Survival misperception, time inconsistency, and implications for life-cycle saving and welfare

Some empirical studies firmly reveal that people tend to form overly pessimistic survival expectations for relatively less distant ages and overly optimistic survival expectations for relatively more distant ages. We incorporate this observation into a life-cycle continuous time overlapping-generations model of consumption/saving with a general form for a subjective survival function. Resulting time-inconsistent optimal control problem has been analytically solved. At the micro level, time inconsistency leads to higher consumption at young and old ages, but this alone fails to improve lifetime well-being since micro-level decisions made with a lack of information about true mortality are suboptimal. In general equilibrium, however, such time inconsistent behavior with survival misperception is conducive to aggregate capital accumulation and greater equilibrium bequest income. The latter effects can produce substantial welfare gains. We also note that empirically observed old age optimistic bias is an important phenomenon, as it helps to avoid unrealistic very old-age debt accumulation within a life-cycle model. In addition, if for a given level of optimistic bias we increase early-life pessimism, this would result in slower capital accumulation, lower bequest income, and thus be detrimental to welfare. Since recent literature reports that young-age survival pessimism has grown over time, it raises some concerns.