Sweden's distribution of disposable income is very even, with a Gini coefficient of just 0.31. Yet its wealth distribution is extremely unequal, with a Gini coefficient of 0.79. Moreover, Swedish wealth inequality is to a very large extent driven by the large fraction of households with zero or negative wealth. In this paper, we ask to what extent the ambitious public pension scheme is responsible for these features of the data. To address this question, we study the properties of two overlapping generations economies with uninsurable idiosyncratic income risk. The first has a pension system modeled on the actual one, the second has no public pension scheme at all. Our findings support the view that the public pension scheme is to a large extent responsible for the features of the data that we focus on.