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Abstract
Two articles (Hugonnier et al., 2013; Cordoba and Ripoll, 2017) have proposed a recursive formulation of utility functions combining a positive value of life, preference homotheticity, and a constant elasticity of substitution. However, when the elasticity of substitution is below one and mortality rates take plausible values, this recursive formulation admits only a unique solution where utility is constant and equals zero everywhere. Non-constant solutions may only exist if mortality rates are assumed to remain low at all ages, namely in a world of perpetually young agents. Such solutions are therefore unsuitable for studying the value of life in demographically relevant settings and yield counterfactual predictions for saving behavior. We conclude this clarifying paper by reviewing various recursive specifications that can be used to study the value of life with no such problems.
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