Precautionary saving and the notion of ambiguity prudence
Introduction
From the early works of Leland (1968), Sandmo (1970), and Drèze and Modigliani (1972), it is well known that the addition of a pure risk affecting future incomes may result in an increase in current savings. This precautionary saving motive has been shown to occur if the marginal utility of future consumption is convex, in which case the agent is said, in the words of Kimball (1990), to be prudent, or more precisely risk prudent. In this context, risk prudence measures the willingness to accumulate wealth to face future risk, which by definition corresponds to a situation in which the probabilities associated with the possible outcomes are perfectly known.
However, if the future wealth of an economic agent is not only risky but is ambiguous in the sense that the probabilities of the possible outcomes depend on an external parameter for which the agent has prior beliefs, under which conditions does the optimal level of saving increase? To answer this question, I consider a simple two-period consumption–saving problem in the presence of ambiguity, and consider non-neutral ambiguity attitudes.1 Ambiguity takes the form of a second order prior probability distribution over the set of plausible first order distributions of the future income. I use the theory developed by Klibanoff et al., 2005, Klibanoff et al., 2009 (hereafter, KMM) to deal with ambiguity. This model has the advantage of making a distinction between ambiguity aversion and risk aversion, and is tractable enough to allow the application of the well developed machinery of the expected utility sequentially on first and second order probability distributions.
Section snippets
The model
The notion of ambiguity prudence is a concept closely related to Kimball’s concept of risk prudence, but which is due to the presence of ambiguity. To study this concept, I consider a very simple two-period model which is not only risky but also ambiguous: probabilities of second-period final wealth are not objectively known, instead they consist of a set of probabilities, depending on an external parameter for which the agent has prior beliefs.2
Conclusion
Analogously to what Kimball (1990) did in the risk theory literature, this letter defines the notion of ambiguity prudence as an individual characteristic leading him to save an extra amount of money if his future income is ambiguous. Sufficient conditions to observe ambiguity prudence are proposed considering both individual’s tastes and perception of ambiguity.
Acknowledgments
I thank Louis Eeckhoudt and an anonymous referee for helpful comments and suggestions. The research leading to this result has received funding from the FRS-FNRS.
References (13)
- et al.
Consumption decisions under uncertainty
J. Econom. Theory
(1972) - et al.
Recursive smooth ambiguity preferences
J. Econom. Theory
(2009) Risk, ambiguity, and the Savage axioms
Quart. J. Econ.
(1961)- Gierlinger, J., Gollier, C., 2008. Socially efficient discounting under ambiguity aversion. Working...
The Economics of Risk and Time
(2001)Choosing between risky prospects: the characterization of comparative statics results, and location independent risk
Manag. Sci.
(1989)