1. Families consider all educational alternatives and select the one with the highest value for their child
2. Better home life increases the quality of home schooling ("better" here and below could be, but does not have to be, a judgment on whether parents themselves are good people. I'd assume the most important elements of having a "better home life" have to do with available resources and the capacity to support and teach your kid, not variance in whether someone is a "good parent" or a "nice person").
3. Better communities increase the quality of public schooling
4. Quality of home life and quality of communities are highly correlated
5. There's an opportunity cost associated with home schooling (this is of course taken into account in #1)
It seems to me that these are all pretty defensible, and the conclusion I'm coming up with is that the people who will benefit from home schooling (and therefore select into it, according to #1) are those people who have a high, positive differential between the quality of their home life and the quality of their communities. The distribution of the impact of homeschooling over the underlying distribution of community quality therefore depends on the joint distribution of home life and community quality. Equalizing expenditures on public education across diverse communities should reduce the benefit of home schooling in previously low quality communities and increase the benefit in previously high quality communities.
It doesn't get at the impact, but an interesting first step in looking at this would be to look at whether policy changes around public school financing lead to this change in selection into home schooling.
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