NBER WORKING PAPER SERIESSTAY-AT-HOME ORDERS IN A FISCAL UNION
Mario J. Crucini
Oscar O'Flaherty
Working Paper 28182
http://www.nber.org/papers/w28182

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
December 2020

The authors thank participants in the 2020 SEA conference and the Vanderbilt Economics
Macroeconomics and International Brown Bag for helpful comments. We thank Michael
McGuire for excellent research assistance. The views expressed herein are those of the authorsand 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 They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies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.
© 2020 by Mario J. Crucini and Oscar O'Flaherty. All rights reserved. Short sections of text, notto exceed two paragraphs, may be quoted without explicit permission provided that full credit,including © notice, is given to the source.

Stay-at-Home Orders in a Fiscal Union
Mario J. Crucini and Oscar O'Flaherty
NBER Working Paper No. 28182
December 2020
JEL No. E3,E47,E62,H12,H23,H7
ABSTRACTState and local governments throughout the United States attempted to mitigate the spread of
Covid-19 using stay-at-home orders to limit social interactions and mobility. We study the
economic impact of these orders and their optimal implementation in a fiscal union. Using an
event study framework, we find that stay-at-home orders caused a 4 percentage point decrease in
consumer spending and hours worked. These estimates suggest a $10 billion decrease in spending
and $15 billion in lost earnings. We then develop an economic SIR model with multiple locations
to study the optimal implementation of stay-at-home orders. From a national welfare perspective,
the model suggests that it is optimal for locations with higher infection rates to set stricter
mitigation policies. This occurs as a common, national policy is too restrictive for the economiesof mildly infected areas and causes greater declines in consumption and hours worked than are
optimal.

Mario J. Crucini
Department of Economics
Vanderbilt University
Box 1819 Station B
Nashville, TN 37235-1819
and NBER
mario.j.crucini@vanderbilt.edu
Oscar O'Flaherty
Vanderbilt University
Department of Economics
VU Station B #351819
2301 Vanderbilt Place
Nashville, TN 37235-1819
USAoscar.oflaherty@vanderbilt.edu

1Introduction

State and local governments throughout the United States attempted to mitigate the outbreak of Covid-19 using stay-at-home orders to limit social interactions and mobility. Many
praised these policies for slowing the spread of the virus while others protested them due totheir perceived negative impact on the economy. The implementation of stay-at-home orders
also created conflict between policy makers. Some called for a nationwide order while others
believed discretion should be left to state and local governments.
This paper studies the economic and political controversy associated with stay-at-homeorders and their implementation, both empirically and theoretically. Empirically, we use
an event-study framework to estimate the marginal impact of stay-at-home orders on theeconomy. We build a daily, state-level panel of labor market and consumer spending variables
using data from the time-clock company Homebase and non-profit organization Opportunity
Insights. Our main sample spans several weeks before the issuance of the first stay-at-homeorder in March up to the first reopening in April. Both hours worked and consumer spending
were already declining before the first statewide stay-at-home order was issued on March
19th. Thus, the economic decline was likely attributed to a combination of governmentissued policies and behavioral responses by consumers and firms to the health risks posed by
the pandemic. The event-study framework allows us to separate these economic effects by
exploiting differences across states that issued a stay-at-home order and those that did not.
Controls for the daily, case load of infections in each state and non-essential business closures
help isolate the impact of stay-at-home orders. The control for non-essential closures also
helps approximate the cumulative effect of mitigation policy.
Stay-at-home orders negatively impacted the labor market. Hours worked initially declines by 2 percentage points and continues downward to a trough of 6 percentage points(pp) two weeks after the order is enacted. High-income workers experience larger declines in
employment compared to low-income workers. Early-treated states experience about twice1the decline in hours worked (4pp) relative to late-treated states (2pp). Non-essential businessclosures did not exacerbate or mitigate the labor market response.
Stay-at-home orders also decreased consumer spending by 4 percentage points for several
weeks. In contrast to employment, spending declines are larger in magnitude among lowincome consumers compared to high-income consumers. Consumer anticipation effects varyacross sectors. For example, we find evidence of stockpiling in grocery and food stores, but
not in accommodation and food services. Early and late-treated states experience similar
post-treatment declines in spending. However, stockpiling in the pre-treatment period is
primarily driven by early-treated states. Unlike employment, non-essential business closures
did exacerbate the consumer spending response.
The baseline estimates suggest that stay-at-home orders decreased consumer spendingby $10 billion and total earnings by $15 billion. They also suggest that stay-at-home orders
account for 10%-25% of the total employment decline observed during our sample. The nonessential business closure estimates suggest that the cumulative effect of mitigation policy is
at least as large in magnitude as implied by the stay-at-home order estimates. The results
are not driven by outliers. Lastly, in response to the virus, some counties implemented theirown stay-at-home orders before their respective states. We also conduct our analysis at thecounty-level to account for these orders and find similar impacts compared to our baseline
estimates.
In order to study the optimal implementation of stay-at-home orders, we extend theSusceptible-Infected-Recovered (SIR) model of Eichenbaum et al. (2020) to multiple locations. Each location initially experiences an idiosyncratic virus shock. Following this, thevirus can spread through both consumption and employment within a given location. This interaction captures the natural societal responses to the virus as people reduce their economic
activity in order to limit their risk of infection. Although locations are closed economies withrespect to their economic transactions, individuals may also spread the virus across locations
by travelling from place to place. Thus, the economic activity of one location is dependent2

upon other locations due to virus spillovers. The model incorporates travel cost across locations in order to specify the extent of virus spillovers. Lastly, in response to the transmissionof the initial virus shocks, an aggregate social planner can implement mitigation policy—
proxied by a consumption tax—to maximize the welfare of the country. Mitigation policy
is able, but not required, to vary across locations. This allows for economic and welfare
comparisons between a common national policy and location-specific policy.
The main contribution of our model is the cross-sectional distribution of consumption,
hours worked, and infection rates that it generates. The single-location model of Eichenbaum
et al. (2020) is equivalent to our multiple-location model if and only if the initial infection
rates of locations are symmetric and travel costs across locations are zero. If either of theserestrictions fails to hold, then aggregate dynamics will depend on the behavior of the crosssection.
We explore the behavior of the cross-sectional distribution and dynamics in the modelthrough an application using US Census region data. The model suggests that travel costacross locations plays a significant role in the spread of the virus in the US. Allowing forcomplete pass-through of virus transmission overestimates the infection rates of every Census
region. In contrast, allowing for no virus transmission across regions tends to underestimate
the infection rates seen in the data. We propose a method to determine the rate of transmission across locations through the associated travel costs. This method provides a good
fit of both the cross-sectional distribution and dynamics in the US Census data, and theprocedure is generalized for use in other applications.
Lastly, we turn our analysis to optimal policy with multiple locations. From a national
welfare perspective, it is optimal for locations with higher infection rates to set stricter
mitigation policies. A common, national policy is too restrictive for mildly infected locations
and causes greater consumption and employment declines than are optimal in these areas.
Stricter policy in more severely affected locations causes infection rates, and subsequently
mitigation policy, to converge over time. Thus, our finding that policy should be set at a3

local level is contingent on sufficient asymmetries in the infection rates of locations.
Other research has examined the empirical relationship between the economy, the spreadof Covid-19, and the ensuing policy responses (Baker et al., 2020; Binder, 2020; Chetty et al.,2020; Rojas et al., 2020). Our empirical contribution is closely related to other differencein-difference estimates that find negative effects of stay-at-home orders on the labor market(Allcott et al., 2020; Baek et al., 2020; Bartik et al., 2020; Beland et al., 2020; Gupta et al.,2020; Kong and Prinz, 2020; Lin and Meissner, 2020) and consumer spending (Allcott etal., 2020; Coibion et al., 2020; Goolsbee and Syverson, 2020). Importantly, our estimates forboth the employment and spending effects are found using an event study specification using
data at a daily frequency which builds on many of these papers. The high frequency data
allows us to provide a clear characterization of both when and where stay-at-home orders
were issued. The event study specification allows us to assess whether our results are driven
by differences in observable pre-treatment trends across treated and control states, for which
we do not find evidence. Of the papers mentioned above, our paper is most closely related to
Allcott et al. (2020) who find similar results for both consumer spending and hours worked.
The Opportunity Insights data allows us to analyze these effects by consumer and worker
income quartiles as well as by industry, which are both new results.
Our paper is also related to the quantitative theoretical literature of infectious diseasemodelling (Kermack and Mckendrick, 1927; Angulo et al., 2013; Zakary et al., 2017; Bisin
and Moro, 2020) and its application to economic activity and mitigation policy (Acemoglu
et al., 2020; Atkeson, 2020; Jones et al., 2020). We extend the model of Eichenbaum et al.
(2020) to multiple locations. This allows us to illustrate how the economy in one location canbe affected by the spread of the virus in other locations. Antràs et al. (2020) and Fajgelbaum
et al. (2020) also study the economic spillovers of virus transmission across locations. Antràs
et al. (2020) focus primarily on endogenous trade adjustments while Fajgelbaum et al. (2020)
assess cross-location mitigation policy such as travel restrictions. In contrast, our analysis
centers on domestic mitigation policies such as stay-at-home orders. Overall, these models

4provide complementary, rather than contradictory, results which help to more fully characterize the economic effects of virus transmission across locations and the subsequent policy
responses. Lastly, Baek et al. (2020) develop a model with stay-at-home orders characterized
as an exogenous productivity or demand shock. By explicitly modelling the spread of thevirus, we are able to endogenously model mitigation policy such as stay-at-home orders.1
This allows us to evaluate their economic impact as well as their optimal implementation in
response to the spread of the virus.
The rest of the paper proceeds as follows. Section 2 presents a timeline of the spread of
Covid-19 throughout the U.S., the subsequent economic and policy responses, and formalizes the event study specification. Section 3 presents the baseline event study results androbustness checks. Section 4 describes the economic SIR model. Section 5 compares themultiple-location model with the single-location model, applies the multiple-location model
to Census region data, and presents the results for optimal mitigation policy. Section 6
concludes.

2

Empirical Framework: Isolating the economic impact of stay-at-home orders

We begin by creating a daily panel of several labor market and consumer spending variables.
Our panel spans from March up to April 24, the first day a stay-at-home order was lifted.
This allows our analysis to focus specifically on the initial virus outbreak and asymmetricpolicy responses across states. The second subsection provides a timeline of the outbreakof the virus, the enactment of stay-at-home orders, and the economic response during thisperiod. The third subsection formalizes our event-study specification.
2.1

Variable Definitions

Baseline Labor Variables We obtain our primary labor market measures from the timeclock company Homebase.2 Homebase helps over 60,000 businesses track the hours worked
12This is one of the novel contributions of Eichenbaum et al. (2020) which remains in our extension.
An interactive database from Homebase can be found here: https://joinhomebase.com/data/5

of 1 million hourly employees. Their data provides three labor-market measures: businesses
open, employees working, and hours worked. A business is defined as open if at least one
employee clocked in for a given day. Employees working is counted as the number of uniqueemployees who clocked in at least once. Hours worked is then determined from the timecards of all employees. Total hours worked is the primary outcome variable as it corresponds
to the model developed in Section 4. All variables are measured at the state level. Eachvariable is normalized relative to the median for that day of week using data from January
4, 2020 through January 31, 2020.

Supplemental Labor Variables We supplement our Homebase data with an employment
measure constructed by the non-profit organization Opportunity Insights (OI) in Chetty etal. (2020). Employment is normalized relative to the average level from Jan. 4-31. This
employment data provides several advantages and disadvantages compared to the Homebase
data. The first advantage is that the OI data is available at both the state and county level.
This allows us to account for stay-at-home orders issued by individual counties. Second,
employment is measured by low (<$27,000 per year), medium ($27,000-$60,000), and highincome (>$60,000) earners at both the state and county level.3 Lastly, the state-level data isdisaggregated into four NAICS sectors: Professional and Business Services, Education and
Health Services, Retail and Transportation, Leisure and Hospitality.
However, the OI data has several disadvantages. The OI data is constructed using workerlevel data from Earnin and firm-level payroll data from Paychex and Intuit.4 This createsthe conflict that observations are recorded when workers are paid rather than the specificdate they are employed as in the time-clock data from Homebase. To circumvent this issue,
Chetty et al. (2020) make the assumption that individuals are employed for all days in their
pay period. If a stay-at-home order occurred in the middle of an individual’s pay period,
employment effects would not be seen until their next pay period. Thus, the implications of
3
These are approximate measures. Quartiles are based upon the hourly wage distribution in 2019. Income
levels are more accurately < $13.00/Hour, $13.00 − $29.17, and > $29.17/Hour.
4
Please see Chetty et al. (2020) for a more detailed description of their employment series.

6this assumption are too strong for an event study analysis which hinges upon variation at thetime of treatment. To account for the difference between the end of the pay period and thedate of employment, we lag the data by an additional week.5 Lastly, their employment series
is constructed as a seven-day look-back moving average. This attenuates the overall effect ofa one-day change in employment which is of primary interest in the context of stay-at-homeorders. For these reasons, we use the Homebase data for our baseline estimates on the labormarket and the OI data for comparisons and robustness checks.6

Expenditure Variables We use credit and debit card spending data from Affinity Solutions
to estimate changes in consumer expenditures. This expenditure data is also constructed by
Chetty et al. (2020) and is available at more granular levels than the Homebase data. At
the state level, expenditure data is provided by income quartile. Consumers are consideredhigh-income if they live in a ZIP code with median income in the top quartile of ZIP codes.
Similarly, low-income consumers live in the bottom quartile of ZIP codes. Middle-income
consumers are then defined as living in the second and third quartiles. Expenditure datais also separated into several merchant groups defined by Affinity Solutions: Apparel andGeneral Merchandise, Entertainment and Recreation, Grocery, Health Care, Restaurants
and Hotels, Transportation. Total expenditure data is also available at the county level,but is not available by income quartile or merchant group. A seven-day look-back moving
average is taken for all consumption variables, and then measured relative to the median forthat day of week using data from January 4, 2020 through January 31, 2020.7
5

Chetty et al. (2020) use Earnin data only for workers that are paid weekly or bi-weekly. They make theassumption that there is a one-week lag from the end of the pay period to the date an individual is paid.
By lagging their employment series an additional week, we essentially shift the data to the beginning of thetwo-week pay cycle and assume there is no lag between the end of the pay period and payment date. Chetty
et al. (2020) also convert weekly employment data from Paychex to daily by assuming that employment isconstant within each week. Lagging an additional week also helps control for the effects of this assumption.
6
Appendix Figure A.1 plots these two measures for comparison.
7
See Chetty et al. (2020) for a full description of the construction of the expenditure series.

7

Figure 1: Coronavirus outbreak by US state

Note: This figure plots the natural log of cases per 1,000 residents for each state. To account for periods ofzero infection in the beginning of our sample, we add one to the number of cases for all observations before
calculating the infection rate. The black line represents the national total. Data is obtained from USAFacts.

Infection variables Our daily panel spanning this period uses cases reported by the nonprofit organization USA Facts.8 Cases are reported at the county level which we thenaggregate to the state level. Primary source information for infections and tests comes fromthe CDC and state and local health agencies. Population data are obtained from the US
Census to calculate case load per capita.

2.2

Context and timeline

The United States recorded its first case of the novel coronavirus disease of 2019 (Covid-19)
on January 20th, 2020 when a man from the state of Washington became ill after a visit toWuhan, China. The timing and spread of the virus differed across states after this initialinfection. To see this, Figure 1 plots the natural log of cases per capita for each state fromMarch 9th through April 24th. West Virginia was the last state to document a confirmed
case on March 17th, almost two months after the first case in Washington. At this point,
8

Specifically, cases and deaths are obtained from the website: https://usafacts.org/visualizations/coronavirus-covid-19-spread-map/.

8

Table 1: Timeline of Stay-at-Home Orders
March 15

March 16

March 17

March 18

March 19
California

March 20

March 21

March 22
Illinois
New Jersey

March 23
New York
OregonWashington

March 24
Connecticut
DelawareLouisiana
Massachusetts
Michigan
New Mexico
Ohio

March 25
Hawaii
Idaho
IndianaWest Virginia
Wisconsin

March 26
Colorado
Vermont

March 27
KentuckyMarch 28
Minnesota
Montana
New Hampshire
Rhode Island

March 29
AlaskaMarch 30
KansasVirginia

March 31
North Carolina
MarylandApril 1
Arizona
District of Columbia
NevadaTennessee

April 2Maine
Pennsylvania
Texas

April 3
FloridaGeorgia

April 4
Mississippi

April 5
AlabamaApril 6
Missouri

April 7

April 8South Carolina

April 9April 10

April 11

Note: This table presents the timeline of the enforcement of stay-at-home orders. Some policies began at
a specific time of the day such as 6:00am or 6:00pm. Orders that occur after noon are recorded on thefollowing day. Dates of stay-at-home orders are obtained from the New York Times.

Montana had a case rate similar to the national total. However, low case growth led themto have the least cases per capita on April 24th. In contrast, persistently high case growthin New York led them to maintain the highest case rate per capita from mid-March throughthe end of April.
As infection rates grew, many local and state governments issued various social distancing
policies to help limit personal contact and combat the spread of the coronavirus. Our analysis
centers on statewide stay-at-home orders. These orders generally closed all non-essential
businesses, and encouraged people to stay at home except for essential activities such as
shopping for food or seeking medical care. Over 90% of the US population was placed undera stay-at-home order in the span of three weeks across forty-two states and the District of9Columbia. Table 1 documents the timeline of these stay-at-home orders.9 California was thefirst state to announce an order on March 19th. Twenty-five additional states issued orders
the following week. South Carolina was the last state to issue an order on April 8. Someorders were issued to start at a specific time of the day (e.g. 6:00am or 6:00pm). As ourpanel is at a daily frequency and cannot capture this, we consider states with orders enacted
after Noon to start treatment the following day.10
Despite widespread recognition of their need from a public health perspective, stay-athome orders were met with opposition. Protests over the economic impact of these orders
occurred in many states (NBC News, 2020; Fox News, 2020). One protester in New Jersey
said, “Businesses are suffering, unemployment checks are not being sent, landlords are notgetting rent. We feel like these directives are causing more suffering than is necessary.”(NJ.com, 2020) A poll conducted in May estimated that 35% of people “strongly or somewhat
agreed” that restrictions and closures had been too severe (USA Today, 2020).
Figure 2 plots the the response of hours worked and consumer expenditures during theoutbreak of Covid-19 from March 9th to April 24th. The red line represents the averageover states which issued a stay-at-home order, and the blue line depicts those that did not.
Standard errors are shaded in their respective colors. Both panels show that employment
and expenditure were declining before the first statewide stay-at-home order was issued on
March 19th. We also see that these declines differed across treatment groups throughout
most of the sample.
Panel (a) shows that total hours worked in states which issued a stay-at-home orderdeclined by 34% on March 18th. On this date, states that did not issue an order only had
a decline of 23%. As a stay-at-home order had not yet been issued, they cannot accountfor this economic decline or the 11 percentage point (pp) difference across groups. However,these differences did grow over time. On April 23rd, the day before the first lifting of a stay9

Appendix Figure A.2 presents a timeline of the percentage of the US population under a stay-at-homeorder.
10
Primary source information for state announcements was compiled by the New York Times: https://www.nytimes.com/interactive/2020/us/coronavirus-stay-at-home-order.html

10Figure 2: Economic Response to Covid-19(a) Hours Worked(b) Expenditure

Note: This figure plots the time series of spending and hours worked for states which issued a stay-at-homeorder (red) and states that did not (blue) from March 9th to April 24th. Estimates are averages over statesin their respective treatment groups. Shaded regions represent the standard error for that date. Hours andexpenditure data are provided by Homebase and Affinity Solutions, respectively.

at-home order, declines in hours worked were 54% and 35% for the treated and untreatedgroups, respectively. Thus, the differences in hours worked across groups had grown by 8
percentage points from March 18th (11pp) to April 23rd (19pp). Panel (b) shows a similar
pattern in expenditures. The percentage point difference in expenditure across groups grewby 2 percentage points from on March 18th (3pp) to on April 23rd (5pp).11

2.3

Event Study Specification

The simple analysis above helps provide the intuition behind a difference-in-differences estimation. Although it provides suggestive evidence that stay-at-home orders may have contributed to the economic decline of states, it does not account for differences in characteristics
of states as in Figure 1 or the variation in treatment timing in Table 1. To account for thesecomplications, the following event study specification is estimated:
k6=−1

yit = αi + γt + ΓXit +X

βk I(StayHomeit = k) + it(1)−10≤k≤15
11

Appendix Table A.1 performs a similar analysis with the remaining labor, expenditure, and infection
variables.

11This empirical strategy strategy uses variation in both when and where stay-at-home orders
were issued. Our primary outcome variable, yit , is either hours worked or consumption
expenditures in state i at time t. State fixed effects, αi , control for both observable andunobservable differences across states that do not change over time. Time fixed effects, γt ,control for variables that affect all states in a given period such as the weekly seasonalityof hours worked seen in Panel (a) of Figure 2 or national news about the coronavirus.
Our sample begins on March 9th, ten days before the first statewide stay-at-home order in
California, and ends on April 23rd, the day before the first statewide reopening in Alaska.
StayHomeit represents the current date relative to the date a stay-at-home order was issued
in a given state. This variable is always equal to −1 for non-treated states which serve as
the control group.
The coefficients of interest, the βk ’s, represent the average difference between the control
and treated group at period k relative to the difference at k = −1, the day before the order isenacted for treated states. We present estimates for event times k ∈ [−10, 15]. Event times
0 to 15 estimate the causal effect of a stay-at-home order on hours worked and consumption
expenditures. These estimates represent the average treatment effect for the treated (ATT).
Event times -10 to -2 serve as a falsification test that our results are not driven by pre-existing
differences in trends between the treatment and control groups before a stay-at-home orderis issued. All of our presented estimates use a balanced set of states. This means ourcoefficients do not reflect changes in the composition of the treatment group.12
Goodman-Bacon and Marcus (2020) raise substantive issues and provide recommendations when using a difference-in-differences design in the context of Covid-19. Our baseline
specification contains several controls to help us address these issues. Namely, we include acontrol for log cases per capita and a similar event study variable for non-essential businessclosures.13 The inclusion of a measure of case incidence helps us to separate the endogenous
12

For example, if we extended the event times to k ∈ [−10, 16], South Carolina would not be included in
the estimate of k = 16 due to the timing of its stay order (recall Table 1). Thus, β16 would be partiallydriven by this change in the composition of the treated group.
13
Non-essential business closures at the state level are obtained from Raifman et al. (2020).

12

Figure 3: Effect of Stay-at-Home Orders on the Economy(a) Hours Worked(b) Expenditure

Note: This figure plots the stay-at-home order event study coefficients estimated from Equation 1. Subcaptions represent the dependent variable. Dashed lines represent 95% confidence intervals using robust standard
errors. The red line plots the difference-in-difference estimate. Observations are at the state-by-day level.
Hours and expenditure data are obtained from Homebase and Affinity Solutions, respectively.

responses of individuals and firms to the risk of infection from the economic impact of stayat-home orders. Controlling for non-essential business closures helps separate the effect ofthese complementary policy tools and avoid possible confounding effects of the two.14

3

Results: Effect of Stay-at-Home Orders on the Economy

Figure 3 analyzes the effect of stay-at-home orders on the economy. Panel (a) shows thatpre-trends in hours worked are slightly elevated eight to ten days before a stay-at-homeorder, but are flat 1-7 days before a stay-at-home order is enacted. Differences in trends are
statistically insignificant at the 95% level using robust standard errors for the entire pretreatment period. Hours worked declined by 4 percentage points (s.e. = 0.39) on averageafter a stay-at-home order. These effects vary over time. Immediately after the order, treatedstates experience over a 2 percentage point decrease in hours. This effect is persistent witha slight downward trend. Fifteen days after the order, treated states experience a trough14

Our main results analyze the effect of stay-at-home orders on the economy. Non-essential business closure
estimates can be found in Section 3.4 and Appendix A.1.

13

decline of −6 percentage points. Effects are statistically significant for the entire posttreatment period.
Panel (b) plots the coefficients for statewide expenditure. Expenditures experience astatistically significant 4pp decline five days after the order. This effect remains stable andsignificant up to fifteen days after the order. We do not find statistically significant differencesin pre-trends before a stay-at-home order. However, they do exhibit a 1 percentage point
upward trend. It is known that consumers would often stockpile items, such as toilet paper,in the days preceding a stay-at-home order. This upward trend may be representative of theconsumer anticipation effect. In this case, our event study estimates for expenditure may bebiased towards finding a negative effect and overstate the effect of the order.
Table 2 provides several alternative specifications and further explores the extent of
the anticipation effect in the baseline results of Figure 3.15 T-values are presented to ease
comparison across specifications. The baseline results are provided in columns (1) and (4)for reference. Results for employment and businesses open in columns (2) and (3) test therobustness of the benchmark labor market results. Immediately after the order, we seeslightly weaker effects of -2.03pp and -2.46pp in employment and businesses open comparedto the baseline estimate of -2.50pp in hours worked. Both variables also suggest a slightdownward trend with an estimated decrease of about 5.6pp fifteen days after the order isenacted.
The baseline results represent the average effect of statewide stay-at-home orders ontreated states’ economic activity. However, some counties issued local orders before theirstate did. These policies could bias the estimates towards not finding a result. To account for
this, we also estimate Equation 1 using county-level orders as the basis for treatment. In thiscase, a county is counted as treated if it issued a stay-at-home order, or if the state it resides
in did.16 As the Homebase dataset does not contain county-level information, this is only
15

Additional robustness checks for population-weighted regressions, outliers, and composition effects canbe found in Appendix Table A.3. These checks have no significant effects on the results.
16
Data for county-level stay-at-home orders and non-essential business closures and their timing is obtained from https://ce.naco.org/?dset=COVID-19&ind=Emergency\%20Declaration\%20Types. Over

14

Table 2: Effect of Stay-at-Home Orders on the Labor Market and Expenditures
Labor Variables (Per. Pt.)

Expenditure Variables (Per. Pt.)

Hours Worked Employment Businesses Open State Level County Level Low Income Middle Income High Income
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

Days
-7

-0.98
(-0.93)-0.16(-0.16)0.37(0.38)-0.94(-1.49)-0.91(-1.35)

0.19
(0.2)

-1.05
(-1.42)-0.39(-0.55)-2

0.91(1.11)

0.88(1.19)

0.7
(0.9)

-0.33
(-0.63)-0.44∗(-2.48)-0.29(-0.33)-0.47(-0.81)

0.13(0.19)

0-2.50∗(-3.12)-2.03∗(-2.78)-2.46∗(-3.45)-0.34(-0.63)-0.33∗(-2.07)-0.4(-0.45)-0.35(-0.61)-0.21(-0.32)5-2.81∗(-3.38)-2.59∗(-3.53)-2.62∗(-3.55)-2.83∗(-5.53)-2.72∗(-3.89)-2.41∗(-2.9)-3.12∗(-5.52)-2.52∗(-3.92)10-3.44∗(-3.79)-3.27∗(-4.02)-4.14∗(-5.22)-4.26∗(-8.02)-3.66∗(-3.8)-4.24∗(-4.59)-4.62∗(-8.21)-3.21∗(-4.85)15-6.14∗(-7.08)-5.68∗(-7.08)-5.59∗(-6.91)-3.97∗(-5.36)-2.88∗(-2.54)-3.03∗(-2.59)-4.2∗(-5.84)-3.62∗(-5.25)Observations

2,346

2,346

2,346

2,346

73,451

2,254

2,346

2,300

Note: This table presents the stay-at-home order event study coefficients estimated from Equation 1.
Columns represent the dependent variable. Observations are at the state-by-day level except column (5)which uses county-by-day observations. Counties begin treatment on the date they issued a stay-at-homeorder or the date the state they reside in issued an order. T-values are presented using robust standard
errors for state estimates and standard errors clustered at the state-level for county estimates. Labor andconsumption variables come from Homebase and Affinity Solutions, respectively.
* denotes estimates significant at the 95% level.

estimated for the consumption data from Affinity Solutions in column (5). Furthermore, we
expect spending and saving patterns to be related to one’s income level. This heterogeneity
may lead to differences in consumption smoothing. We test this hypothesis in columns(6)-(8).17
Columns (4) and (5) of Table 2 are similar in terms of their coefficient estimates. However,we see that the county estimates are statistically significant at the 95% level two days before
100 counties issued a stay-at-home order before their state did. Appendix Figure A.3 plots counties by
their treatment status to gain an understanding of the cross-sectional variation induced by the county orders.
17
Observations may differ across specifications due to missing values. Specifically, high-income expenditure
data is missing for Montana, and low-income data is missing for Alaska and Vermont. Columns (7) and (8)in Appendix Table A.3 re-estimate our baseline results when removing these states from the sample toprovide evidence that these differences across income quartiles are not driven by differences in the sample
composition.

15

and the day the order is enacted.18 This implies that the anticipation effect mentioned
earlier is statistically significant. Middle-income earners in column (7) and our baseline
estimates have similar upward pre-trends as evidenced by days -7 and -2. However, these
upward trends are not as apparent for low (6) and high (8) income consumers. This suggeststhat the anticipation effect is mostly driven by middle-income consumers. This is further
exemplified as all of the significant point estimates are larger in magnitude for middleincome consumers compared to low and high-income estimates. Despite this, we still findstatistically significant estimates for both high and low-income consumers 5-15 days after anorder is enacted. Lastly, comparing columns (6) and (8), we see that low-income consumers
see a trough marginal decline in expenditure of 4.2pp which occurs ten days after the order.
High-income consumers see a smaller trough decline of 3.6pp fifteen days after the order.

3.1

Opportunity Insights Employment Measure

Chetty et al. (2020) mention that the Homebase employment composition skews towards
restaurant and retail workers. In contrast, they show that their employment measure moreaccurately tracks nationally representative statistics such as the Quarterly Census of Employment and Wages (QCEW) and the Occupational Employment Statistics (OES). To explore
the possibility that our results our driven by the Homebase composition, we re-estimate
Equation 1 using the OI employment measure at the county-level. This serves the dual
purpose of accounting for county-level stay-at-home orders.
Figure 4 plots the results using the Opportunity Insights employment measure as thedependent variable. Observations are at the county level. Dashed lines represent 95% confidence intervals using standard errors clustered at the state level. Panel (a) plots the effectof issuing a stay-at-home order on total employment. There is no evidence of differential
trends up to ten days before the issuance of an order. There is a statistically significant 1
percentage point decline in employment five days after the order. Similar to the baseline
18

Standard errors for the county-level estimates are clustered at the state level.

16Figure 4: Opportunity Insights Employment Measure(a) Total Employment(b) Low Income (< $27K)(c) Middle Income ($27K − $60K)(d) High Income (> $60K)

Note: This figure plots the stay-at-home order event study coefficients estimated from Equation 1. Subcaptions represent the dependent variable. Employment data is obtained from Opportunity Insights. Observations are at the county-by-day level. Counties begin treatment on the date they issued a stay-at-home order
or the date the state they reside in issued an order. Dashed lines represent 95% confidence intervals using
standard errors clustered at the state level.

estimates, the effect on employment is amplified over time and remains statistically significant for the remainder of the fifteen day post-period. After fifteen days, the effect peaks at-3.8 percentage points. Overall, the Opportunity Insights data provides similar estimates as
the Homebase data, but the seven-day moving average has created a significant lag in theemployment effects compared with Column two of Table 2. The Day 15 estimate of -3.76pp
from the OI data is more similar to the Day 10 estimate of -3.44pp from the Homebase data.
The Day 10 and Day 5 estimates are respectively (-2.28pp, -2.81pp).
Panels (b)-(d) plot the employment response by worker’s yearly income level. We see

17heterogeneous effects across the income distribution. Low-income workers (< $27K/Year)experience slightly more than a 2 percentage point decline in employment fifteen days after astay-at-home order. This estimate is statistically insignificant, as are all other point estimates
for low-income workers. We see the strongest effect of -5pp in middle-income workers ($27K−$60K) fifteen days after an order. All post-period estimates are statistically significant for
middle-income workers. However, we do find statistically significant estimates of a downward
trend in employment in the ten days leading up to the order. High-income workers (> $60K)
experience a significant 3pp decline in employment fifteen days after the order. High-income
workers also have a slight downward trend in employment leading up to the issuance of anorder, but these estimates are statistically insignificant.19,20

3.2

Heterogeneity across Sectors and the Anticipation Effect

Our baseline expenditure estimates showed some evidence of an anticipation effect by consumers. This is likely the result of stockpiling goods in the days preceding a stay-at-homeorder. Many consumers shifted their spending from food services, such as restaurants, togrocery and food stores during the pandemic (Cavallo, 2020). These markets and their goods
vary significantly in their ability to be stockpiled. An expenditure anticipation effect would
be expected for groceries, but not restaurant meals, for example. We now turn to an exploration of the heterogeneous effects in expenditures and the anticipation effect across several
consumption categories.
Figure 5 plots the results of Equation 1 for (a) Grocery and Food Stores, (b) Appareland General Merchandise Stores, (c) Accommodation and Food Services, and (d) Arts &19

Workers may shift in the income distribution over time due to wage cuts. As an example, low-income
workers may see an increase in employment after a stay-at-home order if middle-income workers on thethreshold see a decrease in wages. Chetty et al. (2020) provide evidence that wages for individuals who
remained employed during this period of the pandemic were largely unchanged. This suggests, given thesignificance levels in each panel and the large differences in magnitude across panels, that it is unlikely thatshifts in the wage distribution will affect the overall qualitative story presented in Panels (b)-(d). Although,these shifts may affect the quantitative interpretation.
20
Appendix Table A.4 compares the county-level results in Figure 4 with the event study results at the statelevel. Additional heterogeneity checks at the state level for employment by NAICS sector are in Appendix
Figure A.5.

18

Figure 5: Heterogeneity across Consumption Expenditures(a) Grocery and Food Stores(b) Apparel and General Merchandise(c) Accommodation and Food Services(d) Arts & Recreation

Note: This figure plots the stay-at-home order event study coefficients estimated from Equation 1. Subcaptions represent the dependent variable. Expenditure data come from Affinity Solutions. Merchant groups
are defined by Affinity Solutions. Observations are at the state-by-day level. Dashed lines represent 95%
confidence intervals using robust standard errors.

Recreation as the dependent variable. Observations are at the state level. Dashed lines
represent confidence intervals at the 95% confidence level using robust standard errors. All
panels suggest similar dynamics in the post-treatment period. There is an initial decline
in expenditure which experiences a statistically significant trough decline 6-8 days after astay-at-home order is issued. After 6-8 days, expenditures begin to recover. However, theseeffects differ significantly in their magnitudes across sectors. Grocery and food stores exhibit
the largest decrease in expenditures of 10 percentage points. In contrast, accommodationand food services only experience a 2pp decline. Trough declines are about 3pp for both
apparel & general merchandise stores and arts & recreation expenditures.
19Pre-trends also vary significantly across specifications. The anticipation effect seen in ourbaseline expenditure results appears to be driven primarily by grocery stores and generalmerchandise stores. Panel (a) of Figure 5 shows that grocery and food stores experienced
a statistically significant upward trend of 4pp in the days preceding a stay-at-home order.
Apparel and general merchandise stores also see an upward trend that starts at -3pp ninedays before the issuance of an order. These upward trends are completely absent in the tendays preceding an order for accommodation and food services as well as arts & recreation
expenditures. Panels (c) and (d) provide further evidence that our baseline estimates are
not significantly driven by consumer anticipation effects, and that stay-at-home orders hadlarge impacts on the economy.21

3.3

Identifying Variation induced by Treatment Timing

Recent work has emphasized the impact that treatment timing can have on difference-indifference and event study estimates (Goodman-Bacon, 2018; Callaway and Sant’Anna, 2020;
Abraham and Sun, 2020). Goodman-Bacon (2018) shows that the baseline DD estimates(red lines in Figure 3) can be expressed as the weighted average of the 2x2 DD estimatesfor each cohort of treatment timing.22,23 There are 19 cohorts in our framework (C0 ={ControlStates}, C1 = {CA}, C2 = {IL, N J}, ..., C18 = {SC}).
Each treated cohort has a DD estimate with the control group for a total of 18 estimates.24
Figure 6 plots these estimates for hours worked. Cohorts are divided into two groups, thosethat received treatment before March 29th (Early, blue circles) and those that received
21

Appendix Figure A.6 contains additional heterogeneity checks for Transportation & Warehousing and
Health Care Services.
22
2x2 stands for two-period/two-group. Intuitively, the two periods are pre/post treatment. Groups aredefined their treatment-timing. DD coefficients are then estimated for each two-group combination, hence
2x2.
23
Weights rely on three main factors: (1) when units are treated, (2) the size of the treatment cohort, and(3) the length of the sample. Please see Goodman-Bacon (2018) for a full discussion on the estimation ofthese weights.
24
The Goodman-Bacon (2018) decomposition also contains DD estimates across treated cohorts. In ourcase, this results in a total of 18 (treated/control) + 153 (treated/treated) = 171 observations. Appendix
Figure A.4 provides the full decomposition for both hours worked and consumption expenditures.

20

Figure 6: Effect of Treatment Timing on Hours Worked DD Estimate

Note: This figure plots the results of a Goodman-Bacon (2018) decomposition on our difference-in-difference
estimate. The dependent variable is hours worked. The y-axis is the treatment-timing cohort DD estimate.
The x-axis is the weight for the respective estimates. Cohorts are further divided into two groups: Treatment
occured before March 29th (Early, blue circles), Treatment occured on or after March 29th (Late, red
triangles). Hours worked data is obtained from Homebase. Observations are at the state-by-day level.

treatment on or after March 29th (Late, red triangles).25 Each treatment-cohort/control
DD estimate is negative, so hours worked decreased after treatment for all cohorts relative
to the control group. However, there is a significant difference in the DD estimates acrossthe early/late treatment groups. Early treated groups, on average, experience about twice
the relative decline in hours worked (14.8pp) compared to late treated groups (7.5pp).

3.3.1

Refined Event Study Specification

Figure 6 suggests that there may be heterogeneity in the estimated treatment effects acrosstreatment cohorts. We refine the event study specification in Equation 1 to test this hypoth25

Stay-at-home orders occurred over four weeks (recall Table 1). March 29th is used as the determinant
for late treatment as it groups the first two weeks (Early) and last two weeks (Late).

21

esis:
yit = αi + γt + ΓXit +

G
X

k6=−1

X

βkg I(i ∈ g)I(StayHomeit = k) + it(2)

g=1 −10≤k≤15

where g specifies the group that state i belongs to. Notice that, compared to Equation 1, βk
is now allowed to vary across groups, βkg . We again consider the two groups of Early (Before
March 29th) and Late (On or After March 29th) treatment. Thus, formally, our specification
is
k6=−1

yit = αi + γt + ΓXit +X

βkEarly I(i ∈ Early)I(StayHomeit = k)

−10≤k≤15
k6=−1

+

X

βkLate I(i ∈ Late)I(StayHomeit = k) + it−10≤k≤15

This specification is similar but not equivalent to the specification in Abraham and Sun(2020) as we relax their assumption that groups must belong to the same treatment-timing
cohort.26

3.3.2

Results

Figure 7 plots the results of Equation 2 with the early treatment estimates in blue and latetreatment in red. Similar to Figure 6, Panel (a) suggests that early treated states experience
about twice the relative decline in hours worked than later treated states. Early treatedstates experience about a 4pp decline in hours worked for the entire post-period while latetreated states experience a 2pp decline. Panel (b) estimates similar expenditure declines
after the issuance of a stay-at-home order in early and late treated states, but significantly
different pre-trends. The consumer anticipation effect appears to be driven primarily by
early treated states which see a 3pp increase in expenditures before an order is enacted.
26

This specification is also similar to stratifying the event study by early and late treatment groups.

22

Figure 7: Effect of Treatment Timing on Event Study Estimates(a) Hours Worked(b) Expenditure

Note: This figure plots the stay-at-home order event study coefficients estimated from Equation 2. Subcaptions represent the dependent variable. Treated states are divided into two groups: Treatment occured
before March 29th (Early, blue), Treatment occured on or after March 29th (Late, red). Observations areat the state-by-day level. Hours and expenditure data are obtained from Homebase and Affinity Solutions,
respectively.

3.4

Non-essential Business Closures

Section 2.3 mentioned that the specification in Equation 1 also includes an event-study
covariate for non-essential business closures. The cumulative effect of implemented policies
may be of interest in addition to the individual effect of stay-at-home orders. Figure 8 plots
our baseline estimates for hours worked and total expenditure side-by-side with non-essential
business closures in blue and stay-at-home orders in red. Dashed lines represent confidence
intervals at the 95% confidence level using robust standard errors. Standard errors areomitted for stay-at-home orders since they are shown in Figure 3. Panel (a) shows that
non-essential business closures did not have a statistically significant effect on hours worked.
This may be the result of a break in pre-trends before their issuance.
Panel (b) shows that non-essential closures did have a statistically significant effect on
expenditures 4-10 days after their implementation with a trough on Day 6. The significant
point estimates have a range from a 1-2 percentage point decline in expenditures. We findno evidence of a break in pre-trends up to ten days before the order. The pre-trends also23

Figure 8: Effect of Non-essential Business Closures on the Economy(a) Hours Worked(b) Expenditure

Note: This figure plots the non-essential business closure event study coefficients (blue) and stay-at-homeorder event study coefficients (red) estimated from Equation 1. Subcaptions represent the dependent variable.
Dashed lines represent 95% confidence intervals using robust standard errors. Observations are at the stateby-day level. Hours and expenditure data are obtained from Homebase and Affinity Solutions, respectively.

show that the consumer anticipation effect seen for stay-at-home orders is not evident for
non-essential business closures. This may be due to differences in the supply and demand
implications between the two policies as non-essential business closures directly targeted the
supply side (firms) of the market while stay-at-home orders directly targeted both supply(firms) and demand (consumers). An analog of Table 2 with robustness/heterogeneity checks
for non-essential business closures can be found in the appendix. The results are similar
to Figure 8 in that we find null effects of non-essential business closures as in Panel (a)or mitigated effects with limited statistical significance compared to stay-at-home orders
as in Panel (b). Overall, the inclusion of non-essential business closures suggest that the
cumulative effect of mitigation policy in response to Covid-19 is at least as great as ourestimates from stay-at-home orders.

3.5Interpretation of Event Study Results

The event study estimates represent the average effect of issuing a stay-at-home order onhours worked and consumer expenditure for treated states. The previous sections presented

24

these results as percentage point effects (e.g. 4pp decrease in hours worked). These percentage point effects can be used to estimate the absolute and cumulative effects of stay-at-homeorders for treated states. Recall that all variables are measured relative to January 4-31. The
average amount of consumer spending per day from Jan. 4-31 was $21.82 billion (Chetty etal., 2020). To estimate the absolute effect of a stay-at-home order, we multiply the event
study estimates by $21.82 billion. The baseline estimate for consumer spending fifteen days
after a stay-at-home order was -3.97%. The absolute effect is then -3.97%*$21.82 = $0.87
billion. The cumulative effect after fifteen days can be found by summing the absolute effectfor all of the post-treatment days (0-15). For consumer expenditures, this equates to $10.5
billion. However, this estimate assumes that the entire US was treated. We then multiply$10.5 billion by the percentage of the population that was placed under a stay-at-home orderto account for this.27 The final estimate of the cumulative effect of stay-at-home orders on
consumer spending is then 95%*$10.5 billion = $9.94 billion.
Panel A of Table 3 plots the cumulative spending loss for treated states calculated above
in Column (1). The bracketed terms are calculated by summing the upper 95% confidenceband and the lower band from our baseline expenditure estimates (Figure 3) over the entire
post-period. This results in a range from $6.28 billion to $13.61 billion. A similar analysis isconducted for earnings per worker and total earnings for states that issued a stay-at-homeorder.28 This suggests a cumulative loss of $80 per worker shown in Column (2). We aggregate this effect over treated states by multiplying the January BLS non-farm employment
numbers (152 million) by the percent of the treated population in the US. This suggests
about a $15.5 billion loss in earnings in the first fifteen days after a stay-at-home order.
Bartik et al. (2020) show that stay-at-home orders had significant effects for almost 30 days
27
This uses the simplifying assumption that consumer spending per capita is equal across states as we do
not have access to the actual percentage of consumer spending by treated states.
28
We first calculate the average earnings per worker per day in January. To do this, we obtain averagehourly earnings ($28.43) and average weekly hours (34.3) from the BLS for all employees on private payrollsin January. Average daily earnings can then be calculated as the hourly earnings multiplied by average
daily hours, $28.43*(34.3/7) = $139.31. The cumulative effect for earnings per worker is then calculated bysumming our baseline event study estimates for hours worked multiplied by the daily wage.

25

Table 3: Cumulative and Relative Effects of Stay-at-Home Orders
Panel A: Spending and Hours Worked
Total Spending(1)

Earnings Per Worker(2)

Total Earnings(3)$21.92 billion/day$139.31/day$26.23 billion/day$9.94 billion[6.28, 13.61]$82.40[44.19, 120.61]$15.51 billion[8.32, 22.71]

Stay-at-Home Orders(1)

BLS Employment(2)

CPS Supplement(3)

Employment Loss

5,797,349

21,909,000

49,839,000

Relative Effect

100%

26.5%

11.6%

January Benchmark
Cumulative Effect (Days 0-15)

Panel B: Employment

Note: This table presents the cumulative effect of stay-at-home orders on consumer spending and hours
worked in Panel A. The cumulative effects are obtained by summing the stay-at-home order event-study
coefficients of Equation 1 and multiplying this sum by the reported January benchmarks. We then multiply
this result by the percent of the population that experienced a stay-at-home order during our sample period.
Numbers in brackets present the confidence interval for the calculated cumulative effect by summing the 95%
lower and upper confidence bands for the event-study coefficients. The January benchmark for consumer
spending is obtained from Chetty et al. (2020). To obtain January benchmarks for earnings per worked
and total earnings, we use BLS data on average private hourly earnings (CES0500000003), average private
weekly hours (CES0500000002), and total nonfarm employment (CES0000000001). Column (1) of Panel
B uses the difference-in-difference estimate for employment to compute the employment loss from stay-athome orders. The BLS employment loss is computed by subtracting the BLS estimate of total nonfarm
employment in April 2020 by the estimate in January 2020. The employment loss in Column (3) is obtained
from the supplemental Covid-19 questions used in the May 2020 CPS. The relative effect is then calculatedby dividing the employment loss from stay-at-home orders by the total employment loss in the respective
columns.

after their issuance. Given this, our results likely serve as a lower bound for the cumulative
effect of stay-at-home orders.
Panel B of Table 3 plots the relative employment loss from stay-at-home orders. Unlike
consumer spending and hours worked, the effect of stay-at-home orders on employment
should not be measured cumulatively. For example, an individual who becomes unemployed
one day after a stay-at-home order is likely to be unemployed two days after the orderas well. The cumulative effect would then count this individual more than once in the
total employment loss. To circumvent this issue, we express the average effect of stay-at-26home orders on employment relative to the total employment loss during our sample. The
average effect of stay-at-home orders can be found by multiplying the difference-in-difference
estimate for employment (-4%) by total employment in January (152 million).29 As before,
this estimate is scaled by the percent of the population under a stay-at-home order during
this period which results in -4%*95%*152 million = -5.8 million. We normalize this 5.8
million employment loss relative to the total employment loss to isolate the relative impact
of stay-at-home orders. The BLS employment estimate for April (130 million) suggests that22 million jobs were lost in total. The relative effect is then computed by dividing the= 26%.
employment loss from stay-at-home orders by the total employment loss, 5.8M
22M
In May, the BLS added several questions to the the Current Population Survey (CPS)
to help gauge the effects of the coronavirus on the labor market (BLS, 2020). One of thequestions was “At any time in the last 4 weeks, were you unable to work because youremployer closed or lost business due to the coronavirus pandemic?”30 The survey resultsfrom this supplemental question suggest 50 million people were unable to work. Column(3) of Panel B uses this estimate as the total employment loss which results in a 11.6%
contribution of stay-at-home orders to the total employment loss.

4

Model Framework: Optimal mitigation policy with multiple locations

The empirical results of the previous section showed that stay-at-home orders had a significant effect on the economy. Beyond general concerns about the economic impact of theorders, policy makers often argued about how to best implement them. On April 1st, inregards to issuing a nationwide stay-at-home order, President Trump responded “There aresome states that are different. There are some states that don’t have much of a problem .
. . You have to give a little bit of flexibility.” (Press Briefing, 2020) Dr. Anthony Fauci
expressed a different opinion the next day saying, “I just don’t understand why we’re not do29

See Appendix Table A.2 for difference-in-difference estimates. As before, non-farm employment in January is obtained from the BLS.
30
The CPS is conducted during the week of the 19th. Thus, the four weeks before May 19th slightly
abstracts from the sample period of our analysis.

27ing that [issuing a federally-mandated stay-at-home order]. We really should be.” (Politico,
2020)
This section builds on our empirical results by developing an economic framework toanalyze virus transmission and optimal mitigation policy in a fiscal union such as the UnitedStates. The model will allow us to address virus transmission across locations. Thus, theeconomic activity of one location depends upon the spread of the virus in other locations.

4.1

Initial Conditions

We model the United States as a multi-location, closed economy version of the SIR macromodel in Eichenbaum et al. (2020). We interpret these locations as states which we denoteby i ∈ [1, N ], where N is the total number of states. The initial population in a state
as a fraction of the national population is written as P opi,0 ∈ (0, 1].31 A fraction of thestate population becomes infected at t = 0, Ti,0 = i . All agents are initially susceptible,
Si,0 = 1 − Ti,0 . Thus, active infections in state i at date 0 is Ii,0 = Ti,0 . This allows states tovary in both initial population and initial infections.

4.2

Virus Transmission

As in Eichenbaum et al. (2020), we assume the virus is transmitted within a state throughconsumption and employment. We further allow the virus to transfer within and acrossstates through an exogenous variable. For a given Home state, which we denote by H, thistransmission mechanism at time t is given by:

S
I
SI
TH,t = πs1 (SH,t CH,t)(IH,t CH,t)+πs2 (SH,t NH,t)(IH,t NH,t)+πs3 SH,tN
X

d(1−τH,i)(Ii,t P opi,0 ) (3)

i=1

S
I
where CH,tis consumption at time t by susceptible agents in the Home state, and CH,tisS
I
consumption by infected agents. Similarly, NH,tand NH,t
are hours worked by susceptible
31

The initial population of a state equals one if and only if N = 1.

28

dand infected agents in the Home state, respectively. Note that τH,irepresents the travel costdbetween locations H and i. This yields an interpretation of 1 − τH,ias the percentage ofsusceptible agents in state H that interact with infected agents in state i. The parameters
πs1 , πs2 , and πs3 are the probability of transmitting the virus through each of the threeassociated mechanisms.
The first two terms of our transmission mechanism, apart from the location indices, areidentical to those in Eichenbaum et al. (2020). The substantive difference between the twomodels is the presence of the third term. This is evident by the fact that our model replicatesdEichenbaum et al. (2020) if we assume that the travel cost between states, τH,i, equals zeroand infection rates are symmetric, or in the trivial case of modelling one location. The thirdand novel mechanism is similar in spirit to the empirical model of Adda (2016), but we loosen
the restriction that the travel cost is equal between all pairs of states. Our only assumptionsdd∈ [0, 1] to= 0, and (2) τH,i
are that (1) travel cost within a state is equal to zero, τH,H

prohibit negative transmission across locations.
The spread of the virus in each state can then be modeled by iterating

St+1 = St − Tt

(4)

It+1 = (1 − πr − πd )It + Tt

(5)

Rt+1 = Rt + πr It(6)

Dt+1 = Dt + πd It(7)where the state index i is suppressed for notational simplicity. Tt follows the transmission
mechanism in Equation 3 in each state. Rt and Dt represent the total fraction of recoveredand deceased. The parameters πr and πd represent the probability an infected person recovers
or dies.

29

4.3

The Economy

We assume that states are closed economies with the exception of virus transmission.32
This allows us to isolate the economic spillovers of virus transmission across locations while
replicating the Eichenbaum et al. (2020) results as a special case. This allows us to focus
specifically on the economic effects of the cross-state virus transmission mechanism, andsimplifies the solution to the state-level decision problems. In the text that follows, thelocation index i is suppressed except where needed for clarity of exposition. Individual state
economies can be written as follows:

Households We assume agents’ discounted lifetime utility depends on their infection statusj ∈ (s, i, r). As infection status follows the transition matrix presented in Equations 3-7,
lifetime utility of the various agents can be written asr
Utr = u(crt , nrt ) + βUt+1hiir
Uti = u(cit , nit ) + β (1 − πr − πd )Ut+1+ πr Ut+1+ πd × 0hisi
Uts = u(cst , nst ) + β (1 − πI,t )Ut+1+ πI,t Ut+1

(8)
(9)
(10)

where ct is consumption, nt is hours worked, and πI,t represents the probability a susceptible
agent becomes infected. In the model, this is found by dividing Equation 3 by St whichyieldsπI,t = πs1 (CtS )(It CtI ) + πs2 (NtS )(It NtI ) + πs3NXd(1 − τH,i)(Ii,t P opi,0 )

(11)

i=1

The remainder of the economic environment follows Eichenbaum et al. (2020). Prefer32

The closed economy assumption abstracts from endogenous trade fluctuations and international policy
such as travel restrictions in response to the virus. Antràs et al. (2020) and Fajgelbaum et al. (2020)
develop open-economy models to analyze these avenues. Importantly, these papers provide support that thequalitative results in Section 5 are likely to hold if we relax the closed economy assumption.

30

ences of agents in each state take the functional form,θu(cjt , njt ) = ln cjt − (njt )22(12)Consumers maximize utility over an infinite horizon subject to the budget constraint(1 + µct )cjt = wt φj njt + Γt

(13)where wt is the real wage, φ is labor productivity, and Γt are lump-sum transfers from thegovernment financed by the tax on consumption, µct . Intuitively, the consumption tax can beviewed as a proxy for mitigation policies such as stay-at-home orders as it creates a tradeoff
between mitigating the spread of the virus and negatively impacting the economy.33

Firms In each state, a continuum of representative firms maximize profits

Π t = Y t − w t Nt

(14)

where Nt is hours worked and Yt = ANt is output.
Government Each state government is subject to a balanced-budget requirement:µct St cst + It cit + Rt crt = Γt (St + It + Rt )(15)

for all t.34
33

The interpretation of the consumption tax as a proxy for mitigation is discussed more in Section 5.3.
Requiring the government budget constraint to hold at the state level implies that fiscal transfers acrossstates are equal to zero. Loosening this restriction to hold at the national level—net fiscal transfers are
zero—would create the opportunity to study optimal transfers across locations. This is a possible avenue for
future research to study the effect of large fiscal programs such as the Paycheck Protection Program or theCares Act, but it is not as relevant for our analysis of mitigation policies such as stay-at-home orders.
34

31

Table 4: Baseline Model Parameters

Parameter
(1)

Value
(2)

Panel A: New Parameters
State Population (Baseline)
Initial State Infection Rate (Baseline)
Travel Cost (Baseline)

P opi0
i0
d
τH,i

1
N

0.001

Panel B: Eichenbaum et al. (2020)
Initial Country Population
Initial Country Infected
Productivity
Labor Productivity (Susceptible)
Labor Productivity (Infected)
Labor Productivity (Recovered)
Disutility of labor
Discount Rate
Probability of consumption infection
Probability of labor infection
Probability of exogenous infection
Probability of recovery
Probability of death
Consumption Tax

P opAgg
0
Agg
A
φs
φi
φr
θ
β
πs1
πs2
πs3
πr
πd
µct

1
0.001
10
1
0.8
1
9
0.981/52
0.0185
1.84960.2055
7× 0.9918
7× 0.01
18
0

|H−i|
N

Note: This table presents the parameters used in our baseline model specification in Section 5. Panel A
presents variables specific to our multiple-location model. Panel B presents the baseline parameters used in
Eichenbaum et al. (2020) which remain in our model.

5Model Implications: Multiple locations and optimal policy

We illustrate the dynamics of our model through several numerical examples. First, we
compare the SIR macro model with one location to our multiple location model. We use thebaseline parameters in Eichenbaum et al. (2020) for this exercise (see Table 4). Eichenbaum
et al. (2020) study how various parameterizations affect the dynamics of the single-location
model, so we do not replicate that sensitivity analysis here. Various changes to their parameters are unlikely to significantly affect the main contribution of our model which isthe cross-sectional distribution we obtain. However, our model does contain several new32

parameters: (1) state population, (2) initial state infection rates, and (3) travel cost acrosslocations. The second subsection develops a procedure to parameterize travel costs acrosslocations which we apply to US Census region data. This application allows us to performa sensitivity analysis to study the effect that travel cost across locations has on the crosssectional distribution of infection rates.35 In turn, we study how the cross-section affects theaggregate dynamics of the model. Lastly, we study optimal mitigation policy when there are
multiple locations with asymmetric infection rates.

5.1

Multiple-location model vs single-location model

Figure 9 plots results from our simulated model with one location (blue) and twenty-one
locations (red). The grey lines represent the individual states. The red line is the national
total computed as the population-weighted average of the grey lines. All states in the country
are symmetric in terms of their initial populations and initial infected. Thus, these resultsdwhere N is the total number ofare entirely driven by our travel cost which is τH,i
= |H−i|N

locations in the country.36 As mentioned earlier, setting travel cost to 0 when initial infection
rates are symmetric would result in all states following the blue line.
Panel (a) of Figure 9 plots the simulated fraction of susceptibles. With one location, we
see that about 45% of the country’s population becomes infected by the end of the sample.
The multiple-location results suggest that a little less than 30% of the population contracts
the virus. Furthermore, the spread of the virus is not symmetric across locations even though
the initial conditions are. This creates a cross-section in which 25% of the state population
contracts the virus in the least affected state while over 30% contract it in the most severely
impacted state.
Panel (b) of Figure 9 plots the simulated infection rates for both models. We see that the35

The appendix contains a full sensitivity analysis of state population, state infection rates, and travel
cost across locations.
36
This travel cost is selected as it meets the assumptions that (1) travel cost within a state is equal to0, and (2) τH,i ∈ [0, 1] for all state pairs. The dynamics of the cross-section will depend on the travel costselected. Figures 10 and A.8 provide a more in-depth analysis of the effect of different travel costs on the
cross-sectional distribution.

33

Figure 9: Multiple-location Model vs Single-location Model(a) Susceptibles(b) Infections(c) Consumption(d) Hours Worked

Note: This figure plots the results of simulations using the baseline SIR macro model with one location(blue) and our extended multiple-location version (red). Grey lines are produced from the multiple-location
model and represent individual states. The red line is the national total from the multiple-location model,
or equivalently the population-weighted average of the grey lines. Twenty-one locations were simulated.

baseline SIR macro model suggests a peak infection rate of 3.5% at about 30 weeks. With
multiple locations, the country-wide peak occurs almost 20 weeks later and is much lower
at about 1.5%. There are two interesting results seen in the cross-section of peak infection
rates. Not only do peak infection rates differ across states, but they also differ in their timing.
The intuition for this can be seen in Panels (c) and (d) which plot the percent deviation of
consumption and hours worked from their steady state values. As states experience more
infections, susceptible agents endogenously choose to decrease their consumption and hours
to lower their probability of being infected. In turn, this contributes to earlier turning points
34

in the infection rate.

5.2

Application to US Census Region Data

The previous subsection showed the capability that our model has to generate a crosssectional distribution of economic variables and infection rates. We demonstrated the imd
portant role played by the travel cost across locations, τH,i
. Although our chosen travel costfunction is convenient to illustrate the differences between the single and multiple-location
models, it is impractical for applied settings. In this section, we develop a procedure to
parameterize trade costs across locations. We then apply the procedure to US Census region
data to illustrate the advantages of this approach.

5.2.1

Calibration Procedure

Panel A of Figure 10 plots the spread of the virus in the US by Census Region (Midwest,
Northeast, South, West) and the national total (dashed line) from May 6th through August
26th. National and Census region data are obtained by aggregating the county-level infection
and population data from Section 2. The daily data are transformed to a weekly frequency
in accordance with the model. The following steps are followed to generate simulations fromthe model:
1. Set Number of Locations (N )2. Set Initial Population of Locations (P op0 )3. Set Susceptible Percent of Population (St )4. Set New Infections (Tt )5. Set Active Infections (It )d
6. Set Parameters (τH,i, πs1 , πs2 , πs3 )37

In this application, the number of locations is set equal to the number of Census regions,N = 4. The corresponding vector of populations by region is P op0 = (20.9%, 17.2%, 38.1%, 23.8%)
37

Appendix A.2.2 provides details on why these parameters are chosen to fit the data.

35

for the Midwest, Northeast, South, and West respectively. The percent of susceptibles at eachdate is 1 less the cumulative fraction of the population that has been infected up to that date,tP
St = 1 −Tk . On May 6th, the susceptible vector is St = (99.7%, 98.9%, 99.8%, 99.8%).
k=0

The number of new infections per capita for the week ending on May 6th were Tt =(0.07%, 0.11%, 0.04%, 0.03%). We approximate current active infections as It = Tt +(1−πr −πd )Tt−1 . This approximation produces It = (0.11%, 0.22%, 0.06%, 0.05%). We then jointly
set the travel cost across locations as well as the other parameters to minimize the sum ofsquared errors between susceptible population percentages in the model and the data,38

min

d ,π ,π ,πτH,is1 s2 s3

Aug26
4
X
X

Data
M odel 2(Si,t− Si,t)(16)i=1 t=M ay6dd
As in Section 4, we impose the restrictions on travel cost: τH,i
∈ [0, 1] and τH,i
= 0 forH = i. We also impose the restrictions that the virus transmission parameters are positive
πs1 , πs2 , πs3 ≥ 0. This process yields estimates of (πs1 = 0.0009, πs2 = 1.53, πs3 = 0.732).
5.2.2Interpretation of Transmission Matrix

Table 5 provides a summary of the initial conditions and the calibrated parameters fromthis procedure. Among the more interesting estimation results are those pertaining to theddas the transmission matrix as it relates to. We refer to the set of 1 − τH,i
travel costs, τH,i

the interaction between susceptible agents in region H with infected individuals in regiondi. Specifically, 1 − τH,irepresents the probability that a susceptible individual in region H

interacts with an infected individual from region i.39 Rows represent the virus destinationd(H), and columns the virus origin (i). Thus, the first row represents the vector 1 − τM
idwest,i .

As we imposed the restriction that susceptible and infected agents fully interact withindregions, we see that 1 − τM
idwest,M idwest = 1. The second column produces an estimate of38

The appendix provides a more detailed procedure to match both the time series of susceptibles andconsumer spending in the Census region data.
39d
In a reduced-form manner, our calibration procedure for 1−τH,icaptures the average real-life interactions
across regions over the sample period (e.g. travel to and from college, vacations, visits to care for dependents).

36

Table 5: Initial Conditions for Census Region Application (May 6)

Panel A: Initial Conditions
Percentage of US Population (P op0 )Susceptible (St )New Infections (Tt )Active Infections (It )Midwest

Northeast

South

West

20.9%
99.7%
0.07%
0.11%

17.2%
98.9%
0.11%
0.22%

38.1%
99.8%
0.04%
0.06%

23.8%
99.8%
0.03%
0.05%

Parameter

Value

πs1
πs2
πs3

0.00091.53
0.732

Panel B: Transmission Parameters
Probability of consumption infection
Probability of labor infection
Probability of exogenous infectiond)Panel C: Transmission Matrix (1 − τH,i

Virus Destination (H)MidwestMidwest
Northeast
South
West

1.00
1.1e-40.009
0.220

Virus Origin (i)Northeast
South
0.216
1.00
0.472
0.391

0.030
5.6e-4
1.00
0.264

West
0.326
0.001
0.247
1.00

Note: This table presents the initial conditions and parameters used in the Census region application. PanelA presents the initial conditions for each Census region on May 6th. Panels B and C present the estimatedparameters from solving Equation 16.

d
1 − τM
idwest,N ortheast = 0.216. This suggests that, over the sample period of May 6th throughAugust 26th, susceptible agents in the Midwest interacted with 21% of infected agents fromthe Northeast on average. The third and fourth columns suggest that susceptibles in the
Midwest interacted at lower rates with the South (3%) but higher rates with the West(32.6%).
The transmission matrix suggests that there is substantial and highly asymmetric interaction across regions as most elements are non-zero and unequal. One exception is the row
for the Northeast region, 1 − τNd ortheast,i , in which the cross-region estimates are all close to
zero. This suggests the susceptible agents in the Northeast have not interacted with infected37

agents of other regions. In contrast, the Northeast contributed significantly to the spreadof the virus to other regions. The two largest elements of the matrix are the transmission
to the South from the Northeast (47.2%) and to the West from the Northeast (39.1%). It
is reassuring that the transmission matrix backed out of this SIR economic model accords
with the statement by Yale epidemiologist, Nathan Grubaugh, “We now have enough data
to feel pretty confident that New York was the primary gateway for the rest of the country”(New York Times, 2020).

5.2.3

Results

Panel B of Figure 10 plots the results using the above procedure and then simulating ourmodel for 17 weeks in accordance with the length of the sample period. We see that the model
performs well in replicating the cross-sectional distribution. The susceptible populationin the data for the week starting on August 26 is StData = (98.7%, 98.3%, 97.9%, 98.4%)
for the Midwest, Northeast, South and West. The model produces susceptible estimatesof StM odel = (98.7%, 98.3%, 97.7%, 98.3%). We also see that the model performs well in
replicating the individual time series for each region as well as the crossing patterns acrossregions. In the data, the South first surpasses the Midwest in their cumulative cases per
capita on July 1st and subsequently surpasses the Northeast on August 5th. In the model,
these dates are June 24th and August 12th. Lastly, the West experiences higher cumulative
cases per capita than the Midwest starting on July 15th, and the model predicts a crossingon July 22nd.

Comparative Statics Panels C and D emphasize the importance of modelling the interaction of virus transmission across locations. We again present the two extreme cases of nodtransmission across regions (τH,i= 1 for all H 6= i) and complete pass-through of infectionsdacross locations (τH,i= 0). The remaining parameters are the same as in Panel B. Thus,ddifferences across panels are due entirely to differences in the transmission matrix, 1 − τH,i.

38

Figure 10: US Census Region Data vs Model (Susceptibles)

Note: This figure plots the susceptible percentage of the population in the United States and each Census
region. Panel A plots the observed time series in the data. Panel B plots the model fit after jointly optimizingdthe travel distance across locations and the transmission parameters (τH,i, πs1 , πs2 , πs3 ). Panels C and D
present comparative static exercises using πs1 , πs2 , and πs3 from Panel B. Panel C allows no virus transmission
across Census regions. Panel D allows complete pass-through of the virus across regions. Infection data is
obtained from USA Facts.

Panel C plots the results for no transmission across regions. This underestimates the infection rates of all regions compared to the data. The percentage of susceptible individuals
predicted by the model on August 26 are now StM odel = (99.3%, 98.3%, 99.1%, 99.6%). The
model now predicts only one cumulative infection rate crossing. Cumulative infections in theSouth exceeds the Midwest on July 22nd, several weeks past the equivalent data moment.
Panel D plots the results when there is complete pass-through of infections across locations. This provides the opposite result and significantly overestimates the spread of thevirus. The model now predicts that all regions have converged with ∼57% of their population contracting the virus by August 26th. Table 6 summarizes the results of our Census
39

Table 6: US Census Region Data vs Model Prediction (August 26)
Panel A: Cumulative Infections
Data
Calibrated ModelNo Transmission
Complete Pass-throughAggregate

Midwest

Northeast

South

West

1.8%
1.8%
0.9%
56.5%

1.3%
1.3%
0.7%
56.4%

1.7%
1.7%
1.7%
56.8%

2.1%
2.3%
0.9%
56.4%

1.6%
1.7%
0.4%
56.4%

Panel B: Crossing Patterns
South > Midwest

South > Northeast

West > Midwest

July 1
June 24
July 22NA

August 5
August 12
NA
NA

July 15
July 22NANA

Data
Calibrated ModelNo Transmission
Complete Pass-throughNote: This table presents the results of our Census region application. Panel A plots the cumulative infections
on August 26th. Panel B plots the dates in which a given Census region passed another region in cumulative
infections. Both panels present the results seen in the data and three model simulations: (1) the calibrated
model using the parameters in Table 5, (2) allowing no virus transmission across locations, and (3) allowing
complete pass-through of the virus across locations.

region application for ease of comparability across model specifications. Overall, the model
simulations suggest that the virus was transmitted partially, but not fully, across locationsin the US.

5.3

Optimal Mitigation Policy

The previous subsection showed that there is substantial interaction across regions in the
US. Importantly, the Census region application also suggests that there is not complete passthrough of the virus across locations. This section builds on this finding by analyzing optimal
mitigation policy when initial infection rates are asymmetric and the virus is partially, but
not fully, transmitted across locations.

5.3.1

Planner’s Problem

The equilibrium conditions in the appendix show that infected agents do not internalize thenegative externalities they impose on other agents in the economy. This creates the role40

for government intervention to help mitigate virus transmission through the consumption
tax of the model, µct . This tax can be viewed as a proxy for containment measures as thegovernment can reduce the consumption and hours worked of infected agents by increasingµct .40 However, like stay-at-home orders, the consumption tax does not specifically target
infected agents. This creates a tradeoff between decreasing transmitted infections, Tt , andnegatively affecting the economy.
To formalize this in a multiple-location model, assume that a social planner sets µct tomaximize the population-weighted average of the discounted lifetime utility of all agents:

max U0 =
µct

N
X



P opi0 Si0 Ui0S + Ii0 Ui0I + Ri0 Ui0R

(17)

i=1

where lifetime utility of an agent of type j ∈ (s, i, r) follows Equations 8-10. This problem
best describes a national government which maximizes the above welfare function with theability, but not the requirement, to restrict state governments to follow the same policy
rule.41 This allows us to evaluate the tradeoffs that exist between national mandates assuggested by Dr. Fauci and allowing state-level discretion as implied by President Trump.

5.3.2

Results

Figure 11 plots the results of a two-location simulation using the optimal policy rule derived
from the welfare function in Equation 17. Both states have an initial population of 12 . We
consider one state to be severely infected (blue) with an initial infection of 1%, and thedother to have a mild infection (red) of 0.1%. As before, we set τH,i
= |H−i|. The dashedNlines illustrate the baseline consumption tax rate of zero in all periods. The optimal policyof the severely and mildly infected states differs for almost 20 weeks. During this period, the40
Importantly, the event study results in Section 3 showed that stay-at-home orders did indeed reduce
spending and hours worked which provides empirical support for the use of the consumption tax as a proxyfor mitigation policy.
41
State governments are likely to place different weights on the welfare of their constituents and the welfareof the rest of the country. Our planning problem allows us to abstract from this complication. It is within
this context that our model is that of a fiscal union.

41

Figure 11: Optimal Mitigation Policy

Note: This figure plots the results of a 2-location SIR macro model with (solid lines) and without (dashedlines) policy intervention. Both locations have an initial population of 12 . Initial infections to 1% and 0.1%
for the severe (blue) and mild (red) infected locations, respectively.

severely infected state sets a higher consumption tax to mitigate their infection rate. Aftertwenty weeks, the infection rates of the two states converge which leads to similar mitigation
policies.
These results suggest that it is not optimal to set a nationwide mitigation policy. Appendix Figure A.9 plots an analogous simulation when restricting both states to the same
policy rule to understand this result. A common, national policy leads to similar virus transmission dynamics in both states compared to Figure 11. However, the mildly infected stateexperiences significantly larger declines in consumption at the onset of the pandemic. Simply

42put, a nationwide mandate is too restrictive for the economy of the mildly infected state anddoes not help contribute to the mitigation of the virus relative to local mandates. These
results suggest that policy should be set at a local level contingent on sufficient asymmetries
in infection rates.

6

Conclusion

We show that stay-at-home orders reduced consumption and employment by 4 percentage
points using an event study framework. Our estimates suggest that stay-at-home orders
contributed to the total employment loss by almost 6 million employees. This accounts for
10%-25% of the total employment decline that occurred during our sample period. Cumulatively, stay-at-home orders contributed a loss of about $10 billion in consumer spending and$15 billion in total wages.
We pair our empirical findings with an economic SIR model to evaluate virus transmission
and optimal mitigation policy in a fiscal union. We show that travel costs are important for
both the aggregate and cross-sectional estimation of the virus spread and economic equilibrium. The extended model is shown to fit both the infection transmission and consumption
time series at the Census region level. Lastly, we find that it is optimal for states to set theirown mitigation policies when infection rates are asymmetric. Our model, combined with
our simulation approach, demonstrates the value of data-driven public policy decisions thatfactor in the economic and health consequences of Covid-19 as well as the value of local andstate policy discretion.

43

References
Abraham, Sarah and Liyang Sun, “Estimating Dynamic Treatment Effects in Event
Studies with Heterogeneous Treatment Effects,” Journal of Econometrics, 2020.
Acemoglu, Daron, Victor Chernozhukov, Ivan Werning, and Michael Whinston,“Optimal Targeted Lockdowns in a Multi-Group SIR Model,” NBER Working Paper,
2020.
Adda, Jérôme, “Economic activity and the spread of viral diseases: Evidence from highfrequency data,” Quarterly Journal of Economics, 2016, 131 (2), 891–941.
Allcott, Hunt, Levi Boxell, Jacob C Conway, Billy A Ferguson, Matthew
Gentzkow, and Benny Goldman, “What Explains Temporal and Geographic Variation in the Early US Coronavirus Pandemic?,” NBER Working Paper No. 27965, 2020.
Angulo, Jose, Hwa Lung Yu, Andrea Langousis, Alexander Kolovos, Jinfeng
Wang, Ana Esther Madrid, and George Christakos, “Spatiotemporal Infectious
Disease Modeling: A BME-SIR Approach,” PLoS ONE, 9 2013, 8 (9).
Antràs, Pol, Stephen J Redding, and Esteban Rossi-Hansberg, “Globalization andPandemics,” NBER Working Paper No. 27840, 2020.
Atkeson, Andrew, “What Will be the Economic Impact of Covid-19 in the US? Rough
Estimates of Disease Scenarios,” NBER Working Paper, 2020.
Baek, Chaewon, Peter B Mccrory, Todd Messer, and Preston Mui, “Unemployment
Effects of Stay-at-Home Orders: Evidence from High Frequency Claims Data,” IRLE
Working Paper, 2020.
Baker, Scott R, Robert A Farrokhnia, Steffen Meyer, Michaela Pagel, and Constantine Yannelis Booth, “How Does Household Spending Respond to an Epidemic?
Consumption during the 2020 COVID-19 Pandemic,” The Review of Asset Pricing Studies,
2020.
Bartik, Alexander W, Marianne Bertrand, Feng Lin, Jesse Rothstein, and Matt
Unrath, “Measuring the Labor Market at the Onset of the Covid-19 Crisis,” NBER
Working Paper No. 27613, 2020.
Beland, Louis-Philippe, Abel Brodeur, and Taylor Wright, “COVID-19, Stay-AtHome Orders and Employment: Evidence from CPS Data,” IZA Working Paper, 2020.
Binder, Carola, “Coronavirus Fears and Macroeconomic Expectations,” Review of Economics and Statistics, 2020.
Bisin, Alberto and Andrea Moro, “Learning Epidemiology by Doing: The Empirical
Implications of a Spatial-SIR Model with Behavioral Responses,” NBER Working Paper
No. 27590, 2020.

44

BLS, “Supplemental data measuring the effects of the coronavirus (COVID-19) pandemic on the labor market,” https://www.bls.gov/cps/effects-of-the-coronavirus-covid-19pandemic.htm, 2020.
Callaway, Brantly and Pedro H.C. Sant’Anna, “Difference-in-Differences with Multiple
Time Periods,” Working Paper, 2020.
Cavallo, Alberto, “Inflation with Covid Consumption Baskets,” NBER Working Paper
No. 27352, 2020.
Chetty, Raj, John N Friedman, Nathaniel Hendren, and Michael Stepner, “How
Did COVID-19 and Stabilization Policies Affect Spending and Employment? A New RealTime Economic Tracker Based on Private Sector Data,” NBER Working Paper No. 27431,
2020.
Coibion, Olivier, Yuriy Gorodnichenko, and Michael Weber, “The Cost of theCovid-19 Crisis: Lockdowns, Macroeconomic Expectations, and Consumer Spending,”
NBER Working Paper No. 27141, 2020.
Eichenbaum, Martin S, Sergio Rebelo, and Mathias Trabandt, “The Macroeconomics of Epidemics,” NBER Working Paper No. 26882, 2020.
Fajgelbaum, Pablo, Amit Khandelwal, Wookun Kim, Cristiano Mantovani, andEdouard Schaal, “Optimal Lockdown in a Commuting Network,” NBER Working Paper
No. 27441, 2020.
Fox News, “Coronavirus shutdown: What states have seen protests against stayat-home orders,” https://www.foxnews.com/us/coronavirus-shutdown-what-states-haveprotested-against-stay-at-home-orders, 2020.
Goodman-Bacon, Andrew, “Difference-in-Differences with Variation in Treatment Timing,” NBER Working Paper No. 25018, 2018.
and Jan Marcus, “Using Difference-in-Differences to Identify Causal Effects of COVID19 Policies,” Working Paper, 2020.
Goolsbee, Austan and Chad Syverson, “Fear, Lockdown, and Diversion: Comparing
Drivers of Pandemic Economic Decline 2020,” NBER Working Paper No. 27432, 2020.
Gupta, Sumedha, Laura Montenovo, Thuy D Nguyen, Felipe Lozano Rojas,
Ian M Schmutte, Kosali I Simon, Bruce A Weinberg, and Coady Wing, “Effectsof Social Distancing Policy on Labor Market Outcomes,” NBER Working Paper No. 27280,
2020.
Jones, Callum J, Thomas Philippon, and Venky Venkateswaran, “Optimal Mitigation Policies in a Pandemic: Social Distancing and Working from Home,” NBER Working
Paper, 2020.

45

Kermack, William Ogilvy and Anderson G Mckendrick, “A Contribution to the
Mathematical Theory o f Epidemics,” Proceedings of the Royal Society of London, 1927.
Kong, Edward and Daniel Prinz, “Disentangling policy effects using proxy data: Whichshutdown policies affected unemployment during the COVID-19 pandemic?,” Journal of
Public Economics, 9 2020, 189.
Lin, Zhixian and Christopher Meissner, “Health vs. Wealth? Public Health Policies
and the Economy During Covid-19,” NBER Working Paper No. 27099, 2020.
NBC News, “’Fire Gruesome Newsom!’: Stay-at-home protests in California andacross the country,” https://www.nbcnews.com/politics/politics-news/re-open-now-stayhome-protests-held-across-country-n1198121, 2020.
New York Times, “Travel From New York City Seeded Wave of U.S. Outbreaks,”
https://www.nytimes.com/2020/05/07/us/new-york-city-coronavirus-outbreak.html, 2020.
NJ.com,“‘Open New Jersey now!’
Protesters in Trenton demandGov.
Murphylift
coronavirus
lockdowns
despiterisingdeathtoll,”
https://www.nj.com/coronavirus/2020/04/open-jersey-now-protestors-in-trenton-callon-gov-murphy-to-lift-coronavirus-lockdowns.html, 2020.
Politico, “Fauci endorses national stay-at-home order: ‘I just don’t understand why we’re
not doing that’,” https://www.politico.com/news/2020/04/03/fauci-endorses-nationalstay-at-home-order-162794, 2020.
Press Briefing, “Remarks by President Trump, Vice President Pence, and Members of
the Coronavirus Task Force in Press Briefing,” https://www.whitehouse.gov/briefingsstatements/remarks-president-trump-vice-president-pence-members-coronavirus-taskforce-press-briefing-16/, 2020.
Raifman, Julia, Kristen Nocka, David Jones, Jacob Bor, Sarah Ketchen
Lispon, Jonathan Jay, and Philip Chan, “Non-essential Closure Dates,”
https://tinyurl.com/statepolicysources, 2020.
Rojas, Felipe Lozano, Xuan Jiang, Laura Montenovo, Kosali I Simon, Bruce A
Weinberg, and Coady Wing, “Is the Cure Worse than the Problem Itself? Immediate
Labor Market Effects of COVID-19 Case Rates and School Closures in the US,” NBER
Working Paper, 2020.
USA
Today,“Partisandivideover
economygrows,
but
Americansmoreworriedabout
theirhealth:Exclusivepoll,”
https://www.usatoday.com/story/news/nation/2020/05/29/coronavirus-poll-dividedover-economy-americans-worry-health/5264864002/, 2020.
Zakary, Omar, Mostafa Rachik, and Ilias Elmouki, “On the analysis of a multiregions discrete SIR epidemic model: an optimal control approach,” International Journalof Dynamics and Control, 9 2017, 5 (3), 917–930.
46

A

Appendix

A.1

Data

A.1.1

Summary Statistics
Figure A.1: Heterogeneous Response to Covid-19 by Income and Sector(a) Employment by Income Level(b) Employment by Sector(c) Expenditure by Income Level(d) Expenditure by Sector

Note: This figure plots the aggregate time series of employment and consumption expenditures from March
9th to April 24th. Employment data is obtained from Homebase and Opportunity Insights. Expenditure
data is sourced from Affinity Solutions. Panel (a) plots the employment response by income level. Panel (b)plots the employment response by sector. Panel(c) plots the expenditure response by income level. Panel (d)plots the expenditure response by sector. All variables are measured relative to their respective counterparts
from January 4th-31st.

47

Figure A.2: Timeline of Stay-at-Home Orders(a) New States with Order(b) Percent of Population with Order

Note: This figure plots the number of new states that issued a stay-at-home order from March 18th throughApril 9th in Panel (a). Panel(b) plots the percent of the total US population under a stay-at-home orderfrom March 9th through April 24th. Dates of stay-at-home orders are obtained from the New York Times.

48

Table A.1: Balance across states
March 18 (Pre-treatment)

April 23 (End of Sample)(1)
Treatment
Mean/SD(2)
Control
Mean/SD(3)
Difference(1) - (2)(1)
Treatment
Mean/SD(2)
Control
Mean/SD(3)
Difference(1) - (2)Cases

208.95(506.52)

29.38(18.4)

179.5819,644(42,255)

2,256(1,290)17,388Population (in millions)

7.20(7.74)

2.18(1.31)

5.03

7.20(7.74)

2.18(1.31)

5.03

Cases per 10,000 Residents

2.46(3.25)

1.51(0.76)

0.95

238
(279)

109
(51)

129

Businesses Open

-0.22
(0.08)-0.14(0.06)

-0.08

-0.46
(0.08)-0.29(0.07)-0.17

Employment

-0.34
(0.1)

-0.23
(0.1)

-0.12

-0.55
(0.09)

-0.37
(0.1)

-0.18

Hours Worked

-0.34
(0.1)

-0.23
(0.1)

-0.11

-0.54
(0.1)

-0.35
(0.11)-0.19

Expenditures (Total)-0.03(0.04)

0.00(0.04)

-0.03

-0.20
(0.08)-0.15(0.08)-0.05

Expenditures (Low Income)-0.04(0.09)-0.01(0.08)

-0.03

-0.17
(0.12)-0.12(0.12)-0.04

Expenditures (Middle Income)-0.03(0.04)

0.01(0.04)

-0.03

-0.20
(0.07)-0.14(0.08)-0.06

Expenditures (High Income)-0.04(0.05)-0.03(0.06)

-0.01

-0.26
(0.06)-0.19(0.06)

-0.07

43

8

51

43

8

51

Number of observations

Note: This table presents means and standard deviations for outcomes of interest and other observablecharacteristics at the state level by treatment status for March 18th and April 23rd. Treatment is definedby the issuance of a statewide stay-at-home order. March 18th is the day before the issuance of the firststatewide stay-at-home order. April 23rd is the day before the first lifting of a stay-at-home order. The
third column reports the difference in means between the two groups. Low income expenditure is missing
for Alaska and Vermont. High income expenditure is missing for Montana. This affects the number ofobservations for these variables.

49

Figure A.3: Counties by Treatment Status

Note: This figure plots counties that remain in our final sample by their treatment status. Stay-at-homedata at the county level is obtained from the National Association of Counties. Statewide orders are obtained
from the New York Times. Counties that issued a stay-at-home order before their state are shaded in dark
blue. Counties that did not issue a stay-at-home order but reside in a state that did are shaded in light blue.
Counties that did not experience a county-level or state-level stay-at-home order are shaded in grey-blue.
Counties missing from our combined dataset are not shaded and labelled as NA.

50

A.1.2Difference-in-difference Estimates
Table A.2: Difference-in-difference Estimates
Labor Variables (Per. Pt.)

Expenditure Variables (Per. Pt.)

Hours Worked

Employment

Businesses OpenState Level

Low Income

Middle Income

High Income

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Stay-Home Order−3.954(0.394)−4.009(0.386)−4.719(0.359)−1.869(0.253)−1.964(0.370)−1.959(0.277)−1.913∗∗∗(0.266)

Business Closure−3.103∗∗∗(0.411)−2.983∗∗∗(0.406)−3.690∗∗∗(0.383)−0.216(0.267)−0.771∗(0.411)−0.460(0.283)−0.384(0.271)

2,346

2,346

2,346

2,346

2,254

2,346

2,300

Observations

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

Note: This table presents difference-in-difference estimates for stay-at-home orders and non-essential businessclosures. Coefficients are jointly estimated in the same regression. Column names represent the dependent
variable. Robust standard errors are reported. All observations are at the state-by-day level. Labor market
and expenditure variables come from Homebase and Affinity Solutions, respectively.
∗
p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.0151

Figure A.4: Goodman-Bacon (2018) Decomposition(a) Hours Worked (All 2x2)(b) Expenditure (All 2x2)(c) Hours Worked (Early vs Late)(d) Expenditure (Early vs Late)

Note: This figure plots the results of a Goodman-Bacon (2018) decomposition on our difference-in-difference
estimate for hours worked in Panel A and expenditure in Panel B. The dependent variable is hours worked.
The y-axis is the treatment-timing cohort DD estimate. The x-axis is the weight for the respective estimates.
The top panel plots all 2x2 difference-in-difference coefficients. Estimates are divided into two groups: Both
Treated (blue circles) and Treated vs Untreated (red triangles). In the bottom panel, only the treated vsuntreated DD estimates are plotted. Estimates are further divided into two groups: Treatment occured before
March 29th (Early, blue circles), Treatment occured on or after March 29th (Late, red triangles). Hours
worked and expenditure data is obtained from Homebase and Affinity Solutions, respectively. Observations
are at the state-by-day level.

52A.1.3

Additional Event Study Estimates

Table A.3: Effect of Stay-at-Home Orders on the Economy (Composition Effects)
Hours Worked (Homebase, State, Per. Pt.)
Days

Total Expenditure (Affinity Solutions, State, Per. Pt.)

Drop California Drop New York Pop. Weighted Drop California Drop New York Pop. Weighted Drop Alaska/Vermont Drop Montana
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

-7
(t-value)-1.17(-1.1)-0.82(-0.77)-0.57(-0.64)-0.92(-1.43)-0.92(-1.43)-0.63(-1.09)-0.91(-1.53)-0.9(-1.44)-2

0.89(1.09)

0.9(1.07)

0.91(1.03)-0.34(-0.63)-0.34(-0.63)-0.45(-0.83)-0.26(-0.48)-0.27(-0.52)0-2.61∗(-3.25)-2.29∗(-2.84)-2.06∗(-2.55)-0.37(-0.66)-0.37(-0.66)-0.23(-0.41)-0.3(-0.53)-0.34(-0.63)5-2.88∗(-3.43)-2.84∗(-3.37)-2.59∗(-3.28)-2.98∗(-5.86)-2.98∗(-5.86)-2.25∗(-4.14)-2.78∗(-5.29)-2.8∗(-5.53)10-3.59∗(-3.93)-3.39∗(-3.69)-3.23∗(-3.83)-4.38∗(-7.99)-4.38∗(-7.99)-3.25∗(-5.75)-4.17∗(-7.94)-4.18∗(-7.95)15-6.31∗(-7.25)-6.09∗(-6.97)-5.36∗(-5.79)-4.03∗(-5.28)-4.03∗(-5.28)-2.83∗(-3.65)-4∗(-5.28)-3.87∗(-5.21)

Observations

2,300

2,300

2,346

2,300

2,300

2,346

2,254

2,300

Note: This table presents estimates of equation 1 for several specifications. All estimates are conductedat the state level. T-values are presented using robust standard errors for state estimates. Hours worked
and total expenditure variables come from Homebase and Affinity Solutions, respectively. Specifications(1) and (4) drop California from the sample. Specifications (2) and (5) drop New York from the sample.
Specifications (3) and (6) weight regressions by state population. Specification (7) shows that composition
effects are not driving our results in Column (6) of Table 2. Similarly, specification (8) shows that Column(8) of Table 2 is not driven by composition effects.
* denotes estimates significant at the 95% level.

53

Table A.4: Opportunity Insights Employment Measure (State vs County)
State Employment (Per. Pt.)

County Employment (Per. Pt.)

Days

Total
(1)

Low
(2)

Middle
(3)

High
(4)

Total
(5)

Low
(6)

Middle
(7)

High
(8)

-7
(t-value)

0.71(1.55)

0.23(0.33)

0.92(1.83)

0.68
(1.8)

0.37
(0.94)-0.04(-0.06)0.73∗(2.27)

0.44(1.36)-2

0.15(0.39)

0.09(0.15)

0.19(0.44)

0.12(0.37)

0.1(1.39)

0.04(0.38)

0.15∗(2.69)

0.08(1.59)

0-0.17(-0.46)-0.13(-0.22)-0.21(-0.49)-0.13(-0.44)-0.12(-1.73)-0.06(-0.49)-0.18∗(-3.61)-0.09(-1.95)5-1.02∗(-2.82)-0.74(-1.35)-1.29∗(-3.05)-0.76∗(-2.61)-0.95∗(-2.17)-0.54(-0.75)-1.32∗(-4.52)-0.76∗(-3.09)10-2.01∗(-4.38)-1.41∗(-2.00)-2.62∗(-5.18)-1.69∗(-4.89)-2.28∗(-2.75)-1.46(-1.07)-3.00∗(-5.15)-1.82∗(-4.31)15-2.67∗(-5.05)-1.56(-1.88)-3.67∗(-6.46)-2.75∗(-6.29)-3.76∗(-3.12)-2.3(-1.15)-4.99∗(-5.65)-3.16∗(-5.08)Observations

2,346

2,300

2,300

2,346

34,937

23,912

26,55816,415

Note: This table presents estimates of equation 1 for the Opportunity Insights employment data. Specifications (1)-(4) are estimated at the state level, and columns (5)-(8) at the county level. T-values arepresented using robust standard errors for state estimates and standard errors clustered at the state-level forcounty estimates. Low-income workers make < $27K per year. Middle-income workers make $27K − $60K.
High-income workers make > $60K per year.
* denotes estimates significant at the 95% level.

54

Figure A.5: Opportunity Insights Employment Measure by NAICS Sector(a) Retail and Transportation(b) Professional Services(c) Education and Health(d) Leisure and Hospitality

Note: This figure plots the results of our event study presented in Equation 1. Employment data is obtained
from Opportunity Insights. Observations are at the state level. Dashed lines represent 95% confidence
intervals using robust standard errors. Retail and Transportation is NAICS supersector 40, Professional
Services (60), Education and Health (65), Leisure and Hospitality (70).

55

Figure A.6: Heterogeneity across Consumption Expenditures (Extra)(a) Transportation and Warehousing(b) Health Care Services

Note: This figure plots the results of our event study presented in Equation 1. Expenditure data come fromAffinity Solutions. Merchant groups are defined by Affinity Solutions. Observations are at the state level.
Dashed lines represent 95% confidence intervals using robust standard errors.

Table A.5: Effect of Non-essential Business Closures on the Economy
Labor Variables (Per. Pt.)
Days

Expenditure Variables (Per. Pt.)

Hours Worked Employment Businesses Open State Level County Level Low Income Middle Income High Income
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

-7
(t-value)

4.12∗(3.23)

3.45∗(2.94)

3.74∗(3.28)-0.25(-0.34)-0.26(-0.37)-1.71(-1.56)-0.22(-0.27)-0.31(-0.41)-2

0.96(0.94)

0.71(0.79)

1.11(1.22)-0.02(-0.04)-0.06(-0.29)-0.31(-0.3)-0.03(-0.04)-0.2(-0.26)0-0.44(-0.48)-0.27(-0.33)-0.85(-0.96)-0.12(-0.2)

0.06
(0.4)

-0.31
(-0.3)-0.08(-0.11)-0.42(-0.63)5-0.82(-0.84)-0.76(-0.89)-1.6(-1.76)-1.73∗(-3)-1.42∗(-2.08)-2.54∗(-2.75)-1.93∗(-2.92)-1.93∗(-2.72)10-0.88(-0.89)-0.58(-0.65)-1.74(-1.92)-1.1(-1.83)-1.51(-1.49)-1.95(-1.91)-1.16(-1.84)-1.99∗(-2.59)15

0.33(0.35)

0.14(0.16)-1.78(-1.97)0.06(0.08)

0.01(0.01)-1.37(-1.13)-0.11(-0.16)-0.64(-0.88)Observations

2,346

2,346

2,346

2,346

73,451

2,254

2,346

2,300

Note: This table presents estimates of equation 1 for several specifications with non-essential business closures as the covariate of interest. All estimates are conducted at the state level except column (5) which
provides county level estimates. T-values are presented using robust standard errors for state estimates andstandard errors clustered at the state-level for county estimates. Labor and consumption variables comefrom Homebase and Affinity Solutions, respectively.
* denotes estimates significant at the 95% level.

56

A.2

Model

A.2.1

Equilibrium Conditions

Our model can be summarized by the following first-order conditions:Susceptible1− (1 + µct )λsbt + λπIt πs1 (It Ct ) = 0
cst−θφs nst + Aλsbt + λπIt πs2 (It NtI ) = 0si− Ut+1) − λπIt = 0β(Ut+1

(18)
(19)
(20)

Infected1− (1 + µct )λibt = 0i
ct−θφi nit + Aλibt = 0

(21)
(22)

Recovered1− (1 + µct )λrbt = 0
crt−θφr nrt + Aλrbt = 0

(23)
(24)

Market Clearing

A.2.2

St cst + It cit + Rt crt = Ct

(25)

St nst + It nit + Rt nrt = Nt

(26)

Parameters chosen to Optimize Modeld, πs1 , πs2 , πs3 ) to best fit the data. We chose these parameters
In Section 5.2, we optimize (τH,ias they summarize the endogenous labor responses by susceptible agents in the model without
policy intervention. Recall that the probability of being infected is

πI,t = πs1 (CtS )(It CtI ) + πs2 (NtS )(It NtI ) + πs3NXd(1 − τH,i)(Ii,t P opi,0 )

(27)

i=1
d
Optimizing the parameters (τH,i, πs1 , πs2 , πs3 ) directly controls the probability of being infected. Furthermore, the equilibrium conditions show that the lagrange multiplier for thisconstraint isisλπIt = β(Ut+1− Ut+1)(28)

57

In the steady-state, this can be re-written asisλπI = β(Uss
− Uss
)

(29)

where
s
Uss
=

1
us
1 − β ss

(30)

i
Uss
=

1
(uiss + βπr urss )1 − β(1 − πr − πd )(31)

However, in the steady-state, usss = urss . Substituting and simplifying, Equation 29 can be
re-written as!
ββ 2 πr
i
s
λπI =
uss +
uss − usss
(32)
1 − β(1 − πr − πd )1 − β(1 − πr − πd )λπI = (uiss − usss ) + c(33)

where c is a constant that depends on the discount factor and the probabilities of recoveringand dying. Substituting for steady-state utility, we obtainθθ
λπI = [(log(ciss ) − (niss )2 ) − (log(csss ) − (nsss )2 )] + c22isλπI = log(css ) − log(css ) + c 1/2 !
 1/2 !
1
1
λπI = log Aφi− log A+cθθλπI = log(φi ) + c

(34)
(35)
(36)
(37)

Thus, the endogenous response by susceptible agents to decrease their probability of infection
can be summarized by the loss in labor productivity and c. One could potentially treat φiand β, which affects c, as free parameters. However, the other components of c, πr and πdare set to match their empirical counterparts and should not be treated as free parameters.
A.2.3

Extended Model Calibration Procedure

Section 5.2.1 provided a procedure to calibrate our model in applied settings. This procedure
focused solely on matching the time series of susceptibles in the model to that in the data.
We extend this procedure to match both the time series of susceptibles and consumption in
the data. The following steps are followed to generate simulations from the model:
1. Set Number of Locations (N )2. Set Initial Population of Locations (P op0 )3. Set Susceptible Percent of Population (St )58

4. Set New Infections (Tt )5. Set Active Infections (It )d
6. Set Parameters (µct , τH,i
, πs1 , πs2 , πs3 )The first five steps are identical to the procedure in Section 5.2.1. Step six now includes
the consumption tax, µct , in the calibration procedure. This increases the number of calibrated parameters by N ∗ T , where N is the number of locations and T is the number oftime periods in the application. Due to the increase of parameters, we use the following four
step procedure for calibration:d
Step One Jointly set (τH,i, πs1 , πs2 , πs3 ) to match the empirical time series of susceptibles.

min

Aug26 4X
X

d ,π ,π ,πτH,is1 s2 s3Data
M odelSi,t− Si,t2(38)

i=1 t=M ay6

Step Two Jointly set µct to match the empirical time series of consumption holding thedcalibrated transmission parameters fixed (τH,i, πs1 , πs2 , πs3 ) fixed.
minµct

Aug26 4
X
X

Data
M odelCi,t− Ci,t2(39)

i=1 t=M ay6

Step Three Repeat Step One holding the calibrated consumption taxes, µct , fixed.
dStep Four Jointly set (µct , τH,i
, πs1 , πs2 , πs3 ) to match both the inverse-variance weighted
time series of susceptibles and consumption.

22 P
4 Aug26
4 Aug26
PP  Data
P  Data
M odelM odelCi,t − Ci,t
Si,t − Si,t
i=1 t=M ay6
i=1 t=M ay6




+
min
d ,π ,π ,π
Data
Data
µct ,τH,is1 s2 s3
var Si,tvar Ci,t(40)

subject todd(µct , τH,i
, πs1 , πs2 , πs3 ) ≥ 0.9 ∗ (µct , τH,i
, πs1 , πs2 , πs3 )

(41)

d
d
(µct , τH,i
, πs1 , πs2 , πs3 ) ≤ 1.1 ∗ (µct , τH,i
, πs1 , πs2 , πs3 )

(42)

d
d
As in Section 5.2.1, we impose the restrictions on travel cost: τH,i
∈ [0, 1] and τH,i
= 0
for H = i and that the virus transmission parameters are positive πs1 , πs2 , πs3 ≥ 0 for all
steps in the calibration procedure. Figure A.7 plots both the time series for susceptibles andconsumption in the data and the model after following this extended procedure. Overall,
the results are similar to those in Figure 10 with the addition of matching the time series ofconsumption in the data.

59

Figure A.7: Extended US Census Region Application

Note: Panel A plots the observed time series of susceptibles in the United States and each Census region fromMay 6 through August 26. Panel B the observed consumption paths. Panels C and D plot the equivalentmodel fits for susceptibles and consumption, respectively, after jointly optimizing the consumption taxes,d, πs1 , πs2 , πs3 ). Infection data
the travel distance across locations, and the transmission parameters (µct , τH,i
is obtained from USA Facts. Consumption data is obtained from Affinity Solutions.

A.2.4

Additional Comparative Statics

Figure A.8 plots the results of a three-location SIR model under different parameterizations.
Columns represent different initial conditions. The first column uses initial populations of 13
and initial infections of 0.1% for all states. The second column uses the initial population
across states, P op0 = (36.6%, 56.5%, 6.9%), while maintaining the same initial infections.
The third column randomizes the initial infections of locations, T0 = (0.16%, 0.05%, 0.16%),
using the randomized populations from the second column.42 Rows represent the travel costused. We require that aggregate initial population and infections are equal 1 and 0.1%,
respectively, for all simulations. Thus, differences in the aggregate must be attributed to thecross-sectional interactions rather than initial aggregate conditions. All other parameters
42

These population and infection rates were determined using a random draw. The random draws are thenscaled to maintain the same initial aggregate conditions as our baseline simulation. The actual dynamics
will depend on the specific random draw, but will not change the qualitative comparative static results.

60

remain the same as in Table 4.
No Transmission across Locations The first row plots the results using no interaction acrossdlocations, τH,i
= 1 for H 6= i. Panel (a) shows that, with symmetric locations and notransmission across locations, all locations have the same time series for the fraction ofsusceptible agents. Panel (b) shows that virus transmission within a state is increasing in
its population. The intuition is that individuals are more likely to catch the virus froma larger number of people in more populous states. Panel (c) shows that different initialinfection conditions can create crossing patterns in the cross-section. For these particularrandomized population and initial infection draws, we see that State 2 takes about twenty
and forty weeks to surpass States 3 and 1, respectively, in cumulative infections. This differsfrom Panel (b) where states with higher population always experience higher cumulative
infections than lower populated states.
d.
Partial Transmission The second row simulates the same scenarios using τH,i
= |H−i|N
Comparing Panels (1a) and (2a) show that asymmetric travel costs across locations can leadto cross-sectional heterogeneity of outcomes even when initial population and infections are
symmetric. Panel (2b) shows that, as in Panel (1b), initial population affects both the crosssectional and aggregate time series. Panel (2c) shows that allowing for virus transmission
across locations mitigates, but does not eliminate, the effect that initial infections has on
the cross-sectional crossing patterns.

Full Transmission The third row plots the results using no travel cost across locations,d= 0. Panel (3a) shows that when there is full transmission of the virus across locations
τH,ithat our model replicates Eichenbaum et al. (2020) when locations are symmetric. Thisis also the case when locations have different populations in Panel (3b). Our transmission
mechanism in Equation 3 shows that idiosyncratic initial infection rates are needed to generate a departure from Eichenbaum et al. (2020) when travel cost is zero. However, Panel (3c)shows that the consequences of idiosyncratic infection rates are small when there is complete
virus pass-through across locations even with asymmetric population sizes.
Overall, Panels (1a)-(1c) show that both initial population and initial infection rates canhave significant consequences for the dynamics of our model. Comparing these panels totheir counterparts in Panels (2) and (3) show that the extent of these consequences depends
heavily on the modelling of virus transmission across locations. In the limiting case of no
travel cost across locations, our model converges to the single-location model of Eichenbaum
et al. (2020) regardless of initial population and infection symmetry. Figure A.8 also showsthat cross-sectional assumptions have important implications for aggregate dynamics. In themost severe cases, over 50% of the total population becomes infected after 100 weeks as seen
in Panel 3 with full transmission across locations. However, Panel (1a) suggests that lessthan 20% of the nation becomes infected when there is no transmission across locations. Our
results suggest that our model is not only important for modelling cross-sectional behavior,
but also aggregate dynamics even when holding aggregate initial conditions fixed.

61

Figure A.8: Comparative Statics (Susceptibles)d
1. No Transmission, τH,i
= 1 for H 6= i(a) Pop = (33.3%, 33.3%, 33.3%)(b) Pop = (36.6%, 56.5%, 6.9%) (c) Pop = (36.6%, 56.5%, 6.9%)
Infections = (0.1%, 0.1%, 0.1%) Infections = (0.1%, 0.1%, 0.1%) Infections = (0.16%, 0.05%, 0.16%)d
2. Partial Transmission, τH,i
= |H−i|Nd
3. Full Transmission, τH,i=0

Note: This figure plots the path of susceptibles using a 3-state SIR macro model. In all specifications,aggregate initial infections are equal to 0.001. Columns represent different initial conditions. The firstcolumn presents results when locations are symmetric. The second column randomizes the population oflocations. The third column randomizes the initial infections of locations using the populations from thesecond column. Rows represent the travel cost used. The first row plots the results using no interactiondacross locations. The second row uses τH,i
= |H−i|N . The third row plots the results using no travel costacross locations.

62A.2.5National Mitigation Policy
Figure A.9: Optimal National Policy

Note: This figure plots the results of a 2-location SIR macro model restricted to a common, national policy.
Both locations have an initial population of 21 . Initial infections to 1% and 0.1% for the severe (blue) andmild (red) infected locations, respectively.

63