Dear avid readers:
This may seem naive...but why do we care about causality in the LR?
We want to teast out causal effects so that we know "de-worming-> increases school attendance", and isn't confounded by some other thing that's driving up school attendance.
But who cares..if my sample is big enough and I see a positive correlation, then in general I know deworming affects something that affects school attendance.
Even if we determine whether de-worming and increased school attendance is not causal, and don't implement the program, it doesn't mean we'll figure out the variable that is, and why not still implement the program?
Perhaps it is because we are concerned that:
1) if it's a confouder that increase school attendance via de-worming, what is it, and what if it drops off?
2) if it's a confonder and we dont' know what it is, then we can't scale this up
What if the market and people that de-worming is offered to is pretty constant. Why do we care about causality then?
Just something I've been kicking around on runs...
Reader1: I think that we care about it for the two reasons that you mentioned
-- if we implement de-worming but the correlation is actually due to a
third variable that may "drop off" or that may have a change in how it
is correlated with the other variables (or something else happens that
impacts that third variable such that the correlation changes) then
the de-worming stops working and we do not know why or what we are to
do then. so causal is most important with respect to policy
implications. But if the third variable is very stable and the
correlations do not change, then from a policy perspective, the
de-worming works so who cares? the only reason we might care in that
case would be if there were a cheaper or more tenable policy option
that we are blind to because we ignored the potential third variable.
In terms of defining relationships, I believe causality does not matter.
Reader 2: The thing about de worming as an intervention is that it is super cheap and it works. In fact, it probably the cheapest thing you could do other than nothing. The only way this study is interesting in an economic sense is if school attendance post deworming goes down. kids lives are improved in other dimensions and you now have a tradeoff to study. But this is not the result, so we are done and nothing is surprising. Now we can see how more costly interventions compare.
Reader 3: I agree, causality is key for policy. Suppose there is only correlational evidence of deworming and schooling. i.e. we observe that some villages have implemented deworming programs and these villages also have greater educational attainment than villages that have not implemented deworming. one possible 'threat" to a causal interpretation of this evidence is that the villages that deworm might also happen to have higher than average income (or lower than average income if these programs are sponsored by donors and targeted at poor villages) and it is income that is really causing differential investments in education and educational attainment.
If a government is deciding whether to invest in a deworming program, there is no guarantee at all -- based on this evidence -- that schooling will improve if a deworiming program is implemented in the villages that have not already implemented the program. hence the need for an RCT.
but maybe you are thinking about the mechanisms- proximal vs. ultimate causes... rather than correlations?