Full text
NBER WORKING PAPER SERIES
WAS PANDEMIC FISCAL RELIEF EFFECTIVE FISCAL STIMULUS? EVIDENCE
FROM AID TO STATE AND LOCAL GOVERNMENTS
Jeffrey Clemens
Philip G. Hoxie
Stan Veuger
Working Paper 30168
http://www.nber.org/papers/w30168
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
June 2022
We are grateful to John Kearns for outstanding research assistance. Clemens thanks the Hoover
Institution for support as a Visiting Fellow. We thank Michael Farquharson, Scott Ganz, Richard
Grossman, Duncan Hobbs, Ben Hyman, Ellen McGrattan, José Luis Montiel Olea, Valerie
Ramey, Andres Santos, Daniel Shoag, Michael Strain, Kaspar Wuthrich, and seminar attendees at
the American Enterprise Institute, the Hoover Institution, and the Stanford University Department
of Economics for their comments, help, and suggestions. The views expressed herein are those of
the authors and do not necessarily reflect the views of the National Bureau of Economic
Research.
NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.
© 2022 by Jeffrey Clemens, Philip G. Hoxie, and Stan Veuger. All rights reserved. Short sections
of text, not to exceed two paragraphs, may be quoted without explicit permission provided that
full credit, including © notice, is given to the source.
Was Pandemic Fiscal Relief Effective Fiscal Stimulus? Evidence from Aid to State and Local
Governments
Jeffrey Clemens, Philip G. Hoxie, and Stan Veuger
NBER Working Paper No. 30168
June 2022
JEL No. E6,H1,H7
ABSTRACT
We use an instrumental-variables estimator reliant on variation in congressional representation to
analyze the effects of federal aid to state and local governments across all four major pieces of
COVID-19 response legislation. Through September 2021, we estimate that the federal
government allocated $855,000 for each state or local government job-year preserved.
Our baseline confidence interval allows us to rule out estimates of less than $433,000. Our
estimates of effects on aggregate income and output are centered on zero and imply modest if any
spillover effects onto the broader economy. We discuss aspects of the pandemic context, which
include the surprising resilience of state and local tax revenues as well as of broader
macroeconomic conditions, that may underlie the small employment and stimulative impacts
we estimate in comparison with previous research.
Jeffrey Clemens Stan Veuger
Department of Economics American Enterprise Institute
University of California, San Diego 1789 Massachusetts Avenue
9500 Gilman Drive #0508 Washington, DC 20036
La Jolla, CA 92093 stan.veuger@aei.org
and NBER
jeffclemens@ucsd.edu
Philip G. Hoxie
Department of Economics,
First Year Commons
University of California San Diego
9500 Gilman Dr. #0508
La Jolla, CA 92093
phoxie@ucsd.edu
I Introduction
Fiscal transfers from the federal government to state and local governments play an important role In
the US federal system. During the COVID-19 pandemic, federal fiscal assistance reached unprecedented
levels, with aid to state and local governments spanning four legislative vehicles and summing to almost
$1 trillion.2
The motivation for federal fiscal stabilization arises from state and local balanced-budget constraints.
When state and local governments face downturns, these constraints would, in the absence of federal
relief, prevent them from contributing to countercyclical policy. As revenues decline and spending needs
rise, compliance with the rules dictates tax increases and a search for budgetary savings. Savings may
come from wage freezes and layoffs for members of the public-sector work force. Figure 1, for example,
illustrates the reductions in state and local government employment that took place from the start of
the pandemic through September 2021. These reductions can, in turn, lead to deteriorating service
delivery just as needs run high.
Over the course of the pandemic, federal fiscal assistance has been distributed through a variety of
channels, including general aid to states, general aid to local governments, and aid appropriated for
specific functions of state and local government. A primary purpose of this aid was to limit the severity
of public-sector layoffs and to increase the pace at which it would ultimately recover (Driessen and
Gravelle, 2020; The White House, 2021; US Department of the Treasury, 2021b). This is motivated, at
least in part, by standard concerns for macroeconomic stabilization. Our analysis thus undertakes to
understand the extent to which federal assistance achieved this objective. We also assess the overall
impact of federal fiscal assistance on the labor market more broadly, as well as on aggregate income and
output.
The key challenge to estimating the effects of fiscal stabilization funds is a standard endogeneity
concern: stabilization efforts are undertaken when and where economic conditions are poor, such that
they correlate negatively with employment. To overcome this impediment, we adopt an instrumental-
variables strategy. Specifically, we draw on existing work demonstrating that federal fiscal assistance to
state and local governments exhibited a strong bias towards small states, which enjoy disproportionate
representation in the US Congress (Clemens and Veuger, 2021a). Crucially, as our analysis confirms, the
dollars driven by the US Congress’s bias towards small states were orthogonal to a rich set of measures
of the pandemic’s direct effects on states and on the health of their populations. This and additional
evidence support the validity of variations in states’ over- and under-representation as an instrument.
Applying our instrumental-variables strategy, we estimate that federal fiscal assistance has had a
modest impact on employment by state and local governments. In our preferred specification, we
estimate that the federal government had to allocate nearly $855,000 to preserve a job-year through
September of 2021. Our baseline estimates are sufficiently precise that we can rule out estimates that
less than $433,000 was needed to preserve a job-year over this time period.
We next assess the effects of federal fiscal assistance on the broader labor market. In our analysis of
private-sector employment, we cannot reject the null hypothesis of no effect, though our estimate is
2
The 2009 American Recovery and Reinvestment Act (ARRA), in comparison, included some $223 billion for three
years of fiscal relief for state and local governments (Inman, 2010).
2
imprecise. Our estimates for real wages and salaries are also near zero, but in this instance come with
sufficient precision to rule out substantial impacts on total payroll. In sum, we find little evidence of
meaningful spillovers from state and local government aid to the overall labor market, though we
cannot rule out nontrivial impacts on employment.
We present additional analyses of effects on aggregate income and output. These estimates can be
described as being of an “open economy relative multiplier” (Nakamura and Steinsson, 2014) or a
“regional transfer multiplier” (Corbi et al, 2019; Pennings, 2021). They also center on zero, implying that
fiscal stabilization dollars have had little overall impact on economic activity in the pandemic context.
Our estimates of effects on income and output are sufficiently precise to allow us to rule out substantial
effects, in particular across the period of heightened fiscal uncertainty. To illustrate the evolving
magnitude of our multiplier estimates, we present impulse response functions using the local-projection
method for each of our outcomes of interest (Jorda, 2005; Ramey, 2016).
Our multiplier estimates are small relative to several prominent estimates from other settings (Suárez-
Serrato and Wingender, 2016; Corbi et al., 2019; Shoag, 2013 and 2016). Later, we discuss the key
features of the setting we analyze that, in our view, are the most plausible explanations for this
difference.
Our primary contribution is to the literature on the macroeconomic effects of federal fiscal assistance.
There are many papers in this literature. Some examples include Fleck (1999), Chodorow-Reich et al.
(2012), Suárez-Serrato and Wingender (2016), Corbi et al. (2019), and Pennings (2021). Other papers
have estimated conceptually similar objects using other sources of windfall gains to state and local
government budgets (Shoag, 2013 and 2016).3 What differentiates our work from these earlier analyses
is both the context and the magnitude of the spending shocks generated by our instrument.4
Papers set in the period immediately following the Global Financial Crisis (e.g., Chodorow-Reich et al.,
2012) or in the Great Depression (e.g. Fleck, 1999) can be described as coming from eras of secular
stagnation or rampant demand shortfalls (Eichengreen, 2015; Summers, 2015; Eggertson et al., 2019).
The period we study, on the other hand, is characterized by a transition from the Great Recession’s low-
inflation environment to one of rapidly increasing prices, suggesting a different imbalance between
aggregate demand and supply.
In addition, the standard transmission mechanisms for multiplier effects may have been blunted by
pandemic restrictions on service provision and spending and by the public-health situation more
broadly. This macroeconomic context may lead one to expect smaller employment and stimulative
effects. In fact, it has been argued that the provision of social insurance, not aggregate-demand
management, was and should have been at the heart of the economic-policy response to the pandemic
(Romer and Romer, 2022). While we believe there is truth to that line of argument, in particular as far as
the Paycheck Protection Program (PPP) and Unemployment Insurance (UI) components of the relief
3
These papers do not estimate a traditional balanced budget multiplier because the spending they analyze is
financed by windfall gains, as observed by Clemens and Miran (2012).
4
Fishback (2017), Ramey (2019), and Chodorow-Reich (2020) provide overviews of the even more extensive
literatures on the effects of fiscal policy more broadly defined on employment, output, and other variables of
interest. Nakamura and Steinson (2014), as well as Ramey (2016 and 2019) and Chodorow-Reich (2020), provide
frameworks for interpretation of the different estimates in these literatures.
3
efforts were concerned, policymakers explicitly intended for the state and local aid component to help
preserve employment, maintain quality of state and local service delivery, and support aggregate
demand.5
Our context also differs from the Great Recession setting in key respects related to state and local
government finances and operations. State government revenues, as has now been widely documented,
were far more robust to the pandemic’s effects than had been anticipated (Clemens and Veuger, 2021b;
National Association of State Budget Officers, 2021). By reducing expenditures, pandemic related limits
on service provision (e.g., transportation to schools) further alleviated strains on state budgets. While
some new expenditure needs directly related to the public-health crisis arose, in overall terms states
were less liquidity-constrained than had been anticipated and thus had less cause to make rapid use of
fiscal assistance dollars. While the remaining federal dollars will either be spent or used to finance
reductions in taxes over time, their impact on states’ economies will come after, rather than during, the
period of pandemic-driven uncertainty and potential revenue and aggregate-demand shortfalls.
Finally, the magnitude of the spending shocks induced by our instrument is quite large. Variations in
states’ over- and underrepresentation predict considerable variations in states’ funding allocations. As
can be seen in Figure 2, allocations to the most over-represented states exceeded allocations to the
least-represented states by several thousand dollars per capita.6 This is considerably more variation than
studies of fiscal stabilization efforts are typically able to analyze.
We also contribute to the literature on state and local government budgets over the course of the
pandemic. Initial papers in this literature sought to forecast the magnitudes of the revenue shortfalls
faced by various levels of government within the United States (Auerbach et al., 2020; Clemens and
Veuger, 2020a, 2020b; Chernick et al., 2020; Gordon, Dadayan, and Rueben, 2020; Whitaker, 2020a;
2020b). Additional analyses have considered the pandemic’s implications for spending needs (Gordon
and Reber, 2020; Clemens, Ippolito, and Veuger, 2021). Researchers have also explored the effects of
initial state and local aid allocations on the extent of public sector layoffs in April 2020 (Green and
Loualiche, 2020). We offer the first systematic analysis of the regional employment, income, and output
multiplier effects of federal allocations to state and local governments across the four major pieces of
COVID-19 response legislation.
The paper is organized at follows. In Section II we introduce the data sets and sources on which our
analysis relies. We turn to our empirical strategy in Section III. Sections IV and V present our empirical
results for state and local government employment and the broader economy, respectively. We
conclude with a discussion of our findings in Section VI.
5
This is reflected in policy documents (e.g., as above, Driessen and Gravelle, 2020; The White House, 2021; US
Department of the Treasury, 2021b), in the contemporary policy debate (e.g. Bartik, 2020; McNichol et al., 2020;
Zandi, 2020), as well as in the explicit association of some elements of state and local aid with specific functions of
those levels of government (e.g. education, health care).
6
The differential between the most and least well-represented states exceeds one-third of the combined, annual
per capita state and local government revenues from own sources of a typical state in recent years.
4
II Data
We analyze the fiscal assistance resulting from four major pieces of legislation during the COVID-19
pandemic: the CARES Act, the Families First Coronavirus Response Act (FFCRA), the Response and Relief
Act (RRA), and the American Rescue Plan Act (ARPA).7 Taken together, these packages constituted a
massive relief effort that provided as much as $6 trillion in income support to households, a mix of
loans, grants, and tax relief to firms and non-profits, funding for (public) health efforts, and
intragovernmental grants to subnational governments. This final category includes almost $900 billion in
funds for state, local, territorial, and tribal governments, as well as the District of Columbia. We focus on
the impact of these funds across the 50 states.
Following Clemens and Veuger (2021a), data from the Committee for a Responsible Federal Budget
(CRFB, 2021) form the foundation for our fiscal assistance variables.8 We supplement the CRFB data with
information from several sources.9 For the bulk of our analysis, we combine the aid disbursed by each
bill into one variable to avoid interactions and inconsistencies between timing, expectations, and
changes in behavior associated with the political process of passing such massive bills. Our main
independent variable is the grand total of aid distributed to each state per resident in millions of dollars.
Figure 2 provides an initial look at the distribution of funds across the four pieces of legislation. Dollar
values are expressed on a per capita basis. Throughout this paper, we define a state’s population
according to the U.S. Census Bureau (2021) official count estimated during the 2020 census. Panel A
shows that the distribution of money across states has not been equal, with smaller states receiving
relatively more per person than larger states.
In this paper’s analysis, we use a state’s number of congressional representatives per million residents
to instrument for federal aid per capita.10 Clemens and Veuger (2021a) establish a relationship between
the relative representation of states in Congress and the amount of aid they were allocated during the
pandemic. Smaller states, such as Wyoming, receive relatively more representation per capita as each
state is guaranteed two senators regardless of population, ensuring that Wyomingite voices are
relatively more powerful in legislative negotiations. Congressional representation is measured using
rosters of the House of Representatives and Senate during the 116th and 117th Congresses from Lewis et
al. (2021). Of note, Congressional representation in 2020 was allocated according to state population in
7
This section’s description of COVID-19 relief legislation draws heavily on the description from Clemens and
Veuger (2021a). Readers interested in detailed legislative histories should look to the more expansive discussion
there.
8
We use data from the CRFB’s COVID-19 Money Tracker as of August 19th, 2021.
9
As in Clemens and Veuger (2021a), “[w]e obtain information on the distribution of transit funds for the RRA and
ARPA from the US Federal Transit Administration (2021a, 2021b). Data on the allocation of ARPA assistance to non-
public schools come from the US Office of Elementary and Secondary Education (2021). We obtain estimates of
ARPA section 9817 matching increases from Chidambaram and Musumeci (2021). We approximate the allocation
of ARPA section 9819 federal matching funds for uncompensated care using FY2021 estimates of federal
disproportionate share hospital allotments by state from the Medicaid and Chip Payment Access Commission
(2021).” The Coronavirus Capital Projects Fund outlined in ARPA is distributed according to guidance from the
United States Department of the Treasury (2021a).
10 # 𝑜𝑓 𝑅𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑎𝑡𝑖𝑣𝑒𝑠𝑠 +# 𝑜𝑓 𝑆𝑒𝑛𝑎𝑡𝑜𝑟𝑠𝑠
Congressional representation per million residents is calculated as , for each
𝑃𝑜𝑝𝑠,𝑦2020 /1,000,000
state s. Clemens and Veuger (2021a) show that assigning greater weight to the number of senators does not
qualitatively affect the estimated importance of congressional over- and under-representation.
5
the 2010 census, thus ensuring that Congressional representation is not affected by COVID-19-induced
variations in population. Panel B shows the relationship between federal aid and our instrument.
The main outcome of interest in our analysis is state and local employment. The US Bureau of Labor
Statistics employs several approaches to estimate employment levels. We primarily rely on employment
counts from the Quarterly Census of Employment and Wages (QCEW), and use Current Employment
Statistics (CES) data for robustness checks. The QCEW counts the monthly unemployment insurance
records of 10.9 million establishments to estimate the number of “covered workers who worked during,
or received pay for, the pay period that included the 12th day of the month” (US Bureau of Labor
Statistics, 2021c). Estimates are broken down by establishment location and NAICS industry code. The
CES, on the other hand, is based on a set of 697,000 establishments monthly, over the same time period
as the QCEW, to approximate employment across states and industries. Generally speaking, the QCEW
estimates are more detailed and precise, but their publication lags that of the CES numbers by several
months. 11 As such, estimates that rely on the QCEW are based on data through September 2021 while
estimates that rely on the CES use data through December 2021. We also analyze the effects of fiscal
assistance on state-wide aggregate income and output as reported by the Bureau of Economic Analysis
(BEA).
Table 1 presents summary statistics on the full set of variables used in our analysis. Because some of the
variables we use in our analyses are available for different time periods, not all variables have the same
number of observations. Notably, variables derived from the QCEW have fewer observations than
variables derived from the CES. Additionally, some of the variables we analyze are reported at a monthly
frequency while others are reported at a quarterly frequency. Further details on the definitions of key
variables can be found in Appendix Table 1.
III Empirical Strategy
We seek to identify the direct impact of COVID-19 relief funds to state and local governments on
employment during the COVID-19 pandemic. Equation (1) presents a “naïve” OLS model of the
relationship between per capita aid and changes in the per capita employment of state and local
governments:
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦 (1)
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
In the equation above, is the arithmetic change in per capita state and local
𝑃𝑜𝑝𝑠,𝑦2020
government employment in state s during month m and year y of the pandemic relative to the same
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
month in 2019. 𝑃𝑜𝑝 is the total per capita funding (in millions of dollars) to state and local
𝑠,𝑦2020
11
It should be noted that the QCEW excludes up to 700,000 state and local government employees that are
sampled in the CES survey. Excluded employees include elected officials, members of a legislative body or judiciary,
state National Guardsmen, and temporary employees serving during a declared emergency. Students employed in
a work-study program do not enjoy Unemployment Insurance (UI) coverage and are therefore not captured by the
QCEW either. For an in-depth discussion of UI coverage, see US Department of Labor (2020).
6
governments in state s pooled across all four COVID-19 relief bills. This variable is time-invariant. 𝑋𝑠,𝑚,𝑦
is a vector of state-level demographic, economic, and political controls, which we discuss in greater
detail below and in Appendix Table 1.
OLS estimates of 𝛽1 from equation (1) are subject to potential biases linked to the endogeneity of fiscal
assistance allocations. If policymakers allocated more money to states with worse outbreaks of COVID-
19, for example, then federal aid would be correlated with any variations in employment that were
driven by variations in the severity of the pandemic. This would introduce downward bias as it would
generate a spurious, negative correlation between aid dollars and employment outcomes. A more direct
form of reverse causality may also arise if, for example, the severity of states’ public-sector layoffs
shaped federal aid allocations. In this case, the employment shock determines the amount of aid given,
creating a spurious negative relationship.
We adopt an instrumental-variable approach to address these challenges. We draw on evidence from
Clemens and Veuger (2021a), who show that a state’s per capita representation in Congress has two
relevant features. First, it is strongly predictive of variations in per capita federal aid allocations. Second,
as discussed in more detail below, it is orthogonal to a rich set of measures of the pandemic’s direct
effects on states and on the health of their populations. This leads us to estimate the following set of
equations:
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 (2a)
= 𝛼 + 𝛽1 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦 .
𝑃𝑜𝑝𝑠,𝑦2020
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑 (2b)
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦 .
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
In the first-stage regression (2a), 𝑃𝑜𝑝 is regressed on 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of
𝑠,𝑦2020
representatives and senators per million residents in 2020, and a set of additional controls 𝑋𝑠,𝑚,𝑦 , the
components of which we discuss below. 𝑋𝑠,𝑚,𝑦 , encompasses a baseline set of controls discussed further
in this section and additional robustness controls defined in Appendix A1. Robust standard errors are
clustered at the state level. In our baseline analysis, we weight observations by state population, though
we present robustness analyses in which we weight each state equally. Fitted values from the first stage
(2a) are used to estimate the second stage (2b).
A valid instrument satisfies both the relevance and exogeneity (or exclusion) restrictions. To serve as a
good instrument, congressional representation needs to be statistically related to the amount of aid
disbursed by the federal government. If the relationship is not strong and the relevance restriction is
failed, the fitted value will not pick up the exogenous variation needed to estimate a correctly specified
second stage. As established by Clemens and Veuger (2021a), the relationship between representatives
per million and COVID-19 relief aid is very strong. On a per capita basis, as can be seen in Figure 2, Panel
A, small states received much more money than large states. These same small states are over-
represented in Congress, a status that provides them with an advantage in the political bargaining
process. Figure 2, Panel B shows that, for those states with more than two congressional representatives
per million residents, the amount of aid scales almost proportionately with representation. However,
7
there is no such relationship for those states with less representation. Thus, congressional
representation per resident is a strong instrument for the relative amount of aid received by a state. We
evaluate the strength of the instrument formally in the Results section.
The exogeneity restriction requires that, conditional on other independent variables, congressional
representation be structurally unrelated to other factors that influence state and local government
employment during the pandemic. Here it thus becomes relevant to discuss the variables we include in
𝑋𝑠,𝑚,𝑦 . In our baseline specification, the vector 𝑋𝑠,𝑚,𝑦 includes the log of state s’s official 2020 Census
population (the level of which is used to construct other variables that require population), the share of
population in state s that lives in a local jurisdiction eligible for financing through the Federal Reserve’s
Municipal Liquidity Facility,12 and the arithmetic changes in state and local government employment per
capita and private employment per capita in state s between December 2018 and December 2019,
respectively. As proxies for the stringency of COVID-related restrictions on economic activity, the
average Oxford Stringency Index (OSI) value for state s during March 2020 and the average OSI value for
state s during month m and year y are also included.13
We advance several arguments and pieces of evidence in support of the exogeneity restriction required
for equation (2b) to yield a causal estimate of the effect of federal fiscal assistance. First, we emphasize
that our instrument’s conditional exogeneity is plausible. Since representation imperfectly scales with
population, some states will be relatively over-represented; for example, Montana’s roughly 1 million
residents enjoy three votes per million in Congress (2 senators and 1 representative) while 3 million
Arkansans enjoy only 2 votes per million (2 senators and 2 representatives). At the same time, excepting
an unlikely epidemiological relationship between state population numbers and the novel coronavirus,
the number of congressional seats has no direct impact on local employment beyond its influence on
the legislative priorities of Congress.
Importantly, the data support the general argument that the degree of a state’s over- or under-
representation was largely unrelated to the needs it faced as a consequence of the pandemic. Clemens
and Veuger’s (2021a) analysis of the small-state advantage shows that it is more or less orthogonal to an
extensive set of proxies for dimensions of state and local government funding needs, including states’
revenue shocks, economic shocks, the size of their public sector, and acreage of federal land. Appendix
Table 2, a version of Clemens and Veuger’s (2021a) Appendix Table 5 with the sum of federal funds
across all four bills taking the place of the funds in each individual bill as the dependent variable,
illustrates this for the current setting. Controlling for various dimensions of perceived need does not
qualitatively affect the relationship between our instrument and the amount of federal funds allocated.
12
Access to the Federal Reserve’s Municipal Liquidity Facility (MLF) has been described as a major contributor to
settling municipal bond markets during the coronavirus’s initial outbreak (Haughwout et al., 2021). Based on
Federal Reserve Board (2021) guidance, we estimate the share of states’ 2020 populations residing in a
municipality eligible for local MLF financing (in addition to state MLF financing, which was accessible to all).
13
Information on the stringency of government restrictions comes from Oxford’s COVID-19 Government Response
Tracker (OxCGRT). This source provides daily index values of government restrictions for all 50 states since January
6, 2020. OxCGRT averages policy stringency across eight dimensions: school closures; workplace closures; public
event cancellations; gathering restrictions; public transportation closures; stay-at-home orders; restrictions on
internal movement; and international travel bans. This variable ranges from 0 (no restrictions) to 100 (the highest
possible level of restrictions across all eight dimensions). In all regressions, OSI is rescaled by dividing by 100 so
that it ranges from 0 to 1.
8
Even with this initial supporting evidence, however, the exogeneity assumption requires further
justification. It is possible, for example, that small states may have been differentially impacted by the
pandemic, which may thus have differentially impacted their employment. A larger outbreak of COVID-
19 will cause more people to limit mobility either voluntarily or due to health reasons. Social distancing
necessarily translates into less spending on services, the taxation of which provides the revenues many
state and local governments use to pay employees. Another possibility is that small states may have
adopted a different set of policy responses to the pandemic, and that those policy responses may have
exerted independent influence on economic activity. On this point, it is useful to note that, as shown by
Clemens and Veuger (2021a), the over-representation of small states is less correlated with political
partisanship than is commonly assumed. We provide additional evidence on a number of these issues by
exploring our results’ robustness to altering the sets of covariates we include in 𝑋𝑠,𝑚,𝑦 . In particular, we
implement specifications that include covariates that are associated with the pandemic’s health effects,
with the stringency of states’ policy responses to the pandemic, with states’ political leanings, and with
additional proxies for states’ pre-pandemic economic trends.
An additional potential concern is that the fiscal assistance that is predicted by our instrument might be
correlated with other elements of the federal government’s pandemic relief packages. This is a natural
concern in light of the fact that fiscal relief for state and local governments accounts for roughly one
sixth (or $1 out of $6 trillion in total relief spending) of the federal relief packages. We are able to
provide direct evidence on this potential concern with respect to three of the largest programs through
which the federal government provided relief to business and households, namely the PPP, the
Economic Impact Payments (EIP, or “stimulus checks”), and federal funding for enhanced UI benefits. In
Appendix Table 3, we report results from an analysis in which we put the per capita spending from each
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
of these programs on the left-hand side of Equation (2b). The point estimate on 𝑃𝑜𝑝 thus tells us
𝑠,𝑦2020
how many dollars in spending through these major programs are correlated with each dollar in fiscal
relief of states and localities as predicted by our instrument. The estimates in Panel A reveal that in our
baseline specification there is no significant relationship between the spending predicted by our
instrument and the federal spending through PPP, EIP, and UI. Indeed, the sum of the three coefficients
is remarkably close to 0. In Appendix Table 4, we place the PPP, EIP, and UI spending variables on the
left-hand side of Equation (2a). The results show directly that our instrument is uncorrelated with
spending through these programs in our first-stage regression.
A final potential concern is that small and large states may simply have been on different pre-pandemic
trends. Indeed, because the data provide reason to worry that this was the case, our baseline
specifications include pre-pandemic trends in the dependent variables as controls. An exploration of the
robustness of our estimates to alternative approaches to controlling for this potential concern will be an
important component of our analysis.
We present further evidence, discussed in more detail below, in the form of “pre-trend tests.” That is,
we confirm that the spending variations that are isolated by our instrument do not predict changes in
employment over the months that preceded the pandemic’s onset and the first pieces of legislation that
we analyze.
Equations (2a) and (2b) can be described as pooled panel regressions. To recover impulse response
functions, we also estimate sets of horizon-specific estimates at the monthly level for our employment
9
data and at the quarterly level for our data on macroeconomic aggregates. These period-by-period
regressions are described by equations (3a) and (3b):
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
= 𝛼 + 𝛽1 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦 (3a)
𝑃𝑜𝑝𝑠,𝑦2020
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑 (3b)
𝑃𝑜𝑝𝑠,𝑦2020
= 𝛼 + 𝛽1 𝑃𝑜𝑝 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦 .
𝑠,𝑦2020
In equations (3a) and (3b), m and y iterate over the month-year pairs from January 2020 to September
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
2021. In this specification, is still the total amount of aid per capita allocated to a state since
𝑃𝑜𝑝𝑠,𝑦2020
the beginning of the pandemic. This change in methodology has two main advantages. First, for the set
of regressions estimated from April 2020 onwards we are able to establish a time series of the effect
that relief aid has had on employment. It is unlikely that money allocated in March would have its full
effect by April, so estimating equations (3a) and (3b) month by month enables us to examine if and
when COVID-19 aid significantly cushioned employment. Second, our estimates for months that precede
the pandemic provide tests for the presence of divergent pre-trends. Instrumented COVID-19 relief aid
should not be related to employment outcomes in any month before money was actually legislated.
Figure 4, analyzed further in the Results section, presents this pre-trend test.
The coefficient 𝛽1 estimated in equations (2b) and (3b) is the primary object of economic interest. In
addition to summarizing the relationship between COVID-19 relief aid and state and local government
employment, 𝛽1 can be transformed into an intuitive metric for evaluating the efficacy of fiscal relief.
Specifically it can be transformed into an estimate of the dollars spent per job-year saved. In equation
(2b), the coefficient 𝛽1 identifies the average number of jobs recovered for an additional $1 million in
̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
federal aid across an 18-month (1.5 year) interval. Since 𝑃𝑜𝑝 is defined as the amount of aid per
𝑠,𝑦2020
capita in millions of dollars, the ratio $1,000,000/(𝛽1 ∗ 1.5) is the number of federal dollars needed to
recover one state or local government job-year during the pandemic.14 If 𝛽1 is large, the government will
have spent relatively little money to preserve or create each job-year.
IV Results: State and Local Employment
Together, the CARES Act, FFCRA, RRA, and ARPA represent an unprecedented transfer of money from
the federal government to state and local governments. We focus first on assessing the extent to which
this transfer helped sustain state and local employment through the crisis, before turning to broader
macroeconomic impacts in the next section.
14
Since the CES data extend to December 2021, the amount of money spent for each job-year saved is equivalent
to $1,000,000/(𝛽1 ∗ 21/12) using the regression results found in the appendix.
10
State and Local Government Employment During the Pandemic
We begin by describing the declines in state and local government employment that occurred during the
pandemic. Figure 1 provides time series evidence on the magnitude of the COVID-19 shock’s initial
impact on state and local government employment, as well as on the evolution of that impact over time.
It uses QCEW data to summarize per capita changes in state government employment, local government
employment, and state and local government employment combined. The changes are calculated
relative to the same calendar month in 2019 (e.g., the first value is a change calculated from January
2019 to January 2020, while the final value is a change calculated from September 2019 to September
2021). Appendix Figure 1 summarizes these changes using employment data from the CES. Both sources
identify the same general trend: a sharp decline in government employment during the spring that was
partially undone during the summer of 2020, followed by additional, but much slower, recovery through
late 2021. Appendix Figure 2 presents the same data in percent change terms, echoing the significance
of the contraction in employment and the lagging pace of the recovery.
Figure 1 shows that local employment has been durably affected by the COVID-19 shock. By June 2020,
local government employment had shrunk by 7.6 percent nationally; it remained 3.2 percent below its
2019 level as of September 2021. State government employment suffered a smaller initial shock and
was 2.1 percent below its 2019 levels as of September 2021. By June 2020, combined state and local
government employment had shrunk by over 1.2 million nationally (6.4 percent below 2019 levels); in
September 2021 it remained 500,000 jobs (or 3.0 percent) below its 2019 levels.15 As in the general
labor market, impediments to full employment in the state and local government sector continued to
linger through the 2021 calendar year.
First-Stage Relationship Between Federal COVID-19 Relief and Congressional Representation
The first-stage relationship between state and local aid and relative congressional representation is
strong, as shown earlier in Figure 2. Panels A and B in Figure 3 present coefficients on 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠
as in equation (3a). In Panel A the dependent variable is, in each month, the cumulative total of per
capita aid to state and local governments across the four major pieces of relief legislation. In Panel B the
dependent variable is the running total, rather than the cumulative total, of federal aid per capita. In all
months after March 2020, the coefficient on the instrumental variable is both economically substantial
and statistically significant at the 1 percent level. In Panel B, estimates for months extending from April
2020 through March 2021 are around $650 per capita and primarily reflect the small-state bias
embedded in the CARES Act. The coefficients rise to roughly $1,000 beginning in April 2021, reflecting
the additional small-state bias embedded in the ARPA. The estimates in Panel A are consistently at
roughly $1,000, reflecting that the dependent variable is the cumulative total of fiscal assistance
regardless of the month in the sample.
Our baseline first-stage F-statistic of 57.79 exceeds the traditional rule-of-thumb threshold value of 10
used to reject a null hypothesis of weak instruments (Stock and Yogo, 2005). Montiel Olea and Pflueger
(2013) propose a test for weak instruments that allows for errors that are not conditionally
homoscedastic and serially uncorrelated. Based on the routine introduced by Pflueger and Wang (2015),
15
Appendix Figure 1 replicates Figure 1 with CES estimates and tells a very similar story.
11
our baseline F-statistic also allows us to reject at the 95% confidence level the null hypothesis that the
approximate asymptotic bias of our 2SLS estimator exceeds 10% (23.11), or even 5% (37.42) of the bias
in our OLS estimator. Similarly reassuring are the results of Angrist and Kolesár (2022, Figure 2), which
suggest that the median bias in our 2SLS estimator is negligible relative to the bias in our OLS estimator.
The strength of our instrument also bears on the potential relevance of violations of the monotonicity
assumption (i.e., the “no defier” assumption, which in our setting requires that states with higher values
of our instrument are never made less likely to be exposed to the treatment of greater federal fiscal
assistance). As noted by Angrist, Imbens, and Rubin (1996), “the stronger the instrument, the less
sensitive the IV estimand is to violations of the monotonicity assumption.” All of this is particularly
reassuring given the (justified) concerns over weak instruments in this literature, as discussed by Ramey
(2016).
Our first-stage is also robust to the combination of baseline controls included in the regression, as
evidenced by Appendix Table 5. The estimated F-statistic remains large with the separate addition of
each control shown.
Federal COVID-19 Relief and State and Local Government Employment
Column 2 of Table 2 presents the second stage of our 2SLS baseline specification using QCEW data from
April 2020 through September 2021. The coefficient on total aid per capita, 0.780, implies that the
federal government had to allocate nearly $855,000 per job-year saved. That amount corresponds to
over 12 times median household income.16
While our baseline estimate of federal dollars allocated per job-year saved is high, our estimate
nonetheless implies a substantial number of job-years saved due to the historically large quantity of aid
provided. A back-of-the-envelope calculation using $837 billion as the total amount of aid disbursed and
$855,000 as the cost to save one job-year implies that 980,000 public-sector job-years were saved in
aggregate. For reference, roughly 1.9 million state and local workers lost their jobs in the initial stages of
the pandemic. Our estimates suggest that, in the absence of federal aid, additional public sector job
losses would have occurred during the summer of 2020. Instead, public-sector employment commenced
its slow recovery.
Alternative Specifications
Based on our discussion of the statistical issues associated with estimating equation (1), we would
expect the OLS estimate to be attenuated towards zero. Column 1 of Table 2 presents the OLS estimates
of equation (1), again using QCEW data from April 2020 through September 2021. As expected, the
coefficient on aid per resident using the 2SLS specification is substantially more positive than the OLS
estimate, confirming that the OLS estimate is biased downward.
Our baseline estimates of equation (2b) may be biased if our instrument, representatives per million
residents, is correlated with related state characteristics such as pre-pandemic macroeconomic
16
This also exceeds the 2020 average annual salary of federal, state, and local government workers of $62,765 by a
factor of close to 14 (US Bureau of Labor Statistics 2021b).
12
performance or the severity of COVID-19 outbreaks. We present several robustness checks to
investigate whether our estimates are sensitive to the addition of controls for such factors. Columns 3
through 7 of Table 2 show estimates with additional sets of controls to account for such variables as the
outbreak of COVID-19, the state political environment, and variations in voluntary and involuntary social
distancing.17 Column 3 adds as controls the share of votes won by Donald Trump in a given state during
the 2020 presidential election, the average OSI value during the last week of March 2020, and the
percentage change in mobility in retail and recreational areas as measured by Google. In Column 4, we
add the total and new number of per capita COVID-19 cases and deaths in the previous month. In
Column 5, we add the arithmetic change in a state’s real output per capita from Q4 2018 to Q4 2019 as
an additional economic control. Column 6 combines all of these controls in one regression. Column 7
presents a specification in which the log of population is the only covariate in 𝑋𝑠,𝑚,𝑦 .
Across the specifications in Table 2, the coefficient on total federal aid per capita remains modest and
either statistically indistinguishable from zero or marginally statistically distinguishable from zero. The
smallest 2SLS estimate is from the “Simple” specification in column 7, which is biased downward
because it incorporates no measure to account for variations in employment growth that pre-date the
pandemic. We emphasize that even the largest estimate in Table 2 is modest in magnitude. The
estimate from Column 4 implies that $640,000 was required to save a full-year government job. In our
most aggressively controlled specification (Column 5), the price for each job-year saved is nearly $1.5
million.
As additional robustness checks, we present estimates in which we do not weight states according to
population and in which we estimate state and local employment using CES data rather than QCEW
data. Weighted and unweighted specifications have different interpretations. Unweighted specifications
are more appropriately interpreted as shedding light on the experience of a typical state, while
population-weighted estimates are more appropriately interpreted as shedding light on the typical
impact of each dollar spent. In analyses of federal fiscal assistance from the ARRA, for example, Ramey
(2019) takes issue with Chodorow-Reich (2020)’s attempts to estimate the aggregate impact of the
ARRA using unweighted regressions. Ramey argues that while Chodorow-Reich (2020)’s unweighted
approach is satisfactory to analyze cross-state differences, the approach is not sufficient to comment on
the overarching impact of federal stimulus. As shown in Appendix Table 7, unweighted estimates tend to
be closer to zero in our setting.18 Appendix Table 8 shows that we similarly obtain smaller estimates
when analyzing CES employment data rather than QCEW employment data. The CES data and
unweighted estimates thus imply employment impacts smaller than the already modest impacts we
estimate in our baseline specification.
Finally, we test the robustness of our results by relying on an instrument that is similar in spirit to ours
but constructed differently. We again estimate equation (2b), but this time with the interaction between
a small-state indicator and state population as the instrument, as in Green and Loualiche (2020).
Appendix Figure 5 summarizes the results of this specification using the QCEW estimates of
17
The additional sets of controls are described in detail in Appendix Table 1. Appendix Table 6 is the first-stage
counterpart to Table 2.
18
Appendix Figure 4 presents the coefficient plot for unweighted regressions using QCEW state and local
government employment data. Aside from observations not being weighted by state population, the baseline
regressions used for Figure 4 and Appendix Figure 4 are otherwise identical. Note that the coefficient plot still does
not show a positive impact of the COVID-19 relief aid to state and local governments.
13
employment. As in Figure 4, the point estimates average modestly under 1, indicating that each $1
million in aid preserved modestly less than 18 public sector job-months across the 18 months in our
sample. This provides reassuring evidence that our findings are not sensitive to the functional form we
use to instrument for fiscal assistance with variations in states’ political representation.
Pre-Trends
In addition to examining the first-stage F-statistics for an indication of the strength of the instrument, it
is also prudent to conduct “pre-trend” tests to provide additional evidence on the plausibility of the
exclusion restriction. If the exclusion restriction is satisfied, the instrument ought not to be correlated
with employment trends prior to the onset of the pandemic. The bottom row of Table 2 shows that the
coefficient on federal aid per capita from regressing equation (2b) with data from January to March
202019 (our ‘pre-pandemic’ period) is statistically insignificant and practically small, suggesting there is
no14 uncontrolled trend prior to April 2020.20 The near-zero and insignificant pre-trend coefficients
suggest the lack of a strong relationship between over-represented states and employment prior to the
COVID-19 shock.
Evolution of Employment Effects over the Course of the Pandemic
Timely delivery of funds has been a central issue for the federal government’s COVID-19 response. As
there is a delay between the announcement of funding allocations, the disbursement to state treasuries,
and the actual spending by state and local governments, it may be useful to examine the coefficient on
federal aid per capita over the course of the pandemic in order to identify any trends over time. This
timing component is an important aspect of the overall policy landscape.
Figure 4 shows the local-projection impulse response of state and local government employment to
total federal aid per capita in millions of dollars, with equation (3b) estimated month by month. While
the coefficient on the aid variable is generally positive, indicating that more federal support translated
into jobs saved, the effect is economically modest and tends, in most months, to be statistically
indistinguishable from zero. An important takeaway from Figure 4 is the lack of a discernible impact of
the relief aid until June 2020. State and local governments may react to federal decisions with a lag, and
it was not clear if it was safe to bring employees back until summer 2020.21 Since summer 2020, and
through the third quarter of 2021, the coefficient has settled around one.
19
As the QCEW is surveyed during the second week of each month, March 2020 employment figures are estimated
prior to the large-scale shutdowns that shocked normal business conditions.
20
These estimates are presented in greater detail in Appendix Table 9. The magnitudes of the coefficients are
roughly one-fifth of those in Table 2, which are already quite low in practical terms, and present negative signs.
21
This stands in interesting contrast with the practically immediate impact of federal relief on municipal credit
markets observed by Haughwout et al. (2021).
14
V Results: The Macroeconomy
Aid to state and local governments may support broader economic activity in two ways. First, supporting
employment in the public sector buoys incomes among those employees who retain their jobs. The
money they continue to spend can support employment in the private sector. It should be noted that
the forced and voluntary social distancing experienced during the pandemic may limit this transmission
mechanism. Second, more aid to state and local governments may also fortify their abilities to provide
basic services, health-related relief, and investment that contain the economic damage of the pandemic.
Table 3 presents estimates of the effects of aid to states and localities on several macroeconomic
indicators. Columns 1 and 2 apply our baseline model to public and private employment using monthly
data. Columns 3, 4, and 5 examine the broader economy at a quarterly frequency using real, annualized
total wages and salaries (government plus private) per capita, state GDP per capita, and personal
income per capita from the Bureau of Economic Analysis (2021).22 In each instance, the regression
includes the outcome variable’s pre-pandemic trend as a control variable.23
The estimate of the impact on private employment in Column 2 is similar in size to our estimate for
public-sector employment, but very imprecisely estimated. We take this as not providing strong
evidence for an effect in either direction. Our findings in Column 3 indicate that an additional $1 in aid
to state and local governments decreased annualized real wages and salaries per capita by $0.05. This
result is insignificant at traditional confidence levels. Columns 2 and 3 thus provide little evidence of
meaningful spillovers from state and local government aid to the overall labor market.
Columns 4 and 5 analyze two broader measures of aggregate economic activity. First, Column 4 uses
annualized, seasonally-adjusted state real GDP per capita (in millions of chained 2012 dollars). The
estimate in column 4 suggests that an additional $1 in relief funds predicts a per-year reduction in GDP
per capita of $0.23, while the estimate in Column 5 shows that an additional $1 in relief funds predicts a
per-year increase in aggregate income per capita of $0.44. These results are statistically
indistinguishable from zero at traditional confidence levels, and we interpret them in combination as
suggesting a null impact on aggregate income and output.
We subject the full set of results in Table 3 to a set of robustness checks that gauge the potential
relevance of the covariates we include, of the functional form in which we include those covariates, and
the potential role of either the largest or smallest states in driving our results. In Appendix Table 10, we
replace the log of states’ populations with an indicator for whether a state was “small” in the sense that
it benefited from the CARES Act’s floor function. In Appendix Table 11, we consider a more saturated
specification in which the covariates include cubic polynomials in all baseline covariates other than
population.24 In Appendix Table 12 we reduce the control set to include solely the log of each state’s
22
We convert nominal wages and salaries and nominal personal income from the Bureau of Economic Analysis into
real terms with the national seasonally-adjusted personal consumption expenditure deflator, with a base year of
2012 equal to 100.
23
The personal income regression in column 5, for example, includes as a control the change in real personal
income per capita from the fourth quarter of 2018 through the fourth quarter of 2019. It excludes as controls the
pre-pandemic trends in public and private employment. The inclusion of these additional controls has a modest
impact on the estimated effect of federal fiscal assistance.
24
This specification also serves to address concerns raised by Blandhol et al. (2022) regarding the interpretation of
instrumental-variables estimators.
15
population, as in the “simple” specification from Column 7 of Table 2. The results in Appendix Tables 10,
11, and 12 provide evidence that our overall conclusions are not sensitive to the covariates we have
included or their functional form. Point estimates for the macroeconomic indicators we analyze tend to
change only modestly across this full set of specifications. The point estimate for state and local
government employment is more sensitive in that the estimates in Appendix Tables 10 and 12 are
negative and near 0. On balance, the estimates thus reinforce the conclusion that federal fiscal
assistance had little economic impact during the pandemic.
In Panel A of Appendix Table 13 we drop the three most and least represented states from the sample,
while in Panel B we drop the five most and least represented states from the sample. The results in
Panel A reveal that the point estimates are little changed by dropping the three most and least
represented states. Additionally, the first stage F-statistic declines only moderately from when we
remove these most extreme states from the sample. The results in Panel B reveal that after removing
the five most and least represented states from the sample, our first stage F-statistics decline
substantially. The second stage point estimates differ only moderately from their counterparts in Table
3, but the precision of the estimates is reduced substantially by dropping 10 states that contribute
substantially to the variation in our instrument from the sample.
Appendix Table 14 presents results in which we moderately change the construction of our outcome
variables. Specifically, for the regressions reported in Appendix Table 14, we define the changes in each
outcome relative to a base period of either December 2019 or the fourth quarter of 2019. Calculating
changes relative to a common month conforms more closely with the conventional approach to
estimating local-projection impulse response functions (Ramey, 2016). This contrasts with our baseline
approach in that it will not net out seasonal effects. As shown in columns 3 through 5, this change has
very little effect on the estimates we obtain for outcomes we construct using seasonally adjusted data
from the BEA. By contrast, columns 1 and 2 reveal that the standard errors on our estimates rise for
outcomes constructed using QCEW data, which are not seasonally adjusted. Qualitatively, these
estimates reinforce the overall impression that federal fiscal assistance dollars had at most a moderate
effect on employment by state and local governments, an imprecisely estimated effect on private
employment and a modest if any stimulative impact on the overall economy.
In a final robustness check, Appendix Table 15 presents estimates in which we augment the set of
controls with an additional lag in the dependent variable. For our estimates of the effect on state GDP,
for example, we add the growth in per capita state GDP from the fourth quarter of 2017 to the fourth
quarter of 2018 as a supplement to the baseline control set, which included growth from the fourth
quarter of 2018 to the fourth quarter of 2019. This robustness check is motivated by insights from
Ramey (2022) regarding the desirability of controlling for more rather than fewer lags when estimating
local-projection impulse response functions. Ramey (2022) draws in part on econometric advances from
Montiel Olea and Plagborg-Møller (2021), who show that lag-augmented local projections have
attractive inference properties. The results in Appendix Table 15 show that the inclusion of an additional
lag has essentially no effect on either the point estimates of interest or the estimated standard errors.
Additionally, the earlier lags in the dependent variables have very little predictive power, in particular
when compared with the more recent lags. In our setting, our baseline specification’s inclusion of a
16
single lag thus appears to be sufficient to capture the information available from the history of the
dependent variable.25
Evolution of Macroeconomic Effects over the Course of the Pandemic
Figure 5 presents evidence on the impulse response of macroeconomic outcomes to federal fiscal
assistance. Panels A through Panel D present local-projection estimates of the effect of federal aid on
private employment, on wage and salary earnings, on real personal income, and on real GDP. In all
cases, the impact of the federal aid to sub-national governments remains small and statistically
indistinguishable from zero over time.
VI Discussion
In this section, we evaluate the fiscal aid to state and local governments as a component of the broader
COVID-19 relief effort, place our results in the context of the literature on fiscal multipliers, and discuss
some of the caveats typical of our empirical strategy.
Job Creation
In the release of the final rule on State and Local Fiscal Recovery Funds, Deputy Secretary of the
Treasury Wally Adeyemo said, “[the COVID-19 relief funds] ensure that governments across the country
have the flexibility they need to vaccinate their communities, keep schools open, support small
businesses, prevent layoffs, and ensure a long-term recovery.” In this paper, we show that the
unprecedented level of transfers from the federal government to the sub-national level has had a
modest impact on government employment and has not translated into detectable gains for private
businesses or for states’ overall economic recoveries.
Our baseline results imply that $855,000 in federal spending was needed to preserve a state or local
government job-year during the pandemic. The confidence intervals on our estimates are sufficiently
precise to rule out estimates of less than $433,000, while we do not find significant additional effects in
the broader labor market.
These estimates do not compare favorably with estimates for the other major element of the COVID-19
relief packages that had the intent of preserving employment or stimulating economic activity. The PPP,
which has itself been criticized for having a modest job-preserving impacts per dollar spent, has been
estimated to cost much less per job year saved. Autor et al. (2022a and 2022b), for example, refer to
their estimate that the PPP cost between $169,000 and $258,000 per worker-year retained as reflecting
a “very substantial cost” and “high costs per job.” Autor et al. (2022b) describe their estimates as being
“broadly similar” to estimates from Chetty et al. (2020) and Hubbard and Strain (2020), who analyzed
25
The apparent sufficiency of a single lag may relate to the fact that our estimation relies on cross-sectional
variation in federal fiscal assistance. Insights from Ramey (2016 and 2022) and from Montiel Olea and Plagborg-
Møller (2021) are developed with a primary emphasis on time series variation.
17
the Paycheck Protection Program using complementary data sources. Faulkender et al. (2020) present
even lower estimates of between $50,000 and $75,000 per job preserved by the PPP.
The employment effects of other elements of the pandemic relief bills have been less widely studied
than those of the Paycheck Protection Program. Haughwout et al. (2021) study the Municipal Liquidity
Facility (MLF) and estimate that while the program had desirable effects on secondary market yields and
primary issuance, its implications for employment were overshadowed by those of the type of direct
federal aid analyzed in this paper. Early on in the pandemic, Chetty et al. (2020) assessed that the
Economic Impact Payments or “stimulus checks” had been so ineffective in sustaining or raising
employment levels that it “raise[d] the specter of a jobless recovery.”
Minimizing expenditures per job created or preserved is of course not the be all and end all of even
explicitly countercyclical policies.26 Unemployment insurance benefits are a particularly salient
demonstration of this, and the policy response to the COVID-19 pandemic included dramatic expansions
and extensions of such benefits. These were, inter alia, the Federal Pandemic Unemployment
Compensation (FPUC) and Pandemic Unemployment Assistance (PUA) programs. Estimates by Holzer et
al. (2021), who analyzed the termination of enhanced unemployment benefits in the summer of 2021,
which varied in timing across states, imply that these programs reduced employment by one job-year
for each $125,000 in spending. The effects of enhanced unemployment benefits were likely smaller
during the pandemic’s initial months, when pandemic restrictions would have rendered workers’ labor
supply preferences a less binding constraint.
A comparison with past fiscal relief efforts can be obtained by looking to research on the effects of the
American Recovery and Reinvestment Act (ARRA). Ramey (2019) provides a range of ARRA employment
multiplier estimates from $50,000 to $112,000 per job-year. The estimation approach, an instrumental-
variables approach that relies on Medicaid formulas, Department of Transportation formulas, and a
combination of multiple agency formulas, as well as the specific estimate of $50,000 come from
Chodorow-Reich (2020); an estimate as low as $26,000 can be found in Chodorow-Reich et al. (2012).
Wilson (2012) follows a similar formula-based approach and arrives at an estimate of $125,000 per job.
Conley and Dupor (2013) use variation in states’ budget positions and ARRA highway funding to
estimate that the Act’s implied cost of creating a job-year was $202,000. Our estimates of the dollars
spent per job-year preserved by COVID-19 era federal support for state and local governments thus far
exceed those from the ARRA context.
Fiscal Multipliers
Turning to our results for output and income, we estimate that relief funds had little if any effect on GDP
and income across the six quarters that extend from Q2 of 2020 through Q3 of 2021. There is an
extensive literature drawing on a wide range of methodological approaches and historical episodes that
provides context for our estimate of these spending multipliers. In a review of estimates of government
spending multipliers using national data, Ramey (2019) reports that most macroeconomic analyses find
a multiplier between 0.5 and 0.8, including for the ARRA. Chodorow-Reich (2020), on the other hand, in
26
We study the extent to which federal aid to state and local governments affected testing and vaccine delivery
during the pandemic in Clemens, Hoxie, Kearns, and Veuger (2022).
18
a review of multipliers estimated using cross-sectional approaches, argues the findings in that literature
translate into national multipliers between 1.5 and 2. Our estimates are most similar to Pennings’ (2021)
estimated multipliers for temporary household transfer payments financed by the federal government
and to Dupor et al.’s (2022) estimates of local consumption multipliers for the ARRA. Below, we discuss
several conceptual considerations that are relevant for interpreting our estimates and comparing them
with estimates from other contexts.
A first set of factors relates to the fact that our estimates are of subnational multipliers as opposed to
aggregate multipliers. As Ramey (2019) points out: “In some instances, the subnational multipliers are
expected to be higher than the aggregate multipliers, whereas in other instances they are expected to
be lower. There is no general rule.”
The relevant spending in this case is financed by (future) national taxpayers. Whether and how
taxpayers in states and localities differ in how they take account of these (future) tax liabilities
compared to a situation in which the spending is financed at the state and local level is an open
question. To the extent that such differences exist, our setting is probably more similar to one of open-
ended deficit financing than one with offsetting (scheduled) tax increases or Ricardian equivalence
dynamics. Within a New Keynesian framework, Pennings (2022) finds that the difference between
locally and externally financed multipliers are smaller than commonly presumed, in particular when the
government spending shock is temporary rather than persistent.
A second set of factors relate to the macroeconomic and public health context. Our estimates do not
come from an era of secular stagnation or rampant demand shortfalls (Eichengreen, 2015; Summers,
2015; Eggertsson et al., 2019). This contrasts with papers set in the period immediately following the
Global Financial Crisis (e.g. Chodorow-Reich et al., 2012). Our estimates may therefore be lower (cf.
Ramey, 2019).
Additionally, the effects of federal fiscal relief may not yet have been fully realized, as the pandemic is
not over and the monies had not all been spent within the time periods we analyze. As state and local
governments continue to use federal transfers to raise their spending, effects on output and income
may begin to accumulate. While effects may begin to accumulate, however, it is relevant to emphasize
that our analysis extends beyond the period in which it was plausible to think states were in financial
dire straits (Clemens and Veuger, 2021b), and into a period of elevated inflation. To the extent that
stimulative effects accumulate in subsequent quarters, they will likely affect prices in addition to
quantities and will presumably be offset to a degree by monetary policy.27 This would imply that their
aggregate, national effect will be smaller than it would be if monetary policy remained passive, as
illustrated by Dupor et al.’s (2022) modeling exercise.28 They find that a local consumption multiplier of
0.20 translates into an aggregate multiplier of 0.41 at the zero lower bound, but that the aggregate
multiplier turns negative if the monetary authority responds to inflationary pressures.
It is also relevant to note that COVID-19 mitigation measures were in place throughout the period we
analyze, though their intensity varied across place and time. Maximizing broader economic activity was
27
This counterproductive time delay is at the heart of a classic critique of fiscal policy as countercyclical policy
(Anderson and Jordan, 1968; Friedman and Heller, 1969; Auerbach, 2002). It is also an argument for keeping state
and local fiscal assistance linked to formulaic automatic stabilizers less vulnerable to excess.
28
See also Jo and Zubairy (2022).
19
thus not necessarily the only or even main goal policymakers had in mind when designing pandemic
relief. That said, even conditions of restricted supply may call for demand stimulus, which can then have
its normal desirable effects (as in Guerrieri et al., 2022). Additionally, as we have noted above,
preventing layoffs and stimulating the economic recovery were explicitly stated goals of the fiscal relief
studied here. The assessment presented here is thus a key component of any overall appraisal of the
federal government’s response to the COVID-19 crisis.
20
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Figure 1: Change in State and Local Government Employment per Capita
Note: This figure shows the change in national state and local government employment per capita relative to the same month
in 2019 over the course of the pandemic. Each variable shown is calculated as the arithmetic difference in employment in a
given month and the same month in 2019 divided by 2020 population. The employment data come from the Quarterly Census
of Employment and Wages (QCEW). State, local, and state plus local employment are shown separately. This figure uses data
from the US Bureau of Labor Statistics (2021b) and US Census Bureau (2021).
27
Figure 2: Distribution of COVID-19 Relief Funds per Resident
Panel A: Total Federal Aid to State and Local Governments per Resident and Population
Panel B: Total Federal Aid to State and Local Governments per Resident and Congressional Representation
Note: This figure shows the appropriation of COVID-19 relief funds to state and local governments by state. Funds are
calculated as the sum across the CARES Act, Families First Coronavirus Response Act, Response and Relief Act, and American
Rescue Plan Act on a per resident basis. Panel A displays the total federal aid to state and local governments per resident in USD
millions on the y-axis and state population (on a log scale) on the x-axis. Note that any state with a population less than
Connecticut is a ‘small state,’ a state that received the floor level of funding mandated in the CARES Act. Panel B displays total
federal aid to state and local governments per resident in USD millions on the y-axis and the number of congressional
representatives per million residents in 2020 on the x-axis. This figure uses data from the Committee for a Responsible Federal
Budget (2021), US Federal Transit Administration (2021a, 2021b), US Census Bureau (2021), Chidambaram and Musumeci
(2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and
Lewis et al. (2021).
28
Figure 3: Relationship Between Federal Aid to State and Local Governments per Resident and
Representatives Per Million Residents
Panel A: Aggregate Total Aid to State and Local Governments
Panel B: Running Total Aid to State and Local Governments
Note: This figure displays the regression coefficient (and its 95% confidence interval) on representatives per million residents in
2020 from a variation of the first stage used to estimate equation (2a):
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
= 𝛼 + 𝛽1 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where is the total of federal aid to state and local governments per resident in state s pooled across all four bills.
𝑃𝑜𝑝𝑠,𝑦2020
𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 is the number of Representatives and Senators per million residents in 2020. Included is a set of state-level
controls 𝑋𝑠,𝑚,𝑦 . This includes the log of 2020 official Census population, the share of a state’s population living in a town eligible
for financing through the MLF, the change in state and local and private employment per capita (QCEW) between December
2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index.
Note that unlike for our baseline regressions, the dependent variables is not scaled in USD millions. Panel A uses the total
29
amount of aid given by September 2021, while Panel B uses the running total of aid given through each month. The passage of
the CARES Act and ARPA can be seen in the coefficients for April 2020 and April 2021, respectively. The national appropriation
of funds is summarized in Appendix Figure 3. The regressions are weighted by state population and clustered at the state level.
Between April 2020 and September 2021, the minimum first stage F-statistic is 30.10 (October 2021) and the maximum is 59.05
(May 2020). This figure uses data from the Committee for a Responsible Federal Budget (2021), US Census Bureau (2021),
Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and
Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b), US Department of the Treasury
(2021a), Federal Reserve Board (2021), and Hale et al. (2020).
30
Figure 4: Local-Projection Impulse Response of State and Local Government Employment to COVID-19
Relief Aid
Note: This figure displays the coefficient (and the 95% confidence interval) on predicted total federal aid to state and local
governments per resident (USD millions) in the regression outlined in equation (3b):
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where m and y iterate over the month-year pairs from January 2020 to September 2021. is the total amount of federal
𝑃𝑜𝑝𝑠,𝑦2020
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
aid allocated to a state per resident in USD millions since the pandemic began. is the arithmetic change
𝑃𝑜𝑝𝑠,𝑦2020
in state and local government employment per capita in state s relative to the same month in 2019. Estimates use the QCEW
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
employment data for the dependent variable. The ratio $1,000,000/(𝛽1 ∗ [ ]) represents the amount of
12
money spent to save one state or local government job-year. Included is a set of state-level controls 𝑋𝑠,𝑚,𝑦 . This includes the log
of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the
change in state and local and private employment per capita (QCEW) between December 2018 and December 2019, and the
March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index. Observations are weighted by state
population and standard errors (in parentheses) are clustered by state. Table 2 shows pooled regressions run using data from
April 2020 to September 2021. The figure uses data from the Committee for a Responsible Federal Budget (2021), US Federal
Transit Administration (2021a, 2021b), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip
Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US
Bureau of Labor Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), and Hale et al.
(2020).
31
Figure 5: Local-Projection Impulse Response of Macroeconomic Outcomes to COVID-19 Relief Aid
Note: This figure displays the coefficient (and the 95% confidence interval) on predicted total federal aid per resident (USD
millions) in a variation of the regression outlined in equation (3b):
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦.
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where t and y iterate over the month-year (quarter-year) pairs from January (Q1) 2020 to September (Q3) 2021. is the
𝑃𝑜𝑝𝑠,𝑦2020
total amount of federal aid to state and local governments per resident (USD millions) allocated to a state s since the pandemic
∆𝑌𝑠,𝑡,𝑦−𝑦2019
began. presents the change in a given macroeconomic variable per capita relative to the same time period in 2019.
𝑃𝑜𝑝𝑠,𝑦2020
Equation (3b) is modified to reflect the wider range of outcome variables. Panel A presents the change in private employment
per capita relative to the same month in 2019, as measured by the QCEW. Panel B presents the change in annualized real,
seasonally-adjusted total wages for all employees per capita relative to the same quarter in 2019, as recorded by the BEA.
Panels C and D present the changes relative to the same quarter in 2019 in seasonally-adjusted, annualized real state GDP per
capita in USD millions and seasonally-adjusted, annualized real personal income per capita in USD millions, respectively. 𝑋𝑠,𝑡,𝑦
denotes a vector of controls. This includes the log of 2020 official Census population, the share of a state’s population living in a
town eligible for financing through the MLF, the March 2020 and contemporaneous month averages of a state’s Oxford
Stringency Index, and the change in the dependent variable between the end of 2018 and 2019. The private employment
regressions include both the pre-trends for public and private employment. Observations are weighted by state population and
standard errors are clustered at the state level. Pooled regression results are presented in Table 3. The figure uses data from
the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a, 2021b), US Census Bureau
(2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary
and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021a, 2021b), US Department of the
Treasury (2021a), Federal Reserve Board (2021), and Hale et al. (2020).
32
Table 1: Summary Statistics
N Mean Std. Dev. Min Max
Change in State and Local Employment per Capita Relative to Same
Month in 2019 (QCEW) 1050 -0.0022 0.0018 -0.0090 0.0028
Change in State Employment per Capita Relative to Same Month in
2019 (QCEW) 1050 -0.0003 0.0008 -0.0085 0.0030
Change in Local Employment per Capita Relative to Same Month in
2019 (QCEW) 1050 -0.0019 0.0016 -0.0077 0.0019
Change in State and Local Employment per Capita Relative to Same
Month in 2019 (CES) 1200 -0.0029 0.0021 -0.0103 0.0023
Percent Change in State and Local Employment per Capita Relative
to Same Month in 2019 (QCEW) 1050 -0.0367 0.0213 -0.0645 0.0116
Percent Change in State and Local Employment per Capita Relative
to Same Month in 2019 (CES) 1200 -0.0026 0.0013 -0.0040 0.0007
Total Aid to State and Local Governments per Resident (USD
Millions) 1200 0.0028 0.0009 0.0018 0.0059
Senators and Representatives per Million Residents 1200 2.1368 0.8849 1.3021 5.1928
Log of 2020 State Population 1200 15.2183 1.0138 13.2668 17.4938
Share of Population in City Eligible for Municipal Liquidity Facility 1200 0.4232 0.1897 0.1472 0.8393
Change in State and Local Employment per Capita from Dec 2018 to
Dec 2019 (QCEW) 1200 0.0004 0.0005 -0.0008 0.0017
Change in Private Employment per Capita from Dec 2018 to Dec
2019 (QCEW) 1200 0.0039 0.0037 -0.0073 0.0119
March 2020 Average Oxford Stringency Index Level 1200 0.4339 0.0520 0.3214 0.5502
Contemporaneous Oxford Stringency Index Level 1200 0.4588 0.2014 0 0.9293
Share of Votes Won by Donald Trump in 2020 Election 1200 0.5003 0.1026 0.3038 0.6950
Final Two Weeks of March 2020 Average Oxford Stringency Index
Level 1200 0.7302 0.0830 0.4907 0.8519
Percent Change in Retail Mobility Relative to February 2020
Baseline (Previous Month) 1200 -0.0888 0.1292 -0.6053 0.3223
New COVID-19 Deaths per 100,000 (Previous Month) 1200 9.3721 11.2599 0 112.0507
Total COVID-19 Deaths per 100,000 (Previous Month) 1200 97.9668 89.5351 0 346.6714
New COVID-19 Cases per 100,000 (Previous Month) 1200 630.0612 698.3465 0 4617.22
Total COVID-19 Cases per 100,000 (Previous Month) 1200 5834.311 5453.198 0 21206.34
Change in Real State GDP per Capita from 2018 to 2019 1200 1162.88 773.44 -768.45 2812.25
Change in Private Employment per Capita Relative to Same Month
in 2019 (QCEW) 1050 -0.0197 0.0201 -0.0990 0.0231
Change in Real State GDP per Capita Relative to Same Month in
2019 (USD Millions) 350 -0.0008 0.0024 -0.0086 0.0046
Change in Real State GDP per Capita from Q4 2018 to Q4 2019 (USD
Millions) 350 0.0012 0.0008 -0.0008 0.0028
Change in Real Personal Income per Capita Relative to Same Month
in 2019 (USD Millions) 350 0.0034 0.0024 -0.0011 0.0105
33
Change in Real Personal Income per Capita from Q4 2018 to Q4
2019 (USD Millions) 350 0.0009 0.0006 -0.0006 0.0023
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021a,
2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT
Election and Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021).
34
Table 2: State and Local Government Employment Impact of COVID-19 Relief Aid
OLS Baseline Political COVID-19 Economic Combined Simple
(1) (2) (3) (4) (5) (6) (7)
Total Aid per Resident (USD millions) 0.176 0.780** 0.562 0.532* 1.040* 0.452 -0.0619
(0.241) (0.387) (0.345) (0.296) (0.534) (0.327) (0.274)
Log(Population) 0.000314* 0.000467** 0.000539*** 0.000439** 0.000578** 0.000545*** 0.000214
(0.000182) (0.000194) (0.000163) (0.000195) -0.000246 (0.000174) (0.000216)
Share of Population Eligible for MLF -0.000513 -0.00131 0.000129 -0.000855 -0.00136 0.000323
(0.000776) (0.000975) (0.000759) (0.000783) (0.00108) (0.000731)
Change S&L Employment 0.398 0.559** 0.171 0.325 0.751** 0.104
per Resident (Dec 2018 – Dec 2019) (0.243) (0.265) (0.219) (0.253) (0.299) (0.216)
Change Private Employment per Resident (Dec 0.110*** 0.134*** 0.140*** 0.104*** 0.203** 0.130***
2018 – Dec 2019) (0.0377) (0.0424) (0.0318) (0.0391) (0.0803) (0.0493)
Average OSI (March 2020) -0.00425* -0.00528** -0.000946 -0.00506** -0.00453* -0.000554
(0.00251) (0.00230) (0.00259) (0.00244) (0.00233) (0.00301)
Average OSI (Current Month) -0.00353*** -0.00373*** -0.00104*** -0.00251*** -0.00364*** 0.000226
(0.000553) (0.000479) (0.000315) (0.000494) (0.000526) (0.000509)
Political and Mobility Controls N N Y N N Y N
COVID-19 Controls N N N Y N Y N
Economic Controls N N N N Y Y N
Dep. Var. Mean -0.0026 -0.0026 -0.0026 -0.0026 -0.0026 -0.0026 -0.0026
Aggregate Impact Coef. 0.264 1.17** 0.843 0.798* 1.56* 0.678 -0.0929
Observations 900 900 900 900 900 900 900
R2 0.352 0.326 0.473 0.374 0.321 0.503 0.032
First-Stage F-Statistic N/A 57.79 49.01 215.15 21.81 104.01 140.62
P-value on Test for Pre-Trends 0.513 0.416 0.616 0.372 0.063 0.137 0.435
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an equation of the following form for all months pooled:
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
35
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all four bills. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of Representatives and Senators per million residents in 2020, according to equation (2a). is the
𝑃𝑜𝑝𝑠,𝑦2020
arithmetic change in state and local government employment per capita in state s relative to the same month in 2019, as measured by the QCEW. The ratio $1,000,000/(𝛽1 ∗
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
[ ]) represents the amount of money spent to save one state or local government job-year. Included is a set of state-level controls 𝑋𝑠,𝑚,𝑦 . This includes the
12
log of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the change in state and local and private
employment per capita (QCEW) between December 2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index.
Observations are weighted by state population and standard errors (in parentheses) are clustered by state. This table shows pooled regressions run using data from April 2020 to
September 2021, the period during which the federal government appropriated money to state and local governments. The first column presents the “naïve” OLS specification
according to equation (1). 𝑋𝑠,𝑚,𝑦 additionally denotes a vector of robustness controls as indicated immediately following the coefficients of interest. Political and mobility
controls include Donald Trump’s vote share in the 2020 presidential election, the average Oxford Stringency Index level during the last week of March 2020, and the change in
retail mobility relative to early 2020. COVID-19 controls include the total and new number of cases and deaths per 100,000 recorded during the previous month. Economic
controls include the change in state real GDP per capita between 2018 and 2019. The aggregate impact coefficient denotes the total impact over the pandemic implied by the
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
annualized coefficient (scaled by [ ] as described above).
12
*** p<0.01, ** p<0.05, * p<0.1
36
Table 3: Macroeconomic Impact of COVID-19 Relief Aid
State and Local State Real State Real
Govt Private Total Wages GDP per Personal
Employment Employment per Capita (USD Capita (USD Income (USD
per Capita per Capita millions) Millions) Millions)
(1) (2) (3) (4) (5)
Total Aid per Resident (USD 0.780** 1.008 -0.0452 -0.229 0.442
millions) (0.387) (3.367) (0.319) (0.592) (0.520)
Log(Population) 0.000467** 5.90e-05 -6.78e-05 -0.000140 0.000234
(0.000194) (0.00220) (0.000173) (0.000334) (0.000270)
Share of Population Eligible for -0.00131 -0.0140 -0.000470 -0.00138 0.000198
MLF (0.000975) (0.0102) (0.000499) (0.00105) (0.000751)
Change S&L Employment
0.559** 5.185**
per Resident (Dec 2018 – Dec
2019) (0.265) (2.445)
Change Private Employment per 0.134*** 1.512***
Resident (Dec 2018 – Dec 2019) (0.0424) (0.416)
Change in Dependent Variable 1.589*** 0.976*** 0.994***
(End-2018 – End-2019) (0.240) (0.224) (0.307)
Average OSI (March 2020) -0.00528** -0.0255 0.00219 0.00503 0.00223
(0.00230) (0.0211) (0.00228) (0.00367) (0.00348)
Average OSI (Current Month) -0.00373*** -0.0880*** -0.00572*** -0.0134*** 0.00294***
(0.000479) (0.00385) (0.000605) (0.00113) (0.000632)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0026 -0.0234 0.0004 -0.0010 0.0039
Aggregate Impact Coef. 1.17** 1.512 -0.0678 -0.344 0.663
Observations 900 900 300 300 300
R2 0.326 0.665 0.612 0.558 0.133
First-Stage F-Statistic 57.78 57.78 59.51 56.27 61.27
P-value on Test for Pre-Trends 0.416 0.692 0.472 0.318 0.853
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an
equation of the following form for all months pooled:
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
four bills. Equation (2b) is modified to reflect the wider range of outcome variables. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million residents in 2020, according to
∆𝑌𝑠,𝑡,𝑦−𝑦2019
equation (2a). presents the change in a given macroeconomic variable per capita relative to the same time period in
𝑃𝑜𝑝𝑠,𝑦2020
37
2019. For example, Column 1 uses the change in state and local government employment per capita, identical to Table 2
Column 2, while Column 4 uses the change in annualized state GDP per capita in USD millions relative to the same quarter in
2019. All employment variables use QCEW estimates. Column 3 uses the annualized real total wages in USD millions, for all
employees, as measured by the BEA. Columns 4 and 5 use seasonally-adjusted, annualized real state GDP per capita in USD
millions and seasonally-adjusted, annualized real personal income per capita in USD millions. Included is a set of state-level
controls 𝑋𝑠,𝑡,𝑦 . This includes the log of 2020 official Census population, the share of a state’s population living in a town eligible
for financing through the MLF, the change in state and local and private employment per capita (QCEW) between December
2018 and December 2019 (for employment regressions), the March 2020 and contemporaneous month/quarter averages of a
state’s Oxford Stringency Index, and the change in the dependent variable between the end of 2018 and 2019 (if not already
included). The aggregate impact coefficient denotes the total impact over the pandemic implied by the annualized coefficient
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
(scaled by [ ] as described above). This table shows pooled regressions run using data from April 2020 to
12
September 2021 for monthly dependent variables or Q2 2020 to Q3 2021 for quarterly variables, the periods during which the
federal government appropriated money to state and local governments.
*** p<0.01, ** p<0.05, * p<0.1
38
Appendix Figure 1: Change in State and Local Employment per Capita: CES Data
Note: This figure shows the change in national state and local government employment per capita relative to the same month
in 2019 over the course of the pandemic. The variable shown is calculated for a given job category as the arithmetic difference
in employment in a given month and the same month in 2019 divided by 2020 population. This figure displays Current
Employment Statistics (CES) estimates. State, local, and state plus local employment are shown separately. This figure uses data
from the US Bureau of Labor Statistics (2021a) and US Census Bureau (2021).
39
Appendix Figure 2: Percent Change in State and Local Employment per Capita, QCEW and CES
Panel A: Percent Change in State and Local Government Employment per Capita Relative to Same Month in 2019,
QCEW
Panel B: Percent Change in State and Local Government Employment per Capita Relative to Same Month in 2019,
CES
Note: This figure shows the percent change in national state and local government employment per capita relative to the same
month in 2019 over the course of the pandemic. Panel A shows this variable using the QCEW estimates of employment while
Panel B displays the CES estimates. State, local, and state plus local employment are shown separately. This figure uses data
from the US Bureau of Labor Statistics (2021a, 2021b) and US Census Bureau (2021).
40
Appendix Figure 3: Federal Funds to State and Local Governments Appropriated per Resident
Nationally Over Time
Note: This figure shows the appropriation of COVID-19 relief funds to state and local governments over time. Funds are shown
for the CARES Act, Families First Coronavirus Response Act, Response and Relief Act, and American Rescue Plan Act on a per
resident basis. The charts displays the national average aid per resident over the course of the pandemic. Increases in funds are
matched with the first QCEW sample period following the passage of a COVID-19 relief bill. For instance, since the CARES Act
was passed in late March 2020, the first observed employment data since its passage is during the second week of April 2020.
Unlike the variable used in our baseline regressions, the variable in the figure is not scaled in USD millions.
41
Appendix Figure 4: Local-Projection Impulse Response of State and Local Government Employment to
COVID-19 Relief Aid, Unweighted
Note: This figure displays the coefficient (and the 95% confidence interval) on predicted total federal aid to state and local
governments per resident (USD millions) in the regression outlined in equation (3b):
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where m and y iterate over the month-year pairs from January 2020 to September 2021. is the total amount of federal
𝑃𝑜𝑝𝑠,𝑦2020
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
aid to state and local governments per resident (USD millions) allocated to state s. is the arithmetic
𝑃𝑜𝑝𝑠,𝑦2020
change in state and local government employment per capita in state s relative to the same month in 2019, as measured by the
QCEW. Included is a set of state-level controls 𝑋𝑠,𝑚,𝑦 . This includes the log of 2020 official Census population, the share of a
state’s population living in a town eligible for financing through the MLF, the change in state and local and private employment
per capita (QCEW) between December 2018 and December 2019, and the March 2020 and contemporaneous month averages
of a state’s Oxford Stringency Index. Observations are not weighted by population, and standard errors are clustered at the
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
state level. The ratio $1,000,000/(𝛽1 ∗ [ ]) represents the amount of money spent to save one state or local
12
government job-year. The figure uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit
Administration (2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access
Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), and Hale et al. (2020).
42
Appendix Figure 5: Local-Projection Impulse Response of State and Local Government Employment to
COVID-19 Relief Aid: Green and Loualiche (2020) Specification
Note: This figure displays the coefficient (and the 95% confidence interval) on predicted total federal aid to state and local
governments per capita (USD millions). The instrument used in the first stage presented below (equation A) differs from the
method outlined in equation (3a); federal aid to state and local governments per capita is instrumented using the interaction
between the log of 2020 state population and an indicator for state size, akin to the strategy employed in Green and Loualiche
(2020):
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
= 𝛼 + 𝛽1 (𝑙𝑛(𝑃𝑜𝑝)𝑠,𝑦2020 ∗ 𝑆𝑚𝑎𝑙𝑙𝑆𝑡𝑎𝑡𝑒𝑠 ) + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦 (A)
𝑃𝑜𝑝𝑠,𝑦2020
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦 (B)
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where m and y iterate over the month-year pairs from January 2020 to September 2021. is the total amount of federal
𝑃𝑜𝑝𝑠,𝑦2020
aid to state and local governments per resident (USD millions) allocated to state s. 𝑆𝑚𝑎𝑙𝑙𝑆𝑡𝑎𝑡𝑒𝑠 equals 1 for state s if it
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
received the minimum CARES Act funding and 0 otherwise. is the arithmetic change in state and local
𝑃𝑜𝑝𝑠,𝑦2020
employment per capita in state s relative to the same month in 2019 as measured by the QCEW. Included is a set of state-level
controls 𝑋𝑠,𝑚,𝑦 . This includes the log of 2020 official Census population, the share of a state’s population living in a town eligible
for financing through the MLF, the change in state and local and private employment per capita (QCEW) between December
2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index.
The regressions are weighted by state population and clustered at the state level. The ratio $1,000,000/(𝛽1 ∗
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
[ ]) represents the amount of money spent to save one state or local government job-year. The figure uses
12
data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census
Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of
Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b), US Department of
the Treasury (2021a), Federal Reserve Board (2021), and Hale et al. (2020).
43
Appendix Table 1: Variable Descriptions and Sets of Control Variables
Variable Description Source
Change in State and The arithmetic change in state and local US Bureau of Labor Statistics (2021a, 2021b); US
Local Employment per government employment between a given month Census Bureau (2021)
Capita Relative to in 2020 or 2021 and the same month in 2019,
Same Month in 2019 divided by the 2020 state population.
Total Aid to State and Funds appropriated to each state by Congress in Committee for a Responsible Federal Budget (2021);
Local Governments COVID-19 relief bills divided by the 2020 state US Federal Transit Administration (2021a, 2021b);
per Resident (USD population, in nominal USD millions. US Census Bureau (2021); Chidambaram and
Millions) Musumeci (2021); Medicaid and Chip Payment
Access Commission (2021); US Office of Elementary
and Secondary Education (2021)
Senators and Number of House plus the number of Senate seats US Census Bureau (2021); Lewis et al. (2021)
Representatives per per 1,000,000 people in each state, according to
Million Residents the 2020 estimate of population and
Congressional seats.
Log of 2020 State The natural logarithm of 2020 state population US Census Bureau (2021)
Population
Share of Population in The share of a state’s 2020 population living in a US Census Bureau (2021); Federal Reserve Board
City Eligible for city or town deemed eligible for financing through (2021)
Municipal Liquidity the Federal Reserve’s Municipal Liquidity Facility.
Facility
Change in State and The arithmetic difference in state and local US Bureau of Labor Statistics (2021a, 2021b); US
Local Employment per government employment between December Census Bureau (2021)
Capita from Dec 2018 2018 and December 2019, divided by the 2020
to Dec 2019 state population.
Change in Private The arithmetic difference in state and local US Bureau of Labor Statistics (2021a, 2021b); US
Employment per government employment between a given month Census Bureau (2021)
Capita from Dec 2018 in 2020 or 2021 and the same month in 2019,
to Dec 2019 divided by the 2020 state population.
March 2020 Average The monthly average level of a state’s Oxford Hale et al. (2021)
Oxford Stringency Stringency Index during March 2020, divided by
Index Level 100.
Contemporaneous The monthly average level of a state’s Oxford Hale et al. (2021)
Oxford Stringency Stringency Index, divided by 100.
Index Level
Share of Votes Won The percentage of votes cast in a state for Donald MIT Election and Data Science Lab (2017)
by Donald Trump in Trump in the 2020 US Presidential election. Proxy
2020 Election for attitudes toward COVID-19.
Final Two Weeks of The monthly average level of a state’s Oxford Hale et al. (2021)
March 2020 Average Stringency Index during the final fourteen days in
Oxford Stringency March, divided by 100. Proxy for seriousness with
Index Level which states initially responded to COVID-19.
Percent Change in Monthly-average percentage change in foot traffic Google LLC (2021)
Retail Mobility in retail and recreation areas relative to the
Relative to February median level of traffic during the January 3, 2020
to February 6, 2020 baseline period
44
2020 Baseline
(Previous Month)
New COVID-19 The number of reported COVID-19 cases and Dong, Du, and Gardner (2020)
Cases/Deaths per deaths, divided by state population in hundred-
100,000 (Previous thousands.
Month)
Total COVID-19 The number of cumulative COVID-19 cases and Dong, Du, and Gardner (2020)
Cases/Deaths per deaths, divided by state population in hundred-
100,000 (Previous thousands.
Month)
Change in Real State The arithmetic change in real gross state product US Bureau of Economic Analysis (2021)
GDP per Capita from per capita from Q4 2018 to Q4 2019, in 2012 US
2018 to 2019 dollars.
Change in Private The arithmetic change in private employment US Bureau of Labor Statistics (2021b); US Census
Employment per between a given month in 2020 or 2021 and the Bureau (2021)
Capita Relative to same month in 2019, divided by the 2020 state
Same Month in 2019 population.
Change in Real State The arithmetic change in real, seasonally-adjusted US Bureau of Economic Analysis (2021); US Census
GDP per Capita and annualized gross state product between a Bureau (2021)
Relative to Same given quarter in 2020 or 2021 and the same
Month in 2019 (USD month in 2019 divided by the 2020 state
Millions) population, in 2012 USD millions.
Change in Real State The arithmetic change in real, seasonally-adjusted US Bureau of Economic Analysis (2021); US Census
GDP per Capita from and annualized gross state product between Q4 Bureau (2021)
Q4 2018 to Q4 2019 2018 and Q4 2019 divided by the 2020 state
(USD Millions) population, in 2012 USD millions.
Change in Real The arithmetic change in real, seasonally-adjusted US Bureau of Economic Analysis (2021); US Census
Personal Income per and annualized real personal income between a Bureau (2021)
Capita Relative to given quarter in 2020 or 2021 and the same
Same Month in 2019 month in 2019 divided by the 2020 state
(USD Millions) population, in 2012 USD millions.
Change in Real The arithmetic change in real, seasonally-adjusted US Bureau of Economic Analysis (2021); US Census
Personal Income per gross state product between Q4 2018 and Q4 Bureau (2021)
Capita from Q4 2018 2019 divided by the 2020 state population, in
to Q4 2019 (USD 2012 USD millions.
Millions)
Change in Real Total The arithmetic change in real, seasonally-adjusted US Bureau of Economic Analysis (2021); US Census
Wages per Capita and annualized total wages for all employees in a Bureau (2021)
Relative to Same state between a given quarter in 2020 or 2021
Month in 2019 (USD and the same month in 2019 divided by the 2020
Millions) state population, in 2012 USD millions.
Change in Real Total The arithmetic change in real, seasonally-adjusted US Bureau of Economic Analysis (2021); US Census
Wages per Capita and annualized total wages for all employees in a Bureau (2021)
from Q4 2018 to Q4 state between Q4 2018 and Q4 2019 divided by
2019 (USD Millions) the 2020 state population, in 2012 USD millions.
45
Appendix Table 2: Total State and Local Funds per Resident, Congressional Representation, and Proxies for Funding Needs
(1) (2) (3) (4) (5) (6) (7) (8)
Representatives and Senators per Million 1,334*** 995.1*** 1,105*** 1,367*** 902.0*** 1,286*** 1,417*** 992.2***
Residents (112.5) (175.9) (130.8) (133.2) (154.6) (113.3) (134.0) (120.9)
Log(Population) 419.5*** 262.0*** 165.1 443.6*** 153.5 411.2*** 366.8*** 101.9*
(90.19) (94.08) (98.90) (112.6) (104.7) (90.22) (66.10) (53.60)
Tax Shortfall per Capita 0.853** -0.424
(0.345) (0.272)
Average Q4 2020 Unemployment per Capita 37,186*** 19,019***
(10,451) (5,362)
Percent Change in Personal Income Q4 2019 -42.48 -62.90***
to Q4 2020 (49.07) (20.67)
Total State and Local Spending per Capita 0.104*** 0.107***
(0.0249) (0.0246)
Acres of Federal Land per Capita 2.574*** 1.680
(0.729) (1.342)
Log Population Density 166.6** 69.78*
(65.36) (39.45)
Political and Mobility Controls N N N N N N N N
COVID-19 Controls N N N N N N N N
Economic Controls N N N N N N N N
Dep. Var. Mean 2826.21 2826.21 2826.21 2826.21 2826.21 2826.21 2826.21 2826.21
Observations 900 900 900 900 900 900 900 900
R2 0.496 0.635 0.709 0.518 0.758 0.501 0.572 0.872
First-Stage F-Statistic 140.62 32.00 71.34 105.36 34.04 128.80 111.81 67.39
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an equation of the following form for all months pooled:
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
= 𝛼 + 𝛽1 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD) in state s pooled across all four bills. is regressed on 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 ,
𝑃𝑜𝑝𝑠,𝑦2020
the number of Representatives and Senators per million residents in 2020, according to equation (2a). Included is a set of state-level controls 𝑋𝑠,𝑚,𝑦 . This includes the log of 2020
46
official Census population, the predicted tax shortfall for state and local governments divided by the state population, the average number of unemployed persons each month
in the fourth quarter of 2020 per capita, the percentage change in personal income between the fourth quarter of 2019 and the fourth quarter of 2020, the total direct
expenditures from state and local governments per capita in 2019, the acres of federal lands per capita, and the log of population density for state s. These controls are inspired
by the analysis in Clemens and Veuger (2021a). Observations are weighted by state population and standard errors (in parentheses) are clustered by state. This table shows
pooled regressions run using data from April 2020 to September 2021, the period during which the federal government appropriated money to state and local governments.
*** p<0.01, ** p<0.05, * p<0.1
47
Appendix Table 3: COVID-19 Relief Aid and Other Federal Stimulus Efforts
PPP Funds per UI Funds per EIP Funds per
Resident (USD Resident (USD Resident (USD
Millions) Millions) Millions)
(1) (2) (3)
Total Aid per Resident (USD millions) 0.0498 -0.116 0.0672
(0.158) (0.261) (0.0583)
Frequency Monthly Monthly Monthly
Observations 1050 1050 1050
R2 0.487 0.531 0.285
First-Stage F-Statistic 57.69 57.69 57.69
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), the US Bureau of Economic Analysis (2021), Walczak and Funkhouser (2021), the US Small Business Administration (2022) to estimate an equation of
the following form for all months pooled:
𝑌𝑠 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦.
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
Where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all four bills. Equation (2b) is modified to reflect the
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
wider range of outcome variables. In a first stage regression, is instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million
𝑃𝑜𝑝𝑠,𝑦2020
𝑌𝑠
residents in 2020, according to equation (2a). presents the total amount allocated per resident in millions USD through the Paycheck Protection Program (column 1),
𝑃𝑜𝑝𝑠,𝑦2020
Unemployment Insurance (column 2), and Economic Impact Payments (column 3). Included is a set of state-level controls 𝑋𝑠,𝑡,𝑦 . This includes the log of 2020 official Census
population, the share of a state’s population living in a town eligible for financing through the MLF, the change in state and local and private employment per capita (QCEW)
between December 2018 and December 2019, the March 2020 and contemporaneous month/quarter averages of a state’s Oxford Stringency Index. Observations are weighted
by state population and standard errors (in parentheses) are clustered by state. This table shows pooled regressions run using data from April 2020 to December 2021.
*** p<0.01, ** p<0.05, * p<0.1
48
Appendix Table 4: Reduced Form Relationship Between Congressional Representation and Other Federal Aid
Federal Aid per Resident (USD Millions)
PPP UI EIP
(1) (2) (3)
Representatives per Million 5.12e-05 -0.000120 6.92e-05
Residents (0.000168) (0.000268) (5.79e-05)
Log(Population) -4.71e-06 0.000139 8.71e-07
(9.45e-05) (0.000214) (3.93e-05)
Share of Population Eligible for 0.000756* 0.00144* -0.000308*
MLF (0.000387) (0.000809) (0.000170)
Change S&L Employment per -0.268** -0.709*** 0.0804*
Resident (Dec 2018 – Dec
2019) (0.103) (0.258) (0.0419)
Change Private Employment -0.0317 -0.0252 0.00129
per Resident (Dec 2018 – Dec
2019) (0.0207) (0.0514) (0.00811)
Average OSI (March 2020) 0.00156 0.00589** -0.000143
(0.000973) (0.00255) (0.000388)
Average OSI (Current Month) 8.25e-05 0.000615** -7.99e-05**
(5.25e-05) (0.000238) (3.56e-05)
Political and Mobility Controls N Y N
COVID-19 Controls N N Y
Economic Controls N N N
Dep. Var. Mean 0.0028 0.0028 0.0028
Obs 1,050 1,050 1,050
R2 0.474 0.560 0.385
F-Statistic 0.09 0.20 1.43
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), the US Bureau of Economic Analysis (2021), Walczak and Funkhouser (2021), the US Small Business Administration (2022) to estimate an equation of
the following form for all months pooled:
𝑌𝑠
= 𝛼 + 𝛽1 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020
49
𝑌𝑠
where presents the total amount allocated per resident in millions USD through the Paycheck Protection Program (column 1), Unemployment Insurance (column 2),
𝑃𝑜𝑝𝑠,𝑦2020
and Economic Impact Payments (column 3). 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 is the number of Representatives and Senators per million residents in 2020. Included is a set of state-level
controls 𝑋𝑠,𝑚,𝑦 . This includes the log of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the change in
state and local and private employment per capita (QCEW) between December 2018 and December 2019, and the March 2020 and contemporaneous month averages of a
state’s Oxford Stringency Index. Observations are weighted by state population and standard errors (in parentheses) are clustered by state. Regressions are run using data
spanning April 2020 to December 2021. These regressions are analogous to those found in Appendix Table 6.
*** p<0.01, ** p<0.05, * p<0.1
50
Appendix Table 5: First-Stage Robustness to One-By-One Addition of Baseline Controls
(1) (2) (3) (4) (5) (6) (7)
Representatives and Senators per Million 1,334*** 1,198*** 1,333*** 1,277*** 1,172*** 1,315*** 1,031***
Residents (112.5) (116.7) (99.42) (109.5) (122.2) (108.9) (135.6)
Log(Population) 419.5*** 299.3*** 441.4*** 438.3*** 288.1*** 406.2*** 219.6***
(90.19) (85.83) (81.61) (88.92) (72.19) (84.09) (78.03)
Share of Population Eligible for MLF 461.7 568.5**
(281.1) (259.1)
Change S&L Employment -318,035** -281,784**
per Resident (Dec 2018 – Dec 2019) (135,911) (111,361)
Change Private Employment per Resident (Dec -31,571* -17,734
2018 – Dec 2019) (18,530) (17,904)
Average OSI (March 2020) 2,430* 1,370
(1,302) (1,081)
Average OSI (Current Month) 507.8** 299.7**
(202.0) (123.8)
Political and Mobility Controls N N N N N N N
COVID-19 Controls N N N N N N N
Economic Controls N N N N N N N
Dep. Var. Mean 2826.21 2826.21 2826.21 2826.21 2826.21 2826.21 2826.21
Observations 900 900 900 900 900 900 900
R2 0.496 0.516 0.583 0.532 0.563 0.519 0.668
First-Stage F-Statistic 140.62 105.44 179.71 136.01 91.98 145.95 57.79
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an equation of the following form for all months pooled:
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
= 𝛼 + 𝛽1 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD) in state s pooled across all four bills. is regressed on 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 ,
𝑃𝑜𝑝𝑠,𝑦2020
the number of Representatives and Senators per million residents in 2020, according to equation (2a). Included is a set of state-level controls 𝑋𝑠,𝑚,𝑦 . This includes the log of 2020
official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the change in state and local and private employment per
capita (QCEW) between December 2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index. Observations are
51
weighted by state population and standard errors (in parentheses) are clustered by state. This table shows pooled regressions run using data from April 2020 to September
2021, the period during which the federal government appropriated money to state and local governments.
*** p<0.01, ** p<0.05, * p<0.1
52
Appendix Table 6: First-Stage Robustness (April 2020 – September 2021)
Total Federal Aid to State and Local Governments per Resident
Baseline Political COVID-19 Economic Combined Simple
(1) (2) (3) (4) (5) (6)
Representatives per Million 1,031*** 1,059*** 1,257*** 838.1*** 1,124*** 1,334***
Residents (135.6) (151.3) (85.68) (179.4) (110.2) (112.5)
Log(Population) 219.6*** 232.6** 290.2*** 98.08 215.3*** 419.5***
(78.03) (89.95) (39.46) (106.5) (57.35) (90.19)
Share of Population Eligible for 568.5** 353.7 242.7** 493.9** 202.3
MLF (259.1) (245.4) (116.5) (244.8) (160.2)
Change S&L Employment per -281,784** -198,351* -84,844 -367,334*** -150,940**
Resident (Dec 2018 – Dec 2019) (111,361) (115,011) (60,733) (99,669) (64,116)
Change Private Employment per -17,734 -22,880 4,640 -64,589** -26,384
Resident (Dec 2018 – Dec 2019) (17,904) (16,643) (10,954) (26,478) (17,840)
Average OSI (March 2020) 1,370 1,062 961.3 574.5 -330.2
(1,081) (1,874) (613.6) (779.9) (793.4)
Average OSI (Current Month) 299.7** 223.6* 792.0*** 182.0*** 585.9***
(123.8) (132.2) (231.5) (59.73) (142.3)
Political and Mobility Controls N Y N N Y N
COVID-19 Controls N N Y N Y N
Economic Controls N N N Y Y N
Dep. Var. Mean 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028
Obs 900 900 900 900 900 900
R2 0.668 0.696 0.830 0.748 0.865 0.496
F-Statistic 57.79 49.01 215.15 21.81 104.01 140.62
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the Bureau of Economic Analysis (2021) to estimate an equation of
the following form for all months pooled:
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
= 𝛼 + 𝛽1 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝜀𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
where is the total of federal aid to state and local governments per resident (USD) in state s pooled across all four bills.
𝑃𝑜𝑝𝑠,𝑦2020
𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 is the number of Representatives and Senators per million residents in 2020. Included is a set of state-level
controls 𝑋𝑠,𝑚,𝑦 . This includes the log of 2020 official Census population, the share of a state’s population living in a town eligible
for financing through the MLF, the change in state and local and private employment per capita (QCEW) between December
2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index.
Observations are weighted by state population and standard errors (in parentheses) are clustered by state. Regressions are run
using data spanning April 2020 to September 2021. 𝑋𝑠,𝑚,𝑦 additionally denotes a vector of robustness controls as indicated
immediately following the coefficients of interest. Political and mobility controls include Donald Trump’s vote share in the 2020
presidential election, the average Oxford Stringency Index level during the last week of March 2020, and the change in retail
mobility relative to early 2020. COVID-19 controls include the total and new number of cases and deaths per 100,000 recorded
during the previous month. Economic controls include the change in state GDP per capita between Q4 2018 and Q4 2019.
53
Appendix Table 7: Change in State and Local Government Employment per Capita and Federal Relief Aid: Unweighted Regressions
(April 2020-September 2021)
OLS Baseline Political COVID-19 Economic Combined Simple
(1) (2) (3) (5) (6) (7) (8)
Total Aid per Resident (USD -0.0626 -0.0513 -0.127 -0.0863 -0.0610 -0.159 -0.211
millions) (0.147) (0.213) (0.201) (0.199) (0.256) (0.218) (0.227)
Log(Population) 0.000739 0.000727 0.00151* 0.000834 -4.59e-05 0.000162 -6.81e-05
(0.000924) (0.000985) (0.000888) (0.000945) (0.000260) (0.000237) (0.000214)
Share of Population Eligible for MLF 0.000739 0.000727 0.00151* 0.000834 0.000718 0.00155*
(0.000924) (0.000985) (0.000888) (0.000945) (0.000963) (0.000860)
Change S&L Employment per 0.391** 0.394** 0.241 0.335* 0.377* 0.182
Resident (Dec 2018 – Dec 2019) (0.178) (0.171) (0.201) (0.179) (0.198) (0.203)
Change Private Employment per 0.0682* 0.0685* 0.0626* 0.0545 0.0630 0.0359
Resident (Dec 2018 – Dec 2019) (0.0367) (0.0362) (0.0343) (0.0393) (0.0526) (0.0535)
Average OSI (March 2020) -0.00272 -0.00276 0.00162 -0.00290 -0.00283 0.000420
(0.00276) (0.00291) (0.00434) (0.00288) (0.00267) (0.00411)
Average OSI (Current Month) -
-0.00451*** -0.00452*** 0.00136*** -0.00254*** -0.00452*** 0.000962
(0.000444) (0.000431) (0.000410) (0.000676) (0.000439) (0.000704)
Political and Mobility Controls N N Y N N Y N
COVID-19 Controls N N N Y N Y N
Economic Controls N N N N Y Y N
Dep. Var. Mean -0.0026 -0.0026 -0.0026 -0.0026 -0.0026 -0.0026 -0.0026
Aggregate Impact Coef. -0.0939 -0.0770 -0.1905 -0.1295 -0.0915 -0.2385 -0.3165
Observations 900 900 900 900 900 900 900
R2 0.290 0.290 0.386 0.319 0.297 0.432 0.020
First-Stage F-statistic N/A 294.31 280.59 420.47 211.59 256.16 161.81
P-value on Test for Pre-Trends 0.337 0.182 0.180 0.171 0.022 0.018 0.293
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate equations of the following form for each all months pooled:
54
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid to state and local governments per resident (USD millions) in state s pooled across all four bills. In a first stage regression, 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of Representatives and Senators per million residents in 2020, according to equation (2a). is the
𝑃𝑜𝑝𝑠,𝑦2020
arithmetic change in state and local employment per capita in state s relative to the same month in 2019, as measured by the QCEW. The ratio $1,000,000/(𝛽1 ∗
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
[ ]) represents the amount of money spent to save one state or local government job-year. Included are a set of state-level controls 𝑋𝑠,𝑚,𝑦 . These include the
12
log of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the change in state and local and private
employment per capita (QCEW) between December 2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index.
Observations are not weighted by state population and standard errors (in parentheses) are clustered by state. This table shows pooled regressions run using data from April
2020 to September 2021, the period during which the federal government appropriated money to state and local governments. The first column presents the “naïve” OLS
specification according to equation (1). 𝑋𝑠,𝑚,𝑦 additionally denotes a vector of robustness controls as indicated immediately following the coefficients of interest. Political and
mobility controls include Donald Trump’s vote share in the 2020 presidential election, the average Oxford Stringency Index level during the last week of March 2020, and the
change in retail mobility relative to early 2020. COVID-19 controls include the total and new number of cases and deaths per 100,000 recorded during the previous month.
Economic controls include the change in state real GDP per capita between Q4 2018 and Q4 2019. The p-value of the pre-pandemic (January 2020 to March 2020) trend
coefficients on total aid per capita are presented as indicators of the robustness of the empirical strategy. The aggregate impact coefficient denotes the total impact over the
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
pandemic implied by the annualized coefficient (scaled by [ ] as described above).
12
*** p<0.01, ** p<0.05, * p<0.1
55
Appendix Table 8: State and Local Government Employment and COVID-19 Relief Aid: CES Employment Data
(April 2020-December 2021)
OLS Baseline Political COVID-19 Economic Combined Simple
(1) (2) (3) (4) (5) (6) (7)
Total Aid per Resident (USD 0.0802 -0.101 -0.430 0.0134 0.326 0.0901 -0.908*
millions) (0.379) (0.582) (0.488) (0.456) (0.706) (0.390) (0.539)
Log(Population) 0.000541** 0.000496 0.000519* 0.000499 0.000665* 0.000655*** 0.000157
(0.000244) (0.000316) (0.000266) (0.000307) (0.000345) (0.000233) (0.000375)
Share of Population Eligible for -0.000284 -4.92e-05 0.00138 -0.000284 -0.000114 0.00110
MLF (0.000954) (0.00107) (0.000878) (0.00100) (0.00118) (0.000797)
Change S&L Employment per 0.517 0.492 0.267 0.509 0.639* 0.343
Resident (Dec 2018 – Dec 2019) (0.351) (0.352) (0.306) (0.339) (0.364) (0.262)
Change Private Employment per 0.0555 0.0462 0.0334 0.0680 0.152 0.161***
Resident (Dec 2018 – Dec 2019) (0.0465) (0.0577) (0.0580) (0.0489) (0.103) (0.0574)
Average OSI (March 2020) -0.00914*** -0.00893*** -0.00593 -0.00923*** -0.00749** -0.00523
(0.00303) (0.00310) (0.00493) (0.00311) (0.00307) (0.00447)
Average OSI (Current Month) -0.00253*** -0.00248*** -0.000331 -0.00165*** -0.00240*** 0.000995
(0.000368) (0.000393) (0.000405) (0.000548) (0.000423) (0.000634)
Political and Mobility Controls N N Y N N Y N
COVID-19 Controls N N N Y N Y N
Economic Controls N N N N Y Y N
Dep. Var. Mean -0.0034 -0.0034 -0.0034 -0.0034 -0.0034 -0.0034 -0.0034
Aggregate Impact Coef. 0.1404 -0.1768 -0.7525 0.0235 0.5705 0.1577 -1.5890*
Obs 1,050 1,050 1,050 1,050 1,050 1,050 1,050
R2 0.348 0.346 0.414 0.356 0.379 0.486 0.094
First-Stage F-statistic N/A 51.26 54.81 195.93 16.27 98.41 140.66
P-value on Test for Pre-Trends 0.903 0.820 0.891 0.763 0.299 0.437 0.027
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021b), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021a), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), and the Bureau of Economic Analysis (2021) to estimate an equation of the following form:
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
56
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid to state and local governments per capita (USD millions) in state s pooled across all four bills. In a first stage regression, 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of Representatives and Senators per million residents in 2020, according to equation (2a). is the
𝑃𝑜𝑝𝑠,𝑦2020
arithmetic change in state and local employment per capita in state s relative to the same month in 2019, as measured by the CES. The ratio $1,000,000/(𝛽1 ∗
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
[ ]) represents the amount of money spent to save one state or local government job-year. Included is a set of state-level controls 𝑋𝑠,𝑚,𝑦 . This includes the
12
log of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the change in state and local and private
employment per capita (CES) between December 2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index.
Observations are weighted by state population and standard errors (in parentheses) are clustered by state. This table shows pooled regressions run using data from April 2020 to
December 2021, the period during which the federal government appropriated money to state and local governments. The first column presents the “naïve” OLS specification
according to equation (1). 𝑋𝑠,𝑚,𝑦 additionally denotes a vector of robustness controls as indicated immediately following the coefficients of interest. Political and mobility
controls include Donald Trump’s vote share in the 2020 presidential election, the average Oxford Stringency Index level during the last week of March 2020, and the change in
retail mobility relative to early 2020. COVID-19 controls include the total and new number of cases and deaths per 100,000 recorded during the previous month. Economic
controls include the change in state real GDP per capita between Q4 2018 and Q4 2019. The p-value of the pre-pandemic (January 2020 to March 2020) trend coefficients on
total aid per capita are presented as indicators of the robustness of the empirical strategy. The aggregate impact coefficient denotes the total impact over the pandemic implied
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
by the annualized coefficient (scaled by [ ] as described above).
12
*** p<0.01, ** p<0.05, * p<0.1
57
Appendix Table 9: Pre-trend Test for QCEW Employment and COVID-19 Relief Aid (January-March 2020)
OLS Baseline Political COVID-19 Economic Combined Simple
(1) (2) (3) (4) (5) (6) (7)
Total Aid per Resident (USD millions) 0.0799 -0.117 -0.0735 -0.126 -0.333* -0.282 -0.105
(0.121) (0.145) (0.143) (0.142) (0.179) (0.190) (0.135)
Log(Population) 9.87e-05* 4.85e-05 5.65e-05 4.84e-05 -4.41e-05 -3.62e-05 9.93e-05
(5.57e-05) (5.70e-05) (5.09e-05) (5.53e-05) (6.34e-05) (6.15e-05) (6.2e-05)
Share of Population Eligible for MLF -8.04e-05 0.000180 -5.42e-05 0.000165 0.000218 8.28e-05
(0.000290) (0.000327) (0.000253) (0.000298) (0.000326) (0.000255)
Change S&L Employment per 0.589*** 0.535*** 0.619*** 0.540*** 0.377*** 0.420***
Resident (Dec 2018 – Dec 2019) (0.0724) (0.0991) (0.0929) (0.102) (0.120) (0.140)
Change Private Employment per 0.00644 -0.00105 -0.00180 -0.00602 -0.0590** -0.0523**
Resident (Dec 2018 – Dec 2019) (0.0168) (0.0168) (0.0139) (0.0144) (0.0246) (0.0238)
Average OSI (March 2020) -0.000612 -0.000243 -0.00241* -0.000423 -0.000901 -0.00384***
(0.000936) (0.00111) (0.00144) (0.00105) (0.000872) (0.00114)
Average OSI (Current Month) -0.000492*** -0.000488*** -0.000549*** -0.000551*** -0.000491*** -0.000412***
(4.83e-05) (4.69e-05) (0.000157) (7.84e-05) (4.75e-05) (0.000158)
Political and Mobility Controls N N Y N N Y N
COVID-19 Controls N N N Y N Y N
Economic Controls N N N N Y Y N
Dep. Var. Mean 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005
Observations 150 150 150 150 150 150 150
R2 0.567 0.535 0.616 0.558 0.601 0.678 0.089
First-Stage F-statistic N/A 55.98 45.68 52.93 20.49 19.83 139.04
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration (2021a), US Census Bureau (2021), Chidambaram and
Musumeci (2021), Medicaid and Chip Payment Access Commission (2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor
Statistics (2021b), US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and Data Science Lab (2017), Dong,
Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an equation of the following form:
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑚,𝑦 + 𝑢𝑠,𝑚,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid to state and local governments per resident (USD millions) in state s pooled across all four bills. In a first stage regression, 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is
∆𝑆&𝐿𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑠,𝑚,𝑦−𝑦2019
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of Representatives and Senators per million residents in 2020, according to equation (2a). is the
𝑃𝑜𝑝𝑠,𝑦2020
arithmetic change in state and local employment per capita in state s relative to the same month in 2019, as measured by the QCEW. The ratio $1,000,000/(𝛽1 ∗
58
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
[ ]) represents the amount of money spent to save one state or local government job-year. Included is a set of state-level controls 𝑋𝑠,𝑚,𝑦 . This includes the
12
log of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the change in state and local and private
employment per capita (QCEW) between December 2018 and December 2019, and the March 2020 and contemporaneous month averages of a state’s Oxford Stringency Index.
Observations are weighted by state population and standard errors (in parentheses) are clustered by state. This table shows pooled regressions run using data from January
2020 to March 2020, the period before which the federal government appropriated money to state and local governments. The first column presents the “naïve” OLS
specification according to equation (1). 𝑋𝑠,𝑚,𝑦 additionally denotes a vector of robustness controls as indicated immediately following the coefficients of interest. Political and
mobility controls include Donald Trump’s vote share in the 2020 presidential election, the average Oxford Stringency Index level during the last week of March 2020, and the
change in retail mobility relative to early 2020. COVID-19 controls include the total and new number of cases and deaths per 100,000 recorded during the previous month.
Economic controls include the change in state real GDP per capita between Q4 2018 and Q4 2019.
*** p<0.01, ** p<0.05, * p<0.1
59
Appendix Table 10: Macroeconomic Impact of COVID-19 Relief Aid – Small State Indicator
State and Local State Real State Real
Govt Private Total Wages GDP per Personal
Employment Employment per Capita (USD Capita (USD Income (USD
per Capita per Capita millions) Millions) Millions)
(1) (2) (3) (4) (5)
Total Aid per Resident (USD -0.291 -1.026 -0.134 -0.533 -0.108
millions) (0.259) (2.650) (0.211) (0.369) (0.316)
=1 if ‘small state’ 0.000165 0.00234 0.000302 0.000740* 0.000128
(0.000331) (0.00435) (0.000195) (0.000420) (0.000330)
Share of Population Eligible for 0.000413 -0.0125* -0.000556 -0.00153* 0.00101
MLF (0.000845) (0.00684) (0.000501) (0.000864) (0.000801)
Change S&L Employment
0.257 4.490*
per Resident (Dec 2018 – Dec
2019) (0.229) (2.316)
Change Private Employment per 0.111*** 1.469***
Resident (Dec 2018 – Dec 2019) (0.0430) (0.401)
Change in Dependent Variable 1.605*** 0.946*** 0.885***
(End-2018 – End-2019) (0.226) (0.200) (0.286)
Average OSI (March 2020) -0.00233 -0.0195 0.00277 0.00628* 0.00411
(0.00278) (0.0203) (0.00212) (0.00358) (0.00307)
Average OSI (Current Month) -0.00340*** -0.0874*** -0.00580*** -0.0133*** 0.00320***
(0.000573) (0.00358) (0.000593) (0.00108) (0.000581)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0026 -0.0234 0.0004 -0.0010 0.0039
Aggregate Impact Coef. -0.437 -1.512 -0.201 -0.780 -0.162
Observations 900 900 300 300 300
R2 0.423 0.675 0.625 0.566 0.148
First-Stage F-Statistic 50.59 50.59 59.51 61.51 64.44
P-value on Test for Pre-Trends 0.336 0.885 0.472 0.318 0.853
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an
equation of the following form for all months pooled:
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
four bills. Equation (2b) is modified to reflect the wider range of outcome variables. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million residents in 2020, according to
∆𝑌𝑠,𝑡,𝑦−𝑦2019
equation (2a). presents the change in a given macroeconomic variable per capita relative to the same time period in
𝑃𝑜𝑝𝑠,𝑦2020
2019. For example, Column 1 uses the change in state and local government employment per capita, identical to Table 2
Column 2, while Column 4 uses the change in annualized state GDP per capita in USD millions relative to the same quarter in
60
2019. All employment variables use QCEW estimates. Column 3 uses the annualized real total wages in USD millions, for all
employees, as measured by the BEA. Columns 4 and 5 use seasonally-adjusted, annualized real state GDP per capita in USD
millions and seasonally-adjusted, annualized real personal income per capita in USD millions. Included is a set of state-level
controls 𝑋𝑠,𝑡,𝑦 . This includes an indicator for if state s is considered a ‘small state,’ the share of a state’s population living in a
town eligible for financing through the MLF, the change in state and local and private employment per capita (QCEW) between
December 2018 and December 2019 (for employment regressions), the March 2020 and contemporaneous month/quarter
averages of a state’s Oxford Stringency Index, and the change in the dependent variable between the end of 2018 and 2019 (if
not already included). The aggregate impact coefficient denotes the total impact over the pandemic implied by the annualized
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
coefficient (scaled by [ ] as described above). This table shows pooled regressions run using data from April
12
2020 to September 2021 for monthly dependent variables or Q2 2020 to Q3 2021 for quarterly variables, the periods during
which the federal government appropriated money to state and local governments.
*** p<0.01, ** p<0.05, * p<0.1
61
Appendix Table 11: Macroeconomic Impact of COVID-19 Relief Aid – Saturated Specification
State and Local State Real State Real
Govt Private Total Wages GDP per Personal
Employment Employment per Capita (USD Capita (USD Income (USD
per Capita per Capita millions) Millions) Millions)
(1) (2) (3) (4) (5)
Total Aid per Resident (USD 0.769* -1.664 -0.299 -0.418 -0.0348
millions) (0.416) (2.747) (0.232) (0.544) (0.370)
Log(Population) 0.000514* -0.00168 -0.000126 -0.000221 0.000238
(0.000278) (0.00164) (0.000140) (0.000314) (0.000212)
Share of Population Eligible for -0.00329 -0.0186 0.00611 0.00405 0.0162**
MLF (0.0121) (0.0857) (0.00543) (0.0110) (0.00683)
Change S&L Employment
0.188 8.828
per Resident (Dec 2018 – Dec
2019) (0.429) (5.618)
Change Private Employment per 0.108 1.274*
Resident (Dec 2018 – Dec 2019) (0.0678) (0.667)
Change in Dependent Variable 0.814*** 0.989 -0.0648
(End-2018 – End-2019) (0.258) (0.637) (0.519)
Average OSI (March 2020) 0.124 -3.363 -0.284*** -0.739*** -0.390***
(0.273) (2.072) (0.106) (0.257) (0.135)
Average OSI (Current Month) 0.0370** 0.0731 0.00684 0.0358 0.0306*
(0.0166) (0.171) (0.0178) (0.0410) (0.0183)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Saturated Controls Y Y Y Y Y
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0026 -0.0234 0.0004 -0.0010 0.0039
Aggregate Impact Coef. 1.154* -2.496 -0.443 -0.627 -0.0522
Observations 900 900 300 300 300
R2 0.406 0.757 0.709 0.678 0.194
First-Stage F-Statistic 56.25 56.25 96.21 68.74 71.76
P-value on Test for Pre-Trends 0.454 0.396 0.038 0.240 0.368
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an
equation of the following form for all months pooled:
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑 2 3
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝛽3 𝑋𝑠,𝑡,𝑦 + 𝛽4 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
four bills. Equation (2b) is modified to reflect the wider range of outcome variables. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
∆𝑌𝑠,𝑡,𝑦−𝑦2019
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million residents in 2020.
𝑃𝑜𝑝𝑠,𝑦2020
presents the change in a given macroeconomic variable per capita relative to the same time period in 2019. For example,
Column 1 uses the change in state and local government employment per capita, identical to Table 2 Column 2, while Column 4
62
uses the change in annualized state GDP per capita in USD millions relative to the same quarter in 2019. All employment
variables use QCEW estimates. Column 3 uses the annualized real total wages in USD millions, for all employees, as measured
by the BEA. Columns 4 and 5 use seasonally-adjusted, annualized real state GDP per capita in USD millions and seasonally-
adjusted, annualized real personal income per capita in USD millions. Included is a set of state-level controls 𝑋𝑠,𝑡,𝑦 . This includes
the log of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the
MLF, the change in state and local and private employment per capita (QCEW) between December 2018 and December 2019
(for employment regressions), the March 2020 and contemporaneous month/quarter averages of a state’s Oxford Stringency
2 3
Index, and the change in the dependent variable between the end of 2018 and 2019 (if not already included). 𝑋𝑠,𝑡,𝑦 𝑎𝑛𝑑 𝑋𝑠,𝑡,𝑦
denote the squared and cubed terms of the variables contained in 𝑋𝑠,𝑡,𝑦 . The aggregate impact coefficient denotes the total
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
impact over the pandemic implied by the annualized coefficient (scaled by [ ] as described above). This table
12
shows pooled regressions run using data from April 2020 to September 2021 for monthly dependent variables or Q2 2020 to Q3
2021 for quarterly variables, the periods during which the federal government appropriated money to state and local
governments.
*** p<0.01, ** p<0.05, * p<0.1
63
Appendix Table 12: Macroeconomic Impact of COVID-19 Relief Aid – Simple Specification
State and Local State Real State Real
Govt Private Total Wages GDP per Personal
Employment Employment per Capita (USD Capita (USD Income (USD
per Capita per Capita millions) Millions) Millions)
(1) (2) (3) (4) (5)
Total Aid per Resident (USD -0.0619 -7.894*** -0.0510 -0.203 0.606
millions) (0.274) (2.360) (0.334) (0.422) (0.584)
Log(Population) 0.000214 -0.00227 0.000227 0.000126 0.000555
(0.000216) (0.00169) (0.000202) (0.000225) (0.000355)
Share of Population Eligible for
MLF
Change S&L Employment
per Resident (Dec 2018 – Dec
2019)
Change Private Employment per
Resident (Dec 2018 – Dec 2019)
Change in Dependent Variable
(End-2018 – End-2019)
Average OSI (March 2020)
Average OSI (Current Month)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0026 -0.0234 0.0004 -0.0010 0.0039
Aggregate Impact Coef. -0.093 -11.84 -0.077 -0.305 0.909
Observations 900 900 300 300 300
R2 0.032 0.136 0.038 0.017 0.043
First-Stage F-Statistic 140.62 140.62 139.99 139.99 139.99
P-value on Test for Pre-Trends 0.435 0.686 0.998 0.166 0.858
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an
equation of the following form for all months pooled:
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
Wwhere 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
four bills. Equation (2b) is modified to reflect the wider range of outcome variables. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million residents in 2020, according to
∆𝑌𝑠,𝑡,𝑦−𝑦2019
equation (2a). presents the change in a given macroeconomic variable per capita relative to the same time period in
𝑃𝑜𝑝𝑠,𝑦2020
2019. For example, Column 1 uses the change in state and local government employment per capita, identical to Table 2
Column 7, while Column 4 uses the change in annualized state GDP per capita in USD millions relative to the same quarter in
64
2019. All employment variables use QCEW estimates. Column 3 uses the annualized real total wages in USD millions, for all
employees, as measured by the BEA. Columns 4 and 5 use seasonally-adjusted, annualized real state GDP per capita in USD
millions and seasonally-adjusted, annualized real personal income per capita in USD millions. Included is a set of state-level
controls 𝑋𝑠,𝑡,𝑦 . This includes only the log of the population of state s. The aggregate impact coefficient denotes the total impact
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
over the pandemic implied by the annualized coefficient (scaled by [ ] as described above). This table shows
12
pooled regressions run using data from April 2020 to September 2021 for monthly dependent variables or Q2 2020 to Q3 2021
for quarterly variables, the periods during which the federal government appropriated money to state and local governments.
*** p<0.01, ** p<0.05, * p<0.1
65
Appendix Table 13: Macroeconomic Impact of COVID-19 Relief Aid – Drop Most- & Least-Represented
States
State and Local State Real State Real
Govt Private Total Wages GDP per Personal
Employment Employment per Capita (USD Capita (USD Income (USD
per Capita per Capita millions) Millions) Millions)
(1) (2) (3) (4) (5)
Panel A: Drop 3 Most- & Least-Represented States
Total Aid per Resident (USD 0.972** -4.930 -0.273 -0.299 0.180
millions) (0.469) (4.486) (0.339) (0.574) (0.379)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0027 -0.0229 0.0004 -0.0009 0.0039
Aggregate Impact Coef. 1.458** -7.395 -0.410 -0.449 0.270
Observations 792 792 264 264 264
R2 0.253 0.664 0.635 0.575 0.093
First-Stage F-Statistic 25.69 25.69 35.63 40.50 31.60
P-value on Test for Pre-Trends 0.601 0.578 0.364 0.632 0.776
Panel B: Drop 5 Most- & Least-Represented States
Total Aid per Resident (USD 1.448 -1.035 0.211 0.558 1.006
millions) (1.000) (7.570) (0.502) (0.908) (0.801)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0027 -0.0220 0.0004 -0.0008 0.0039
Aggregate Impact Coef. 2.172 1.553 0.3165 0.837 1.509
Observations 720 720 240 240 240
R2 0.234 0.621 0.656 0.555 0.105
First-Stage F-Statistic 8.88 8.88 16.19 19.35 15.30
P-value on Test for Pre-Trends 0.760 0.717 0.291 0.936 0.946
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an
equation of the following form for all months pooled:
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
four bills. Equation (2b) is modified to reflect the wider range of outcome variables. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million residents in 2020, according to
∆𝑌𝑠,𝑡,𝑦−𝑦2019
equation (2a). presents the change in a given macroeconomic variable per capita relative to the same time period in
𝑃𝑜𝑝𝑠,𝑦2020
2019. For example, Column 1 uses the change in state and local government employment per capita, while Column 4 uses the
change in annualized state GDP per capita in USD millions relative to the same quarter in 2019. All employment variables use
66
QCEW estimates. Column 3 uses the annualized real total wages in USD millions, for all employees, as measured by the BEA.
Columns 4 and 5 use seasonally-adjusted, annualized real state GDP per capita in USD millions and seasonally-adjusted,
annualized real personal income per capita in USD millions. Included is a set of state-level controls 𝑋𝑠,𝑡,𝑦 . This includes the log of
2020 official Census population, the share of a state’s population living in a town eligible for financing through the MLF, the
change in state and local and private employment per capita (QCEW) between December 2018 and December 2019 (for
employment regressions), the March 2020 and contemporaneous month/quarter averages of a state’s Oxford Stringency Index,
and the change in the dependent variable between the end of 2018 and 2019 (if not already included). The aggregate impact
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
coefficient denotes the total impact over the pandemic implied by the annualized coefficient (scaled by [ ]
12
as described above). This table shows pooled regressions run using data from April 2020 to September 2021 for monthly
dependent variables or Q2 2020 to Q3 2021 for quarterly variables, the periods during which the federal government
appropriated money to state and local governments. Panel A excludes observations for the three most over-represented and
under-represented states (Wyoming, Vermont, Alaska; Texas, Florida, California), while Panel B excludes the five most over-
and under-represented states (Wyoming, Vermont, Alaska, North Dakota, Rhode Island; Texas, Florida, California, New York,
North Carolina).
*** p<0.01, ** p<0.05, * p<0.1
67
Appendix Table 14: Macroeconomic Impact of COVID-19 Relief Aid – Relative to End-2019
State and Local State Real State Real
Govt Private Total Wages GDP per Personal
Employment Employment per Capita (USD Capita (USD Income (USD
per Capita per Capita millions) Millions) Millions)
(1) (2) (3) (4) (5)
Total Aid per Resident (USD 1.113 4.471 -0.0384 -0.393 0.359
millions) (0.732) (4.030) (0.300) (0.573) (0.480)
Log(Population) 0.000810*** -0.000175 -6.13e-05 -0.000193 0.000189
(0.000296) (0.00239) (0.000169) (0.000329) (0.000263)
Share of Population Eligible for -0.00220 -0.0227** -0.000478 -0.00137 9.53e-05
MLF (0.00189) (0.0107) (0.000462) (0.00106) (0.000747)
Change S&L Employment
1.092** 6.547**
per Resident (Dec 2018 – Dec
2019) (0.489) (2.786)
Change Private Employment per 0.166** 1.308***
Resident (Dec 2018 – Dec 2019) (0.0682) (0.447)
Change in Dependent Variable 1.277*** 0.686*** 0.748***
(End-2018 – End-2019) (0.211) (0.198) (0.290)
Average OSI (March 2020) -0.00801** -0.0114 0.00277 0.00706* 0.00311
(0.00407) (0.0239) (0.00220) (0.00372) (0.00343)
Average OSI (Current Month) 0.000747 -0.0945*** -0.00579*** -0.0136*** 0.00294***
(0.000630) (0.00457) (0.000641) (0.00114) (0.000620)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0046 -0.0252 0.0001 -0.0014 0.0036
Aggregate Impact Coef. 1.670 6.707 -0.058 -0.590 0.539
Observations 900 900 300 300 300
R2 0.054 0.672 0.589 0.129 0.586
First-Stage F-Statistic 57.78 57.78 59.51 56.27 61.27
P-value on Test for Pre-Trends 0.385 0.106 0.297 0.777 0.443
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an
equation of the following form for all months pooled:
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
four bills. Equation (2b) is modified to reflect the wider range of outcome variables. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million residents in 2020, according to
68
∆𝑌𝑠,𝑡,𝑦−𝑦2019
equation (2a). presents the change in a given macroeconomic variable per capita relative to the last measured value
𝑃𝑜𝑝𝑠,𝑦2020
in 2019. For example, Column 1 uses the change in state and local government employment per capita relative to December
2019, while Column 4 uses the change in annualized state GDP per capita in USD millions relative to Q4 2019. All employment
variables use QCEW estimates. Column 3 uses the annualized real total wages in USD millions, for all employees, as measured
by the BEA. Columns 4 and 5 use seasonally-adjusted, annualized real state GDP per capita in USD millions and seasonally-
adjusted, annualized real personal income per capita in USD millions. Included is a set of state-level controls 𝑋𝑠,𝑡,𝑦 . This includes
the log of 2020 official Census population, the share of a state’s population living in a town eligible for financing through the
MLF, the change in state and local and private employment per capita (QCEW) between December 2018 and December 2019
(for employment regressions), the March 2020 and contemporaneous month/quarter averages of a state’s Oxford Stringency
Index, and the change in the dependent variable between the end of 2018 and 2019 (if not already included). The aggregate
impact coefficient denotes the total impact over the pandemic implied by the annualized coefficient (scaled by
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
[ ] as described above). This table shows pooled regressions run using data from April 2020 to September
12
2021 for monthly dependent variables or Q2 2020 to Q3 2021 for quarterly variables, the periods during which the federal
government appropriated money to state and local governments.
*** p<0.01, ** p<0.05, * p<0.1
69
Appendix Table 15: Macroeconomic Impact of COVID-19 Relief Aid – Adding Additional Lags
State and Local State Real State Real
Govt Private Total Wages GDP per Personal
Employment Employment per Capita (USD Capita (USD Income (USD
per Capita per Capita millions) Millions) Millions)
(1) (2) (3) (4) (5)
Total Aid per Resident (USD 0.780** 1.304 -0.0474 -0.122 0.406
millions) (0.378) (3.536) (0.322) (0.639) (0.508)
Log(Population) 0.000467** 4.25e-05 -6.29e-05 -9.21e-05 0.000218
(0.000195) (0.00218) (0.000189) (0.000343) (0.000288)
Share of Population Eligible for -0.00131 -0.0127 -0.000488 -0.00163 -0.000213
MLF (0.000971) (0.00957) (0.000524) (0.00120) (0.000986)
Change S&L Employment
0.558** 6.898**
per Resident (Dec 2018 – Dec
2019) (0.261) (3.490)
Change Private Employment per 0.134*** 1.921***
Resident (Dec 2018 – Dec 2019) (0.0426) (0.643)
Change in Dependent Variable 1.416*** 0.821*** 0.924***
(End-2018 – End-2019) (0.257) (0.261) (0.281)
Change in Dependent Variable -0.00122 -0.694 0.406 0.265 0.489
(End-2017 – End-2018) (0.136) (0.706) (0.376) (0.332) (0.321)
Average OSI (March 2020) -0.00527** -0.0294 0.00314 0.00498 0.00425
(0.00228) (0.0214) (0.00210) (0.00366) (0.00297)
Average OSI (Current Month) -0.00373*** -0.0881*** -0.00578*** -0.0134*** 0.00318***
(0.000494) (0.00382) (0.000631) (0.00112) (0.000583)
Political and Mobility Controls N N N N N
COVID-19 Controls N N N N N
Economic Controls N N N N N
Frequency Monthly Monthly Quarterly Quarterly Quarterly
Dep. Var. Mean -0.0026 -0.0234 0.0004 -0.0010 0.0039
Aggregate Impact Coef. 1.17** 1.956 -0.0711 -0.183 0.609
Observations 900 900 300 300 300
R2 0.326 0.667 0.552 0.153 0.625
First-Stage F-Statistic 59.53 55.62 67.40 41.37 64.54
P-value on Test for Pre-Trends 0.554 0.714 0.257 0.962 0.441
Note: This table uses data from the Committee for a Responsible Federal Budget (2021), US Federal Transit Administration
(2021a), US Census Bureau (2021), Chidambaram and Musumeci (2021), Medicaid and Chip Payment Access Commission
(2021), US Office of Elementary and Secondary Education (2021), and Lewis et al. (2021), US Bureau of Labor Statistics (2021b),
US Department of the Treasury (2021a), Federal Reserve Board (2021), Hale et al. (2020), Google LLC (2021), MIT Election and
Data Science Lab (2017), Dong, Du, and Gardner (2020), and the US Bureau of Economic Analysis (2021) to estimate an
equation of the following form for all months pooled:
∆𝑌𝑠,𝑡,𝑦−𝑦2019 ̂ 𝑠
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑
= 𝛼 + 𝛽1 + 𝛽2 𝑋𝑠,𝑡,𝑦 + 𝑢𝑠,𝑡,𝑦
𝑃𝑜𝑝𝑠,𝑦2020 𝑃𝑜𝑝𝑠,𝑦2020
where 𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠 is the total federal aid per resident to state and local governments (USD millions) in state s pooled across all
𝑇𝑜𝑡𝑎𝑙𝐴𝑖𝑑𝑠
four bills. Equation (2b) is modified to reflect the wider range of outcome variables. In a first stage regression, is
𝑃𝑜𝑝𝑠,𝑦2020
instrumented using 𝑅𝑒𝑝𝑠𝑃𝑒𝑟𝑀𝑖𝑙𝑙𝑖𝑜𝑛𝑠 , the number of representatives and senators per million residents in 2020, according to
∆𝑌𝑠,𝑡,𝑦−𝑦2019
equation (2a). presents the change in a given macroeconomic variable per capita relative to the same time period in
𝑃𝑜𝑝𝑠,𝑦2020
70
2019. For example, Column 1 uses the change in state and local government employment per capita, identical to Table 2
Column 2, while Column 4 uses the change in annualized state GDP per capita in USD millions relative to the same quarter in
2019. All employment variables use QCEW estimates. Column 3 uses the annualized real total wages in USD millions, for all
employees, as measured by the BEA. Columns 4 and 5 use seasonally-adjusted, annualized real state GDP per capita in USD
millions and seasonally-adjusted, annualized real personal income per capita in USD millions. Included is a set of state-level
controls 𝑋𝑠,𝑡,𝑦 . This includes the log of 2020 official Census population, the share of a state’s population living in a town eligible
for financing through the MLF, the change in state and local and private employment per capita (QCEW) between December
2018 and December 2019 (for employment regressions), the March 2020 and contemporaneous month/quarter averages of a
state’s Oxford Stringency Index, and two annual lags in the dependent variable spanning from 2017 to 2019 (if not already
included). The aggregate impact coefficient denotes the total impact over the pandemic implied by the annualized coefficient
𝑀𝑜𝑛𝑡ℎ𝑠𝑆𝑖𝑛𝑐𝑒𝑃𝑎𝑛𝑑𝑒𝑚𝑖𝑐
(scaled by [ ] as described above). This table shows pooled regressions run using data from April 2020 to
12
September 2021 for monthly dependent variables or Q2 2020 to Q3 2021 for quarterly variables, the periods during which the
federal government appropriated money to state and local governments.
*** p<0.01, ** p<0.05, * p<0.1
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