Theoretical bounds on the value of improved health

Policies that improve health and longevity are often valued by combining expected gains in quality-adjusted life years (QALYs) with a constant willingness-to-pay (WTP) per QALY. This constant is derived by dividing value per statistical life (VSL) estimates by expected future QALYs. We explore the theoretical validity of this practice by studying the properties of WTP for improved health and longevity in a framework that makes minimal assumptions about the shape of an agent's utility function. We find that dividing VSL by expected QALYs results in an upper bound on the WTP for a marginal improvement in the quality of life, as measured by gains in health status or longevity. Calibration results suggest that analysts using this approach to monetize health benefits overestimate the value of a program or policy by a factor of two on average. We also derive a lower bound on the WTP for improved health and longevity that permits a novel empirical test for the descriptive validity of the QALY model. Our calibrations suggest that this lower bound is on average 20% smaller than the actual WTP.