This paper reconsiders the trade-off between efficiency and equality of unemployment insurance in a job search model with precautionary saving. Contrary to Cahuc and Lehmann [2000], we show that a decreasing profile of unemployment benefits is able to alleviate this trade-off when agents can save. It is due to a change in saving time profile and an increase in job search effort. The short term unemployed begins to save when unemployment benefits become declining. When the unemployment episode expands, he becomes long term unemployed and dissaves which enables to support his consumption to a higher level.
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