Implications for Estimating Income Effects Let F(·) be the cumulative distribution of cash-on-hand (x 1 ) (not observed) Thought experiment 1: lottery by choice, as in model Let λ be the fraction of lottery players in the model Thought experiment 2: random compulsory lottery; fraction λ of population We observe lottery winners and non-winners (those that dont play, and those that lose.) Others (notably Imbens et al., 2001) observe those that lose.
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