Disincentive Effects of Unemployment Insurance Benefits — WP 23-11R (December 20, 2024)

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A working paper, WP 23-11R, Disincentive Effects of Unemployment Insurance Benefits, by Andreas Hornstein, Marios Karabarbounis, André Kurmann, Etienne Lalé, and Lien Ta, dated December 20, 2024. The abstract states that the paper provides independent estimates of the disincentive effects arising from the pandemic unemployment benefits, using high-frequency data on small restaurants and retailers from Homebase. It states that employment in low-wage businesses recovered more slowly than employment in neighboring high-wage businesses in labor markets with larger differences in the relative generosity of pandemic UI benefits. According to a labor search model, the disincentive effects reduced the aggregate employment recovery by 3.4 percentage points between April and December 2020.

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Disincentive Effects of
Unemployment Insurance Benefits

WP 23-11R 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 Marios Karabarbounis André Kurmann
FRB Richmond FRB Richmond Drexel University

Etienne Lalé Lien Ta
York University Drexel University

December 20, 2024

Unemployment insurance (UI) acts both as a disincentive for labor supply and as a de-
mand 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 demand
effects by comparing neighboring businesses that largely share the positive impact of UI stimu-
lus. We find that employment in low-wage businesses recovered more slowly than employment
in neighboring 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 3.4
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 as-
sistance and Fernando Alvarez, Mark Bils, Yongsung Chang, Cynthia Doniger, Giovanni Gallipoli, Philip
Jung, Marianna Kudlyak, Guiseppe Moscarini, Pascal Noel, Guido Menzio, Theodore Papageorgiou, Victor
Rios-Rull, Aysegul Sahin, Venky Venkateswaran, as well as seminar participants at the NBER SI 2024 (Micro
and Macro Perspectives of Aggregate Labor Market), SED 2022, Wharton, FRB Philadelphia, FRB St.
Louis, CERGE-EI, SFU, University of Toronto, University of Miami, and Vienna Macro Conference 2023 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 of
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 eli-
gibility 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 modest negative effects on
job-finding rates and employment. What these studies do not clarify, however, is if these lim-
ited 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 controls for confounding demand effects in two ways. First, we differ-
ence out common local demand shifts arising from the UI stimulus by comparing the employ-
ment recovery of low-wage and high-wage businesses within the same labor market, industry,
and price range.1 Second, we account for idiosyncratic demand shifts between neighboring
low- and high-wage businesses by including controls for customer traffic and spending for each

1
Such local differencing not only reduces the bias arising from the demand stimulus of UI but also from
any factor that is correlated with demand shifts and replacement rates as long as the factor is common within
labor markets.

1
individual business.
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 repre-
sentative of small, in-person service sector businesses, mostly restaurants and retail businesses
(Kurmann, Lalé, and Ta, 2021).2 The data provides a panel of businesses with daily data on
employment, the hourly wage, hours worked by each employee, business zip code, and industry
affiliation. We match this data to Yelp to obtain a price range and to Safegraph to obtain
weekly measures of customer traffic and customer expenditures for each individual business.
The link between employment, wages, price range, and customer demand at the individual
business level and at a high frequency is a unique feature of our analysis.
We study the employment recovery in low- versus high-wage businesses before and after
the discontinuation of the CARES Act $600 income supplement.3 Due to the expiration, some
labor markets experience a larger decline in the UI replacement rate gap between low- and
high-wage businesses than others. We find that in labor markets with a larger decline in the
UI replacement gap, employment in low-wage businesses recovers faster than employment in
their high-wage neighbors, thereby closing the employment recovery gap. For this result, it is
crucial to define local labor markets narrowly. When we compare businesses at broader levels
of geographical aggregation (e.g., within state borders) the estimated effect of replacement
rates on the employment recovery gap disappears.
The basic identification assumption is that low- and high-wage businesses in the same labor
market, industry, and price range are not differentially exposed to demand and productivity
shifts. Based on our comprehensive and linked data we collect several pieces of evidence that
support this assumption. First, we confirm that low- and high-wage businesses in the same la-
bor market, industry, and price range are not differentially impacted by local industry demand
shifts (such as the number of customers and spending). Second, we show that the inclusion of
a variety of controls such as health indicators, stay-at-home regulations, school closures, and
differences in measures of business quality and customer demand do not substantially alter
our estimated effects. Finally, we show that even though employment of low-wage businesses
lagged behind employment of their high-wage neighbors during the period of the $600 sup-
plement, hours per employee and hourly wages of low-wage businesses were growing faster.
This correlation is suggestive of differential labor supply shocks not differential demand or

2
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.
3
Whereas the introduction of the income supplement in March 2020 coincides with other widespread
disruptions in the labor market from pandemic-related closures, the removal of the supplement occurs in
August 2020 when the economy is relatively close to its normal capacity and most health-related regulations
have been lifted.

2
productivity shocks.
To quantify the overall impact of the CARES Act on employment recovery we build a
labor search model. As long as the employment decisions of high-wage businesses are affected
by the pandemic UI benefits, our estimate of the employment recovery gap impact of UI alone
does not represent the total impact of UI on employment. With the model, we can construct
a proper counterfactual for the overall employment recovery absent pandemic UI benefits. In
addition, we use the model 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.
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 and constant wage offers. Unemployed work-
ers randomly search for jobs from the wage offer distribution and accept a job if the offered
wage is higher than their reservation wage (McCall, 1970; Albrecht and Axell, 1984). Since UI
benefits depend on a worker’s last wage, 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 vastly overstates the estimated impact of the expiration
of the $600 income supplement on the employment recovery of low- versus high-wage firms.
The exaggerated impact arises in the model not only due to the magnitude of the income

3
supplement but also due to the expansion of the UI eligibility criteria. Using data from the
Current Population Survey (CPS) we document that for the in-person leisure and hospitality
businesses we study, 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 during the period of $600 income
supplement and recovers at an equally fast pace after the expiration.
We reconcile the model with the data by introducing the possibility that workers lose
their UI eligibility if they refuse a job offer. This assumption, which is motivated by UI
law, effectively reduces the outside option for workers and increases the acceptance rates for
low-wage firms. With a probability of losing benefits upon job refusal around 16 percent,
we can match the estimated impact of the expiration of the $600 income supplement on the
employment recovery gap closely.
Based on this extended model, we compute the employment losses relative to a counter-
factual economy without the CARES Act. We find that when implemented in isolation, each
provision of the CARES Act has only 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 3.4 percentage
points higher between April and December 2020. This employment loss represents around
20 percent of the average employment loss in the Leisure and Hospitality sector during the
same period. This large employment decline is due to the sheer size and joint implementation
of the pandemic UI provisions. The model’s implied unemployment duration elasticities are
actually quite modest and in line with the low-to-middle range of pre-pandemic estimates
(e.g., Schmieder and von Wachter, 2016).
Our paper contributes to the literature that studies to what extent 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. (2024)
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 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 employment would have been modestly higher in the absence of
pandemic benefits. We argue that these limited estimated effects likely represent a mix of
disincentive effects, stimulative effects, and possible other confounding local demand shocks.

4
Di Maggio and Kermani (2021) and Hellwig (2021) also estimate the labor market con-
sequences of UI benefits taking into account both the disincentive and stimulative effects of
UI policies. In the spirit of Mian and Sufi (2014), their approach compares the employment
effects in non-tradable sectors — that are more affected by local demand conditions — and
tradable sectors. In contrast, our methodology controls for local demand effects by comparing
relatively homogeneous businesses that are part of the same local market. Thus, our method-
ology 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
Finamor and Scott (2021), like us, use Homebase data to study labor market search at
the state level. They find that a higher replacement rate is not associated with a lower
labor market re-entry of workers. As mentioned, when we conduct our research design at a
similar broad level of geographical aggregation our estimates become small and insignificant,
highlighting 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 eligibil-
ity (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., 2024). 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.

4
See, for example, Hagedorn et al. (2013), Dieterle, Bartalotti, and Brummet (2020), Chodorow-Reich,
Coglianese, and Karabarbounis (2019), and Boone et al. (2021). A direct application of the BCP design is not
well-suited to study the effects of pandemic supplements, because these provisions apply to all counties.

5
2 Research design
Consider the following data-generating process

yj,c,t = α + βRj,c,t + X0j,c,t γ + uj,c,t + εj,c,t , (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

bc (wc,t0 ) + St
Rj,c,t = . (2)
wj,c,t0

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.5 For the average unem-
ployed, 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 .
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., idiosyncratic demand shifts from the stimulus or quality differences). 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 benefit more from the UI stimulus or are
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. Consider two labor markets,
A and B, each populated with two businesses. Average wages paid by the businesses in labor
market A are higher than in labor market B. Because of the pandemic, businesses experience
a large decline in their employment and gradually return to normal. With the same pandemic
supplement S, labor market B has higher average replacement rates than labor market A.

5
This definition implies that a business can potentially match with any unemployed worker in the labor
market, a characteristic of random search models.

6
Figure 1: Example of Research Design

100

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.

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.6 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 low-
and 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
the difference between the average replacement rate in the low-wage section and the high-
wage section of labor market c, and similarly for the other observable factors. As we show

6
This is a relevant concern since Ganong et al. (2024) show that pandemic-UI recipients quickly spent a
substantial portion of their benefits.

7
in empirical Section 3, 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 low-
and 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. It is equally plausible that within labor markets, a business with a high
replacement rate recovers more slowly than a business with a low replacement rate, and this
disparity in recovery increases with 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 shifts that
may be correlated with the generosity of the replacement rates (e.g., local demand shifts due
to pandemic regulations or consumer preferences).
Local differencing does not eliminate components of uj,c,t that differ across neighboring
low- and high-wage businesses, most notably idiosyncratic demand and quality factors. For
example, low- and high-wage businesses may not benefit proportionately from the UI stimulus
or be differentially impacted by the pandemic. We address this issue in two ways.
First, we limit the analysis to a relatively short period around the expiration of the income
supplement and include local industry fixed effects in our regression. Most pandemic-related
restrictions have been lifted for this period, and the economy is relatively close to its normal
capacity. Therefore, persistent differences between low- and high-wage businesses are unlikely
to change much and will be picked up by our local industry fixed effects. Second, we directly
control for observable differences in time-varying idiosyncratic factors in ∆X0c,t . These include
customer traffic, customer spending, and business quality.
Finally, note that our research design only identifies relative employment effects between
neighboring businesses. In Section 5 we use a structural model that matches these relative
employment effects to estimate the aggregate employment effects of the pandemic UI expan-
sion.

3 Data
3.1 Employment and customer traffic
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

8
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. We combine the
HB employment data with Safegraph data tracking the number of mobile devices that have
visited establishments around the U.S. on a weekly basis (foot traffic). In addition, Safegraph
provides information on credit card spending at the business level. We use these measures as
proxies for customer demand.
Our sample covers the period from January 2019 to December 2020 and contains ap-
proximately 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 differ in their employment trajectories during the pandemic. It is therefore
important to incorporate information about a business’ industry. 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 information on the number of customer visits and customer expenditures for each
business derived from anonymized cell-phone and credit card spending data; and (ii) Yelp
data that includes the price range of the business.7
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.
We want to study the relative employment paths of low- and high-wage businesses in local-
industry 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. Finally, to make the distinction between low- and high-wage businesses in a local-
industry cell we drop single business cells. After imposing all of these restrictions we are left
with 4,595 businesses for which we have weekly 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,

7
See Kurmann, Lalé, and Ta (2021) for a detailed description of the matching procedure.

9
foot traffic, 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 comparable to estimates
from the CPS.
As described in our research design, our goal is to compare labor market outcomes of low-
versus 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 local-
industry dummies dc :
wj,c = a + dc + ej,c . (4)

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, industry,
and price range. 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 a separate group. Finally, we bundle businesses into relatively inexpensive (one
and two Yelp dollar signs) and relatively expensive (three and four Yelp dollar signs). Given
our sample, this results in 1,195 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 39.
We measure weekly employment in a business by counting the number of hourly-paid
employees 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 employees 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). Measuring business employment based on
hourly-paid employees is consistent with our classification of businesses into low- vs. high-
wage which is based on hourly wages. We test our results when we include a broader definition
of employment that includes salaried workers (e.g., store managers) in the robustness section.
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

10
Table 1: Employment, Wages, and Customer Demand by Business Type

All Businesses Low-wage High-wage

Wages
Hourly wage ($) 10.9 10.0 11.8
Hours and Employment
# Employees per business 12.8 12.5 13.2
Hours worked (per day) 4.9 4.8 5.0
Separation rate (%) 9.5 9.6 9.3
Hiring rate (%) 12.4 12.5 12.3
Customer demand & characteristics
# In-person visits (per week) 1051 999 1098
Spending per transaction ($) 23.8 22.6 24.8
Share of restaurants and bars 0.86 0.85 0.87
# Businesses 4,595 2,194 2,401

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.

is 12.8 across all businesses which indicates that the HB data capture mainly very small busi-
nesses. Furthermore, low-wage businesses are smaller than high-wage businesses. Employees
work 4.9 hours per day and the hourly wage is $10.9. Even within narrowly defined local
industries, there is sizable dispersion in hourly wages: high-wage businesses pay on average
$1.8 more than low-wage businesses or equivalently, 8 percent more than the average.
Are employees working in low- and high-wage businesses fundamentally different? In
Figure 2 we report hourly wages by decile for low- and high-wage businesses. Specifically, for
each business, we rank the employees that have worked in the business during 2019 by their
average hourly wage. On average, the bottom 10 percent of employees in low-wage businesses
receive around $8 per 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

11
Figure 2: Hourly Wages Within Businesses

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.

employed in t. Table 1 reports weekly separation and hiring rates averaged over all the weeks
in 2019. The weekly hiring rate and job separation rate in the HB data is 12.4 and 9.5 percent,
respectively.8
During a typical week in 2019, high-wage businesses had around 100 additional customers
relative to low-wage businesses while the average customer spent around $2 more in high-wage
businesses. Finally, 86 percent of our sample are restaurants and bars.

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 meet-
ing 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 ad-

8
Both of these numbers are larger than the equivalent values implied by monthly or quarterly data as typ-
ically reported in the literature (e.g., Hyatt and Spletzer, 2013). 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 high-frequency 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).

12
ditional $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 du-
ration 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.

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.
In our regression analysis, equation (3), rather than using the level of the replacement rate,
we use the replacement rate gap, that is, the difference between the average replacement rates
of low- and high-wage businesses in the same labor market as defined in equation (2).9 The
income supplement increases the gap for all labor markets but increases the gap more for labor
markets with a lower overall average hourly wage or a larger difference in the hourly wage
between low- and high-wage businesses. For illustration, 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 the replacement gap is

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 . (5)
wH,c,t0 wL,c,t0 wH,c,t0 wL,c,t0
| {z } | {z }
=ac =δc

Thus, labor markets with lower average hourly wages or larger inequality in hourly wages have

9
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 B).

13
higher scaling factors δc . In addition, note that by adding a labor market fixed effect in our
regression (3) 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
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. Using data from
the CPS, we show in Section 5.5 that this rise in the recipiency rate is not only related to
the expansion of eligibility toward gig and self-employed workers but applies more generally
to workers in the Leisure and Hospitality sector. 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 A first look at the data
We plot the raw time series of employment for low- and high-wage businesses prior and
during the pandemic. Figure 3 shows employment aggregated at the monthly frequency. We
normalize employment by the average 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.
Before the pandemic, low- and high-wage businesses move tightly together. When the
pandemic hits, employment declines to 41 percent of normal in low-wage businesses and to
48 percent of normal in high-wage businesses. Thereafter, employment recovers, but there
remains a sizable gap in recovery rates between low- and high-wage businesses which visibly
narrows in the summer of 2020. In the next section, we use weekly data to show that the
narrowing of the employment recovery gap coincides with the expiration of the $600 income
supplement.10
10
We find that recalls do not play an important role in explaining the differential employment dynamics
between low- and high-wage businesses (see Appendix B.1).

14
Figure 3: Employment Relative to Normal (in percent)

120

100

Jun 19 Sep 19 Dec 19 Mar 20 Jun 20 Sep 20 Dec 20

Notes: Monthly averages of the number of employees. Business employment is normalized by the
average during January and February 2020. Low- and high-wage business classification is based on
local industry sorting as described in the text.

Figure 4 shows hours per employee (left panel) and hourly wages (right panel) aggregated at
the monthly frequency. We normalize both measures by their averages in the business during
our base period. Along the recovery path, hours per employee and hourly wages grow faster
in low-wage businesses, suggesting that supply side channels drive the differential employment
recovery of low- versus high-wage businesses reported in Figure 3.11 If demand differentials
were behind the differences in employment recovery we should see a higher hours per employee
growth and a faster hourly wage growth for high-wage businesses as well. We confirm this
interpretation in the next section where we show that the estimates of the disincentive effects
are not impacted by the inclusion of local demand controls.

4.2 Event study analysis
The initiation of the CARES Act coincided with large disruptions in the labor market from
pandemic-related restrictions making it hard to isolate the effect of UI on employment. Since
the proposed regression (3) from Section 2 estimates the average effect of replacement rate
gaps across time and labor markets it may conflate the pandemic downturn with the effects
of the replacement rate gap. Furthermore, our quantitative model of Section 5 suggests that

11
Although hourly wages grow faster in low-wage businesses, their overall level remains below that of
high-wage businesses during the pandemic, so the classification of low- versus high-wage businesses remains
unchanged.

15
Figure 4: Hours per Employee and Hourly Wages Relative to Normal (in percent)

110
100
105
95

100
90

85 95

80 90
19 p 19 c 19 r 20 20 p 20 c 20 19 p1
9
c1
9
r2
0 20 p2
0
c2
0
Jun Se De Ma Jun Se De Jun Se De Ma Jun Se De

Notes: Monthly averages of hours per employee and hourly wages. Both measures are normalized
by their averages during January and February 2020. Low- and high-wage business classification is
based on local industry sorting as described in the text.

employment adjusts gradually to UI changes. For these reasons, we focus on the weeks before
and after the expiration of the $600 income supplement and estimate the following event-study
regression:

T2
βs 1{s=t} + Z0c,t θ + ∆X0c,t γ + ∆εc,t .
X
∆yc,t = ac + (∆Rc,post − ∆Rc,pre ) (6)
s=T1

Variable ∆Rc,post − ∆Rc,pre is the time-invariant change of the replacement rate gap in labor
market c due to the expiration of the income supplement. We interact this variable with weekly
time dummies to estimate separate disincentive effects for each week t in a time window around
expiration [T1 , T2 ].
Previously we have argued that the replacement rate gap, ∆Rc,t , depends on the local
average wage and the wage gap between low- and high-wage businesses. Consequently, upon
the income supplement expiration, the replacement rate gap declines more for some labor
markets than others. From Figure 5 we can see that there is substantial variation in the
decline of ∆Rc across local industries.12
In regression (6) we add a labor market fixed effect, ac , which captures fixed differences
between low- and high-wage businesses in the same labor market, industry, and price range
12
The full distribution of the decline in the replacement rate, ∆Rc,post − ∆Rc,pre , across labor markets is
given in Appendix B.

16
Figure 5: Replacement Rate Gap around Expiration of $600.

70
60
50
40
30
20
10
0
-3 -2 -1 0 1 2 3 4

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

during the period of analysis. We also control for the employment gap in cell c during the
same week of 2019 in order to capture seasonal factors as well as two sets of observables.
Vector Zc,t includes local-industry-wide controls at week t, namely (1) the number of Covid-
19 deaths in a county as a measure of community health risk; (2) stay-at-home regulations
taking place in local industry c during week t; (3) 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); and (4) local-industry-wide demand conditions during week t. This demand
control utilizes all available information on the total number of customer visits and total
customer spending (relative to the base period of January-February 2020) from all businesses
in Safegraph in cell c during week t.
In addition, we include in vector ∆Xc,t differences in the recovery rate in customer traffic
and customer expenditures among low-wage and high-wage Homebase businesses, in labor
market c and week t, relative to the base period of of January-February 2020. Since we do not
have information on customer visits and credit card spending for all Homebase businesses, we
cannot always construct the within-cell difference. For this reason we use as a baseline the
specification with local-industry-wide controls, Zc,t , and show separately the results using the
specification that also includes within-cell differences, ∆Xc,t .

17
Figure 6: Employment Recovery Around Expiration of $600 (in p.p.)

-2

-4

-6

-8

-2 0 2 4 6 8 10 12

Notes: Estimated β’s from regression (6) reported in percentage points. The regression includes
local-industry-wide controls and local industry fixed effects. Estimates are reported around the
expiration of the $600 income supplement in the summer of 2020. The shaded area represents the
95 percent confidence interval.

In Figure 6 we display the estimated coefficients on the weekly time dummies as well as
their 95 percent confidence intervals when we run the baseline regression with local-industry
controls and local-industry fixed effects. Standard errors are clustered at the local industry
level. The omitted week 0 is the last week of the $600 income supplement. We find that the
pandemic UI benefits disproportionately affected low-wage businesses. In particular, upon
expiration, the coefficients turn negative meaning that in labor markets with a larger drop in
the replacement rate gap between low- and high-wage businesses (from the expiration of the
$600), there is a faster employment recovery in low- relative to high-wage businesses.
By comparing the employment gap between low- and high-wage businesses in the same la-
bor market, industry, and price range, our baseline regression eliminates the effects of common
local demand shifts arising from the UI income supplement. But even within narrow local in-
dustries, high-wage businesses may benefit relatively more from the UI demand stimulus than
low-wage businesses. Thus, when the UI stimulus expires, the demand may shift back toward
low-wage businesses that subsequently increase their employment. It is also possible that the
expiration of the UI stimulus might differentially impact the quality of low- and high-wage

18
Table 2: Effect of $600 Expiration on Employment Gap (in p.p.)

∆yc,t (Employment gap) (1) (2)

Replacement rate gap change
× weekly dummy
4 weeks after expiration −0.80 −1.36
(1.31) (1.24)
8 weeks after expiration −4.80*** −4.35***
(1.47) (1.73)
12 weeks after expiration −5.74*** −4.66**
(1.67) (2.03)
Local-industry controls
Covid-19 deaths −0.93 1.50
(per 100,000 pop.) (1.45) (2.20)
School traffic 0.13 −0.24
(% change) (0.84) (1.07)
Customer visits −0.25 −0.23
(4.38) (6.50)
Customer spending −0.10 −0.02
(0.15) (0.80)
Within-cell differences
Customer visit gap – 0.31
(0.77)
Customer spending gap – 0.28
(0.21)
# Observations 18,848 6,256

Notes: Estimates of parameters in regression (6) with standard errors in parenthesis. All regressions
include cell fixed effects and the employment gap for the same week in 2019. Observations are at
the local industry/week level and reported in percentage points. We winsorize variables at the one
percent level and cluster standard errors at the local industry level.

businesses, which in turn affects demand for their products.
We can evaluate the validity of these concerns using our comprehensive, high-frequency
data. Table 2 shows the estimated coefficients on selected weekly time dummies after the
expiration of the income supplement. Specification (1) is our baseline regression that includes
local-industry controls, and specification (2) adds within-cell differences as controls.
The baseline regression shows that the level of local-industry demand, such as customer

19
visits or spending, does not have a statistically significant impact on the employment gap
of low- and high-wage businesses. In other words, low- and high-wage businesses do not
differentially respond to weekly changes in customer demand. We confirm this result also for
the employment levels of low- and high-wage businesses in the year prior to the pandemic
(Section 4.4).
For specification (2) we find that, as expected, idiosyncratic differences in demand are pos-
itively associated with the employment gap between low- and high-wage businesses. Nonethe-
less, employment in low-wage businesses still recovers faster than employment in high-wage
businesses even after controlling for these idiosyncratic differences.13

Table 3: Effect of $600 Supplement on Relative Employment Recovery (in p.p.)

Estimate per 100 p.p. ∆R − ∆Rt0 −5.7
× Average decline in ∆R 0.46

Effect of $600 supplement −2.6

Notes: The baseline estimate is translated using the average decrease in the replacement rate gap.

Our baseline specification implies that a 100 percentage point decline in the replacement
rate gap, is associated with a 5.7 percentage point rise in low-wage business employment
recovery relative to high-wage business employment recovery 12 weeks after the expiration.
For the average labor market, the expiration of the CARES Act decreases the replacement rate
gap by 46 percentage points, which implies a 2.6 percentage point rise in low-wage employment
recovery relative to high-wage employment recovery 12 weeks after expiration (Table 3). 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.

4.3 The Role of Local Industry Sorting
Our research design controls for demand effects in two ways. First, we compare neigh-
boring businesses that share to some extent the positive impact of UI stimulus. Second, we
13
Note that based on our findings, the slight decline in the estimate is not related to the additional controls,
but to the reduction in the sample size.

20
Figure 7: Expiration of $600: Local Industry vs. State Sorting

Notes: Estimated β’s from regression (6) for local industry sorting (baseline) and when cells are
grouped at the state level. Estimates are reported in percentage points. We winsorize variables at
the one percent level and cluster standard errors at the local industry and state level, respectively.
The shaded area represents the 95 percent confidence interval.

include observable measures of idiosyncratic demand in neighboring low-wage and high-wage
businesses. In Figure 7 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 effect of the replacement rate gap on the employ-
ment rate gap turns positive and becomes statistically insignificant. This happens because we
compare businesses located in areas with different average wages and businesses 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 further confound the estimates. This
exercise explains why we find different results from Finamor and Scott (2021) who find that
with state-fixed effects only a higher replacement rate is not associated with a lower labor
market re-entry of workers in HB data. Thus, our research design highlights the importance
of comparing units within narrow local industries.

21
Figure 8: Share of Stores Closed During the Week (Averaged over a Month)

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).

4.4 Discussion and Robustness
We conduct a series of robustness exercises. A detailed analysis of the estimates is reported
in Appendix C, Table C-5.

Low- vs high-wage response to local demand in 2019 A key identifying assumption is
that low- and high-wage businesses within a local labor market do not differentially react to
demand shocks. We test if this assumption holds prior to the pandemic. We run the following
regression using 2019 data:

yj,c,t = aj + τt + θ0 Demandc,t + θ1 Demandc,t × 1{highwj } + εj,c,t

where yj,c,t is the employment of business j in cell c during week t and demand is either
total customer visits or total spending in cell c and week t both normalized relative to their
base period of January-February 2019. Demand is interacted with a dummy variable taking
the value of one if the business is classified as high-wage. A business is classified as low- or
high-wage based on the 2020 base period as in the baseline specification. We find that θ1 is
not significantly different from zero for either demand measure. Thus, low- and high-wage
businesses in the same location, industry, and price range do not respond differentially to

22
a local demand shift. These results are consistent with the statistically insignificant local
demand effects for employment gaps around the expiration of the UI income supplement we
documented in Table 2.

Effects of hourly wages and hours per employee Did the expiration of the $600 have
an effect on hours per employee and hourly wages? We run the baseline regression (6) using
differences in hourly wages and hours per employee between the low- and high-wage businesses
as the left-hand side variable. Neither variable shows a statistically significant effect. Thus,
the expiration of the income supplement affected the extensive margin of employment but not
the intensive margin or the wages paid (see for example, Jager et al., 2020).

Business closures Our baseline sample includes businesses that operated continuously dur-
ing the pandemic, as well as businesses that closed and re-opened. In fact, most of the HB
businesses are open during the period of the generous income supplement. The average share
of closed stores is 30 percent in April 2020, 16 percent in May 2020, and 7 percent in June
2020, see Figure 8. When we restrict the sample to the businesses that continuously operated
during the pandemic the estimated coefficient at week 12 after expiration increases in absolute
terms to −6.0 and is statistically significant at the one percent level.

Quality of a business We test the robustness of our results by including the difference
in the quality of low- and high-wage businesses as an additional control. Our time-varying
measure of business quality is specific to restaurants that comprise most of the businesses in
our sample. Typically, in higher quality restaurants there are more employees per customer
relative to lower quality restaurants. Thus, our quality measure is total hours worked at the
business divided by the number of customer visits. Based on 2019 data, we find that high-wage
businesses devote, on average, 1.13 hours worked for one customer while low-wage businesses
devote, on average, 1.02 hours worked for one customer. When we also include differences in
quality as part of the controls, the estimated replacement rate gap coefficient at week 12 after
expiration changes to −3.9 and is statistically significant at the 5 percent.

Expanded sample In the baseline sample, local industry sorting is based on Yelp prices,
which drops businesses without price information. As a check, we allow businesses for which
we do not have Yelp-related information to form their own cell. This considerably increases
the sample size to 10,558 businesses. For the expanded sample, the estimated replacement
rate gap coefficient at week 12 after expiration changes to −4.5 and is statistically significant
at the one percent level. Furthermore, in the baseline, we measure business employment
based on hourly employees. When we also include salaried workers (managers) as part of

23
the employment, the estimated replacement rate gap coefficient at week 12 after expiration
changes only slightly to −5.4.

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 −5.3. 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 at week 12 changes to −5.4. In
both cases the estimate remains statistically significant at the one percent level.

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 repli-
cate 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 ex-
panded 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.,
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.14
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 equi-
librium 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

14
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.

24
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).15 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
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 pan-
demic 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)]} , (7)

15
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.

25
where Up(w) and Uy(w) denote the values of being unemployed while being eligible and

ineligible for UI benefits, respectively. These values are given by!®

Und) =U beau] + 34 pve] 00) f marc{Wisa lw), Uneer(w)} du! + [1 = A] Uxerlw)]
H(A = pr) [aC ff mas (Wisse!) Unease} Madu! + [1 — a6] Ureas(w)] |
s)
and
Uvalte) =U foy(w)] +8 { 00e) mas (Wiea(w), Uren w)) Sau! + = 00) Cr psale) }

(9)

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, w;(w), which is implicitly defined by

Note that w;,(w) in (10) 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 y(w) S wri). (11)
Finally, w*,,,, is the lowest acceptable wage for an unemployed worker
Winint = min wy z(w). (12)

min,t> are inactive.

Vacancies with a wage below the lowest acceptable wage, i.e., w < w

16We assume that Ul-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.

26
5.3 Transition of measures
The measure of employed workers and hence, of the filled jobs that receive wage w evolves
according to

ṽt (w)
et+1 (w) = (1 − δ)et (w) + Ft (w) λ(θt )ut , (13)
ṽt

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), (14)
´ 0)
where fR,t (w) = λ(θt ) w0 ≥w∗ (w) ṽt (w
ṽ t
dw0 is the probability that an UI-eligible worker with
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)] , (15)
´ 0)
where fN,t (w) = λ(θt ) w0 ≥w∗ (w) ṽt (w
ṽt
dw0 is the probability that an UI-ineligible unemployed
N,t
is offered a job and accepts it.
Furthermore, we have by definition
ˆ ˆ
ut = uR,t (w)dw + uN,t (w)dw, (16)

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+1 (w) = δet (w) + 1 − Ft (w) vt (w). (17)
θt

The distribution of vacant jobs (active and inactive) is determined by the following equa-
tion:

et (w) + vt (w) = g(w)M, (18)

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

27
∗
unemployed workers, i.e., vacancies with wages w < wmin , or equivalently F (w) = 0, will not
be active and have e(w) = 0. We define all active vacancies as
ˆ
ṽt = vt (w)dw (19)
∗
w≥wmin,t

∗
Aggregating equation (18) over w ≥ wmin,t we have
ˆ
et + θt (1 − et ) = M g(w), (20)
∗
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
( ˆ ˆ )
1
Ft (w) = (1 − pN,t ) uR,t (w0 )dw0 + [uN,t (w0 ) + pN,t uR,t (w0 )] dw0 .
ut ∗ (w)
w0 ≥wR,t ∗ (w)
w0 ≥wN,t
(21)
Furthermore, the aggregate job-finding rate (i.e., the hazard rate of exiting unemployment) is
ˆ
ṽt (w)
JF Rt = λ(θt ) Ft (w)dw, (22)
ṽt

and the aggregate vacancy fill rate is
ˆ
λ(θt ) ṽt (w)
V F Rt = Ft (w)dw. (23)
θt ṽt

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 (7), (8), and (9).
∗ ∗ ∗
2. The reservation wages {wR , wN , wmin }, satisfy equations (10) and (12).

3. The (un)employment and vacancy distributions {e, uR , uN , u, v, ṽ} satisfy equations (13),
(14), (15), (16), (19), and (20).

4. The acceptance rate F (w) satisfies equation (21).

5. Market tightness θ is given by ṽ/u.

28
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 focus-
ing again on separations into non-employment, the weekly job separation rate is δ = 0.016.
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 B-3 in Appendix B). We set the pre-pandemic expiration
probability of unemployment benefits to pN = 0.038, which corresponds to an expected dura-
tion 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,

29
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 E for details) and find a
20 percent share of UI recipients before the pandemic and a 60 percent share for 2020.17 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 B-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 = 0.10 such that wages of filled jobs
at the 75th percentile are 6 percent 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
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 residual-wage distribution.
In the HB data, the 10th percentile of (residual) log wage is 87 percent of the mean (see
Table B-2 in Appendix B). 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

17
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.

30
Table 4: Parameter Values

Parameter Notation Value Target/Reference
Externally set parameters:
Discount factor β 0.9992 4% annual interest rate
Risk aversion γ 2 –
Job separation rate δ 0.016 LEHD
Matching function elasticity η 0.5 Şahin et al. (2014)
Replacement rate, UI ρR 0.51 UI system
Expiration probability pN 0.038 UI system
Calibrated parameters
Total number of jobs M 1.013 Steady state θ = 1.2
Recipiency probability pR 0.15 CPS and IRS data
Matching efficiency κ 0.23 Weekly job finding rate of 0.23
Wage dispersion σ 0.10 Wage dispersion upper half
Replacement rate, non-UI ρN 0.15 Wage dispersion bottom half

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

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.

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. We allocate workers who lose their jobs to UI and non-UI unemploy-
ment 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

31
benefits through the end of July 2020. We model this change as an increase in weekly unem-
ployment 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 2.2 which is the replacement rate during
the CARES Act in our HB sample (see Table B-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)
w, the shift increases uR,3 (w) by Π2t=0 (1 − fN,t (w))(p0R − pR ) N,3
uN,3
∆e. This shift affects 40
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
policy. As various additional changes to UI policy occurred, through Fall 2020 and then 2021,
we focus 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 D.

32
Figure 9: Effects of $600 Expiration on Employment Recovery: Model vs. Data

-5

-10

-15

-20

-25

-30
-2 0 2 4 6 8 10 12

Notes: The figure plots the estimated β’s from regression (6) in the model versus the data. The
shaded area represents the 95 percent confidence interval of the data estimates.

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),
which is appropriate given that the disincentive effects are measured within narrow local
industry markets. We use the model-generated data on employment and replacement rates
to run the exact same regression as in the data (regression (6)) for the same time window.
Figure 9 compares the estimates in the model versus the data. We find that the baseline model
overstates the estimated impact of the expiration of the $600 supplement on the employment
recovery gap by a large degree.
Figure 10 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.

33
Figure 10: Acceptance Rate for Different Job Offers: Model

100

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.

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, UI-
unemployed workers gradually start to accept the offer so that the acceptance rate converges
to its steady state relatively fast and prior to the expiration of the supplement.
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. When the $600 is close to expiring the acceptance rate rapidly
bounces back to its normal levels.
Finally, 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.

34
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
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 9. 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, employment in low-wage firms declines dramatically during the period of $600 income
supplement and recovers at an equally fast pace after the expiration.

6.1 Reconciling the model with the data
In the baseline model employment recovery overstates the effect of the $600 expiration on
the employment recovery gap relative to what we document 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.18
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

18
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.

35
written as follows:

O (w!)

Uns) =U [bre(w)] + Bpne ace [ax {isa (w!) Cralee)} de! = 2000) Uvssr(u)|

+ 8(1 = pr) [d6) f amas {Wey a(u!). (1 — Ue a(w) + xU srw) a
+ B(1 — pnz) [1 — A(A)| Uresi(w). (24)
Accordingly, the reservation wage of UI recipients is given by:
Wit [wre(w)| = (1 — x)URp41(w) + XUN t41(w). (25)
The measure of these workers evolves according to
Unt+i(w) = prsder(w) + [1 — (fre(w) +x — fre(w)))| A —pwelurew), (26)

where, as before, fre(w) = ACA) Josie (w) Pele) yy! is the probability that an Ul-eligible
oMR,t t
worker with previous wage w is offered a job and accepts it. Finally, the measure of UI-

ineligible unemployed evolves according to

une (w) =(1 — pre)de(w) + [L — five(w)] [pr cure(w) + un e(w)] (27)
+x. — fre(w))C = pws)ur), (28)

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.’?

We set the probability of losing eligibility upon job refusal, y = 16.5%, to match the
estimated impact of the $600 expiration on the employment recovery gap between low- and
high-wage businesses 12 weeks after expiration (the estimated coefficient from regression (6)).
Figure 11 shows that the model is able to match the data closely and also reproduces the
gradual decline in the estimated 6’s over time. Search frictions prevent low-wage firms from
recovering their employment all at once. As a result, the $600 expiration has a larger effect
on the employment recovery gap over a longer horizon compared to the weeks closer to the

expiration.

18The extended model can still match the benchmark targets and thus, does not need a re-calibration of
other parameter values.

36
Figure 11: Employment Recovery Gap: Model with UI Loss upon Job Refusal

-2

-4

-6

-8

-2 0 2 4 6 8 10 12

Notes: The figure plots the estimated β’s from regression (6) in the model with the probability of
losing UI upon job refusal versus the data.

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 UI effects
from 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
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 substan-
tial aggregate employment losses. Conditional on the other two provisions being in effect,
the income supplement holds back the employment recovery by 1.6 percentage points, the
extended maximum duration by 1.5 percentage points, and the expanded eligibility by 2.9
percentage points. Without any of the UI policy changes, the employment recovery would
have been, on average, 3.4 percentage points closer to normal between April and December

37
Table 5: Employment Recovery Loss (in percentage points)

Each provision alone
$600 Additional UI Benefits 0.2
Extended Duration of UI Benefits 0.2
Expanded Eligibility of UI Benefits 1.0
Each provision when other provisions are in effect
$600 Additional UI Benefits 1.6
Extended Duration of UI Benefits 1.5
Expanded Eligibility of UI Benefits 2.9
CARES Act (all provisions combined) 3.4

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.

2020. This employment loss represents around 20 percent of the average employment loss in
the Leisure and Hospitality sector during the same period. The employment loss peaks at
almost 8 percentage points about 10 weeks after the initiation of the CARES Act (Figure 12).
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 F for more details). Similarly to Table 5, we calculate the unemployment duration
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 unemploy-
ment duration by 8 percent (from 3.4 weeks to 3.7 weeks). Since in our model, the replacement
rate rises by 343 percent (from 0.51 to 2.2), this implies a duration elasticity of 0.02. In turn,
the extended benefits alone increase unemployment duration by 6 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

38
Figure 12: Employment Losses due to CARES Act UI policies

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.

an elasticity of 0.03. Expanded eligibility increases the expected duration of unemployment
by 19 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 0.04.
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 85 percent implying an elasticity
of 0.24. When the extended benefits provision is activated on top of the other two provisions,
unemployment duration increases by 65 percent implying an elasticity of 0.43. When the
expanded eligibility provision is activated on top of the other two provisions, unemployment
duration increases by 112 percent implying an elasticity of 0.28.
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 im-

39
Table 6: Unemployment Duration Elasticities implied by CARES Act Provisions

Unemployment Duration Elasticity
Each provision alone
$600 Additional UI Benefits +8% 0.02
Extended Duration of UI Benefits +5% 0.03
Expanded Eligibility of UI Benefits +19% 0.04
Each provision when other provisions are in effect
$600 Additional UI Benefits +85% 0.24
Extended Duration of UI Benefits +65% 0.43
Expanded Eligibility of UI Benefits +112% 0.28

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.

pact 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. (2024); 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
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. Our results are robust to a variety
of controls including customer traffic and spending measured at the business level.
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 3.4 percentage points, on average, between April and December 2020. We find
that expanded eligibility of UI benefits is the most disruptive provision and disproportionately

40
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.

41
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45
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 consist of anonymized daily records of individual hours worked and wages of em-
ployees, 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 contain 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 “baseline 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 for which we can assign a consistent NAICS code by matching them
by name and address to Safegraph’s Places of Interest (POI) database (see Kurmann, Lalé, and Ta
(2021) for details). The baseline 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 baseline sample consists of 4,595
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 small business employment for 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 baseline 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,

46
Lalé, and Ta (2021).20
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 baseline 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 baseline 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 Baseline
Sample
10

ref.
0

Employment change
−10

−20

−30

(in % relative to mid−Feb. 2020)
−40

−50

−60

−70

Mar 8 − Mar 14 Mar 22 − Mar 28
Apr 5 − Apr 11 Apr 19 − Apr 25 May 3 − May 9 Oct 4 − Oct 10 Oct 18 − Oct 24
Nov 1 − Nov 7
Nov 15 − Nov 21 Nov 29 − Dec 5 Dec 13 − Dec 19
May 17 − May 23
May 31 − Jun 6 Jun 14 − Jun 20
Jun 28 − Jul 4 Jul 12 − Jul 18 Jul 26 − Aug 1 Aug 9 − Aug 15 Sep 6 − Sep 12 Dec 27 − Jan 2 Jan 10 − Jan 16 Jan 24 − Jan 30
Aug 23 − Aug 29 Sep 20 − Sep 26
Jan 26 − Feb 1 Feb 9 − Feb 15 Feb 23 − Feb 29 Feb 7 − Feb 13

HB sample used in Sections 3−4 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 baseline sample. See text for details.

20
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 baseline
sample since it contains only continuing businesses, that is, they can be temporarily closed in 2020 but must
reopen before the end of 2020.

47
A.3 Representativeness concerning wages, hours, and earnings
The other important dimension in which to assess the representativeness of the HB baseline
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 pertain 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.21 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 $1.5 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 baseline sample is therefore
also broadly representative of small businesses for 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,

21
This restriction only affects average weekly hours worked. Average hourly wage rates are very similar
with or without this restriction.

48
Table A-1: Comparison of Wages, Hours, and Earnings: CPS vs HB Estimation Sample

CPS HB CPS w/OTC HB w/OTC
Hourly wage ($) 12.5 10.9 14.8 13.6
Weekly hours 30.6 30.1 30.6 30.1
Weekly earnings ($) 400.1 328.1 467.2 415.96
# 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 hourly-
paid workers in the leisure and hospitality sector in the CPS and in the HB baseline 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 , (29)

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

49
i in region j.22 We then add the estimated OTC amount, otc
ˆ ij = â0j + â1j wij , to the hourly wage of
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.

B Cross-sectional statistics
Employment, Hours, and Wages Table B-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
less than five employees.

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

Mean SD p(5) p(10) p(25) p(50) p(75) p(90)
# Employees 12.8 9.1 3 4 7 11 16 24
Hours per worker 4.9 1.5 2.6 3.1 3.9 4.8 5.8 6.8
Hourly wage ($) 10.9 2.7 6.6 7.6 9.1 11 12.7 14.2
Residual log-hourly wage ($) 0.0 0.11 -0.19 -0.13 -0.06 0.0 0.06 0.13
Separation rate (%) 9.5 14.0 2.7 3.3 4.7 7.1 11.1 16.6
Hiring rate (%) 12.4 10.0 3.5 4.3 6.2 10.0 15.3 23.0

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,t0
.

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}.
22
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.

50
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 B-3 reports summary statistics for the cross-sectional distribution of the business-level
replacement rate Rj,c,t and the replacement rate gap ∆Rc,t which is calculated as the average re-
placement rate in low-wage businesses of cell c minus the average replacement rate in high-wage
businesses of cell c. In addition, we report the distribution of the difference in the replacement rate
gap across labor markets, after and before the expiration of the income supplement (∆Rpost −∆Rpre ).
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 2.23 and the median to 2.14.
In normal times the replacement rate gap is on average 0.13, with a median of 0.08. With the CARES
Act, the replacement rate gap increases on average to 0.61 and for the median labor market to 0.34.
Finally, on average, the replacement rate drops by 46 percentage points after the expiration of the
income supplement.
How do the replacement rate R and the replacement rate gap ∆R vary across labor markets and
over time? The left panel of Figure B-2 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.

B.1 Recalls in HB businesses
Fujita and Moscarini (2017) document that a large share of workers returns to their previous
employer after a jobless spell. We focus on businesses that closed and re-opened and examine if,
upon re-opening, the HB businesses disproportionately hired employees who previously worked in the
business. In Figure B-3 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 (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. Our findings are in accord with
Ganong et al. (2024) who document that UI supplements did not have substantial effects on recalls.
Our benchmark model abstracts from a recall margin but we expand the baseline model to include
recalls in Appendix G and discuss the results.

51
Table B-3: Replacement Rate Distribution

Mean SD p(5) p(10) p(25) p(50) p(75) p(90)
Replacement rate (R)
Normal Times 0.54 0.09 0.48 0.50 0.50 0.51 0.54 0.62
CARES Act 2.23 0.54 1.61 1.73 1.86 2.14 2.47 2.83
Replacement rate gap (∆R)
Normal Times 0.13 0.16 0.01 0.02 0.04 0.08 0.16 0.28
CARES Act 0.61 0.86 0.03 0.08 0.19 0.34 0.68 1.21
Decline in replacement
rate gap (∆Rpost − ∆Rpre ) -0.46 0.62 -1.51 -0.94 -0.51 -0.26 -0.14 -0.06

Figure B-2: Replacement Rate R and Replacement Rate Gap ∆R

200

150

Replacement Rate
200

150
100

100
50

50
0
0 20 40 60 80
0 Replacement Rate Gap
Jan 20 Apr 20 Jul 20 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.

52
Figure B-3: Recall Rates for Low- and High-Wage Businesses Upon Re-opening

100

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 gray area).

C Robustness results
We report the estimated coefficients from regression:

yj,c,t = aj + τt + θ0 Demandc,t + θ1 Demandc,t × 1{highwj } + εj,c,t

where yj,c,t is the employment of business j in cell c during week t and demand is either total
customer visits or total spending in cell c and week t both normalized relative to their base period
of January-February 2019.
A business is classified as low- or high-wage based on the 2020 base period as in the baseline
specification. We find that θ1 is not significantly different from zero for either demand measure.
Thus, low- and high-wage businesses in the same location, industry, and price range do not respond
differentially to a local demand shift.
Table C-5 reports estimates for the various robustness exercises described in Section 4. In all
exercises we report the interaction of the replacement rate gap decline with the weekly dummy
estimate 12 weeks after the expiration. First, we analyze the response of hours per employee and
hourly wages around the window of expiration. Second, we restrict the sample to the businesses that
continuously operated during the pandemic. Third, we add business quality in the set of time-varying
controls. Fourth, we examine the estimates for an expanded sample of businesses. Specifically, we

53
Table C-4: Demand Effects on the Employment Gap in 2019

Customer visits Customer spending

θ0 0.198* 0.015
(0.114) (0.010)
θ1 −0.125 −0.003
(0.111) (0.011)

Notes: Estimates effects of demand conditions for the employment gap in 2019.

keep businesses for which we could not find information on their price from Yelp. Fifth, we measure
business’ employment including salaried workers. Sixth, we choose a wider base period of July 2019-
February 2020 and finally, we weigh each cell by the number of businesses inside the cell; i.e., more
populated cells take a higher weight.

D 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:

t=0 satisfy equation (7), equation (8), and equation (9),
1. The value functions {Wt , UR,t , UN,t }∞
for all t.

2. The reservation wages {wR,t min,t }t=0 , satisfy equation (10), and equation (12), for all
∗ , w∗ , w∗
N,t
∞

3. The (un)employment and vacancy distributions {et , uR,t , uN,t , ut , vt , ṽt }∞
t=0 satisfy equation (13),
equation (14), equation (15), equation (16), equation (19), and equation (20) for all t.

4. The acceptance rate {Ft (w)}∞
t=0 satisfy equation (21), for all t.

5. Market tightness {θt }∞
t=0 is given by ṽt /ut , for all t

E 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

54
Table C-5: Alternative Empirical Specifications

∆yc,t Time dummy at week 12

Benchmark −5.7***
(1.6)
Hours per employee gap −0.4
(1.5)
Hourly wages gap −0.7
(0.9)
Continuously open businesses −6.0***
(1.7)
Adding business quality −3.9**
(1.8)
Expanding sample −4.5***
(1.4)
Including salaried workers −5.4***
(1.3)
Larger base period −5.3***
(1.7)
Weights −5.4***
(1.5)

Notes: Each line reports the estimates from regression (6) for an alternative specification (reported
in percentage points). We winsorize variables at the one percent and cluster standard errors at the
local industry level.

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.
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.

55
F 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:

∞ h
X i
EDR,t (w) = ξR,t+τ (w) fR,t+τ (w) + ξN,t+τ (w) fN,t+τ (w) × (τ + 1) . (30)
τ =0

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
∞
X
EDN,t (w) = ζt+τ (w) fN,t+τ (w) × (τ + 1) . (31)
τ =0

Let εU
i,t denote the unemployment duration elasticity arising from a policy change from x to x̃, for

56
workers in unemployment state i € {R, N}. We have:

ey (w) = = 1 (32)
© _
In the final step, we aggregate across all unemployed workers:
1
ey = un (urge (w) eRe (w) + une (w) ey (w)) dw (33)

GA 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 6°). But we also allow the
separated workers to be in touch with their previous employers with a probability 1—6?. Unemployed
workers who are in touch with their old employers are indexed as i = 1 and unemployed workers
who are not are indexed as 7 = 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:

W, (w) =U (w) + 8 [(L — 8°) Wear (w) + 6° ((L— prt) UN eri (W) + PRtU Rr (w))]

where Ure 4, and U Ne 4, 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

receiving UI, and who is in touch with the employer is given by:

Ung (w) = 0°URy (w) + (1-8?) |r U (bre (w)) + Bmax {Wisi (w),Uneps (w)})

+ (=r) |U (br (w)) +8

PN,t (0 — ()) Une (w)

+A (04) ff max {Weer (0) Ther (w)} 2 ar) + (1—pwa) (0 ~ (64) er (w)

+0 (64) / max {Wit () Uh eg (w)} ae) | .

Notice that at time period t, with probability 6?, an unemployed loses touch with the employer and
receives UR which is defined below. With probability 1 — 6? an unemployed stays in touch with
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 W;,)(w) or continuing to be

57
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 py.

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:

Uns (w) =U (bre (w)) + B

PN (0 — A (4)) UN t+ (w)

+064) [ mar(Wesr (0) Wer (w)} ae) + = pre (0 — A (6:)) Ug (W)

+d (61) / max {Wis (x) U8 p43 (w)} 1a) | .

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:

Uns (w) = PUN (w) + (1-6?) |r (U (by) + Bmax {Wes (w) UX 41 (w)})

+ (1—r) |U (bn) + 8 (1 — (4)) Une (w)

+A (0) f max {Wiss (2) Uh esr ()} 1 a |

UR, (w) =U (by) + B (a — (01) US p41 (w) + (84) / max {Wr (0) U8 p44 (w)} 2) ir)

Let A(w,w’) 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 w’. 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:
Ary (w,w') = 1 {Wir (w’) > Ursa (w)}

Av t (w, w') =1 {Wet (w’) > UN 1 (w)}

Note that as in the baseline model, these definitions for time t refer to decisions made in ¢ + 1.

The law of motion for employment is similar to the baseline with an additional inflow of recalled

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workers who accept their old job at wage w:

ers1 (w) = (1— 0°) ex (w) + (1-6?) Alyy (w, wv) (uns (w) + ups (w))

+ (6) nw) F, (w) iy (34)
t
F,,(w), the probability that a job offer w gets accepted, is
1
Fa (w) = 2 (f= pore) (6a (2) + whe (2)) Af (0.0) a

+ / (1 — pyy) (1-6) (1 r) ub, (0) Akg (ar,w) de
+ / ((6P ub g (1c) + uy, (e)) + Drv (Pak (oe) + up, (0))) AX, (a w) de

+f (1-6) (1—r) uk, («) Aly (a, w) ir) |
The transition equations for unemployment are given by:

UR (w) = (1-6?) O° DR tet (w)

+ (1- A) f Ake (w2) ae) (1 —pye) 1 =r) = uh

UR td (w) = 6?d* pret (w)

+ (1-0) [ Ake ose) 1) a) (1 — pyrg) (Sub (w) + why (er)

UN eqs (w) = (1 — 6?) 5° (1 — pry) ee (w ;

+ (1-a¢ = (6) [Ae w a) (1 =r) (1 = 8) (uh (w) + pvaerky (w))

UN att (w) = 65° (1 — pry) ee (w) + . - i (1— Als (w,w)) (uxy (w) + upg (w))

(Daa — (r) ) | Are w a) (Sune (a) + UN ¢ (x)) + PN, (Ours (a) + Ure (x))) .

with a = f (( —(1-—d?)r) (uh (x) + URt (x)) +unzt (x) + urR¢ (x)) dx and % = { 0; (x) dx. We
have the assumption of a fixed number of jobs as in the baseline:

er (w) + Ung (w) + Up, (w) + ve (w) = g (w) M. (35)

Labor market tightness is given by: 7
6, = 24 (36)

Ut
We set the weekly job separation rate as 6° = 0.016 as in the baseline. The matching technology

parameter « = 0.15 is set to match a job finding rate equal to 0.23. Parameter 6? = 0.17 matches a

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recall share of hires equal to 33 percent, consistent with our data. Given that the average duration
of recalls in HB data is about 4 weeks, we set r = 0.23, i.e. one-fourth of a month.
The effective probability of losing UI upon job refusal in the model with recall, i.e., the probability
a worker stays in touch with the employer and that the employer recalls the worker back to work,
is (1 − δ p )r = 0.19. In the reduced-form model in the main text, the probability of losing UI upon
job refusal is equal to χ = 0.165 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. Our parameterized recall model generates similar dynamics
around the expiration of the income supplement the baseline.

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