scores of the pupils who pass goes from 18 to 30, meanwhile I have no idea of the score taken by those who did not pass (they may have taken 2 like 17 and I don't know). So I was thinking to run my regressions only on pupils who pass the exam and utilize data on failing students to apply Heckman correction, but i was wondering if it is possible or non sense.

And in the second case how should i treat insufficient marks? ( I was also thinking to insert a dummy variable which indicates whether the student has already attempted the exam before,
but I don't think it makes sense because:

i) there are two cases of students that repeat (those who have gone wrong and those who aim for a higher grade)
ii) students who repeat exam usually they are the ones that do the worst, but -at the same time- having already taken the exam should increase the chances of passing it

So I am in trouble with my research design and I don't know how to deal with failing students...

[FernandoRios]

Hi Chiara
Reading your setup again, perhaps you can treat that as a censored variable? (Tobit type model).
After all, it is not that you know nothing about those student's grades. What you know is that they fail. thus their grade is lower than 18.
(17 or lower).
So, I think you could either use a tobit model or perhaps a hurdle model? Where the prob of passing is different from the grade obtained. (this combines a probit and truncated model)
HTH
Fernando

[Chiara Tasselli]

Fernando,
many thanks for your interest and suggestions.

I have never worked with tobit and hurdle model, but by looking at them I realize that are better than Heckman correction which should implies that students select themselves into the situation to pass or not (if that were the case, I don't think I would have the problem of insufficiencies :P lol ).

(I also got a clearer view of my sample that luckily is censored rather than truncated> a mean limit observations (pupils that didn't pass) are in the sample (only the value of the insufficient grade is censored))

!! Many many thank at you and Jeff for your time. !!
Any further advice is welcome.

[Chiara Tasselli]

Good morning,
Can I ask another question about how to deal with failing grades?
As mentioned above, I only see sufficient marks (> 18 ), What is my lower bound: 18 or 17?

, ll(18) or , ll(17)

?
Many thanks in advance for your time.