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How do you want to think about poster fixed effects? Other things equal, some posters receive more zaps than others.
Thinking through it, I believe that anything which is predictable and/or a function of effort needs to go into the first regression (zaps on quality), because the point is to measure how much "surprise" there was in previous zaps. So to the extent that user FE captures known factors, including the users' own typical effort levels, it would go into the first regression.
Thanks for asking the question, it was clarifying for me to type that out.
I also wonder what kind of bias is introduced by zappers learning about posters.
This is a KBC, after all. If quality is consistently high, but not increasing, I’d expect zaps to increase, which will look like the writer learning to make better posts.
Would be curious to hear what you think of how I map this to empirics.
I write zap amount zi as:
where qi is quality of the post. Although effort is not observable, we assume that quality is. And since quality is increasing in expectation with respect to effort, the hypothesis we test is that the quality of the subsequent post is increasing in the user's history of positive zap surprises.
We'll assume we can measure qi by writing qi=Xiβ, where Xi is a bunch of observable post characteristics, then running the regression equation above.
We then run a regression of qi for the user's next post on the average of their prior zap surprises (average of lnzi−qi for prior posts) and look for a positive coefficient.
I may be getting ahead of my skis because I haven't actually tested this regression yet.