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Job losers exhibit significant heterogeneity in wealth holdings and in the marginal propensity to consume transitory income. We consider potential sources of this heterogeneity, whether (some of) the unemployed face borrowing constraints, and the implications of this heterogeneity for unemployment insurance. We show theoretically how the

optimal benefit can depend significantly on borrowing constraints, and on other (non-

precautionary) savings motives. We report empirical evidence that (i) a quarter of job

losers cannot borrow for current consumption, (ii) this constraint is binding for a much

smaller fraction, and (iii) that \'excess sensitivity\' is not limited to the constrained.