In my one experience with a charter school lottery, the charter school made it quite difficult to enter the lottery; and to find out if your kid was selected, you had to go there and ask them. And, it appeared, it wasn't a random lottery at all. My son was known to the founders of the school as a star student, so when I showed up and nervously asked if his name had been picked, I was told, Don't worry about it, of course he's in.
This is a very good point. There have been some very good comments on the use of charter school lotteries as a gold standard. I think there are persuasive reasons to be concerned, even if the lotteries are fair. However, it would be in the self interest of charter schools to accept a few "star students" outright rather than lave their selection to chance. Insofar as this happens at all, we would no longer have randomization (and thus would be unable to use these lotteries to estimate causal effects, even if the other concerns were not present).
So it seems increasingly hard to treatment there lotteries as a valid instrumental variable.
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