Preferences Yielding the "Precautionary Effect"

TL;DR

This paper provides a geometric characterization of when the difference of two convex functions is convex, linking it to economic models to better understand the precautionary effect in decision-making under uncertainty.

Contribution

It introduces a geometric approach to determine convexity of function differences and applies this to analyze the precautionary effect in economic decision models.

Findings

Characterization of convexity for the difference of two convex functions.

Application of the geometric characterization to economic utility models.

Unification of existing literature on the precautionary effect.

Abstract

Consider an agent taking two successive decisions to maximize his expected utility under uncertainty. After his first decision, a signal is revealed that provides information about the state of nature. The observation of the signal allows the decision-maker to revise his prior and the second decision is taken accordingly. Assuming that the first decision is a scalar representing consumption, the \emph{precautionary effect} holds when initial consumption is less in the prospect of future information than without (no signal). \citeauthor{Epstein1980:decision} in \citep*{Epstein1980:decision} has provided the most operative tool to exhibit the precautionary effect. Epstein's Theorem holds true when the difference of two convex functions is either convex or concave, which is not a straightforward property, and which is difficult to connect to the primitives of the economic model. Our main contribution consists in giving a geometric characterization of when the difference of two convex functions is convex, then in relating this to the primitive utility model. With this tool, we are able to study and unite a large body of the literature on the precautionary effect.