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Redistributive Unemployment Benefit and Taxation

  • Homa Esfahanian and Ali Moghaddasi Kelishomi ORCID logo EMAIL logo

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.

JEL Classification: D82; H21; J64; J65

Corresponding author: Ali Moghaddasi Kelishomi, School of Business and Economics, Loughborough University, Epinal Way, Loughborough LE11 3TU, UK, E-mail:

Acknowledgments

We thank Melvyn Coles, Jan Eeckhout and Kenneth Burdett for their valuable comments.

Appendix

A.1 Proof of Lemma 1

To hold R constant, a first order Taylor expansion on (5) implies d b , d τ , d w 0 must satisfy

(21) d R = 1 1 τ d b τ 1 τ d w 0 + b + d w 0 ( 1 τ ) 2 d τ = 0 .

Hence the constraint dR = 0 requires (dw 0, dτ) satisfy:

(22) τ d w 0 b + d w 0 ( 1 τ ) d τ = d b .

As a policy perturbation satisfying (22) ensures dR = 0, Eq. (10) and the constraint dC 0 = 0 additionally requires d b , d τ , d w 0 satisfy

d b + α r R w ̄ ( w w 0 ) d F ( w ) d τ α r τ [ 1 F ( R ) ] d w 0 = 0

which we rearrange as:

(23) α r R w ̄ ( w w 0 ) d F ( w ) d τ α r τ [ 1 F ( R ) ] d w 0 = d b

Thus, for db ≠ 0, (22) and (23) imply dR = dC 0 = 0 if and only if (dw 0, dτ) satisfy:

τ b + d w 0 ( 1 τ ) α r τ [ 1 F ( R ) ] α r R w ̄ ( w w 0 ) d F ( w ) d w 0 d τ = 1 1 d b .

Let Δ = α τ r R w ̄ ( w w 0 ) d F ( w ) [ 1 F ( R ) ] b + d w 0 ( 1 τ ) . Then as long as Δ ≠ 0, perturbation d b , d τ , d w 0 holds dR = dC 0 = 0 if and only if:

d w 0 d τ = α r R w ̄ ( w w 0 ) d F ( w ) + b + d w 0 ( 1 τ ) Δ τ [ 1 + α r [ 1 F ( R ) ] ] Δ d b .

Consider then the first order impact of this policy perturbation on the objective function; i.e

r d V u = [ w 0 R ] d τ + τ d w 0 .

Substituting out (dτ, dw 0) using the above implies:

r d V u = [ w 0 R ] τ [ 1 + α r [ 1 F ( R ) ] ] Δ + τ α r R w ̄ ( w w 0 ) d F ( w ) + b + d w 0 ( 1 τ ) Δ d b .

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

[ w 0 R ] 1 + α r [ 1 F ( R ) ] + α r R w ̄ ( w w 0 ) d F ( w ) + b + d w 0 ( 1 τ ) = 0 .

Rewriting this equation for b and simplifying yields Lemma 1.

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Received: 2021-04-06
Revised: 2021-12-22
Accepted: 2022-03-13
Published Online: 2022-06-13

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