PRECAUTIONARY SAVING IN THE SMALL AND IN THE LARGE

PRECAUTIONARY SAVING IN THE SMALL AND IN THE LARGE

February 1989 | Miles S. Kimball
This paper establishes an isomorphism between the theory of precautionary saving and the Arrow-Pratt theory of risk aversion, allowing the application of risk aversion concepts to precautionary saving. It shows that the strength of the precautionary saving motive can be measured similarly to risk aversion, with the index of absolute prudence, $\eta(\theta, \delta)$, and relative prudence, $\theta \eta(\theta, \delta)$, playing analogous roles to absolute and relative risk aversion. The paper demonstrates that the optimal response of decision variables to risk, including precautionary saving, can be analyzed using these measures. It also shows that the Dreze-Modigliani substitution effect can be interpreted as a result of the precautionary saving motive being stronger than risk aversion in the case of decreasing absolute risk aversion and weaker than risk aversion in the case of increasing absolute risk aversion. The paper further explores the effects of decreasing, increasing, or constant absolute prudence on precautionary saving, including the impact of uncertainty on the marginal propensity to consume. It also considers the effects of multiple independent risks and concludes that precautionary saving is more significant than risk aversion when absolute risk aversion is decreasing. The paper provides a comprehensive analysis of the relationship between precautionary saving and risk aversion, demonstrating the utility of the Arrow-Pratt framework in understanding optimal decision-making under uncertainty.This paper establishes an isomorphism between the theory of precautionary saving and the Arrow-Pratt theory of risk aversion, allowing the application of risk aversion concepts to precautionary saving. It shows that the strength of the precautionary saving motive can be measured similarly to risk aversion, with the index of absolute prudence, $\eta(\theta, \delta)$, and relative prudence, $\theta \eta(\theta, \delta)$, playing analogous roles to absolute and relative risk aversion. The paper demonstrates that the optimal response of decision variables to risk, including precautionary saving, can be analyzed using these measures. It also shows that the Dreze-Modigliani substitution effect can be interpreted as a result of the precautionary saving motive being stronger than risk aversion in the case of decreasing absolute risk aversion and weaker than risk aversion in the case of increasing absolute risk aversion. The paper further explores the effects of decreasing, increasing, or constant absolute prudence on precautionary saving, including the impact of uncertainty on the marginal propensity to consume. It also considers the effects of multiple independent risks and concludes that precautionary saving is more significant than risk aversion when absolute risk aversion is decreasing. The paper provides a comprehensive analysis of the relationship between precautionary saving and risk aversion, demonstrating the utility of the Arrow-Pratt framework in understanding optimal decision-making under uncertainty.
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