ISSN (Print) 0473-453X

Discussion Paper No. 1163

ISSN (Online) 2435-0982

WORKING FROM A DISTANCE:PRODUCTIVITY DISPERSION
AND LABOR REALLOCATION
Jingping Gu
Dongya Koh
Andrew Liu

February 2022

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Working from a Distance:
Productivity Dispersion and Labor Reallocation∗
Jingping Gu

Dongya Koh
Andrew Liu
University of Arkansas
February 17, 2022
Abstract

Following the shocks of the COVID-19 pandemic, the economy may be significantly
changed relative to the pre-pandemic world. One critical shift induced by the COVID19 pandemic is a need for physical distance (at least 6 feet apart) between workers andcustomers. In this study, we examine the impacts of social distancing in the workplaceon employment and productivity across industries. Using our constructed measureof adaptability to social distancing, we empirically find that industries that are more
adaptive to social distancing had less decline in employment and productivity during
the pandemic. Using this empirical evidence, our model predicts that employment andproductivity dispersion would induce labor reallocation across sectors, while imperfectlabor mobility may result in a long road to economic recovery.
Keywords: COVID-19, social distancing, productivity, labor reallocation, economic
recoveryJEL Codes: E24, E27, J24, J64∗

Dongya Koh gratefully acknowledges financial support from the Joint Usage/Research Center at ISER,
Osaka University and JSPS KAKENHI Grant Number JP21H04397. We would like to thank Raul
Santaeulalia-Llopis, Javier Birchenall and Kieran Walsh for valuable comments. We have also benefited
from the seminar and conference participants at the Sam M. Walton College of Business at the Universityof Arkansas, ESCoE Conference on Economic Measurement 2020, and UCSB Macro Group.

1

Introduction

Despite a gradual reopening of the economy after a few weeks of business closures, oureconomy after the recent COVID-19 shock may look completely different from the prepandemic world. One critical change due to COVID-19 is a need for physical distance (atleast 6 feet apart) between workers. Although recent technologies have aided our transition
to a new, socially distanced working environment, the efficiency of this new working style
may vary across types of businesses. Some industries can more easily implement social
distancing1 (such as consulting, IT related works, data analysis, and education services). On
the other hand, some industries suffer a productivity drop after adopting social distancing
among workers (such as construction sites, food processing sites, hospitals, dental clinics,
and some elements of the media industry).
This study sheds light on the effects of social distancing on productivity dispersion as
it differs across industries and the consequential effects on labor reallocation. We constructmeasures of how easily an industry can adopt social distancing in their workplace using theAmerican Community Survey (ACS). We find that there is a positive relationship between
the adaptability to social distancing and employment and productivity changes; that is, more
adaptive industries had less decline in employment and productivity because of the pandemic.
Correspondingly, we find that less adaptive industries experienced a larger dispersion in
employment and productivity responses due to COVID-19.
Publicly available data allows us to empirically document only the immediate responsesof the U.S. economy to the pandemic shock.2,3 However, the post-pandemic projection of
economic recovery is of more interest to the public. Therefore, we calibrate a multisector
model of labor reallocation and predict the persistent effects of a pandemic shock on labor
reallocation across industries and on economic recovery. The calibrated model predicts
that productivity dispersion across industries induces labor reallocation from less adaptive
industries to more adaptive industries, while imperfect labor mobility across sectors slows
down progress toward economic recovery.
Our prediction of economic recovery from the pandemic shock may depend on the productivity adjustment of less adaptive industries. If less adaptive industries were to implement
1

We define social distancing in a broader sense, not only keeping 6-feet distance among workers andcustomers but also working remotely or encompassing all the preventive actions taken by firms and industries
after COVID-19.
2
At the time of this writing, the latest public data available was July 2020 monthly data from the Bureauof Labor Statistics (BLS) or the second quarter data of 2020 in the Bureau of Economic Analysis (BEA).
3
The pandemic shock can be interpreted as not just an exogenous outbreak of COVID-19 but also nationwide lockdown and social distancing policies implemented by the U.S. government.

1

a technological shift resulting in increasing productivity back to the pre-pandemic level,
then the aggregate economy may recovery more rapidly. On the contrary, if less adaptive
industries fail to adjust to a new environment and therefore persistently suffer inefficient
productivity, the economic recovery may be slow. These scenarios are two extremes, and themost likely outcome will fall somewhere in between.

2

Related Literature

In contrast with recent slowdowns associated with an economy under lockdown, COVID19-related research has been vigorously produced at a rapid pace. One topic of interestin the literature measures the effect of social distancing on working conditions during the
COVID-19, as exemplified in a study by Dingel and Neiman (2020) that combines Occupational Information Network (O*NET) surveys and some information from the U.S. Bureau ofLabor Statistics (BLS) to investigate which occupations may be conducted remotely in different industries, cities, and countries. This paper examines various countries and finds thatlower-income economies have a lower percentage of jobs that can be performed at home.
Brynjolfsson et al. (2020) conducted their own online survey for the U.S. to explore who
continued commuting to the office or working from home during COVID-19. Mongey et al.
(2020) further examined two different measures: the likelihood that jobs could be performed
from home and the personal proximity in the workplace.
Another avenue of research that are closely related to our work examines the effect ofthe pandemic shock on particular markets. For example, Cowan (2020) uses the Current
Population Survey (CPS) data from February to April 2020 to examine the short-run effects
of COVID-19 on the U.S. labor market and a particular population’s working status. Oneof the most closely related research is Gregory et al. (2020) where they calibrate a searchtheoretic model using Longitudinal Employer and Household Dynamics (LEHD) and theSurvey of Income and Program Participation (SIPP) from 1997-2014 to forecast the U.S.
labor market recovery after the pandemic. Despite the similarity of their prediction on aslow recovery to our results, the source of their recovery in the model is mainly driven byworker productivity and a corresponding job finding rate. In contrast, our focus herein ison the decline of the firm’s productivity and, therefore, labor demand due to the requiredsocial distancing among workers.

2

3

Empirical Evidence

In this section, we empirically examine how social distancing in the workplace affects productivity across various industries. The dispersion of productivity across industries critically
hinges on the differences in adaptability to social distancing, or how easily industries canimplement social distancing in their workplace. First, we construct measures of adaptability
to social distancing. Second, we empirically show that those industries that are more flexible
to practicing social distancing or work from home tend to have less decline in employment
and productivity, according to the data from the second quarter of 2020, which captures theimmediate response to unexpected COVID-19 shocks.
3.1

Measuring the Adaptability to Social Distancing

Some industries (e.g., IT, consulting, banking, etc.) easily leveraged recent technologicaladvances, such as high home internet bandwidth and secure video call features, to implementsocial distancing in the workplace and enable workers to work from home with only minor
disruptions to workflow. Conversely, some industries (e.g., construction, nail salons, dental
clinics, etc.) simply require a physical presence, and have been unable to adopt social
distancing in the workplace. Such sectoral differences in adaptability to social distancing may
create productivity dispersion across industries after the outbreak of COVID-19. To examine
the link between the adaptability to social distancing and productivity across industries, weconstruct a measure of how easily industry can adopt social distancing in their workplace.
For this, we use the American Community Survey (ACS) of the U.S. Census. ACS is anannual survey that asks about occupations, education, commuting to work, and housing of
U.S. citizens to better understand people’s life patterns and determine the distribution offederal and state funds. We use the latest 2018 ACS 1-year Public Use Microdata Sample,
with data collected from Jan. 1. 2018 to Dec. 31, 2018, for a variety of geographic areas
with more than 65,000 respondents. For the measure of adaptability to social distancing,
we use one survey question in ACS that asks about “transportation to work.” The survey
provides information on how many workers in the 2-6 digit 2017 NAICS code commute totheir workplace by “car/truck/van” “taxi/cab,” “motorcycle,” “bicycle,” “walked,” “worked
at home,” etc. Using this 2018 survey information, we compute the share of workers who
worked at home in an industry i. This pre-pandemic survey informs us of the degree of thephysical presence of workers at a workplace in each industry at baseline. This information
can be used as a proxy for how adaptive an industry would be to transitioning to remote
work after COVID-19.

3

Table 1 shows the share of workers who worked at home by a 2-digit industry. An industry with the highest adaptability to social distancing is “professional, scientific, and technicalservices” with 15% of workers in that industry worked at home prior to the pandemic (excluding missing responses). They are mostly professional workers (e.g., lawyers, engineers,
computer programmers, researchers, and consultants) who provide specialized services totheir customers online. In contrast, the lowest fraction working from home was workers in“accommodation and food services” with only 1.7% of workers working at home. Overall,tertiary and quaternary sectors (e.g., services, information, finance, and insurance) tend tohave a higher share of workers working from home. In contrast, primary and secondary
sectors (e.g., mining, manufacturing, and utilities) tend to have a lower share of workers
working at home.
Notable exceptions are agriculture and education services. The share of workers working
from home is the second highest in the agriculture sector, with 13% of agricultural workers
working from home, mainly because farming is usually performed on a farm adjacent to thefarmer’s house. In contrast, education services only have 3.3% of workers providing services
from home because the provision of online courses was limited in public education systems
prior to COVID-19. However, this has now clearly changed among the educational sector.
This result suggests that the share of workers working at home prior to the pandemic may
not be a perfect measure for the “potential” adaptability to social distancing. Nonetheless,the measure is informative of the adaptability to working from home as there might be lessadjustment cost for industries where larger fractions of workers are already remotely working.
Also, one advantage of using this measure as a proxy for the adaptability to social distancing
is that the measure is classified into 274 detailed levels of sub-industries.4
It is important to note that our measure of adaptability to social distancing is interpreted
as the fraction of jobs in industry i that can be performed from home. When an industry
consists of job types that are less restricted by the physical location, the industry may
exhibit higher share of workers working at home and greater adaptability to social distancing.
Indeed, in the paper by Dingel and Neiman (2020), feasibility to work from home wasconstructed from occupational characteristics and classified by industry level according tothe occupational composition within each industry. In our Online Appendix, we show that
our measure is positively correlated with the measure from this prior paper. Further, we
confirm that our empirical findings are robust with their measure.
4

Dingel and Neiman (2020)’s measure of feasibility of working at home that we discuss in our Online
Appendix is aggregated into the classification of 108 sub-industries, while another measure constructed fromthe American Time Use Survery is classified into 19 industries.

4

3.2

Employment and Productivity Responses to COVID-19

Immediately after the COVID-19 outbreak, the unemployment rate in the U.S. increased
from 3.5% (February) to 4.4% (March) before skyrocketing to 14.7% in April. The temporary
suspension of economic activities and nationwide lockdown were the leading cause of thisunemployment surge.
Employment Responses. We use monthly employment data by industry, available from
BLS, and relate it to our measure of adaptability to see if the drop in employment ineach industry is affected by the adaptability to social distancing. Panel (a) of Figure 1
demonstrates the employment decline between the fourth quarter of 2019 and the second
quarter of 2020, as it relates to the share of workers who worked at home prior to thepandemic by industry.5 As expected, industries with a higher pre-pandemic share of workers
working at home experienced a less-severe drop in employment. For example, “professional,
scientific, and technical services,” which had the highest share of workers who worked athome, experienced a minor 2.3% drop in employment due to the pandemic. In contrast,“accommodations and food services,” which had only 1.7% of workers who worked from homeprior to the pandemic, experienced a 23.8% employment decrease following the COVID-19
shock. A log-linear line weighted by the employment share of industry in the figure showsa positive relationship between adaptability to social distancing and employment responses
to COVID-19.
From the figure, it is apparent that the dispersion of employment growth also varied by
the adaptability to social distancing. For instance, for industries in the range of 0 to 5%
share of workers who worked at home prior to the pandemic, the employment growth ranged
from a 33.9% decline (“Amusements, gambling, and recreation industries,” a sub-industry in“ Arts, entertainment, and recreation”) to 0.6% decline (“Utilities” industry). However, forindustries in the range of 10 to 20% of workers who worked at home, the employment growth
ranged from 4.6% employment decline (“Real estate and rental and leasing” industry) to 1.6%
employment decline (“Computer systems design and related services,” a sub-industry in the“Professional, scientific, and technical services” industry). In sum, less adaptive industries
experienced a greater decline in employment, on average, as well as a larger dispersion of
employment responses to the pandemic.
Productivity Responses. Firms and institutions have had to focus attention on ensuring
the health and well-being of their employees and customers during the COVID-19 pandemic.
5

The employment growth in monthly frequency from January of 2020 to April, May, June, or July of2020 shows the similar positive relationship.

5

To prevent the spread of infection, social distancing and face mask regulations have been
implemented in most of the areas in the U.S. Additionally, for example, some grocery stores
have replaced cashier checkout counters with all self-checkouts. Most restaurants offer curbside pickup and have reduced the number of tables for dining. These adjustments either
under-utilize installed capital or replace current employees with new capital, both of which
result in decreased number of workers, as shown in panel (a) of Figure 1. This implies thatthe productivity or efficiency of production should also be affected by the pandemic shockin a manner that varies by the adaptability to a new business style.
We compute the productivity changes after COVID-19 by industry using the data before
the pandemic (the fourth quarter of 2019) and right after the pandemic outbreak (the second
quarter of 2020). Our objective is to examine if adaptability to social distancing is associatedwith changes in productivity. We assume that the production function of real value-addedof an industry i in period t takes a Cobb-Douglas form:6
αi 1−αiLi,tYi,t = Ai,t Ki,t(1)where K indicates real net stock of capital, L indicates the number of employees, α indicatesthe capital income share, and A indicates total-factor productivity (TFP). By taking logs
on this production function, we compute the industry-specific TFP, Ai,t , as the residual.
For this calculation, we use “Real Gross Value Added” from GDP-by-Industry accounts
in BEA for Yi,t , Employment by industry from BLS current employment statistics for Li,t ,7“Real Net Stock of Capital” from BEA Fixed Asset Table 3.2ESI for Ki,t , and “Componentsof Value Added by Industry” from GDP-by-Industry accounts in BEA to construct capitalincome share in industry i, αi .
Of these public data series, the BLS monthly employment data is available for the mostrecent month (e.g., July 2020 at the time of this writing). BEA real value-added is quarterly
data, and the latest available are from the second quarter of 2020. The rest of the BEA data
are all annual data, available up to 2019. Due to the unavailability of some data, we have toimpose an assumption that the capital income share across industries (αi ) and the real net
6
To check the sensitivity of the functional form, we compare our accounting calculation of industryspecific productivity with a nonparametric estimation of technology efficiency in our Online Appendix. One
advantage of nonparametric analysis is that the model allows more flexible functional form, and therefore,
the Cobb-Douglass production function is no longer needed to estimate industry productivity.
7
We confirm that the empirical results remain unchanged with the annual “Hours Worked by Full-Timeand Part-Time Employees by Industry” from BEA NIPA Table 6.9D. In this study, we prefer to use the BLS
monthly employment data over total hours of work from BEA for a direct comparison to the employment
responses shown in panel (a) of Figure 1.

6

stock of capital across industries (Ki,t ) remain stable before and after the shock. This assumption is not critical for the dynamics of productivity because the real net stock of capitaland capital income share are far less responsive to an aggregate shock than employment andoutput in the short run.8 Thus, we compute the recent productivity at a quarterly frequency
before and after the pandemic outbreak by taking 2019 data for the capital income shareand the real stock of capital.
Taking a log difference of two data points, 2019Q4 and 2020Q2, we can identify theimmediate response of industry productivity to the pandemic shock.9 Panel (b) of Figure
1 shows the productivity growth from 2019Q4 to 2020Q2 for 2-4 digit industries, sortedby the adaptability measure that we constructed in the previous section. Though weaker
than the employment, the productivity responses also exhibit a positive relationship withadaptability to social distancing. Three sub-industries with relatively large employment
share that experience a large drop in productivity are “Air transportation” (72.3% drop),“amusement, gambling, and recreation” (16.5% drop), “Transportation and warehousing”(11.3% drop). These industries are unable to provide their service remotely.
Analogous to the employment growth, the productivity responses to the pandemic shock
are also dispersed across industries. Even though the dispersion of productivity over theshare of workers working at home is not as evident as the dispersion of employment, for theindustries with the share of workers working at home ranging from 0 to 5%, the productivity
growth ranges from a 72.3% decline (“Air transportation”) to 0.9% growth (“Broadcasting
and telecommunications”). On the other hand, for the industries with the larger share ofworkers working at home, ranging from 10 to 20%, the productivity growth ranges from a
2.4% decline (“Professional, scientific, and technical services”) to 1.6% decline (“Computer
systems design and related services”).
Statistical Significance. Using the employment and productivity data constructed above,
we test the statistical significance of the effect of social distancing implemented in each industry after the pandemic spread of COVID-19 on the employment and productivity decline.
We regress the employment growth and productivity growth before (2019Q4) and right after
8

Assuming that real net stock of capital and capital income share remain unchanged is more valid with a
two-quarter change in 2019Q4-2020Q2 than a one-year change in 2019Q2-2020Q2. Even though the aggregate
capital income share is known to be procyclical to aggregate shocks, the cyclicality of sectoral capital shareis not well known.
9
The assumption on the 2019 net stock of capital and capital income share implies that our calculated
productivity growth is almost identical to the growth rate of labor productivity. With more data being
available soon, we will be able to observe the one-year change of TFP Ai,t in each industry with timevarying capital and capital income share.

7

COVID-19 (2020Q2) on the log of the adaptability measure. The estimating equation is∆ log Ri = α + β log(W F Hi ) + εi(2)where ∆ log Ri takes either a log difference of employment or productivity of an industry ifrom pre-pandemic t to post-pandemic t + 1; and log(W F Hi ) indicates a pre-pandemic measure of adaptability to social distancing of industry i in log. Our conjecture that industries
with higher flexibility to social distancing tend to experience less decline in employment andproductivity from COVID-19 predicts β > 0.
The results from this estimation are shown in Table 2. We take different measures ofadaptability to social distancing for the estimation.10 For our measures of adaptability
to social distancing and Dingel and Neiman (2020)’s measure, the positive effect on theemployment growth and productivity growth are statistically significant. More specifically,as the ACS share of workers working at home increases by 1%, the employment decline
mitigates by 7.6%. Similarly, when Dingel and Neiman (2020)’s measure of feasibility towork from home increases by 1%, the employment decline is reduced by 6.4%.
The productivity responses also exhibit a statistically significant, positive relationshipwith adaptability to social distancing. For instance, when ACS measure increases by 1%, theproductivity grows by 3.9%. Similarly, productivity growth rises by 3.2% when Dingel andNeiman (2020)’s measure increases by 1%. These results support the notion that industries
that were less able to adapt to remote work and social distancing suffered greater impacts
on employment and productivity in the wake of the pandemic.11

4

A Multisector Model of Labor Reallocation

Empirical evidence shows the immediate responses of employment and productivity to COVID19 shock. However, the projection of economic recovery after the shock is a more timely
question to examine than the immediate responses. Unfortunately, data at the time of thiswriting cannot answer this question. Instead, we exploit a model to predict the short-run
and medium-run responses of the economy after the shock. In this section, we use a multisector search model by Chodorow-Reich and Wieland (2020) to examine labor reallocation
across industries, given the sectoral productivity responses to an aggregate pandemic shock.
10

The construction of alternative measures is described in detail in our Online Appendix.
We also checked the responses of real wage to the pandemic shock in our Online Appendix. We findthat the average wage responses to the shock are negligible, while the wage growth becomes more dispersed
after the shock.
11

8

4.1

Model

Time is discrete. Let there be I industries in the economy. Each sector i produces ahomogeneous good yi,t . Labor is the only factor input in the good production. Equivalently,
one can assume that capital is fixed and cannot be reallocated across sectors:
yi,t = Ai (νt )ei,t .

(3)Ai (νt ) is a sector-specific productivity responding to an aggregate social-distancing restriction νt . From our empirical evidence, we assume that the sector-specific productivity
depends only on the economy-wide social distancing restriction. The functional form could
differ by sectors as the social distancing restriction affects each sector differently. While we
do not restrict the functional form, it is sensible to assume that at least after some level ν, Ai
is weakly decreasing in νt . We also assume that the firms can only hire from a sector-specificlabor market. In the directed search literature, the assumption means that each sector isalso a sub-market (Moen, 1997; Delacroix and Shi, 2006; Shi, 2009).
1−η η
Workers and firms match according to a sector-specific matching function M vi,txi,twhere M indicates a matching efficiency, η indicates a bargaining power of workers, vi,t isthe measure of vacancy, and xi,t is the measure of job searchers. Because there are multiple
sectors, and we assume that not everyone in a sector can be reallocated within a period, themeasure of job searchers is not proportional to the measure of unemployed workers. Let θi,tdenote the market tightness in sector i which is defined as vi,t /xi,t .

Employed workers are separated exogenously at a rate δ. After the realization of theseparation shock, the workers receive a reallocation shock at an exogenous rate λ every
period. In line with recent literature on semi-directed search (see e.g., Pilossoph (2014);
Kennan and Walker (2011); Chodorow-Reich and Wieland (2020)), the workers who receive
the reallocation shock draws a vector of idiosyncratic taste shock {εi,t }Ii=1 across sectors.
The taste shock is additive to the worker’s value function, which allows workers flowing fromlow-productivity sectors to high-productivity sectors and vice versa. The taste shock εi,t follows a Type I extreme-value distribution with parameters (−ργ, ρ). With the distributional
assumption of the taste shock, the conditional choice probabilities have a multinominal logit
form (McFadden, 1973, 1981).
Firm in sector i receives the real marginal revenue product pi,t by selling the intermediate
good and pays the real wage cost wi,t to workers. Firms post vacancy vi,t at a cost κ.
Assuming a free entry condition, the expected value of vacancy becomes zero. Bellman
9equations for filled job and vacancy posting are illustrated as
Ji,t = pi,t − wi,t + β(1 − δ)Ji,t+1(4)

κ = q(θi,t )Ji,t(5)

where β is a discount factor, and δ is an exogenous job separation rate.
Employed workers receive the sector-specific wage wi,t . When receiving the separation
shock, the worker enters the unemployment pool immediately and search for jobs. When
receiving the reallocation shock, the worker chooses to switch to the sector that has thehighest expected continuation value, augmented by the taste shocks. Unemployed workers
receive unemployment benefit z which is common across sectors. Denote the value functionof the employed worker in sector i at period t by Wi,t . The value function of unemployedworker searching a job in sector i at period t is denoted as Ui,t . Then, the worker’s recursive
Bellmen equations are specified as
Wi,t = wi,t + β{[(1 − δ) + δ(1 − λ)f (θi,t+1 )]Wi,t+1 + δ(1 − λ)(1 − f (θi,t+1 ))Ui,t+1 }+ βδλ Eε max{(1 − f (θj,t+1 ))Uj,t+1 + f (θj,t+1 )Wj,t+1 + εj,t }j(6)
Ui,t = z + β{(1 − δλ)[f (θi,t+1 ))Wi,t+1 + (1 − f (θi,t+1 ))Ui,t+1 ]}+ βδλ Eε max{(1 − f (θj,t+1 ))Uj,t+1 + f (θj,t+1 )Wj,t+1 + εj,t }j(7)
where Eε takes an expectation over the idiosyncratic taste shocks {εi,t }Ii=1 . The discrete
choices Eε maxj {(1 − f (θj,t+1 ))Uj,t+1 + f (θj,t+1 )Wj,t+1 + εj,t } with Type I extreme value tastePshocks εj can be written as ρ log j exp{(1 − f (θi0 ))Uj0 + f (θi0 )Wj0 }/ρ.
We characterize three laws of motion for employment ei,t , unemployment ui,t , and job
searcher xi,t over time:IX
xi,t+1 = δ(1 − λ)ei,t + (1 − δλ)ui,t + πi δλ(ej,t + uj,t )(8)

jei,t+1 = (1 − δ)ei,t + f (θi,t+1 )xi,t+1(9)

ui,t+1 = (1 − f (θi,t+1 ))xi,t+1(10)where πi denotes the transition probability to sector i conditional on receiving a reallocation10

shock. The laws of motion show that both the reallocation shock and the social-distancing
shock are important for the measure of job searchers and hence the employment and theunemployment. In particular, the social-distancing shock affects xi,t by changing the probability that the workers switch to sector i.
Finally, we assume that the market wage is determined by the Nash bargaining scheme
between firms and workers, wi∗ , but is constrained by the downward nominal wage rigidity:
wi = max{wi∗ , (1 − χ)wi,t−1 /Πi,t }.

(11)

Denote Πi the gross producer price index, and the nominal wage cannot fall by χ percent.
4.2

Calibration

To examine the effect of productivity dispersion across sectors and differential speed of
sectoral adjustment to pandemic shocks on the aggregate recovery, we calibrate the modelwith two sectors, I = 2. As demonstrated in the empirical evidence of productivity dispersion
associated with adaptability to social distancing, we assume two sectors in which, without
loss of generality, sector 1 is less adaptive to social distancing and thereby receiving a larger
productivity drop followed by a slow adjustment of their production efficiency. In contrast,
sector 2 is more adaptive to social distancing and hence recovering the productivity fairly
quickly after having a mild productivity decline. The rest of the model parameters are takenfrom Chodorow-Reich and Wieland (2020). Cost of vacancy (κ) and matching efficiency (M )are calibrated to match job finding rate f (θ) = 0.5 and job filling rate q(θ) = 0.75. The
calibrated model parameters are shown in our Online Appendix.
4.3

Quantitative Analysis of Pandemic Shocks

We simulate the model with two sectors in which the productivity of two sectors declines andrecovers at a different rate specified as Ai,t+1 = (1 − αi )Ā + αi Ai,t + σi νt given an aggregate
pandemic shock (νt ) at period 0. Two sectors’ productivity in the steady state is normalized
to Ā = 1 for simplicity. Receiving a one unit of negative aggregate shock at period 0, we
assume that sector 1 exhibits σ1 = 0.1 of productivity decline and α1 = 0.9 of persistence ofthe shock over time, whereas sector 2 exhibits σ2 = 0.05 and α2 = 0.1. The simulated pathsof productivity are shown in panel (a) of Figure 2. We numerically solve and demonstrate
the impulse responses of aggregate unemployment as well as sectoral variables to one-time
pandemic shock at t=0.
Panel (b) of Figure 2 shows the impulse response of market tightness for each sector. The
11

steady-state market tightness for both sectors is 0.666. After the aggregate shock at time
0, the market tightness for sector 1 drops by 91% while it only drops by 14.8% for sector 2.
The larger decline for sector 1 attributes to a constant decrease in job search after the shock(panel (c)) and to job vacancy plummeting without a subsequent rise afterward (panel (d)).
On the other hand, a tiny and temporary drop in productivity in sector 2 results in a small
drop of vacancy followed by a rapid increase, which is also offset by a rapid increase in thejob search.
Unemployment of workers previously working in sector 1 starts falling after a one-time 2%
jump at time 1 (panel (e)). The fall is due to a large drop in market tightness, which results
in a decline in job-finding rate in sector 1, leading to a mild decline in job search. Intuitively,
workers in sector 1 are shifting to more adaptive and relatively more productive sector 2.
Conversely, the inflow of workers from sector 1 overcrowds sector 2 and, as a consequence,
the unemployment in sector 2 rises rapidly. An aggregated effect of pandemic shock withthe reallocation of workers is shown in panel (f) of Figure 2. The unemployment rate rises
by almost 2.42 percentage points in two periods after the shock. The economy recovers to
0.05 percentage point in 6 periods as more workers in sector 1 transition to sector 2. This
simple scenario—without considering the second and third waves of COVID-19— informs
us that even though some industries’ productivity suffers from adopting social distancing,workers are reallocated to more adaptive and productive industries. Therefore, the economy
can exhibit an optimistic quick recovery from the pandemic shock. We now experimentwith some changes in critical factors of the economy to explore changes in the projection of
economic recovery.12
Adaptability to Pandemic Shocks Because of its work characteristics, some industries
are more flexible to implement social distancing in their working environment than otherindustries. Our empirical evidence in the previous section demonstrates that the industrylevel work-from-home index as a proxy for the adaptability to social distancing nonlinearly
relates to the employment and productivity growth after the pandemic shock. This evidence
implies that some industries are more vulnerable to pandemic shock, suffering productivity
drops after adopting social distancing in the working environment. Therefore, we experimentwith how the adaptability of each sector to pandemic shocks may affect economic recovery.
We consider a case where the persistence of the productivity in sector 1 changes while
holding the persistence of sector 2 constant. The results are shown in panel (a) of Figure 3.
12Note that in our model simulation, we do not take into account the second and third waves of pandemic
shocks. Therefore, our simulation results exhibit an optimistic view of the recovery from the one-time
pandemic shock.

12

When sector 1 adjusts their productivity fairly quickly with α1 = 0.5, the labor reallocation
across sectors almost disappears. Although the immediate response of productivity of sector
1 to the aggregate shock is still twice as large as that of sector 2, the productivity of sector 1
returns to the original level in 7 periods. A quick recovery of the productivity in sector one
reduces the decline of market tightness to almost half of the benchmark case. This reduction
is mainly driven by the reduction of worker reallocation from sector 1 to sector 2. Given theperfect foresight of this productivity projection, an outflow of workers in sector 1 to sector
2 disappears, and therefore, the rise of unemployment in both sectors remain minor as the
productivity recovers in a short period of time. Likewise, the rise of aggregate unemployment
due to the shock is only a third of the benchmark case and returns to the original level in 6
periods. If the productivity of sector 1 takes an even shorter period of adjustment (α1 = 0.1),
the fall of market tightness becomes even smaller. The unemployment in sector 1 becomesalmost negligible immediately after the shock. The impact on aggregate unemployment isalso negligible that the peak is only 25% of the peak in the benchmark case.13
Reallocation of Labor across Sectors We can explore the effect of the reallocation friction(λ) on sectoral variables and aggregate unemployment along the transition path. Panel (b)of Figure 3 shows the impact of labor reallocation on the labor market under the productivity
dispersion across sectors. The steady-state market tightness for both sectors does not changeby the reallocation friction. However, when there is no labor reallocation across sectors(λ = 0), each sector is on its own. Therefore, the job search rate in sector 1 mildly rises, while
there is no rise in job search in sector 2. This implies that the rise of the unemployment rate
in sector 2 is negligible, while the unemployment becomes larger in sector 1. In aggregate,
the unemployment rate is 0.54 percentage point higher than the benchmark case.
In contrast, as we assume perfect labor mobility across sectors (λ = 1), more job searchoccurs in sector 2 with a faster decline of search in sector 1. As more reallocation to sector 2
takes place along the transition path, more job search concentrating in a productive sector
drives a higher unemployment rate in sector 2, whereas the unemployment rate in a lessproductive sector falls even more than the benchmark case. In aggregate, the unemployment
rate is 0.25 percentage points lower than the benchmark case. This finding informs usthat the higher reallocation friction across sectors obstructs an economic recovery from thepandemic shock.
13

We only show impulse responses of sectoral and aggregate unemployment to save space of this paper.
All the simulated impulse responses are shown in our Online Appendix.

13

Downward Nominal Wage Rigidity Finally, we experiment the effect of downward nominal
wage rigidity (DNWR). We explore how the economic recovery might change by the presenceof DNWR.Given the aggregate adverse shock in the economy, the productivity of both sectors
falls. Under the flexible wage, the market wage falls accordingly as the productivity declines
to optimize the allocation of labor. However, the downward adjustment of market wage isconstrained by the DNWR imposed on both markets. As a result, the wage rigidity engenders
more fluctuations in employment and labor mobility across sectors.
More fluctuations under DNWR is shown in panel (c) of Figure 3. The market tightness
plummets at period 0 in sector 1 under a strong rigidity (χ = 0.0035), while the drop is mild
under the weaker rigidity (χ = 0.1). This is because market wage falls under the flexible wage
system to respond to the productivity decline, and hence a sudden drop of vacancy after theshock in sector 1 vanishes. However, under DNWR the wage fails to reflect the productivity
decline which induces a large drop of vacancy in sector 1. Had the wage be flexibly adjusted
to the productivity decline, more workers in sector 1 would remain in the sector with alower wage, which would have resulted in less unemployment in sector 1. In aggregate,
the unemployment under the flexible wage would have been almost 6% of unemployment in
the benchmark case. In other words, the wage rigidity may disrupt an adjustment to thepandemic shock and, as a consequence, excessively slows down the economic recovery.

5

Conclusion

Recent evidence confirms that the shock of COVID-19 induced changes in employment andproductivity that varied across industries. Some industries with higher adaptability to social
distancing were less vulnerable to the changes necessitated by the pandemic. While thedispersion of employment and productivity may be expected to lead to the reallocationof labor across industries, imperfect labor mobility obstructs that reallocation. Our model
prediction of labor reallocation due to the dispersion of productivity shows that the economic
disruption may depend on the degree of labor mobility and the speed of adjustment to social
distancing, especially in less adaptive industries. The extent of recovery from the pandemic
may also depend on these factors.

14

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15

Table 1: The Share of Workers Worked at Home by 2-digit Industry
Industry (2-digit)
Professional, Scientific, and Technical Services
Agriculture, Forestry, Fishing, and Hunting
Real Estate and Rental and Leasing
Information
Finance and Insurance
Administrative and support and waste management services
Arts, Entertainment, and Recreation
Other Services, Except Public Administration
Wholesale Trade
Management Of Companies And Enterprises
Construction
Health Care and Social Assistance
Retail Trade
Transportation and Warehousing
Manufacturing
Educational Services
Mining, Quarrying, and Oil and Gas Extraction
Public Administration
Utilities
Accommodation and Food Services

16

Share
.150
.130
.110
.099
.090
.071
.070
.067
.064
.058
.044
.040
.034
.034
.033
.033
.031
.025
.022
.017

Figure 1: Employment/Productivity Decline by the Adaptability to Social Distancing(a) Employment Responses(b) Productivity Responses

Notes: Panel (a) and (b) shows the relationship between the share of workers working at home in 2018 andthe average employment growth and productivity growth from 2019Q4 to 2020Q2, respectively. The size ofeach circle indicates the share of employment in each (sub-)industry. The dashed line indicates a log-linear
line of the scatterplots. Note that sub-industries with more than 20% drop in productivity are not shown inpanel (b).

Table 2: Effects of Social Distancing on Employment and Productivity Growth
Employment Growth(1)log(ACS WFH)

(2)

Productivity Growth(3)0.0756***(0.0180)log(ATUS WFH)

(1)

(2)

(3)

0.0391**(0.0158)
0.0667**(0.0257)

log(DN WFH)

0.0349(0.0200)
0.0635***(0.0101)

0.0323***(0.0101)

Constant

0.153**(0.0582)

0.0552(0.0528)0.000489(0.0157)

0.0704(0.0510)0.0195(0.0411)-0.0132(0.0156)

Observation

35

17

64

35

17

64

Note: Standard errors in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. ACS WFH indicates ourwork-from-home (WFH) measure from American Community Survey. ATUS WFH and DN WFH are
alternative measures from American Time Use Survey and Dingel and Neiman (2020), respectively, that we
describe in our Online Appendix.

17

Figure 2: Impulse Responses of Labor Market to a Pandemic Shock(a) Sectoral Productivity(b) Sectoral Market Tightness(c) Sectoral Job Search(d) Sectoral Vacancy(e) Sectoral Unemployment(f) Aggregate Unemployment

18

Figure 3: Counterfactual Impulse Responses of Labor Market(a) Persistence of Shocks in Sector 1
Sectoral Unemployment

Aggregate Unemployment(b) Reallocation of Labor
Sectoral Unemployment

Aggregate Unemployment(c) Nominal Wage Rigidity
Sectoral Unemployment

Aggregate Unemployment

Notes: Panel (a) shows the impulse response of sectoral unemployment and aggregate unemployment withthe various persistence levels of productivity in sector 1 after the pandemic shock at period 0. Panel (b)shows the impulse response of sectoral unemployment and aggregate unemployment with the various levelsof reallocation friction (λ). Panel (c) shows the impulse response of sectoral unemployment and aggregate
unemployment with the various nominal wage rigidity (χ).

19