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Disincentive Effects of
Unemployment Insurance Benefits

WP 23-11

Andreas Hornstein
Federal Reserve Bank of Richmond
Marios Karabarbounis
Federal Reserve Bank of Richmond
André Kurmann
Drexel University
Etienne Lalé
York University
Lien Ta
Drexel University

Disincentive Effects of Unemployment Insurance Benefits∗
Andreas Hornstein
FRB Richmond

Marios Karabarbounis
FRB Richmond

Etienne Lalé
York University

André Kurmann
Drexel University

Lien Ta
Drexel University

November 1, 2023
Unemployment insurance (UI) acts both as a disincentive for labor supply and as a demand stimulus which may explain why empirical studies often find limited effects of UI on
employment. This paper provides independent estimates of the disincentive effects arising
from the largest expansion of UI in U.S. history, the pandemic unemployment benefits. Using
high-frequency data on small restaurants and retailers from Homebase, we control for local
demand effects by comparing neighboring businesses that largely share the positive impact
of UI stimulus. We find that employment in low-wage businesses recovered more slowly than
employment in high-wage businesses in labor markets with larger differences in the relative
generosity of pandemic UI benefits. According to a labor search model that replicates the
estimated employment differences between low- and high-wage businesses, the disincentive
effects from the pandemic UI programs held back the aggregate employment recovery by 4.7
percentage points between April and December 2020.

JEL Classification: E24, E32, J64, J65
Keywords: Unemployment Insurance, Disincentive Effects, Search and Matching Models

∗
Emails:
andreas.hornstein@rich.frb.org, marios.karabarbounis@rich.frb.org, ak3386@drexel.edu,
elale@yorku.ca, ltt46@drexel.edu. We thank Matt Murphy and Kushal Patel for excellent research assistance and Fernando Alvarez, Mark Bils, Yongsung Chang, Cynthia Doniger, Giovanni Gallipoli, Marianna
Kudlyak, Pascal Noel, Guido Menzio, Theodore Papageorgiou, Victor Rios-Rull, Aysegul Sahin, Venky
Venkateswaran as well as numerous seminar and conference participants for their comments. Any opinions
expressed are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of
Richmond or the Federal Reserve System.

1

Introduction

Unemployment insurance (UI) not only acts as a disincentive for workers to supply labor.
It also stimulates consumption, and therefore labor demand, by raising the disposable income
of the unemployed. These two opposing effects are hard to distinguish empirically. Yet, having
independent estimates of the disincentive effects of UI is of critical importance. It informs
policymakers about the full implications of UI provisions and allows economists to properly
discipline and evaluate quantitative labor search models often used for policy analysis.
In this paper, we develop an estimation framework that isolates the disincentive effects
arising from the largest expansion of UI programs in U.S. history, the pandemic unemployment
benefits. We then use a calibrated search and matching model to quantify the disincentive
effects of each of the various provisions of the pandemic UI programs on labor market recovery.
Beginning with the March 2020 CARES Act the U.S. federal government relaxed UI eligibility criteria, extended maximum UI duration, and supplemented state benefits to such a
degree that for many recipients UI payments considerably exceeded what they had earned in
their previous job (Ganong, Noel, and Vavra, 2020). Yet, the overall message from existing
studies (reviewed below) is that pandemic UI benefits had only modestly negative effects on
job-finding rates and employment. What these studies do not clarify, however, is if these limited estimated effects represent small disincentive effects or a small net effect from opposing
labor supply and demand channels.
The small net effect on employment may arise for the following reasons. Average wages
paid differ widely across local labor markets. With a uniform UI income supplement, labor
markets with lower average wages have higher average replacement rates. Thus, businesses
in low-wage markets find it relatively more difficult to attract workers, and employment in
these markets recovers more slowly than in high-wage markets. But at the same time, the
unemployed in these low-wage labor markets experience a relatively larger increase in their
purchasing power, thereby increasing labor demand and helping the employment recovery.
Thus, a standard difference-in-difference estimator may show that in labor markets with higher
replacement rates, businesses recover faster and not slower.
Our research design adds one more difference by considering the employment recovery gap
between low-wage and high-wage businesses within the same local labor market and then
applies a standard fixed effect estimator to these gaps. By comparing low- and high-wage
businesses we difference out common demand shifts arising from the UI stimulus and construct
a measure of the disincentive effects of UI benefits only. The basic identifying assumption to
eliminate the bias from the confounding demand effects is that neighboring low- and highwage businesses share the positive demand effects of the UI stimulus. Our research strategy
not only reduces the bias arising from the demand stimulus of UI but also from any factor
1

that is correlated with demand shifts and replacement rates as long as the factor is common
within labor markets.
Our identifying assumption is more likely to hold the more local the labor market and
the more homogeneous the businesses in that market. To that end, we apply the proposed
research design to data from Homebase, a scheduling and payroll administration provider used
by thousands of small businesses in the U.S. The data is representative of small, in-person
service sector businesses, such as restaurants and retail businesses (Kurmann, Lalé, and Ta,
2021).1 The data provides us with a panel of businesses with daily data on employment, the
hourly wage, hours worked by each employee, business zip code, and industry affiliation. In
addition, we match each business with indicators of quality and price from Yelp and daily
customer visits based on cell phone tracking data from Safegraph.
We first establish a link between the pandemic UI benefits and the employment recovery
gap using an event study approach. We document that while the income supplement of $600
per week under the CARES Act is in effect, the employment recovery in low-wage businesses
significantly lags the employment recovery in neighboring high-wage businesses. But upon
expiration of the income supplement of $600, in the summer of 2020, employment in low-wage
businesses rapidly gains ground and nearly closes the employment recovery gap with their
high-wage neighbors.
Second, we analyze how the employment recovery gap varies with the relative generosity
of the pandemic income supplement of $600. According to our estimates, for the median labor
market, the rise in the replacement rates from the income supplement of $600 held back the
employment recovery in low-wage businesses by 1.5 percentage points more than high-wage
businesses.2
To quantify the overall impact of the CARES Act on employment recovery we build a
labor search model. As long as high-wage businesses are also affected by the pandemic UI
benefits—either directly or through general equilibrium effects—the employment recovery gap
that we estimate may not represent the aggregate effect of UI on employment. The model
allows us to construct a proper counterfactual which is the employment recovery gap in the
absence of pandemic UI benefits. In addition, the model allows us to separately quantify
the impact of each provision included in the CARES Act: the $600 weekly supplement, the
extension of maximum duration of benefits, and the expanded eligibility of beneficiaries.
1
As we document in Appendix A, employment in Homebase businesses tracks administrative data very
closely. In addition, we show that average hourly wages and average employee hours are broadly comparable
to estimates from the Current Population Survey. For a more detailed discussion see Kurmann, Lalé, and Ta
(2021).
2
We also show that in labor markets with a higher replacement rate gap, hours per employee as well as
hourly wages increase relatively faster in low-wage businesses which supports our arguments that our estimates
capture differential labor supply constraints instead of differential demand or productivity effects.

2

We should note that our quantitative model is focused directly on the disincentive effects of
UI and does not capture the stimulative effects of UI nor other pandemic-related confounding
factors such as re-opening restrictions. This is consistent with our empirical design that
estimates disincentive effects net of demand effects and other common labor market factors.
This also allows us to work within the standard class of search and matching models without
imposing additional structure.
In our search model, firms post idiosyncratic, constant over time, wage offers drawn from
an exogenously given distribution. Unemployed workers randomly search for jobs that pay
different wages and accept a job if the offered wage is higher than their reservation wage
(McCall, 1970; Albrecht and Axell, 1984). UI benefits are a function of the worker’s past
wage so that the reservation wage distribution is an equilibrium object (as in Ljungqvist and
Sargent, 1998, 2008).
In the model, not all unemployed receive UI, as benefits are restricted based on eligibility
and maximum duration. Unemployed who are part of the non-UI state are more keen to accept
job offers even from the lower end of the wage distribution. Hence, we calibrate the flow value
of the non-UI state such that, conditional on observed UI recipiency and UI replacement rates,
the model generates a realistic equilibrium residual wage dispersion. Generating a realistic
residual wage dispersion is challenging for standard labor search models (Hornstein, Krusell,
and Violante, 2011). In our model, the presence of the non-UI state substantially increases
the residual wage dispersion.
We expose the model to a large separation shock, consistent with the evidence of the
decline in employment at the onset of the pandemic followed by a large expansion of UI
benefits consistent with the provisions of the CARES Act: income supplement, extension of
benefit duration, and expanded eligibility. We solve for the equilibrium transitional dynamics
of employment in low- and high-wage firms as they return to their steady state.
We find that the baseline model overstates the magnitude of the employment recovery
gap by a large degree, driven mainly by the large decline in low-wage employment. What
is surprising is that the expansion of the UI eligibility criteria alone has a bigger impact
on the decline of low-wage employment than either the generous income supplement or the
extended maximum duration of pandemic benefits on their own. Using data from the Current
Population Survey (CPS) we document that the share of unemployed workers who received
benefits during 2020 nearly tripled compared to the pre-pandemic period. As a result, in the
model, the CARES Act drains the pool of non-UI unemployed which is the main source of
employees for the low-wage firms, so that employment in these firms declines dramatically.
We present a reduced-form solution that can reconcile the model with the data. We
introduce a probability that workers lose their UI eligibility if they refuse a job offer. This

3

assumption effectively reduces the outside option for workers and increases the acceptance
rates for low-wage firms. With a 10 percent probability of losing benefits upon job refusal, we
can match the estimated employment recovery gap closely.
Based on this extended model, we compute the employment losses relative to a counterfactual economy without the CARES Act. We find that when implemented in isolation, each
provision of the CARES Act only has a modest effect. When implemented jointly, however,
the UI programs generate substantial disincentive effects. Specifically, without any of the UI
policy changes, the employment recovery would have been on average about 4.7 percentage
points higher between April and December 2020. This employment loss represents around 25
percent of the average employment loss in the Leisure and Hospitality sector during the same
period.3
Our paper contributes to the literature studying the labor market consequences of UI
benefits by separating the disincentive from the stimulative effects of UI policies. Two papers that also make this distinction are Di Maggio and Kermani (2021) and Hellwig (2021).
Both rely on a comparison in employment between non-tradable sectors — that are more
affected by local demand conditions — versus tradable sectors (in the spirit of Mian and Sufi,
2014). In contrast, our methodology controls for local demand effects by comparing relatively
homogeneous businesses that are part of the same local market. Thus, our methodology is
conceptually closer to the border-county-pair (BCP) research design which has been used extensively to study the effects of expanded UI duration in the aftermath of the 2007-08 financial
crisis.4
Our paper also contributes to the literature studying the extent to which pandemic UI
held back the labor market recovery. So far, this literature has found that pandemic UI
benefits had only modest negative effects on job-finding rates and employment. Ganong et
al. (2022) use individual bank account data and document that the weekly $600 supplements
during the first four months of the CARES Act had only a moderate effect on job-finding
rates. Petrosky-Nadeau and Valleta (2021) arrive at a similar conclusion using CPS data.
Marinescu, Skandalis, and Zhao (2021) find that pandemic UI slightly decreased search effort
The unemployment duration elasticities implied by the model are also modest and in line with the lowto-middle range of pre-pandemic estimates (e.g., Schmieder and von Wachter, 2016). The overall employment
impact turns out to be large, however, due to the sheer size of the UI provisions as well as their joint
implementation.
4
Hagedorn et al. (2013) compare adjacent counties in different states that experience changes in UI for reasons tied to the state’s performance and find that increasing the duration of benefits increased unemployment
rates substantially. In contrast, Dieterle, Bartalotti, and Brummet (2020) and Boone et al. (2021) find, using a
similar BCP research design but accounting for cross-border spillovers and a longer sample, respectively, that
the negative effects of UI were small. Subsequent research that uses data on job applications and variation in
the real-time measurement error of the unemployment rate also finds a limited effect of UI (e.g., Marinescu,
2017; Chodorow-Reich, Coglianese, and Karabarbounis, 2019). A BCP design is not well-suited to study the
effects of pandemic supplements because these provisions occurred simultaneously across counties.
3

4

but did not decrease vacancy creation. Coombs et al. (2021) compare job finding rates in
states that withdrew early from the pandemic UI benefits in the summer of 2021 to states
that retained the benefits and find that in the absence of pandemic benefits, employment would
have been modestly higher. We argue that the limited effects estimated in the aforementioned
papers likely represent a mix of disincentive effects, stimulative effects, and possible other
confounding local demand shocks.
A notable study is Finamor and Scott (2021) who, like us, use Homebase data but use
variation at a relatively broad geographical level, namely a state. They find that a higher
replacement rate is not associated with a lower labor market re-entry of workers. When we
conduct our research design at a similar broad level of geographical aggregation our estimates
become small and insignificant which highlights the importance of comparing units within
narrow local industries.
Finally, our paper contributes to the literature using structural models to quantify the
effects of UI benefits. Typically, existing models focus on a single aspect of the UI policy such
as the replacement rate (e.g., Landais, Michaillat, and Saez, 2018), the maximum duration of
benefits (e.g., Nakajima, 2012; Kekre, 2021; Mitman and Rabinovich, 2022), expanded eligibility (e.g., Michaud, 2023), or one-time additions to usual benefits via income supplements as in
the pandemic UI benefits (e.g., Petrosky-Nadeau and Valleta, 2021; Ganong et al. (2022)). In
contrast, our model quantifies the impact of the CARES Act taking into account all aspects of
the pandemic UI policies: income supplements, expanded eligibility, and extended maximum
duration. We show that first, expanded eligibility was the most disruptive of the UI policies
especially for low-wage businesses, and second, that the large disincentive effects arise from
the interaction of these UI policies.
The paper is organized as follows. Section 2 describes the research design. Section 3
outlines the data and Section 4 estimates the disincentive effect of pandemic UI benefits on
employment recovery. Section 5 sets up the quantitative model and the calibration. Section 6
describes the model results. Finally, Section 7 concludes.

2

Research design
Consider the following data-generating process
yj,c,t = α + βRj,c,t + X0j,c,t γ + uc,j,t + εj,c,t ,

5

(1)

where yj,c,t is employment for business j (normalized by its value in some initial period t0 ) in
labor market c and period t, and Rj,c,t is the business-specific replacement rate defined as
Rj,c,t =

bc (wc,t0 ) + St
.
wj,c,t0

(2)

This replacement rate measures how much the average unemployed worker in labor market c
receives in UI payments relative to the wage offered by business j. For the average unemployed,
UI receipts depend on state-level benefits bc (wc,t0 ) where wc,t0 is the average hourly wage in
labor market c in the initial (pre-pandemic) period t0 as well as the pandemic UI income
supplement St (translated into per-hour units). Finally, wj,c,t0 is the average hourly wage of
business j in t0 .
Our empirical design could equally be applied to workers instead of businesses. In such
a case, variable yj,c,t would be some labor market indicator for worker j (e.g., employment
status) in labor market c and period t, and Rj,c,t would be the worker-specific replacement
rate. The reason we focus on businesses instead of workers is that in our data (analyzed in
detail in Section 3) workers typically work for short periods before permanently exiting the
sample. Thus, we cannot guarantee a long balanced panel unless we analyze the employment
recovery from the perspective of employers.
The coefficient β captures the negative impact of a higher replacement rate on business
employment, i.e., it is a measure of the disincentive effect. Business employment is also affected
by observable factors, Xj,c,t , and unobserved factors, uj,c,t , that are potentially correlated with
Rj,c,t . Unobserved factors can include, on the one hand, common effects such as demand
shifts by the UI stimulus in labor market c and, on the other hand, idiosyncratic features of
businesses (e.g., productivity). Finally, εj,c,t denotes a classical error that is, by assumption,
uncorrelated with Rj,c,t .
Unbiased estimation of β requires that E[Rj,c,t uj,c,t | X0j,c,t ] = 0. If UI benefits stimulate
local demand or if they are otherwise positively correlated with local demand conditions, then
β̂ is biased upwards (making the estimated coefficient less negative than the actual disincentive
effect). On the other hand, if high-wage businesses are at the same time more productive and
therefore less affected by a negative shock such as the pandemic, then this implies a downward
bias of β̂.
Figure 1 gives a visual example of the identification concern. In this example, there are
two labor markets, A and B, each populated with two businesses (assumed to have the same
productivity). Labor market A is populated by relatively high-wage businesses while labor
market B is populated by relatively low-wage businesses.
As a consequence of the pandemic, businesses experience a large decline in their employ-

6

Figure 1: Example of Research Design

100

80

60

40
0

1

2

3

4

5

6

7

8

9

10 11 12 13 14

Notes: A hypothetical example of labor market recovery highlighting the identification concerns.

ment and gradually recover back to normal. With the same pandemic supplement S, on
average, labor market B has higher replacement rates relative to labor market A. But despite
the higher average replacement rate in labor market B relative to labor market A, the average
employment recovery in labor market B is faster than in labor market A. This occurs because
unemployed workers in labor market B experience a larger increase in their purchasing power
compared to labor market A which translates to a higher demand for local output.5 As a
result, a typical estimation of regression (1) with fixed effects across location and time is not
enough to estimate β without bias. This estimator cannot detect the confounding demand
effects that shift the average employment recovery higher in labor market B.
We therefore propose to eliminate the confounding demand effects by averaging across lowand high-wage businesses of the same labor market c and then taking the difference. This
results in the regression
∆yc,t = β∆Rc,t + ∆X0c,t γ + ∆uc,t + ∆εc,t .

(3)

where ∆yc,t ≡ yL,c,t − yH,c,t is the difference between the average employment-to-normal in
the low-wage section and the high-wage section of labor market c, ∆Rc,t ≡ RL,c,t − RH,c,t is
5
This is a relevant concern since Ganong et al. (2022) show that pandemic-UI recipients quickly spent a
substantial portion of their benefits. Using county-level correlations, we also verify that the generosity of the
$600 weekly supplement is positively correlated with changes in consumer spending at the beginning of the
pandemic (see Appendix B).

7

the difference between the average replacement rate in the low-wage section and the highwage section of labor market c, and similarly for the other observable factors. As we show in
empirical Section 3, and also demonstrate in the simple example below, the replacement rate
gap in low-wage labor markets is larger than in high-wage labor markets.
The idea behind our design is that the component of uj,c,t that is common between lowand high-wage businesses is eliminated. It is plausible that the stimulative effects arising
from local demand shocks are largely shared between neighboring businesses and therefore
differenced out. Within labor markets, the business with a relatively high replacement rate
has more difficulty recovering relative to the business with a relatively low replacement rate,
and this difference is wider the larger the difference in the replacement rates. For example, in
Figure 1, the employment recovery gap in labor market B is larger than in labor market A
because the replacement rate gap is also larger. As a result, our local industry estimator picks
up the negative correlation between the replacement rate gap and the employment recovery
gap by differencing out common demand effects.
Note that our strategy not only deals with common demand effects arising from the UI
stimulus but with any type of common demand shifts that may be correlated with the generosity of the replacement rates (e.g., local demand shifts due to pandemic regulations or shifts
in consumer preferences). At the same time, our strategy does not eliminate components of
uj,c,t that are not common (e.g., productivity). But as long as the difference in productivity
between neighboring low- and high-wage businesses remains constant over time, we can obtain an unbiased estimate by adding labor market fixed effects in regression (3). This is the
main regression specification we analyze in the empirical analysis of Section 4. Finally, note
that our research design identifies relative effects between neighboring businesses that do not
necessarily represent aggregate effects. In Section 5 we rely on a structural model to translate
our estimates into aggregate UI effects.
Example of research design We demonstrate more precisely our arguments using a simple
example. Assume, as in Figure 1, that there are two labor markets, A and B, each populated
with a low-wage and a high-wage business, j = {L, H}. The wage of business j in labor
market c is given by wj,c = (1 + εj )wc where wc is the average wage in the labor market and
εj ∈ {−, }. Labor market A is populated by relatively high-wage businesses while labor
market B is populated by relatively low-wage businesses, i.e., wA > wB . For simplicity, we
assume that the dispersion  is the same in both labor markets. Assuming a proportional
pre-pandemic UI replacement rate ρ, the business-specific replacement rate is
Rj,c,t



ρwc + St
ρwc + St
St
−1
=
=
= ρ(1 + εj )
1+
.
wj,c
wc (1 + εj )
ρwc
8

(4)

In addition, we assume for simplicity that Xj,c,t = 0 for all j, c, t, and that the demand shifter
of business j is given by
St
uj,c,t = ψj
,
(5)
ρwc
where ψj gives the sensitivity of employment in business j when the relative purchasing power
St
increases. The demand shift is stronger in labor market B, because the relative purchasing
ρwc
power increases more than in labor market A when the supplement S is in effect.
To simplify the analysis we define T1 and T2 as periods where the income supplement is or
is not in effect, respectively (indexed by τ = {T1 , T2 } so that ST1 > 0 and ST2 = 0). Second,
xc,τ is the average
ofi variable x across businesses of labor market c in period τ . For example,
h
ρ
Sτ
1 + ρw
.
Rc,τ = 1−
2
c
The typical estimator with fixed effects across labor markets and time cannot eliminate the
correlation between the replacement rate R and demand shifts u. Defining ∆c,τ as differences
in variables between both time periods and labor markets, we have:
∆c,τ y c,τ = [y A,T2 − y A,T1 ] − [y B,T2 − y B,T1 ]


1
ST1
1
+
∆c,τ Rc,τ = [RA,T2 − RA,T1 ] − [RB,T2 − RB,T1 ] =
−
1 − 2
wA w B


ST1
1
1
−
+
.
∆c,τ uc,τ = [uA,T2 − uA,T1 ] − [uB,T2 − uB,T1 ] = ψ
ρ
wA wB
Thus, a regression of ∆c,τ y c,τ on ∆c,τ Rc,τ generates a biased coefficient since ∆c,τ Rc,τ remains
correlated with the unobserved component ∆c,τ uc,τ . Instead, our local industry design transforms the data in terms of differences between businesses of the same labor market c. Just
for comparison with the previous estimator, we denote the operator differencing variables between businesses of the same labor market as ∆j∈c . For the baseline specification (3) we use
the simpler notation ∆ to denote the differencing of variables between businesses of the same
labor market and rely on fixed effects to demean other dimensions of the data. This gives us:
∆j∈c yj,c,τ = yL,c,τ − yH,c,τ


∆j∈c Rj,c,τ = RL,c,τ − RH,c,τ

Sτ
= 1+
ρwc

∆j∈c uj,c,τ = uL,c,τ − uH,c,τ = (ψL − ψH )



2ρ
1 − 2



Sτ
.
ρwc

The basic identification assumption behind our research design is that ψL = ψH , i.e.,
demand effects arising from the UI stimulus equally benefit low- and high-wage businesses in
the same narrowly defined labor market c. The weaker assumption that neighboring businesses

9

only partially share the benefits from the UI stimulus is still able to reduce the bias from the
demand component.
i For example, if ψH = χψL with χ ≤ 1 then Cov(∆j∈c Rj,c,τ , ∆j∈c uj,c,τ ) =
h
Sτ
2
) which tends to 0 as χ → 1.
(1 − χ)ψL ρ(1−2 ) V ( w
c
Furthermore, as we mentioned, our local industry estimator cannot eliminate unobserved
factors that are not common between low- and high-wage businesses, most notably productivity. But to the extent that the difference in productivity between low-wage and high-wage
businesses is time-invariant, we can eliminate its effect by further differencing the data along
Sτ
the labor market dimension. For example, if uj,c,τ = ψj ρw
+ zj , where zj is the productivity
c
of business j, we can eliminate the time-invariant difference zL − zH from the unobserved
component by adding labor market fixed effects.

3

Data

3.1

Employment data (Homebase)

We use data from Homebase (HB), a scheduling and payroll administration provider used
by thousands of small businesses in the U.S. Most of these businesses are restaurants and
retail businesses that are individually owned and operated. The data provides us with a panel
of businesses with daily data on employment, hourly wages, and hours worked. Given the
nature of HB businesses, workers typically work for short periods before permanently exiting
the sample. Thus, to guarantee a long balanced panel we analyze the employment recovery
from the perspective of employers instead of individual workers.
Our HB data covers the period from January 2019 to December 2020 and contains approximately 140,000 unique businesses. We construct a benchmark sub-sample for which (1)
businesses are assigned to industries, (2) the sample is “balanced”, (3) we have the average
wage of businesses, and (4) there are at least two businesses for every local-industry cell.
Industries differed in their employment trajectories during the pandemic. It is therefore
important to incorporate information about the industry where the business operates. The
HB data contains a business address but does not include consistent information on its industry classification. Based on the name and address of HB records we can match individual
businesses to (i) Safegraph’s Places of Interest (POI) data, which provides us with consistent
industry coding for each business based on the North American Industry Classification System
(NAICS) as well as the number of customer visits for each business derived from anonymized
cell-phone data; and (ii) Yelp data that includes indicators of quality and price range of the
business.6 After matching businesses to industries, we are left with 30,665 businesses for which
6

See Kurmann, Lalé, and Ta (2021) for a detailed description of the matching procedure.

10

we know their location and industry.
We are interested in how employment in businesses recovers during the pandemic, allowing
for temporary business closures and differences in pre-pandemic trends. For this purpose, we
construct a “balanced” sample by requiring that businesses are in the sample all of 2019, but
may temporarily close in 2020. In our sample, businesses will shut down, especially in March
and April 2020, but we do require that they re-open and operate at least until December 2020.
This restriction leaves us with 9,335 businesses.
We want to study the relative employment paths of low- and high-wage businesses in localindustry cells. Thus, we restrict the sample to businesses that track not only the number of
employees but also payroll, that is, we have information on both the business’ employment
and wages. This decreases the number of businesses to 6,550. To make the distinction between
low- and high-wage businesses in a local-industry cell we drop single business cells which leaves
us with 4,219 businesses for which we have daily information.
With the baseline sample we can analyze each business along the pre-pandemic period (i.e.,
to control for seasonal patterns) and across multiple store characteristics (location, industry,
price range, etc.). In Appendix A we show that employment recovery dynamics of the baseline
sample is broadly similar to the recovery dynamics of the full HB sample, and Kurmann, Lalé,
and Ta (2021) have shown that employment in the full HB sample tracks well employment in
the Leisure and Hospitality sector. In addition, we show that the average hourly wages and
hours per employee in our baseline HB sample are closely comparable to estimates from the
CPS.
As described in our research design, our goal is to compare labor market outcomes of lowversus high-wage businesses within local industry cells. To that end, we sort businesses as
follows. Let wj,c denote the log of the average hourly wage for business j in local-industry cell
c, computed over all hourly wages paid to business employees in our base period, January and
February 2020. Thus, a business is characterized by its pre-pandemic average hourly wage.
Local industry sorting then is based on a simple regression of business wages wj,c on localindustry dummies dc :
wj,c = a + dc + ej,c .
(6)
The residual êj,c is the business’ deviation (in percentage terms) from the local industry
average. We classify a business as a high (low) wage business if the residual wage is higher
(lower) than the local-industry average, i.e., êj,c > 0 (êj,c < 0).
A local industry is a set of businesses that share the same geographical area and industry.
We define a geographical area by its four-digit zip code. On average, this definition bundles
four neighboring zip codes. We define an industry at the two-digit level of NAICS, except
for restaurants and bars (NAICS 722410, 722511, 722513, and 722515), which we define as
11

Table 1: Employment, Hours, and Wages by Business Type

All Businesses

Low-wage

High-wage

6.4
6.7
11.3
8.3
9.9
4.03
0.41
0.85
0.30
4,219

6.0
6.6
10.3
8.6
10.2
4.01
0.44
0.84
0.30
2,037

6.9
6.7
12.2
8.1
9.6
4.05
0.39
0.86
0.29
2,182

# Employees per business
Hours worked (per day)
Hourly wage ($)
Separation rate (%)
Hiring rate (%)
Yelp rating (1-5)
Share with $1 Yelp price
Share of restaurants and bars
Share of businesses in rural areas
# Businesses

Notes: Averages are calculated for operating businesses in 2019. Low- and high-wage business
classification is based on local industry sorting as described in the text.

a separate group. Given our sample, this results in 1,134 local-industry cells with two or
more businesses. Most cells have few businesses: the 25th percentile cell has 2 businesses, the
median cell has 3 businesses, and the 90th percentile cell has 7 businesses. The largest number
of businesses in a cell is 32.
We measure weekly employment in a business by counting the unique bodies that worked
for at least one day during the week in the business. If the business does not operate during
the week, we set the number of bodies to zero. Our definition aligns with the way official
employment statistics are constructed based on monthly or quarterly payroll data (e.g., the
Current Employment Statistics).
Table 1 reports statistics by business type (low- and high-wage within a local industry cell)
averaged over all the days the business operated in 2019. The average number of employees is
6.4 across all businesses which indicates that the HB data capture mainly very small businesses
(Kurmann, Lalé, and Ta, 2021). Furthermore, low-wage businesses are on average smaller
than high-wage businesses. On average, employees work 6.7 hours per day and the hourly
wage is $11.3. Even within narrowly defined local industries, there is sizable dispersion in
hourly wages: high-wage businesses pay on average $1.9 more than low-wage businesses or
equivalently, 7 percent more than the average.
In Figure 2 we report hourly wages by decile for low- and high-wage businesses. On
average, the bottom 10 percent of employees in low-wage businesses receive around $8 per

12

Figure 2: Hourly Wages Within Businesses
16

14

12

10

8
1

2

3

4

5

6

7

8

9

10

Notes: We sort employees in every business based on their hourly wage. We report the average
hourly wage for each decile in the wage ladder during 2019.

hour while the bottom 10 percent in high-wage businesses receive around $10 per hour. The
wage difference remains constant across the wage ladder. Hence, the wage differences do not
arise from a few special employees at the top of the ladder but likely from some business fixed
effect that affects uniformly the bottom and the top of the wage ladder.
Returning to Table 1, the weekly hiring rate is defined as the number of workers who work
in week t but not in t − 1 divided by the number of employed in t. The weekly separation rate
is the number of workers who worked in t − 1 but not in t divided by the number of employed
in t. Table 1 reports weekly separation and hiring rates averaged over all the weeks in the
sample. The weekly hiring rate and job separation rate in the HB data is 9.9 and 8.3 percent,
respectively. Both of these numbers are larger than the equivalent values implied by monthly
or quarterly data as typically reported in the literature (e.g., Hyatt and Spletzer, 2013).7
Concerning industry and location, our sample consists of 85 percent of restaurants and
bars, 70 percent of the businesses are in metro areas and 30 percent in rural areas. Finally,
the Yelp data, on average, rate low- and high-wage businesses of the same local industry
similarly, and have high-wage businesses slightly more expensive.

7
Closer inspection reveals that this difference arises because a substantial fraction of employees in the HB
data miss work for a week or two and then return to the same business within the same month. The highfrequency weekly HB data capture these transitions, whereas they largely disappear in the time-aggregated
monthly and quarterly data (for a related discussion, see Davis et al. (2013)).

13

3.2

Pandemic unemployment insurance benefits

The CARES Act which was signed on March 27, 2020, and intended to ameliorate the
effects of pandemic lockdown measures, set off the largest expansion of UI programs in U.S.
history. The Act extended UI eligibility to self-employed and gig workers and those not meeting state requirements on previous work experience through the Pandemic Unemployment
Assistance (PUA) program. In addition, the Act increased benefits from the beginning of
April 2020 through the end of July 2020 in that everyone who qualified for UI received an additional $600 in weekly benefits through the Federal Pandemic Unemployment Compensation
(FPUC) program. Finally, the Act increased the duration for which benefits could be received
by an additional 13 weeks beyond state benefit exhaustion through the Pandemic Emergency
Unemployment Compensation (PEUC) program which in combination with increased UI duration at the state level implied that eligible workers did not exhaust benefits until at least
the end of 2020.
After FPUC expired, the Trump administration issued an executive order on August 8,
2020, for Lost Wage Assistance (LWA) that was set to $300 per week. The program was
designed to last for six weeks but states did not disperse the benefits immediately after the
expiration of FPUC. Only seven states started handing out benefits in August 2020 and most
states first started to hand out benefits during the week of September 6th and September
13th . A subsequent $300 weekly supplement was further extended between January 2021 and
September 2021 together with expanded eligibility provisions. For our analysis, we focus on
the UI policies implemented during 2020 (i.e., the CARES Act) and not during 2021. The
CARES Act was implemented relatively fast in response to an unanticipated shock. It is more
difficult to argue that the subsequent policies that started in 2021 were similarly unanticipated.
Replacement rate effects Ganong, Noel, and Vavra (2020) estimate that the $600 FPUC
supplement led to a massive increase in replacement rates, nearly tripling typical benefit levels
and raising the median replacement rate to 145%, with three-quarters of eligible workers
receiving more in UI benefits than their previous labor earnings.
We plot the impact of the FPUC supplement on our measures of local industry replacement
rate gaps, ∆Rc,t , in Figure 3. The replacement rate gap is the difference between the average
replacement rates of low- and high-wage businesses in the same labor market with the businesslevel replacement rate defined as in equation (2). In normal times the replacement rate gap is
not zero as the low-wage businesses have higher implied replacement rates (about 7 percentage
points higher for the median labor market). When the pandemic UI programs come into effect
the gap increases for all labor markets but increases more so for the labor markets with either
a lower overall average hourly wage or a larger difference in the hourly wage between low- and
14

Figure 3: Variation in the Replacement Rate Gap

80

60

40

20

0
Jan 20

Apr 20

Jul 20

Oct 20

Notes: We plot the difference in replacement rates (∆R) between the low- and the high-wage labor
market, by week at the 25th , the median, and the 75th percentile of the distribution. The difference
is reported in percentage points.

high-wage businesses.8 To see this algebraically, assume that we have two businesses in labor
market c with the low-wage business paying wL,c,t0 and the high-wage business wH,c,t0 . Then
we have that
bc (wc,t0 ) + St bc (wc,t0 ) + St
−
∆Rc,t =
wL,c,t0
wH,c,t0
which can be written as:
wH,c,t0 − wL,c,t0 wH,c,t0 − wL,c,t0
∆Rc,t = b(wc,t0 )
+
St .
wH,c,t0 wL,c,t0
wH,c,t0 wL,c,t0
|
{z
} |
{z
}
=ac

(7)

=δc

Labor markets with generally low hourly wages or larger inequality in hourly wages have
higher scaling factors δc . In addition, note that by adding a labor market fixed effect in our
regressions we can eliminate the constant ac but not the scaling factor δc .
Eligibility effects What has received less attention in the discussion of pandemic UI is how
the increased UI recipiency through an expansion of UI eligibility has affected labor market
8
The average replacement rate in a labor market, Rc,t , is strongly correlated with the difference in the
replacement rates between low- and high-wage businesses within the labor market, ∆Rc,t (see Appendix C).

15

outcomes. Larrimore, Mortenson, and Splinter (2023) use IRS data and estimate that the
number of UI recipients in 2020 was more than twice that number in 2010 during the Great
Recession. The increase in recipiency together with the increased benefits means that total UI
benefits paid in 2020 were more than three times those paid in 2010. It is difficult to isolate
the effects of UI eligibility extensions in the data but they come through clearly in our labor
search model of the UI disincentive effects presented in Section 5.

4

Effects of pandemic UI benefits on employment

We show that in our HB sample, the presence of generous UI benefit supplements during
the pandemic slows down the employment recovery of low-wage businesses relative to that of
high-wage businesses.

4.1

Event study analysis

As a first step, we characterize the employment recovery of low-wage businesses relative
to high-wage businesses following the pandemic in March 2020, and how the relative recovery
relates to broad changes in the magnitude of UI benefits. For this purpose, we estimate the
following weekly regression for 2020 data:
∆yc,t =

X

bs 1{s=t} + X0c,t γ + δ∆yc,t,2019 + εc,t ,

(8)

s

where ∆yc,t = yL,c,t /yL,c,t0 −yH,c,t /yH,c,t0 is the employment recovery rate gap which is expressed
in percentage points and is calculated using the difference in average employment among lowwage and high-wage businesses, in labor market c and week t, relative to the base period t0
of January-February 2020.
The weekly dummies capture the average weekly employment recovery gap controlling for
a set of observables, Xc,t , and one-year lagged employment gaps. The observables include
(1) the number of Covid-19 deaths in a county as a measure of community health risk; (2)
the percentage change in visits in schools by week and county relative to January 2020 as
a measure of disruptions in schooling (Kurmann and Lalé, 2023); (3) the difference in the
number of weekly customers between the low- and high-wage businesses in cell c (relative
to the base period of January-February 2020); and (4) the difference in price range between
low- and high-wage businesses as measured in Yelp. Finally, we include the one-year lagged
employment gap, to control for potential seasonal factors.
Figure 4 shows the estimated coefficients on the weekly time dummies as well as their 95
percent confidence intervals. We also mark the period from April 2020 to August 2020 when
16

Figure 4: Employment Recovery Around UI Programs
2
0
-2
-4
-6
-8
-10

Jan 20

Apr 20

Jul 20

Oct 20

Jan 21

Notes: Estimated b’s from Regression 8. The coefficients represent the average low-wage business
employment minus the average high-wage business employment (both relative to their pre-pandemic
level). Dates of initiation and expiration of the income supplement are reported. The shaded area
represents the 95 percent confidence interval.

the CARES Act provided an additional $600 weekly supplement and the subsequent period
when the Lost Wages Assistance (LWA) program provided a $300 weekly supplement for six
weeks. We can see that after an initial bigger drop of employment in low-wage businesses
at the onset of the pandemic, low-wage businesses are catching up with high-wage businesses
and the employment gap narrows from the end of March 2020 to early April 2020. With the
arrival of the CARES Act the employment gap not only stops closing, but it starts to widen
until the $600 weekly supplement expires at the end of July 2020. Thereafter, employment
in low-wage businesses rapidly gains ground and partially closes the employment gap to the
high-wage businesses.9

9
For a detailed evaluation of pre- and post-pandemic trends in the time series of employment, hours per
employee, hourly wage, separation, and hiring rates, for low- and high-wage businesses during 2019 and 2020,
see Appendix D.

17

Table 2: Effect of Pandemic UI Replacement Rate
Employment gap

∆yc,t

(1)
Replacement rate gap
(per 100 p.p.)
Covid-19 deaths
(per 100,000 pop.)
School traffic
(% change)
Customer visits gap
# Observations

Hours per employee gap

(2)

(3)

−6.52*** −5.73*** 0.41
(1.32)
(1.34)
(0.60)
−1.28
−1.45
−0.21
(0.98)
(1.04)
(0.42)
1.61***
1.78*** −0.02
(0.44)
(0.45)
(0.18)
–
7.52***
–
–
(0.76)
–
59,065
51,834
52,741

(4)
0.39
(0.62)
−0.11
(0.43)
−0.13
(0.19)
0.61***
(0.22)
46,700

Hourly wages gap
(5)

(6)

1.88***
1.52**
(0.65)
(0.63)
0.65*
0.75*
(0.37)
(0.39)
−0.51*** −0.57***
(0.15)
(0.16)
–
−0.50***
–
(0.18)
48,952
43,519

Notes: Estimates from regression 9 including the control variables. Observations are at the local
industry/week level. We winsorize variables at the one percent level and cluster standard errors at
the local industry level.

4.2

The effect of income supplements on employment recovery

We now evaluate the direct effect of the pandemic income supplements in our local industry
sample by replacing the weekly fixed effects in equation (8) with the replacement rate gaps:
∆yc,t = β∆Rc,t + X0c,t γ + δ∆yc,t,2019 + ac + ηc,t .

(9)

Essentially, we are estimating regression (3) described in Section 2. For this regression, we
also include a cell fixed effect ac to control for time-invariant differences between low- and
high-wage businesses, most notably constant differences in their productivity. Finally, we
also estimate the impact of replacement rate gaps on the recovery rate for several alternative
left-hand side variables: employment, average hours per employee, and hourly wages.
Table 2 shows the regression results. Estimates are reported with and without customer
traffic as a control variable. Each observation represents a cell in a particular week during
2020. There are fewer observations when we include customer traffic as a control since this
variable is not available for all businesses. Similarly, there are fewer observations for the
alternative dependent variables hours per employee and hourly wages since businesses with
employment information do not have information on hours and wages for every week of 2020.
In our preferred specification that controls for customer traffic, a 100 percentage point
increase in the business replacement rate gap, is associated with a 5.7 percentage point decline
in low-wage business employment relative to high-wage business employment. For the median
18

labor market the CARES Act increases the replacement rate gap by 27 percentage points,
see Figure 3, which implies a 1.5 percentage point decline in low-wage employment relative
to high-wage employment. This estimate should be interpreted as the effect of the $600 UI
supplement on the employment recovery of low- vs. high-wage businesses conditional on the
presence of the other CARES Act provisions. We emphasize this interpretation since in the
structural model of Section 5 we show that the combined effect of the UI policies is much
larger than the sum of their individual effects.
Table 3: Effect of $600 Supplement on Employment Recovery (in p.p.)
Estimate per 100 p.p. ∆R
× Median increase in ∆R

Effect of $600 supplement

−5.7
0.27

−1.5

Notes: The baseline estimate in Table 2 is translated using the median increase in the replacement
rate gap in Figure 3.

Two pieces of evidence corroborate our claim that our estimates do not arise from productivity differences between low- and high-wage businesses. First, when we control for differential
customer visits the estimated employment effect changes little. Second, an increase in the replacement rate gap is associated with a positive but not significant increase in hours per
employee gap of 0.3 percentage points, and a positive and statistically significant increase in
the hourly wage gap by 1.5 percentage points.10 These findings suggest that the pandemic
UI generated stronger labor supply constraints for low-wage businesses which reacted to these
constraints by increasing the hours worked by their existing employees and by raising their
wages at a faster pace. Had the faster employment gains in high-wage businesses been driven
by differential productivity shifts (as opposed to UI) we should expect their hours per employee
and hourly wages to also grow faster than in low-wage businesses.

4.3

Discussion and robustness

The basic identification assumption to control for demand effects is that neighboring businesses share most of the positive impact of UI stimulus. We find this a plausible assumption,
10
This result differs from Jager et al. (2020) who analyze the sensitivity of wages to UI benefits using four
UI reforms in Austria between the period 1976-2001 and find that wages in that case are insensitive to UI
benefits changes.

19

Figure 5: Share of Stores Closed During the Week (Averaged over a Month)

50

40

30

20

10

0
Dec 19

Mar 20

Jun 20

Sep 20

Dec 20

Notes: Share of stores with zero employees in a week reported in percent (monthly average).

especially if the neighborhood is defined in a narrow way (e.g., four-digit zip code in our
baseline). As an exercise, we explore how the estimates change if we define a local industry
more broadly. In particular, we compare low- and high-wage businesses within a U.S. State.
Using such broad variation, the estimated coefficient for the replacement rate gap is −0.4
and statistically insignificant. The decline (in absolute value) in the employment response is
natural since businesses located in relatively low-wage areas benefit more from the relatively
faster increase in the purchasing power of the unemployed in these areas. It is also possible
that separate regions experienced different local demand shocks during the pandemic which
may additionally confound the estimates.
This exercise explains why we find different results from Finamor and Scott (2021) who
also use HB data but use state fixed effects and find that a higher replacement rate is not
associated with a lower labor market re-entry of workers. Thus, our research design highlights
the importance of comparing units within narrow local industries.
Another concern is the extent of business closures in HB while the $600 income supplement
is dispersed. Figure 5 shows that the average share of closed stores is 30 percent in April 2020,
16 percent in May 2020, and 7 percent in June 2020. Thus, most of the HB businesses are
open during the period of the generous income supplement.
Next, we conduct a series of robustness exercises. We focus on the implications for the

20

estimated coefficient for the replacement rate gap in the employment gap regression. A detailed
analysis of the estimates is reported in Table E-5, Appendix E.
Continuously open businesses Our baseline sample includes businesses that operated
continuously during the pandemic and businesses that closed and re-opened. If we restrict
the sample to the businesses that continuously operated during the pandemic the estimated
coefficient on the replacement rate gap declines from −5.7 to −3.9. This attenuation implies
that part of the disincentive effect operates through low-wage businesses remaining closed at
higher rate than high-wage businesses.
Tips and commission Recorded hourly wages in HB likely represent base rates and do not
include overtime, tips, and commissions (OTC). OTC is particularly relevant in the Leisure
and Hospitality sector, which accounts for the majority of the HB sample. To address this
concern, we use information from the CPS and adjust individual wage rates in the HB data
with an OTC amount estimated from the CPS data (see Appendix A for details). With the
imputed wages that include tips and commissions, the estimated coefficient on the replacement
rate gap is −3.7.
Broader sample In the baseline sample, we remove businesses for which we could not find
information on their price and quality from Yelp. If we include businesses for which we do not
have Yelp-related information, the sample size almost doubles to 7,958 businesses. For the
expanded sample the estimated replacement rate gap coefficient increases in absolute value
from −5.7 to −6.6.
Base period and weights In the baseline specification we have normalized our time series
with respect to the base period of January-February 2020. When we widen the base period
to July 2019-February 2020, the estimate of the replacement rate gap coefficient decreases in
absolute value to −5.2. Also, the benchmark specification weighs each cell equally. Once we
weigh each cell by the number of businesses inside the cell, i.e., more populated cells take a
higher weight, the coefficient on the replacement rate gap increases only slightly in absolute
value to −6.0.
Recalls Fujita and Moscarini (2017) document that a large share of workers returns to their
previous employer after a jobless spell. We examine if, upon re-opening, the HB businesses
disproportionately hired employees who previously worked in the business. In Figure 6 we
plot the recall rate (the share of employees that have previously worked in the business) before
and after the business’ closing and re-opening. We center the plots around re-opening week
21

Figure 6: Recall Rates for Low- and High-Wage Businesses Upon Re-opening

100
90
80
70
60
50
-10

-5

0

5

10

15

20

Week Since Re-opening
Notes: Weekly averages for recall rates. Week “0” is re-opening week. Closing week and closing spell
differs across businesses (represented by the grey area).

(denoted as “week 0”). Week -1, depicted as a shaded area in the plots, represents the time
businesses were closed. Recall rates are high only during the first month of re-opening and
then converge to pre-pandemic levels. In addition, high-wage businesses have higher recall
rates than low-wage businesses but the difference also disappears after the first month. In
sum, the recall margin does not seem to play an important role for our HB sample.11 Our
benchmark model, presented in the next section, abstracts from a recall margin. We expand
the baseline model to include recalls in Appendix I and discuss the results.

5

A model for the disincentive effects of pandemic UI

In this section, we build a labor search model and explore if we can quantitatively replicate the estimated disincentive effects of pandemic UI policies. Building on McCall (1970)
and Albrecht and Axell (1984), we analyze how the job acceptance decision is affected by expanded UI benefits. The model features probabilistic eligibility of UI among the unemployed,
probabilistic expiration of UI benefits, and benefits that depend on past wages as in, e.g.,
11
Our findings are in accord with Ganong et al. (2022) who document that UI supplements did not have
substantial effects on recalls.

22

Ljungqvist and Sargent (1998, 2008).

5.1

Environment

Time is discrete and the discount factor is β. The economy is populated by a unit measure
of workers and a fixed measure of firms, M . Workers are either employed or unemployed.
A worker’s utility is increasing and concave in consumption, U(c). Workers cannot save and
consumption is equal to the wage w when employed and to an income supplement b when
unemployed. Workers do not derive utility from leisure.12
Each firm (business) consists of one job that is characterized by (constant) wage w drawn
from an exogenous distribution with probability density function g (w). Note that the equilibrium offer distribution will differ from g(w) since not all offers will be accepted. There is
no exit or entry of jobs. Instead, when a filled job gets hit by a separation shock δ it becomes
vacant. The measure of vacancies that offer wage w is denoted v(w). We distinguish between
active vacancies (total measure of ṽ) and inactive vacancies (total measure of v − ṽ). When
a vacancy has zero probability of being accepted it remains inactive in which case it does not
influence the matching process.
Employed workers separate from their jobs with probability δ and become unemployed.
With probability pR newly separated workers are eligible for UI benefits and the level of
benefits is a function of the previously earned wage, bR (w). These are the UI-unemployed.
Workers ineligible for UI, the non-UI unemployed, receive social benefits that also depend on
the past wage, bN (w).13 We assume that both benefits are increasing functions of the wage.
Finally, in each period, UI unemployed lose eligibility with probability pN and become non-UI
unemployed.
Every period, unemployed workers randomly receive a new job offer with probability λ(θ),
where θ = ṽ/u denotes labor market tightness defined as the ratio of total active vacancies ṽ
to all unemployed workers u, whether or not they are UI-eligible. Matching of unemployed
workers with vacancies is governed by a constant returns to scale function, implying that
vacancies meet unemployed workers with probability λ(θ)/θ. The total probability of receiving
a job offer that pays wage w is λ(θ)ṽ(w)/ṽ where ṽ(w) is the measure of active vacant jobs
paying wage w and ṽ is the measure of all active vacancies. Upon receiving a job offer with
wage w0 , an unemployed worker with previous wage w will accept the offer if the wage exceeds
12
We essentially assume that the non-pecuniary benefits from not working are small for workers who are
at their borrowing constraint. These benefits are likely to be further reduced by the time spent searching for
a job and the direct disutility from being unemployed.
13
Adding heterogeneity to the non-UI unemployed eases the computation of the transition and is not crucial
for our results. Hence, we choose a simple way to add heterogeneity without introducing an additional state
variable.

23

the reservation wage associated with the value of remaining unemployed, w∗ (w).
After characterizing the steady state of this environment, we model the Covid-19 pandemic as a large one-time separation of employed workers into unemployment, followed by
an unanticipated expansion of UI. To capture the various aspects of the CARES Act, this
expansion consists of a temporary increase in the level of benefits for UI-eligible workers,
a temporary increase in the probability of becoming UI-eligible upon job separation, and a
temporary increase in the probability of remaining UI-eligible while unemployed.

5.2

Value functions

We describe the value functions of employed and unemployed workers. We use a time
subscript when parameters or functions change along the transition from their steady state
value. The value of a worker employed at wage w is
Wt (w) = U(w) + β {(1 − δ)Wt+1 (w) + δ [pR,t UR,t+1 (w) + (1 − pR,t )UN,t+1 (w)]} ,

(10)

where UR (w) and UN (w) denote the values of being unemployed while being eligible and
ineligible for UI benefits, respectively. These values are given by14



ˆ
ṽt (w0 ) 0
0
dw + [1 − λ(θt )] UN,t+1 (w)
UR,t (w) = U [bR,t (w)] + β pN,t λ(θt ) max {Wt+1 (w ), UN,t+1 (w)}
ṽt


ˆ
ṽt (w0 ) 0
0
+(1 − pN,t ) λ(θt ) max {Wt+1 (w ), UR,t+1 (w)}
dw + [1 − λ(θt )] UR,t+1 (w)
ṽt
(11)
and


ˆ
ṽt (w0 ) 0
0
UN,t (w) = U [bN (w)] + β λ(θt ) max {Wt+1 (w ), UN,t+1 (w)}
dw + [1 − λ(θt )] UN,t+1 (w) .
ṽt
(12)
The value functions are increasing in the wage since flow utility is increasing in the wage,
either directly when employed or indirectly when unemployed because benefits are increasing
in the prior wage. Thus, a job offer is accepted if the associated wage exceeds the reservation
wage, wi∗ (w), which is implicitly defined by
 ∗

Wt+1 wi,t
(w) = Ui,t+1 (w) for i ∈ {R, N } .

(13)

14
We assume that UI-eligible unemployed learn whether their benefits expire before receiving a job offer.
This timing assumption is consistent with the fact that, at least under normal circumstances, benefits duration
is known in advance. However, alternative timing assumptions would generate very similar quantitative results.

24

∗
Note that wi,t
(w) in (13) captures the decision to work in period t + 1, not t. This somewhat
unusual definition helps streamline notations.
The reservation wage of non-UI unemployed is lower than the reservation wage of a UI
unemployed since the benefits of non-UI unemployed are uniformly lower
∗
∗
wN,t
(w) ≤ wR,t
(w).

(14)

∗
is the lowest acceptable wage for an unemployed worker
Finally, wmin
∗
∗
wmin,t
= min wN,t
(w).
w

(15)

∗
, are inactive.
Vacancies with a wage below the lowest acceptable wage, i.e., w < wmin,t

5.3

Transition of measures

The measure of employed workers and hence, of the filled jobs that receive wage w evolves
according to
et+1 (w) = (1 − δ)et (w) + Ft (w)

ṽt (w)
λ(θt )ut ,
ṽt

(16)

where F (w) denotes the job acceptance rate, i.e., the probability that a random unemployed
worker accepts a job offer paying wage w (to be defined below).
The measure of UI-eligible unemployed evolves according to
uR,t+1 (w) = pR,t δet (w) + [1 − fR,t (w)] (1 − pN,t )uR,t (w),

(17)

´
0)
dw0 is the probability that an UI-eligible worker with
where fR,t (w) = λ(θt ) w0 ≥w∗ (w) ṽt (w
ṽ
t
R,t
previous wage w is offered a job and accepts it. The measure of UI-ineligible unemployed
evolves according to
uN,t+1 (w) = (1 − pR,t )δet (w) + [1 − fN,t (w)] [pN,t uR,t (w) + uN,t (w)] ,

(18)

´
0)
where fN,t (w) = λ(θt ) w0 ≥w∗ (w) ṽt (w
dw0 is the probability that an UI-ineligible unemployed
ṽt
N,t
is offered a job and accepts it.
Furthermore, we have by definition
ˆ
ut =

ˆ
uR,t (w)dw +

25

uN,t (w)dw,

(19)

where uR,t (w) denotes the measure of unemployed workers receiving benefits bR,t (w) and
uN,t (w) the measure of unemployed workers who instead receive bN (w).
The measure of vacancies (active or inactive) paying wage w evolves according to

λ(θt )
vt (w).
vt+1 (w) = δet (w) + 1 − Ft (w)
θt


(20)

The distribution of vacant jobs (active and inactive) is pinned down by the following
equation:
(21)

et (w) + vt (w) = g(w)M,

where g(w) is the exogenous distribution of wage offers and M is the measure of firms (or
total jobs, filled and vacant). As mentioned, vacancies with wages that are not acceptable to
∗
, or equivalently F (w) = 0, will not
unemployed workers, i.e., vacancies with wages w < wmin
be active and have e(w) = 0. We define all active vacancies as
ˆ
ṽt =

(22)

vt (w)dw
∗
w≥wmin,t

∗
we have
Aggregating equation (21) over w ≥ wmin,t

ˆ
et + θt (1 − et ) = M

g(w),

(23)

∗
w>wmin,t

∗
where we have used that e is zero at wage levels less than wmin,t
, θ = uṽ , and that all workers
in the economy are of measure one.
Given these definitions, the job acceptance rate F (w) can be expressed as

1
Ft (w) =
ut

(

ˆ

ˆ
uR,t (w0 )dw0 +

(1 − pN,t )
∗ (w)
w0 ≥wR,t

)
[uN,t (w0 ) + pN,t uR,t (w0 )] dw0

.

∗ (w)
w0 ≥wN,t

(24)
Furthermore, the aggregate job-finding rate (i.e., the hazard rate of exiting unemployment) is
ˆ
JF Rt = λ(θt )

ṽt (w)
Ft (w)dw,
ṽt

(25)

ṽt (w)
Ft (w)dw.
ṽt

(26)

and the aggregate vacancy fill rate is
λ(θt )
V F Rt =
θt

ˆ

26

5.4

Stationary equilibrium

∗
∗
∗
A stationary equilibrium is a set of value functions {W, UR , UN }, reservation wages {wR
, wN
, wmin
},
job acceptance rate F , distributions {e, uR , uN , u, v, ṽ}, and market tightness θ such that:

1. The value functions {W, UR , UN } satisfy equations (10), (11), and (12).
∗
∗
∗
2. The reservation wages {wR
, wN
, wmin
}, satisfy equations (13) and (15).

3. The (un)employment and vacancy distributions {e, uR , uN , u, v, ṽ} satisfy equations (16),
(17), (18), (19), (22), and (23).
4. The acceptance rate F (w) satisfies equation (24).
5. Market tightness θ is given by ṽ/u.

5.5

Calibration

We calibrate the model parameters such that the steady state fits pre-pandemic averages
in the U.S. service sector. A summary of our parameters and calibration strategy is given in
Table 4.
As in our empirical analysis, we specify the model’s period to a week. Thus, we set
β = 0.9992, consistent with an annual real interest rate of 4 percent. For the worker’s
1−γ
utility function, we use a constant relative risk aversion specification U (x) = x 1−γ−1 with a
coefficient of relative risk aversion γ = 2. The total number of jobs is set to M = 1.013 so
that the equilibrium derived θ = 1.2 which was the vacancy-to-unemployment ratio before the
pandemic.
Matches are given by a Cobb-Douglas matching function: m = κu1−η ṽ η . Based on Şahin
et al. (2014), we set the elasticity of matches to vacancies η = 0.5. We set κ to match the
pre-pandemic average job-finding rate for low-wage workers. Many workers in the Leisure
and Hospitality sector are characterized by relatively short employment and non-employment
spells. Thus, instead of targeting monthly job-finding rates from CPS or other surveys, which
are potentially subject to time-aggregation issues, we use evidence on vacancy fill rates and job
separation rates from JOLTS and LEHD. We estimate vacancy fill rates from JOLTS following
Davis et al. (2013) and then use LEHD data to account for the hires undercounted in JOLTS.
For the Leisure and Hospitality sector, for the period 2015-2019, we find an adjusted weekly
vacancy fill rate of V F R = 0.28 when we focus on hires from non-employment. Based on
labor market tightness θ = 1.2, we get a target job-finding rate equal to JF R = 0.23.
The job separation rate is based on LEHD data. For the same time period and focusing again on separations into non-employment, the weekly job separation rate is δ = 0.016.
27

Together, the job-finding rate and separation rate imply an unemployment rate equal to 6.4
percent.
For pre-pandemic unemployment benefits, we specify the function bR (w) = ρR w and set
the replacement rate ρR = 0.51, which is the median replacement rate prior to the pandemic
implied by our HB data (see Table C-3 in Appendix C). We set the pre-pandemic expiration
probability of unemployment benefits to pN = 0.038, which corresponds to an expected duration of 26 weeks equal to the maximum number of regular unemployment benefits eligibility
in most U.S. States.
The benefit recipiency probability after job separation, pR , combines UI eligibility with
UI takeup. From the March CPS-ASEC, we calculate the fraction of those who reported
receiving UI in the previous calendar year, conditional on being unemployed for at least one
week following employment in Leisure and Hospitality. For the period 2010-2019, the average
of this share is about 12.5%. However, linking CPS data with IRS tax data Larrimore,
Mortenson, and Splinter (2023) shows that only about half of CPS respondents who receive
UI benefits during an unemployment spell report these payments. We adapt their procedure
to adjust UI recipiency rates in the March CPS data (see Appendix G for details) and find a
20 percent share of UI recipients before the pandemic and a 60 percent share for 2020.15 The
last estimate will be relevant for the CARES Act experiment that is described in the next
section. To compute the model-equivalent statistic we generate a panel of workers using Monte
Carlo simulation and ask the workers the same question asked in the CPS. The estimated
probabilities are pR = 0.14 for the steady state and p0R = 0.70 for the pandemic experiment.
To match the equilibrium wage distribution (displayed in Table C-2 in the appendix), we
use the dispersion of the firm wage distribution, σ, to match the upper half of the equilibrium
wage distribution, and we use the non-UI replacement rate, ρN , to match the lower half of the
wage distribution.
We assume that the exogenous firm wage distribution g(w) is log-normal with a mean
normalized to one and standard deviation σ. We set σ = 0.11 such that wages of filled jobs
at the 75th percentile are 7% higher than for the median filled job, similar to what we observe
within local-industry cells in our HB data prior to the pandemic.
Standard search models do not generate much wage dispersion at the lower end of the wage
distribution. Hornstein, Krusell, and Violante (2011) show that unemployed workers will turn
down low-wage offers, given observed transition rates out of unemployment and reasonable
calibrations of the flow return to unemployment. Introducing a non-UI state that has a
15
Our measure for the combined eligibility and take-up rate of UI is lower than the recipiency rates estimated
in Birinci and See (2022) using 1996-2016 SIPP data (equal to 0.35). But Birinci and See (2022) also note
that eligibility and take-up shares are lower for low-income groups, such as the kind of workers that comprise
our HB sample.

28

Table 4: Parameter Values
Parameter

Notation

Value

Target/Reference

β
γ
δ
η
ρR
pN

0.9992
2
0.016
0.5
0.51
0.038

4% annual interest rate
–
LEHD

M
pR
κ
σ
ρN

1.013
0.15
0.23
0.11
0.15

Steady state θ = 1.2
CPS and IRS data
Weekly job finding rate of 0.23
Wage dispersion upper half
Wage dispersion bottom half

Externally set parameters:
Discount factor
Risk aversion
Job separation rate
Matching function elasticity
Replacement rate, UI
Expiration probability

Şahin et al. (2014)

UI system
UI system

Calibrated parameters
Total number of jobs
Recipiency probability
Matching efficiency
Wage dispersion
Replacement rate, non-UI

Notes: The table reports the parameter values of the model. The model period is set to be one week.

sufficiently low utility flow, together with preferences that have a sufficiently high curvature,
allows us to increase wage dispersion for the bottom half of our wage distribution. In the
HB data, the 10th percentile of (residual) log wage is 88 percent of the mean (see Table C2 in Appendix C). We are able to match this target through a non-UI replacement rate of
ρN = 0.15.
Before continuing, it is instructive to compare our calibration of ρN to direct calibrations in
the literature based on data from U.S. social assistance programs. Pavoni and Violante (2007)
compute the median allotment of food stamps and find that it is worth $397 per month. Given
the average monthly wage of $1,500 in their model, this implies a replacement ratio of social
assistance equal to 26 percent. Foster and Rojas (2018) report that the average recipients of
TANF and SNAP receive $3,072 and $3,928 per year, which yields $135 of social assistance
per week. Compared to average hourly earnings from the CPS for NAICS 71-72, this puts the
replacement ratio at almost 30 percent. While these replacement ratios are higher than the
ρN = 0.15 that we obtain from our indirect calibration, we note that these empirical estimates
also include recipients that are non-attached to the labor force over the long-term so that the
social supplements likely replace a larger share of their previous market income. In contrast,
in our environment, non-UI unemployed are attached to the labor force and generally return
to employment relatively quickly.

29

5.6

Transitional dynamics

We model the pandemic transition as an initial shock to employment, followed three weeks
later by an unanticipated UI expansion. First, in period t = 0 we reduce employment in
high-wage and low-wage businesses such that, consistent with the HB data, total employment
declines by 60 percent, and employment of low-wage businesses declines about 8 percentage
points more than employment of high-wage businesses. We allocate workers who lose their
jobs to UI and non-UI unemployment based on the steady state recipiency probability.
Second, the UI system changes at t = 3, i.e., three weeks after the initial separation shock,
which corresponds to the first week of April 2020. The changes involve the magnitude of
benefits, the duration for which benefits are paid, and the set of workers who are eligible to
receive the benefits. We assume that these changes were not anticipated as of t < 3, and that
their expiration is anticipated.
The CARES Act provided supplemental benefits of $600 per week on top of usual state
benefits through the end of July 2020. We model this change as an increase in weekly unemployment benefits from bR (w) = 0.51w to b0R (w) = 0.51w + S that lasts for 16 weeks, setting
S such that the average replacement rate equals about 2.0 which is the median replacement
rate during the CARES Act in our HB sample (see Table C-3 in appendix).
In addition, the CARES Act extended benefits for 13 weeks beyond the usual state-level
duration of benefits so that, effectively, benefits did not expire until the end of December 2020.
We model this change as a decrease in the benefit expiration probability from pN = 0.038 to
p0N = 0 that lasts for 39 weeks.
Finally, the CARES Act expanded eligibility, among others, to part-time workers and
workers who previously did not qualify for benefits due to insufficient quarterly earnings. In
addition, it is likely that the more generous UI increased take-up rates among the eligible. We
model this as an increase in the recipiency probability from pR = 0.14 to p0R = 0.7 targeting
a 60 percent share of unemployed who have reported receiving UI during 2020 in the CPS.
We assume that a share of workers who lost their jobs at t = 0 and were not eligible for UI
during the first three weeks of the recession become eligible once the CARES Act comes into
effect (at t = 3). Without this assumption we cannot match the high pandemic UI recipiency
share we document from the CPS. The size of unemployed who shift to eligibility at t = 3 is
given by the number of separated workers (∆e) who would have taken UI had eligibility been
available from t = 0 and provided they did not find a job until t = 3. Thus, at each wage
u
(w)
∆e. This shift affects 40
w, the shift increases uR,3 (w) by Π2t=0 (1 − fN,t (w))(p0R − pR ) N,3
uN,3
percent of non-UI unemployed workers.
All three policy changes are assumed to be unexpected when they start, but their expiration
is fully anticipated as announced. We also assume that there are no follow-up changes to UI
30

Figure 7: Difference in Employment Recovery in Low- and High-wage Jobs: Model vs. Data

0
-5
-10
-15
-20

-5

0

5

10

15

20

25

30

35

Notes: The figure plots the average low-wage business employment minus the average high-wage
business employment (both relative to their pre-pandemic level). “Model with CARES Act” is the
benchmark model and “Model without CARES Act” is the benchmark model with the separation
shock but not the CARES Act provisions. Data represent the estimated b’s from Regression 8.

policy. As various additional changes to UI policy occurred, through Fall 2020 and then 2021,
we focus most of our analysis on the implications for the 16 weeks for which supplemental
benefits were initially expected to be in place.
We solve for the perfect foresight transition equilibrium as follows. We assume that the
economy converges to the pre-pandemic steady state after some time T . We guess a path
for market tightness, {θt }Tt=0 , and the measure of vacancies {vt (w)}Tt=0 . We solve the value
functions and reservation wages starting from period T and moving backward. Next, we
simulate forward the transition paths for employment, unemployment, and vacancies using
the value functions and transition equations and obtain a new guess for the paths of market
tightness and vacancies. We repeat the process until this algorithm converges. The transition
path is defined formally in Appendix F.

6

Quantitative results

Our quantitative analysis focuses on the disincentive effects of UI as represented by the
employment recovery gap between low-wage and high-wage jobs. The quantitative model does
not capture demand effects or other common labor market factors (e.g., pandemic restrictions),
31

Figure 8: Acceptance Rate for Different Job Offers: Model

100
80
60
40
20
0
0

10

20

30

40

50

Notes: The figure reports the fraction of unemployed (in regular benefits and social assistance) that
would accept the wage offered by a business, each week. Businesses offering $10 and $11.0 dollars per
hour are low-wage businesses and the business offering $13 dollars per hour is a high-wage business.
Dates of initiation and expiration of the CARES Act provisions are reported.

which is appropriate given that the disincentive effects are measured within narrow local
industry markets. Figure 7 compares the employment recovery gap with our estimates from
Figure 4. We find that the baseline model overstates the decline in the employment recovery
gap by a large degree.
Figure 8 helps to understand why the baseline model performs poorly. We plot acceptance
rates, F (w), for three businesses that offer $10.0 and $11.0 per hour (low-wage businesses) and
$13.0 per hour (high-wage business), respectively. Businesses can attract different groups of
unemployed. The high-wage business offering $13 per hour can attract all types of unemployed
workers (both those without UI benefits and those with benefits) and that is why F (w) is 100
percent in the steady state. The same is true for the low-wage business offering $11 per hour.
The low-wage business offering $10 per hour can only attract from the non-UI unemployed
(the uN set) and that is why the acceptance rate is around 80 percent in the steady state.
The CARES Act has two major effects. First, it decreases the acceptance rates of the
UI-unemployed (the uR group) by offering $600 per week and extending the duration of the
benefits. Second, it increases the pool of the UI-unemployed and decreases the pool of the
non-UI unemployed by expanding eligibility.
Initially, the UI-unemployed reject the $13 offer. The rejection is temporary though and
lasts only for a few weeks. Anticipating the expiration of the pandemic supplement, UI32

Figure 9: Employment Recovery Gap: CARES Act UI Provisions

0
-2
-4
-6
-8
-10

-5

0

5

10

15

20

25

30

35

Notes: The figure plots the average low-wage business employment minus the average high-wage
business employment (both relative to their pre-pandemic level) when only one of the CARES Act
provisions is in effect: (a) the income supplement of $600, (ii) the extended maximum duration, and
(iii) the expanded eligibility. Data represent the estimated b’s from Regression 8. Dates of initiation
and expiration of the $600 income supplement are reported.

unemployed workers gradually start to accept the offer so that the acceptance rate converges
to its steady state relatively fast.
The business offering $11 per hour also experiences a rejection from the UI-unemployed.
But on top of that the share of non-UI unemployed in total unemployment (who accept its
offer) immediately declines due to the expanded eligibility. The share of non-UI unemployed
then continues to shrink because first, new unemployed are continuously allocated to uR which
continues to increase (thus, shrinking the share of non-UI unemployed to total unemployment),
and second, because UI-unemployed now accept job offers at a relatively lower rate and their
share increases even more. As a result, the acceptance rate continues to decline and only
bounces back when the $600 supplement is close to expiring and the UI-unemployed again
start to accept the business’ offer.
The business offering $10 per hour recovers at the slowest pace. This business also experiences a decline in acceptance rates because the share of the non-UI unemployed shrinks.
For this business, the expiration of the $600 supplement does not immediately improve the
acceptance rates because the business was not attracting workers from the UI-unemployed in
the first place. Over time, however, the share of non-UI unemployed is increasing because the
33

relative acceptance rate of UI-unemployed has now increased. But this process is very slow
and only when the eligibility extension expires (around week 42) can this business begin its
employment recovery.
The behavior of the relative offer acceptance rates at low- and high-wage businesses helps
us understand the employment gap dynamics in Figure 7. The low-wage businesses hire mainly
from the pool of non-UI unemployed, which prior to UI eligibility extension represented about
80 percent of the unemployed (since only about 20 percent of workers in this segment of the
labor market receive UI benefits). But with expanded eligibility the UI recipiency rate sharply
increases and the low-wage businesses have a substantially smaller pool to hire from. As a
result, the employment recovery gap between low- and high-wage businesses is quite large in
the model relative to the data. The gap is widening until the $600 benefits are about to expire
and the acceptance rates of UI unemployed increase again.
Figure 9 analyzes the employment gap between low- and high-wage businesses when only
one of the pandemic UI policy provisions is in effect. We find that the $600 income supplement
and the extended duration of benefits alone generate too little of a response. The expanded
eligibility provision has the strongest effect on the employment recovery gap but the shape
of the recovery does not match data well. In the next section, we present a model where all
provisions are in effect and the model can generate an employment recovery gap close to the
data.

6.1

Reconciling the model with the data

The baseline model generates a low-wage employment gap that is much larger than in the
data. In this section, we propose a reduced-form solution to reconcile the model with the
data: a probability of losing UI eligibility upon refusal of a job offer.16
In the baseline model, UI recipients can reject a wage offer without losing their UI status.
According to UI law, an unemployed who refuses suitable work loses eligibility. In addition,
employers can themselves contest the eligibility of a claimant. However, it is difficult to
determine how prevalent such denials were for unemployed who refused to return to work.
Still, for workers, losing the eligibility status could be perceived as a real possibility.
Assume that unemployed workers who reject an offer, lose their eligibility status with
probability χ. As a result, the value function for an unemployed who receives UI benefits is

16
Boar and Mongey (2020) consider multiple other possibilities that can explain why some workers returned
to work in spite of the generous UI benefits such as workers being unable to return to their old job even if
they wanted to or lower wages after an unemployment spell. Their proposed solutions are less likely to apply
to our sample of restaurant businesses where worker tenure is typically short-lived.

34

Figure 10: Employment Recovery Gap: Model with UI Loss upon Job Refusal

0
-2
-4
-6
-8
-10

-5

0

5

10

15

20

25

30

35

Notes: The figure plots the average low-wage business employment minus the average high-wage
business employment (both relative to their pre-pandemic level) in the model with the probability
of losing UI upon job refusal with and without the CARES Act. Data represent the estimated b’s
from Regression 8.

written as follows:
ˆ


ṽt (w0 ) 0
UR,t (w) = U [bR,t (w)] + βpN,t λ(θt ) max {Wt+1 (w ), UN,t+1 (w)}
dw + [1 − λ(θt )] UN,t+1 (w)
ṽt


ˆ
ṽt (w0 ) 0
0
+ β(1 − pN,t ) λ(θt ) max {Wt+1 (w ), (1 − χ)UR,t+1 (w) + χUN,t+1 (w)}
dw
ṽt


0

+ β(1 − pN,t ) [1 − λ(θt )] UR,t+1 (w).

(27)

Accordingly, the reservation wage of UI recipients is given by:
 ∗

Wt+1 wR,t
(w) = (1 − χ)UR,t+1 (w) + χUN,t+1 (w).

(28)

The measure of these workers evolves according to
uR,t+1 (w) = pR,t δet (w) + [1 − (fR,t (w) + χ(1 − fR,t (w)))] (1 − pN,t )uR,t (w),

(29)

´
0)
dw0 is the probability that an UI-eligible
where, as before, fR,t (w) = λ(θt ) w0 ≥w∗ (w) ṽt (w
ṽ
t
R,t
worker with previous wage w is offered a job and accepts it. Finally, the measure of UI-

35

ineligible unemployed evolves according to
uN,t+1 (w) =(1 − pR,t )δet (w) + [1 − fN,t (w)] [pN,t uR,t (w) + uN,t (w)]
+ χ(1 − fR,t (w))(1 − pN,t )uR (w),

(30)
(31)

where the last term measures the flow of UI recipients whose benefits did not expire but were
lost by rejecting a job offer. All other model equations are the same.17
We set the probability of losing eligibility upon job refusal, χ, equal to 10 percent in
order to match the employment recovery gap we estimated in the data. Figure 10 compares
the employment recovery gap between low- and high-wage businesses in the transition. The
employment recovery gap in this model matches the data closely. First, the model generates
the abrupt decline in the employment gap once the CARES Act comes into effect (at t=3)
without generating too steep of a decline. Second, the model captures well the faster recovery
of low-wage businesses once the $600 supplement expires. The employment recovery gap when
the $600 supplement is in effect (i.e., during the first sixteen weeks of the CARES Act) is about
1.7 percentage points lower than when the $600 supplement has expired, which is fairly close
to our empirical estimate of 1.5 percentage points.
Thus, the introduction of a small probabilistic loss of UI eligibility increases the incentives of UI-unemployed to accept low-wage offers, and the model can match the differential
employment recovery we estimated in the data. In Appendix I, we study a version of the
baseline model where unemployed workers can be recalled by their former employer and UI
is denied for those who refuse to return to work upon getting recalled. In such a model,
the probability of UI loss upon job refusal is effectively the probability of being recalled to a
previous employer.

6.2

Aggregate employment losses from pandemic UI benefits

We compute the effect of the CARES Act on employment recovery and quantify separately
the impact of each provision. We study the employment losses within the model with a
probabilistic UI loss upon job refusal which is able to closely replicate the estimated differential
employment recovery we document in the data.
In Table 5 we compute the employment loss of each UI policy provision when implemented
separately when combined with the other two policies, and finally, the overall employment
losses from all UI policy provisions. To measure the employment loss associated with a policy
we compute the difference between the employment-to-normal level when the policy is in effect
17
The extended model can still match the benchmark targets and thus, does not need a re-calibration of
other parameter values.

36

Table 5: Employment Recovery Loss (in percentage points)

Each provision alone
$600 Additional UI Benefits
Extended Duration of UI Benefits
Expanded Eligibility of UI Benefits

0.3
0.3
1.2

Each provision when other provisions are in effect
$600 Additional UI Benefits
Extended Duration of UI Benefits
Expanded Eligibility of UI Benefits

2.1
2.3
3.9

CARES Act (all provisions combined)

4.7

Notes: The table reports the employment recovery loss with respect to each CARES Act provision
using simulated data from the transition equilibrium. In the top three lines, the losses are computed
when the other two provisions are inactive while the middle three lines compute the losses when the
other two provisions are in effect. Estimates are reported in percentage points.

to the employment-to-normal level when the policy is not in effect and take the average over
the period April to December 2020.
The aggregate employment recovery loss associated with each UI policy when implemented
separately is modest. However, when combined, the pandemic UI policies generate substantial
aggregate employment losses. Conditional on the other two provisions being in effect, the
income supplement holds back the employment recovery by 2.1 percentage points, the extended
maximum duration by 2.3 percentage points, and the expanded eligibility by 3.9 percentage
points. Without any of the UI policy changes, the employment recovery would have been,
on average, 4.7 percentage points closer to normal between April and December 2020. This
employment loss represents around 25 percent of the average employment loss in the Leisure
and Hospitality sector during the same period. The employment loss is non-linear (Figure 11),
peaking at almost 8 percentage points about 10 weeks after the initiation of the CARES Act.
Thereafter, the disincentive effect gradually diminishes as the $600 supplement expires and
the expanded eligibility and extended duration policies draw closer to an end.
In sum, our quantitative results underline the importance of jointly taking into account
the different UI policy changes brought about by the CARES Act.

6.3

Unemployment duration elasticities

Using the model’s transition path we compute unemployment duration elasticities (see
Appendix H for more details). Similarly to Table 5, we calculate the unemployment duration
37

Figure 11: Employment Losses due to CARES Act UI policies

8
6
4
2
0
0

5

10

15

20

25

30

35

Notes: The figure reports the aggregate loss of pandemic UI programs as a percent of normal
employment. Separate losses for each program are reported by simulating the model with only
a single provision at a time.

elasticity of each of the three UI provisions when implemented alone and when implemented
in combination.
Table 6 reports the results. The $600 supplement alone increases the average unemployment duration by 11 percent (from 3.5 weeks to 3.9 weeks). Since in our model, the replacement rate rises by 292 percent (from 0.51 to 2.0), this implies a duration elasticity of 0.03. In
turn, the extended benefits alone increase unemployment duration by 8 percent. According to
the CARES Act, benefits did not expire until the end of the year (39 additional weeks) when
the usual duration of state-level benefits would be in effect. Thus, the (potential) duration
of benefits rose from 26 weeks to 65 weeks, or an increase of 150 percent, which generates
an elasticity of 0.05. Expanded eligibility increases the expected duration of unemployment
by 20 percent. The model inferred probability of receiving benefits rose from 14 percentage
points to 70 percentage points, or by 400 percent which generates an elasticity of 0.05.
Table 6 also reports the duration elasticities of each of the provisions conditional on the
other two provisions being in effect. For example, when the $600 is activated on top of the
other two provisions, unemployment duration increases by 83 percent implying an elasticity
of 0.28. When the extended benefits provision is activated on top of the other two provisions,
unemployment duration increases by 68 percent implying an elasticity of 0.45. When the
expanded eligibility provision is activated on top of the other two provisions, unemployment

38

Table 6: Unemployment Duration Elasticities implied by CARES Act Provisions

Unemployment Duration

Elasticity

Each provision alone
$600 Additional UI Benefits
Extended Duration of UI Benefits
Expanded Eligibility of UI Benefits

+11%
+8%
+20%

0.03
0.05
0.05

Each provision when other provisions are in effect
$600 Additional UI Benefits
Extended Duration of UI Benefits
Expanded Eligibility of UI Benefits

+83%
+68%
+104%

0.28
0.45
0.26

Notes: The table reports the unemployment duration elasticity with respect to each CARES Act
provision. The upper panel assumes the other two provisions are not in effect and the lower panel
that the other two provisions are in effect. The duration elasticity is calculated using simulated data
from the transition experiment.

duration increases by 104 percent implying an elasticity of 0.26.
Our numbers are in the low-to-middle range of existing estimates. With respect to the
duration elasticity out of benefit extensions, Katz and Meyer (1990) find estimates between
0.3-0.5. Johnston and Mas (2018) and Landais (2015) find even larger elasticities between
0.4-0.8. On the lower end of the estimates Rothstein (2011) estimates an elasticity of 0.06
and Farber and Valletta (2015) estimate an elasticity of 0.15. Schmieder and von Wachter
(2016) report a similarly large divergence in the estimates of the duration elasticity of benefit
supplements. For the U.S., the median is 0.38, and the range is from 0.1 to 1.2.
Although the duration elasticities implied by our model are modest, the employment impact of the CARES Act turns out to be large due to the sheer size of the UI programs as well
as their joint implementation.

7

Conclusion

Our paper asks if the limited effects of the pandemic UI benefits on employment, as
estimated by several studies (e.g., Coombs et al. (2021); Marinescu, Skandalis, and Zhao,
2021; Ganong et al. (2022); and others), arise from small disincentive effects or represent a
mix of disincentive and stimulative effects acting in opposite ways?
Based on high-frequency data on small restaurants and retailers, we find that employment
in low-wage businesses recovers significantly slower than employment in neighboring high-wage
39

businesses in labor markets with larger differences in UI replacement rates. Our research design
controls for the local stimulative effects of UI programs by comparing neighboring businesses
that largely share the positive effects of the UI stimulus.
A search and matching model augmented to include a probability of losing UI eligibility
upon job refusal can replicate the disincentive effects we estimate from the data. According
to the model, the disincentive effects of pandemic UI programs held back the employment
recovery by 4.7 percentage points, on average, between April and December 2020. We find
that expanded eligibility of UI benefits is the most disruptive provision and disproportionately
decreases employment in low-wage businesses.
We conclude that the disincentive effects of pandemic UI programs are sizable and the
limited effects typically estimated in the literature likely reflect a mix of disincentive and
stimulative effects.

40

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44

Appendix: For Online Publication
A

Details about Homebase data and representativeness
In this appendix, we provide additional details about the Homebase (HB) data and assess its

representativeness. For an even more detailed analysis, see Kurmann, Lalé, and Ta (2021).

A.1

Details about HB data

The HB data consists of anonymized daily records of individual hours worked and wages of
employees, linked longitudinally to the establishment where they work and the firm that owns the
establishment (although almost all firms are single-establishment firms). The data is recorded in real
time and is used by many of the businesses for payroll processing. The majority of establishments
are in sectors associated with in-person services: retail trade (NAICS 44-45), education and health
(NAICS 61-62), leisure and hospitality (NAICS 71-72), and other services (NAICS 81).
The raw HB data contains about 140,000 unique establishments (called businesses in the main
text and below) between January 2019 and December 2020. To assess the representativeness of the
HB data, we distinguish between the ”full sample” and the ”estimation sample”. The full sample
consists of all businesses that are active for at least three consecutive weeks with at least 40 weekly
tracked hours across its employees, and that we can match by name and address to Safegraph’s
Places of Interest (POI) database to attribute a consistent NAICS code (see Kurmann, Lalé, and Ta
(2021) for details). The estimation sample is a subset of this full sample and consists of businesses
that are present in the sample all of 2019 and at the end of 2020, report consistent wage information
for their employees, and have at least one neighboring business in the same local industry cell (see
the main text for details).
The full sample consists of over 51,000 businesses with over 500,000 unique employees, covering
2377 counties with a total population of over 300 million. The estimation sample consists of 4,219
businesses with over 80,000 unique employees, covering 527 counties with a total population of about
220 million. As these statistics suggest, essentially all businesses are small, employing fewer than 50
workers.

A.2

Representativeness concerning employment dynamics

As documented in Kurmann, Lalé, and Ta (2021), the full sample provides a weekly estimate of
employment of small businesses in in-person industries in the U.S. that fits administrative data very
closely. Here, we explore the extent to which the employment dynamics in the estimation sample fit
the employment dynamics in the full sample. To do so, we compute weekly employment relative to
mid-February 2020 with each sample using the recursive weighted estimator proposed by Kurmann,

45

Lalé, and Ta (2021).18
Figure A-1 shows the resulting employment estimates for 2020 in leisure and hospitality, the
sector accounting for over 80 percent of all businesses in the estimation sample. Results are similar
for the other sectors. Overall the fit is very good. While the decline in employment during the
first weeks of the pandemic is somewhat larger in the full sample than in the estimation sample, the
difference is well within reasonable range compared to other estimates (e.g., Cajner et al. (2020)).
From June 2020 onward, the two estimates then move closely together.

Figure A-1: Comparison of HB Employment Dynamics: HB Full Sample versus Estimation
Sample
10

ref.
Employment change
(in % relative to mid−Feb. 2020)

0

−10

−20

−30

−40

−50

−60

Feb 7 − Feb 13

Jan 24 − Jan 30

Dec 27 − Jan 2

Jan 10 − Jan 16

Nov 29 − Dec 5

Dec 13 − Dec 19

Nov 15 − Nov 21

Nov 1 − Nov 7

Oct 4 − Oct 10

Oct 18 − Oct 24

Sep 20 − Sep 26

Sep 6 − Sep 12

Aug 9 − Aug 15

Aug 23 − Aug 29

Jul 26 − Aug 1

Jun 28 − Jul 4

HB sample used in Sections 3−4

Jul 12 − Jul 18

Jun 14 − Jun 20

May 31 − Jun 6

May 3 − May 9

May 17 − May 23

Apr 19 − Apr 25

Apr 5 − Apr 11

Mar 8 − Mar 14

Mar 22 − Mar 28

Feb 23 − Feb 29

Jan 26 − Feb 1

Feb 9 − Feb 15

−70

Full sample from Kurmann, Lalé, and Ta (2021)
(estimates for small businesses in Leisure & Hospitality)

Notes: The figure shows the estimated employment change for small businesses in the leisure and hospitality
sector as implied by the full HB sample versus the estimation sample. See text for details.

18
The full sample contains businesses that disappear entirely from HB, some of which close permanently
and some of which simply stopped using the HB service. For an estimate of total employment it is important to
distinguish between the two, Kurmann, Lalé, and Ta (2021). No such adjustment is needed for the estimation
sample since it contains only continuing businesses, that is, they can be temporarily closed in 2020 but must
reopen before the end of 2020.

46

A.3

Representativeness concerning wages, hours, and earnings

The other important dimension in which to assess the representativeness of the HB estimation
sample is concerning wages, hours worked, and earnings of workers. We use the monthly Outgoing
Rotation Group (ORG) files from the Current Population Statistics (CPS) survey to perform this
assessment. Since the HB wage and hours data pertains to employees reporting actual hours worked,
we retain CPS data for hourly-paid workers only, and we drop all observations with either imputed
hours or imputed wages. For sample size reasons, we do not restrict the CPS to workers who respond
that they are employed in small businesses.
In the CPS-ORG files, hourly-paid workers provide information on actual hours worked, the
hourly wage rate, and weekly overtime, tips, and commissions (OTC) for the main job. We compute
the average hourly wage and average weekly hours over all observations in 2019, using the regular
sampling weights. Average weekly earnings are then computed as average hourly wage times average
weekly hours. To compute the average hourly wage with OTC, we divide the sum of average weekly
earnings plus weekly OTC with average weekly hours.
In the HB data, we have daily data on the hourly wage and hours worked for each employee.
Closer inspection of the data reveals that a substantial fraction of employees average fewer than
20 hours of work per week, either because this is not their main job or because they are part-time
workers/work irregularly (i.e., full-time for a few days and then not at all for a few days). While
interesting, this means that average weekly hours from the HB data are not directly comparable to
the CPS data, which only contains data for the main job. For the below comparison, we restrict
the HB sample to employees who work at least 3 days in a given week and business.19 With this
restriction in place, we sum the hours of all remaining workers to the weekly level and then, as in the
CPS, compute average hourly wages and average weekly hours across all observations in 2019. As
above, we provide results for the leisure and hospitality sector, both because this is the sector where
most of the HB businesses are active and because this is where the CPS sample is largest. Results
would be similar for the other sectors for which we have data. Table A-1 reports the results. As
the first two columns show, the average hourly wage in the CPS is about $1 higher than in the HB
sample, while average weekly hours are essentially the same. Hence average weekly earnings in the
CPS are somewhat higher than in the HB sample. Given that the CPS contains hourly-paid workers
not only from small businesses but also larger businesses that pay higher wages on average, this
difference should not come as a surprise. We conclude that the HB estimation sample is therefore
also broadly representative of small businesses in in-person industries with regard to wages, hours,
and earnings.
A potential caveat to this conclusion is that hourly wages recorded by HB may not include OTC,
either because they are paid out intermittently and not reported, or because businesses generally
only record the base wage rate. This is particularly relevant for the leisure and hospitality sector,
19
This restriction only affects average weekly hours worked. Average hourly wage rates are very similar
with or without this restriction.

47

Table A-1: Comparison of Wages, Hours, and Earnings: CPS vs HB Estimation Sample

CPS

HB

CPS w/OTC

HB w/OTC

Hourly wage ($)
Weekly hours
Weekly earnings ($)

12.5
30.6
400.1

11.3
30.1
347.0

14.8
30.6
467.2

13.6
30.1
415.96

# Observations

10,508

1,067,934

10,508

1,067,934

Notes: This table reports average hourly wages, average weekly hours, and average weekly earnings for hourlypaid workers in the leisure and hospitality sector in the CPS and in the HB estimation sample. For the CPS,
only data for the main job is considered. For HB, only workers with at least 3 days of work in a given week and
business are considered. Averages are computed over all observations in 2019 (monthly for the CPS, weekly
for HB). The first two columns report hourly wage and weekly earnings statistics without overtime, tips, and
commissions (OTC). The last two columns report hourly wage and weekly earnings statistics with OTC. See
text for details.

which accounts for the majority of the HB sample. As the third column of Table A-1 shows, average
hourly wages in the CPS are indeed substantially higher than HB hourly wages once OTC is included.
This raises two related questions. First, how to adjust the HB wage data for OTC when computing
UI replacement rates? Second, do businesses identified as low- vs high-wage differ systematically
in the extent to which they report OTC, and therefore, is our identification of low- and high-wage
businesses robust to including OTC?
To address these questions, we use information from the CPS. In the ORGs, the reported hourly
wage rate for hourly-paid workers excludes OTC. As a first step, we therefore consider the relationship
between the hourly wage rate and hourly OTC (i.e., reported weekly OTC divided by actual hours
worked). There is a clear kink in this relationship around the federal minimum wage of $7.25/hour:
for workers with an hourly wage rate below $7.25, there is an approximately 1:1 negative relationship
with hourly OTC, whereas, for workers with an hourly wage rate above $7.25, hourly OTC is constant
around $2 on average. This difference is consistent with federal minimum wage law, which mandates
that for tipped workers, the minimum base wage is $2.13/hour as long as tips and base wage add up
to $7.25/hour or more.
Given this finding, we adjust individual wage rates in the HB data with an OTC amount estimated
from the CPS data. Specifically, we run the following regression on CPS hourly-paid workers in
Leisure & Hospitality, separately for those with hourly wages below $7.25 and for those with hourly
wages at or above $7.25:
otcij = a0j + a1j wij + εij ,

(32)

where otcij and wij denote, respectively, the hourly OTC amount and the hourly wage rate of worker

48

ˆ ij = â0j + â1j wij , to the hourly wage of
i in region j.20 We then add the estimated OTC amount, otc
each worker in our HB sample.
As the fourth column of Table A-1 shows, the OTC-adjusted HB hourly wage is on average $2.30
higher than the baseline HB hourly wage. This difference is the same as for the CPS, which is not
surprising since the OTC adjustment is inferred from CPS data.
Given this OTC adjustment, we can now address the above questions. First, how to adjust
HB wage data when computing UI replacement rates? Since pre-pandemic state replacement rates
are around 0.5 (within eligibility bounds), this matters primarily for computing replacement rates
including the weekly pandemic supplement of $600 during Summer 2020, respectively $300 during
part of Fall 2020 and Spring 2021. When we use weekly OTC-adjusted earnings from our HB sample,
we obtain a median replacement rate of around 2. Since we obtain a very similar replacement rate
distribution with weekly earnings computed as HB hourly wage rate (without OTC) times 35 weekly
hours, we use this approximation as the baseline in the main text (also see Appendix C).
Second, we find that workers in businesses classified as low-wage receive on average a larger
OTC adjustment than workers in businesses classified as high-wage. While taking into account OTC
reverses the identification of some businesses, our regression results are all robust to this change and,
in some cases, even stronger (see Appendix E for details). Moreover, it is important to remember
that the OTC adjustment proposed here is based on estimates from CPS data that, for many regions,
are surrounded by substantial uncertainty due to the small sample size. Hence, the OTC adjustment
is at best a rough approximation. For these reasons, we base the analysis in the main text on
unadjusted hourly wages.

B

Pandemic UI generosity and economic outcomes across counties
In this appendix, we document the relative generosity of pandemic UI supplements across counties

and their relationship with economic outcomes.

B.1

Relative generosity of pandemic UI supplements

As described in the main text, from the beginning of April 2020 to the end of July 2020, the
federal government supplemented state-level UI benefits with an additional $600 per week through
the Federal Unemployment Compensation (FPUC) program. During parts of Fall 2020 and then
again from January 2021 through September 2021, additional supplements of $300 per week were
paid out. Since weekly earnings of likely UI recipients vary substantially across different parts of the
U.S., the relative generosity of these supplements also varies substantially.
To quantify the spatial variation in relative generosity implied by the $600 weekly FPUC supplement, we compute the ratio of the $600 to average weekly earnings of in-person service workers
20
We define regions by micropolitan and metropolitan statistical areas. To increase the sample size for
this regression, we use CPS-ORG data for 2018 and 2019. For regions with less than 10 observations, we use
state-level averages.

49

Figure B-2: Change in Relative Generosity of UI from $600 Supplement

1.15 − 4.61
1.07 − 1.15
1.00 − 1.07
0.94 − 1.00
0.86 − 0.94
0.46 − 0.86
No data

Notes: The figure reports the change in relative generosity of pandemic UI implied by the $600 weekly FPUC
supplement across U.S. counties, measured as the ratio of the $600 weekly supplement to average county
weekly earnings for in-person service workers. See text for details.

across U.S. counties. Average weekly earnings are measured for 2019 from the Quarterly Workforce
Indicators (QWI). In-person service sectors are defined as retail trade (NAICS 44-45), education and
health (NAICS 61-62), leisure and hospitality (NAICS 71-72), and other services (NAICS 81). We
only retain counties for which the QWI provides actual data and for which we have employment data
from HB.
As Figure B-2 shows, the $600 weekly supplement implies large spatial variations in the change
of UI generosity across counties, ranging from about 50 percent on the West Coast, the Northeast,
and Florida to over 200 percent in the Midwest and the Central South region of the U.S.21

B.2

Relation to changes in spending and employment at the onset
of the pandemic

To illustrate the potential importance of stimulative effects of UI and other demand confounds
that occurred around the start of pandemic UI, we report cross-country scatter plots of the relative
generosity of the $600 weekly FPUC supplement (measured as above) against the change in consumer
21
Note that comparing the relative generosity of the FPUC across counties here is analogous to comparing
the difference between replacement rates of low-wage and high-wage businesses across local industries in the
text since the effect state UI programs is differenced out.

50

spending and the change in in-person service sector employment between the end of March 2020 and
end of April 2020 (i.e., the first month of FPUC payments) as a percent of the January 2000 February 2000 average. The county-level consumer spending data is from Chetty et al. (2020) based
on credit- and debit-card spending data from Affinity, while county-level employment for in-person
service sectors comes from Kurmann, Lalé, and Ta (2021) based on HB data.
As Figure B-3 shows, there is a pronounced positive relation between the change in the generosity
of UI implied by the $600 weekly supplement and the change in consumption and employment.
Further inspection of the data reveals that this effect is robust to various controls, including industry
and state fixed effects. We also find similar results with regard to small business revenues (using data
from Womply by Chetty et al. (2020)); and we find that around the expiration of the $600 weekly
supplement at the end of July, there is a corresponding negative (although substantially smaller)
relation of the two variables with the relative generosity measure.
We take this evidence as highly suggestive of stimulus effects of the $600 supplement and, potentially, other local labor market confounds that obscure the disincentive effects of UI during the
first few months of the pandemic. In other words, research designs that exploit simple variations in
UI generosity around the beginning and end of pandemic UI supplements do not identify a disincentive effect but an equilibrium effect that combines disincentive and stimulus effects and, potentially,
other confounds. As explained in Section 2, our local-industry design differences out these demand
confounds, at least to the extent that they affect low- and high-wage businesses equally.

C

Cross-sectional statistics

Employment, Hours, and Wages

Table C-2 shows the cross-section of key labor market vari-

ables for 2019. The statistics are computed when the businesses are in operation. The table shows
that HB data covers small businesses. On some days, a significant fraction of businesses operate with
one or two employees. Even businesses at the 90th percentile that employ on average 12 employees
would be considered small by normal standards. We winsorize the hourly wage at $7 per hour.
Workers reporting an hourly wage lower than this threshold are likely compensated by tips which we
cannot verify in our data. This adjustment does not affect the division of businesses in low-wage vs.
high-wage (and hence, the empirical estimates) but affects the cross-sectional dispersion we target
in the model. Without this adjustment, the residual of the log-hourly wage at the 10th percentile
would be -0.15 instead of -0.12.
Replacement rates

To conduct our empirical analysis we compute a replacement rate at the

business level. The procedure to calculate business-level replacement rates is as follows:
1. The average daily hourly wage of business j in cell c in the base period January-February 2020
is wj,c,t0 . We multiply this wage by 7 hours times 5 days times 13 (52) weeks to obtain a
q
quarterly (annual) measure of business-level earnings, wj,c,t
.
0

51

Figure B-3: Generosity of Pandemic UI Supplement vs. Changes in Consumption and Employment

Notes: The figure reports binned scatter plots of the relative generosity of the $600 weekly supplement against
the change in average county-level consumption (left) and the change in in-person service sector employment
(right) between the end of March 2020 and end of April 2020 as a percent of baseline, which is the January
2000 to February 2000 average. See text for details.

52

Table C-2: Employment, Hours, and Wage in the Cross-section

# Employees
Hours per worker
Hourly wage ($)
Residual log-hourly wage ($)
Separation rate (%)
Hiring rate (%)

Mean SD
6.4
5.1
6.7
1.6
11.3
2.7
0.0
0.09
8.3
13.9
9.9
19.3

p(5) p(10)
1
2
4.3
4.9
7.2
8.0
-0.16 -0.12
0.0
0.0
0.0
0.0

p(25)
3
5.7
9.5
-0.05
0.0
0.0

p(50)
5
6.5
11.3
0.0
3.1
3.1

p(75) p(90)
8
12
7.5
8.5
13.0
14.7
0.07
0.13
12.5
22.5
13.1
24.6

2. We take the average of quarterly or annual earnings in cell c denoted as wqc,t0 .
3. We combine wqc,t0 with state-level formulas for unemployment insurance income to derive the
weekly amount of UI that an unemployed in cell c receives, denoted b(wc,t0 ).
4. b(wc,t0 ) + St is the total weekly amount of UI that an unemployed in cell c receives during
week t of the pandemic, where St = {$0, $300, $600}.
5. We divide the total weekly supplement b(wc,t0 ) + St by the weekly earnings in business j, equal
to wj,c,t0 × 7 × 5. This gives us the business-replacement rate Rj,c,t which measures the amount
of UI an unemployed would receive in labor market c and period t relative to what he/she can
receive by being employed in business j.

Table C-3: Replacement Rate Distribution

Mean

SD

p(5)

p(10)

p(25)

p(50)

p(75)

p(90)

Replacement rate (R)
Normal Times
CARES Act

0.54
2.11

0.13
0.55

0.41
1.54

0.43
1.62

0.47
1.78

0.51
2.00

0.57
2.32

0.66
2.68

Replacement rate gap (∆R)
Normal Times
CARES Act

0.12
0.51

0.16
0.65

0.01
0.03

0.02
0.08

0.04
0.18

0.07
0.34

0.57
0.61

0.22
1.00

Table C-3 reports summary statistics for the cross-sectional distribution of the business-level
replacement rate Rj,c,t as well as the replacement rate gap ∆Rc,t which is calculated as the average
replacement rate in low-wage businesses of cell c minus the average replacement rate in high-wage
businesses of cell c.

53

150

50

100

150

200

100

Replacement Rate

200

Figure C-4: Replacement Rate R and Replacement Rate Gap ∆R

0

50
0

0
Jan 20

Apr 20

Jul 20

20

40
60
Replacement Rate Gap

80

Oct 20

Notes: The left panel shows the time series of the average replacement rate R in the labor market
and the average difference (gap) in replacement rate between the low- and high-wage business of the
labor market, ∆R. The right panel shows a binscatter of R and ∆R across labor markets and weeks.
The plot is restricted to gaps lower than 100 percent.
In normal times (i.e., during 2019), the mean replacement rate is 54 percent and the median
is 51 percent. During the CARES Act (specifically, between April 2020 and June 2020 where the
additional $600 is in effect), the average replacement rate increased to 2.11 and the median to 2.00.
In normal times the replacement rate gap is on average 0.12, with a median of 0.07. With the CARES
Act, the replacement rate gap increases on average to 0.51 and for the median labor market to 0.34.
How do the replacement rate R and the replacement rate gap ∆R vary across labor markets and
over time? The left panel of Figure C-4 shows the average time series path of R and ∆R which move
together as they are both influenced by the pandemic income supplement St . In the right panel,
we plot a binscatter of Rc,t and ∆Rc,t across labor markets and weeks. Labor markets that have a
higher difference in the replacement gap also experience higher average UI replacement rates.

D

Trends before and during the pandemic
We plot the raw time series of labor market variables for low- and high-wage businesses during

2019 and 2020. The left panel of Figure D-5 shows employment and the right panel of Figure D5 shows employment during operating weeks, i.e., without counting the zero observations. Both
employment measures are aggregated at the monthly frequency. In these figures, we make two
adjustments to the weekly employment data. First, we normalize weekly employment by the average
weekly employment in the business in our base period, i.e., January-February 2020. This way we
can measure how far businesses are from their “normal” levels. Second, we seasonally adjust the
employment data where seasonal factors are computed based on the average monthly number of

54

Figure D-5: Employment (Left Panel) and Employment Cond. on Operation (Right Panel)
120

120

100

100

80

80

60

60

40

40

r
Ma

19 n 19 p 19 c 19 r 20 n 20 p 20 c 20
Ju
Se De
Se De Ma Ju

0
9
0
9
0
9
0
9
r 1 un 1 ep 1 ec 1 ar 2 un 2 ep 2 ec 2
a
J
J
S
S
D
D
M
M

Notes: Monthly averages of the number of employees. The left panel includes days of inactivity
and the right panel is average conditional on operation. Business employment is normalized by the
average during January and February 2020 and is seasonally adjusted. Low- and high-wage business
classification is based on local industry sorting.
employees during 2019.
Before the pandemic, low- and high-wage businesses move broadly together. When the pandemic
hits, employment declines to 46 percent of normal in high-wage businesses and around 41 percent
of normal in low-wage businesses. Naturally, the decline in the restaurant and retail sector is much
larger than the economy-wide decline in employment (around 15 percent). Thereafter, employment
recovers, but there remains a sizable gap in recovery rates between high- and low-wage businesses.
Specifically, the employment recovery gap is about 8 percentage points between April 2020 and
July 2020 (when the $600 income supplement is in effect) and decreases to about 6 percentage points
after July 2020, i.e., when the income supplement expires. This raw comparison of averages coincides
with our baseline estimate that the $600 supplement decreased low-wage employment recovery by
1.5 percentage points. The right panel of Figure D-5 shows average employment during operating
weeks. In this case, the employment recovery gap is about 6 percentage points between April 2020
and July 2020 and decreases to about 4 percentage points after July 2020.
The left panel of Figure D-6 plots average hours worked (once more normalized by the JanuaryFebruary 2020 level) while the right panel plots the average hourly wage. Before the pandemic,
average hours worked for low- and high-wage businesses coincide, while average hourly wages grew
faster for high-wage businesses than for low-wage businesses. As the pandemic hits, average hours
worked decline for both types of businesses for a couple of months and then revert roughly back to
their trend. Notably, hours recover faster for low-wage businesses up to August 2020. Regarding

55

Figure D-6: Hour per Employee (Left Panel) and Hourly Wage (Right Panel)
15

105

14
13

100

12
11
95

10
9

90

8

0
9
0
9
0
9
0
9
r 1 n 1 ep 1 ec 1 ar 2 un 2 ep 2 ec 2
J
S
S
D
D
M
Ma Ju

0
9
0
9
0
9
0
9
r 1 n 1 ep 1 ec 1 ar 2 un 2 ep 2 ec 2
J
S
S
D
D
M
Ma Ju

Notes: The left panel shows monthly averages of weekly hours per employee for low- and high-wage
businesses. The time series are normalized by the average during January and February 2020. The
right panel shows monthly averages of weekly hourly wages for low- and high-wage businesses and is
reported in levels.
hourly wages, we observe a temporary hump at the beginning of the pandemic. This hump arises
mostly due to selection: when employment declines the highest-paid employees are retained. The
pre-pandemic trend in average hourly wages is reversed along the recovery: low-wage businesses
increased their hourly wage faster than high-wage businesses. From January 2020 to December
2020, the hourly wage increased 5.9 percent for low-wage businesses and 4.3 percent for high-wage
businesses.
Finally, Figure D-7 shows the weekly separation and hiring rate (averaged over a month). Separation rates are higher for low-wage businesses before the pandemic and so are hiring rates. At the
beginning of the pandemic, low-wage businesses experience larger separation rates and lower hiring
rates relative to high-wage businesses which explains the divergence in employment recovery between
groups.

E

Regression results and robustness
We quantify the employment recovery gap between low- and high-wage businesses, by estimating

the following regression in the main text:
∆yc,t =

X

bs 1{s=t} + X0c,t γ + δ∆yc,t,2019 + εc,t .

s

56

Figure D-7: Separation Rate (Left Panel) and Hiring Rate (Right Panel)

20
10
15
8
10
6

5

0

4
r

Ma

19

Jun

19

9
0
9
20 p 20 c 20
p1 c1 r2
Se De Ma Jun Se De

0
9
0
9
0
9
0
9
r 1 un 1 ep 1 ec 1 ar 2 un 2 ep 2 ec 2
J
J
S
S
D
D
M

Ma

Notes: Monthly averages of weekly separation (left panel) and hiring rates (right panel) for low- and
high-wage businesses, reported in percent.
In the text, we discuss how the estimated weekly fixed effects correlate with the pandemic UI
supplements. Here we discuss the controls and the seasonal coefficient. The control variables Xc,t
include the following variables. First, the number of Covid-19 deaths which are obtained from Covid
Act Now (see Kurmann, Lalé, and Ta, 2021). The upper panel in Figure E-8 shows the national time
trends for Covid-19 cases (per 10,000,000 population) and deaths (per 100,000 population). Second,
the percentage change in visits to schools (right panel in Figure E-8).
Third, our controls include the difference in the number of weekly customers between the lowand high-wage businesses in cell c (relative to the base period of January-February 2020). Both
schooling and customer traffic are based on cell phone traffic data from Safegraph.
Fourth, we include the difference in the price range between low- and high-wage businesses as
measured in Yelp. Finally, we control for the employment gap in variable y between low- and highwage businesses for local industry c at the same week t of 2019 (denoted as ∆yc,t,2019 ). Table E-4
shows the estimates from Regression 8.
Table E-5 reports estimates for the various robustness exercises described in Section 4. First, we
restrict the sample to the businesses that continuously operated during the pandemic. Second, we
sort businesses into low- and high-wage based on OTC-adjusted wages, as described in Appendix A.
Third, we examine the estimates when we look at a broader sample of businesses. Specifically, we
keep businesses for which we could not find information on their price and quality from Yelp. Fourth,
we choose a wider base period of July 2019-February 2020. Fifth, we weigh each cell by the number
of businesses inside the cell; i.e., more populated cells take a higher weight.

57

Figure E-8: COVID-19 Cases and Deaths and School Traffic
50

140
0

120
100

-50

80
-100

60
40

-150

20
-200
21
O

ct

1
l2
Ju

A

pr

21

21
n
Ja

20
O
ct

0
l2
Ju

20
pr
A

Ja

n

20

ct
21
O

Ju
l2

1

1
pr
2
A

21
Ja
n

20
O

ct

0
l2
Ju

20
A

pr

Ja
n

20

0

Notes: The left panel shows Covid-19 reported cases and deaths and the right panel shows percent
change in school traffic.

Table E-4: Estimates from Regression 8
∆yc,t

Estimate

S.E.

Weekly dummies

Figure 3

–

Covid-19 deaths (per 100,000 pop)

1.29∗∗∗

(0.37)

School traffic (% change)

1.16∗∗∗

(0.38)

−3.14∗∗∗

(0.24)

∆yc,t,2019

2.27∗∗∗

(0.39)

Customer visits

1.12∗∗∗

(0.19)

# Observations

97,546

Yelp Price Range

Notes: Estimates from regression 8 including the control variables. Observations are at the local
industry/week level. We winsorize variables at the one percent. We cluster standard errors at the
local industry level.

F

Definition of equilibrium transition path
We describe the equilibrium along the transition path. Given the initial job separation at t = 0

and a path for the UI policy parameters {bR,t , pR,t , pN,t }∞
t=0 a transitional dynamics equilibrium
∗
∗
∗
∞
is a sequence of value functions {Wt , UR,t , UN,t }∞
t=0 , reservation wages {wR,t , wN,t , wmin,t }t=0 , job
∞
∞
acceptance rate {Ft }∞
t=0 , distributions {et , uR,t , uN,t , ut , vt , ṽt }t=0 , and market tightness {θt }t=0 such

that:

58

Table E-5: Alternative Empirical Specifications

Employment gap Hours per employee gap Hourly wages gap

∆yc,t

(1)

(2)

(3)

Benchmark

−5.73***
(1.34)

0.39
(0.62)

1.52**
(0.63)

Continuously open businesses

−3.94**
(1.58)

0.99
(0.70)

2.59***
(0.78)

Sorting with OTC-adjusted wages

−3.70***
(0.89)

0.69*
(0.42)

1.02**
(0.50)

Broader sample

−6.62***
(1.24)

0.97
(0.61)

1.54***
(0.57)

Larger base period

−5.22***
(1.35)

0.65
(0.67)

1.54***
(0.67)

Weights

−6.04***
(1.21)

0.27
(0.57)

0.73
(0.67)

Notes: Each line reports the estimates from regression 9 for an alternative specification. We winsorize
variables at the one percent and cluster standard errors at the local industry level.
1. The value functions {Wt , UR,t , UN,t }∞
t=0 satisfy equation (10), equation (11), and equation (12),
for all t.
∞
∗ , w∗ , w∗
2. The reservation wages {wR,t
min,t }t=0 , satisfy equation (13), and equation (15), for all
N,t

t.
3. The (un)employment and vacancy distributions {et , uR,t , uN,t , ut , vt , ṽt }∞
t=0 satisfy equation (16),
equation (17), equation (18), equation (19), equation (22), and equation (23) for all t.
4. The acceptance rate {Ft (w)}∞
t=0 satisfy equation (24), for all t.
5. Market tightness {θt }∞
t=0 is given by ṽt /ut , for all t

G

Calibration of recipiency rate
In our calibration, we adjusted UI recipiency rates in the March CPS data by adapting the

procedure of Larrimore, Mortenson, and Splinter (2023) (LMS). The authors use CPS and IRS data
and document that there is substantial underreporting of UI recipiency (and benefit amounts) in
the March CPS. They provide IRS estimates of UI recipiency by income centiles for each tax year
from 1999 until 2021. We adapted their code to adjust UI recipiency rates in the March CPS data.

59

Specifically, for each centile of the income distribution, LMS’s procedure compares the raw number
of UI recipiency in the CPS with that from the IRS data; if the latter is larger (which happens to be
the case in almost every centile of the distribution), they randomly allocate the number of missing
UI recipients so that the sum of the raw and imputed UI recipients in this centile matches the IRS’s
estimate. We perform a similar allocation, but prioritize the allocation of missing UI receipts to
workers who have been working for at least part of the previous year and have been unemployed
for at least one quarter. This adjustment is motivated by the fact that, within any centile, these
individuals are more likely to have received UI benefits compared to any randomly selected individual.

H

Calculation of duration elasticities
We measure the unemployment duration elasticity over a policy change x along the transition.

We consider three policy changes: (i) the income supplement where x denotes dollar amounts, (ii)
the maximum duration of benefits where x denotes weeks, and (iii) the set of eligible workers for UI
where x is a probability.
To calculate the unemployment duration elasticity, let us first define survival functions for workers
who receive UI benefits at the beginning of t. ξi,t+τ (w) is the probability that these workers are still
unemployed by the end of time t + τ and at that point their status is i ∈ {R, N }. In the baseline
model, the survival function ξR,t+τ (w) satisfies the relation:
ξR,t+τ (w) = ξR,t+τ −1 (w) (1 − fR,t+τ −1 (w)) (1 − pN,t+τ ) , τ = 1, 2, . . . ,
starting from
ξR,t (w) = 1 − pN,t .
For the survival function ξN,t+τ (w), we can exploit the following mutually exclusive events. For a
worker who started unemployment as R in t, and is N at the end of t + τ , it must be that she was
either (i) R at the end of t + τ − 1 and became N during period t + τ , or (ii) already N at the end
of t + τ − 1. As a result, we have
ξN,t+τ (w) = ξR,t+τ −1 (w) (1 − fR,t+τ −1 (w)) pN,t+τ + ξN,t+τ −1 (w) (1 − fN,t+τ (w)) , τ = 1, 2, . . .
starting from
ξN,t (w) = pN,t .
Putting it all together, the expected unemployment duration of an unemployed who is in state R
(that is to say receiving UI benefits) at t and with previous wage w is:
EDR,t (w) =

∞ h
X

i
ξR,t+τ (w) fR,t+τ (w) + ξN,t+τ (w) fN,t+τ (w) × (τ + 1) .

τ =0

60

(33)

Next, we compute the expected unemployment duration of an unemployed worker who is in state
N in period t. We define the following survival function
ζt+τ (w) = ζt+τ −1 (w) (1 − fN,t+τ −1 (w)) , τ = 1, 2, . . .
which allows us to compute
EDN,t (w) =

∞
X

ζt+τ (w) fN,t+τ (w) × (τ + 1) .

(34)

τ =0

Let εU
i,t denote the unemployment duration elasticity arising from a policy change from x to x̃, for
workers in unemployment state i ∈ {R, N }. We have:
εU
i,t (w) =

˜ i,t (w)
ED
EDi,t (w) −
x̃
x −1

1
.

(35)

In the final step, we aggregate across all unemployed workers:
εU
t

I

1
=
ut

ˆ


U
uR,t (w) εU
R,t (w) + uN,t (w) εN,t (w) dw

(36)

A Model with Recalls
We expand the baseline model by adding recall unemployment. As in the baseline model, workers

are separated from their employer with some probability (denoted here δ s ). But we also allow the
separated workers to be in touch with their previous employers with a probability 1−δ p . Unemployed
workers who are in touch with their old employers are indexed as i = 1 and unemployed workers
who are not are indexed as i = 0. Unemployed who are in touch with their previous employers can
be recalled to their old job with some probability r.
We assume that upon separation, the unemployed keep in touch with their previous employers.
As a result, the value function for an employed worker is:



1
1
Wt (w) = U (w) + β (1 − δ s ) Wt+1 (w) + δ s (1 − pR,t ) UN,t+1
(w) + pR,t UR,t+1
(w)
1
1
where UR,t+1
and UN,t+1
are the value functions for an unemployed with and without UI benefits,

respectively, that is still in touch with the employer. The value function for an unemployed worker

61

receiving UI, and who is in touch with the employer is given by:
"
1
UR,t
(w)

=δ

p

0
UR,t
(w)

p




0
+ (1 − δ ) r U (bR,t (w)) + β max Wt+1 (w) , UN,t+1
(w)

"

"
1
(1 − λ (θt )) UN,t+1
(w)

+ (1 − r) U (bR,t (w)) + β pN,t
ˆ
+λ (θt )



ṽt (x)
1
1
max Wt+1 (x) , UN,t+1 (w)
dx + (1 − pN,t ) (1 − λ (θt )) UR,t+1
(w)
ṽt

ˆ

ṽt (x)
1
dx
,
+λ (θt ) max Wt+1 (x) , UR,t+1 (w)
ṽt

Notice that at time period t, with probability δ p , an unemployed loses touch with the employer and
0 , which is defined below. With probability 1 − δ p an unemployed stays in touch with
receives UR,t

the employer in which case two possibilities arise. First, with probability r an unemployed can be
recalled to the previous job. In this case, the unemployed receives at t the unemployment benefit and
the next period makes a choice between working at the old employer Wt+1 (w) or continuing to be
unemployed. The basic assumption in this formulation is that UI is denied for an unemployed who
has been contacted by the former employer and refused to return to work. Second, with probability
1 − r, an unemployed is not recalled to the old job. In this case, as in the baseline model, an
unemployed loses the UI benefits only if they expire which occurs with probability pN .
The value function for an unemployed worker receiving UI and who is not in touch with the
previous employer (i = 0) is similar to the baseline model:
"
0
UR,t
(w)

0
(1 − λ (θt )) UN,t+1
(w)

= U (bR,t (w)) + β pN,t
ˆ
+λ (θt )



ṽt (x)
0
0
dx + (1 − pN,t ) (1 − λ (θt )) UR,t+1
(w)
max Wt+1 (x) , UN,t+1 (w)
ṽt

ˆ

ṽt (x)
0
+λ (θt ) max Wt+1 (x) , UR,t+1 (w)
dx ,
ṽt

We report below the value functions of unemployed workers in social assistance, when they are in
touch and when they are not in touch with their previous employer:
"
1
UN,t
(w)

=δ

p

0
UN,t
(w)

p




0
+ (1 − δ ) r U (bN ) + β max Wt+1 (w) , UN,t+1
(w)
"

1
+ (1 − r) U (bN ) + β (1 − λ (θt )) UN,t+1
(w)

ˆ
+λ (θt )

62

max



1
Wt+1 (x) , UN,t+1
(w)

ṽt (x)
dx
ṽt


,

0
UN,t
(w)



ˆ

ṽt (x)
0
0
dx .
= U (bN ) + β (1 − λ (θt )) UN,t+1 (w) + λ (θt ) max Wt+1 (x) , UN,t+1 (w)
ṽt

Let A(w, w0 ) be an indicator that takes the value of 1 if an unemployed worker whose previous job
paid w accepts an offer for a job that pays w0 . Notations become very cumbersome if we define
reservation wages as in the baseline model, so let us instead work with the following indicators for
the decision to accept a job:





i
AiR,t w, w0 = 1 Wt+1 w0 > UR,t+1
(w)





i
AiN,t w, w0 = 1 Wt+1 w0 > UN,t+1
(w)
Note that as in the baseline model, these definitions for time t refer to decisions made in t + 1.
The law of motion for employment is similar to the baseline with an additional inflow of recalled
workers who accept their old job at wage w:
et+1 (w) = (1 − δ s ) et (w) + (1 − δ p ) rA0N,t (w, w) u1N,t (w) + u1R,t (w)
+ λ (θt )




ṽt (w)
Ft (w) ūt
ṽt

Ft (w), the probability that a job offer w gets accepted, is
ˆ


1
Ft (w) =
(1 − pN,t ) δ p u1R,t (x) + u0R,t (x) A0R,t (x, w) dx
ũ
ˆt
+ (1 − pN,t ) (1 − δ p ) (1 − r) u1R,t (x) A1R,t (x, w) dx
ˆ





+
δ p u1N,t (x) + u0N,t (x) + pN,t δ p u1R,t (x) + u0R,t (x) A0N,t (x, w) dx

ˆ
p
1
1
+ (1 − δ ) (1 − r) uN,t (x) AN,t (x, w) dx ,
The transition equations for unemployment are given by:
u1R,t+1 (w) = (1 − δ p ) δ s pR,t et (w)


ˆ
ṽt (x)
1
+ 1 − λ (θt ) AR,t (w, x)
dx (1 − pN,t ) (1 − r) (1 − δ p ) u1R,t (w) ,
ṽt
u0R,t+1 (w) = δ p δ s pR,t et (w)


ˆ


ṽt (x)
0
+ 1 − λ (θt ) AR,t (w, x)
dx (1 − pN,t ) δ p u1R,t (w) + u0R,t (w) ,
ṽt
u1N,t+1 (w) = (1 − δ p ) δ s (1 − pR,t ) et (w)


ˆ


ṽt (x)
1
+ 1 − λ (θt ) AN,t (w, x)
dx (1 − r) (1 − δ p ) u1N,t (w) + pN,t u1R,t (w) ,
ṽt

63

(37)





u0N,t+1 (w) = δ p δ s (1 − pR,t ) et (w) + (1 − δ p ) r 1 − A0N,t (w, w) u1N,t (w) + u1R,t (w)


ˆ





ṽt (x)
0
+ 1 − λ (θt ) AN,t (w, x)
dx
δ p u1N,t (x) + u0N,t (x) + pN,t δ p u1R,t (x) + u0R,t (x) ,
ṽt
with ũt =

´




´
(1 − (1 − δ p ) r) u1N,t (x) + u1R,t (x) + uN,t (x) + uR,t (x) dx and ṽt = ṽt (x) dx. We

have the assumption of a fixed number of jobs as in the baseline:
et (w) + u1N,t (w) + u1R,t (w) + vt (w) = g (w) M.
Labor market tightness is given by:
θt =

ṽt
ũt

(38)

(39)

We set the weekly job separation rate as δ s = 0.016 as in the baseline. The matching technology
parameter κ = 0.15 to match a job finding rate equal to 0.23. Parameter δ p = 0.17 matches a recall
share of hires equal to 33 percent. Given that the average duration of recalls in HB data is about 4
weeks, we set r = 0.23.
The effective probability of losing UI upon job refusal in the model with recall is (1 − δ p )r = 0.19,
i.e., the probability a worker stays in touch with the employer and that the employer recalls the
worker back to work. In the reduced-form model in the main text, the probability of losing UI upon
job refusal is equal to χ = 0.10 in order to match the employment recovery gap we documented in
the data. Thus, our reduced-form parameterization is reasonably close to the parameter values in
a model with recall unemployment. To highlight this argument, Figure I-9 plots the employment
recovery gap in the data, in the model with UI loss upon job refusal and in the model with recalls.
The model with recalls can also capture closely the dynamics of the employment recovery gap.

64

Figure I-9: Employment Recovery Gap: Model with Recalls

0
-2
-4
-6
-8
-10

-5

0

5

10

15

20

25

30

35

Notes: The figure plots the average low-wage business employment minus the average high-wage
business employment (both relative to their pre-pandemic level) in the model with the probability
of losing UI upon job refusal and the model with recalls. Data represent the estimated b’s from
Regression 8.

65