Hyperbolic discounting and state-dependent commitment

In a stochastic economy with uninsurable endowment risk, we establish a condition under which hyperbolic-discounting consumers commit to a future consumption path using both illiquid assets and borrowing constraints as commitment devices. There is the possibility that a state-dependent commitment can be adopted as an equilibrium consumption strategy. On a path leading to low future endowment, the current self can commit to its own optimal consumption path, which is undesirable for future selves. In contrast, along the path with a high future endowment, the current self cannot make a commitment and must accept a consumption allocation that future selves will revise. Thus, depending on what stochastic state will arise, people cannot fully utilize the available commitment devices in risky situations.