In response to the global COVID-19 pandemic, the U.S. federal government, through the CARES Act, FFCRA, RRA, and ARPA, provided as much as "$6 trillion in income support to households, a combination of loans, grants, and tax relief to firms and non-profits, funding for (public) health efforts, and intragovernmental grants to sub-national governments." These federal funds included "roughly $900 billion in aid to state and local government entities." And a recent paper, What Do State Do With Fiscal Windfalls? Evidence from the Pandemic, by Jeffrey Clemens (UCSD--econ.) et al., focuses on how state governments deployed this federal aid.
To do so, the paper benefits from a unique dataset constructed from a rich array of sources and an estimation strategy that levers variations across states with "low vs. high levels of per resident representation in the U.S. Congress." More specifically, owing to the possibility that federal aid to states may be endogenous along many dimensions, the paper deploys "an instrumental-variable approach to estimate the effect of federal relief to state and local governments on the revenue and expenditure decisions of state governments."
Among the findings include that "for every $1000 of committed federal aid per capita, $645 appears as increased intergovernmental grant revenue in states over the years 2020-2022." When it came to deploying the federal funds, state governments emphasized "General Government Expenditures ($379 per $1000 of federal aid) and state and local pension contributions ($72 per $1000 of federal aid)." An excerpted abstract follows.
“Using variation in federal pandemic-era fiscal aid to states driven by the strength of political representation, we find that incremental pandemic-era fiscal aid to states was most likely to end up in the categories of general administrative service spending and employee pension benefit funding. Spending on categories that motivated the aid in the first place, such as healthcare, education, and infrastructure, may also have responded but does not show robust patterns. Total state government revenues and expenditures had increased by around 70 cents per incremental windfall dollar of committed federal funds by 2022. Of this, the statistically significant categorical spending effects are 38 cents to general government expenditures (the residual that in principle excludes healthcare, education, infrastructure, and other functional categories) and 7 cents to pension funding, even though the latter use was inconsistent with the objectives of the legislation.”

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