Social security, optimal retirement, and savings

Whether or not there will be private wealth accumulation in addition to the acquisition of social security claims generally depends on the replacement ratio. However, if retirement is variable, so is the replacement ratio. Studying an actuarially fair system in presence of uncertain lifetimes and borrowing constraints, it can be shown that the (exogenously fixed) contribution rate determines the optimal retirement date. Optimal retirement then induces (no) private accumulation, if the contribution rate falls short of (is greater or equal than) a benchmark rate. Moreover, this benchmark rate maximizes the induced social security benefit payments and individual welfare. Defining two ranges of contribution rates according to whether they exceed or fall short of the benchmark, it is then demonstrated that the retirement date always decreases with increasing contribution rates within the upper range. Given the case with private accumulation, we are able to derive sufficient conditions which ensure that this conclusion carries over - thus, supplementing earlier research reporting ambiguous reactions.