The services provided by the liability side of banking are examined in an economy in which everyone is identical ex ante and banks are uninsured. Demand equity deposit claims are shown to provide all the service that can be provided by demand debt claims without the risk of banking panics as long as there is not both aggregate uncertainty about liquidity demands and asymmetry of information about the quality of bank assets. Demand debt claims are conjectured to have evolved because both these conditions were met historically. Given the rapid development of financial market, these conditions may no longer hold and thus demand equity claims may offer a viable alternative to government-insured demand debt claims. With demand equity claims, only insurance against fraud need be provided to insure a safe deposit system.