We consider a simple overlapping generations model with bequests where agents care about their consumption relative to that of others. It is shown that, under some parameter values, the distribution of bequests diverges and only a fraction of agents leaves bequests in the long run. Then, the introduction of an unfunded social security system promotes capital accumulation, as opposed to the standard result in the literature. We also show that an expansion of the social security system causes the bequest distribution to diverge more slowly, suggesting its mitigating effect on wealth concentration.