A methodology for measuring the impact of risk prudence on economic decisions with application toward consumption, risk sharing, and social security

Kimball (1990) introduces risk prudence both as a definition from derivatives of a utility function and as a measure of the precautionary saving motive. This dissertation explores the question “what is the magnitude of impact of prudence?” In a variety of settings, the sign of the impact can be determined analytically without specifying a functional form of the utility, but to determine the magnitude of impact requires the specification of a functional form. As it turns out, the commonly used utility functions provide little help in assessing the impact of prudence since they do not have a parameter to specify the level of prudence. A Kimball and Weil (1992) decomposition of absolute prudence into its two additive components (absolute risk aversion, and an additional prudence factor) shows that the additional prudence factor is parameterless for both exponential and log-power utility, hence suggesting the need to create a utility function that does have a prudence parameter. This is accomplished using the Brockett-Golden (1987) approach, and one such utility function is introduced here as the Brockett-Golden-Inverse-Gaussian (BG-IG) utility function. The BG-IG is a first step in exploring the magnitude of impact, since it has a prudence parameter, and since it can reduce to both exponential and log-power levels of prudence, allowing comparisons. Results suggest the magnitude of impact is significant in the consumption decision only when the inter-temporal discount differs significantly from one, or when the reference wealth level is either low or with high variability. However, the magnitude seems more significant for the risk sharing aspects of a simple insurance decision. In general, the results suggest the need to create additional utility functions that have even more prudence than that of the exponential, log-power and BG-IG classes. And with the introduction of the BG-IG there are now additional consumer preference models to test empirically