Present-bias and the value of sophistication: Splurging vs. smoothing

This paper develops a dynamic wealth management model for risk-averse agents displaying present-bias in the form of hyperbolic discounting. The agent chooses optimal consumption and labor supply policies and allocates her funds between a risk-free asset, a traded liquid asset, and a non-traded illiquid asset. We characterize these policies for both sophisticated and naive present-biased agents. There are three results. First, sophisticated agents overconsume more and supply less labor than their naive counterparts if and only if their elasticity of intertemporal substitution (EIS) is greater than one. This result arises from the interplay of the smoothing and the splurging effect, which exactly cancel out when the EIS equals one. As a result, sophistication is welfare reducing (increasing) when EIS is high (low). Second, higher stock market volatility and worsening investment opportunities make the sophisticated agent relatively better off than her naive counterpart. Finally, when borrowing constraints are binding and absorbing asset illiquidity serves as a commitment device to mitigate overconsumption and thereby increase welfare.