A continuous-time value function approach to VSL and VSI valuation. Working paper

I present a simple analytical model in continuous time where individuals can be either healthy or ill, and have constant transition between the states and constant mortality rates in each state. The values from being in each of the two live states are represented by two Bellman dynamic programming equations. This leads to simple expressions for lifetime values of remaining in each of the states, values of statistical life in good health (VSL) and of statistical illness (VSI), the value of improved health, and the value of health investments. Changes in background risks have intuitively reasonable effects on VSL and VSI, while a “dead-anyway effect ” only appears in the valuation of health investment but not in expressions of VSL or VSI. I argue that my model is appropriate for VSL and VSI analysis when interventions have immediate effects on health risks, but less so when risks are delayed. More care than hitherto ought to be taken, in selecting models for such analyses. Key words: Value of statistical life; value of statistical illness; mortality risks; background risks