The Great Lockdown and the Big Stimulus: Tracing the Pandemic Possibility Frontier — NBER Working Paper
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NBER Working Paper No. 27794, The Great Lockdown and the Big Stimulus: Tracing the Pandemic Possibility Frontier for the U.S., by Greg Kaplan, Benjamin Moll and Giovanni L. Violante, September 2020. The abstract states that the paper provides a quantitative analysis of trade-offs between health outcomes and the distribution of economic outcomes under alternative policy responses to the COVID-19 pandemic, integrating an expanded SIR model of virus spread into a macroeconomic model with income and wealth inequality. It summarizes the findings through a distributional pandemic possibility frontier and states that the economic welfare costs of the pandemic are large and heterogeneous for all combinations of health and economic policies considered.
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NBER WORKING PAPER SERIES
THE GREAT LOCKDOWN AND THE BIG STIMULUS:
TRACING THE PANDEMIC POSSIBILITY FRONTIER FOR THE U.S.
Greg Kaplan
Benjamin Moll
Giovanni L. Violante
Working Paper 27794
http://www.nber.org/papers/w27794
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
September 2020
We thank Zhiyu Fu and Brian Livingston for outstanding research assistance. We are grateful to
Ralph Luetticke, Ron Milo, Tommaso Porzio, Anna Schrimpf and many (virtual) seminar
participants for their useful comments. We have previously presented a preliminary version of
this paper under the title "Pandemics According to HANK." The views expressed herein are those
of the authors and do not necessarily reflect the views of the National Bureau of Economic
Research.
At least one co-author has disclosed a financial relationship of potential relevance for this
research. Further information is available online at http://www.nber.org/papers/w27794.ack
NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.
© 2020 by Greg Kaplan, Benjamin Moll, and Giovanni L. Violante. All rights reserved. Short
sections of text, not to exceed two paragraphs, may be quoted without explicit permission
provided that full credit, including © notice, is given to the source.
The Great Lockdown and the Big Stimulus: Tracing the Pandemic Possibility Frontier for
the U.S.
Greg Kaplan, Benjamin Moll, and Giovanni L. Violante
NBER Working Paper No. 27794
September 2020
JEL No. E0
ABSTRACT
We provide a quantitative analysis of the trade-offs between health outcomes and the distribution
of economic outcomes associated with alternative policy responses to the COVID-19 pandemic.
We integrate an expanded SIR model of virus spread into a macroeconomic model with realistic
income and wealth inequality, as well as occupational and sectoral heterogeneity. In the model, as
in the data, economic exposure to the pandemic is strongly correlated with financial vulnerability,
leading to very uneven economic losses across the population. We summarize our findings
through a distributional pandemic possibility frontier, which shows the distribution of economic
welfare costs associated with the different aggregate mortality rates arising under alternative
containment and fiscal strategies. For all combinations of health and economic policies we
consider, the economic welfare costs of the pandemic are large and heterogeneous. Thus, the
choice governments face when designing policy is not just between lives and livelihoods, as is
often emphasized, but also over who should bear the burden of the economic costs. We offer a
quantitative framework to evaluate both trade-offs.
Greg Kaplan Giovanni L. Violante
Department of Economics Department of Economics
University of Chicago Princeton University
1126 E 59th St Julis Romo Rabinowitz Building
Chicago, IL 60637 Princeton, NJ 08540
and NBER and NBER
gkaplan@uchicago.edu violante@princeton.edu
Benjamin Moll
London School of Economics
Houghton Street
London WC2A 2AE
United Kingdom
and NBER
b.moll@lse.ac.uk
1 Introduction
The COVID-19 pandemic has fueled a global health and economic crisis of unprecedented
severity. Six months into the pandemic, the death toll in the U.S. is approaching 200,000
and, despite massive fiscal stimulus, we are in the midst of the deepest economic contraction
in modern history. Since person-to-person contact is essential for a substantial fraction of
the U.S economy to function, and since such close contact allows the virus to spread easily,
both fatalities and economic losses are unavoidable.
It is thus not surprising that much of the debate around the appropriate policy response
to the pandemic hinges on one question: how large is the trade-off between saving lives and
preserving livelihoods? Our goal in this paper is to contribute to this debate by quantifying
this trade-off, focusing on the distributional effects of the pandemic and associated policy
responses, across different types of workers and households.
Exposure and vulnerability to the pandemic Our analysis builds on the observation
that those individuals who are most financially exposed to the pandemic are also the most
financially vulnerable.
The key dimension of heterogeneity for economic exposure to the pandemic is occupation.
Workers in occupations that both require social interaction, and have little flexibility to work
remotely (such as waiters, hairdressers, and dentists), have experienced especially large drops
in their earnings. In contrast, the earnings of workers in occupations that produce goods and
services that do not require social interactions, and have high flexibility to work from home
(such as lawyers, academics, and finance professionals) have been left relatively unscathed.
Whether these different labor market experiences translate into differences in economic
welfare depends on households’ financial vulnerability. The key dimensions of heterogeneity
for vulnerability are the size and composition of household balance sheets, eligibility for
government transfers, and the ability to increase labor supply to compensate for the fall in
income. Jointly, these factors explain the extent to which losses in income and wealth due
to the pandemic translate into a fall in consumption and economic welfare.
Using individual and household-level micro data, we document that those individuals who
work in rigid social-intensive occupations tend to have particularly low earnings, wealth and
buffers of liquid assets. On the other hand, workers in flexible occupations with low exposure
to the social sector tend to have higher earnings, robust balance sheets and enough liquid
wealth to weather the storm. This strong positive correlation between economic exposure to
the pandemic and financial vulnerability suggests that the effects of the pandemic have been
extremely unequal across the population. There is thus a great deal of scope for economic
and health policies, with appropriate patterns of redistribution, to both contain the virus
and mitigate the economic losses of the most affected households.
1
Integrated epidemiological and heterogeneous agent macroeconomic model To
evaluate the scope of these possibilities, we integrate an expanded SIR model of virus spread
into a heterogeneous-agent incomplete-markets macroeconomic model, which we calibrate to
epidemiological, clinical, macroeconomic and cross-sectional data for the U.S. economy.
The epidemiological block of the model consists of a SEIR model à la Kermack and
McKendrick (1927) with two additional features: (i) a constraint on ICU (Intensive Care
Unit) capacity, which leads to a higher death rate when violated; (ii) feedback from economic
behavior to the dynamics of the pandemic that makes the transmission rate of the virus
depend endogenously on individual work and consumption choices.
The economic block of the model builds on the heterogeneous-agent incomplete-market
literature. In addition to modeling income risk, wealth and portfolio heterogeneity, we in-
troduce a number of new ingredients that are central to understanding the impact of the
pandemic and policy responses: (i) three types of goods: regular goods, social goods and
home-produced goods; (ii) three types of labor: in the workplace, remote, and home pro-
duction; and (iii) occupations that differ with respect to their flexibility for remote work,
their use in production of regular versus social goods, and how essential they are for pro-
viding critical goods and services. These elements are important for capturing household
heterogeneity in economic exposure to the pandemic and financial vulnerability. Finally, in-
dividuals’ disutility from working in the workplace, and their utility from consuming social
goods, both depend on the extent of the virus. This feature captures voluntary social dis-
tancing behaviors that lead to a fall in economic activity even in the absence of a lockdown.
Pandemic possibility frontier To summarize the trade-offs between health and eco-
nomic outcomes for different policy alternatives, we advocate the use of a distributional
pandemic possibility frontier (PPF). Figure 1 shows an example of a PPF for our baseline
experiments in which we vary the length of a workplace and social sector lockdown, with and
without fiscal support. Different policy scenarios are represented on the frontier with two
cost metrics: (i) deaths due to the virus (horizontal axis), and (ii) economic welfare costs
for those alive (vertical axis).
Most existing analyses of the welfare costs of the pandemic or lockdown policies use
a single number, such as lost GDP or unemployment, as a summary. In contrast, our
heterogeneous agent approach allows us to account for the fact that welfare losses are very
unevenly distributed across the population, by computing individual-specific welfare costs.
We measure these costs as a compensating variation in terms of liquid wealth: the one-time
wealth transfer, expressed as a multiple of each individual’s pre-pandemic monthly income,
that would make them indifferent in terms of economic outcomes between experiencing
the pandemic and associated policy response versus the pre-pandemic steady-state. The
distributional PPF reports not only the average welfare cost for each policy scenario, but
also the dispersion in these costs. For example, the shaded area in Figure 1 shows the 10th
2
10 Mean w/o Fiscal Support
Economic Welfare Cost (Multiples of Monthly Income)
p10-p90 w/o Fiscal Support
Mean w/ Fiscal Support
p10-p90 w/ Fiscal Support
17-M
8 Lockdoonth
wn
12-Month
6 Lockdown
4
US Lockdown
US Policy Laissez
-f aire
2
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Deaths (% of Population)
Figure 1: Pandemic Possibility Frontier summarizing our main results. Laissez-faire: no lockdown
and no fiscal support. U.S. lockdown: lockdown without fiscal stimulus. U.S. policy: lockdown
plus fiscal stimulus. Each point corresponds to lockdowns of different durations.
and 90th percentiles of economic welfare costs, with and without fiscal support
Relative to existing approaches, an important advantage of our frontier is that it allows
for a quantitative comparison of different policy scenarios without taking a stand on the
monetary value of life. Instead, we present policy makers with a menu of policy options that
can be evaluated against subjective indifference curves, and we identify suboptimal policies
that lie on the wrong side of the frontier. One of our objectives is to identify policies that
shift the frontier inward, thus allowing for the same number of fatalities with lower economic
costs, or vice-versa.
Main findings Our first finding is that, for all health and economic policies that we
consider, the economic welfare costs are large and very heterogeneous. For example, the
point labelled “US Lockdown” in Figure 1 shows that with a 2-month lockdown, the average
economic welfare loss is above 3 months of income, and the 90-10 ratio of economic costs
is above 2. Even in the laissez-faire scenario without any lockdown or fiscal intervention
(point labelled “Laissez-faire”), in which fatalities are highest, the average economic costs
of the pandemic are around 2 months of income, also with substantial heterogeneity. This
is because individuals react to rising infections and deaths by endogenously reducing both
social consumption and supply of workplace hours.
With or without a lockdown, the largest welfare costs accrue to households in the middle
of the income distribution. Households at the bottom of the distribution depend largely on
3
government transfers and so are less affected, whereas those at the top of the distribution
mostly work in flexible jobs. However among those in rigid occupations, the identities of
those hit hardest is affected by the lockdown. In the laissez-faire scenario, only workers
in social-intensive occupations suffer large earnings drops, whereas under the workplace
lockdown, the earnings of workers in all occupations are also hit very hard.
Our second finding is that the slope of the PPF varies tremendously with the length
of the lockdown. This finding reconciles conflicting opinions on the existence of a trade-off
between lives and livelihoods, on the basis of different views about where exactly we are
on the frontier. Two features of the pandemic are critical for this non-linearity: limited
ICU capacity and the eventual arrival of a vaccine. The two flatter segments of the frontier
correspond to lockdown durations that either reduce the time for which the ICU capacity
constraint binds (right portion, shorter lockdowns) or avoid a second wave of infections just
before the arrival of the vaccine (left portion, longer lockdowns). The steep section of the
frontier reflects the fact that lockdowns of intermediate durations are unnecessarily long if
the argument is preventing the ICU constraint from binding (flattening the curve) and not
long enough if the argument is preventing a second wave of infections.
Our third finding is that the U.S. fiscal policy response implemented in the Spring of 2020
(CARES Act) succeeded in mitigating economic welfare losses by around 20% on average,
while leaving the cumulative death count effectively unchanged. However, the stimulus
package made the economic consequences of the pandemic more unequal. This is because
the stimulus package redistributed heavily toward low-income households, while middle-
income households gained little from the stimulus package but will face a higher future tax
burden. This redistribution, together with the large fraction of hand-to-mouth households in
the bottom of the income distribution, allows the model to replicate the somewhat puzzling
empirical finding that labor incomes have fallen more for poor households than for rich ones,
and have remained persistently low, while consumption expenditures of the poor initially
fell by the most but then recovered more quickly than those of the rich (Cox et al., 2020;
Chetty et al., 2020).
Our fourth finding concerns alternative policy responses that offer a more favorable trade-
off than blunt lockdowns. We show that exempting workers in social-intensive occupations
from the workplace lockdown leads to lower economic welfare costs for a sizable part of the
population, for a given fatality rate. An even more effective policy is to impose Pigouvian
taxes on social consumption and work in the workplace, with revenues rebated to the work-
ers employed in rigid and social-intensive occupations, respectively. These more targeted
policies all generate a flatter average PPF with a more favorable trade-off between lives and
livelihoods. However, they come at the cost of more unequal economic welfare losses, a fea-
ture which would have to be appropriately managed through fiscal redistribution for these
policies to be feasibly implemented in practice.
4
When tracing the pandemic possibility frontier for the U.S., we focus our attention on
lockdown and fiscal stimulus policies, since these are the health and economic policies that
have actually been implemented in the U.S. on a large scale. Additionally, we consider the
smart policies described in the preceding paragraph. We do not evaluate some alternative
policies that may potentially further flatten or shift inward the PPF, such as contact tracing,
widespread testing, border closures and mandatory quarantines. Quantifying how these
policies affect the trade-offs that we analyze is an important task for future work.
Related literature The literature on the macroeconomic implications of COVID-19 is
already vast and still growing. In existing work, macroeconomists have addressed many
dimensions of the complex interaction between the epidemic and the economy, such as:
basic calculations of the ‘lives vs economy’ trade-off (e.g. Hall et al., 2020); externalities
in individual distancing decisions and socially optimal lockdowns (e.g. Alfaro et al., 2020;
Alvarez et al., 2020; Atkeson, 2020; Eichenbaum et al., 2020; Farboodi et al., 2020; Jones
et al., 2020; Krueger et al., 2020; Moser and Yared, 2020; Piguillem and Shi, 2020; Rachel,
2020; Toxvaerd, 2020); smarter and more targeted policies in alternative to indiscriminate
lockdowns (e.g. Acemoglu et al., 2020; Akbarpour et al., 2020; Alon et al., 2020b; Azzimonti
et al., 2020; Baqaee et al., 2020; Berger et al., 2020; Dorn et al., 2020; Favero et al., 2020;
Glover et al., 2020; Gollier, 2020; Grimm et al., 2020); the relative importance of demand and
supply shocks (e.g. Baqaee and Farhi, 2020; Brinca et al., 2020; Guerrieri et al., 2020); the
long-run implications of the virus for the economy (e.g. Barrero et al., 2020; Kozlowski et al.,
2020); the role of fiscal stimulus and monetary policy (e.g. Bayer et al., 2020; Carroll et al.,
2020; Coibion et al., 2020a; Elenev et al., 2020; Faria e Castro, 2020; Ganong et al., 2020); the
labor market outcomes of different demographic groups (e.g. Adams-Prassl et al., 2020; Alon
et al., 2020a; Bick and Blandin, 2020; Brotherhood et al., 2020; Cajner et al., 2020; Coibion
et al., 2020b; Gregory et al., 2020; Hur, 2020; Mongey et al., 2020); the empirical dynamics
of income and consumption in the aggregate and across the distribution (e.g Carvalho et al.,
2020; Chetty et al., 2020; Cox et al., 2020; Hacioglu et al., 2020).
We discuss specific connections to the literature in the main body of the paper. The rest
of the paper is organized as follows. Section 2 outlines the model. Section 3 describes the
parameterization. Section 4 contains all the model simulations. Section 5 concludes.
2 Model
Our model has two building blocks: an epidemiological block and an economic block. The
epidemiological block consists of a standard compartmental SEIR model à la Kermack and
McKendrick (1927) (see e.g. Hethcote, 2000) with two modifications. First, we introduce an
Intensive Care Unit (ICU) state to capture the possibility that an overwhelmed health care
5
system leads to a higher death rate. Second, we include a two-way feedback between the
dynamics of the pandemic and individual work and consumption choices.
We model households in the tradition of the heterogeneous-agent incomplete-markets
macroeconomics literature. Households face uninsurable idiosyncratic income and health
risks, and can hold both liquid and illiquid assets. This asset structure leads to realistic con-
sumption and saving behavior, including a sizable aggregate marginal propensity to consume
(MPC). Into this relatively standard framework, we introduce some less standard ingredients
that are important for understanding the impact of the pandemic and lockdown policies.
First, households consume three different types of goods: regular goods, social goods
and home-produced goods. The defining feature of social goods is that consuming them
requires social interaction with other individuals. High social interaction translates into
faster transmission of the disease. Examples of social consumption include dining in a
restaurant, going to a movie, and traveling by air.
Second, households can supply three types of labor: market work in the workplace (i.e.
on-site), market work from home (i.e. remote work), and home production. The presence of
these different types of consumption goods and labor services allows us to capture substitu-
tion along these margins in response to the pandemic and lockdown.
Third, households work in different occupations, which differ along three dimensions:
(i) Flexibility: In less flexible occupations, remote hours are a poor substitute for work-
place hours. This introduces a labor supply effect whereby some occupations’ effective
hours of labor fall in response to the pandemic or to lockdowns.
(ii) Sectoral Intensity: Some occupations are primarily employed in the production of
social goods, while others are primarily employed in the production of regular goods.
This introduces a labor demand effect whereby the demand for some occupations’ labor
services falls in response to the pandemic or to lockdowns.
(iii) Essentiality: Workers in some occupations are permitted to continue working on-site
during a lockdown.
The model is set in continuous time and there is no aggregate uncertainty. We focus on
perfect-foresight transitional dynamics that follow the unexpected arrival of various combi-
nations of the pandemic, lockdown and fiscal stimulus policies. In our benchmark we assume
flexible prices. In Appendix A.3 we consider an extension with price rigidities in which a
monetary authority sets the nominal interest rate by operating a monetary policy rule.
2.1 Epidemiological Model
The economy is populated by a continuum of individuals with initial population size N0 = 1.
At any point in time, each individual is in one of five health states. St individuals are
6
susceptible to the disease; Et are exposed, meaning they have contracted the virus but are
not yet infectious (the disease is in the incubation period); It are infectious, meaning these
are active infections that can spread the virus; Ct are critically ill, meaning they are in
intensive care and may ultimately die; and Rt have recovered from the disease. The total
population size is Nt = St + Et + It + Ct + Rt which declines below one when individuals
die of the disease. For future reference, we refer to the vector et = [St , Et , It , Ct , Rt ]T as the
economy’s epidemiological state.
Susceptible individuals contract the virus and become exposed at rate βt It /Nt , where
It /Nt is the population share of infectious individuals. Exposed individuals become infec-
tious at rate λE . Individuals exit the infectious state at rate λI , with one of two outcomes:
with probability χ they become critically ill and require ICU care, and with probability
1 − χ they recover. Critically ill individuals exit the ICU at rate λC , again with one of two
outcomes: with probability P (Ct , Cmax ) they die and with probability 1 − P (Ct , Cmax ) they
recover. Because of the ICU constraint, the death probability out of the C state depends
on the number of critically ill patients Ct and the ICU capacity Cmax (more on this below).
Finally, recovered individuals may become susceptible again at rate λR , which we set to 0.1
We summarize these movements in the following continuous-time transition matrix:
−βt NItt βt NItt
0 0 0
0
−λE λE 0 0
At = 0 0 −λI λI χ λI (1 − χ) . (1)
0 0 0 −λC λC (1 − P (Ct , Cmax ))
λR 0 0 0 −λR
Individual transitions across health states give rise to a system of differential equations
for the economy’s epidemiological state, given by
ėt = AT
t et , et = [St , Et , It , Ct , Rt ]T . (2)
This is the standard system of differential equations of a compartmental model written in
matrix form. For example, the first, second and third equations read
It It
Ṡt = −βt St + λR Rt , Ėt = βt St − λE Et , İt = λE Et − λI It
Nt Nt
Our model features a two-way feedback between economic behavior and the dynamics of
the pandemic. To model the feedback from economic behavior to infections we assume that
1
While we set λR = 0 in most of our exercises, this parameter allows for the possibility of partial, rather
than permanent, immunity.
7
the transmission rate of infections is given by
βt = β(Cst , Lwt , t), (3)
where Cst is aggregate social consumption and Lwt is aggregate workplace hours. The func-
tion β is increasing in its first two arguments. Social consumption and workplace hours
are defined in more detail in the next section. The parameterization of the function β is
described in Section 3. Other recent macroeconomic analyses of the COVID-19 crisis feature
similar reduced-form feedback mechanisms (see e.g. Eichenbaum et al., 2020).
We assume that when the number of critical patients exceeds the fixed ICU capacity
Cmax , the death probability conditional on being critically ill is higher:
P (Ct , Cmax ) = δC + ∆C max {Ct − Cmax , 0} /Ct , (4)
where δC > 0 is the death probability for those patients who have an ICU bed and ∆C ∈
[0, 1 − δC ] is the excess death probability for those patients who do not obtain an ICU bed.
Under these assumptions, COVID-19 deaths evolve as Ḋt = λC Ct P (Ct , Cmax ), where Dt
denotes cumulative deaths. Individuals in all health states are also at risk of death from
other causes, which occurs at the lower Poisson rate δN . Each person dying of other causes
is replaced by a newborn in the susceptible state.2
2.2 Economic Model
Individuals The economy is populated by a continuum of individuals, indexed by their
holdings of liquid assets b, illiquid assets a, idiosyncratic labor productivity z, occupation
j and health status h.3 Labor productivity follows an exogenous Markov process that we
describe in detail in Section 3. At each instant in time t, the state of the economy is the
joint distribution µt (da, db, dz, j, h).
Individuals receive a utility flow U from three types of goods: regular consumption ct
(the numeraire), social consumption st and a home-produced good ht . They also receive a
disutility flow V from supplying three types of labor: work in the workplace `wt , remote work
`rt , and labor input into home production `ht which produces goods one-for-one, ht = `ht .
2
In the current draft we also assume that each person dying of COVID-19 is replaced by a newborn in the
recovered state. This simplifies computations because it leaves the total population size unaffected. While
we do not expect this assumption to affect our conclusions in a quantitatively noticeable fashion (because
even without replacing COVID-19 deaths by newborns, the level of the population would not change much
in absolute terms), we plan to relax this assumption in later drafts.
3
Throughout the text, we use the term individuals to describe the unit at which economic decisions
are made. We also sometimes interchangeably use the term households, particularly when we bring the
model to the data in Section 3. This fuzziness in terminology is due to an inherent tension between the
model’s economic and epidemiological blocks: while households are the more natural units for economic
decision-making, disease transmission occurs at the individual level.
8
U is strictly increasing and strictly concave in its three inputs. V is strictly increasing and
strictly convex. Preferences are time-separable and, conditional on surviving, the future is
discounted at rate ρ ≥ 0:
∞ h i
E0 e−ρt U (ct , υs (Ḋt )st , ht ) − V (υ` (Ḋt )`wt , `rt , `ht ) dt, (5)
0
where the expectation is taken over realizations of idiosyncratic productivity and health
shocks and also takes into account life expectancy in different health states. A healthy
individual faces a baseline death rate δN , whereas a critically ill individual faces death rate
P (Ct , Cmax ) defined in (4). Because of the law of large numbers, and the absence of aggregate
shocks, there is no economy-wide uncertainty.
Both the utility from consuming social goods and the disutility from supplying work in
the workplace depend on the state of the pandemic through the terms υs (Ḋt ) and υ` (Ḋt )
where Ḋt is the excess death rate in the population at time t. This formulation allows us to
capture, in a reduced-form fashion, the behavioral response of individuals to increasing death
rates: as Ḋt rises, the marginal utility of social consumption falls and the marginal disutility
of workplace hours increases. The formulation is therefore conceptually similar to the way
that feedback from pandemic to behavior is modeled in Farboodi et al. (2020), Eichenbaum
et al. (2020) and others. Below we explain how our formulation is closely related to the
calculations of the value of statistical life (VSL), a mapping that helps in parameterizing
this feedback.
Individuals are employed in different occupations, indexed by j ∈ J. Occupations are
imperfect substitutes in production and therefore pay occupation-specific wages wj per ef-
ficiency unit of hours worked. An occupation’s flexibility is denoted by φj ∈ [0, 1], which
describes how much less productive are remote hours than workplace hours in that occu-
pation. The labor income of an individual with average efficiency units z = 1 working in
occupation j equals wtj (`wt + φj `rt ). A fully rigid occupation has φj = 0 and a fully flexible
occupation has φj = 1.
Individuals can save in liquid assets b and illiquid assets a. Assets of type a are illiquid in
the sense that individuals incur a cost for depositing into or withdrawing from their illiquid
account. We use dt to denote an individual’s deposit rate (with dt < 0 corresponding to
withdrawals) and χ(dt , at ) to denote the flow cost of depositing at a rate dt for an individual
with illiquid holdings at . In equilibrium, the presence of the transaction cost implies that the
illiquid asset earns a higher real return than the liquid asset so that rta > rtb . Short positions
are not allowed in either asset.
9
An individual’s asset holdings evolve according to:
ḃt = (1 − τt )wtj zt (`wt + φj `rt ) + rtb bt + Tt − dt − χ(dt , at ) − ct − pst st (6)
ȧt = rta at + dt (7)
bt ≥ 0, at ≥ 0. (8)
Net liquid savings ḃt are given by the individual’s income flow (composed of labor earnings
taxed at rate τt , interest payments on liquid assets, and government transfers Tt ) net of
deposits into (dt > 0) or withdrawals from (dt < 0) the illiquid account, transaction costs
χ(dt , at ), and consumption expenditures ct + pst st . Net illiquid savings ȧt equal interest
payments on illiquid assets plus net deposits from the liquid account dt .
Individuals differ in their health state h which also determines their ability to supply
labor. All individuals other than the critically ill can supply labor. Although individuals are
in one of five true underlying health states S, E, I, C and R, we assume that only critically
ill C individuals know their true health state while others cannot distinguish which of the
four remaining states S, E, I or R they are in. This assumption reduces the individual state
space from five to two, since we only need to keep track of whether individuals are able to
supply labor, which we denote by h = a, or critically ill, h = c.4
Individuals that are able to supply labor (h = a) maximize (5) subject to (6)–(8). They
take as given the dynamics of the pandemic (2), the equilibrium paths for real wages in differ-
ent occupations {wtj }t≥0 , j = 1, ..., J, the real return to liquid assets {rtb }t≥0 , the real return
to illiquid assets {rta }t≥0 , the relative price of social goods {pst }t≥0 and taxes and transfers
{τt , Tt }t≥0 . Critically ill individuals (h = c) solve a different problem that is described in
Appendix A.2. Rather than choosing consumption optimally the government provides them
with fixed amounts of regular and social consumption c and s.
As we explain below, {rtb }t≥0 , {wtj }t≥0 , {rta }t≥0 and {pst }t≥0 are determined by market
clearing conditions for bonds, capital, labor and social goods.
Sectors and occupations There are two production sectors, indexed by i: the regular
consumption sector (i = c) and the social sector (i = s). Intermediate producers in each
sector produce using capital Ki and the labor input of occupation j, Nij :
" σ
# σ−1
X 1
j σ j
σ−1
Yi = Zi Niαi Ki1−αi , Ni = ξi Ni σ
, i = c, s. (9)
j∈J
The sectoral intensity parameters (ξcj , ξsj ) describe the importance of labor from each occu-
pation j for production in each of the two sectors. Importantly, these sectoral intensities
4
One implication of this assumption is that we cannot allow for testing in this version of the model. While
somewhat unrealistic, this assumption drastically simplifies computation of individuals’ economic decisions.
10
Occupation
Type Examples
Essential Nurse, Firefighter, Mail carrier, Subway operator
C-intensive Flexible Economist, Writer, Software developer, Accountant
C-intensive Rigid Carpenter, Electrician, Astronomer, Biologist
S-intensive Flexible Sec. school teacher, Therapist, Property manager
S-intensive Rigid Cook, Waiter, Dancer, Travel guide
Table 1: Examples of different types of 3-digit occupations grouped by their sectoral intensity and
their degree of flexibility (i.e. ability to work remotely). See Section 2.2 for details.
differ across occupations, which implies that some occupations are more intensely employed
in the production of social goods than others. Intermediate producers rent capital at rate
rtk in a competitive capital market and hire labor at wage wtj in competitive labor markets
for each occupations j.
Table 1 clarifies the distinction between the flexibility and the sectoral intensity dimen-
sions of occupational heterogeneity. For example, software developers and accountants are
occupations with high flexibility and low social intensity, because workers in these occupa-
tions can effectively work remotely and are typically employed in sectors that produce goods
whose consumption does not involve much social interaction with other individuals. In our
simulations of the pandemic and lockdown, neither the demand nor supply of labor in these
occupations will be strongly affected. In contrast, waiters and travel guides are occupations
in which workers cannot effectively work from home, and are employed in sectors that pro-
duce social goods. During the pandemic and lockdown, both demand and supply of labor in
these occupations will be strongly affected.
The third dimension of occupational heterogeneity is that some occupations are deemed
essential. Our definition of essential occupations are those which cannot be effectively per-
formed remotely (low flexibility), but are not subject to government-mandated work from
home orders. Examples of essential occupations include nurses and mail carriers. Although
the labor supply of essential occupations is not affected by the lockdown, the pandemic does
induce a moderate fall in labor demand for these occupations because some of them are
intensive in the social sector.5
Monopolistic competition and final goods production In each sector i = c, s, a com-
petitive representative final-goods producer aggregates a continuum of intermediate inputs
5
Examples of essential occupations that have seen a sharp fall in demand include health-care occupations
not directly involved in the hospitalizations caused by the virus, such as dentists and physical therapists.
11
indexed by w € [0, 1]
1 =1
n= ( Vi(w) de) , t=6,8
0
where € > 0 is the elasticity of substitution across goods. Cost minimization implies that
demand for intermediate good w is
. Te 1 *_
Each intermediate good w is produced by a monopolistically competitive producer with
6
production function (9) who takes this demand curve as given.
Investment fund _ Illiquid assets are equity claims on an investment fund. Thus, at every
date t the value of the fund A; equals households’ aggregate stock of illiquid assets f adju.
The investment fund owns the economy’s capital stock AK; and makes the economy’s in-
vestment decision subject to an adjustment cost ®(,), where 1; is the investment rate, i.e.
investment as a fraction of the capital stock. The fund also owns shares of the intermediate
producers in the regular and social goods sectors (Os, O.) that represent claims on the
future stream of monopoly profits Il, in each of the two sectors, 7 = c,s. We denote the
price of these shares by q}.
The investment fund solves the problem
{44,9ct,Ost}edo0
Ay := max | 7 Io reas fc — ty — O(,)| Ky + S (Hin Oin — uo} dt
0
1=C,8
subject to K, = (4—6)K;, with Ko, Oo and O49 given. It follows that the optimal investment
rate 1, satisfies 1+ ’(v,) = q* where gf is the fund’s shadow value of capital; (ii) the value of
the fund is given by A; = qf K, + qOu + @O.; and (iii) the illiquid asset return r? satisfies
the no-arbitrage condition
po Te PU) Fe = Oe) HGF _ Mee + ae _ Use +a
i= = = ;
k
; ; (10)
Cn Or d+
This condition implies that the value of equity in each sector is given by qi = f° ede 4ST, dr
fori=c,s.’
°In equation (9) we ignored dependence of production on w. This is because all intermediate producers
within a sector 7 are symmetric and therefore make the same production and pricing decisions, and so
Y;(w) = Y;,i = c,s. In our baseline model with flexible prices, the only role of monopolistic competition is
that firms charge a positive markup =; over marginal costs. In Appendix A.3 we consider the case with
sticky prices in which case monopolistic competition opens the door to modeling a dynamic price-setting
decision subject to price adjustment costs.
"In Alves et al. (2020) we formally derive equation (10) in a one-sector model. The extension of the proof
12
Government The government is the sole issuer of liquid assets in the economy, which are
real bonds of infinitesimal maturity B?. It faces exogenous expenditures G, and administers
a progressive tax and transfer scheme on individual labor income w?z(é,, + ¢/€,), consisting
of a proportional tax rate 7% and transfers 7; Ya, b, z,h) that can depend on the individual
state. We also allow the government to subsidize wage payments and profits at rates (Guz, Sat)
to capture a potentially important aspect of the fiscal response to the pandemic. The
government intertemporal budget constraint reads:
BE+ (ri sue) f whe [Enu() + 67 2,(-)] din = Ga [TEC d+ S(T + Tha) + 7B. (11)
Lockdowns _ Lockdowns are government executive orders that affect the economy in two
ways.
1. Lockdowns constrain economic activity in the social goods through bans on dining in
and closure of non-essential businesses. We model this component by assuming that
the governments limits utilization of capital, i.e. capacity, in the social sector. Hence
during the lockdown, the production function (9) in the social goods sector becomes
Y, = Z.(ksK,)°NP © with O<K, <1 (12)
where &, measures the degree of capital utilization allowed by the government.
2. Lockdowns also constrain the supply of workplace hours through stay-at-home orders.
We model this component by imposing the additional constraint on household labor
supply
Oo <ni(@,4+0) with O<nKi <1. (13)
where «7 measures the maximum share of work that can be performed in the work-
place.®
The parameters «, and KJ are policy parameters. If k, = Kj = 0 there is a full lockdown:
sector s is shut down completely and on-site work is banned. If 0 < Kz, KJ < 1 the economy
is partially locked down. Denoting essential occupations by 7 = E, we assume that KP = 1
always, meaning that essential occupations can continue to work in the workplace even
during a lockdown. Because we let the virus transmission rate 6, depend on the aggregate
level of social consumption and workplace hours (see equation (3)), both types of lockdown
to two sectors is straightforward, so we omit it.
8An alternative formulation would impose the constraint on the level of workplace hours directly rather
than on the share @, < «}. Both specifications capture the spirit of the stay-at-home orders, but the former
is more computationally tractable.
13
taper the growth of the pandemic.
Our specification implies that lockdowns affect the same behavioral margins as the pan-
demic itself. During the pandemic, individuals voluntarily substitute away from social con-
sumption and workplace hours. During a lockdown, the government forces them to substitute
along the same margins. A distinction is that the lockdown constrains the supply of social
goods whereas voluntary substitution away from social goods lowers the demand for those
goods.
2.3. Equilibrium
Given an initial condition for the pandemic Zp, a lockdown policy { Fist, Ki,} and a path for
fiscal variables {Gi, Ths Swts Sts Te (+) bso
for the pandemic state vector {e;},.9, individual and firm decisions, distributions {/1},59,
t>0°
an equilibrium in this economy is defined as paths
government debt {B7/},.,. and prices such that, at every time t: (i) the state of the pandemic
is determined by the law of motion (2); (ii) individuals and firms maximize their objective
functions taking as given equilibrium prices, taxes, and transfers; (iii) the distribution pu;
satisfies aggregate consistency conditions; (iv) the government budget constraint holds; and
(v) all markets clear.
There are 12 markets in our economy: liquid and illiquid asset markets, the capital mar-
ket, labor markets for the five occupations, goods markets for regular and social consumption
goods, and share markets for the equity of social and regular goods producers.
The liquid asset market clears when
Bi = Bi, (14)
where BY is the stock of outstanding government debt and B? = f bdj, is total individual
holdings of liquid bonds. The capital market clears when capital demand by the two sectors
equals capital supply by the fund
Ka + Ke = Ky.
The markets for stocks of each sector 7 clear when 0, = 1 for 7 = c,s, where we have
normalized the total number of sectoral shares to one. This implies that individuals’ holdings
of illiquid assets A, = f adj equal the value of capital plus the equity value of monopolistic
producers:
A= Gf Ki t+ a +@. (15)
°Note an important difference between the workplace lockdown and the social sector lockdown. Under
the former, those employed in S-intensive flexible occupations (e.g., an event planner or a museum curator)
can work remotely and keep earning their wages. Under the latter, they cannot.
14
The labor market for each occupation clears when
Ni, + Ni, = [Gulab a) + p€,(a,b,z,a))dju, 7 € I (16)
Finally, the markets for regular and social goods clear when
Yu = Cat+l+Gi+ x1, Yor = Cyt. (17)
Here, Cy and C are total consumption expenditures in the two sectors, J; is gross additions
to the capital stock K;, G; is government spending, and the last term reflects transaction
costs, which we interpret as financial services.
3 Parameterization
3.1 Epidemiological Model
In this section we describe our parameter choices for the epidemiological block of the model.
The data that underlies these choices is rapidly evolving, and we plan to make updates as
new information becomes available. Our choices reflect the state of knowledge at the time
of writing in August 2020. The resulting parameter values are summarized in Table 2.
Epidemiological parameters The basic reproduction number Ro(t) := 3;/A; varies over
time in our model because the transmission rate (3; is time-varying (see discussion below).'°
We set the initial basic reproduction to R#"* := Ro(0) = 2.5. This value is based on Liu et all.
(2020), who reviewed 12 studies that estimate the basic reproduction number for COVID-19
and conclude that Ro is likely in the range of 2-3.
Together with the average duration of infection Ting = 1/Az, the initial basic reproduction
rate Rim* determines the dynamics of the infection pool at the onset of the pandemic, when
the behavioral response is still largely absent. From the system of equations for the dynamics
of the pandemic (1) and (2), one obtains:
. . S Rinit —]
inf
where the second approximate equality holds because in the early stages of the pandemic,
10Throughout the paper, we use Ro(t) to refer to what the average number of secondary cases would be if
the entire population were fully susceptible and remained so throughout the epidemic. This is a arguably an
abuse of epidemiological terminology because epidemiologists often reserve Ro to mean the average number
of secondary cases in a fully susceptible population, i.e. our Ro(0). Our terminology is convenient simply
because 6;/; appears frequently in our analysis.
15
Parameter Value
Epidemiological
Average duration of Exposure (latent period) Tat > AB=1/Tat 5.0 days
Average duration of Znfectious Tint > Ar = 1/Tine 4.3 days
Initial basic reproduction number Rint 2.5
Initial transmission rate Bo = Rint [Tint 0.58
Initial condition Io 6.5 x 10-4
Behavioral
Final basic reproduction number Rene 2
Month at which learning starts tirn 4
Speed of learning AB 2
Behavioral elasticities V3 = VR 0.8
Clinical
Pr of exiting Znfectious and becoming Critical x 0.02
Average duration of Critical state Teri > AG = 1/Teri 10 days
Infection fatality rate IFR 0.01
Pr of dying when Critical & C < Cmax Ye 0.33
Pr of dying when Critical & C > Cmax 60 + Ac 1
ICU Capacity / Adult Population Cmax 0.00024
Rate at which Recovered become Susceptible again AR 0
Month at which vaccine arrives tyac 24
Table 2: Parameterization of the epidemiological/clinical block of the model.
the entire population is susceptible S, ~ N;. This equation states that the initial growth
rate of infections is (Rj"* — 1) /Tine- In most countries the initial growth rate of infections in
the first week was around 35%, which implies Ti, = 4.3.'' This estimate is within the ‘best
estimate’ interval of 4-5 days reported in the compendium by Bar-On et al. (2020). The same
authors report ‘best estimates’ for the median latent period (the time between exposure and
becoming infective) between 3 and 4 days. A median of 3.5 days implies Tia, = 1/Ag = 5.
Behavioral parameters The infection transmission rate (3; varies over the course of the
pandemic, because individuals alter their behavior either voluntarily, or due to a lockdown.
As indicated by the arguments of equation (3), we allow for three behavioral channels:
changes in social consumption (C,;), changes in workplace hours (L,,;) and exogenous learn-
ing about best-practice behavior during a pandemic, such as wearing face masks (t). We
assume the following isoelastic functional form for the function B(Cy, Lut, t):
a Cst " Lut "
Br = Br (=) (=) ; (19)
See, for example, https: //www.ft.com/coronavirus-latest, which collects data on the evolution of infec-
tions across countries. The first week is defined as the week after the first 3 cases were officially detected.
16
107 10 Pow
ce}
5 oes og °
2@l0r £ -10
Fa} 2
9) i = 9) i
g -20 4 Over 90% of population 3 20 Over 90% of population
g in lockdown S in lockdown
by =
B30} ° ' -30} | 5
x ® (o}
Oo oc °
= -4o} ° -40 + ol
° Og? £ {os}
-50} Pen GG oP | -50+ %
fe}
-60 1 1 1 1 1 -60 1 1 1 1 1
Feb 18 Mar 03 Mar 17 Mar 31 Apr 14 Apr 28 Feb 18 Mar 03 Mar 17 Mar 31 Apr 14 Apr 28
Date 2020 Date 2020
Figure 2: Percentage decline in mobility for ‘workplace’ (left panel) and ‘retail and recreation’
(right panel) in the US relative to the baseline (median value, for the corresponding day of the
week, during the 5-week period Jan 3 - Feb 6, 2020). These are the empirical proxies for hours
worked in the workplace and expenditures on social good in the model. The circles are the raw
data, the solid fitted lines are 7-day moving averages to filter out seasonality. Source: Google
COVID-19 Community Mobility Reports.
where 6, captures the exogenous reductions in transmission rates through learning about
best-practice behavior. The parameter vg measures the elasticity of the transmission rate to
changes in social consumption and workplace hours.!”
According to Ferguson et al. (2020), shelter-in-place measures can reduce contacts out-
side households by up to 75% under full compliance. Real-time estimates of the effective
reproduction number R,; = Ro(t) x S; = 3;/A; x S; for the U.S. imply reductions of R, of
around two-thirds (with some notable variation across states) after the lockdown was put
in place.'? Since lockdowns were put in place early in the pandemic when S; ~ 1, these
estimates imply a reduction in Ro(t) by a similar amount.
Google COVID-19 Community Mobility Reports offer an indication of the magnitude
of the decline in social consumption and on-site work, as they chart physical movements
between different categories of places, including retail & recreation and workplace.'* These
data, summarized in Figure 2, show that over the period where most U.S. states were under
a full lockdown, activity in retail and workplace declined by roughly 50% compared to mid
February 2020. Under the assumption that the reduction in workplace and in retail &
recreation mobility are good proxies for the cutback in onsite work hours and expenditures
!2The quadratic matching nature of the SIR model means that what matters is for transmission is average
hours worked of the susceptible times average hours worked of the infectious. In our model the two are
the same, which justifies the use of the average across population groups in (19). The Cobb-Douglas spec-
ification captures the idea that there is a complementarity between the reduction in workplace and retail
activities in containing the spread of the virus. An alternative specification without complementarity is
13 These estimates are provided by The COVID Tracking Project and available at https://rt.live.
4See https: //www.google.com/covid19/mobility.
17
on social goods, respectively, a fall in R0 (t) from 2.5 to 0.82 (−66% from 2.5) implies νβ = 0.8.
The exogenous component β̃t captures reductions in the transmission rate βt that arise
from changes in social norms about cheap preventive measures, such as wearing masks,
washing hands, etc. We specify this time path in terms of R̃0 (t) := β̃t /Tinf , which is the
exogenous component of the basic reproduction number (i.e. the basic reproduction number
R0 (t) in the absence of behavioral feedback from social consumption or workplace hours).
To capture the typical path of learning dynamics, we assume that R̃0 (t) = (1 − ω(t))R0init +
ω(t)R0end with R0end < R0init . We assume that ω(t) = 1/(1 + e−λβ (t−tlrn ) ) follows a logistic
learning curve as in Griliches (1957) and can be interpreted as the fraction of the population
who have learned about best-practice behaviors. We set R0end = 2 so that the exogenous
component of the transmission rate R̃t declines by 20% from its initial value of R0init = 2.5
over the course of the pandemic.15 We set tlrn = 4 months and λβ = 2 which implies that
most of the learning takes place within 4 months.
Clinical parameters The clinical parameters of the model are taken from Ferguson et al.
(2020) (a.k.a the Imperial College Report), most of which are in line with the estimates from
Zhou et al. (2020) using data from the Wuhan episode. According to this report, the average
duration of the critical state Tcri = 1/λc is 10 days, the death probability conditional on being
critical is 33%, and the overall infection fatality rate (IFR) is around 0.66%, which is also the
midpoint of the estimate in Bar-On et al. (2020). Because only critically ill individuals die
in our model, IFR = χ × 33% which requires setting χ, the probability of becoming critical
when exiting the I state, to 2%.16
We parameterize ICU capacity Cmax as the number of ICU beds relative to the initial
population, which we interpret as the U.S. adult population of roughly 250 million people.
According to the Harvard Global Health Institute, there are around 60, 000 ICU beds avail-
able in U.S. hospitals, implying Cmax = 0.00024.17 We assume that when the health care
system is at capacity, all critically ill who exceed the number of available beds die with
certainty.
Finally, we assume that a vaccine yielding full immunity starts being distributed in month
tvac = 24 after the initial outbreak of the virus, and the entire population is vaccinated very
rapidly.
15
Some empirical papers studying the efficacy of masks and other cheap preventive measures argue for
even larger drops in R0 of up to 40% (see e.g. Mitze et al., 2020). We have also experimented with such
larger drops and these alternative assumptions do not affect our main results much.
16
The Imperial College report sets χ to 1.5%, the product of a 5% hospitalization rate and 30% probability
of ending in ICU when hospitalized. Wu and McGoogan (2020) estimate χ between 3% and 5% using data
for China.
17
Source: https://globalpandemics.org/our-data/hospital-capacity.
18
Figure 3: ‘Naive’ dynamics of pandemic without behavioral response (i.e., β0 fixed at 0.58) and
without lockdowns.
Benchmark pandemic dynamics We interpret t = 0 as 1 March 2020 and set I0 =
6.5 × 10−4 at this date. With this initial condition, our baseline simulations that include
the endogenous behavioral feedback and a lockdown designed to mimic the one in the U.S.,
imply that there are around 100,000 deaths after 3 months, as in the data.18
For ease of comparison with other studies, Figure 3 plots the counterfactual dynamics
of the pandemic in the absence of any behavioral feedback (tlrn = ∞, νβs = νβ` = 0) and
without any lockdown or other interventions, which we refer to as the naive model dynamics.
The naive model dynamics predict a peak of active infections of approximately 9% of the
population after less than 3 months and a final cumulative infections of approximately 87% of
the population. Therefore, total infections overshoot quite dramatically the herd immunity
threshold of 1 − 1/R0init = 60%. Cumulative deaths are roughly 1.6% of the population, and
hence almost three times as large as the number implied by the baseline IFR of 0.66%, i.e.
0.66% × 87% = 0.57%, because the ICU constraint binds for almost three months during
the pandemic. These extremely dire clinical predictions are based on the naive version of
the model that abstracts from both the behavioral response and public health interventions,
both of which happened in reality and which we incorporate in our full model.
3.2 Economic Model
3.2.1 Production
Sectors The Bureau of Economic Analysis’s (BEA) 2-digit 2017 NAICS industry classifi-
cation contains 21 private sector industries.19 We allocate each of these industries to either
the regular (c) or social (s) sectors based on the degree of social interaction, either with
18
Source: https://covidtracking.com/data/us-daily.
19
Source: Table ‘Components of Value Added by Industry,’ https://www.bea.gov.
19
NAICS code Sector C (value added share: 0.74) NAICS code Sector S (value added share: 0.26)
11 Agriculture, forestry, fishing, and hunting 44-45 Retail trade
21 Mining 481-482-483 Air, rail, and water transportation
22 Utilities 485-487-488 Transit and scenic transportation
23 Construction 61 Educational services
31-32-33 Manufacturing 62 Health care and social assistance services
42 Wholesale trade 531-532-533 Real estate, rental and leasing services
484-486 Truck and pipeline transportation 71 Arts, entertainment, and recreation services
491-492 Postal transportation 72 Accommodation and food services
493 Warehousing and storage 81 Other services (excluding P.A.)
51 Information
52 Finance and insurance
– Housing services
54-55 Professional, technical, and scientific services
56 Management and administrative services
Table 3: Classification of 2-digit NAICS industries into c and s sectors.
other customers or with workers, required to consume them. According to our classification,
reported in Table 3, the total value added share of the c sector is 0.74 and the value added
of the s sector is 0.26. Using industry-level labor shares, we also compute the implied labor
shares in the two sectors. We find that the social goods sector is much more labor intensive
than the regular goods sector, with a 54% larger labor share.20
Occupations We assume that individuals work in one of J = 5 occupations. One of these
occupations, labeled E, consists of essential workers who are not affected by the lockdown.
The four non-essential occupations are differentiated in terms of their flexibility (F for more
flexible, R for more rigid) and their sectoral intensity (C for more intensive in production of
regular goods, S for more intensive in production of social goods). So for example, occupation
CF contains workers who can work from home with relatively little loss in productivity, and
produce goods or services that entail relatively little social interaction.21
To calibrate occupation-level parameters, we categorize each of the 430 5-digit 2010
SOC occupation codes as either flexible or rigid, based on the analysis of O*NET data in
Dingel and Neiman (2020a), and our own analysis of American Time Use Survey (ATUS).
In Appendix B.1, we show that the employment weighted correlation between these two
measures is 0.8. We use the O*NET based classifications for our calculations. We categorize
20
Some industries map cleanly into the regular or social goods sector. For example, food services (e.g.
restaurants), other services (e.g. hairdressers), and entertainment (e.g. movie theaters) fit naturally in the
s sector, whereas mining, manufacturing, and finance fit naturally in the c sector. Within more ambiguous
industries, we separated out 4-digit sub-industries into different sectors. For example, in the transportation
industry, we included rail, air and transit transportation in the s sector, but we included postal, pipeline
and truck transportation in the c sector. Similarly, in the real estate, rental and leasing sector, we included
real estate (e.g. services from housing) in the c sector, but we included other rental services (e.g. services of
real-estate and car-rental agents) in the s sector.
21
Recall that Table 1 illustrates several examples of occupations in each of the five groups.
20
Occupation Share of Share of Average Employment
Type φj Lab Inc C Lab Inc S ξcj ξsj Earnings Share
E 0.01 0.211 0.353 0.191 0.356 44, 745 0.308
CF 0.99 0.535 0.118 0.575 0.141 79, 422 0.211
CR 0.10 0.191 0.041 0.181 0.043 44, 813 0.133
SF 0.99 0.028 0.193 0.025 0.193 50, 619 0.104
SR 0.10 0.035 0.295 0.028 0.267 32, 000 0.244
Table 4: The five occupation groups in the model: Essential (E) , C-intensive Flexible (CF ),
C-intensive Rigid (CR), S-intensive Flexible (SF ), S-intensive Rigid (SR). Sectoral labor shares,
employment and earnings. Earnings are in 2017 dollars.
each occupation as either C-intensive or S-intensive based on their relative labor shares in
the industries in each sector, as reported in Table 3. We define essential workers as those
in both occupations with low flexibility and industries that are classified by the Department
of Homeland Security as “critical infrastructure workers”. Appendix B.1 contains a detailed
description of this procedure.
Table 4 reports the average earnings and employment shares of each of the five occupa-
tions and the share of total labor income in the C and S sectors going to each occupation.
Average annual earnings are highest for the C-intensive flexible occupations ($79,000) and
lowest for the S-intensive rigid occupations ($32,000).
Technology We set the flexibility indexes {φj } for the essential and flexible occupations
very close to 0 and 1, respectively to respect the nature of these definitions. For the rigid
occupations we set the index to 0.10 which allows for the small amount of remote work that
we observe in the data for these groups. The ten share parameters {ξcj , ξsj } in the intermediate
goods production function are set to match the occupational labor income shares in the c
and s sectors reported in Table 4. The capital share parameters αc and αs are set to replicate
an aggregate labor share of 0.60, with the ratio of labor shares in the two sectors calibrated
to 1.54, as estimated from BEA data and described above.
The elasticity of substitution across occupations is set to 1.25 in both sectors. With this
value, the drop in labor earnings of the five occupations in our baseline experiment matches
closely the drops observed in US data between March and May (source: Monthly CPS). We
set the within-sector elasticity of substitution across intermediate goods producers in both
sectors to 10 (c = s = 10).
The functional form for the capital adjustment cost is φ(ι) = δk1ϑ (ι − δk )2 . We set ϑ,
which measures the elasticity of the investment rate to (small changes in) the shadow price
of capital, to 4. This value yields a drop in investments around 10% in Q2:2020, in line with
the aggregate U.S. data.22 The annual depreciation rate on capital δk is set to 10%.
22
Series: Private Non-residential Fixed Investment (PNFI) in FRED, https://fred.stlouisfed.org/.
21
E CF CR SF SR
Median net liquid wealth ($) 1,312 18,375 1,013 8,916 875
Share of Hand-to-Mouth 0.453 0.272 0.465 0.327 0.499
Share of Poor HtM 0.186 0.069 0.195 0.097 0.255
Share of Wealthy HtM 0.267 0.203 0.270 0.230 0.244
Liquid rate wedge (%) 0 0.2 -0.7 1.2 -1.0
Table 5: Median net liquid wealth holdings, and hand-to-mouth (HtM) shares by occupational
group. Source SIPP, Waves 1-4 2014.
3.2.2 Households
Asset returns and transaction costs We choose the following function form for house-
hold transaction costs: χ
d 2
χ (d, a) = χ1 a. (20)
a
The restriction (χ1 > 0, χ2 > 1) ensures the function is increasing and convex in d. Under
these assumptions, deposit rates are finite, |dt | < ∞, and hence individual’s holdings of
assets never jump.23
We choose the two parameters of the transaction cost function (χ1 , χ2 ) to generate a total
share of hand-to-mouth households of 40%, of which two-thirds are wealthy hand-to-mouth
households as in the 2016 Survey of Consumer Finances (SCF 2016). In both model and
data, we define a household as hand-to-mouth if its holdings of liquid wealth are less than
$1,000 and as wealthy hand-to-mouth if, in addition, its holdings of illiquid wealth are more
than $1,000.24
We choose the real interest rate on liquid assets rb to match an overall median holdings
of liquid wealth of $3,500 (SCF 2016). The annualized calibrated value of rb is 2.8%.
In our model, the main determinant of whether households are able to weather income
shocks is their holdings of liquid wealth. It is thus important that the model is consistent with
heterogeneity across occupations in liquid wealth. Table 5 shows median net liquid wealth
for each of the five occupation groups, together with the share of total, poor and wealthy
hand-to-mouth households in each group. Since the publicly available SCF micro-data does
not contain detailed occupation information, these statistics are based on data from the
23
Scaling by illiquid assets a delivers the desirable property that marginal costs χd (d, a) are homogeneous
of degree zero in (d, a) so that the marginal cost of transacting depends on the fraction of illiquid assets
transacted, rather than the raw size of the transaction. Because the transaction cost is infinite at a = 0, for
computational purposes we replace the term a with max {a, a}, where the threshold a > 0 is a small value
(around $500) that guarantees costs remain finite even for individuals with a = 0.
24
Our definitions of liquid and illiquid net worth are the same as in Kaplan et al. (2014) and Kaplan et al.
(2018). Net liquid wealth is defined as banks deposits plus directly held mutual funds, stocks and bonds
times an adjustment of 5% of liquid assets for cash holdings (not recorded in the SCF) net of credit card
debt. Net illiquid wealth is the sum of housing net worth and wealth in retirement accounts, plus other
small items like CDs and life insurance.
22
Survey of Income and Program Participation (SIPP Waves 1-4, 2014).2° Table 5 reveals
that workers in rigid and essential occupations are significantly more financially vulnerable
than those in flexible occupations. To match this heterogeneity in median liquid wealth,
we introduce an occupation-specific wedge in the liquid rate which should be interpreted as
a reduced-form catch-all for heterogeneity in financial sophistication, intermediation costs,
informational frictions, structural barriers to financial markets and behavioral phenomena.
We normalize the wedge for essential workers to zero.
The aggregate quarterly MPC in the model is 0.14. As extensively discussed in Kaplan
and Violante (2020), it is the combination of uninsurable risk and two-asset structure that
enables the model to simultaneously generate a large amount of aggregate net worth and a
high aggregate MPC (roughly 10 times the MPC in a representative agent model) without
preference heterogeneity.
Preferences We choose the discount rate p to replicate a ratio of total illiquid net worth
to annual GDP of 4.5 (SCF 2016) which, in turn, implies a steady-state annualized value of
r? = 0.05.
We assume the following functional form for period utility U(c, us(D)s, h)—V (ve(D) lu, ls ln)
in (5)
dy gi
: ~ \\ O=1 o-1\ 0-1
U(cv(D)sh) = -— + e7— Fs (v(D)s rth ) (21)
with y,y, > 0 and @> 1 and
ire ~ _ én én \ Tq
with ¢, y, yn > 0 and 7 = 0.
We set 7 = 1.7° We choose vy; so that the output share in the s sector is 26%. Estimates
of the elasticity of substitution between market consumption and home, @, using micro
data typically obtain values just below 2 (e.g., Aguiar and Hurst, 2007a). We set 6 = 2
because s goods are arguably more substitutable with home production than the whole
market consumption bundle. The shifters vu, and vu, are normalized to one in steady-state.
25We can construct measures of liquid and illiquid wealth in the SIPP that are very close to those in
the SCF. We define hand-to-mouth households as described above for the SCF. The total share of HtM
households in SIPP is 40%, and the fraction of wealthy HtM among these is around 60%, consistent with
the SCF. Median household liquid wealth in SIPP is somewhat smaller than in the SCF, so we rescale all
SIPP observations by a constant factor to match the SCF median. See Appendix B.2 for details.
26Note that 1/7 denotes both the intertemporal elasticity of substitution for both consumption goods and
the static elasticity of substitution between c and the composite (s,h) bundle. To assess whether the latter
elasticity is in the right ballpark, we construct quantities and price indexes for c and s goods for the US
economy from 1947 to 2019. Time-series regressions of log relative quantities on log relative prices also yield
an elasticity around one. See Appendix B.3 for details.
23
We set the Frisch elasticity of labor supply 1/¢ to 1. The parameter 7 governs the degree
of substitution between supplying labor remotely and in the workplace. When 7 — ov,
workplace and remote hours are perfect substitutes in preferences. We normalize the time
endowment to one and set (Ye, Yn, 7) to match three moments about hours worked: (i) total
market hours ¢,, + ¢, equal to 0.34; (ii) remote market hours as a share of total market
hours ¢,./(€u + ,) equal to 0.10; (iii) home production hours as a share of total hours worked
Cn/ (lw + & + €n) equal to 0.18. The first two moments are taken from Aguiar and Hurst
(2007b, Table 2). The third moment is computed from the most recent wave of ATUS for
2019.”
Finally we set the exogenous level of consumption of the two goods (c, s) for the critically
ill to 0.14, which is roughly 20% of average consumption expenditures.
Optimal labor supply Lemma 1 in Appendix A characterizes optimal decisions for the
three types of labor supply and three types of consumption goods. With our specification
for the disutility of labor in (22), the optimal share of workplace hours in total market hours
in the absence of a lockdown is given by
_ lw _ uD)"
(23)
Sy:
where ¢ is the individual’s occupation flexibility index and u,(D) is the additional disutility
of workplace hours due to the virus.
The share of workplace hours is decreasing in flexibility @ and equals one if @ = 0, so
that individuals in fully rigid occupations only work onsite. Whenever @ > 0, this share
is decreasing in disutility ve(D), so individuals substitute toward remote work when deaths
from the virus increase. The size of both of these margins of substitution is governed by the
elasticity parameter 7. It follows from (23) that the labor lockdown constraint (13) binds
whenever Kj is less than this unconstrained share of workplace hours. Symmetric expressions
hold for demands for social and home-produced goods.
Feedback from virus to economic activity We parameterize the disutility functions
that govern feedback from the virus to the economic decisions using the functional forms,
u,(D) = exp (—2D"") , ue(D) = exp (rb") ; (24)
One advantage of these functional forms is that the disutility of workplace hours con-
nects directly to calculations of the value of a statistical life (VSL). Re-arranging the static
7Bick and Blandin (2020) estimate similar numbers for the pre-lockdown period.
24
optimality condition for labor supply we obtain the relationship
ν1
log wit = γ`0 ν`0 Ḋt ` + γ`1 Xit , (25)
where β 0 = η(1+ζ)
1+η
and Xit is a vector of individual correlates, that includes hours worked
and consumption. The relationship between the hourly wage and death rate in equation (25)
can be interpreted as a compensating differential for fatality risk, and is the foundation for
most empirical estimates of VSL (see Kniesner and Viscusi, 2019, for a survey).
The specification in (24) allows for a nonlinear effect of fatality risk on compensating
wage differentials. This nonlinearity is important in our context because death rates at the
peak of the pandemic, when the ICU constraint binds, are one to two orders of magnitudes
larger than the average fatality risk in a typical occupation.28 When ν`1 < 1, the wage
premium demanded in exchange for additional risk increases less than linearly with the level
of death risk. This property, which implies that the VSL is decreasing in the level of fatality
risk, is consistent with empirical evidence from high-risk occupations.29
We set the disutility parameters for workplace hours to ν`0 = 8.0 and ν`1 = 0.6 to match a
VSL of around $10M for quarterly death rates of the order of 1/10,000 and a VSL of around
$4M for quarterly death rates of the order of 1/1,000, based on the estimates in Lavetti
(2020). Appendix B.4 contains further details of this calculation.
We set the curvature parameter for the disutility of social consumption to be the same
as the curvature for workplace hours, νs1 = ν`1 = 0.6. We choose νs0 = 16 to obtain the
same percentage declines in workplace hours and social consumption from the behavioral
feedbacks during the pandemic.
Wage dynamics The stochastic component of individual productivities zijt for an indi-
vidual i in occupation j follows a jump-drift process in logs. Jumps arrive at a Poisson
0
rate λzj . Conditional on a jump, a new log-productivity state zijt is drawn from a Normal
2 0 2
distribution with mean zero and variance σzj , zijt ∼ N (0, σzj ). Between jumps, the process
drifts toward zero at rate βzj . Formally, the process for zj,it is
dzijt = −βzj zijt dt + dΛjt ,
We estimate the parameters {λzj , σzj , βzj } using data on household wages from the PSID
28
In 2020:Q1 there were around 100,000 COVID-19 related deaths in the US. This corresponds to an
average fatality risk of 1/2,500, compared to an average quarterly fatality risk in typical VSL calculations
of 1/100,000.
29
Greenstone et al. (2014) emphasize non-linearities in the context of risky military occupations such as
infantry, and Lavetti (2020) estimates non-linearities in the context of Alaskan fisheries, which have the
largest death rate across all US civilian occupations (around 1/1,000 quarterly).
25
Moments Essential C int-Flex C int-Rigid S int-Flex S int-Rigid
Variance (lag 0) 0.229 0.322 0.235 0.314 0.311
Variance (lag 2) 0.115 0.126 0.124 0.141 0.130
Kurtosis (lag 2) 9.87 8.85 7.77 8.61 8.74
Total observations 10,2507 83,473 30,002 14,994 40,712
Parameters Essential C int-Flex C int-Rigid S int-Flex S int-Rigid
λzj 0.0346 0.0365 0.0649 0.0346 0.0425
σzj 0.736 0.790 0.627 0.814 0.764
βzj 0.0348 0.0315 0.0481 0.0390 0.0338
Years btw shocks 7.23 6.85 3.85 7.22 5.89
Half life of shocks 19.9 22.0 14.4 17.8 20.5
Table 6: Top table. Panel-data moments estimated on PSID biannual data 1997-2017. Dingel
and Neiman (2020b) occupation classification. Bottom table: Parameter estimates via minimum
distance. The parameters are expressed at quarterly frequency, the model period.
(1997-2017).30 We classify households in the PSID into the five occupation groups based
on the occupation of the main earner in the household. For each occupation, we compute
the following moments: (i) variance of log earnings, (ii) variance of 2-year log change in
earnings and (iii) kurtosis of 2-year log-change in earnings. These moments are sufficient for
identification (see Kaplan et al. (2018)). We estimate the parameters by minimum distance.
The empirical moments and parameter estimates for each occupation group are reported
in Table 6.
3.2.3 Government
The government supplies all the liquid assets in the economy in the form of risk-free govern-
ment debt. Given our calibration of household liquid assets, steady-state government debt
B g is 58 percent of annual GDP.
We set the proportional labor income tax rate to τ = 0.25 and assume that in steady-state
the transfer function T (·) is lump-sum and equal to 5 percent of output, which is equivalent to
around $7,000 per household per year. In steady-state, 23 percent of households receive a net
transfer from the government. Expenditures are determined residually from the government
budget constraint.
30
We define household wages as household labor income divided by household hours worked. Our definition
of labor income includes wages, commissions, overtime, and bonuses. We restrict our sample to household-
year observations with at least 520 hours worked and with an hourly wage above the federal minimum wage
for that year.
26
Parameter Value Moment to Match Value
Technology
Sectoral TFP Zc = Zs 1 Normalization –
Labor share in C sector αc 0.59 Labor share in C sector (BEA) 0.53
Labor share in S sector αs 0.90 Labor share in S sector (BEA) 0.81
Elast. of subst. across occup. σc 1.25 Earnings drop across occup. in Q2 (CPS) –
Elast. of subst. for intermediates c = s 10 Profit share 0.10
Depreciation rate δk 0.10 External –
Elast. of inv. to price of K ϑ 4 Investment drop in Q2 (BEA) 10%
Transaction costs
Scale of transaction cost χ1 0.32 Total Share of Hand-to-Mouth (SCF) 0.40
Convexity of transaction cost χ2 1.27 Share of Wealthy Hand-to-Mouth (SCF) 0.26
Preferences
Discount rate (annualized) ρ 0.025 Illiquid wealth-income ratio (SCF) 4
IES 1/γ 1 External –
Weight on S good ϕs 1.31 Share of value added in S sector (BEA) 0.26
Elasticity of substitution (s, h) θ 2 External –
Preference shifters υ` = υs 1 Normalization –
Frisch elasticity 1/ζ 1 External –
Elasticity of substitution (`w , `r ) η 83.0 Hours worked remotely (ATUS) 0.10
Weight on remote market work ϕ` 9.94 Hours worked in the market (ATUS) 0.34
Weight on home work ϕh 3.56 Hours worked at home (ATUS) 0.18
Consumption of the critically ill c, s 0.14 External –
Government
Labor income tax τ 0.25 Tax revenues 0.15 · GDP
Lump-sum transfer T 0.05 Transfers to households 0.05 · GDP
Government debt (liquid wealth) Bg 0.58 Liquid wealth held by hh (Flow of Funds) 0.58 · GDP
Table 7: Summary of some of the parameter values and targeted moments for technology, trans-
action costs, preferences, and government. Remaining ones are reported in Tables 3-6. Quarterly
GDP is normalized to 1 in the model.
4 Numerical Experiments
We organize our experiments around three scenarios. In Section 4.1, we consider a Sweden-
like ‘laissez-faire’ scenario without government intervention. We use this scenario to develop
a baseline counterfactual in which behavioral feedback is the only force limiting the spread
of the virus. In Section 4.2, we consider a US-like scenario that includes the type and
duration of lockdown that was observed in the United States, but without any economic
stimulus package. We use this scenario to compare the trade-offs between economic and
health costs under counterfactual lockdowns of different lengths and intensities. In Section
4.3, we consider a scenario that includes the complex economic stimulus program enacted
by the US government, in addition to the lockdown. We use this scenario to analyze the
effect of each component of the stimulus program on the trade-off, to examine the effects of
counterfactual stimulus programs, and to interpret the observed time-series of consumption
27
for different types of households. Finally, in Section 4.4 we consider the effects of smart
containment and stimulus policies that can improve the trade-off between lives and economic
welfare.
Government finances during the pandemic We assume that the monetary authority
has access to a storage technology for final goods, and has accumulated a sufficient quantity
of goods to provide short-term financing to the government during the pandemic. The
monetary authority uses these goods to buy the additional government debt that is needed
to cover the shortfall in tax revenues and finance the stimulus program. This assumption is
intended to capture the role of central banks in preventing the sharp rise in governments’
borrowing costs that would be required if the private sector had to absorb the additional
debt.31 In the long-run, we assume that the government repays the additional debt it issues
during the pandemic by smoothly raising the labor income tax rate.
Economic welfare costs We measure the economic welfare costs of the pandemic us-
ing compensating variation in liquid wealth. Consider a particular pandemic scenario that
includes a specification of both lockdown and stimulus policies. Fix an individual at a
particular point in the state space (a, b, z, h, j) in the initial steady-state. We measure the
economic cost of the pandemic for this individual as the size of the one-time liquid wealth loss
that would make them indifferent between experiencing and not experiencing the pandemic.
Denote the individual’s steady state value function by V̄ and the value function immediately
after the onset of the pandemic by V0 . The economic welfare cost is given by the value of
Ω(a, b, z, h, j) that solves
V0 (a, b, z, h, j) = V̄(a, b + Ω, z, h, j).
We report this compensating variation as a multiple of each individual’s steady-state
monthly disposable income (after tax earnings + asset income + transfers). This yields a
distribution of economic welfare costs across households, which we use to summarize the
distributional consequences of the pandemic. We measure the aggregate economic costs of
a pandemic scenario as the mean or median of this distribution of income multiples.
4.1 Laissez-Faire Scenario
In this section we examine a scenario without any government-mandated lockdown or fiscal
stimulus. This scenario forms a useful counterfactual benchmark with which to compare
31
For a description of central banks’ responses to the pandemic, we refer to https://research.stlouisfed.
org/publications/economic-synopses/2020/04/21/central-bank-responses-to-covid-19.
28
2.5
(a) Reproduction Number 1.8
(b) Infectious (% of Population) 0.200
(c) Monthly Death Rate (%)
R0 1.6 Actual
Effective R 0.175 No ICU Constraint
2.0 1.4 0.150
1.2
1.5 0.125
1.0
0.100
0.8
1.0 0.075
0.6
0.4 0.050
0.5
0.2 0.025
0.0 0.0 0.000
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
(d) Output (%) 10
(e) Consumption (%) 10
(f) Investment and Share Price (%)
0
Investment
0 5 Share Price
10
10 0
20
20
5
30
30
10
40 Y 40 C
Regular Y Regular C 15
50 Social Y 50 Social C
20
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
(g) Hours (%) (h) Labor (%) (i) Government Debt
Quarterly GDP
400 2.70
60 20 Labor Productivity
40 Labor Income 2.65
200 10
20 2.60
0 0 0 2.55
20 2.50
200 10
40 2.45
60 20
400 2.40
80 Workplace Hrs.
Home Hrs. Remote Hrs. 30 2.35
100 600
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
Figure 4: Laissez-faire counterfactual: dynamics of key variables
alternative policy interventions, and should not be used to compare model predictions with
data.
Aggregate dynamics Figure 4 displays the aggregate dynamics of key epidemiological
and economic variables. We will use versions of this figure to describe each alternative
scenario that we examine.32
The top row of Figure 4 displays epidemiological variables: the basic reproduction number
32
In all experiments aggregate output, consumption and investment are expressed in real terms by using
expsh
their respective deflators. For example, the consumption deflator is pst st , where expshst is the household
expenditure share on goods s at date t, since (i) the price of regular consumption is normalized to 1 at all
t and (i) the consumption aggregator in preferences is Cobb-Douglas. The deflator for output is analogous,
but with the share of s in value added instead of expenditures. The investment deflator is one at all times.
Equity price and labor earnings are deflated with the consumption price index.
29
R0 (t), the effective reproduction number R0 (t) × St , the fraction of infectious individuals
It /Nt , the death rate Ḋt and a counterfactual death rate in the absence of constraint on
ICU capacity. This latter variable helps to see the number of additional deaths that are due
to the ICU constraint binding.
Without a lockdown, infections would peak at around 1.5% of the population (around
3.75 million) in May. At this level of infections, the ICU constraint binds. Total cumulative
deaths are about 0.3% of the population, but would be less than half without the ICU
constraint. The high level of deaths at the peak of the pandemic triggers a strong behavioral
response, which leads to a rapid decline in the basic reproduction number R0 , from 2.5 to
below 1 within the first two months. The effective reproduction number also drops below 1,
and then remains roughly constant at or just below 1 for the remainder of the pandemic, in
line with microfounded models of voluntary social distancing.33
The remainder of Figure 4 shows key macroeconomic aggregates. Aggregate output falls,
with the majority of the drop concentrated in the social sector, due to the endogenous
reduction in demand for social goods. The initial contraction is severe and short-lived, but
the recovery is slow: a year later the economy is still 3% below trend. Despite the sharp
drop in social consumption expenditures, regular consumption rises only very slightly for
two reasons. First, households substitute social good spending with more home production
(home hours increase by 50%, panel (g)). Second, labor income decreases sharply (panel(h)).
Also aggregate investment falls (panel (f)) since the shadow value of additional capital is
much reduced due to the preference-driven decline in demand and labor input. Even in the
absence of fiscal stimulus, the large fall in economic activity leads to a considerable budget
deficit and an increase in the debt-to-GDP ratio around 3% (panel (i)).
Occupation dynamics Figure 5 shows the dynamics of labor income (left panel) and
consumption (right panel) for the five occupation groups. There are large differences across
occupations in the extent of the drop in labor income. Workers in the S-intensive rigid (SR)
occupations experience an average fall in labor income of nearly 35%, whereas those in the
C-intensive flexible (CF) occupations experience a decline of only 6%. Both labor supply
and labor demand account for this large difference. Workers in the two rigid occupations
supply fewer efficiency hours of labor when they substitute remote work for onsite work.
The demand for workers in the two S-intensive occupations falls as consumers reduce their
demand for social goods. While both forces are active, the labor demand effect accounts for
a larger fraction of the differential falls in labor income across occupations.
In this laissez-faire scenario, labor income decreases also for essential occupations (by
around 23%) because a substantial fraction of these workers are employed in the production
of social goods and services (see Table 4).
33
See e.g. Farboodi et al. (2020) for a discussion of this effect.
30
(a) Labor Income (%) (b) Total Consumption (%)
0
0
5
10 5
15
10
20 E: Essential E: Essential
25 CF: C-intensive, Flexible 15
CF: C-intensive, Flexible
CR: C-intensive, Rigid CR: C-intensive, Rigid
30 SF: S-intensive, Flexible SF: S-intensive, Flexible
35 SR: S-intensive, Rigid 20 SR: S-intensive, Rigid
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month
(c) Regular Consumption (%) (d) Social Consumption (%)
2.0 E: Essential 0
CF: C-intensive, Flexible
1.5 CR: C-intensive, Rigid 10
1.0 SF: S-intensive, Flexible
SR: S-intensive, Rigid 20
0.5
0.0 30 E: Essential
0.5 CF: C-intensive, Flexible
1.0
40 CR: C-intensive, Rigid
SF: S-intensive, Flexible
1.5 50 SR: S-intensive, Rigid
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month
Figure 5: Laissez-faire counterfactual: distributional effects across occupations
The fall in labor income translates into a fall in spending that is ordered in the same
way across occupations but is much more compressed. The decline in total consumption is
driven by the collapse in S-sector consumption for all occupations caused by the behavioral
response to the pandemic. Regular consumption rises slightly, through substitution, only for
the least affected occupations.
Summarizing, in the laissez-faire scenario, both consumption and investment drop sharply.
The decline in consumption is driven by the endogenous reduction in demand for the social
goods. The co-movement between consumption and investment is attributable to a fall in
aggregate productivity caused by workers in rigid occupations (nearly 70% of the workforce)
cutting workplace hours and being less productive while working remotely. The economic
consequences of the virus vary across workers in occupations with different degrees of flexi-
bility and different exposure to the harder-hit S sector.
4.2 Lockdown Scenarios
In this section we examine a scenario with a government-mandated lockdown that mimics
those implemented in the US in the Spring of 2020, but without fiscal stimulus. As with the
laissez-faire scenario, this is a counterfactual scenario that should not be used to compare
model predictions with data.
31
(a) Workplace Lockdown (%) (b) Social Sector Lockdown (%)
60
80
50
40 60
30
40
20
20
10
0 0
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month
Figure 6: The two components of the baseline lockdown
Parameterization of lockdown A lockdown consists of time paths for the constraints
on the share of workplace hours in total market hours for each occupation κj`t t≥0 (see
equation (12)), and on the fraction of the capital stock in the S sector that can be used for
production {κst }t≥0 (see equation (13)). We assume that the workplace labor lockdown does
not affect essential occupations κE
`t = 0 but is common across the other four occupations.
Based on the evidence presented in Section 3.1, we calibrate the size of both lockdowns
to generate a 50% reduction in workplace hours and social consumption, relative to mid-
February 2020. Recall that t = 0 corresponds to 1 March 2020. We assume that the lockdown
starts on 1 April 2020 (at t = 1) and lasts until 1 June 2020 (t = 3), after which it is released
quickly and is completely over by end of August 2020 (t = 5). The resulting time paths for
the lockdown parameters are displayed in Figure 6, with the two-month lockdown period
indicated by the grey shaded area. This lockdown scenario is designed to mimic the US
lockdown in the Spring of 2020.34
Aggregate dynamics Figure 7 displays key epidemiological and macroeconomic variables
for the baseline lockdown scenario and Figure 8 contrasts them with the laissez-faire coun-
terfactual. Three features of these dynamics stand out.
First, the initial wave of infections is dampened as a result of the lockdown, with death
rates peaking at around 2.5%, down from 12% in the laissez-faire scenario. This comes at
34
At the time of writing in August 2020, it is unclear whether additional lockdowns will be mandated. Our
baseline scenarios assume that there will be no such additional lockdowns, even in the case of a second wave
of infections. It is thus crucial that our results about the future evolution of the pandemic are interpreted
as conditional on this assumption about future lockdown policy. Similarly, all our conclusions in this section
about the efficacy of lockdowns should be interpreted as statements about US-style lockdowns that are
relatively short-lived and released quickly. We will relax these assumptions when we consider alternative
lockdown policies below.
32
2.5
(a) Reproduction Number 1.8
(b) Infectious (% of Population) 0.200
(c) Monthly Death Rate (%)
R0 1.6 Actual
Effective R 0.175 No ICU Constraint
2.0 1.4 0.150
1.2
1.5 0.125
1.0
0.100
0.8
1.0 0.075
0.6
0.4 0.050
0.5
0.2 0.025
0.0 0.0 0.000
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
(d) Output (%) 10
(e) Consumption (%) 10
(f) Investment and Share Price (%)
0
Investment
0 5 Share Price
10
10 0
20
20
5
30
30
10
40 Y 40 C
Regular Y Regular C 15
50 Social Y 50 Social C
20
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
(g) Hours (%) (h) Labor (%) (i) Government Debt
Quarterly GDP
400 2.70
60 20 Labor Productivity
40 Labor Income 2.65
200 10
20 2.60
0 0 0 2.55
20 2.50
200 10
40 2.45
60 20
400 2.40
80 Workplace Hrs.
Home Hrs. Remote Hrs. 30 2.35
100 600
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
Figure 7: Counterfactual with lockdown but no fiscal policy: dynamics of key variables
the cost of a deeper and longer recession. Output falls by 17% for around 2 months under
the lockdown, compared with a drop of around 14% for 1 month without the lockdown.
Second, the lockdown leads to a second wave of infections that is as large as the first wave
and is longer lived. Infections start rising again at the beginning of July (t = 4) and reach a
peak around November (t = 8), before slowly tapering off only in the summer of 2021. By
the end of the pandemic, the lockdown reduces the cumulative number of deaths by around
one-third, relative to the laissez-faire scenario. The second wave of infections brings with
it a prolonged double-dip recession that is about half as large as the first. Both drops in
output are concentrated in the social sector. However, in the first contraction investment
also plays a major role, whereas in the second it doesn’t. The reason is that the first recession
is driven by the lockdown which dramatically decreases labor input and, as a result, capital
productivity, whereas the second one is caused by a decline in the demand for the social
33
0.12
(a) Monthly Death Rate (%) (c) Labor Income (CF: C-intensive, Flexible) (%) (e) Labor Income (SF: S-intensive, Flexible) (%)
0 0
Laissez-faire
0.10 Full Lockdown
10 10
0.08
20 20
0.06
30 30
0.04
40 40
0.02 Laissez-faire Laissez-faire
Full Lockdown Full Lockdown
0.00 50 50
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month
(b) Output (%) (d) Labor Income (CR: C-intensive, Rigid) (%) (f) Labor Income (SR: S-intensive, Rigid) (%)
0 0 0
5 10 10
10 20 20
15 30 30
20 40 40
Laissez-faire Laissez-faire Laissez-faire
Full Lockdown Full Lockdown Full Lockdown
25 50 50
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month
Figure 8: Comparison between laissez-faire and lockdown
sector which is not very intensive in capital.
Third, the distributional implications of the lockdown are different from those of the
laissez-faire. The lockdown is extremely costly for the C-intensive rigid occupations whose
earnings fall by 35%, compared with 12% in the laissez-faire scenario. This is because in the
laissez-faire scenario the demand for regular goods does not fall much so those workers can
continue to produce and be paid. This is true also for the C-intensive flexible occupations,
whose earnings are also affected by the lockdown because of imperfect substitutability across
occupations in production. In contrast, the S-intensive occupations are hit similarly hard in
both cases.
Lockdown decomposition In Figure 9 we decompose the dynamics in the lockdown
scenario into contributions from the social sector and workplace components.
The top row of Figure 9 shows that the workplace labor lockdown is somewhat more
effective at suppressing infections, and hence deaths than the social sector lockdown, but
comes with larger economic cost (compare the red and green lines in the second panel).
The reason is that by limiting the amount of onsite work across the board, the workplace
lockdown prevents those employed in rigid occupations in the C sector from working and,
through imperfect substitutability across occupations, heavily affects total production in a
sector of the economy that accounts for 3/4 of GDP.
The decompositions in Figure 9 also highlight the dynamic trade-offs involved with differ-
ent types of lockdowns. In the absence of further lockdown orders, an initial lockdown that
34
0.12
(a) Monthly Death Rate (%) (b) Labor Income (CF: C-intensive, Flexible) (%) (c) Labor Income (SF: S-intensive, Flexible) (%)
0 0
Laissez-faire
0.10 Full Lockdown
Social Sector Lockdown 10 10
0.08 Workplace Lockdown
20 20
0.06
30 30
0.04 Laissez-faire Laissez-faire
40 Full Lockdown 40 Full Lockdown
0.02 Social Sector Lockdown Social Sector Lockdown
Workplace Lockdown Workplace Lockdown
0.00 50 50
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
(d) Output (%) (e) Labor Income (CR: C-intensive, Rigid) (%) (f) Labor Income (SR: S-intensive, Rigid) (%)
0 0 0
5 10 10
10 20 20
15 30 30
Laissez-faire Laissez-faire Laissez-faire
20 Full Lockdown 40 Full Lockdown 40 Full Lockdown
Social Sector Lockdown Social Sector Lockdown Social Sector Lockdown
Workplace Lockdown Workplace Lockdown Workplace Lockdown
25 50 50
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
Figure 9: Role of different lockdown components
is more effective at lowering infections during the first half of 2020 comes at the cost of not
only a deeper contraction, but also a larger second wave of infections and deeper associated
recession in 2020:Q4, and a slower recovery in 2021 (compare solid orange and dashed green
lines).
Pandemic possibility frontier (PPF) Figure 10 displays a distributional pandemic
possibility frontier that offers a more systematic analysis of the tradeoffs between health and
economic outcomes under different lockdown policies. Each vertical segment on the frontier
corresponds to a lockdown scenario of different length. Longer lockdowns are those towards
the left of the frontier, with fewer total deaths; shorter lockdowns are those towards the right
of the frontier, with more total deaths. The thick dash-dot line traces out the combinations
of mean economic welfare costs and total death rates that are achievable with lockdowns of
different lengths. The shaded regions indicate different percentiles of the economic welfare
cost distribution corresponding to each lockdown length. The laissez-faire and baseline 2-
month lockdown discussed above are indicated on the frontier.
Regardless of the length of lockdown, the economic welfare costs of the pandemic are
large and heterogeneous. In the baseline 2-month lockdown, the average economic welfare
cost is around 3.4 times monthly income, with a 90-10 percentile ratio that ranges from less
than 2.2 times to nearly 4.5 times monthly income. Both the size and heterogeneity in the
economic costs of the pandemic increase with the length of the lockdown. The mean cost of
a 12-month lockdown is nearly 7 times monthly income, with a 90-10 ratio of 4.5 to 8.5 times
35
Mean
Economic Welfare Cost (Multiples of Monthly Income)
10 p25-p75
p10-p90
p5-p95
17-Mon
t
8 Lockdo h
wn
12-Month
Lockdown
6
4
US Lockdown
Laissez-fa
ire
2
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Deaths (% of Population)
Figure 10: Counterfactuals with lockdown but no fiscal policy: frontier
monthly income. Therefore both mean and dispersion of economic losses roughly double as
the lockdown is extended from 2 to 12 months.35
The non-convex shape of the mean frontier reflects the different mechanisms through
which the lockdown affects the spread of the virus at different durations. Moving from the
rightmost point of the frontier (laissez-faire), the frontier is initially relatively flat, reflecting
the fact that short lockdowns (less than 2 months) induce relatively small economic costs
but drastically reduce deaths. This sizable reduction in deaths is due to two effects of such
short lockdowns: (i) preventing the ICU capacity constraint from binding; and (ii) buying
time for people to learn best-practice behaviors so that R0 falls.
Longer lockdowns (between 2 and 12 months) incur a less favorable trade-off between
deaths and economic welfare, as reflected in the steeper portion of the frontier. This follows
from the epidemiological dynamics inherent in SIR models. In the absence of ICU constraints
and declines in R0 , the best that a temporary lockdown can do is to eliminate pandemic
overshoot, i.e. to reach the herd immunity threshold without the virus still circulating
(see e.g. Rachel, 2020; Moll, 2020). This limits the number of lives that can be saved by
lengthening the lockdown, but the economic costs continue to increase steeply with the
duration of the lockdowns.
35
Table 9 in Appendix D summarizes cumulative deaths and welfare costs at different points of the pan-
demic possibility frontiers for these experiments as well as all the others in the paper.
36
(a) Economic Welfare Cost (b) Lockdown - Laissez-faire
0.20
4
0.15
3
0.10
2 Laissez-faire
US Policy 0.05
1 US lockdown
0.00
1 2 3 4 5 6 7 8 9 10 4 3 2 1 0 1 2
Earnings Deciles Economic Welfare Cost
(c) Fiscal - Lockdown (d) Fiscal - Laissez-faire
0.4
0.3
0.3
0.2 0.2
0.1 0.1
0.0 0.0
4 3 2 1 0 1 2 4 3 2 1 0 1 2
Economic Welfare Cost Economic Welfare Cost
Figure 11: Panel (a): economic welfare losses by initial position in the distribution of earnings.
Panel (b): distribution of economic welfare losses (multiples of monthly income) from imposing the
lockdown relative to the laissez faire. Panel (c): from lockdown plus the fiscal stimulus relative to
the lockdown only. Panel (d): from lockdown plus the fiscal stimulus relative to the laissez-faire.
As the arrival of the vaccine nears, additional lives can be saved by relatively short
extensions of the lockdown that incur little additional economic costs. This is why the
frontier flattens as the lockdown is extended beyond 12 months.
Welfare cost distribution Panel (a) of Figure 11 illustrates the distribution of economic
welfare losses across the earnings distribution. Everyone loses from the pandemic, both under
lassez-faire and under lockdown, but households who lose the most, perhaps surprisingly, are
always those in the middle of the distribution. The economic losses of the poorest ones are
limited because the main source of their income is not labor, but government transfers which
remain unchanged. 36
Comparing the green and the blue line in panel (a) reveals that the economic losses of the
lockdown are quite uniform across the distribution. Panel (b) confirms this impression: the
entire distribution of economic welfare losses is compressed between 0.5 and 1.5 of monthly
income, with a mean economic loss around 1.
36
Combining this analysis with that of the pandemic possibility frontier implies that households at the
top of the band in Figure 10 are those around the 30th percentile and households at the bottom of the band
are those in the 99th percentile.
37
(a) Transfers (% of Quarterly GDP) (b) PPP Subsidies (%) (c) Withdrawal Cost (%)
Check Wage 0
3.0 UI 50
Profit
2.5 5
40
2.0 10
30
1.5
15
20
1.0
10 20
0.5
0.0 0 25
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
Figure 12: Components of fiscal stimulus package in model
4.3 Fiscal Stimulus Scenario
In this section we add to the lockdown scenario a set of economic stimulus measures that
mimic the Coronavirus Aid, Relief, and Economic Security (CARES) Act. The simulations
in this section are intended to be compared with US data and are our point of departure for
counterfactual stimulus and containment strategies.
Modeling the CARES act We focus on the four most important components of the
CARES act for household welfare. Appendix C contains a detailed description of these
different stimulus policies and how we incorporate them in our model economy. Here we
provide only a summary.37
(i) The Economic Impact Payments (EIP) program consisted of one-time stimulus
payments with amounts which depended on family size and were phased out at high
income levels. To match the total outlays reported by the Department of Treasury
($260B), we set the payment per household to $1,900. We model these payments as
flow transfers paid out evenly over 1.5 months. This allows us to capture delays that
occurred during the rollout of the program and heterogeneity in the exact timing of
the payments.
(ii) Several expansions to the Unemployment Insurance (UI) program consisted of
additional payments to unemployed workers and extended eligibility. We model UI
as transfers that compensate for the shortfall of individuals’ labor incomes relative to
their steady state values, based on the replacement rates calculated by Ganong et al.
(2020). For low-income households these replacement rates exceeded 100%.
37
The CARES act was passed by Congress at the end of March. In our simulations, we assume that the
policy is implemented on April 15.
38
2.5
(a) Reproduction Number 1.8
(b) Infectious (% of Population) 0.200
(c) Monthly Death Rate (%)
R0 1.6 Actual
Effective R 0.175 No ICU Constraint
2.0 1.4 0.150
1.2
1.5 0.125
1.0
0.100
0.8
1.0 0.075
0.6
0.4 0.050
0.5
0.2 0.025
0.0 0.0 0.000
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
(d) Output (%) 10
(e) Consumption (%) 10
(f) Investment and Share Price (%)
0
Investment
0 5 Share Price
10
10 0
20
20
5
30
30
10
40 Y 40 C
Regular Y Regular C 15
50 Social Y 50 Social C
20
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
(g) Hours (%) (h) Labor (%) (i) Government Debt
Quarterly GDP
400 2.70
60 20 Labor Productivity
Labor Income 2.65
40
200 10
20 2.60
0 0 0 2.55
20 2.50
200 10
40 2.45
60 20 2.40
400
80 Workplace Hrs.
Home Hrs. Remote Hrs. 30 2.35
100 600
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
Figure 13: Lockdown plus fiscal stimulus: dynamics of key variables
(iii) The Paycheck Protection Program (PPP) was intended as an employment sub-
sidy. Some researchers, however, have argued that PPP may not have been as effective
at protecting employment as the program’s name suggests (see e.g. Chetty et al., 2020;
Granja et al., 2020) since firms were not required to demonstrate that funds provided
under the program were used to finance payroll expenses for workers that would have
been otherwise laid-off. We therefore model the PPP as part wage subsidy and part
profit subsidy (ςwt , ςπt in the model), with each component amounting to 50% of the
PPP’s $669 billion budget.
(iv) Tax penalties for retirement account withdrawals were temporarily waived and
withdrawal limits were relaxed. We model this policy as a reduction in the scale
parameter χ1 in the adjustment cost function in equation (20).
Figure 12 plots the magnitudes and timing of these four elements of the CARES act that
we feed into the model. In line with the data, components (ii)-(iv) expire on August 1st.
39
(a) Effective R (b) Labor Income (%) (c) Workplace Hours (%)
2.5 No CARES 5 0 No CARES
Check + UI 0 10 Check + UI
2.0 Full CARES Full CARES
5 20
1.5
10 30
1.0 15
40
20 No CARES
0.5 50
25 Check + UI
0.0 Full CARES 60
30
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
(d) Monthly Death Rate (%) (e) Consumption (%) (f) Share Price (%)
0.030
No CARES 0 1 No CARES
0.025 Check + UI Check + UI
Full CARES 5 0 Full CARES
0.020
10 1
0.015
0.010 15 2
No CARES
0.005 20 Check + UI 3
0.000 Full CARES
25 4
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
Figure 14: Effect of different stimulus components
CARES act decomposition Figure 13 displays the analogous aggregate dynamics to
those in Figures 4 and 7 for the model with fiscal stimulus. Figure 14 plots a subset of
these variables alongside their counterparts in the scenario with a lockdown but no stimulus,
together with an intermediate stimulus package that contains only the EIP payments and
expanded UI benefits.
The top two panels in Figure 14 show that the stimulus package has barely any effect
on the initial dynamics of the virus. However, the effective reproduction number is slightly
lower in the second wave, which just prevents the ICU constraint from binding and lowers
fatalities in the second wave. The reason for the lower transmission rate is that the PPP
raises asset prices. The higher asset prices lead people to work fewer hours in the workplace
due to a wealth effect. Lower workplace hours leads to fewer infections
The impact of the stimulus package on economic aggregates is substantial. Both the
transfer programs (EIP, UI) and PPP boost aggregate consumption throughout the lock-
down and in its immediate aftermath. We revisit these effects on consumption below in
our discussion of the distributional dynamics of consumption. The CARES act boosts con-
sumption by around 6 percentage points, with about 4 points coming from PPP and the
remainder from UI and EIP.
Because we model the PPP as part labor subsidy and part profit subsidy, its two main
effects are on labor income and firms’ profitability. Figure 14(b) shows that PPP reduces
the fall in labor income by around half, and Figure 14(f) shows that the fall in the stock
market by around 4 percentage points.
The costs of the stimulus package can be seen in the large increase in government debt
Figure 13(i). After eighteen months the debt-GDP ratio increases by about 12% above its
40
10
Mean
Economic Welfare Cost (Multiples of Monthly Income)
p25-p75
p10-p90
8 p5-p95
17-Month
Lockdown
12-Month
6 Lockdown
4
US Policy
No Lockdo
wn
2
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Deaths (% of Population)
Figure 15: Lockdown plus fiscal stimulus: distributional frontier
pre-pandemic level, compared with an increase of 3% without the CARES act.
Pandemic possibility frontier Figure 15 displays the pandemic possibility frontier for
lockdowns of different lengths in the presence of the stimulus package. The stimulus package
does not alter the shape of the frontier, but it shifts down the frontier and widens the
distribution of economic costs, especially for short lockdowns, by substantially lowering the
welfare losses for about a quarter of households.
This comparison is most clearly seen in Figure 1 in the Introduction. The downward shift
in the frontier reflects the role of the stimulus package in raising household consumption.
The stimulus package lowers the average economic cost of the lockdown by around 20%,
from 3.4 times monthly income to 2.7 times monthly income. The success of the policy is
the mirror image of the failure of Ricardian equivalence in the model.
The top-right panel of Figure 11 reports the distribution of welfare losses (negative num-
bers are gains) from the combination of lockdown and fiscal stimulus relative to a scenario
without fiscal stimulus. Almost all households gain from the CARES Act. The top-left panel
of the figure clarifies that gains are concentrated below the median. The CARES act was
highly redistributive. It is especially interesting that the poorest tercile of the distribution is
economically better off even compared to laissez-faire (these are the households with negative
values in the bottom-right panel). Thus, under the combined lockdown and fiscal stimulus
policy, the bottom quintile of the earnings distribution are better off in terms of both lives
41
(a) Labor Income (%) (b) Consumption (%)
0
0
5
10
10
20 Bottom Quartile Bottom Quartile
15
2nd Quartile 2nd Quartile
30 3rd Quartile 20
3rd Quartile
Top Quartile Top Quartile
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month
Figure 16: Labor income and consumption across pre-pandemic income distribution
and economic welfare than in the laissez-faire scenario.
Distribution of consumption and earnings We can use our model to interpret recent
empirical evidence on household labor income and consumption in the early stages of the
pandemic in the US. Cajner et al. (2020) find that labor incomes have fallen most for house-
holds at the bottom of the income distribution and have remained low. These households
disproportionally work in hospitality and other rigid, S-intensive occupations. At the same
time, Cox et al. (2020) and Chetty et al. (2020) find that consumption expenditures of poor
households have recovered more quickly than expenditures of rich households.
Our model reproduces these apparently contradicting patterns of consumption and labor
income, and offers an intuitive explanation. Figure 16 displays the paths of average labor
incomes and consumption in each quartile of the income distribution, over the first four
months of the pandemic. As in the data, in the model labor incomes fall most for the lowest
quartile of the pre-pandemic income distribution and remain persistently low. Also as in the
data, the drop in expenditures is much more uniform across the distribution, but recovers
fastest for the households in the bottom quartile. The reason, as illustrated in Figure 17, is
that the stimulus package had very heterogeneous effects across the income distribution.
Figure 17 decomposes the dynamics of labor income, total income and consumption into
contributions from each major component of the stimulus program, for the top and bottom
quartiles of the income distribution.
Panels (a) and (d) shows PPP leads to earnings gains for workers across the income
distribution. UI benefits, instead, slightly disincentivizes labor supply at the bottom of the
distribution, where replacement rates widely exceeded 100%. Together, the CARES act
mitigated the fall in earnings for all workers, but the drop in labor earnings was still at least
42
(a) Labor Income (%) (b) Total Income (%) (c) Consumption (%)
0 5
100 No CARES No CARES
Check + UI Check + UI
80 Full CARES 0 Full CARES
10
Bottom Quartile
60 5
20 40 10
20
30 15
No CARES 0
Check + UI 20
40 Full CARES 20
25
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
(d) Labor Income (%) (e) Total Income (%) (f) Consumption (%)
5
No CARES 5 No CARES No CARES
5 Check + UI Check + UI Check + UI
Full CARES Full CARES 0 Full CARES
0 0
5 5
Top Quartile
5
10 10 10
15 15 15
20 20
20
25 25
25
Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul Apr Jul Oct 2021 Apr Jul
Month Month Month
Figure 17: Effect of different stimulus components across pre-pandemic income distribution
10 percentage points deeper at the bottom of the earnings distribution. Panels (b) and (f)
show the stark contrast in the dynamics of total income (including fiscal transfers) between
the top and bottom quartiles of the income distribution. Through the lens of our model, the
combined effect of the various elements of the CARES Act is that income-poor households
experienced large increases in their total incomes.38 Since many of these households are
liquidity constrained, their consumption expenditures follow income closely: they first fall
and then rise (panel (c)). Richer households are rarely liquidity constrained and, as a result,
display more pronounced forward-looking behavior. Because the economic outlook is bleak,
these households cut consumption and save a larger fraction of their income, including the
additional one from the government. These patterns are consistent with empirical evidence
in Baker et al. (2020) and Coibion et al. (2020a) that recipients of stimulus checks consumed
a sizable fraction of them in the first weeks after receipt, and that households with lower
earnings, greater income drops, and lower levels of liquidity displayed stronger spending
responses.
38
When interpreting the large percentage increase it is important to keep in mind that the average starting
income of this population group is very low, so large percentage increases still corresponds to small absolute
amounts.
43
4.4 Smart Containment and Fiscal Policies
So far, we have only analyzed workplace and social sector lockdowns as policies to contain
the virus. These forms of blunt lockdowns have been the main policy instrument used by
the U.S. and other countries to contain the spread of the virus.39 Blunt lockdowns have the
advantage of being both (i) quickly implementable, and (ii) effective at rapidly curtailing
infections when ICU use is near capacity. In the initial phase of an unexpected epidemic they
are thus a sensible policy response. However, blunt lockdowns also have the disadvantage
of being costly in terms of economic welfare, in the absence of adequate social insurance
provision. Are there other instruments that can achieve a better trade-off between lives and
the economy, as measured by a flatter and more inward locus for the pandemic possibility
frontier? In this section, we explore three alternatives.
Smart exemptions from workplace lockdown As with the lockdowns implemented in
the U.S. and most of Europe, the workplace lockdown in our baseline scenario applies to all
non-essential business, including firms in the C-sector. However, based on the findings of
Section 4.2, an economy-wide workplace lockdown might be excessive.
Panel (b) in Figure 18 plots the pandemic possibility frontier (PPF) for a workplace
lockdown that exempts C sector businesses and allows their employees to work on-site. The
main effect of this loosening is to change the labor supply of workers in rigid C-intensive
occupations. Panel (a) shows how the PPF compares to the PPF in the full lockdown
scenario. This looser lockdown generates a flatter PPF, particularly at long durations. But
even with only a 2 months lockdown, this looser lockdown would have saved roughly the
same number of lives with 10% lower welfare costs. One limitation of the looser lockdown,
however, is that the maximum achievable reduction in deaths is smaller than for the full
lockdown.
Pigouvian taxes rebated smartly The virus generates a negative externality: individ-
uals do not internalize that when they consume social goods or work in the workplace, they
risk contracting the virus, which imposes costs on other individuals. These costs are due
to (i) higher disutility of work and lower utility of social consumption (since these utilities
depend on the average death rate); (ii) higher probability of contracting the virus and being
hospitalized and hence unable to work and consume; and (iii) lower residual ICU capacity
and so possibly higher death rates for the critically ill.
A natural remedy for such negative externalities is a Pigouvian tax on either social
consumption or on-site work.40 However, in a model with heterogeneity and market incom-
39
An important exception is the use of border closures in combination of with test and tracing in a handful
countries, such as Australia and New Zealand).
40
Note that this is the opposite of the U.K.’s “Eat Out to Help Out” policy, which subsidizes social
44
10
(a) Comparison 10
(b) Lockdown w/ C Sector Exempted
Mean: US Lockdown Mean
Mean: Lockdown w/ C Sector Exempted p10-p90
Mean: Social Consumption Tax p25-p75
8 Mean: Workplace Hours Tax 8
21-Month
6 6 17-Month
12-Month
4 4
2-Month
Laissez-faire
2 2
0 0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
10
(c) Social Consumption Tax 10
(d) Workplace Hours Tax
Mean Mean
p10-p90 p10-p90
p25-p75 p25-p75
8 8
6 21-Month 6
17-Month 21-Month
12-Month
17-Month 12-Month
4 4
2-Month
Laissez-faire Laissez-faire
2-Month
2 2
0 0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Deaths (% of Population) Deaths (% of Population)
Figure 18: Panel (a): mean pandemic possibility frontier (PPF) for three “smart policies” and
for the baseline lockdown. Each dot on the frontier represents a different duration for the policy.
Panel (b): C-intensive occupations exempted from the lockdown. Panel (c): Pigouvian tax of 30%
on social consumption with revenues rebated to the S-intensive occupations. Panel (d): Pigouvian
tax of 30% on workplace earnings with revenues rebated to the rigid occupations.
pleteness, either tax is particularly bad for a subset of individuals – in the case of a tax on
social consumption, those working in the social sector; in the case of a tax on on-site work,
those in rigid occupations. We offset these costs by rebating the revenues lump-sum to the
affected workers.
Panel (c) of Figure 18 traces the PPF for a 30% tax on social consumption that is kept
in place for different durations. The revenues from this tax are rebated to workers in S-
intensive occupations. So, for example, instead of the government mandating the closure of
restaurants, bars, gyms and hair salons, the government imposes a 30% tax on the sales of
these establishments, and rebates the revenues to both flexible and rigid workers in these
businesses.
The social consumption tax generates a PPF (orange line in panel (a)) that is even
flatter than the PPF from the lockdown with smart exemptions (green line in panel (a)),
consumption.
45
with most of the gain in trade-off coming at long durations. However, keeping the tax on
social consumption in place for an extended period leads to extremely unequal outcomes
across the distribution of households. The reason is that although the targeted rebate is
successful at containing the economic losses of workers employed in S-intensive occupations,
the cost of the tax falls heavily on households in C-intensive occupations, especially those
in rigid jobs who cut their workplace hours for fear of contracting the virus.
An alternative Pigouvian tax policy is to impose a tax on hours worked in the workplace
and to rebate the proceeds to workers in rigid occupations. This tax targets the labor supply
margin as the source of the negative externality, as opposed to the social consumption margin.
Panel (d) of Figure 18 traces the PPF for a 30% tax on workplace hours with different
durations. This policy generates the flattest PPF. With a tax on workplace hours in place
for 2 months, the mean economic welfare loss is about 2 times monthly income, which is
about the same as in the laissez faire scenario, but with a substantially smaller number of
deaths – by around 0.1% of the population.
The distributional outcomes of the tax on workplace hours are also unequal at long
durations. Workers in the rigid occupations gain the most from this policy, because it
essentially insures their labor earnings. Workers in the flexible occupations gain the least,
not because of the direct effect of the tax (which they don’t pay because they work from
home), but because their productivity suffers due to the low labor supply of their colleagues
in rigid occupations.
Figure D1 plots PPFs by occupations for all these alternative policy simulations alongside
those for the lockdown scenario with and without fiscal stimulus.
Summarizing, an important lesson from these experiments is that there exist targeted
policies which offer a more favorable average trade-off between lives and livelihoods than
blunt lockdowns. There are two important limitations to these policies which would need
to be addressed if they were implemented in practice. First, targeted lockdown and tax
policies entail a more unequal distribution of economic welfare costs. Second, there are
limits to the total reduction in deaths that can be achieved by different policies, as indicated
by the vertical segments in panel (a) of Figure 18. An example we have explored that
illustrates both of these features is to exclude essential occupation from the tax on workplace
hours in panel (d). With this alternative policy, the dispersion in economic welfare costs
is substantially reduced but so is the maximum possible reduction in deaths that can be
achieved by extending the duration of the tax.
5 Conclusion
We provide a quantitative analysis of the trade-offs between lives and economic outcomes as-
sociated with the COVID-19 pandemic, under the lockdown and fiscal policies implemented
46
in the U.S., as well as under alternative counterfactual policy scenarios. We focus on the
distributional implications of these policies across workers and households. Different in-
dividuals have different degrees of economic exposure and vulnerability to the pandemic.
Heterogeneity in exposure is related to the extent to which an individual works in a rigid
occupation and/or and occupation that is used intensively in the production of social goods
and services. Heterogeneity in vulnerability is related to households’ access to liquid sav-
ings and eligibility for government transfers. We find that in U.S. data, the most exposed
individuals are also the most vulnerable, which opens the door to very unequal economic
consequences of the pandemic.
Our model simulations suggest that a representative household perspective of the pan-
demic that ignores this heterogeneity would miss some first-order effects of both the lockdown
and fiscal policies. The economic welfare costs of the pandemic are large and heterogeneous
regardless of the policy response. Even smart containment and fiscal policies that offer a
more favorable trade-off in terms of mean outcomes entail very uneven outcomes. Thus,
whereas most of the emphasis in public debate has been on the extent of the trade-off that
governments face in terms of lives and livelihoods, we emphasize the equally important and
inescapable choice over which parts of the population should carry the heaviest burden of
the economic costs. Through our focus on a distributional pandemic possibility frontier, our
paper offers a framework to integrate these different aspects of the policy trade-offs.
Partly because of a constraint on space, and partly because we are not aware of data that
can be used for calibration, we have not run counterfactuals where some of the funds used
for fiscal support are diverted toward investing in health outcomes. Such investments might
include education campaigns about wearing face masks and physical distancing, widespread
testing and tracing, better treatments for COVID-19 and vaccine development. Through the
lens of our model such investments not only improve health outcomes but also have positive
distributional effects, because more effective suppression of the virus enables workers in rigid
occupations and the social good sector to return to work sooner.
Finally, looking ahead, our model predicts that, in the absence of a tight lockdown in
the Fall of 2020, the U.S. will experience a second wave of the virus and another (milder)
recession: the recovery will be W shaped and very prolonged. Moreover, the distributional
implications of the second wave will be much closer to those observed under our laissez-faire
counterfactual, with the economic costs falling more heavily on the most vulnerable parts of
the population, and thus quite different from the distribution of costs during the first wave
in the Spring of 2020. This discrepancy calls for a distinct, more targeted, policy response.
47
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