Self-Control and Saving for Retirement

This paper builds the first calibrated life-cycle simulation model of “hyperbolic” consumers – whose discount rates decline with horizon, setting up a conflict between a patient long-run self and an impatient short-run self – and compares it with the standard “exponential” consumer model used to evaluate tax-deferred saving vehicles such as 401(k) plans. In a one-asset economy the two types’ calibrated consumption and wealth profiles look “nearly indistinguishable,” but the hyperbolic model also generates two signatures that do show up in US survey data: a higher incidence of binding liquidity constraints, and the anomalously low “missing” precautionary-saving coefficient that Dynan (1993) found empirically. When a second, partially illiquid asset – a stylized 401(k)-style defined-contribution (DC) plan with an early-withdrawal penalty – is added, hyperbolic consumers respond much more strongly than exponential consumers: with the authors’ preferred risk-aversion calibration, DC plans raise the steady-state net national saving rate by 61-102 percent for exponential households versus 81-134 percent for hyperbolic households (depending on the match rate and penalty), and the welfare gain from gaining access to the DC plan is far larger for hyperbolic households, because they value the plan’s illiquidity as a commitment device on top of the same tax benefit that exponential households value alone. These gaps shrink sharply for both types of households once risk aversion is raised from 1 to 3, so the model’s verdict on how much DC plans raise national saving and welfare turns on a risk-aversion parameter the authors say is “not know[n]” with confidence.

David I. Laibson | Macro Paper Warehouse

Self-Control and Saving for Retirement