In an overlapping generations economy with incomplete insurance markets, the introduction of an employment fund (akin to the one introduced in Austria in 2003, also known as `Austrian backpack') can enhance production effciency and social welfare, if it complements, and in part substitutes, the two classical systems of public insurance: pay-as-you-go pensions and unemployment insurance (UI). We show this in a calibrated dynamic general equilibrium model with heterogeneous agents of the Spanish economy (2014). A `backpack' (BP) employment fund is an individual (across jobs) transferable fund, which earns the economy interest rate as a return and is financed with a small payroll tax (a BP tax). The worker can use the fund if he or she becomes unemployed or retires. To complement the existing Spanish pension and UI systems with a 2% BP tax would be preferred to the status quo by more than 90% of the households of the calibrated economy, a percentage that can be higher with a more substantial BP (i.e. higher BP tax). Our model also provides a framework where other reforms (e.g. a partial, or complete, substitution of current unsustainable pension systems) can be quantitatively assessed.The ADEMU Working Paper Series is being supported by the European Commission Horizon 2020 European Union funding for Research & Innovation, grant agreement No 649396