On Multivariate Prudence

In this paper we extend the theory of precautionary saving to the case in which uncertainty is multidimensional and we develop a matrix-measure of multivariate prudence. Furthermore, we characterize comparative prudence, decreasing and increasing prudence, the effect of uncertainty on the marginal propensity to consume out of wealth, and the Drèze-Modigliani substitution effect in this multivariate setting. We also characterize the concept of multivariate downside risk aversion as a multivariate preference for harm disaggregation. We show that our definition is equivalent to a positive precautionary saving motive. We propose an alternative measure of the intensity of downside risk aversion and show that this measure is useful in understanding several economic problems that involve multivariate preferences.