FOUR ESSAYS ON THE ECONOMICS OF EDUCATION Note that Theorem 2 does not rule out equilibria in which some families live inlower-μ than do some higher-income families. I refer to these as unsorted (or imperfectlysorted) equilibria. They arise when the peer group advantage of high-income communitiesover low-income communities is large enough to overcome deficits in school effectiveness.28For fixed income and effectiveness distributions, unsorted equilibria become harder tomaintain as the weight that families place on peer group relative to school quality falls:...
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