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You're getting to this in one of your next steps, but as I'm sure you expected I have questions about bias and endogeneity.
It helps that you can show the relationship holds within territories, so we know it's not just some artifact of composition. However, there still are lots of other things going on.
  1. Reverse causality: Some territories might raise their fees because they have low volume but expect that volume to be inelastic. I think this describes what @realBitcoinDog did with ~HealthAndFitness and it's what @jeff was doing with ~econ before he handed it over to me.
  2. Spurious correlation: There may have simply been lower fees when territories were first introduced, which corresponded to a busier time at SN. During the early price discovery process founders were fairly slow to raise fess because no one had any idea what the optimal fees were. Unless somewhat higher fees caused the decline of SN activity (maybe it did!), then this is a problem.
  3. Selection: Territories have different focuses. ~news is geared towards higher volume shorter posts, while ~mostly_harmless is for more thoughtful content. I suspect the intention of the territory is doing work in addition to the fees.
I'm sure we'll both think of more, but that's enough to start with.
Some sort of dif-in-dif design could get at the reverse causality issue.
You might be able to use a relative measure of fees and activity to check the spurious correlation problem.
I bet something as simple as territory fixed effects will take care of the selection issue.
Yeah next up is probably a two way fixed effects regression with time effects and territory effects. Can throw in bitcoin price as a regressor as well.
If, as I'm imagining it, it'll be a territory-by-week panel, there will probably be lots of zeros. I wonder if you know how to efficiently run a tobit model with lots of fixed effects
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I'd probably start with the subsample of territories that have posts almost every week.
Have you looked at the distribution of post output by territory? I suspect the territories that have posts every week account for 95%+ of total posts.
I forget exactly when asinh has problems, but it can perform more or less like a log that accepts zeros.
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