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\begin_body

\begin_layout Title
\noindent

\series bold
What Explains Temporal and Geographic Variation in the Early US COVID-19 Pandemic?
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\begin_layout Author
\noindent
Hunt Allcott,

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 Stanford University and NBER
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E-mail:
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allcott@stanford.edu,
 leviboxell@gmail.com,
 jacob.conway@chicagobooth.edu,
 billyf@stanford.edu,
 gentzkow@stanford.edu,
 bgoldman@cornell.edu.
 We thank Zane Kashner and Peng Zhang for their excellent research assistance.
 We thank SafeGraph,
 Facteus,
 and Homebase for providing access to the data.
 We also thank the SafeGraph and Homebase COVID-19 response communities respectively for helpful input.
 We also thank Christopher Avery,
 Christopher Meissner,
 David McAdams,
 an anonymous referee,
 and seminar participants at Harvard University and Stanford University for their feedback and comments.
 This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No.
 DGE-1656518.
 Any opinions,
 findings,
 and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation We also acknowledge funding from the Stanford Institute for Economic Policy Research (SIEPR),
 the John S.
 and James L.
 Knight Foundation,
 the Sloan Foundation,
 and the Institute for Humane Studies.
 Previously circulated beginning in May 2020 as 
\begin_inset Quotes eld
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Economic and Health Impacts of Social Distancing Policies during the Coronavirus Pandemic.
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Levi Boxell,
 
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Independent
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\series default
Jacob Conway,
 
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University of Chicago
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Billy Ferguson,
 
\shape italic
Stanford University
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Matthew Gentzkow,
 
\shape italic
Stanford University and NBER
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Benny Goldman,
 
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Cornell University
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\begin_layout Abstract
\noindent
We provide new evidence on the drivers of the early US COVID-19 pandemic and develop a methodology that future researchers can use to similarly analyze the outbreaks of new diseases.
 We combine an epidemiological model of disease transmission with quasi-random variation arising from the timing of stay-at-home-orders to estimate the causal roles of policy interventions and voluntary social distancing.
 We then relate the residual variation in disease transmission rates to observable features of cities.
 We estimate significant impacts of policy and social distancing responses,
 but we show that the magnitude of policy effects was modest,
 and most social distancing was driven by voluntary responses.
 Moreover,
 we show that neither policy nor rates of voluntary social distancing explained a meaningful share of geographic variation.
 The most important predictors of which cities were hardest hit by the pandemic were exogenous characteristics such as population and density.
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\begin_layout Section
Introduction
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\begin_layout Standard
The course of the COVID-19 pandemic in the US varied dramatically across space and time.
 In the early months,
 the epicenter was primarily large cities on the West Coast and in the Northeast.
 Slow growing outbreaks in Seattle and San Francisco were followed by rapid surges of cases in cities such as New York and Boston.
 Other large cities such as Dallas,
 Atlanta,
 Phoenix,
 Miami,
 and Denver were largely spared.
\end_layout

\begin_layout Standard
Popular discussion and prior work has pointed to a number of plausible drivers of this variation,
 with policy differences as one leading explanation.
\begin_inset Foot
status open

\begin_layout Plain Layout
For example,
 New York Governor Andrew Cuomo was frequently blamed for the severity of the crisis in New York,
 with critics citing his slow response to the pandemic and his derision of Mayor De Blasio's earlier suggestion of closing down New York City (Gold and Robinson 2020).
\end_layout

\end_inset

 However,
 evidence below and in prior work clearly shows that substantial behavioral changes preceded the first stay-at-home orders,
 and that mobility levels remained significantly depressed even after many of these policies were lifted—
suggesting voluntary social distancing behaviors may have been important.
 Other potential drivers include physical characteristics of cities such as population size and density that might have affected virus transmission rates,
 or connections via international flights to early overseas epicenters such as China and Italy.
\end_layout

\begin_layout Standard
In this paper,
 we provide new evidence on the importance of policy relative to these other factors during the first months of the US pandemic (through April 2020).
 Our empirical strategy exploits short-run changes around the onset of policy in event-study and difference-in-difference specifications within the context of an SIRD (Susceptible,
 Infected,
 Recovered,
 Deceased) model of disease transmission.
 By taking the ratio between the estimated effects of policy on disease transmission and the estimated effects of policy on social distancing behaviors,
 we are able to provide causal estimates for the change in disease transmission rates per unit change in social distancing—
allowing us to decompose the role that policy and social distancing behaviors played in driving temporal and geographic variation during the early pandemic period.
 We then relate the residual variation in disease transmission rates to observable features of cities.
\end_layout

\begin_layout Standard
We begin by using event-study designs to estimate the short-run effects of stay-at-home orders on social distancing.
 We measure social distancing using visits to points of interest (POIs) such as shops,
 parks,
 hospitals,
 and other places measured in cell phone location data aggregated by a company called SafeGraph.
 We combine POI visits with data on the implementation date of stay-at-home orders at the Combined Statistical Area (CSA) level.
 Our estimates suggest that POI visits dropped by 18 percent on the day after a stay-at-home order was implemented.
 We complement our GPS data with information on consumer spending and small business employment—
finding that consumer spending dropped by 7 percent and employment dropped by 12 percent.
\end_layout

\begin_layout Standard
We next estimate the effects of stay-at-home orders on disease transmission in the context of an SIRD epidemiological model (Kermack and McKendrick 1927).
 Infected people infect Susceptible people at rate 
\begin_inset Formula $\beta_{t}$
\end_inset

 and recover at rate 
\begin_inset Formula $\gamma$
\end_inset

.
 The reproduction number 
\begin_inset Formula $\mathcal{{R}}$
\end_inset

—
the number of people to whom one Infected person transmits the virus—
is 
\begin_inset Formula $\beta_{t}/\gamma$
\end_inset

.
 If a stay-at-home order is modeled as a proportional effect 
\begin_inset Formula $\tau$
\end_inset

 on the contact rate,
 then we can estimate 
\begin_inset Formula $\tau$
\end_inset

 in a linear regression framework with the natural log of the number of new cases on the left-hand side.
 We find that stay-at-home orders reduced the contact rate by 9 to 14 percent for different plausible values of 
\begin_inset Formula $\gamma$
\end_inset

.
 We show that our estimator performs well when estimated on data simulated from a SIRD model.
\end_layout

\begin_layout Standard
We use these estimates to examine the share of the temporal variation in health,
 social distancing,
 and economic outcomes that can be attributed to stay-at-home orders versus voluntary and other policy responses.
 Consistent with other work released around the same time as our initial May 2020 working paper,
 we find that much of the reduction in POI visits pre-dated stay-at-home orders (Brzezinski et al.
 2020;
 Chetty et al.
 2024;
 Gupta et al.
 2021;
 Sears et al.
 2023).
 We calculate that by mid-April 2020,
 the short run effects of stay-at-home orders accounted for only 16 percent of observed social distancing,
 16 percent of observed reductions in economic activity (measured by small business employment),
 and 13 percent of the reduction in contact rate.
\end_layout

\begin_layout Standard
Next,
 we use our previous estimates to compute the counterfactual transmission rates if policy,
 and subsequently social distancing rates,
 were equalized across all CSAs.
 We find that neither policy nor social distancing rates explain the geographic variation in transmission rates.
 Rather,
 fixed differences across CSAs were the primary drivers.
 Using a lasso model to select features of the data that are highly predictive of differential transmission rates,
 we find that population and population density explain nearly half of the average differences across high and low transmission CSAs,
 with racial composition and partisanship explaining a smaller share.
 Our model accurately predicts transmission rates in epicenters,
 such as New York City.
 These results suggest that much of the observed variation across CSAs was not driven by different policy or voluntary behavioral responses,
 but was driven by invariant characteristics of CSAs.
\end_layout

\begin_layout Standard
Lastly,
 we use our estimates to examine the effect of counterfactual policies on the overall prevalence of the virus in the United States.
 While policy explains a small proportion of the temporal variation in case growth and an even smaller proportion of the geographic variation,
 policy still led to an important reduction in cases.
 Absent the observed policy response,
 there would have been 494,000 more confirmed cases by April 30th,
 2020 and 14,800 more deaths.
 In contrast,
 a uniform stay-at-home order implemented on March 17th,
 2020 (the effective date of the first county-level stay-at-home order) would have resulted in 154,000 fewer cases by April 30th.
\end_layout

\begin_layout Standard
We emphasize a number of important caveats.
 Our GPS-based social distancing measure captures overall movement patterns without distinguishing activity with a high vs.
\begin_inset space \space{}
\end_inset

low risk of virus transmission.
 Our measures of economic cost only consider two dimensions of policies' overall economic impact,
 and these are captured imperfectly.
 Our measure of health impact relies on the assumptions of our SIRD model,
 is overall relatively imprecise,
 and may be biased by factors such as endogenous reporting of COVID-19 cases.
 In each case,
 we are able to capture only short-term,
 on-impact effects.
 We provide a set of data points that speak to the benefits and costs of social distancing policies but stop well short of a comprehensive welfare analysis.
 Moreover,
 our analysis focuses on the early onset of the pandemic.
 Predictors and drivers of temporal or geographic variation later in the pandemic may have been different.
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\begin_layout Plain Layout
For example,
 Wallace et al.
 (2023) show that excess death rates during the COVID-19 pandemic were higher for Republican voters after COVID-19 vaccines were made available to all adults (May 2021),
 but not before.
\end_layout

\end_inset

 Our analysis also does not distinguish whether policy- and social distancing-induced reductions in cases during the onset of the pandemic permanently avoided these negative health outcomes,
 or whether they instead delayed these infections (potentially still 
\begin_inset Quotes eld
\end_inset

flattening the curve
\begin_inset Quotes erd
\end_inset

 and avoiding health care capacity constraints and unvaccinated infections).
\begin_inset Foot
status open

\begin_layout Plain Layout
See Budish (2024) for analysis of mitigation policies sufficient to keep the effective reproduction number below one,
 resulting in falling infections until a vaccine or cure can be developed.
 See Rachel (2024) for analysis of how temporary mitigation policies might increase the likelihood of subsequent waves in the absence of a vaccine or cure.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Our work connects to several research areas.
 First,
 a series of recent papers used GPS data from SafeGraph or similar providers to quantify social distancing and estimate the effects of stay-at-home orders and other policies (Alexander and Karger 2023;
 Allcott et al.
 2020;
 Chen et al.
 2020a;
\begin_inset Note Note
status open

\begin_layout Plain Layout
Keith Chen
\end_layout

\end_inset

 Engle et al.
 2020;
 Goolsbee and Syverson 2021;
 Painter and Qui 2021;
 Sears et al.
 2023).
 Second,
 several recent papers have studied the effects of stay-at-home policies on economic outcomes (Baker et al.
 2020;
 Bartik et al.
 2020;
 Chen et al.
 2020b
\begin_inset Note Note
status open

\begin_layout Plain Layout
IMF paper,
 not Keith chen
\end_layout

\end_inset

;
 Chetty et al.
 2024;
 Kong and Prinz 2020;
 Lin and Meissner 2020).
 Third,
 another set of papers quantified the effects of regulation on health outcomes (Childs et al.
 2021;
 Flaxman et al.
 2020;
 Fowler et al.
 2020;
 Friedson et al.
 2021;
 Greenstone and Nigam 2020;
 Lasry et al.
 2020;
 Lin and Meissner 2020).
 Collectively,
 these contemporaneous literatures have reached a growing consensus (supported by our analysis) that the majority of social distancing was voluntary rather than policy-induced.
 However,
 these literatures have not fully pinned down the drivers of pandemic outbreaks or the causal effect of policy and social distancing on health outcomes.
 In the epidemiological literature,
 there is a set of what economists might call 
\begin_inset Quotes eld
\end_inset

structural
\begin_inset Quotes erd
\end_inset

 models that use Bayesian techniques to estimate the reproduction number 
\begin_inset Formula $\mathcal{{R}}$
\end_inset

;
 these estimates often pay less attention to identifying the causal effect of policies on 
\begin_inset Formula $\mathcal{{R}}$
\end_inset

 (Cori et al.
 2013;
 Thompson et al.
 2013).
 In the economics literature,
 there is a set of papers that use reduced form event-study approaches to estimate the effects of policies on some measure of disease transmission,
 but many of these papers are not closely tied to structural models of disease transmission.
 Our paper forms a bridge between these two lines of work by deriving simple linear estimating equations (which are useful for standard quasi-experimental analysis) from structural epidemiological models and using these estimates to decompose the role of various drivers in explaining the temporal and geographic variation of virus transmission in the early months of a pandemic.
\begin_inset Foot
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Desmet and Wacziarg (2021),
 Knittel and Ozaltun (2020),
 and Kuchler et al.
\begin_inset space \space{}
\end_inset

(2022) examine spatial variation in COVID cases and/or deaths in the United States without employing the framework of an SIRD model.
\end_layout

\end_inset

 Our methodology may also serve as a blueprint for future researchers seeking to analyze the outbreaks of new diseases.
\end_layout

\begin_layout Section
Data
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name "sec:data"

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\begin_layout Subsection
Policy Data
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name "subsec:data_policy"

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\end_layout

\begin_layout Standard
We explore both stay-at-home and business closure policies in this paper.
 Due to the decentralized policy response of states,
 cities,
 and counties,
 there is no single resource documenting non-pharmaceutical interventions (NPIs) in the United States.
 To get the best coverage of these NPIs,
 we combine data from four sources and define both our stay-at-home and business closure policies by sequentially assigning enforcement dates by data source.
 We prioritize the data sources in the following way (first to last priority):
 the New York Times (Mervosh et al.
 2020a),
 Keystone Strategy,
 a crowdsourcing effort from Stanford and University of Virginia,
 and Hikma Health.
 Once a state enacted a policy,
 the counties inherited the policy of the state.
 In Appendix Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:policy_source_table"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

,
 we provide summary statistics reporting the share of county policies from each source.
 We visualize the distribution of county stay-at-home order implementation dates over time in Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:order-timing"
plural "false"
caps "false"
noprefix "false"
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.
 Additional detail on data construction can be found in Appendix Section 
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plural "false"
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.
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\begin_layout Subsection
Social Distancing Data
\end_layout

\begin_layout Standard
The data on social distancing behaviors come from SafeGraph,
 a data company that aggregates anonymized location data from about 45 million mobile devices
\begin_inset Note Note
status open

\begin_layout Plain Layout
Source:
 https://www.safegraph.com/dashboard/covid19-shelter-in-place?s=US&d=05-01-2020&t=counties&m=index
\end_layout

\end_inset

 and numerous applications in order to provide insights about physical points of interest (POIs).
 POIs include restaurants,
 coffee shops,
 grocery stores,
 retail outlets,
 hospitals,
 and many other business establishments.
 For each POI,
 SafeGraph reports the daily number of unique device visits along with information on the POI's industry and location.
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\begin_layout Plain Layout
See 
\begin_inset CommandInset href
LatexCommand href
name "https://web.archive.org/web/20201024234927/https://docs.safegraph.com/docs/weekly-patterns"
target "https://web.archive.org/web/20201024234927/https://docs.safegraph.com/docs/weekly-patterns"
literal "false"

\end_inset

 for additional information on the data's construction.
\end_layout

\end_inset

 For each CSA,
 we construct the total number of visits to POIs in that CSA for a given day.
\end_layout

\begin_layout Subsection
Economic Data
\end_layout

\begin_layout Standard
Our analysis uses economic data from two sources.
 We incorporate spending on approximately 10 million
\begin_inset Note Note
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\begin_layout Plain Layout
Source:
 SafeGraph/Placekey consortium comment from Facteus team,
 https://placekey-community.slack.com/archives/C01080G2TD0/p1585693155347700
\end_layout

\end_inset

 debit cards in data from Facteus,
 a financial data provider that directly partners with banks.
 This sample consists of traditional debit cards issued by banks,
 general purpose debit cards issued by merchants,
 payroll cards issued by employers,
 and government alimony disbursement cards.
 Lower- and middle-income individuals are represented more heavily in this data than in the US population.
 We construct the total number of transactions and dollar amount spent by cards from a given home CSA on a given day.
\begin_inset Foot
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\begin_layout Plain Layout
To protect privacy,
 Facteus injects a small amount of mathematical noise into key record attributes.
 This has very minimal impact on aggregate data.
 More information on this differential privacy procedure can be found at 
\begin_inset CommandInset href
LatexCommand href
name "https://web.archive.org/web/20210519180241/https://www.facteus.com/products/data-products/"
target "https://web.archive.org/web/20210519180241/https://www.facteus.com/products/data-products/"
literal "false"

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.
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\begin_layout Standard
We also source information on employment from Homebase,
 a company providing scheduling and time tracking software to over 60,000 small businesses.
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Additional information regarding Homebase's data can be found at 
\begin_inset CommandInset href
LatexCommand href
name "https://joinhomebase.com/data/"
target "https://joinhomebase.com/data/"
literal "false"

\end_inset

.
\end_layout

\end_inset

 For each day,
 we analyze the number of work hours and individuals employed by Homebase partner firms in a given CSA.
\end_layout

\begin_layout Subsection
Health Data
\end_layout

\begin_layout Standard
We pull case and death counts by day at the county level from a continually-updated repository by the New York Times that aggregates reports from state and local health agencies.
 For all dates up to the first available data,
 we assume no cases nor deaths.
 We collect state-level testing and hospitalization data from the Covid Tracking Project.
\end_layout

\begin_layout Subsection
Demographic Data
\end_layout

\begin_layout Standard
We supplement the policy and outcome data with data on CSA characteristics.
 For our measure of partisanship,
 we use the Republican vote share in the 2016 presidential election (MIT Election Data and Science Lab 2018).
 Following Allcott et al.
 (2020),
 we use the SafeGraph OpenCensus data to assign demographic variables such as race,
 income,
 occupation,
 and commuting to the various geographies analyzed.
 The SafeGraph OpenCensus data is derived from the 2016 5-year ACS at the census block group level.
 We add the urban share of the population from the 2010 Census.
 We also use average seasonal temperatures by geography from Wu et al.
 (2020),
 which is ultimately sourced from gridMET (Abatzoglou 2013).
 To characterize potential global migration flows for transmission,
 we use flight data from the OpenSky Network (Schäfer et al.
 2014;
 Olive 2019).
\end_layout

\begin_layout Section
Effects on Social Distancing and Economic Outcomes
\begin_inset CommandInset label
LatexCommand label
name "sec:mobility-econ"

\end_inset


\end_layout

\begin_layout Standard
Our main results are at the Combined Statistical Area (CSA) by order date level (i.e.,
 we group counties within a CSA who received a stay-at-home order on the same day together) using data from February 1,
 2020 to April 30,
 2020.
\begin_inset Foot
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\begin_layout Plain Layout
See Appendix 
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:data_appendix"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 for detail regarding CSAs and the benefits of conducting our analysis at the CSA level.
\end_layout

\end_inset

 We call our unit of observation a 
\begin_inset Quotes eld
\end_inset

CSA
\begin_inset Quotes erd
\end_inset

 for simplicity.
 To estimate the causal effect of these stay-at-home orders,
 we estimate the following event-study specification
\begin_inset Formula 
\begin{equation}
Y_{it}=\mu_{i}+\delta_{t}+\sum_{k=-21,k\not=-1}^{k=21}\omega_{k}{\bf 1}_{\{t-T_{i}=k\}}+\epsilon_{it}\label{eq:event-study}
\end{equation}

\end_inset

where 
\begin_inset Formula $Y_{it}$
\end_inset

 is the outcome of interest in CSA 
\begin_inset Formula $i$
\end_inset

 during time 
\begin_inset Formula $t$
\end_inset

,
 
\begin_inset Formula $\mu_{i}$
\end_inset

 is a CSA fixed effect,
 
\begin_inset Formula $\delta_{t}$
\end_inset

 is a date fixed effect,
 and 
\begin_inset Formula ${\bf 1}_{\{t-T_{i}=k\}}$
\end_inset

 is an indicator for the days relative to the first stay-at-home order 
\begin_inset Formula $T_{i}$
\end_inset

.
\begin_inset Foot
status open

\begin_layout Plain Layout
For CSAs without a stay-at-home order in our sample,
 
\begin_inset Formula ${\bf 1}_{\{t-T_{i}=k\}}$
\end_inset

 is always set to zero.
\end_layout

\end_inset

 Standard errors are clustered at the CSA level irrespective of order timing.
 Earlier and later time periods are pooled in the 
\begin_inset Formula $k=-21$
\end_inset

 and 
\begin_inset Formula $k=21$
\end_inset

 time indicators respectively.
\end_layout

\begin_layout Standard
Panels A–C of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:event_study-1"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 show clear effects of stay-at-home orders on social distancing and economic outcomes.
 Panel A shows that a stay-at-home order decreased POI visits by 17.8 percent (se = 1.3) by the day after the order's effective start date (
\begin_inset Formula $k=1$
\end_inset

).
 This decrease persisted and was relatively stable throughout the window of analysis.
 Panel B estimates that a stay-at-home order decreased consumer debit spending (in total $) by 7.1 percent (se = 0.9) by the day after an order's effective start date.
 Panel C estimates a 12.3 percent (se = 1.5) reduction in the number of employees working in our Homebase sample on the day following an order's implementation.
\end_layout

\begin_layout Standard
In Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:te_heterogeneity"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 Panel A,
 we find no evidence of heterogeneous policy effects on mobility by implementation date.
 In Panel B,
 we also find similar policy effects on mobility in majority Democrat vs.
\begin_inset space \space{}
\end_inset

majority Republican CSAs.
 Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:event_study_bus_simultaneous"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 analyzes the effects of mandatory business closure orders,
 which induced less negative mobility and spending responses than stay-at-home orders but which caused a comparable reduction in employment.
\end_layout

\begin_layout Section
Effects on Health Outcomes
\begin_inset CommandInset label
LatexCommand label
name "sec:health"

\end_inset


\end_layout

\begin_layout Subsection
SIRD Model
\end_layout

\begin_layout Standard
We start with a discrete-time SIRD model (Kermack and McKendrick 1927),
 suppressing notation for different geographies 
\begin_inset Formula $i$
\end_inset

.
 In outlining this model,
 we make the assumption that there are no health spillovers across geographies.
 Furthermore,
 we abstract from issues around testing and the endogeneity of stay-at-home order timing.
\end_layout

\begin_layout Standard
The population is defined by 
\begin_inset Formula 
\begin{equation}
S_{t}+I_{t}+R_{t}+D_{t}=N\label{eq:pop}
\end{equation}

\end_inset

where 
\begin_inset Formula $S_{t}$
\end_inset

,
 
\begin_inset Formula $I_{t}$
\end_inset

,
 
\begin_inset Formula $R_{t}$
\end_inset

,
 and 
\begin_inset Formula $D_{t}$
\end_inset

 are the number of susceptible,
 infected,
 recovered,
 and deceased individuals at time 
\begin_inset Formula $t.$
\end_inset

 Dynamics in the SIRD model are defined by the transition probabilities between states.
 The laws of motion are given by:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
S_{t+1}-S_{t}=-\beta_{t}S_{t}\frac{I_{t}}{N}\label{eq:motion_s}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
I_{t+1}-I_{t}=\beta_{t}S_{t}\frac{I_{t}}{N}-\gamma I_{t}\label{eq:motion_i}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
R_{t+1}-R_{t}=(1-\kappa)\gamma I_{t}\label{eq:motion_r}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
D_{t+1}-D_{t}=\kappa\gamma I_{t}\label{eq:motion_d}
\end{equation}

\end_inset

where 
\begin_inset Formula $\beta_{t}$
\end_inset

 is the contact rate that governs the speed at which new infections propagate,
 
\begin_inset Formula $\gamma$
\end_inset

 is the rate at which infected individuals recover,
 and 
\begin_inset Formula $\kappa$
\end_inset

 is the proportion of recovered individuals that die.
 We treat the recovery rate 
\begin_inset Formula $\gamma$
\end_inset

 and death rate 
\begin_inset Formula $\kappa$
\end_inset

 as fixed parameters during the time period we analyze.
\end_layout

\begin_layout Standard
Defining the total number of cases to be 
\begin_inset Formula $C_{t}=I_{t}+R_{t}+D_{t}$
\end_inset

 and combining equations (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_i"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

),
 (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_r"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

),
 and (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_d"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

),
 we get that new cases evolve as 
\begin_inset Formula 
\begin{equation}
C_{t+1}-C_{t}=\beta_{t}S_{t}\frac{I_{t}}{N}\label{eq:new_cases}
\end{equation}

\end_inset

We make the simplifying assumption that 
\begin_inset Formula $S_{t}\approx N_{t}$
\end_inset

 so that we can treat the ratio 
\begin_inset Formula $\frac{S_{t}}{N_{t}}=1$
\end_inset

.
 As of May 1,
 less than 0.5 percent of the US population had a confirmed case on or before this date—
making this approximation reasonable—
though the true case count may have been greater.
 This allows us to replace equations (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_s"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) and (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_i"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) with
\begin_inset Formula 
\begin{equation}
C_{t+1}-C_{t}=\beta_{t}I_{t}.\label{eq:motion_c}
\end{equation}

\end_inset

Furthermore,
 we can write 
\begin_inset Formula 
\begin{equation}
I_{t}=(C_{t}-C_{t-1})+(1-\gamma)I_{t-1}.\label{eq:I_t}
\end{equation}

\end_inset

Given initial conditions 
\begin_inset Formula $C_{0}$
\end_inset

,
 
\begin_inset Formula $I_{0}$
\end_inset

,
 the contact rate 
\begin_inset Formula $\beta_{t}$
\end_inset

,
 and the recovery rate 
\begin_inset Formula $\gamma$
\end_inset

,
 equations (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_c"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) and (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:I_t"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) define the dynamics of cases over time.
\end_layout

\begin_layout Subsection
Estimation Framework
\end_layout

\begin_layout Standard
A key parameter of interest for policymakers is the contact rate 
\begin_inset Formula $\beta_{t}$
\end_inset

.
 As social distancing increases,
 the contact rate decreases—
yielding fewer new cases.
 The contact rate 
\begin_inset Formula $\beta_{t}$
\end_inset

 is proportionally related to the reproduction number 
\begin_inset Formula $\mathcal{{R}}_{0t}$
\end_inset

 as 
\begin_inset Formula $\mathcal{{R}}_{0t}=\beta_{t}/\gamma$
\end_inset

.
 A proportional effect on the contact rate 
\begin_inset Formula $\beta_{t}$
\end_inset

 will have the same proportional effect on the reproduction number 
\begin_inset Formula $\mathcal{{R}}_{0t}$
\end_inset

.
\end_layout

\begin_layout Standard
We suggest it is natural to think of stay-at-home orders as a proportional effect (
\begin_inset Formula $\tau$
\end_inset

) on the contact rate that would occur in the absence of policy interventions (
\begin_inset Formula $\tilde{{\beta}_{t}}$
\end_inset

).
 That is,
 the contact rate is 
\begin_inset Formula $\beta_{t}=\tilde{{\beta}_{t}}(1+\tau)$
\end_inset

 under a stay-at-home order as opposed to 
\begin_inset Formula $\tilde{{\beta}}_{t}$
\end_inset

.
\end_layout

\begin_layout Standard
Applying this substitution and taking logs of equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_c"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

),
 we get 
\begin_inset Formula 
\[
\log(C_{t+1}-C_{t})=\log(I_{t})+\log(\tilde{\beta}_{t})+\log(1+\tau{\bf 1}_{\{t\geq T_{i}\}}).
\]

\end_inset

where 
\begin_inset Formula ${\bf 1}_{\{t\geq T_{i}\}}$
\end_inset

 denotes an indicator for being under a stay-at-home order.
 We then use an event-study framework to estimate the impact of treatment
\begin_inset Formula 
\begin{equation}
\log(C_{i,t+1}-C_{it})=\alpha\log(I_{it})+\delta_{t}+\xi_{it}+\sum_{k=-14,k\not=-1}^{k=21}\omega_{k}{\bf 1}_{\{t-T_{i}=k\}}+\epsilon_{it},\label{eq:event-study-1}
\end{equation}

\end_inset

where,
 relative to equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:event-study"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

),
 
\begin_inset Formula $\xi_{it}$
\end_inset

 is an indicator for the non-binned event-study window.
\begin_inset Foot
status open

\begin_layout Plain Layout
The event-study window indicator is required for normalization when geography fixed effects are excluded.
 We exclude geography fixed effects because they bias estimates in our simulations (see Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:simulations_alt"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

).
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The 
\begin_inset Formula $\omega_{k}$
\end_inset

 coefficients can be interpreted as estimates of 
\begin_inset Formula $\tau$
\end_inset

 while 
\begin_inset Formula $\delta_{t}$
\end_inset

 and 
\begin_inset Formula $\xi_{it}$
\end_inset

 control for variation in 
\begin_inset Formula $\beta_{t}$
\end_inset

 over time unrelated to the policy.
 Even though 
\begin_inset Formula $I_{t}$
\end_inset

 is not directly observed,
 given initial conditions 
\begin_inset Formula $C_{0}=I_{0}$
\end_inset

 and 
\begin_inset Formula $\gamma$
\end_inset

,
 no additional data is required to construct the time-path for 
\begin_inset Formula $I_{t}$
\end_inset

 beyond the growth in cases.
 Below,
 we use values for 
\begin_inset Formula $\gamma$
\end_inset

 suggested by the epidemiology literature and examine robustness to alternative values.
 Note that one test of the model and its assumptions is whether 
\begin_inset Formula $\hat{\alpha}=1$
\end_inset

.
\end_layout

\begin_layout Standard
In Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:simulations"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

,
 we show that this estimator performs well when estimated on data simulated from an SIRD model,
 and contrast this with the poor performance of other specifications used in the literature.
\end_layout

\begin_layout Subsection
Results
\end_layout

\begin_layout Standard
A key input into the estimation process is 
\begin_inset Formula $\gamma$
\end_inset

 which is the inverse of the average infectious period for COVID-19.
 We report estimates using a range of values for 
\begin_inset Formula $\gamma.$
\end_inset

 On one extreme,
 we set 
\begin_inset Formula $\gamma=0$
\end_inset

 which implies 
\begin_inset Formula $I_{it}=C_{it}$
\end_inset

 or an infinite infectious period.
 On the other extreme,
 we set 
\begin_inset Formula $\gamma=1$
\end_inset

 which implies an average infectious period of 1 day.
 Early indications in the literature suggested an infectious period of 4.4 to 7.5 days (Anderson et al.
 2020).
 As of May 8,
 2020,
 the CDC website recommended home isolation until at least 10 days have passed since symptoms first appeared,
 whereas the UK NHS recommended a minimum of 7 days.
\begin_inset Foot
status open

\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
name "https://web.archive.org/web/20200508003242/https://www.cdc.gov/coronavirus/2019-ncov/if-you-are-sick/steps-when-sick.html"
target "https://web.archive.org/web/20200508003242/https://www.cdc.gov/coronavirus/2019-ncov/if-you-are-sick/steps-when-sick.html"
literal "false"

\end_inset

 and 
\begin_inset CommandInset href
LatexCommand href
name "https://web.archive.org/web/20200522075042/https://www.nhs.uk/conditions/coronavirus-covid-19/what-to-do-if-you-or-someone-you-live-with-has-coronavirus-symptoms/staying-at-home-if-you-or-someone-you-live-with-has-coronavirus-symptoms/"
target "https://web.archive.org/web/20200522075042/https://www.nhs.uk/conditions/coronavirus-covid-19/what-to-do-if-you-or-someone-you-live-with-has-coronavirus-symptoms/staying-at-home-if-you-or-someone-you-live-with-has-coronavirus-symptoms/"
literal "false"

\end_inset


\end_layout

\end_inset

 We view the range of 
\begin_inset Formula $\gamma=1/3$
\end_inset

 (an infectious period of three days on average) and 
\begin_inset Formula $\gamma=1/12$
\end_inset

 (an infectious period of twelve days on average) as limits to the range of likely values.
\end_layout

\begin_layout Standard
Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:table_agg_reg"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 reports our estimates using case data and stay-at-home orders.
 To reduce instances where 
\begin_inset Formula $\log(C_{i,t+1}-C_{it})$
\end_inset

 is undefined,
 we group counties by the interaction between their cumulative statistical area and the timing of their stay-at-home order.
\begin_inset Foot
status open

\begin_layout Plain Layout
For simplicity,
 we subsequently refer to these CSA-timing groups as CSAs.
\end_layout

\end_inset

 We restrict attention to CSA-days with at least 10 cases,
 the set of CSAs to either never treated CSAs or CSAs which are observed for at least 8 days before and 20 days after the order,
 and the time period prior to May 1,
 2020.
 Because of the imprecision of the estimates,
 we estimate an aggregated event study specification (see table notes).
 In general,
 
\begin_inset Formula $\gamma$
\end_inset

 is positively correlated with the estimated treatment effects of stay-at-home orders on case prevalence.
\end_layout

\begin_layout Standard
Using likely values of 
\begin_inset Formula $\gamma$
\end_inset

,
 we find a negative estimated effect of stay-at-home orders on case prevalence though these estimated effects have wide confidence intervals.
 Setting 
\begin_inset Formula $\gamma=1/6$
\end_inset

,
 which implies an average infectious period of 6 days,
 our baseline estimates suggest that stay-at-home orders decreased the contact rate 
\begin_inset Formula $\beta_{t}$
\end_inset

 (i.e.,
 the rate of new cases) by 9.1 percent (se = 4.8) relative to their pre-order levels.
 Consistent with the data coming from an SIRD data generating process,
 estimates for 
\begin_inset Formula $\alpha$
\end_inset

 are close to 1.
\end_layout

\begin_layout Standard
Panels D and E of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:event_study-1"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 report the full event-study plot for 
\begin_inset Formula $\gamma=0$
\end_inset

 which sets 
\begin_inset Formula $I_{t}=C_{t}$
\end_inset

,
 along with our preferred value of 
\begin_inset Formula $\gamma=1/6$
\end_inset

.
 Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:event_study_health_alt_gamma"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 reports the full event studies for the other values of 
\begin_inset Formula $\gamma.$
\end_inset


\end_layout

\begin_layout Section
Explaining Variation in Outcomes
\begin_inset CommandInset label
LatexCommand label
name "sec:Variation"

\end_inset


\end_layout

\begin_layout Subsection
Temporal Variation
\begin_inset CommandInset label
LatexCommand label
name "sec:temp-variation"

\end_inset


\end_layout

\begin_layout Standard
In this section,
 we compute the share of the overall change in each outcome that is attributable to stay-at-home and business closure orders.
 Secular trends in the outcomes were prominent over our time period as individuals made voluntary behavioral changes (e.g.,
 Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:trends"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

).
\end_layout

\begin_layout Standard
To examine the share of aggregate changes explained by policy,
 we first compute the average total percent reduction in the outcome as
\begin_inset Formula 
\begin{equation}
\text{Total}\Delta=\frac{Y_{T}-Y_{0}}{Y_{0}}
\end{equation}

\end_inset

where 
\begin_inset Formula $Y_{t}$
\end_inset

 is the weighted average of the level of the outcome in week 
\begin_inset Formula $t$
\end_inset

 taken over geographies that enacted the corresponding order during our time period.
 
\begin_inset Formula $t=0$
\end_inset

 is the first week of February,
 and 
\begin_inset Formula $t=T$
\end_inset

 is the third week of April.
 We average across days in the week when computing 
\begin_inset Formula $Y_{t}$
\end_inset

 to remove any day-of-week effects.
\begin_inset Foot
status open

\begin_layout Plain Layout
Most CSAs did not have any cases in early February,
 so the pre-period levels cannot be estimated from the data when examining the overall change in the contact rate 
\begin_inset Formula $\beta_{t}$
\end_inset

.
 Since we must choose 
\begin_inset Formula $\gamma$
\end_inset

 for each specification and the reproduction number 
\begin_inset Formula $\mathcal{{R}}_{0}$
\end_inset

 is 
\begin_inset Formula $\beta_{t}/\gamma$
\end_inset

,
 we can recover 
\begin_inset Formula $\beta_{t}$
\end_inset

 in the pre-period by specifying 
\begin_inset Formula $\mathcal{{R}}_{0}$
\end_inset

.
 Anderson et al.
 (2020) and D'Arienzo and Coniglio (2020) provide an overview of estimates of the initial reproduction rate 
\begin_inset Formula $\mathcal{{R}}_{0}$
\end_inset

,
 ranging from 2.5 to 3.5.
 Our preferred reproduction rate is 
\begin_inset Formula $\mathcal{{R}}_{0}=$
\end_inset

 3.0.
 We then compute 
\begin_inset Formula $Y_{T}$
\end_inset

 and 
\begin_inset Formula $Y_{\mathcal{T}(i)}$
\end_inset

 using equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_c"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) and the assumed 
\begin_inset Formula $\gamma$
\end_inset

 value;
 we use the assumed 
\begin_inset Formula $\mathcal{{R}}_{0}$
\end_inset

 when (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_c"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) is undefined in our data.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Next,
 we compute the average policy-induced change relative to baseline levels as
\begin_inset Formula 
\begin{equation}
\text{Policy}\Delta=\frac{1}{N}\sum_{i}w_{i}\frac{{\omega_{k}\times Y_{\mathcal{T}(i)}}}{Y_{0}}
\end{equation}

\end_inset

where 
\begin_inset Formula $\omega_{k}$
\end_inset

 is the estimated treatment effect from Sections 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:mobility-econ"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:health"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

,
 
\begin_inset Formula $w_{i}$
\end_inset

 are geography population weights that sum to 
\begin_inset Formula $N$
\end_inset

,
 and 
\begin_inset Formula $\mathcal{T}(i)$
\end_inset

 is the period prior to the order's implementation for geography 
\begin_inset Formula $i$
\end_inset

.
 We account for uncertainty induced by the estimation of 
\begin_inset Formula $\omega_{k}$
\end_inset

 in the standard errors,
 and treat the values of 
\begin_inset Formula $Y_{t}$
\end_inset

 as given.
 We set 
\begin_inset Formula $k=1$
\end_inset

 in our baseline specification and examine robustness to alternative assumptions.
\end_layout

\begin_layout Standard
Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:decomp_plot"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 presents the ratio 
\begin_inset Formula $\text{Policy}\Delta/\text{Total}\Delta$
\end_inset

 for our social distancing,
 employment,
 and health outcomes.
\begin_inset Foot
status open

\begin_layout Plain Layout
Debit card transactions and total spending,
 according to the Facteus data,
 did not have a similarly strong decrease between February and April.
 As a result,
 the decomposition of this small reduction (or increase in the case of total spending) into a voluntary and mandatory portion is more difficult to interpret.
 We note that Farrell et al.
 (2020) find a decrease in consumer spending when using data sources other than Facteus' debit card panel.
\end_layout

\end_inset

 We compute this estimate separately for stay-at-home orders and mandatory business closure orders.
 Appendix Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:table_decomp"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 reports 
\begin_inset Formula $\text{Total}\Delta$
\end_inset

 and 
\begin_inset Formula $\text{Policy}\Delta$
\end_inset

 individually for the stay-at-home orders,
 the business closure orders,
 and the simultaneous implementation of both orders.
\end_layout

\begin_layout Standard
We estimate that stay-at-home orders explain 16.2 percent of the change in POI visits,
 15.6 percent of the change in total wages,
 16.0 percent of the change in total employment,
 and 13.1 percent of the change in the contact rate 
\begin_inset Formula $\beta_{t}$
\end_inset

 when setting 
\begin_inset Formula $\gamma=1/6$
\end_inset

 and 
\begin_inset Formula $\mathcal{R}_{0}=3.0$
\end_inset

.
 Overall,
 while stay-at-home orders only explain a small proportion of the overall changes in social distancing and case growth,
 they do not appear inefficient.
 Stay-at-home orders have a wage cost per unit of social distancing that is 0.96 times as large as the average cost across voluntary behavioral changes and other government orders and has a relative employment cost that is 0.99 times as large.
\begin_inset Foot
status open

\begin_layout Plain Layout
That is,
 
\begin_inset Formula $\frac{.156}{.162}/\frac{1-.156}{1-.162}=0.96$
\end_inset

 and 
\begin_inset Formula $\frac{.160}{.162}/\frac{1-.160}{1-.162}=0.99$
\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
In contrast to the stay-at-home orders,
 the employment cost per unit of social distancing for business closures is relatively high.
 Our estimates suggest that business closure orders have a wage cost per unit of social distancing that is 2.25 times larger than the average cost across voluntary behavioral changes and other government orders and has a relative employment cost that is 1.91 times greater.
\begin_inset Foot
status open

\begin_layout Plain Layout
That is,
 
\begin_inset Formula $\frac{.182}{.090}/\frac{1-.182}{1-.090}=2.25$
\end_inset

 and 
\begin_inset Formula $\frac{.159}{.090}/\frac{1-.159}{1-.090}=1.91$
\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Appendix Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:table_decomp_appendix"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 considers alternative estimators and provides qualitatively similar conclusions.
\end_layout

\begin_layout Subsection
Geographic Variation
\begin_inset CommandInset label
LatexCommand label
name "sec:geo-variation"

\end_inset


\end_layout

\begin_layout Standard
We next examine factors that explain the geographic variation in health outcomes.
\end_layout

\begin_layout Standard
To formalize the comparison across CSAs,
 we extend our parameterization of the contact rate 
\begin_inset Formula $\beta_{it}$
\end_inset

 as a function of social distancing behaviors along with date and CSA fixed effects
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\log(\beta_{it})=\Lambda_{0}\Delta\log(POI_{it})+\theta_{i}+\rho_{t}+\nu_{it}\label{eq:beta_param}
\end{equation}

\end_inset

where 
\begin_inset Formula $\Delta\log(POI_{it})$
\end_inset

 is the change in the log of POI visits between March 1,
 2020 and 
\begin_inset Formula $t$
\end_inset

,
 
\begin_inset Formula $\theta_{i}$
\end_inset

 are CSA fixed effects,
 
\begin_inset Formula $\rho_{t}$
\end_inset

 are date fixed effects,
 and 
\begin_inset Formula $\nu_{it}$
\end_inset

 are residuals unobserved by the econometrician.
 We use our constructed series for 
\begin_inset Formula $I_{it}$
\end_inset

 and the case growth 
\begin_inset Formula $C_{i,t+1}-C_{it}$
\end_inset

 to define 
\begin_inset Formula $\beta_{it}$
\end_inset

 as in equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_c"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) assuming 
\begin_inset Formula $\gamma=1/6$
\end_inset

.
 Note that we can use the ratio of the treatment effects of stay-at-home orders on social distancing behaviors in Section 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:mobility-econ"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 and on the contact rate from Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:table_agg_reg"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 to provide a 
\emph on
causal
\emph default
 estimate 
\begin_inset Formula $\hat{\Lambda}_{0}$
\end_inset

 for the change in the contact rate per change in social distancing.
 Constraining 
\begin_inset Formula $\Lambda_{0}$
\end_inset

 to be the estimated ratio from our event-study specifications,
 we estimate equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:beta_param"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) via a fixed effects estimator.
\begin_inset Foot
status open

\begin_layout Plain Layout
To implement the regression constraint and avoid taking the log of zero,
 we set 
\begin_inset Formula $\beta_{ik}=\frac{1}{1,000,000}$
\end_inset

 when 
\begin_inset Formula $\beta_{ik}<\frac{1}{1,000,000}$
\end_inset

 and we estimate
\begin_inset Formula 
\[
\log\left(\beta_{it}\right)-\hat{\Lambda}_{0}\Delta\log(POI_{it})=\theta_{i}+\rho_{t}+\nu_{it}
\]

\end_inset

where we use the same estimating sample as in Section 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:health"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 restricted to the period between March 15 and April 30,
 2020,
 and we set 
\begin_inset Formula $\hat{\Lambda}_{0}=\frac{.091}{.178}=.51$
\end_inset

.
 We do not use population weights.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:add_decomp_table"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 reports the average difference in log contact rates 
\begin_inset Formula $\log(\beta_{it})$
\end_inset

 across various groups of CSAs with high and low average case growth.
 To understand the role of social distancing and policy in explaining differences between these groups,
 we use equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:beta_param"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) and our previous event-study estimates to obtain the predicted log contact rates if (i) stay-at-home policies had been equated across all CSAs and (ii) if changes in social distancing had been equated across all CSAs.
 Our estimates suggest that little to none of the average geographic variation in log contact rates were explained by differences in social distancing behaviors or policy.
 The timing of virus onset,
 accounted for by 
\begin_inset Formula $\rho_{t}$
\end_inset

,
 also did little to explain these average differences.
\begin_inset Foot
status open

\begin_layout Plain Layout
Appendix Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:var_decomp_table"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 reports the share of the cross-CSA variance in log contact rates 
\begin_inset Formula $\log(\beta_{it})$
\end_inset

 explained by each set of covariates and provides similar conclusions as the additive decomposition in Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:add_decomp_table"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
These results suggest the vast majority of differences across CSAs were driven by the estimated fixed effects 
\begin_inset Formula $\theta_{i}$
\end_inset

.
\begin_inset Foot
status open

\begin_layout Plain Layout
Appendix Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:table_summary"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 reports summary statistics for all CSAs,
 CSAs with above median average contact rates,
 and CSAs with below median average contact rates;
 and provides analogous conclusions.
\end_layout

\end_inset

 We next turn to examining which observable factors help explain the variation in the estimated CSA fixed effects.
\end_layout

\begin_layout Standard
To examine the determinants of these fixed differences across CSAs,
 we first perform the descriptive exercise of regressing the CSA fixed effects 
\begin_inset Formula $\theta_{i}$
\end_inset

 on CSA-level covariates using OLS.
 Panel A of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:determinants_fe"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 shows the standardized coefficient estimates from univariate regressions.
 Panel B of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:determinants_fe"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 shows the corresponding coefficients when controlling for log population.
 While many variables were significant predictors in the univariate regressions,
 only racial composition (share Black,
 Asian,
 and Other) and partisanship (Republican vote share) were significant predictors after controlling for log population.
\end_layout

\begin_layout Standard
Next,
 we formalize the prediction exercise using the full set of covariates and lasso to select and penalize coefficients.
\begin_inset Foot
status open

\begin_layout Plain Layout
We exclude the log number of tests as of April 30th from the lasso exercise for endogeneity reasons.
\end_layout

\end_inset

 We choose the lasso penalty to maximize out-of-sample fit in a 10-fold cross-validation without using population weights.
 Lasso selects variables that cover population (log population and log population density),
 racial composition (share Black and Other),
 and partisanship (Republican vote share).
\begin_inset Foot
status open

\begin_layout Plain Layout
This analysis of the strongest predictors of differences in contact rates across geographies might help to identify the most critical characteristics to incorporate into heterogeneous SIR models (see Ellison 2024 for detail regarding these models).
\end_layout

\end_inset

 Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:scatter_fit"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 shows the fit of the predicted fixed effects from the lasso regression and the estimated fixed effects 
\begin_inset Formula $\hat{\theta}_{i}$
\end_inset

.
 Overall,
 the model performs well—
accurately predicting the contact rate fixed effect for NYC and other major CSAs but performing less well on smaller CSAs.
\end_layout

\begin_layout Standard
Using the lasso estimates,
 we return to the additive decomposition in Table 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:add_decomp_table"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

.
 We recompute the log contact rates after equating various subsets of covariates using the estimated coefficients from our lasso model.
 Overall,
 the covariates in our lasso model explained 54.8 percent of the difference between CSAs with above-median case growth and CSAs with below-median case growth.
 The population variables,
 log population and log population density,
 were the primary predictors—
explaining 48.2 percent of the above-below median difference in CSAs by themselves with partisanship explaining smaller shares.
\end_layout

\begin_layout Standard
These results suggest fixed differences across locations played a larger role in explaining differential case growth early on in the pandemic than policy or observed social distancing behaviors.
 Predictors and drivers of temporal or geographic variation later in the pandemic may have been different.
 The 
\begin_inset Formula $S=N$
\end_inset

 assumption was also less tenable during later periods in the pandemic as the recovered population grew—
thus,
 complicating an analysis of this later period.
\end_layout

\begin_layout Subsection
Counterfactuals
\begin_inset CommandInset label
LatexCommand label
name "subsec:Counterfactuals"

\end_inset


\end_layout

\begin_layout Standard
Lastly,
 we conduct several counterfactual exercises.
 Our exercises take the form of constructing alternate sequences of contact rates 
\begin_inset Formula $\{\beta_{ik}\}_{k=0}^{t}$
\end_inset

 and using the SIRD model outlined above to compute counterfactual cases given observed initial conditions 
\begin_inset Formula $I_{0}=C_{0}$
\end_inset

.
\begin_inset Foot
status open

\begin_layout Plain Layout
We restrict 
\begin_inset Formula $\beta_{ik}\geq\frac{1}{1,000,000}$
\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
In Panel C of Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:decomp_plot"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

,
 we compute various counterfactual contact rate sequences 
\begin_inset Formula $\{\beta_{ik}^{c}\}_{k=0}^{t}$
\end_inset

 and examine how these alternative sequences would have shaped the evolution of total cases in our sample.
 Assuming a proportional impact of stay-at-home orders on social distancing behaviors as estimated in Section 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:mobility-econ"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

,
 a uniform stay-at-home order implemented on March 17 (when the San Francisco Bay Area implemented their stay-at-home order) would have resulted in 154,000 fewer cases by April 30th,
 or a 19.5 percent reduction in cases.
\begin_inset Foot
status open

\begin_layout Plain Layout
To implement,
 we counterfactually reduce the log of POI visits by .178 after March 17 for CSAs not under an order at that time.
\end_layout

\end_inset

 If,
 instead,
 we assume that stay-at-home orders caused social distancing behaviors to fall to a fixed level at 35 percent of baseline levels,
 a uniform stay-at-home order implemented on March 17 would have resulted in 494,000 fewer cases,
 or a 62.5 percent reduction in cases.
 If all CSAs followed the social distancing behaviors of the counties in the San Francisco Bay Area that were the first to initiate stay-at-home orders,
 there would have been 349,000 fewer cases in our sample,
 or a 44.1 percent reduction.
 Lastly,
 removing the proportional effect of all policy would have resulted in 494,000 more cases,
 or a 62.4 percent increase in cases.
\end_layout

\begin_layout Standard
While policy explains a small proportion of the temporal or geographic variation in case growth,
 policy still has led to a non-trivial reduction in cases over time.
 As of September 4,
 2020,
 the observed case fatality rate in the United States was 3 percent.
\begin_inset Foot
status open

\begin_layout Plain Layout
See https://coronavirus.jhu.edu/data/mortality accessed on September 4,
 2020.
\end_layout

\end_inset

 Based on this observed case fatality rate,
 the stay-at-home policies saved 14,800 lives while a further 10,500 lives could have been saved if all CSAs followed the social distancing behavior of the counties in the San Francisco Bay Area that were the first to initiate stay-at-home orders during the initial period of the pandemic.
\end_layout

\begin_layout Standard
This counterfactual analysis comes with three important caveats.
 First,
 we have assumed that there were no spillover effects from stay-at-home orders to geographies outside of the implementing CSA,
 as we do not have information on the matrix of potential cross-CSA spillovers.
 While this limitation is mitigated by our use of CSAs (which combine areas with significant cross-geography employment),
 if stay-at-home orders reduced contact rates in other geographies,
 then our counterfactuals are likely to underestimate the impacts of counterfactual policies.
 A second key limitation of our analysis is that the wide confidence intervals in our estimated impacts on health outcomes (see Section 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:health"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) similarly lead to significant imprecision in our health counterfactuals.
 Finally,
 our analysis assumes that stay-at-home orders cause a proportional reduction in the log of POI visits that is uniform across geographies and time periods.
 While Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:te_heterogeneity"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 Panel A provides empirical support for the assumption of uniform effects across different implementation dates during this period,
 it is plausible that effects may be heterogeneous across geographies.
 The existing literature provides mixes evidence regarding potential heterogeneity.
 Painter and Qui (2021) estimate that stay-at-home orders have larger effects on mobility in Democratic counties (which were more likely to implement these orders) than in Republican counties.
 If observed stay-at-home orders are positively selected on their potentially heterogeneous treatment effects,
 this would lead our counterfactuals to overestimate magnitudes from implementing these policies in geographies that did not in fact issue such orders.
\begin_inset Foot
status open

\begin_layout Plain Layout
We thank an anonymous referee for contributing this point and suggesting heterogeneity tests.
\end_layout

\end_inset

 In contrast and consistent with our homogeneity assumption,
 Alexander and Karger (2023) estimate fairly uniform responses to stay-at home orders across the country (including by county-level political leanings,
 and particularly after controlling for differences in the timing of stay-at-home orders).
 In Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:te_heterogeneity"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

 Panel B,
 we estimate similar impacts on mobility in majority Democrat vs.
\begin_inset space \space{}
\end_inset

majority Republican CSAs.
\begin_inset Foot
status open

\begin_layout Plain Layout
Estimated treatment effect magnitudes are slightly larger in majority Democrat CSAs,
 but this difference is not statistically significant at standard significance levels for the day following the implementation of the stay-at-home order.
\end_layout

\end_inset


\end_layout

\begin_layout Section
Conclusion
\end_layout

\begin_layout Standard
We use event studies and a model-driven regression framework to provide new decompositions on the role of policy in driving the spatial and temporal variation in case transmission during the early months of the COVID-19 pandemic.
 We find that policy was responsible for roughly 13 percent of the change in virus contact rates between early March and mid-April 2020.
\begin_inset Foot
status open

\begin_layout Plain Layout
This finding is consistent with a growing consensus that most social distancing during this time period was voluntary rather than policy-driven (e.g.,
 Goolsbee and Syverson 2021),
 and further extends this analysis to quantify impacts on subsequent health outcomes.
\end_layout

\end_inset

 Moreover,
 policy explained little-to-none of the differences in average contact rates between CSAs with high- and low-contact rates;
 in other words,
 policy and social distancing choices were not the primary reason that areas like New York City experienced relatively severe outbreaks during the early pandemic period.
 Rather,
 the most important predictors of which cities were hardest hit by the pandemic were exogenous characteristics such as population and density.
\end_layout

\begin_layout Standard
These results inform the debate about the role policy played in the initial months of the COVID pandemic.
 While our results suggest that policy explained a small proportion of the overall spatial and temporal variation,
 this does not mean that (a) policy was inefficient or (b) policy was not important.
 We find evidence that policy was no less costly in the short-run than voluntary social distancing behaviors.
 Additionally,
 our counterfactual estimates suggest a uniform stay-at-home policy implemented on March 17th would have resulted in a 20 percent reduction in cases by April 30th.
\end_layout

\begin_layout Standard
The empirical strategy that we have developed can similarly be used to study potential future pandemics,
 as researchers can use this methodology to rapidly identify the causal effects of policy and voluntary responses,
 and to analyze the drivers of initial outbreaks.
\end_layout

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References
\end_layout

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\begin_layout Standard
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\end_layout

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target "http://www.climatologylab.org/gridmet.html"
literal "false"

\end_inset

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target "https://institute.jpmorganchase.com/institute/research/household-income-spending/initial-household-spending-response-to-covid-19"
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target "https://www.theguardian.com/commentisfree/2020/may/20/andrew-cuomo-new-york-coronavirus-catastrophe"
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\emph on
Proceedings of the Royal Society of London.
 Series A,
 Containing Papers of a Mathematical and Physical Character
\emph default
.
 115(772):
 700–721.
\end_layout

\begin_layout Standard
Knittel,
 Christopher R.,
 and Bora Ozaltun.
 2020.
 What does and does not correlate with COVID-19 death rates.
 
\emph on
NBER Working Paper 27391.
\end_layout

\begin_layout Standard
Kong,
 Edward,
 and Daniel Prinz.
 2020.
 The impact of non-pharmaceutical interventions on unemployment during a pandemic.
 
\emph on
Journal of Public Economics
\emph default
.
 189.
 104257.
\end_layout

\begin_layout Standard
Kuchler,
 Theresa,
 Dominic Russel,
 and Johannes Stroebel.
 2022.
 JUE Insight:
 The geographic spread of COVID-19 correlates with the structure of social networks as measured by Facebook.
 
\emph on
Journal of Urban Economics.

\emph default
 127:
 103314.
\end_layout

\begin_layout Standard
Lasry,
 Arielle,
 Daniel Kidder,
 Marisa Hast,
 Jason Poovey,
 Gregory Sunshine,
 Nicole Zviedrite,
 Faruque Ahmed,
 and Kathleen A.
 Ethier.
 2020.
 Timing of community mitigation and changes in reported COVID-19 and community mobility―four US metropolitan areas,
 February 26–April 1,
 2020.

\emph on
 CDC Morbidity and Mortality Weekly Report.
 
\emph default
69:
 451-457.
\end_layout

\begin_layout Standard
Lin,
 Zhixian and Christopher M.
 Meissner.
 2020.
 Health vs.
\begin_inset space \space{}
\end_inset

wealth?
 Public health policies and the economy during COVID-19.
 
\emph on
NBER Working Paper 27099.
\end_layout

\begin_layout Standard
Mervosh,
 Sarah,
 Denise Lu,
 and Vanessa Swales.
 2020a.
 See which states and cities have told residents to stay at home.
 
\emph on
The New York Times.

\emph default
 Accessed at 
\begin_inset CommandInset href
LatexCommand href
target "https://www.nytimes.com/interactive/2020/us/coronavirus-stay-at-home-order.html"
literal "false"

\end_inset

.
\end_layout

\begin_layout Standard
Mervosh,
 Sarah,
 Jasmine C.
 Lee,
 Lazaro Gamio,
 and Nadja Popovich.
 2020b.
 See how all 50 states are reopening.
 
\emph on
The New York Times.
 
\emph default
Accessed at 
\begin_inset CommandInset href
LatexCommand href
target "https://www.nytimes.com/interactive/2020/us/states-reopen-map-coronavirus.html"
literal "false"

\end_inset

.
\end_layout

\begin_layout Standard
MIT Election Data and Science Lab.
 2018.
 County presidential election returns 2000-2016.
 Harvard Dataverse.
 https://doi.org/10.7910/DVN/VOQCHQ.
\end_layout

\begin_layout Standard
Olive,
 Xavier.
 2019.
 Traffic,
 a toolbox for processing and analysing air traffic data.
 
\emph on
Journal of Open Source Software.

\emph default
 4(39).
\end_layout

\begin_layout Standard
Painter,
 Marcus,
 and Tian Qiu.
 2021.
 Political beliefs affect compliance with COVID-19 social distancing orders.

\emph on
 Journal of Economic Behavior & Organization.
 
\emph default
185:
 688–701.
\end_layout

\begin_layout Standard
\align block
Rachel,
 Lukasz.
 2024.
 The second wave.
 
\emph on
Review of Economic Design.

\emph default
 Forthcoming.
\end_layout

\begin_layout Standard
Schäfer,
 Matthias,
 Martin Strohmeier,
 Vincent Lenders,
 Ivan Martinovic,
 and Matthias Wilhelm.
 2014.
 Bringing up OpenSky:
 A large-scale ADS-B sensor network for research.
 
\emph on
Proceedings of the 13th IEEE/ACM International Symposium on Information Processing in Sensor Networks.
 
\emph default
83–94.
\end_layout

\begin_layout Standard
Sears,
 James,
 J.
 Miguel Villas-Boas,
 Sofia Berto Villas-Boas,and Vasco Villas-Boas.
 2023.
 Are we #stayinghome to flatten the curve?
 
\emph on
American Journal of Health Economics
\emph default
 9(1):
 71-95
\emph on
.
\end_layout

\begin_layout Standard
Thompson,
 Kimberly M.,
 Mark A.
 Pallansch,
 Radboud J.
 Duintjer Tebbens,
 Steve G.
 Wassilak,
 Jong‐Hoon Kim,
 and Stephen L.
 Cochi.
 2013.
 Preeradication vaccine policy options for poliovirus infection and disease control.
 
\emph on
Risk Analysis.

\emph default
 33(4):
 516–543.
\end_layout

\begin_layout Standard
Vissat,
 Ludovica Luisa,
 Nir Horvitz,
 Rachael V.
 Phillips,
 Zhongqi Miao,
 Whitney Mgbara,
 Yue You,
 Richard Salter,
 Alan E.
 Hubbard,
 and Wayne M.
 Getz.
 2022.
 A comparison of COVID-19 outbreaks across US Combined Statistical Areas using new methods for estimating R0 and social distancing behaviour.
 
\emph on
Epidemics
\emph default
.
 41:
 100640.
\end_layout

\begin_layout Standard
Wallace,
 Jacob,
 Paul Goldsmith-Pinkham,
 and Jason L.
 Schwartz.
 2023.
 Excess death rates for republican and democratic registered voters in Florida and Ohio during the COVID-19 pandemic.
 
\emph on
JAMA Internal Medicine.
\emph default
183(9):
 916-923.
\end_layout

\begin_layout Standard
Wu,
 Xiao,
 Rachel C.
 Nethery,
 Benjamin M.
 Sabath,
 Danielle Braun,
 and Francesca Dominici.
 2020.
 Air pollution and COVID-19 mortality in the United States:
 Strengths and limitations of an ecological regression analysis.
 
\shape italic
Science Advances.
 
\emph on
6(45):
 eabd4049.
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
parindent=2em
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\begin_layout Plain Layout


\backslash
leftskip=0em
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage pagebreak
\end_inset


\end_layout

\begin_layout Standard
\begin_inset CommandInset include
LatexCommand include
filename "figures.lyx"
literal "true"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset CommandInset include
LatexCommand include
filename "../output/health_reg_table_filled.lyx"
literal "true"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset CommandInset include
LatexCommand include
filename "../output/add_decomp_table_filled.lyx"
literal "true"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage pagebreak
\end_inset


\end_layout

\begin_layout Section
\start_of_appendix
Appendix
\begin_inset CommandInset label
LatexCommand label
name "sec:appendix"

\end_inset


\end_layout

\begin_layout Standard
See the replication code for exact details on data construction and estimation.
\end_layout

\begin_layout Subsection
Data Construction Procedures
\begin_inset CommandInset label
LatexCommand label
name "subsec:data_appendix"

\end_inset


\end_layout

\begin_layout Standard
We construct the datasets used in our analysis as follows.
\end_layout

\begin_layout Enumerate
We begin by matching SafeGraph POIs to the counties in which they are located.
 We use latitude and longitude from SafeGraph's August 2020 Core POI dataset,
 along with the 2010 TIGER county shapefile.
\begin_inset Foot
status open

\begin_layout Plain Layout
Downloaded from 
\begin_inset CommandInset href
LatexCommand href
name "https://www.census.gov/geo/maps-data/data/cbf/cbf_counties.html"
target "https://www.census.gov/geo/maps-data/data/cbf/cbf_counties.html"
literal "false"

\end_inset

 on July 24,
 2018.
\end_layout

\end_inset

 We successfully assign 99.9 percent of the POIs to a county.
\end_layout

\begin_layout Enumerate
We then merge the POI-county mapping from (1) onto SafeGraph's Patterns data using the safegraph-place-id variable.
 We sum visits by county for a given day,
 aggregating across POIs.
 Our SafeGraph series ranges from January 1,
 2020 to August 30,
 2020.
\end_layout

\begin_layout Enumerate
We then merge onto the output from (2) a dataset of county-level demographic information constructed as follows.
 We use the Open Census data from SafeGraph,
 aggregating up the data given at the census block group level to the county level.
 We combine this with data on county 2016 Presidential votes shares (MIT Election Data and Science Lab 2018).
 We define the Republican vote share to be the share of votes received by the Republican candidate over the sum of votes across all candidates.
 We exclude counties without valid vote data,
 which drops Alaska and two additional counties (FIPS:
 15005,
 51515).
 We also merge on the urban population share from the 2010 Census.
\begin_inset Foot
status open

\begin_layout Plain Layout
Downloaded from 
\begin_inset CommandInset href
LatexCommand href
name "https://www.census.gov/programs-surveys/geography/technical-documentation/records-layout/2010-urban-lists-record-layout.html"
target "https://www.census.gov/programs-surveys/geography/technical-documentation/records-layout/2010-urban-lists-record-layout.html"
literal "false"

\end_inset

 on June 25,
 2020.
\end_layout

\end_inset

 We also use average seasonal temperatures by geography from Wu et al.
 (2020),
 which is ultimately sourced from gridMET.
 Averages for a given county and season are taken across the years 2010-2016.
\begin_inset Note Note
status open

\begin_layout Plain Layout
Weather data was not available for Hawaii,
 so this particular state is dropped in regressions including weather controls.
 [HI isn't assigned a CSA and we don't use weather for our county-level analysis,
 so this doesn't matter right now.]
\end_layout

\end_inset


\end_layout

\begin_layout Enumerate
We then merge onto the output from (3) the number of incoming international flights for each US county from December 2019 to February 2020 made available by the OpenSky Network (Schäfer et al.
 2014;
 Olive 2019).
\end_layout

\begin_layout Enumerate
We then merge data on Covid-19 health outcomes onto the output from (4).
 We source confirmed Covid-19 cases and deaths by county and day from The New York Times.
 We assume zero cases and deaths for the observations not observed in The New York Times data.
 We drop the four counties which overlap with Kansas City (MO),
 because The New York Times lists these as geographic exceptions where it either does not assign cases to these counties or excludes cases occurring within the city.
 For the five boroughs of New York City,
 we assign cases and deaths based on their population share.
 We also merge data on testing and hospitalizations from the Covid Tracking Project by state and day.
\end_layout

\begin_layout Enumerate
We then merge a dataset of county-level shelter-in-place and business closure order start dates onto the output from (5) and construct an indicator for whether a county had been subject to a shelter-in-place and/or business closure order by a given date.
 It is ultimately sourced from The New York Times,
 Keystone Strategy,
 a crowdsourcing effort from Stanford University and the University of Virginia,
 and Hikma Health.
 The New York Times has been tracking 
\begin_inset Quotes eld
\end_inset

shelter-in-place
\begin_inset Quotes erd
\end_inset

,
 
\begin_inset Quotes eld
\end_inset

stay-at-home
\begin_inset Quotes erd
\end_inset

,
 
\begin_inset Quotes eld
\end_inset

healthy-at-home
\begin_inset Quotes erd
\end_inset

,
 etc.
 policies enacted at the city,
 county and state level (Mervosh et al.
 2020a).
 We use the dates reported by the NYT for our stay-at-home policy.
 The relevant NPIs from Keystone's data are shelter-in-place (SIP) and closure of public venues (CPV) policies.
 Keystone considers an 
\begin_inset Quotes eld
\end_inset

order indicating that people should shelter in their homes except for essential reasons
\begin_inset Quotes erd
\end_inset

 as a SIP intervention and a 
\begin_inset Quotes eld
\end_inset

government order closing gathering venues for in-person service
\begin_inset Quotes erd
\end_inset

 as a CPV intervention.
 We will use Keystone's SIP and CPV dates for our stay-at-home and business closure policies respectively.
 The crowdsourced data collected by a group from Stanford and University of Virginia solicits policy and personal information from survey participants in an online form.
 We use the 
\begin_inset Quotes eld
\end_inset

lockdown
\begin_inset Quotes erd
\end_inset

 and 
\begin_inset Quotes eld
\end_inset

business closed
\begin_inset Quotes erd
\end_inset

 dates for counties from this data.
 Hikma Health,
 a non-profit working on data systems and analysis for healthcare providers,
 has carried out their own crowdsourcing effort to document NPIs.
 We use the county 
\begin_inset Quotes eld
\end_inset

shelter date
\begin_inset Quotes erd
\end_inset

 and 
\begin_inset Quotes eld
\end_inset

work date
\begin_inset Quotes erd
\end_inset

 from Hikma Health in our construction of stay-at-home and business closure policies respectively.
 Given that none of the sources have entirely overlapping policy data,
 we define both our stay-at-home and business closure policies by sequentially assigning enforcement dates when data is available in the order:
 NYT,
 Keystone,
 Stanford/Virginia crowdsource,
 and Hikma Health.
 Once a state enacts a policy,
 the counties inherit the policy of the state.
 We then merge on a dataset of reopening dates at the state level collected by the NYT (Mervosh et al.
 2020b) and curated by Rearc.
\end_layout

\begin_layout Enumerate
We then merge debit card transactions and spending totals from Facteus onto the output from (6).
 Prior to this merge,
 Facteus data is aggregated from the zip code to the county level using a 5-digit zip code to county crosswalk.
\begin_inset Foot
status open

\begin_layout Plain Layout
Downloaded from HUD (
\begin_inset CommandInset href
LatexCommand href
target "https://www.huduser.gov/portal/datasets/usps_crosswalk.html"

\end_inset

) on April 12,
 2020
\end_layout

\end_inset

 Facteus data ranges from Jan 1,
 2020 to August 27,
 2020,
 with missing data on August 7,
 2020.
\end_layout

\begin_layout Enumerate
We then merge employment data from Homebase onto the output from (7).
 Homebase data is aggregated to the county-day level prior to this merge.
 This step completes the construction of the dataset used in our county-level analysis.
 Homebase data ranges from Jan 1,
 2020 to August 31,
 2020.
\end_layout

\begin_layout Enumerate
For analysis at the level of a CSA,
 order date,
 and day,
 we then aggregate the output from (8) to this level.
 We use a county to CSA crosswalk.
\begin_inset Foot
status open

\begin_layout Plain Layout
Downloaded on May 29,
 2020 from the NBER (
\begin_inset CommandInset href
LatexCommand href
target "http://data.nber.org/cbsa-csa-fips-county-crosswalk/cbsa2fipsxw.csv"

\end_inset

),
 which uses delineation files originally sourced from the Census
\end_layout

\end_inset

 We sum countable variables such as POI visits or Covid-19 cases.
 For other variables,
 we take a population-weighted average across counties in a CSA-day with the same social distancing policy start date.
 In our CSA-level analysis,
 we exclude counties not assigned to a CSA.
\end_layout

\begin_layout Standard
CSAs consist of groups of counties that have significant commuting ties across counties within the group.
 More precisely (per 
\begin_inset CommandInset href
LatexCommand href
target "https://www.census.gov/programs-surveys/metro-micro/about/glossary.html"
literal "false"

\end_inset

),
 each CSA consists of two or more adjacent core based statistical areas (CBSAs) that have an employment interchange measure of 15 or more.
 CBSAs in turn consist of the county or counties (or equivalent entities) associated with at least one core (urban area) of at least 10,000 population,
 plus adjacent counties having a high degree of social and economic integration with the core as measured through commuting ties.
 Employment interchange is defined as the sum of the percentage of workers living in the smaller entity who work in the larger entity and the percentage of employment in the smaller entity that is accounted for by workers who reside in the larger entity.
 We use CSAs as our unit of analysis in order to partially capture policy and health spillovers across geographies that have significant commuting ties,
 to avoid instances in which the log of new COVID-19 cases is undefined at the county level,
 and to focus our analysis on metropolitan and micropolitan areas (excluding particularly rural areas that likely had more limited COVID-19 testing capacity).
 This differs from the focus on county-level analysis in much of the existing literature,
 with Vissat et al.
\begin_inset space \space{}
\end_inset

(2022) being one exception that also analyzes variation across CSAs (without analyzing causal effects or incorporating data on policy and social distancing).
 80 percent of the US population resided within CSAs as of April 1,
 2020,
 per data from the US Census (
\begin_inset CommandInset href
LatexCommand href
target "https://www2.census.gov/programs-surveys/popest/tables/2020-2023/metro/totals/csa-est2023-pop.xlsx"
literal "false"

\end_inset

,
 downloaded on August 20,
 2024).
\begin_inset Note Note
status open

\begin_layout Plain Layout
Source:
 https://www2.census.gov/programs-surveys/popest/tables/2020-2023/metro/totals/csa-est2023-pop.xlsx from https://www.census.gov/data/tables/time-series/demo/popest/2020s-total-metro-and-micro-statistical-areas.html
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
SIRD Simulations and Estimation Details
\begin_inset CommandInset label
LatexCommand label
name "subsec:simulations"

\end_inset


\end_layout

\begin_layout Subsubsection
Simulation
\end_layout

\begin_layout Standard
To generate data from an SIRD data generating process,
 we assume a death rate 
\begin_inset Formula $\kappa=.008$
\end_inset

 and an average infectious period of 10 days (
\begin_inset Formula $\gamma=.1$
\end_inset

).
 We assume 
\begin_inset Formula $\beta_{it}$
\end_inset

 evolves as 
\begin_inset Formula $\beta_{it}=\gamma(\mathcal{R}_{i0}e^{\lambda_{i}t}+\mathcal{R}_{1}(1-e^{\lambda_{i}t}))\times(1+\tau T_{it})$
\end_inset

 where 
\begin_inset Formula $\mathcal{R}_{i0}$
\end_inset

 is drawn from a normal distribution with mean 2.4 and standard deviation 0.1,
 
\begin_inset Formula $\mathcal{R}_{1}=.95$
\end_inset

,
 
\begin_inset Formula $\tau$
\end_inset

 is either 0 or -0.1 depending on the simulation,
 
\begin_inset Formula $T_{it}$
\end_inset

 is drawn from a binomial distribution with size 150 and probability 4/15,
 and 
\begin_inset Formula $\lambda$
\end_inset

 is drawn from a normal distribution with mean 
\begin_inset Formula $-0.08$
\end_inset

 and standard deviation 
\begin_inset Formula $0.01.$
\end_inset

 The exponential decay process for 
\begin_inset Formula $\beta_{t}$
\end_inset

 follows Fernández-Villaverde and Jones (2022).
 The initial share of the population infected is drawn from an exponential distribution with rate 
\begin_inset Formula $10,000$
\end_inset

.
 The size of the population is drawn from an exponential distribution with rate 
\begin_inset Formula $1/100,000$
\end_inset

.
\end_layout

\begin_layout Standard
We then follow the laws of motion outlined in the main text,
 updating 
\begin_inset Formula $\beta_{t}$
\end_inset

 each period.
 Note that in constructing the simulations,
 we do 
\emph on
not 
\emph default
use the 
\begin_inset Formula $S/N\approx1$
\end_inset

 assumption but simulate data from the complete model.
 We simulate data for 200 geographies with 150 time periods.
 We then follow the estimation process outlined in the main text and assume that 
\begin_inset Formula $\gamma$
\end_inset

 is the true value used in simulations.
 We drop the event window indicator in equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:event-study-1"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) when including geography fixed effects.
 We also show robustness to incorrectly specifying 
\begin_inset Formula $\tau$
\end_inset

 as half its true value and twice its true value.
\end_layout

\begin_layout Subsubsection
Dave et al.
 (2021)
\end_layout

\begin_layout Standard
Dave et al.
 (2021;
 Figure 4) use an event-study specification with the log of confirmed cases on the left-hand side and geography-specific linear time trends,
 e.g.,
\begin_inset Formula 
\begin{equation}
\log(C_{it})=\mu_{i}+\mu_{i}\times t+\delta_{t}+\sum_{k=-7,k\not=-1}^{k=21}\omega_{k}{\bf 1}_{\{t-T_{i}=k\}}+\epsilon_{it}\label{eq:dave_et_al}
\end{equation}

\end_inset

where 
\begin_inset Formula $\log(C_{it})$
\end_inset

 is the log of confirmed cases in geography 
\begin_inset Formula $i$
\end_inset

 during time 
\begin_inset Formula $t$
\end_inset

,
 
\begin_inset Formula $\mu_{i}$
\end_inset

 is a geography fixed effect,
 
\begin_inset Formula $\delta_{t}$
\end_inset

 is a date fixed effect,
 
\begin_inset Formula ${\bf 1}_{\{t-T_{i}=k\}}$
\end_inset

 is an indicator for the days relative to the first stay-at-home order 
\begin_inset Formula $T_{i}$
\end_inset

,
 and 
\begin_inset Formula $\mu_{i}\times t$
\end_inset

 is a geography-specific linear time trend.
\begin_inset Foot
status open

\begin_layout Plain Layout
In their event-study specification,
 Dave et al.
 (2021) aggregate multiple post-treatment periods into a single treatment effect and include other control variables.
\end_layout

\end_inset

 Following Dave et al.
 (2021),
 we exclude data after April 20,
 2020.
\end_layout

\begin_layout Subsubsection
Estimation Details
\end_layout

\begin_layout Standard
To implement our SIRD estimator,
 we proceed as follows:
\end_layout

\begin_layout Enumerate
We assume zero cases in counties for which none have been reported,
 aggregate county data to the CSA-order timing level (subsequently 
\begin_inset Quotes eld
\end_inset

CSA
\begin_inset Quotes erd
\end_inset

),
 and constrain cumulative cases to be non-decreasing at the CSA level.
 We then make the following restrictions:
\end_layout

\begin_deeper
\begin_layout Enumerate
CSA-days with at least 10 cases,
\end_layout

\begin_layout Enumerate
CSAs that either never receive a stay-at-home order or are observed at least 8 days prior and 20 days after the implementation of the order,
 and
\end_layout

\begin_layout Enumerate
CSA-days between February 1,
 2020 and April 30,
 2020.
\end_layout

\end_deeper
\begin_layout Enumerate
We set 
\begin_inset Formula $C_{i0}$
\end_inset

 to be the number of confirmed cases during the period in which at least 10 cases are confirmed,
 and we define 
\begin_inset Formula $C_{i0}=I_{i0}$
\end_inset

.
\end_layout

\begin_layout Enumerate
We then use equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:I_t"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) to define the full time path of 
\begin_inset Formula $I_{it}$
\end_inset

 for each geography given 
\begin_inset Formula $\gamma$
\end_inset

.
\end_layout

\begin_layout Enumerate
We then estimate equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:event-study-1"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

),
 using 
\begin_inset Formula $\log(\frac{1}{2}+C_{t+1}-C_{t})$
\end_inset

 to avoid taking log of zero when no new cases are observed.
\end_layout

\begin_layout Subsubsection
Other Methods of Estimation in the Literature
\end_layout

\begin_layout Standard
Several previous attempts at estimating the effect of stay-at-home orders have not been model-driven.
 For example,
 Dave et al.
 (2021) use the log of confirmed cases as the outcome in an event-study framework with state-specific linear trends.
\begin_inset Foot
status open

\begin_layout Plain Layout
Friedson et al.
 (2021) use a synthetic control estimator with log cases on the left-hand side to estimate the effect of California's stay-at-home order.
 Lin and Meissner (2020),
 Fowler et al.
 (2021),
 and Courtemanche et al.
 (2020) use various difference-in-difference specifications with 
\begin_inset Formula $\log(C_{i,t+1})-\log(C_{it})$
\end_inset

 on the left-hand side,
 which gives 
\begin_inset Formula $\log(C_{i,t+1})-\log(C_{it})=\log(\beta_{it}I_{it}+C_{it})-\log(\beta_{i,t-1}I_{i,t-1}+C_{i,t-1})$
\end_inset

.
 Lin and Meissner (2020) also perform a matching exercise of counties across state borders.
 Given the nonlinear dynamics of the SIRD model,
 synthetic control or matching estimates may perform better when the model structure is not accounted for parametrically.
\end_layout

\end_inset

 These estimators can produce unexpected results when the data comes from an SIRD data-generating process.
\end_layout

\begin_layout Standard
In Appendix Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:dave_et_al"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

,
 we show that the Dave et al.
 (2021) estimator exhibits substantial pretrends and fails to recover the estimated treatment effect when estimated on simulated data.
 We also apply the estimator to real,
 state-level data as in Dave et al (2021).
 We qualitatively replicate their results when using the 7-day pre-period event window.
 When using a more complete 14-day or 21-day pre-period event window,
 the estimator produces null results with substantial pretrends—
mirroring the estimates from this estimator when using data simulated from an SIRD model.
 To gain intuition for the poor performance of these estimators,
 equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:motion_c"
plural "false"
caps "false"
noprefix "false"
nolink "false"

\end_inset

) implies log cases follow
\begin_inset Formula 
\begin{equation}
\log(C_{i,t+1})=\log(\beta_{it}I_{it}+C_{it}).\label{eq:log_cases}
\end{equation}

\end_inset

Therefore,
 the 
\begin_inset Formula $\omega_{k}$
\end_inset

 coefficients from an event study with log cases on the left-hand side are going to pick up differential trends in a nonlinear function of 
\begin_inset Formula $\beta_{it}$
\end_inset

,
 
\begin_inset Formula $I_{it}$
\end_inset

,
 and 
\begin_inset Formula $C_{it}$
\end_inset

 across treated and non-treated units rather than differential trends in 
\begin_inset Formula $\log(\beta_{it})$
\end_inset

 alone.
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Note that even under the simplifying assumption that 
\begin_inset Formula $C_{it}=I_{it}$
\end_inset

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\begin_inset Formula $\gamma=0$
\end_inset

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 rewriting equation (
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\end_inset

) still gives
\begin_inset Formula 
\[
\log(C_{i,t+1})=\log(1+\beta_{it})+\log(C_{it}).
\]

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