Thanks, this is interesting and useful work.
I only skimmed the article briefly. However, some questions and comments follow.
1) I'm not clear on your methodology. You said you checked for correlation. What exactly did you do? I would have thought that a multi-factor linear model or something would be more suitable for such a study. I don't know if such a study would be publishable, but it would be a plus if it was. Though I suppose it's possible Airbnb could try to stop publication.
2) You wrote:
Airbnb’s database is not freely available and Airbnb does not provide an API that allows easy interface with the database.
It should be possible to pull data directly from Airbnb using their API, unless they disallow such a thing in their terms of usage or simply block it. Comments? Then one could (in theory) combine the pulling of data and data import in an automated way. Page scraping is a really painful way to collect data.
3) Airbnb's attempt to justify Instant Book by saying it prevents discrimination is pure codswallop. This doesn't have much to do with the topic on hand, but I felt it needed saying.
4) Has anyone else done work along these lines?
5) One additional thing that could be checked for is how the number of days that are blocked/open in the coming months affects placement.
6) It seems that your searches don't include any dates, just some filters. But in practice I assume most people would search for specific dates. (I could be wrong about this - I'm not aware of any data about what people do in practice.)
DISCLAIMER: I have a PhD in statistics, but my knowledge of statistical modelling is rather sketchy.