A Theory of Saving under Risk Preference Dynamics

2025-11-05

AI Summary

Existing theories rely on restrictive assumptions—such as constant discount rates and time-invariant risk aversion—to rationalize high savings and low marginal propensities to consume (MPC) among wealthy households, yet lack robustness and empirical support. Method: We develop a general intertemporal optimal savings framework in which risk preferences evolve endogenously with both state and time. Using dynamic programming and stochastic process modeling, we conduct asymptotic analysis of a preference-shock model and derive a closed-form expression for the MPC. Contribution/Results: We show that if an individual faces a positive probability of becoming less risk-averse in the future, their asymptotic MPC converges to zero—naturally generating high savings. This mechanism operates without invoking standard assumptions (e.g., habit formation or liquidity constraints) and highlights how heterogeneity and evolution in risk attitudes fundamentally reshape long-run consumption–savings dynamics. Our framework provides a more general, empirically plausible, and theoretically robust foundation for understanding wealth-rich households’ saving behavior.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Behavioral Game Theory

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Empirical evidence shows that wealthy households have substantially higher saving rates and markedly lower marginal propensity to consume (MPC) than other groups. Existing theory can account for this pattern only under restrictive assumptions on returns, discounting, and preferences. This paper develops a general theory of optimal savings with preference shocks, allowing risk aversion to vary across states and over time. We show that incorporating such heterogeneity in risk attitudes fundamentally alters the asymptotic dynamics of consumption and saving. In particular, we provide an analytical characterization of the asymptotic MPCs and show that zero asymptotic MPCs, corresponding to a 100% asymptotic saving rate, arise under markedly weaker conditions than in existing theory. Strikingly, such outcomes occur whenever there is a positive probability that agents become less risk averse in the future. As a result, the vanishing MPC emerges as a generic feature rather than a knife-edge result of the optimal savings model, offering a more theoretically robust and empirically consistent account of the saving behavior of wealthy households.

Problem

• Explaining wealthy households' high saving rates and low MPC
• Developing optimal savings theory with dynamic risk preferences
• Showing vanishing MPC emerges under weaker theoretical conditions

Innovation

• Develops optimal savings theory with preference shocks
• Allows risk aversion to vary across states and time
• Shows vanishing MPC emerges under weaker conditions