Numerous analyses of the benefits and costs of COVID‐19 policies have been completed quickly as the crisis has unfolded. The results often largely depend on the approach used to value mortality risk reductions, typically expressed as the value per statistical life (VSL). Many analyses rely on a population‐average VSL estimate; some adjust VSL for life expectancy at the age of death. We explore the implications of theory and empirical studies, which suggest that the relationship between age and VSL is uncertain. We compare the effects of three approaches: (1) an invariant population‐average VSL; (2) a constant value per statistical life‐year (VSLY); and (3) a VSL that follows an inverse‐U pattern, peaking in middle age. We find that when applied to the U.S. age distribution of COVID‐19 deaths, these approaches result in average VSL estimates of $10.63 million, $4.47 million, and $8.31 million. We explore the extent to which applying these estimates alters the conclusions of frequently cited analyses of social distancing, finding that they significantly affect the findings. However, these analyses do not address other characteristics of COVID‐19 deaths that may increase or decrease the VSL estimates. Examples include the health status and income level of those affected, the size of the risk change, and the extent to which the risk is dreaded, uncertain, involuntarily incurred, and outside of one's control. The effects of these characteristics and their correlation with age are uncertain; it is unclear whether they amplify or diminish the effects of age on VSL.

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This paper uses new data collected by the author on cigarette taxation in 443 municipalities from 1990 to 2009. These data are combined with state-level price and tax information to measure the relative effects of state and local taxes on cigarette prices.

OpenAI's Gym library contains a large, diverse set of environments that are useful benchmarks in reinforcement learning, under a single elegant Python API (with tools to develop new compliant environments) . The introduction of this library has proven a watershed moment for the reinforcement learning community, because it created an accessible set of benchmark environments that everyone could use (including wrapper important existing libraries), and because a standardized API let RL learning methods and environments from anywhere be trivially exchanged. This paper similarly introduces PettingZoo, a library of diverse set of multi-agent environments under a single elegant Python API, with tools to easily make new compliant environments.

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