Academic journal article Journal of Risk and Insurance

Risk Aversion and the Value of Risk to Life

Academic journal article Journal of Risk and Insurance

Risk Aversion and the Value of Risk to Life

Article excerpt

ABSTRACT

The standard literature on the value of life relies on Yaari's (1965) model, which includes an implicit assumption of risk neutrality with respect to life duration. To overpass this limitation, we extend the theory to a simple variety of preferences that are not necessarily additively separable. The enlargement we propose is relevant for the evaluation of life-saving programs: current practice, we estimate, puts too little weight on mortality risk reduction of the young. Our correction exceeds in magnitude that introduced by the switch from the notion of number of lives saved to the notion of years of life saved.

INTRODUCTION

Billions of dollars are spent every year on mortality reduction programs. Issues like the allocation of funds to medical research or prevention, the design of safety rules, or the wording of environmental bills raise intense debate on the relevance of the choices made by governments and their agencies. For economists, the baseline is that alternative projects should be evaluated with objective criteria to avoid pure waste or dramatic underinvestment in less popular issues.

To back public decisions, some inquiry into individual valuation of life is indispensable. In practice, if we leave apart contingent valuation, the analysis of the wage-risk trade-off is the major source of estimates of people's behavior with respect to risk to life. These surveys are primarily informative about industrial workers. Because public programs affect wider populations whose characteristics may vary considerably and given that the mortality changes considered are often beyond the range experienced by the reference sample, a theoretical support for the interpretation of the data is indispensable.

The choice of the structural life-cycle model that minimizes bias at estimation and extrapolation stages is capital. The standard approach uses additively separable lifecycle models. The intertemporal additivity assumption, which involves an implicit assumption of risk neutrality with respect to length of life, is extremely constraining (Bommier, 2006). Although this model has been severely criticized in other branches of the literature, (1) it remains an almost universal assumption for applied theory papers on the value of life. (2)

In this article, we develop an alternative model, based on recursive von Neumann-Morgenstern utility functions, which relaxes the additivity assumption and thereby introduces what we shall call mortality risk aversion (MRA). (3) Although this extension complicates intermediate calculations, practical difficulties are kept at a reasonable level: formulas for the value of statistical lives are almost as simple as those obtained with the standard additive model. There are therefore no technical difficulties for applying this novel approach to concrete issues. Above all, relaxing additivity warrants a significant gain in accuracy. As a proof of concept, we use empirical results on the wage-risk trade-off to calibrate both the additive and nonadditive models. While the additive model proves unable to fit the data, the generalization proposed provides an excellent fit with reasonable estimated parameters.

To emphasize the importance of accounting for MRA, we compare the benefits of (fictitious) life-saving policies using different methods. The magnitude of the bias caused by the additive separability assumption appears to be uncomfortably big. The type of cost-benefit analysis that is currently recommended for life-saving programs is likely to be strongly biased in favor of the elderly if the decline of the VSL with age is underestimated. The correction we suggest could exceed in magnitude that introduced by the switch from the notion of number of lives saved to the notion of years of life saved.

The empirical wage-risk trade-off is used as a test of alternative theories of the lifecycle preferences. Potentially, a better understanding of life-cycle behaviors would be instructive for many applications not directly related to the value of life literature. …

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