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 economic welfare, assistance programs targeted at these problems can face challenges, as they often rely on simpler measures of hardship such as income or wealth that fail to capture to full complexity of families’ welfare. In this paper, we explore one important dimension – susceptibility to income shocks. We introduce a model of economic welfare that incorporates income, wealth, and income shocks. We analyze this model to show that it can vary, at times substantially, from measures of economic welfare that only use income or wealth.
We then study the problem of how to allocate 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 consider subsidies to agents’ income and wealth and give an efficient optimal allocation mechanism for the min-max objective under a general setting. Likewise, we show that we can give an optimal allocation mechanism for the min-sum objective under natural assumptions on the agents’ wealth and shock distributions. Then, for the general case, we give fully polynomial-time approximation scheme (FPTAS) to optimize for the min-sum objective. We conclude with a discussion contextualizing our work in the broader literature and a discussion of the social and ethical implications of our work.