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I'm looking for the effect of nutritional coffee breaks on MBA performance, and I found that the change to a healthier catering increased the performance of MBA students. Additionally, I want to see if **more exposure to nutritional meals** affects more or less these students' test scores. To do that, I want to use **attendance to measure the intensity of the treatment** (if you attended more, you were more exposed to the treatment). Still, given that the healthier snacks might affect attendance, I first obtain the effect of healthier on attendance, estimating a precise zero. Consequently, can I use attendance as a measure of intensity? or even if I find that healthier coffee breaks do not affect attendance, I should assume that it is endogenous. If the aforementioned answer is correct, can you explain to me why?
Thank you very much.
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$Performance_i = \beta_0 +\beta_1 Attend_i +\varepsilon_i$

It may be that healthier snacks do not affect attendance, but I would be very concerned making an assumption of the form $Cov(Attend_i, \varepsilon_i)=0$. Students who are more likely to perform well are also probably more likely to attend. i.e., there could be an omitted variable, $Motivation_i$ such that $\varepsilon_i =\beta_2 Motivation_i +\eta_i$.

Then $Motivation_i$ is probably correlated with both attendance and performance.

This is tricky. How are you measuring performance? Test scores? Or something else?

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