Recent works have stressed that precautionary savings can provide a level of insurance against unemployment risks that is comparable to the current unemployment insurance (UI) system in average. This paper reconsiders this result by laying stress on the implied insurance and wealth inequalities in an incomplete market model calibrated on the French labor market. Self-insurance is found to increase the permanent inequality in this set-up, due to the history dependence of consumption in the presence of borrowing constraints. This result is fostered when one turns to transitory inequalities as some unemployed persons can be potentially liquidity constrained at a given period.