Tail Risk of Contagious Diseases (2004.08658v1)

Abstract: Applying a modification of Extreme value Theory (thanks to a dual distribution technique by the authors on data over the past 2,500 years, we show that pandemics are extremely fat-tailed in terms of fatalities, with a marked potentially existential risk for humanity. Such a macro property should invite the use of Extreme Value Theory (EVT) rather than naive interpolations and expected averages for risk management purposes. An implication is that potential tail risk overrides conclusions on decisions derived from compartmental epidemiological models and similar approaches.

An Analysis of Tail Risk in Contagious Diseases

The paper "Tail Risk of Contagious Diseases" by Pasquale Cirillo and Nassim Nicholas Taleb rigorously applies Extreme Value Theory (EVT) to assess the tail risk associated with pandemics spanning the last 2,500 years. This investigation reveals the fat-tailed nature of pandemic fatalities, underscoring their potential for existential risk, which is pivotal for robust risk management strategies.

Key Findings

1. Fat-Tailed Distribution Evidence: The paper demonstrates that pandemics exhibit a fat-tailed distribution in terms of fatalities. Specifically, through the examination of historical data, it identifies a power law decay in the survival function of pandemic deaths. The tail parameter ($\xi$) is estimated to be greater than 1, indicating that even the first moment is infinite.
2. Inadequacy of Traditional Models: The authors argue that traditional compartmental epidemiological models, like SIR models, are inadequate for assessing tail risk due to their presumption of averages and other finite moment estimators that fail to capture the statistical properties of pandemics. Instead, EVT emerges as a fitting approach for understanding the extreme risks posed by pandemics.
3. Dual Distribution Technique: To address the epistemological challenge of modeling potential infinite mean phenomena while acknowledging finite upper bounds (world population), the authors employ a dual distribution technique. This technique aids in calculating shadow means that approximate risk more accurately than naive averages.
4. Robustness to Data Variation: Given historical data volatility, robustness analyses involving distorted data and jackknife sampling reinforce the reliability of tail risk estimates. Despite reductions in credible data observations, the fat-tailed nature of pandemics persists.

Implications

The paper has profound implications for the policy and strategic management of pandemic risk. The findings suggest:

• Policy Precautions: Pandemics necessitate a precautionary principle that prioritizes preparedness for low-frequency, high-impact events rather than relying on average outcomes. This approach is aligned with the observed fat-tailed nature of pandemic fatalities.
• Modeling and Forecasting: Embracing EVT in modeling pandemics allows policymakers to focus on extremes and tail exposures, ensuring precautionary measures that are informed by the statistical reality of potentially devastating outcomes.
• Tail-Wags-Dog Phenomenon: The dominance of extremes in fat-tailed distributions implies a need for re-prioritization from the bulk to the tail, where significant risk information resides.

Future Directions

The investigation opens avenues for further research into understanding the generating mechanisms behind these fat tails, such as network analysis of contagion spread and computational models of super-spreaders. Advancements in these areas could refine forecasts and enhance preventive strategies, potentially mitigating pandemic impacts at their onset.

In conclusion, the paper underscores the crucial role of EVT in interpreting and managing pandemic risk, challenging current paradigms and offering a framework that could reshape strategies in public health and beyond.