Before revision:  Furthermore, while almost 50\% of retirees reveal that they do not value leaving bequests, the rest have heterogeneous preference for bequestthat, on average, increases with their savings. On the supply side, we find that firms ' annuitization costs vary across retirees , and the average costs increase with retirees' savings . If these costs were commonly known then the pensions would increase for everyone, but the increment would be substantial only for the high savers.
After revision:  Furthermore, while almost 50\% of retirees reveal that they do not value bequest, and firms are more likely to have low annuitization cost for retirees in the top two savings deciles. Counterfactuals show that under the current mechanism, private information about costs harms only these high savers.