(met_nutritionist) on the number of pizzas eaten in the last two weeks (pizzas_eaten):
pizzas_eaten = βo + β₁ met_nutritionist + u
If you estimate this using OLS, will ẞ₁ represent the causal effect of interest?
(a) No, it would represent the association between met_nutritionist and pizzas_eaten because there are reasons to believe that cov(met_nutritionist, u) ≠ 0.
(b) No, it would represent the association between met_nutritionist and pizzas_eaten because there are reasons to believe that cov(met_nutritionist, u) = 0.
(c) Yes, there is no reason to doubt cov(met_nutritionist, u) = 0.
(d) Yes, it is crystal clear that meeting with a nutritionist would cause people to reduce their pizza consumption.