On the Commitment and partial naïveté: Early withdrawal penalties on retirement accounts

We analyze a portfolio allocation problem in a standard model of conflict within temporal selves who suffer from partial naïveté – the current self holds a deterministic but possibly wrong (underestimation) perception about the present bias of her future selves. The current self can invest in a liquid and a longer-maturity, illiquid asset; the latter offers partial commitment since the future self may prematurely liquidate it at a non-lump-sum cost. If the cost is made prohibitive, no liquidation happens, and the first-best plan laid out by the current self is followed. When such costs are more reasonable, raising them has countervailing income and substitution effects: the current self leaves less illiquid assets for her future self to potentially liquidate, but any given liquidation hurts more in terms of reduced resources available to later selves. In a range, a strengthening of the commitment device of illiquidity is not necessarily welfare increasing for the current self.