Abstract
This paper suggests a simple rule which identifies the coordination between optimal unemployment benefits paid and the tax system in the case of risk neutral workers but with moral hazard and hidden information on the worker’s type. Our model posits that, given a universal, linear income tax scheme, the optimal unemployment benefits paid does not depend on workers’ types. Standard government policy pays a positive replacement rate to unemployed workers. Optimal redistribution, taking moral hazard and adverse selection into account, instead suggests that the benefit paid should be the same for all and only depends on the underlying tax structure.
Acknowledgments
We thank Melvyn Coles, Jan Eeckhout and Kenneth Burdett for their valuable comments.
A.1 Proof of Lemma 1
To hold R constant, a first order Taylor expansion on (5) implies
Hence the constraint dR = 0 requires (dw 0, dτ) satisfy:
As a policy perturbation satisfying (22) ensures dR = 0, Eq. (10) and the constraint dC
0 = 0 additionally requires
which we rearrange as:
Thus, for db ≠ 0, (22) and (23) imply dR = dC 0 = 0 if and only if (dw 0, dτ) satisfy:
Let
Consider then the first order impact of this policy perturbation on the objective function; i.e
Substituting out (dτ, dw 0) using the above implies:
The necessary condition for optimality is dV u/db = 0, otherwise a policy variation with db ≠ 0 exists which strictly increases welfare and satisfies the constraints. Hence a necessary condition for optimality is
Rewriting this equation for b and simplifying yields Lemma 1.
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