Finite Life Expectancy And The Age-Dependent Value Of A Statistical Life
In this short paper, we investigate the behavior of the age-dependent value of a statistical life (VSL) within a lifecycle framework with a finite maximal possible lifespan. Some existing results, obtained under the unrealistic assumption of an infinite life expectancy, are reversed. In particular, we show that when the market interest rate is equal to (or less than) the sum of age-specific mortality rate and the discounting rate in time preference at any age over the remaining lifetime, then VSL declines. We also show that an inverted-U shape of VSL profile over the life cycle emerges under realistically plausible circumstances. An innovation is that we characterize the changes in optimal consumption and instantaneous utility with age, showing that such changes are proportionate to the difference between the sum of age-specific mortality rate and the discounting rate in time preference and the market interest rate, which may prove to be useful in addressing other issues related to VSL.
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