We consider a reform that would replace the current Finnish unemployment insurance (UI) scheme with individual unemployment accounts. The reform would provide additional pensions for individuals who end up with a positive account balance at retirement age without restricting unemployment benefits relative to the current system. At the same time, the reform is likely to improve labour supply incentives, at least for some individuals. The question is whether such a reform would be self-financing. The fiscal effects of the reform depend crucially on the distribution of lifetime unemployment and the extent to which the reform would increase labour supply. We use a micro panel comprising a representative sample of 1/3 of the Finnish population and covering the period 1988-2010 to estimate the distribution of lifetime unemployment and to simulate how the unemployment accounts would evolve. We assume that the reform improves labour supply incentives only via the extensive margin and find that it is likely to be self-financing if the labour supply elasticity at the extensive margin is about 0.16 or higher. We also experiment with integrating UI with the pension system.