Abstract: Disaster policy design needs to weigh the costs and benefits of policy implementation. Social willingness to pay (WTP) is often used to evaluate the benefits of disaster prevention and control policies. This is because the larger the losses caused by disasters, the stronger the willingness of society to pay, and consequently, the greater the perceived benefits of these policies. Disaster probability and scale are two critical variables that characterize disaster loss. In analyzing the benefits of policies aimed at mitigating rare disasters, it is essential to explore how the probability and magnitude of such disasters affect socio-economic dynamics. Nonetheless, there is a significant uncertainty surrounding the consumption losses caused by rare disasters. Previous studies indicate that consumption losses from rare disasters typically follow a fat-tailed distribution. Therefore, this study examines the social willingness to pay to reduce both the probability and the impact size of rare disasters under the fat-tailed uncertainty.
To assess the benefits of rare-disaster policies under the fat-tailed uncertainty, we suppose the economic impact of a rare disaster follows a power-law distribution. However, the rate at which the probability density function tapers off to approach zero in the tail is slow compared to an exponential decay. This fat-tailed uncertainty is characterized by the tail index parameter, which defines the tail behavior of the impact distribution. Consequently, the objective of a rare-disaster policy is to expedite the slimming of the probability density function so it approaches zero in the tail more rapidly. We have developed a straightforward framework to explore how the tail uncertainty affects social welfare and to determine the extent of willingness to pay that society should be prepared to commit in order to mitigate the uncertainty associated with the economic impacts of rare disasters.
The simulation results reveal nuanced dynamics in social responses to disaster risks. As the probability of disasters increases, there is a corresponding rise in the social willingness to pay. Interestingly, while the overall WTP to address disaster risks grows, the WTP to specifically reduce the probability per unit of disaster actually decreases. This implies a declining marginal utility in investments aimed at reducing disaster probabilities. Conversely, an increase in disaster scale not only elevates the general WTP but also boosts the WTP per unit reduction in disaster scale, suggesting heightened sensitivity and concern as disasters grow in magnitude. In scenarios involving large-scale disasters, the society demonstrates a readiness to allocate significantly more resources to curb disaster impacts. Additionally, the study explores the effects of the fat-tailed uncertainty associated with the disaster scale on social WTP. The results indicate that the greater uncertainty in disaster scale leads to increased overall WTP. However, the WTP to reduce the uncertainty per unit of disaster scale diminishes, highlighting a strategic shift in prioritizing broader risk reduction over specific uncertainties as disaster risks escalate.
In this empirical study, consumption data from the World Bank are employed to evaluate the impact of the COVID-19 pandemic on global consumption across various countries and regions. We analyze the social willingness to pay for disaster prevention and control in both developed and developing nations. It is observed that the willingness to pay in developing countries exceeds that in developed countries. This suggests that the epidemic prevention and control policies should differ from developing countries to developed ones. Additionally, the study calculates China’s social willingness to pay for COVID-19 prevention and control using consumption data. Although China shows a higher willingness to pay than developed nations, it displays a lower willingness than other developing countries with similar human development indices. This could be attributed to China’s effective measures in controlling the epidemic’s spread, which have resulted in minimized consumption losses.
Global Risk Report in 2024 suggested that global threats would intensify, such as extreme weather events, adverse outcomes from AI technologies, interstate armed conflicts, and cyber insecurity intensification, so this article’s theoretical framework can be used to assess the benefits of policies designed to mitigate these risks.

Key words: willingness to pay, rare disasters risk, uncertainty, policy design

摘要： 灾难政策设计需要权衡政策实施的成本与收益。社会支付意愿常用来评估灾难防控政策收益,其依赖于灾难损失的大小。灾难概率和规模是刻画灾难损失的两个重要变量。因此,本文基于灾难概率与规模提出了一种评估灾难防控的社会支付意愿理论框架。首先分析了灾难概率与期望规模对社会支付意愿的影响。结果发现,随着灾难概率的增大,社会支付意愿增大,但是减少单位灾难概率的社会支付意愿是下降的。随着灾难规模的增大,社会支付意愿也增大,且减少单位灾难规模的社会支付意愿是上升的。这意味着,社会支付意愿对灾难规模更敏感,特别当灾难规模较大时,为减少灾难规模社会愿意支付更多成本。进一步,考虑到灾难规模的厚尾不确定性,研究了灾难规模不确定性对社会支付意愿的影响。结果发现,随着灾难规模不确定性的增大,社会支付意愿也是增大的,但是减少单位灾难规模不确定性的社会支付意愿是下降的。这为灾难政策设计时如何权衡灾难概率与灾难规模提供了重要参考。

关键词: 社会支付意愿, 灾难风险, 不确定性, 政策设计