DP15283 Optimal allocations to heterogeneous agents with an application to stimulus checks

Author(s): Vegard M. Nygaard, Bent E Sørensen, Fan Wang
Publication Date: September 2020
Date Revised: December 2021
Keyword(s): American Rescue Plan, Consumption inequality, Economic Stimulus Act, Propensity to Consume, Welfare inequality
JEL(s): C6, E21, I38
Programme Areas: Monetary Economics and Fluctuations
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=15283

A planner allocates discrete transfers of size D_g to N heterogeneous groups labeled g and has CES preferences over the resulting outcomes, H_g(D_g) . We derive a closed-form solution for optimally allocating a fixed budget subject to group-specific inequality constraints under the assumption that increments in the H_g functions are non-increasing. We illustrate our method by studying allocations of "support checks'' from the U.S. government to households during both the Great Recession and the COVID-19 pandemic. We compare the actual allocations to optimal ones under alternative constraints, assuming the government focused on stimulating aggregate consumption during the 2008-2009 crisis and focused on welfare during the 2020-2021 crisis. The inputs for this analysis are obtained from versions of a life-cycle model with heterogeneous households, which predicts household-type-specific consumption and welfare responses to tax rebates and cash transfers.