Subsidy Allocations in the Presence of Income Shocks

Poverty and economic hardship are understood to be highly complex and dynamic phenomena. Due to the multi-faceted nature of welfare, assistance programs targeted at alleviating hardship can face challenges, as they often rely on simpler welfare measurements, such as income or wealth, that fail to capture to full complexity of each family's state. Here, we explore one important dimension -susceptibility to income shocks. We introduce a model of welfare that incorporates income, wealth, and income shocks and analyze this model to show that it can vary, at times substantially, from measures of welfare that only use income or wealth. We then study the algorithmic problem of optimally allocating subsidies in the presence of income shocks. We consider two well-studied objectives: the first aims to minimize the expected number of agents that fall below a given welfare threshold (a min-sum objective) and the second aims to minimize the likelihood that the most vulnerable agent falls below this threshold (a min-max objective). We present optimal and near-optimal algorithms for various general settings. We close with a discussion on future directions on allocating societal resources and ethical implications of related approaches. Introduction Understanding and measuring economic hardship is a fundamental question that directly informs the design of policies and assistance programs designed to address the needs of vulnerable individuals and families (Anand and Sen 1997; Atkinson 2003) . A crucial challenge here is the range of factors that play a role in poverty and economic hardship, including health, demographics, social ties, intergenerational dynamics, and many other dimensions (Grusky 2018). Recent studies have sought to address this gap between official measures of welfare and the more complex formulations that might be needed to accurately identify the sources of greatest need. One active and ongoing effort is the Poverty Tracker program (Wimer et al. 2014; 2016) , which surveys approximately 2300 families in New York City, documenting the intricate associations between their circumstances and levels of hardship. As with other studies in this area, the Poverty Tracker study is in part based on the premise