Ting Zhang et al., Small Business and the COVID-19 Pandemic: The Role of Work from Home (2020)
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Research article, Small Business and the COVID-19 Pandemic: The Role of Work from Home, by Ting Zhang and Dan Gerlowski of the University of Baltimore and Zoltan Acs of George Mason University, posted September 29th, 2020 as a preprint. It builds a utility maximization framework with a contagion agglomeration parameter, arguing that work from home (WFH) is a rational choice for small businesses, and compiles a real-time daily and weekly dataset tracking WFH propensity from March 20 through July 28. Estimating fixed-effects, population-averaged generalized linear and two-level mixed-effects panel models, the authors find that WFH rates rose after stay-at-home orders ended and that small businesses in states with higher WFH rates were more likely to see higher operating revenue, better cash flow and lower chances of temporary closure.
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Small Business and the COVID-19 Pandemic: The
Role of Work from Home
Ting Zhang ( tzhang@ubalt.edu )
University of Baltimore
Dan Gerlowski
University of Baltimore
Zoltan Acs
George Mason University
Research Article
Keywords: Work from home, COVID-19, Small Business, Stay-at-home Order JEL: O33, L25, L16, M54,
Posted Date: September 29th, 2020
DOI: https://doi.org/10.21203/rs.3.rs-83264/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License.
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Small Business and the COVID-19 Pandemic:
The Role of Work from Home
Ting Zhang, corresponding author, tzhang@ubalt.edu,
Associate Professor, Merrick School of Business,
Associate Director, Jacob France Institute
University of Baltimore, 1420 N. Charles Street, Baltimore, MD 21201
Dan Gerlowski,
Professor, Merrick School of Business,
University of Baltimore, 1420 N. Charles Street, Baltimore, MD 21201
and
Zoltan Acs,
Director, Center for Entrepreneurship and Public Policy;
University Professor, Schar School of Policy and Government,
George Mason University, 3351 Fairfax Dr., MS 3B1, Arlington, Virginia 22201
Abstract
Work from home (WFH) becomes the new norm in the COVID-19 pandemic. Whether the WFH norm will fade or
accelerate after the stay-at-home mandate ends is unknown. The study builds a theoretical framework based on utility
maximization theory subject to a “contagion” agglomeration parameter and argues that WFH is a rational choice for small
businesses. We compiled an up-to-date real-time daily and weekly multifaceted data set tracking WFH propensity from
March 20 through July 28. Our empirical analysis estimated a variety of fixed-effects panel data models, population-
averaged generalized linear panel-data models with the generalized estimating equation (GEE) approach, and two-level
mixed-effects panel-data models. After controlling for the local pandemic, economic, and demographic factors, we find
that, (1) after the stay-at-home order ended, WFH rate got higher; (2) small businesses in states with higher WFH rate are
more likely to have higher increases in operating revenue, better cash flow and lower chances of temporary closure. Our
robust empirics confirm our theory and hypotheses and demonstrate WFH as a potential force that expedited the “creative
destruction” into a new efficient work paradigm.
Keyword
Work from home, COVID-19, Small Business, Stay-at-home Order
JEL: O33, L25, L16, M54,
Small Business and the COVID-19 Pandemic:
The Role of Work from Home
Introduction
One disruption that the COVID crisis brought to our economy is working from home (WFH). Dingel & Neiman (2020)
found that 37% of jobs in the United States can be performed entirely at home, with variation across cities and industries.
Bartik, et al. (2020b) report that 45% of firms having at least some workers switch to teleworking during the COVID-19
pandemic and over 1/3 of those firms believe that WFH will remain more common at their companies after the COVID-19
crisis ends. Gallup Panel (2020) revealed that the percentage for Americans WFH doubled to over 60% between mid-
March and early April 2020 and 59% U.S. workers who have been teleworking during the pandemic would prefer to
continue WFH as much as possible, once public health restrictions are lifted, while only 41% would prefer to return to
their workplace to work (Breman 2020).
Will this COVID-induced WFH disruption emerge into a Schumpeterian (1934) “creative destruction” that help
businesses grow better in the long run and will small businesses (with less than 500 employees and receipts of at least
$1,000) ride this WFH wave well? While small businesses employ almost 50% of American workers (Bartik, et al.
2020a), in economic crisis small businesses are vulnerable (Kolasa et al. 2010; Kennickell et al. 2017) and
disproportionately negatively affected (Bartz & Winkler 2016). While a rising number of businesses adopt WFH and
while prior literature discussed separately on WFH and on crisis impact on small businesses, whether WFH helps mitigate
the crisis shock on small businesses is unknown.
This paper therefore focuses on examining (1) whether WFH rates continue to rise after singling out the pandemic
severity and related stay-at-home mandate, and (2) how WFH helps small businesses do better in the pandemic. The
exogenous pandemic shock could have expedited the WFH norm as the new Schumpeterian (1934) “creative destruction”:
a norm that we were technically ready but hesitant to adopt. The future path of WFH will impact workplaces, life styles,
and urban structure and planning.
The study builds a theoretical framework based on utility maximization theory subject to business costs, working
hours, wages, and a contagion agglomeration parameter (Krugman 1996; Glaeser 1999), demonstrating conditions when
WFH is a rational choice for businesses. Then, we compiled an up-to-date real-time daily and weekly multifaceted data
set tracking WFH propensity from March 20 through July 28. Relying on our theory and real-time data, our empirical
analysis estimated a variety of fixed-effects panel data models, population-averaged generalized linear panel-data models
with the generalized estimating equation (GEE) approach, and two-level mixed-effects panel-data models.
The next section focuses on our theoretical framework, followed by our two research hypotheses. Then in the
methodology section, we describe our data and present our empirical findings with robustness check After controlling for
the local pandemic, economic, and demographic factors, we find (1) after the stay-at-home order (SHO) ended, WFH rates
got higher; (2) small businesses in states with higher WFH rates are more likely to have an increase in operating revenue,
a better cash flow situation, fewer temporary closures and fewer disruptions of supply chain.
Theoretical Framework
Our theoretical framework is cast in a cost benefit framework where workers and firms seek to be rational maximizing
entities in a constrained environment comparing home and office workplaces. The four key factors of production for a
firm include capital, labor, land, and technology and entrepreneurship (Bade and Parkin, 2018). Under certain technology
conditions (X), it is business owners’, or top managers’, entrepreneurship that determines whether working in traditional
brick-&-mortar offices or WFH. Based on the utility maximization theory, a rational choice is a choice that maximize
one’s utility. From the labor demand perspective, hiring decisions are based on the revenue and cost a marginal employee
would bring.
Employers choose WFH versus brick-&-mortar office if WFH (H) brings more marginal net benefit than work in
the traditional offices (O). Workers are endowed with certain skills and abilities (S) which are dependent on the level and
use of technology available to the worker (X). Better technology will increase S and hence worker marginal productivity.
Facing the pandemic, workers’ working hours (T) is often affected by the pandemic conditions (P), no matter WFH or
working in traditional offices. For employers, they hire employees based on employees’ skills, S(X), and potential
working hours, T(P), because S(X) and T(P) jointly determine potential revenue. Employers’ cost spread to each
employee include employees’ wage (W), capital or equipment, office supply and utility costs (K), and land cost (L). In
the traditional office settings, the marginal revenue of workers also benefits from an agglomeration parameter (A)
(Krugman 1996; Glaeser 1999) with networking and knowledge spillovers (Saxenian 1994). In the pandemic, the location
based agglomeration effect is constrained also by the pandemic conditions (P) with social distancing needs. Therefore,
employers would choose WFH versus working in traditional offices if the marginal revenue per unit of marginal costs of
WFH is larger:
𝑆(𝑋)𝐻 ∗ 𝑇(𝑃)𝐻 𝑆(𝑋)𝑂 ∗ 𝑇(𝑃)𝑂
≥ 𝐴(𝑃) ∗ (1)
𝑊𝐻 ∗ 𝐾𝐻 ∗ 𝐿𝐻 𝑊 𝑂 ∗ 𝐾 𝑂 ∗ 𝐿𝑂
(1) can be further transformed into
𝑆(𝑋)𝐻 𝑇(𝑃)𝐻 𝑊 𝑂 𝐾 𝑂 𝐿𝑂 1
𝑂
∗ 𝑂
∗ 𝐻∗ 𝐻∗ 𝐻∗ ≥ 1 .
𝑆(𝑋) 𝑇(𝑃) 𝑊 𝐾 𝐿 𝐴(𝑃)
For employers, the labor search pool is enlarged beyond the local scope, resulting the employee skills out of
location-unbounded web search, 𝑆 𝐻 , potentially better matched with the job than that out of local search only; for the
𝑆(𝑋)𝐻
same job, WFH would potentially require more technology savviness. Therefore, 𝑆(𝑋)𝐻 > 𝑆(𝑋)𝑂 , 𝑖. 𝑒., > 1.
𝑆(𝑋)𝑂
As for hours committed to work, many WFH workers feel the need to reciprocate the privilege of WFH with
flexibility, autonomy, and saved commuting time by working longer hours and/or harder work (Gajendran & Harrison
2007), mirrored with empirical evidence on longer hours for WFH (Kelliher & Anderson 2010; Mariani 2000) or “hard to
plug off work” in the survey (Buffer 2019). We therefore believe WFH workers work for longer hours than workers in
𝑇𝐻
traditional offices for a work day, i.e., > 1. In the pandemic, working hours in traditional office could be even shorter
𝑇𝑂
𝑇(𝑃)𝐻
to limit social distancing, i.e., > 1.
𝑇(𝑃)𝑂
With a wider labor pool to pick from, employers could potentially push the wage rate from WFH labor lower. As
Mas & Pallais (2017) found, an average worker is willing to give up 8 percent of wages for WFH. This percentage could
be much higher facing a pandemic health threat and high unemployment. Firms may regard WFH as a means to increase
motivation and commitment (Caillier 2012; Eaton 2003). Bourdeau et al (2019) identify a flexibility stigma associated
with WFH as a characteristic violating the work devotion schema that calls for intensive allegiance, dedication, and
undivided attention to the workplace, which could push WFH wages lower. Therefore, wage rate for workers working in
traditional offices, 𝑊 𝑂 , could be higher than wage rate for WFH employees for the same type of work, 𝑊 𝐻 . This means
𝑊𝑂
> 1.
𝑊𝐻
For traditional office settings, business owners are obligated for capital or Administrative & General (A&G) costs
like utilities, equipment, office furniture, supplies, and an office manager’s salary to handle those administrative issues.
In contrast, the home office setup cost for WFH case is often lower for employers: some employers might reimburse some
home office supply and equipment costs and employers might need to pay for the technology to facilitate WFH, but
typically not utility costs (e.g., electricity, gas, internet, telephone cost, insurance, etc.). For most small businesses, the
potentially saved office costs could be even more important and the technology requirement for WFH might not have to
be sophisticated or expensive with current advances in technology. Therefore, those office costs for workers working in
𝐾𝑂
the traditional office setting, 𝐾 𝑂 , is often larger than that for home offices for WFH, 𝐾 𝐻 , 𝑖. 𝑒. , > 1. However, the
𝐾𝐻
concerns about the ability of employers to manage WFH workers (Coenen and Kok 2014) may result in some
management cost, or costs of organizational change and technological investments (see Aguilera, et al. 2016) which could
offset the WFH capital cost advantage. However, in the COVID pandemic, the social distancing requirements (such us
keeping space from each other for at least 6 feet), the cost for Personal Protective Equipment, makes the 𝐾 𝑂 larger, i.e.,
𝐾𝑂
> 1. From the employer perspective, WFH could become a more effective and cheaper way to achieve social
𝐾𝐻
distancing, reduce COVID spread, and lower the cost of losing key employees.
For traditional office settings, business owners are obligated for continuous, often monthly, land costs (L), either
rent or mortgage (and tax) and insurance of the offices. For small businesses, this land costs are often a major operating
costs. In contrast, the home office land cost for the WFH case is often not considered and not reimbursed by the
employers. Therefore 𝐿𝐻 is basically close to 0, except for essential offices. Matthews & Williams (2005) noted that WFH
allowed companies to make considerable savings through lower real estate costs and productivity gains. Therefore,
employers’ land cost for workers working in the traditional office setting, 𝐿𝑂 , is considerably larger than the almost 0
𝐿𝑂 𝐿𝑂
home offices land cost for WFH, 𝐿𝐻 , 𝑖. 𝑒. , 𝐻 → + ∞. With a close to 0 denominator, 𝐻 is reaching positive infinity.
𝐿 𝐿
Given the benefit of agglomeration, A>1, for rational employers not to choose WFH versus from traditional
1
offices in Inequation (1), A has to be a positive infinity to make off-set the joint effect from all the other vectors that is a
𝐴
𝐿𝑂
product of a positive infinity vector ( 𝐻 ) and other vectors that are larger than 1 (i.e.,
𝐿
𝑆(𝑋)𝐻 𝑊 𝑂 𝐾 𝑂 𝑇(𝑃)𝐻
𝑆(𝑋) 𝑂, 𝑊 𝐻, 𝐾 𝐻 , 𝑎𝑛𝑑 𝑇(𝑃)𝑂
). Although A might enhance work efficiency to some extent, A cannot enhance work efficiency
by positive infinity folds. Plus, with the growing technology conditions (X), the benefits of agglomeration (A>1) may be
counter-balanced by the impact of technology and the likelihood of contagion for WFH workers as well, with even
additional benefits such as recorded sessions, meeting transcripts, saved whiteboard images for needed review. Therefore,
𝑆(𝑋)𝐻 𝑊𝑂 𝐾𝑂 𝑇(𝑃)𝐻 𝐿𝑂
the probability for the agglomeration effect A to be larger than ∗ ∗ ∗ ∗ 𝐻 is impossible. As a result, a
𝑆(𝑋)𝑂 𝑊𝐻 𝐾𝐻 𝑇(𝑃)𝑂 𝐿
rational employer would most likely choose WFH over traditional office work. In the pandemic, the agglomeration effect
A is further compromised by social distancing needs and therefore A(P) is even smaller.
Currently WFH still face various barriers. Golden and Eddleston (2020) find empirical support in survey based
research for some negative outcomes in promotions, raises, and career success for those pursuing flexible work
arrangements including WFH. Firms that have not adopted WFH are likely to doubt productivity of WFH workers (see
Aguilera, et al. 2016), though WFH were also found to be more productive than traditional office work (SHRM 2018) due
to reasons such as less absenteeism. Any Schumpeterian “creative destruction” took a painful path to “disrupt” first
before a newer and more productive or economically rational approach finally becomes a norm.
Hypotheses
When COVID-19 started to spread across the US, WFH started to dominate. This was pushed by the health
concerns to limit the virus spread and correspondingly by the government SHO mandate. Although many businesses
remained closed after the SHO was lifted, others reopened to partial or full business. One can easily argue that WFH
would dramatically drop back to where it was before the COVID-19 started after the virus is contained or would be at
least less popular after the SHO ends. However, based on our theoretical framework, since WFH seems a rational choice
for businesses, we believe WFH would be gaining popularity and should not sharply drop because of the end of SHO.
In addition, out of this COVID pandemic, firms have now paid the fixed costs of learning how to make remote
working functional (Bartik, et al., 2020b) and are more aware of the potential of WFH. Many firms did not adopt WFH
before the pandemic either because of ignorance or coordination issues (Bartik, et al. 2020b). After this unexpected
natural experiment and learning by doing experience of WFH in the pandemic, the paid fixed costs to facilitate WFH, the
related work coordination, and the enhanced awareness of the WFH advantages may make WFH a real optimal for many
businesses. Although some companies may return to traditional office setting, many firms may continue adopting WFH
after the SHO ended or even after the pandemic is over. Both surveys in Bartik, et al. (2020b) show that 40% of both large
and small firms expect that at least 40% of their workers who switched to remote work during the crisis will work
remotely after the crisis. Although the pandemic is unpleasant, it could have expedited our economy to utilize the new
technological frontier better. We therefore hypothesize, the popularity of WFH would continue, ceteris paribus:
Hypothesis 1: After controlling for the local pandemic, economic, and demographic conditions, the WFH
rate would not sharply drop after the SHO ended.
Although adopting WFH practices often requires organizational changes, such as surveillance and control or
management of the psycho-sociological distance from the work environment (Belanger 1999; Taskin and Devos 2005;
Wilton et al., 2011), WFH could save turnover cost from businesses because WFH increases employee well-being by
reducing travel-related fatigue, providing a less stressful work environment (Ravi S. & David A. 2007; Redman et al.,
2009) and a better balance between work and family life (Wheatley 2012), reducing the costs of commuting, pollution and
urban congestion (Helminen and Ristimäki 2007; Mokhtarian et al. 2004), and even elevating productivity (Belanger
1999; SHRM 2018). Bailey and Kurland (2002) declare that in almost all empirical articles they examined, WFH was
associated with higher productivity because of less absenteeism (Kitou and Horvath 2008).
A study by Belzunegui-Eraso and Erro-Garcés (2020) showed that WFH is being used by many companies to
keep productivity up during the crisis, and that adopting WFH contributes to a reduced hit to GDP as a result of the crisis.
Bartik, et al. (2020b) also noted that industries that are better suited to remote work also seemed to experience less
productivity loss when switching to remote work. We therefore believe WFH can mitigate the negative economic impact
from the COVID shock and help small businesses do better in the pandemic.
In a pandemic, it is often expected that a small business might temporarily close. Bartik, et al. (2020a) reported
43% of small businesses they surveyed did temporarily close and cited fragile financing with less than one month of cash
on hand. On the other hand, Bartz & Winkler (2016), using German data for the 2009 crisis, identified relative growth
advantages among small businesses due to flexibility. Temporary closures have important implications for the US
workforce. The cash flow position often signals time-to-failure for small businesses. In addition, disruptions in the supply-
chain exhibit challenges that other businesses are facing and have implications about the economy as a whole (Buffington,
et al. 2020). Whether the operating revenue is increased is a direct indicator for business performance. Considering the
potential impacts from financial assistance from the Paycheck Protection Program (PPP), we add those controls as well as
aforementioned controls. Therefore we hypothesize:
Hypothesis 2: A higher (versus lower) WFH rate helps small businesses perform better in the pandemic
with a lower probability of temporary closures, with more operating revenues, and with better cash flow
positions, controlling for local pandemic, economic, demographic, and financial assistance program
conditions.
Methodology
Our analysis demonstrates robustness across various specifications in three types of models: the fixed-effect cross-section
time-series panel-data model, population-averaged generalized linear panel-data models with the generalized estimating
equation (GEE) approach, and two-level mixed-effects panel-data model: Most of the independent variables adopted one-
period lag to capture a sequential effect. In this section, we first explain our empirical models and variables. Then we
present our data sources and variables measures.
Empirical Models and Variables
To test Hypothesis 1, we modeled the sensitivity of the end of SHO on WFH, controlling for local demographic,
economic, and pandemic conditions. Our data is cross-sectional time-series data, assuming correlations over time for each
state (or Washington D.C. (DC)) and independence between 50 states (and DC) in the United States. We started with the
fixed-effect panel data modeling, fixed at the individual states:
4 3
𝑊𝐹𝐻𝑗𝑡 = 𝛽0 + 𝛽1 𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑡 + 𝛾𝑖 ∑ 𝐶𝑂𝑉𝐼𝐷𝑗(𝑡−1) + 𝜂𝑖 ∑ 𝐸𝐶𝑂𝑁𝑗(𝑡−1)
𝑖=1 𝑖=1
4
+𝜃𝑖 ∑ 𝐷𝑒𝑚𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑠𝑗(𝑡−1) + 𝑣𝑗 + 𝜀𝑗𝑡 . (1)
𝑖=1
Our independent variable, 𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑡 is a binary variable labeling the data period after the SHO ended in each
state j and time period t; based on our theory and hypothesis, we expect 𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑡 to show a positive effect on WFH
rates. 𝐶𝑂𝑉𝐼𝐷𝑗𝑡 includes a set of four variables measuring the COVID pandemic severity. 𝐸𝐶𝑂𝑁𝑗𝑡 captures three local
macroeconomic condition measures. 𝐷𝑒𝑚𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑠𝑗𝑡 incorporates four demographic attributes. 𝑣𝑗 is the state-specific
error term; it differs between states, but for any particular state, its value is constant. 𝜀𝑗𝑡 is the idiosyncratic error term.
Considering the fact that states’ demographic attributes data do not capture weekly or even daily changes and
WFH and the pandemic information was limited by March, fixed effects would be limited. We therefore also estimated
population-averaged generalized linear panel-data models with the GEE approach described in Liang and Zeger (1986).
This longitudinal data model do not require the data set to be balanced and allows among- and within-state covariates to
be incorporated straightforwardly. Although the model incorporates an assumption of multivariate normality of a
response vector conditional on covariates, with large samples, estimators of parameters in the models are consistent for
the true values with a deduced approximate normal sampling distribution.
In addition, we also add in industry sector controls in our modeling. Dingel and Neiman (2020) demonstrated
industry sector variations in WFH feasibility in the pandemic. Bartik, et al. (2020b) also noted industries that are better
suited to remote work seem to experience less productivity loss when switching to remote work. We therefore first
integrate industry sector fixed effects to the population-averaged generalized linear panel-data models with the GEE
approach. Then we adopted the two-level (i.e., state and industry sector) mixed-effects model.
As our theoretical framework noted, WFH is subject to local labor market conditions as well as industry sectors.
Individual businesses are interdependent not only in an area where knowledge, information, labor, and social networks
flow and spillover easily, but also correlated in the same industry sector. In this case, fixed-effect logistic regression is
limited, because the assumed independent and identical distribution between individual observations is violated
(McCoach & Adelson 2010) and it does not allow for necessary random effects with an industry sector or a local areas.
Multilevel modeling also enjoys the advantage of allowing for unbalanced sample size across local areas (Raudenbush
1993) shown in this study, compared to clustered standard errors. We want to observe not only variations across states
(fixed state effects) but also random variations across industry sectors (random industry sector effects). In panel data,
random effects are useful for modeling intra-industry sector; that is, states in the same industry sector are correlated
because they share common industry sector level random effects. Mixed-effects modeling contains both fixed effects and
random effects:
4 3
𝑊𝐹𝐻𝑗𝑘𝑡 = 𝛽0 + 𝛽1 𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑘𝑡 + 𝛾𝑖 ∑ 𝐶𝑂𝑉𝐼𝐷𝑗𝑘(𝑡−1) + 𝜂𝑖 ∑ 𝐸𝐶𝑂𝑁𝑗𝑘(𝑡−1)
𝑖=1 𝑖=1
4
+𝜃𝑖 ∑ 𝐷𝑒𝑚𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑠𝑗𝑘(𝑡−1) + 𝑍𝑗𝑘𝑡 𝜇𝑘𝑡 . (2)
𝑖=1
In our two-level mixed-effects panel data model, states are conditional on a set of random effects 𝜇𝑘𝑡 , for k =
1, …. n industry sectors, with industry sector j consisting of j = 1, …. m (m<=51) states’ observations across time periods
(days or weeks) t. Vector 𝑍𝑗𝑘𝑡 is the covariate corresponding to the random effects. The random effects 𝜇𝑘𝑡 are n
realizations from a multivariate normal distribution, with mean 0 and variance δ. The random effects are not directly
estimated as model parameters, but are instead summarized according to the unique elements of variance. Multilevel
mixed-effects modeling have been used extensively in social science studies, such as Rabe-Hesketh and Skrondal (2012),
which analyzes school data from Scotland.
To teste Hypotheses 2, we adopted three similar models. In this case, our dependent variable is business
performance, 𝐵𝑢𝑠𝑖𝑛𝑒𝑠𝑠𝑗𝑘𝑡 , which captures operating revenue, cash flow, temporary closure, or disruption of supply chain.
Since financial assistance from Paycheck Protection Program (PPP) and other programs might impact firms’ revenue,
cash, and performance, we include 𝐹𝐼𝑁𝑗(𝑡−1) to capture nine financial assistance types. The base model, the fixed-effect
panel-data model, is therefore:
4 3
𝐵𝑢𝑠𝑖𝑛𝑒𝑠𝑠𝑗𝑘𝑡 = 𝛽0 + 𝛽1 𝑊𝐹𝐻𝑗𝑘(𝑡−1) + 𝛽2 𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑡 + 𝛾𝑖 ∑ 𝐶𝑂𝑉𝐼𝐷𝑗𝑘(𝑡−1) + 𝜂𝑖 ∑ 𝐸𝐶𝑂𝑁𝑗𝑘(𝑡−1)
𝑖=1 𝑖=1
4 9
+𝜃𝑖 ∑ 𝐷𝑒𝑚𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑠𝑗𝑘(𝑡−1) +€𝑖 ∑ 𝐹𝐼𝑁𝑗(𝑡−1) + 𝑣𝑗 + 𝜀𝑗𝑡 . (3)
𝑖=1 𝑖=1
The two-level mixed-effects model accordingly changes to
4 3
𝐵𝑢𝑠𝑖𝑛𝑒𝑠𝑠𝑗𝑘𝑡 = 𝛽0 + 𝛽1 𝑊𝐹𝐻𝑗𝑘(𝑡−1) + 𝛽2 𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑡 + 𝛾𝑖 ∑ 𝐶𝑂𝑉𝐼𝐷𝑗𝑘(𝑡−1) + 𝜂𝑖 ∑ 𝐸𝐶𝑂𝑁𝑗𝑘(𝑡−1)
𝑖=1 𝑖=1
4 9
+𝜃𝑖 ∑ 𝐷𝑒𝑚𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑠𝑗𝑘(𝑡−1) +€𝑖 ∑ 𝐹𝐼𝑁𝑗(𝑡−1) + 𝑍𝑗𝑘𝑡 𝜇𝑘𝑡 . (4)
𝑖=1 𝑖=1
Based on our theory and hypothesis, we expect our independent variable 𝑊𝐹𝐻𝑗𝑘(𝑡−1) to show a positive effect on our
measures of business performance, 𝐵𝑢𝑠𝑖𝑛𝑒𝑠𝑠𝑗𝑘𝑡 .
Data Sources and Variable Measures
Our main models to test Hypothesis 1 used daily data, starting from March 21, 2020 when the first state started the SHO
till July 28, 2020, the last day we got our data, With one day lagged value for our independent variables, the daily data
actually covers up to 130 days (depending on when a states starts the SHO) from March 20 to July 28, 2020 across all
states (including DC) in the United States. Our data to test Hypothesis 2 are weekly data and include the small business
data of April 26 through June 27, 2020. With one week lagged value for our dependent variables, the weekly data
therefore covers 10 weeks from April 19 to June 27, 2020 over all states (including DC).
Our data comes from multiple data sources. Data for our key variable, WFH, are from the University of
Maryland’s Maryland Transportation Institute (MTI). WFH captures the daily percentage of workforce working from
home. It is calculated using daily mobile device1 location based work trip information and US Department of Labor’s
unemployment claims information. According to Zhang, et al. (2020), MTI first integrated and cleaned location data from
multiple sources representing person and vehicle movements to improve the quality of the mobile device location data
panel and then clustered the location points into activity locations and identified home and work locations at the census
block group level to protect privacy. If an anonymized individual in the sample did not make any trip longer than one-mile
in distance, this anonymized individual was considered as staying at home. The data sources and computational
algorithms have been validated based on a variety of independent datasets such as the National Household Travel Survey
and American Community Survey (ACS), and peer reviewed by an external expert panel in a U.S. Department of
Transportation Federal Highway Administration’s Exploratory Advanced Research Program project2.
The data for small business performance measures are from the US Census Bureau weekly Small Business Pulse
Survey (SBPS). The survey targets toward all nonfarm, single-location employer operating businesses with 1-499
employees and receipts of $1,000 or more in the 50 states, DC, and Puerto Rico. For those single-establishment small
businesses, the decision to choose WFH often falls on business owners or top executives. The survey does not include
businesses in agriculture, railroads, US Postal Service, Central Bank, Funds, Trusts, and other financial vehicles, religious
grant operations and religious organizations, private households, public administration, or with unclassified legal form of
organizations as tax-exempt or unknown.
As a survey conducted by the US Census Bureau, the survey represents the country’s small businesses relatively
well. As an online survey and with the sample restricted to businesses with e-mail addresses, the SBPS survey data comes
with a potential selection issue, if businesses willing to participate in email-based surveys are systematically different
from other businesses, However, since our study is on WFH, the online survey works better for businesses that could
potentially allow WFH. The SBPS may be subject to non-response bias because of lack of response or because some may
have already closed; however, according to Buffington et al. (2020), the estimates in the data have been re-weighted to
adjust for non-response based on prior employment size. In addition, as Buffington et al. (2020) noted, although the
businesses sampled in the SBPS tend to be larger than the average small business, they do not appear to differ
substantially in terms of firm age.
1
Daily feeds of more than 100 Million anonymized devices are used.
2
Titled “Data analytics and modeling methods for tracking and predicting origin-destination travel trends based on mobile device
data”.
Our business performance measures include the percentages of small business that increased (or decreased)
operating revenues and experienced (or not) temporary closure, disruptions in supply chain, no cash flow or cash on hand
for 1-4 weeks, 1-2 months, or 3 months or more. SBPS provides detailed information on the challenges that small
businesses are facing during the COVID-19 pandemic as well as related financial assistance programs such as the PPP.
The main COVID-19 pandemic severity measures (COVID new cases and COVID death rate) are sourced from
Johns Hopkins University (JHU) Center for Systems Science and Engineering (CSSE) Github data repository. The
COVID new cases is measure by the number of COVID cases per 1000 people. COVID death rate is measured as the
percentage of deaths among all COVID-19 cases. The CSSE repository is widely used since the start of pandemic.
Funded by multiple agencies and prestigious institutions3, the CSSE data for the United States are from U.S. county and
state health departments, multiple national government health departments, and data aggregating websites4 combining
reports from local health departments and media reports (Dong et al. 2020).
Our data for days of decreasing COVID cases and COVID exposure are calculated by the MTI. Days of
decreasing COVID cases is used because one federally recommended guideline to reopen is a decline in cases over 14-day
period5. Since many states reopened and ended the SHO without meeting the federal guideline, we feel it necessary to
include this measure in our model to better control the pandemic severity. It measures the number of days with
decreasing COVID-19 cases. Since COVID caseload and death rates are subject to the test availability and people’s
behavior that differ across areas, to fully measure the pandemic severity, we also added a measure, COVID exposure
which captures the number of residents already exposed per 1000 people.
The SHO data (𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑡 ) are from the U.S. COVID-19 Hospital Needs and Death Projections data, compiled
by the Institute for Health Metrics and Evaluation (IHME), University of Washington (IHME 2020). The earliest SHO
started on March 21. Our data focus on the observations since the first SHO started. Therefore 𝐴𝑓𝑡𝑒𝑟𝑆𝐻𝑂𝑗𝑡 has two
values: 0 for when SHO was in effect and 1 for after the SHO ended.
For the economic background data, the unemployment rates are weekly from the US Department of Labor
(USDOL). The median household income is again from the ACS. Employment density information is from the US
Environmental Protection Agency (EPA)’s Smart Location Database (SLD). It captures jobs per acre on unprotected
3
e.g., the JHU, National Science Foundation, National Institute of Allergy and Infectious Diseases and National Aeronautics and
Space Administration (NASA), Bloomberg Philanthropies, Stavros Niarchos Foundation.
4
Those websites Include 1point3acres, Worldometers.info, BNO, and the COVID Tracking Project.
5
See https://www.whitehouse.gov/openingamerica/.
land. According to EPA (2020), the Smart Location Database is a nationwide geographic data resource for measuring
location efficiency for over 90 attributes summarizing characteristics (such as housing density, neighborhood design,
destination accessibility, transit service, employment); most of them are available for every census block group.
The demographic data are from the ACS and include percentages of men, African Americans, Hispanic
Americans, older Americans aged 60 or above. For the influence of financial assistance, in addition to the PPP, other
controlled financial assistance programs in the models include assistance from the Economic Injury Disaster Loans
(EIDL), SBA Loan Forgiveness, Other Federal Programs, State or Local Government, banks, self-fund, family, friends,
and others. Table 1 list the data source, type, time period, and measure for each variable.
<< Insert Table 1 about here >>
Findings
Since our data has two cuts: (1) daily data from March 20 to July 28, and (2) weekly from April 19 to June 27, 2020, we
describe our findings using those two cuts separately. Although when adding industry sector information, the number of
observations increased, the data attributes do not change substantially.
For the daily data, there are 4,551 observations across up to 130 days, 51 states (including Washington DC).
Across states we see vast disparities. Over our observation period, averagely 27% of the US workforce since the start of
states’ SHO worked from home, ranging from the lowest rate in a state at only 5% to the highest at 56%; daily new
COVID caseload was about 122 cases per 1 million people with the mean death rate at about 1.7%; about 12 out of 1000
people were exposed to the COVID-19; the average number of days of decreased caseload was less than 4 days. While the
mean unemployment rate across all states during this period is 21.5%, it varies from the lowest at 8% to the highest at
44%. The median household income was around $63,000, but the highest state almost doubled that of the lowest state’s
value. Similarly we see large racial distribution disparities across states.
<< Insert Table 2 about here >>
Appendix Table A presents the correlation matrix between those variables. We do not detect potential major concerns for
multicollinearity.
Figure 1 shows related (either similar or opposite) trends between WFH, COVID new caseload, unemployment
rate, and time (the start and end of the SHO). Since the start of SHO (starting on March 21, 2020 in some states), new
COVID caseload and WFH were dropping and unemployment rate was rising until around the time when the SHO ended
(starting on April 25, 2020 in some states). Soon after the SHO started to end, the unemployment rate started to tip down,
and WFH and new COVID caseload started to tick up in June. Figure A in Appendix shows detailed variations across
states.
<< Insert Figure 1 about here >>
The intuition from Figure 1 seem to show that the WFH rate change is almost a catching up following the COVID
new caseload changes and unemployment rate. After controlling for the pandemic and unemployment changes, does the
WFH rate change becomes irrelevant? Although the WFH rate has kept rising after the SHO ended, by the time we
conducted this study it has not yet returned to the peak when SHO started, reflecting a very moderate negative correlation
between WFH and the end of SHO (shown in Table A in Appendix), opposite to our Hypothesis 1 expectation.
We therefore estimated multivariate empirical models of this impact, controlling for the local pandemic, economic
and demographic conditions, as shown in Table 3. Model (1) and (2) adopted the fixed-effect panel data models. Model
(3) and (4) adopted the population-averaged generalized linear panel-data models with the GEE approach. Models (1) and
(3) included the time variable, Date, to add the fixed time effect, in addition to the fixed state effects in Models (2) and
(4). All the four models used the daily data and resulted in 4,551 observations.
Across all the four models, WFH demonstrated a consistently strong and higher rate after the SHO ended,
controlling for the local pandemic, economic, and demographic conditions. Models (2) and (4) show that WFH rate is
about 2 percentage points higher after versus before the SHO ended. Models (1) and (3) show an average 0.03 percentage
point daily increase in WFH rate since the SHO started in addition to a 0.5 percentage point increase in WFH rate after the
SHO ended.
<< Insert Table 3 about here >>
This effect is also presented in Figure 2. After the SHO ended, the policy requirement restricting workers to
commute to work was lifted. However when holding local pandemic, economic, and demographic factors constant, this
did not result in a drop in the WFH rate; instead, WFH rate continued to rise. This is consistent with our expectation in
Hypothesis 1. All the four models also clearly evidenced the pandemic and economic impact on WFH rates.
<< Insert Figure 2 about here >>
For our weekly data, most variable summary statistics (shown in Appendix Table B) are similar to that of our
daily data, except that the number of observation dropped to 687 overall and to 333 for small business measures. Among
all the observing small businesses, only 2% of them reported no cash flow at all, 31% reported cash flow to last about 1-4
weeks, 29% reported cash flow to last 1-2 months, and 23% reported cash flow to last 3 months or longer. While all states
have more small businesses reporting a decreasing versus increasing in operating revenue (shown in negative range),
averagely across all states and observing period, 34 percentage of more businesses reported decreasing than increasing
operating revenue. While some state in a certain week reported as high as 29% of small businesses experienced temporary
closures, overall most small business did not experience temporary closure. The number of small businesses that did not
report temporary closures in the survey is 46 percentage point higher than those that did. While some state reported as
high as 8% of business experienced disruption of supply chain, the number of small businesses that did not report
disruption of supply chain is 24 percentage points higher than those that did in the survey.
Considering the fact the WFH rate is much affected by the pandemic and economic conditions (as shown in Table
2), estimating the WFH effect on small business performance needs to control for local pandemic, economic, and
demographic conditions. We first conducted four sets of empirical models with those controls, as well as industry sectors,
to test Hypothesis 2. Appendix Table C Models (5) through (11) presents the estimates in seven two-level mixed-effects
models, each on one business performance measure.
Considering the potential impact of PPP and other financial assistance programs, we also added the financial
assistance control variables in our models in Table 1. The WFH effects on small business performance shown in Table 4
stayed highly similar to those shown in Appendix Table C.
<< Insert Table 4 about here >>
As Models (12) through (18) in Table 4, as well as Models (5) through (11) in Appendix Table C, show, a higher
WFH rate is associated with a better performance for small businesses when controlling for local pandemic, economic and
demographic conditions: one percentage point increase in the WFH rate is associated with a small businesses’ share
increase for (1) a cash flow lasting 1week to 3 month or more, (2) increasing operating revenue, (3) no temporary
closures, and (4) no disruptions in supply chain. Our models also show that the pandemic has negative impacts on small
business performances, consistent with previous literature (see Bartik, et al. 2020a). Although the COVID pandemic itself
naturally bring economic shock to small businesses (such as a decrease in operating revenue, temporary closures, and
disruption in supply chain as shown in Table 4), WFH helped offset small businesses some of those negative shocks, as
expected in Hypothesis 2.
As Models (12) through (15) shows, while a higher WFH rate does not increase the percentage of small
businesses that have no cash flow reserved at all, it is associated with a higher share of small businesses with cash flow
reserve for 1-4 weeks, 1-2 months, or 3 or more months respectively by 0.14, 0.45, and 0.35 percentage points, when
holding local pandemic, economic, demographic, and financial assistance conditions constant. Figure 3 partially illustrates
those effects for observations with the WFH rates for 99.3% of the observation without the two extreme tails. 6 Noting that
the impact is stronger for cash flow reserves longer than one month. Since businesses that have longer cash flow reserves
were probably slightly larger, this is consistent with the finding from the literature (see Aguilera, et al. 2016) that larger
businesses are more likely to adopt WFH.
<<Insert Figure 3 about here>>
Model (16) demonstrates the WFH effect on small businesses’ operating revenue increase. When controlling for
local pandemic, economic, and demographic conditions, each one percentage point increase in a state’s WFH rate is
associated with a 0.6 percentage point net increase in the small businesses’ operating revenue a week later. This positive
WFH effect is reflected in Figure 4 with 95% confidence interval. The left panel of Figure 4 presents the WFH effect for
the 99.3% of the observation without the two extreme tails; the right panel is for all observations.
<<Insert Figure 4 about here >>
6
Figures 3 partially illustrates those effects. Figure 3 omitted observations for WFH rate below 3% and above 50% (i.e., omitting the
two extreme tails at 3% and 50-56%) because those observation only represent 0.7% of the observation, but have a much larger and
more dramatic effect from WFH rates. Presenting those in the graph will visually inflate the WFH effects.
As shown in Model (17), ceteris paribus, a percentage point increase in states’ WFH rates resulted in 0.8
percentage point decrease in the small businesses’ probability of temporarily closures. The left panel of Figure 5 presents
the WFH effect without the two tiny tails; the right panel is for all observations.
<< Insert Figure 5 about here >>
Model (11) shows that each one percentage point increase in states’ WFH rates resulted in 0.4 percentage point
decrease in small businesses’ probability of supply chain disruptions, ceteris paribus. The left panel of Figure 6 presents
the effect without the tiny tails; the right is for all observations.
<< Insert Figure 6 about here >>
The financial assistance from PPP (shown in Table 4) has a positive effect on small business cash flow, temporary
closures, and disruptions in supply chain. This reflects the importance of PPP. However, PPP show a negative effect on
small businesses’ increase in operating revenue, reflecting the fact that businesses receiving assistance from PPP tended to
have lower operating revenue.
This positive WFH rate effect on small business performance in Models (5)-(18)7 and Hypothesis 2 further
confirms our theory and Hypothesis 1. This positive effect confirms WFH as a business rational option and is a driving
force for the rising WFH rates even after SHO ended.
Robustness Check
To gauge the robustness of our empirical form, we not only ran three types of models, we also added different variables to
check whether the effects are consistent. As mentioned above, adding time effects in Models (1) and (3) in Table 3 or
adding controls for financial assistance programs in Models (12)-(18) in Table 4, our findings are consistent and highly
similar respectively to Models (2) and (4) in Table 3 or Models (5)-(11) in Appendix Table C.
7
Models (12) through (18) are in Table 4 and Models (5) through (11) are in Appendix Table C.
We also estimated alternative models. For Hypothesis 1, we further estimated Models (19)-(22) in Appendix
Table D using weekly, instead of daily, data, including fixed industry sector effects, and with the three aforementioned
types of models. All those models show the same strong rising WFH trends after the SHO ended, consistent with Models
(1) through (4) using daily data presented in Table 3,
For Hypothesis 2, to check the robustness of our two-level mixed-effects models [Models (5) through (18)] that
tested Hypothesis 2, again we estimated a set of fixed-effects panel data models [Models (23) -(29) in Appendix Table E],
population-averaged generalized linear panel-data models with the GEE approach [Models (30)- (36) in Appendix Table
F], and population-averaged generalized linear panel-data models with the GEE approach with fixed industry sector
effects [Models (37)-(43) in Appendix Table G]. The positive business effects we found in our two-level mixed-effects
models [Models (5) through (18) 8] are basically the same as the population-averaged generalized linear panel-data models
with the GEE approach and fixed industry sector effects [Models (37) through (43) in Appendix Table G] and not
inconsistent with the other models as well.
The highly consistent effects across the 43 models indicate the robustness of our models. Also, among the fixed-
effects models, those testing Hypothesis 1 explained 33% to 43% of variability of WFH; those testing Hypothesis 2
explained lower variability (up to 12%) for small business performance measures because the relatively limited number of
observations with the weekly data. All those models have a statistically significant F statistics. The chi-square tests are
statistically significant for all the population-averaged generalized panel-data models with the GEE approach and two-
level mixed-effects models. The latter also have high log likelihoods and show significant difference from linear models
via the likelihood ration tests, indicating the advantage of controlling both state and industry sector level variations.
Discussion
Following Schumpeter (1934)’s “creative destruction” argument, although COVID-19 resulted a human health and
economic disaster, this destruction may result in some new creations, innovations, and creative ways to better utilize our
advances in high-tech communication platforms. This “creative destruction”, expedited by the painful COVID-crisis, may
have sped up our learning curve for using and accepting high-tech communication platforms as a norm; this could set a
more efficient and more cost-effective new course of production in the long run. The forced new WFH norm may have
8
Models (12) through (18) are in Table 4 and Models (5) through (11) are in Appendix Table C.
not only expedited WFH-ready firms to implement WFH practice more fully, but may also push other firms to creatively
find new solutions to utilizing the modern communication technology in any possible creative ways. Out of this
disruption, not only our health care system can be reborn mending many exposed weaknesses, the potential of WFH could
be more fully realized. A disruption from the traditional brick-&-mortar offices might result in a new hybrid or a WFH-
dominant new workplace setting. If the new WFH norm really emerges soon, our current human resource practice, real
estate industry, urban sprawling patterns, urban planning, racial segregation, city externalities would all await to be
transformed. This would have huge public policy implications.
More importantly and sadly, the rising WFH popularity would deepen the digital divide and widen the wealth gap.
Dingel & Neiman (2020) noted lower-income economies have a lower share of WFH jobs. Those who haves and have-
nots would be increasingly different, unless more and more jobs can be done via WFH. Otherwise the world would be
more polarized, like what education has divided us in the long human history: on the one hand, high skilled workers who
master digital skills are not only enjoy better pay, better work-life balance (Mas & Pallais 2017) and better control of
their schedules, but also better health with limited exposure to virus or bacteria; on the other hand, workers without digital
skills or digital access often conduct relatively low-paid jobs, remain a life demanded by their bosses’ schedules, and
more importantly, always at the front line to be exposed to any transmutable disease, virus, germs. Dingel & Neiman
(2020)’s contribution on teleworkable jobs offered the timely and critical contribution in the pandemic. When WFH really
becomes the new norm, we hope certain innovation can penetrate WFH better to currently non-teleworkable jobs
eventually. This requires entrepreneurship from often the nimble and creative small businesses.
The internet and globalization are double edged swards: they on the one hand reached out better to the poor with a
larger market, on the other hand made it easier for the large firms to sell and profit more. WFH would further make the
internet and globalization a necessity.
WFH itself is a double-edged sword as well. It not only brings the flexibility and a better work-family balance to
workers [c.f. Gajendran, et al (2007)], but also often blurs the boundaries between work and family (Riggoti et al. 2020).
There is also general managerial concern on control and surveillance for WFH workers (Coenen and Kok 2014), or a
career path concerns with limited in-person presence (Golden and Eddleston 2020), both related to an appropriate psycho-
sociological distance (Belanger, 1999; Taskin and Devos 2005; Wilton et al., 2011). Best practice human resources
policies need to be further discussed for a healthy and sustaining labor relations.
This paper used small business data because small business are often the most vulnerable in the crisis. It is not our
intention to compare the WFH effects for small businesses to that for larger businesses. Small businesses often do not
have as much resources as larger businesses to build robust WFH infrastructure (Vilhelmson and Thulin 2016), including
costs of organizational change and technological investments (Aguilera, et al. 2016). This could have limited some of our
evidence. Since we found positive productive role of WFH in small business performance, the impacts for larger
businesses could be even larger. Although we do not have data on business owners or decision making process, for the
timeliness and limitation of the data availability, this paper relies on the best available data that is publicly available and
well-represented to empirically test the WFH effects.
In this COVID-19 pandemic, social distancing is critical. Whether a small business can adjust its goods and
service to pickup/carry-out/delivery as their only means to serve customers shows how nimble and adaptive to change a
small business is. This could also be related WFH. We initially planned to also model WFH effects on this. However, it
is unclear what types of impact can be expected. Further analysis on this will need to be considered. In addition, fear
factor could affect economic recovery in the pandemic and its aftermath. Before the effective vaccine is found and
prevalent, this fear factor could affect the WFH trajectory. Further research is needed on that.
Conclusion
The study first builds a theoretical framework based on utility maximization theory subject to a “contagion”
agglomeration parameter and argues that WFH is a rational choice for small businesses. We then compiled an up-to-date
real-time daily and weekly multifaceted data set tracking WFH propensity from March 20 through July 28. Using this
data set, we estimated a variety of fixed-effects panel data models, population-averaged generalized linear panel-data
models with the GEE approach, and two-level mixed-effects panel-data models.
Our empirical findings are consistent with our initial expectation and also support the hypotheses drawn from our
theoretical framework. First, WFH has potential attractiveness for employers. In the pandemic, although WFH rate is
dramatically increased due to the COVID pandemic and the SHO mandate, after the SHO ended, WFH rate did not drop
and instead rose, after controlling for local pandemic, economic, and demographic conditions. This paper empirically
supports the idea that WFH could be the new norm.
With various economic and health advantages, WFH has been shown in this study to positively associate with
small business’ operating revenue increases, stronger cash flow positions, and reductions in temporary closure and in
supply chain disruption. These help mitigate the negative pandemic shock and suggest that a policy response include
provisions to promote teleworkable jobs and WFH.
More importantly, if this pandemic brings in major economic structure disruption, WFH could be the opportunity
for Schumpeterian “creative” innovation out of this disruption. As nimble and creative as small businesses have always
been, riding or even leading this WFH wave well would not only help small businesses survive better in the pandemic, it
might make them the vanguard of a new work paradigm. With public policy facilitating WFH with technology and
institution, this new potential may really happen.
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Tables and Figures
Table 1. Data Sources, Types, Time Periods, Measures for all Variables
Time
Variable Name Description Source Data Type
Period
WFH: Work From Home
Percentage of workforce working from home based on
3/21-7/28, Continuous
WFH UMD models. Calculated by MTI based on changes in MTI
daily (%)
work trips and unemployment claims.
AfterSHO: After Stay-Home Order Ended
3/21-7/28,
afterSHO The date is later than the state’s stay-home order end date IHME Dummy
daily
Business: Business Performance Measures
Percentage of businesses reported "increased" (+) or
4/26-6/27, Continuous
Opr Rev "decrease" (-) to the question "In the last week, did this SBPS
weekly (%)
business experience a change in operating revenues?"
Percentage of businesses reported "yes" (+) or "no" (-) to
4/26-6/27, Continuous
Tenp Closure the question "In the last week, did this business SBPS
weekly (%)
temporarily close any of its locations for at least one day?"
Percentage of businesses reported "yes" (+) or "no" (-) to
4/26-6/27, Continuous
Disrpt. Sup Chn the question "In the last week, did this business have SBPS
weekly (%)
disruptions in its supply chain?"
Percentage of businesses reported "No cash available for
business operations" to the question "How would you 4/26-6/27, Continuous
cashFlow0 SBPS
describe the current availability of cash on hand for this weekly (%)
business?"
Percentage of businesses reported "1-4 weeks of business
4/26-6/27, Continuous
cashFlow4w operations" to the question "How would you describe the SBPS
weekly (%)
current availability of cash on hand for this business?"
Percentage of businesses reported "1-2 months of business
4/26-6/27, Continuous
cashFlow2m operations" to the question "How would you describe the SBPS
weekly (%)
current availability of cash on hand for this business?"
Percentage of businesses reported "3 or more months of
business operations" to the question "How would you 4/26-6/27, Continuous
cashFlow3m+ SBPS
describe the current availability of cash on hand for this weekly (%)
business?"
COVID: COVID-19 Pandemic Severity
Number of COVID-19 daily new cases per 1000 people 3/20-7/28, Continuous
New Case / 1k CSSE
(three-day moving average). daily (0/000)
% deaths among all COVID-19 cases. Calculated by MTI
3/20-7/28, Continuous
Death Rt based on number of deaths and estimated total COVID CSSE
daily (%)
cases including confirmed and untested cases.
Number of residents already exposed to coronavirus per 3/20-7/28, Continuous
exposure / 1k MTI
1000 people. Calculated by MTI. daily (0/000)
Number of days with decreasing COVID-19 cases.
3/20-7/28,
Days Decr. Calculated by MTI based on weekly pattern of new daily MTI Continuous
daily
cases.
ECON: Economic Background
3/15-7/28, Continuous
Unemploy Rt Unemployment rate updated weekly. USDOL
weekly (%)
2018,
Median Inc. Median household income from the US Census Bureau ACS Continuous
yearly
Gross employment density (jobs per acre) on unprotected EPA 2013, one Continuous
Emp Density
land. SLD time (%)
DEMO: Demographics
2018, Continuous
% 60+ Percent of population above the age of 60. ACS
yearly (%)
2018, Continuous
% African Am. Percentage of African Americans. ACS
yearly (%)
2018, Continuous
% Hispanic Am. Percentage of Hispanic Americans. ACS
yearly (%)
2018, Continuous
% male Percentage of male. ACS
yearly (%)
FIN: Business Financial Assistance
Percentage of businesses reported "Paycheck Protection
Program (PPP)" to the question "Since March 13,2020, 4/26-6/27, Continuous
Fin_PPP SBPS
has this business requested financial assistance from any weekly (%)
of the following sources??"
Percentage of businesses reported "Economic Injury
Disaster Loans (EIDL)" to the question "Since March 4/26-6/27, Continuous
Fin_EIDL SBPS
13,2020, has this business requested financial assistance weekly (%)
from any of the following sources??"
Percentage of businesses reported "SBA Loan
Forgiveness" to the question "Since March 13,2020, has 4/26-6/27, Continuous
Fin_SBAlnForg SBPS
this business requested financial assistance from any of weekly (%)
the following sources??"
Percentage of businesses reported "Other Federal
Programs" to the question "Since March 13,2020, has this 4/26-6/27, Continuous
Fin_OtherFed SBPS
business requested financial assistance from any of the weekly (%)
following sources??"
Percentage of businesses reported "State or Local
Government" to the question "Since March 13,2020, has 4/26-6/27, Continuous
Fin_StLocGov SBPS
this business requested financial assistance from any of weekly (%)
the following sources??"
Percentage of businesses reported "Banks" to the question
4/26-6/27, Continuous
Fin_Banks "Since March 13,2020, has this business requested SBPS
weekly (%)
financial assistance from any of the following sources??"
Percentage of businesses reported "Self" to the question
4/26-6/27, Continuous
Fin_Self "Since March 13,2020, has this business requested SBPS
weekly (%)
financial assistance from any of the following sources??"
Percentage of businesses reported "Family or Friends" to
the question "Since March 13,2020, has this business 4/26-6/27, Continuous
Fin_FamFriend SBPS
requested financial assistance from any of the following weekly (%)
sources??"
Percentage of businesses reported "Other" to the question
4/26-6/27, Continuous
Fin_Other "Since March 13,2020, has this business requested SBPS
weekly (%)
financial assistance from any of the following sources??"
Table 2. Descriptive Statistics for Daily Data
Variable Obs Mean Std. Dev. Min Max
WFH
WFH 4,551 0.26674 0.09349 0.048 0.557
Date
Date 4,551 22062.9 35.6531 21995 22124
afterSHO 4,552 0.56305 0.49606 0 1
COVID
New Case / 1k (t-1) 4,551 0.1216 0.16573 0 1.007
Death Rt (t-1) 4,551 0.01737 0.00817 0.0032 0.0458
Exposure / 1k (t-1) 4,551 11.5198 12.1186 0.48 52.03
Days Decr. (t-1) 4,551 3.57064 6.49126 0 44
ECON
Unemploy Rt (t-1) 4,551 0.21547 0.07449 0.081 0.444
Median Inc. (t-1) 4,551 62176.3 10649.5 44445 84342
Emp Density (t-1) 4,551 511.443 2569.62 1 16044
Demographics
% 60+ (t-1) 4,551 0.22194 0.02325 0.17 0.27
% African Am. (t-1) 4,551 0.12306 0.11018 0.004 0.461
% Hispanic Am. (t-1) 4,551 0.10943 0.08692 0.015 0.392
% male (t-1) 4,551 0.49291 0.00803 0.4746 0.5221
Figure 1. Trend of WFH, COVID severity, Unemployment, March 21-July 28, 2020
Table 3. Empirical Models for the End of SHO Effect on WFH Rates
Model (1) Model (2) Model (3) Model (4)
GEE Population- GEE Population-
Dependent averaged Generalized averaged Generalized
Variable: Fixed-effects Panel Fixed-effects Panel Linear Panel Data Linear Panel Data
WFH Rates Data Model Data Model Model Model
Std. Std. Std.
Coef. Err. Coef. Err. Coef. Err. Coef. Std. Err.
Independent Variable
afterSHO (t-1) 0.0054 0.0012 *** 0.0176 0.0009 *** 0.0054 0.0012 *** 0.0176 0.0009 ***
Control Variable: Time Effects
Date 0.0003 0.0000 *** 0.0003 0.0000 ***
Control Variables: COVID: COVID-19 Pandemic Severity
New Case / 1k (t-1) 0.0217 0.0036 *** 0.0252 0.0037 *** 0.0223 0.0036 *** 0.0259 0.0037 ***
Death Rt (t-1) -0.7573 0.0965 *** -0.5998 0.0982 *** -0.7231 0.0949 *** -0.5645 0.0967 ***
exposure / 1k (t-1) -0.0001 0.0001 * 0.0004 0.0000 *** -0.0001 0.0001 ** 0.0004 0.0001 ***
Days Decr. (t-1) -0.0001 0.0001 -0.0002 0.0000 *** -0.0001 0.0001 -0.0002 0.0001 ***
Control Variables: ECON: Economic Background
Unemploy Rt (t-1) -0.8093 0.0079 *** -0.7948 0.0080 *** -0.8102 0.0077 *** -0.7959 0.0079 ***
Median Inc. (t-1) (omitted) (omitted) 0.0000 0.0000 *** 0.0000 0.0000 ***
Emp Density (t-1) (omitted) (omitted) 0.0000 0.0000 *** 0.0000 0.0000 ***
Industry
Control Variables: DEMO: Demographics
% 60+ (t-1) (omitted) (omitted) 0.0236 0.4785 0.0720 0.4651
% African Am. (t-
1) (omitted) (omitted) -0.0819 0.1227 -0.0942 0.1193
% Hispanic Am. (t-
1) (omitted) (omitted) 0.2746 0.0853 *** 0.2580 0.0829 ***
% male (t-1) (omitted) (omitted) -4.0208 1.5873 ** -3.7291 1.5430 **
Constant, Random Error, or Random Effect
Constant -6.2795 0.4603 *** 0.4314 0.0018 *** -4.4465 0.9833 *** 2.0800 0.8533 **
sigma_u 0.0710 sigma_u 0.0685
Random Error or sigma_e 0.0212 sigma_e 0.0217
Random Effects rho 0.9184 rho 0.9092
Diagnostics
F test that all F(36, (36,
u_i=0: 4507) 838.97 *** 4508) 795.73
# of Obs # obs 4551 # obs 4551 # obs 4551 # obs 4551
# #
# of Groups # groups 37 # groups 37 groups 37 groups 37
Within 0.8521 Within 0.8451 Link: identity Link: identity
R-Squared B/w 0.1657 B/w 0.2121 Family: Gaussian Family: Gaussian
Overall 0.3938 Overall 0.4274 Corr exchangeable Corr: exchangeable
Wald Wald
F or Wald Chi2 F(7,4507) 3708 *** F(6,4508) 4099 *** chi2(13) 26828 *** chi2(12) 25326 ***
corr(u_i, corr(u_i, Scale Scale
Other Stat Xb) -0.082 Xb) -0.036 Param.: 0.0020 Param.: 0.0020
Figure 2. Marginal Effect of the End of SHO on WFH based on Model (4)
Table 4. WFH Effects on Small Business Performance with Financial Assistance, Multilevel Mixed-effects Models (12)-(18)
Increase
Cash Flow foe 1-4 Cash Flow for 1-2 Cash Flow for 3+ Operating Temporary Disruptino in
No Cash FLow Weeks Months Months Revenue Closure Supply Chain
Model (12) Model (13) Model (14) Model (15) Model (16) Model (17) Model (18)
Coef St. Coef St. Coef St. Coef St. Coef St. Coef St. Coef
. Er. . Er. . Er. . Er. . Er. . Er. . St. Er.
WFH: Work From Home
WFH (t-1) -0.01 0.01 0.14 0.06 ** 0.45 0.09 *** 0.35 0.08 *** 0.61 0.15 *** -0.75 0.18 *** -0.39 0.18 **
Time Effects
- ** ** - ** - 0.0 **
afterSHO (t-1) 0.00 0.00 * 0.03 0.00 * 0.00 0.01 0.01 0.01 ** 0.23 0.01 * 0.24 0.01 * 0.10 1 *
COVID: COVID-19 Pandemic Severity
** - - ** ** 0.1
New Case / 1k (t-1) 0.03 0.00 * 0.06 0.04 0.12 0.06 * 0.09 0.06 0.45 0.11 * 0.43 0.13 * 0.29 3 **
- ** ** 1.1 **
Death Rt (t-1) 0.06 0.04 0.79 0.37 ** 0.91 0.55 * 1.09 0.50 ** 9.72 0.97 * 8.64 1.14 * 4.86 4 *
** ** ** ** 0.0
exposure / 1k (t-1) 0.00 0.00 ** 0.00 0.00 * 0.00 0.00 * 0.00 0.00 * 0.01 0.00 * 0.00 0.00 ** 0.00 0
** ** ** ** 0.0
Days Decr. (t-1) 0.00 0.00 0.00 0.00 * 0.00 0.00 * 0.00 0.00 * 0.00 0.00 * 0.00 0.00 * 0.00 0
ECON: Economic Background
- ** ** ** - ** - 0.1 **
Unemploy Rt (t-1) 0.01 0.01 ** 0.02 0.06 0.39 0.09 * 0.44 0.08 * 1.46 0.16 * 0.93 0.19 * 1.01 9 *
0.0
Median Inc. (t-1) 0.00 0.00 * 0.00 0.00 0.00 0.00 0.00 0.00 ** 0.00 0.00 ** 0.00 0.00 ** 0.00 0
** ** ** 0.0
Emp Density (t-1) 0.00 0.00 0.00 0.00 * 0.00 0.00 * 0.00 0.00 * 0.00 0.00 * 0.00 0.00 * 0.00 0
DEMO: Demographics
- ** - ** - ** ** 0.4
% 60+ (t-1) 0.02 0.02 0.43 0.13 * 1.29 0.20 * 1.11 0.18 * 0.84 0.35 ** 1.49 0.41 * 0.51 2
- - ** - ** - ** - ** ** 0.1
% African Am. (t-1) 0.01 0.00 0.11 0.04 * 0.19 0.06 * 0.29 0.06 * 0.32 0.11 * 0.39 0.12 * 0.26 3 **
** ** ** - ** ** 0.0
% Hispanic Am. (t-1) 0.00 0.00 0.19 0.03 * 0.19 0.04 * 0.16 0.04 * 0.75 0.07 * 0.60 0.09 * 0.23 9 **
- ** - ** - ** 2.2
% male (t-1) 0.06 0.08 4.15 0.72 * 6.94 1.06 * 6.00 0.98 * 3.81 1.88 ** 2.38 2.20 4.37 2 **
FIN: Business Finanical Assistance
** ** - ** - ** - 0.0 **
Fin_PPP 0.00 0.00 0.01 0.01 0.06 0.01 * 0.06 0.01 * 0.14 0.02 * 0.12 0.02 * 0.08 2 *
** ** ** - ** - 0.0
Fin_EIDL 0.00 0.00 0.13 0.01 * 0.31 0.02 * 0.14 0.02 * 0.11 0.03 * 0.02 0.04 0.05 4
** ** 0.1
Fin_SBAlnForg 0.02 0.01 * 0.43 0.05 * 0.08 0.07 0.02 0.06 0.30 0.12 ** 0.16 0.14 0.10 4
- - 0.8
Fin_OtherFed 0.05 0.03 0.16 0.28 0.13 0.42 0.18 0.39 0.53 0.75 0.05 0.87 0.64 8
** - - - - 0.1
Fin_StLocGov 0.02 0.01 * 0.02 0.06 0.09 0.09 0.12 0.08 0.04 0.15 0.43 0.18 ** 0.07 8
** ** - ** 0.1
Fin_Banks 0.03 0.01 * 0.48 0.06 * 0.13 0.09 0.13 0.08 0.13 0.16 0.54 0.19 * 0.06 9
** ** 0.1
Fin_Self 0.01 0.00 ** 0.33 0.04 * 0.14 0.06 ** 0.11 0.05 ** 0.15 0.10 0.34 0.12 * 0.08 2
** - - - 0.6
Fin_FamFriend 0.33 0.02 * 0.22 0.22 0.60 0.32 * 0.73 0.29 ** 0.05 0.57 0.47 0.66 0.09 7
- - - - - 0.7
Fin_Other 0.02 0.03 0.02 0.23 0.02 0.35 0.37 0.32 0.02 0.62 0.28 0.72 0.15 3
Constant & Model Diagnostics
- ** ** ** - ** - - 1.1
Constant 0.03 0.04 2.14 0.37 * 3.54 0.55 * 2.99 0.51 * 2.55 0.98 * 1.92 1.15 * 2.30 5 **
St. St. St. St. St. St. St.
Random-effects Parameters Est. Er. Est. Er. Est. Er. Est. Er. Est. Er. Est. Er. Est. Er.
NAICS Identity
0.0
sd(_cons) 0.00 0.00 ** 0.04 ** ## 0.07 0.01 ** 0.08 0.02 ** 0.06 0.01 ** 0.28 0.05 ** 0.30 5 **
0.0
sd(Residual) 0.01 0.00 ** 0.09 ** ## 0.13 0.00 ** 0.12 0.00 ** 0.24 0.00 ** 0.28 0.00 ** 0.28 0 **
LR test vs. linear ** ** ** ** ** ** **
model:chibar2(01) 9 * 424 * 570 * 901 * 122 * 1371 * 1651 *
Number of obs 2909 2909 2909 2909 2909 2909 2909
Number of groups 17 17 17 17 17 17 17
Obs per Group, min 5 5 5 5 5 5 5
Obs per Group, ave 171 171 171 171 171 171 171
Obs per Group, max 285 285 285 285 285 285 285
151 104 115 105
Wald chi2(12) 488 *** 0 8 *** 0 9 *** 0 617 *** 0 7 *** 0 7 *** 0 171 *** 0
Log likelihood 9147 2837 1694 1929 25 -441 -465
Figure 3 WFH Rate Effects on Small Business’ Cash Flow, Based on Models (12)-(15)
No Cash Flow Cash Flow for 1-4 Weeks
Cash Flow for 1-2 Months Cash Flow for 1-4 Weeks
Note: This graph omitted observations for WFH rate below 3% and above 50% (i.e., omitting two tails at 2% and 51-56%)
because those observation only represent 0.7% of the observations, but have a much larger and more dramatic effect from
WFH rates. Presenting those in the graph will visually inflate the WFH effects.
Figure 4. WFH Effects on Small Business’ Operating Revenue Increase, Based on Model (16)
For WFH Rate between 3-50% (99.3% of observation) For All WFH Rates (2-56%)
Figure 5 WFH Rate Effects on Small Business’ Temporary Closure, Based on Model (17)
For WFH Rate between 3-50% (99.3% of observation) For All WFH Rates (2-56%)
Figure 6 WFH Rate Effects on Small Business’ Disruption in Supply Chain, Based on Model (18)
For WFH Rate between 3-50% (99.3% of observation) For All WFH Rates (2-56%)
Appendix
Table A. Correlation Matrix for the Daily Data
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 WFH 1.00
2 Date 0.06 1.00
3 afterSHO -0.06 0.79 1.00
4 New Case / 1k (t-1) 0.35 0.37 0.21 1.00
5 Death Rt (t-1) 0.01 0.10 0.04 -0.24 1.00
6 exposure / 1k (t-1) 0.37 0.55 0.35 0.62 0.29 1.00
7 Days Decr. (t-1) -0.10 0.11 0.10 -0.07 0.28 0.27 1.00
8 Unemploy Rt (t-1) -0.65 0.10 0.14 -0.30 0.44 -0.04 0.24 1.00
9 Median Inc. (t-1) 0.35 -0.02 -0.15 -0.07 0.10 0.17 0.09 0.00 1.00
10 Emp Density (t-1) 0.48 0.00 -0.03 0.05 0.06 0.19 -0.04 -0.07 0.33 1.00
11 % 60+ (t-1) -0.21 0.00 -0.06 -0.11 0.03 -0.16 0.10 0.02 -0.35 -0.37 1.00
% African Am. (t-
12 1) 0.26 0.02 0.04 0.26 0.12 0.34 -0.07 -0.01 -0.01 0.51 -0.35 1.00
% Hispanic Am. (t-
13 1) 0.22 0.00 0.00 0.14 -0.03 0.21 0.03 0.08 0.18 0.01 -0.35 -0.09 1
14 % male (t-1) -0.37 -0.01 0.04 -0.17 -0.26 -0.39 -0.04 0.10 0.10 -0.39 -0.17 -0.70 0.13 1
Figure A. Trend of WFH, COVID severity, Unemployment by Date and State
Table B. Summary Statistics of the Weekly Data
Variable Obs Mean Std. Dev. Min Max
WFH: Work From Home
WFH 687 0.270 0.092 0.048 0.557
WFH (t-1) 687 0.268 0.092 0.048 0.557
Business: Business Performance Measures
cashFlow0 333 0.021 0.027 0.000 0.119
cashFlow4w 333 0.312 0.087 0.000 0.526
cashFlow2m 333 0.291 0.041 0.143 0.426
cashFlow3m+ 333 0.228 0.054 0.000 0.415
Opr Rev 333 -0.400 0.180 -0.811 -0.052
Tenp Closure 333 -0.464 0.219 -0.863 0.290
Disrpt. Sup Chn 333 -0.239 0.120 -0.624 0.078
Time Effects
afterSHO 687 0.568 0.495 0.000 1.000
COVID: COVID-19 Pandemic Severity
New Case / 1k (t-1) 687 0.115 0.158 0.000 1.007
Death Rt (t-1) 687 0.017 0.008 0.004 0.045
Exposure / 1k (t-1) 687 10.66 11.71 0.480 52.03
Days Decr. (t-1) 687 3.267 6.120 0.000 44.000
ECON: Economic Background
Unemploy Rt (t-1) 687 0.211 0.074 0.081 0.444
Median Inc. (t-1) 687 62171 10659 44445 84342
Emp Density (t-1) 687 506 2553 1 16044
DEMO: Demographics
% 60+ (t-1) 687 0.222 0.023 0.170 0.270
% African Am. (t-1) 687 0.123 0.110 0.004 0.461
% Hispanic Am. (t-1) 687 0.109 0.087 0.015 0.392
% male (t-1) 687 0.493 0.008 0.475 0.522
FIN: Business Financial Assistance
Fin_PPP 333 0.743 0.047 0.551 0.879
Fin_EIDL 333 0.276 0.047 0.125 0.424
Fin_SBAlnForg 333 0.087 0.042 0.000 0.203
Fin_OtherFed 333 0.009 0.013 0.000 0.047
Fin_StLocGov 333 0.045 0.061 0.000 0.317
Fin_Banks 333 0.063 0.038 0.000 0.158
Fin_Self 333 0.096 0.042 0.000 0.193
Fin_FamFriend 333 0.022 0.023 0.000 0.143
Fin_Other 333 0.020 0.021 0.000 0.104
Table C. WFH Effects on Small Business Performance, Multilevel Mixed-effects Models
Increase
Dependent Cash Flow foe 1-4 Cash Flow for 1-2 Cash Flow for 3+ Operating Temporary Disruption in
Variables: No Cash Flow Weeks Months Months Revenue Closure Supply Chain
Model (5) Model (6) Model (7) Model 8) Model (9) Model (10) Model (11)
St. St. St. St. St. St. St.
Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er.
Independent Variable: WFH: Work From Home
WFH (t-1) -0.01 0.01 0.18 0.06 *** 0.54 0.09 *** 0.38 0.08 *** 0.59 0.16 *** -0.94 0.18 *** -0.50 0.18 ***
Control Variable: Time Effects
afterSHO (t-1) 0.00 0.00 *** -0.04 0.00 *** -0.01 0.01 ** 0.00 0.01 0.23 0.01 *** -0.23 0.01 *** -0.10 0.01 ***
Control Variables: COVID: COVID-19 Pandemic Severity
New Case / 1k (t-
1) 0.02 0.00 *** 0.06 0.05 -0.16 0.06 ** 0.02 0.06 -0.26 0.11 ** 0.22 0.13 * 0.17 0.13
-
Death Rt (t-1) 0.09 0.05 * 1.93 0.42 *** 2.03 0.59 *** 1.74 0.53 *** 10.32 1.01 *** 10.45 1.18 *** 5.20 1.17 ***
exposure / 1k (t-
1) 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.01 0.00 *** 0.00 0.00 *** 0.00 0.00
Days Decr. (t-1) 0.00 0.00 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 * 0.00 0.00
Control Variables: ECON: Economic Background
Unemploy Rt (t-
1) -0.01 0.01 * 0.04 0.07 0.43 0.10 *** 0.46 0.09 *** 1.50 0.17 *** -1.17 0.19 *** -1.14 0.19 ***
Median Inc. (t-1) 0.00 0.00 0.00 0.00 0.00 0.00 * 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00
Emp Density (t-1) 0.00 0.00 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00
Control Variables: DEMO: Demographics
% 60+ (t-1) 0.01 0.02 -0.69 0.15 *** -1.58 0.21 *** -1.33 0.18 *** 0.81 0.35 ** 1.88 0.41 *** 0.76 0.41 *
% African Am. (t-
1) -0.01 0.00 -0.19 0.04 *** -0.26 0.06 *** -0.34 0.06 *** -0.31 0.11 *** 0.42 0.13 *** 0.32 0.12 **
% Hispanic Am.
(t-1) 0.01 0.00 *** 0.42 0.03 *** 0.42 0.04 *** 0.27 0.04 *** -0.81 0.07 *** 0.77 0.09 *** 0.24 0.09 ***
-
% male (t-1) -0.04 0.09 -7.25 0.78 *** 10.30 1.11 *** -7.98 0.99 *** 4.77 1.89 ** 2.09 2.20 5.64 2.19 ***
Constant & Model Diagnostics
Constant 0.02 0.04 3.68 0.40 *** 5.23 0.58 *** 4.02 0.51 *** -3.10 0.98 *** -1.95 1.14 * -3.00 1.14 ***
Random-effects St. St. St. St. St. St. St.
Parameters: Est. Er. Est. Er. Est. Er. Est. Er. Est. Er. Est. Er. Est. Er.
NAICS industry Identity
sd(_cons) 0.00 0.00 ** 0.07 0.01 ** 0.10 0.02 ** 0.08 0.02 ** 0.06 0.02 ** 0.28 0.05 ** 0.28 0.05 **
sd(Residual) 0.01 0.00 ** 0.10 0.00 ** 0.14 0.00 ** 0.13 0.00 ** 0.24 0.00 ** 0.28 0.00 ** 0.28 0.00 **
LR test vs. linear
model:chibar2(01) 27.27 *** 694.63 *** 779.48 *** 802.1 *** 118.48 *** 1404.83 *** 2043.56 ***
Number of obs 2909 2909 2909 2909 2909 2909 2909
Number of groups 17 17 17 17 17 17 17
Obs per Group,
min 5 5 5 5 5 5 5
Obs per Group,
ave 171 171 171 171 171 171 171
Obs per Group,
max 285 285 285 285 285 285 285
Wald chi2(12) 124 *** 0 726 *** 0 597 *** 0 441 *** 0 1014 *** 0 933 *** 0 155 *** 0
Log likelihood 8983 2548 1515 1854 -27 -487 -473
Table D. Alternative Models for the End of SHO Effect on WFH
Model (19) Model (20) Model (21) Model (22)
GEE Population- GEE Population-
averaged Generalized averaged Generalized
Fixed-effects Panel Linear Panel Data Linear Panel Data
Data Model Model Model Multilevel Mixed-effects Model
Std.
Coef. Std. Err. Coef. Err. Coef. Std. Err. Coef. Std. Err.
Time Effects
Date
afterSHO
(t-1) 0.030 0.004 *** 0.030 0.004 *** 0.007 0.001 *** 0.023 0.001 ***
COVID: COVID-19 Pandemic Severity
New Case /
1k (t-1) 0.025 0.014 * 0.034 0.014 ** 0.060 0.011 *** 0.048 0.013 ***
Death Rt
(t-1) -1.089 0.370 *** -0.607 0.354 * 0.613 0.165 *** 4.154 0.093 ***
exposure /
1k (t-1) 0.001 0.000 ** 0.001 0.000 ** 0.002 0.000 *** -0.001 0.000 ***
Days Decr.
(t-1) 0.000 0.000 * 0.000 0.000 * 0.000 0.000 *** 0.000 0.000 **
ECON: Economic Background
Unemploy
Rt (t-1) -0.702 0.031 *** -0.717 0.031 *** -0.743 0.021 *** -0.875 0.012 ***
Median Inc.
(t-1) (omitted) 0.000 0.000 *** 0.000 0.000 *** 0.000 0.000 ***
Emp
Density (t-
1) (omitted) 0.000 0.000 ***0.000 0.000 *** 0.000 0.000 ***
Industry Yes
DEMO: Demographics
% 60+ (t-1) (omitted) 0.026 0.466 0.142 0.125 0.083 0.043 *
% African
Am. (t-1) (omitted) -0.123 0.120 -0.038 0.035 -0.021 0.013
% Hispanic
Am. (t-1) (omitted) 0.247 0.083 *** 0.211 0.020 *** 0.289 0.007 ***
% male (t-
1) (omitted) -4.044 1.555 *** -0.480 0.564 -1.686 0.227 ***
Constant, Error Terms, or Random Effect
Constant,
Error
Terms, or
Random
Effect 0.411 0.006 *** 2.225 0.859 *** 0.459 0.298 0.960 0.117 ***
Random-
Random effects
Errors or sigma_u 0.070 Param. Estimate Std. Err.
Random sigma_e 0.032 NAICS: Identity
Effects rho 0.828 sd(cons) 0.001 0.001 **
sd(Resi.l) 0.030 0.000 **
Diagnostics
LR test
F test that F(36, vs. linear
all u_i=0: 644) 58 *** model: chi2(01) 0.070
# of Obs # obs 687 # obs 687 # obs 2909 # obs 2909
# #
# of Groups # groups 37 groups 37 groups 414 # groups 17
Obs per
R2 Group,
Within 0.68 Link: identity Link: identity min 5
Obs per
R-Squared Group,
B/w 0.16 Family: Gaussian Family: Gaussian ave 171
Obs per
R2 Group,
Overall 0.33 Corr: exchangeable Corr: exchangeable max 285
F or Wald Wald Wald Wald
Chi2 F(6,644) 226 *** chi2(28) 1479 *** chi2(28) 2297 *** chi2(12) 13545 ***
corr(u_i, - Scale Scale Log
Other Stat Xb) 0.057 Param.: 0.002 Param.: 0.001 likelih. 6111
Models (19) and (20) followed the design of Models (2) and (4), i.e., using respectively fixed-effects models and
population-averaged generalized linear panel-data models with the GEE approach. Model (21) followed Model
(20), but added the industry sector fixed effects in. Model (22) adopted the two-level mixed-effects model
controlling correlations at the both the state and industry sector levels.
Table E. WFH Effects on Small Business Performance, Fixed-effect Panel Data Models
Cash Flow foe 1-4 Cash Flow for 1-2 Cash Flow for 3+ Increase Operating Disruption in Supply
No Cash Flow Weeks Months Months Revenue Temporary Closure Chain
Model (23) Model (24) Model (25) Model (26) Model (27) Model (28) Model (29)
Coef. St. Er. Coef. St. Er. Coef. St. Er. Coef. St. Er. Coef. St. Er. Coef. St. Er. Coef. St. Er.
WFH: Work From Home
WFH (t-1) -0.01 0.05 0.07 0.16 -0.13 0.10 0.03 0.11 0.54 0.23 ** -0.47 0.27 * -0.24 0.23
Time Effects
afterSHO
(t-1) -0.01 0.00 *** -0.02 0.01 ** 0.00 0.01 0.02 0.01 *** 0.09 0.01 *** -0.08 0.02 *** -0.04 0.01 **
COVID: COVID-19 Pandemic Severity
New Case /
1k (t-1) 0.01 0.02 0.13 0.07 * -0.04 0.05 0.02 0.05 0.19 0.11 * -0.33 0.12 *** 0.02 0.11
Death Rt
(t-1) -0.63 0.45 -0.04 1.43 1.33 0.93 -1.55 0.97 4.55 2.08 ** -5.42 2.38 ** -0.21 2.08
exposure /
1k (t-1) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ** 0.01 0.00 *** -0.01 0.00 *** -0.01 0.00 ***
Days Decr.
(t-1) 0.00 0.00 0.00 0.00 ** 0.00 0.00 ** 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
ECON: Economic Background
Unemploy
Rt (t-1) -0.31 0.07 *** -0.99 0.21 *** 0.37 0.13 *** 0.88 0.14 *** 4.01 0.30 *** -3.99 0.34 *** -2.24 0.30 ***
Median
Inc. (t-1) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted)
Emp
Density (t-
1) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted)
DEMO: Demographics
% 60+ (t-1) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted)
% African
Am. (t-1) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted)
% Hispanic
Am. (t-1) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted)
% male (t-
1) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted) (omitted)
Constant & Model Diagnostics
-
Constant 0.12 0.03 *** 0.55 0.08 *** 0.20 0.05 *** 0.00 0.06 1.77 0.12 *** 0.90 0.14 *** 0.46 0.12 ***
sigma_u 0.03 0.08 0.04 0.06 0.29 0.36 0.15
Page 43 of 47
sigma_e 0.02 0.05 0.03 0.04 0.08 0.09 0.08
rho 0.72 0.69 0.57 0.71 0.93 0.94 0.78
F test that
all u_i=0:
F(36, 289) 6.2 *** 9.02 *** 3.13 *** 6.07 *** 10.38 *** 19.7 *** 5.14 ***
Number of
obs 333 333 333 333 333 333 333
Number of
groups 37 37 37 37 37 37 37
R-Sq
Within 0.41 0.37 0.21 0.52 0.82 0.76 0.58
R-Sq
Bwtween 0.04 0.01 0.04 0.03 0.31 0.42 0.01
R-Sq
Overall 0.04 0.08 0.01 0.12 0.08 0.00 0.12
F(7,4507) 29 *** 24 *** 11 *** 45 *** 183 *** 133 *** 58 ***
corr(u_i,
Xb) -0.64 -0.56 -0.80 -0.73 -0.83 -0.82 -0.81
Table F. WFH Effects on Small Business Performa, population-averaged generalized linear panel-data models with the GEE approach
Increase
Cash Flow foe 1-4 Cash Flow for 1-2 Cash Flow for 3+ Operating Disruption in
No Cash Flow Weeks Months Months Revenue Temporary Closure Supply Chain
Model (30) Model (31) Model (32) Model (33) Model (34) Model (35) Model (36)
St. St. St. St. St. St. St.
Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er.
WFH: Work From Home
WFH (t-1) 0.02 0.04 0.08 0.12 0.01 0.07 0.22 0.08 ** 0.50 0.22 ** -0.39 0.26 -0.36 0.20 *
Time Effects
afterSHO (t-1) -0.02 0.00 *** -0.04 0.01 *** 0.02 0.01 *** 0.05 0.01 *** 0.10 0.01 *** -0.10 0.02 *** -0.08 0.01 ***
COVID: COVID-19 Pandemic Severity
New Case / 1k
(t-1) 0.03 0.02 0.11 0.07 -0.09 0.04 ** -0.03 0.05 0.14 0.11 -0.26 0.12 ** 0.14 0.10
Death Rt (t-1) 0.77 0.26 *** 1.56 0.89 * 0.36 0.50 -1.89 0.62 *** 2.33 1.94 -2.59 2.23 3.91 1.53 ***
Page 44 of 47
exposure / 1k
(t-1) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 *** -0.01 0.00 *** 0.00 0.00 **
Days Decr. (t-
1) 0.00 0.00 * 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 * 0.00 0.00 0.00 0.00 0.00 0.00
ECON: Economic Background
Unemploy Rt
(t-1) -0.11 0.04 *** -0.54 0.14 *** 0.14 0.08 * 0.62 0.10 *** 3.72 0.28 *** -3.68 0.33 *** -1.56 0.23 ***
Median Inc.
(t-1) 0.00 0.00 0.00 0.00 *** 0.00 0.00 ** 0.00 0.00 0.00 0.00 * 0.00 0.00 ** 0.00 0.00
Emp Density
(t-1) 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
DEMO: Demographics
% 60+ (t-1) 0.11 0.11 0.01 0.46 -0.21 0.20 -0.60 0.32 * -3.34 2.75 4.75 3.32 1.08 0.96
% African Am.
(t-1) 0.08 0.03 *** 0.19 0.11 * -0.08 0.05 -0.25 0.08 *** -1.05 0.70 1.09 0.85 0.36 0.24
% Hispanic
Am. (t-1) 0.10 0.02 *** 0.05 0.09 0.04 0.04 -0.14 0.06 ** -0.90 0.49 * 1.01 0.59 * 0.16 0.17
% male (t-1) 0.54 0.45 0.56 1.78 -0.89 0.80 -1.79 1.24 -5.05 9.46 3.34 11.40 2.08 3.63
Constant & Model Diagnostics
Constant -0.29 0.24 0.28 0.96 0.68 0.43 1.05 0.67 2.28 5.20 -2.92 6.27 -1.13 1.96
Number of
obs 333 333 333 333 333 333 333
Number of
groups 37 37 37 37 37 37 37
Link: identity identity identity identity identity identity identity
Family: Gaussian Gaussian Gaussian Gaussian Gaussian Gaussian Gaussian
Correlation: exchangeable exchangeable exchangeable exchangeable exchangeable exchangeable exchangeable
Wald chi2(13) 254 *** 0 221 *** 0 57 *** 0 256 *** 0 1254 *** 0 906 *** 0 321 *** 0
Scale
parameter: 0.00 0.00 0.00 0.00 0.06 0.08 0.01
Page 45 of 47
Table G. WFH Effects on Small Business Performa, population-averaged generalized linear panel-data models with the GEE approach, with
Industry Sector Fixed Effects
Increase
Cash Flow foe 1-4 Cash Flow for 1-2 Cash Flow for 3+ Operating Temporary Disruption in
No Cash Flow Weeks Months Months Revenue Closure Supply Chain
Model (37) Model (38) Model (39) Model (40) Model (41) Model (42) Model (43)
St. St. St. St. St. St.
Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. Er. Coef. St. Er.
WFH: Work From Home
WFH (t-1) 0.00 0.01 0.11 0.07 * 0.34 0.10 *** 0.20 0.09 ** 0.63 0.17 *** -1.04 0.20 *** -0.55 0.19 ***
Time Effects
afterSHO (t-1) 0.00 0.00 *** -0.03 0.00 *** 0.00 0.01 0.02 0.01 *** 0.21 0.01 *** -0.22 0.01 *** -0.10 0.01 ***
COVID: COVID-19 Pandemic Severity
New Case / 1k
(t-1) 0.02 0.01 *** 0.13 0.04 *** -0.12 0.06 ** 0.08 0.05 -0.25 0.11 ** 0.26 0.13 ** 0.22 0.13 *
-
Death Rt (t-1) 0.11 0.05 ** 2.21 0.49 *** 2.15 0.70 *** 1.34 0.63 ** 13.17 1.17 *** 11.92 1.34 *** 5.73 1.24 ***
exposure / 1k
(t-1) 0.00 0.00 ** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.01 0.00 *** 0.00 0.00 0.00 0.00
Days Decr. (t-
1) 0.00 0.00 ** 0.00 0.00 *** 0.00 0.00 0.00 0.00 *** 0.00 0.00 ** 0.00 0.00 0.00 0.00
ECON: Economic Background
Unemploy Rt
(t-1) -0.02 0.01 ** -0.11 0.08 0.34 0.11 *** 0.55 0.10 *** 2.01 0.19 *** -1.69 0.22 *** -1.27 0.20 ***
Median Inc.
(t-1) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00
Emp Density
(t-1) 0.00 0.00 0.00 0.00 *** 0.00 0.00 *** 0.00 0.00 ** 0.00 0.00 ** 0.00 0.00 *** 0.00 0.00
Industry Yes Yes Yes Yes Yes Yes Yes
DEMO: Demographics
% 60+ (t-1) 0.02 0.02 -0.55 0.27 ** -1.59 0.37 *** -1.47 0.33 *** 0.61 0.53 2.57 0.58 *** 0.80 0.47 *
% African Am.
(t-1) -0.01 0.01 -0.14 0.08 * -0.25 0.10 ** -0.40 0.09 *** -0.38 0.15 ** 0.56 0.17 *** 0.32 0.14 **
% Hispanic
Am. (t-1) 0.01 0.00 ** 0.41 0.05 *** 0.44 0.06 *** 0.25 0.06 *** -0.95 0.10 *** 0.85 0.11 *** 0.27 0.09 ***
% male (t-1) -0.01 0.11 -5.55 1.31 *** -8.89 1.79 *** -7.90 1.60 *** 5.04 2.66 * 4.18 2.93 5.33 2.45 **
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Constant & Model Diagnostics
Constant 0.00 0.05 2.74 0.68 *** 4.42 0.93 *** 4.11 0.84 *** -3.37 1.39 ** -3.14 1.53 ** -3.09 1.27 **
Number of
obs 2909 2909 2909 2909 2909 2909 2909
Number of
groups 414 414 414 414 414 414 414
Link: identity identity identity identity identity identity identity
Family: Gaussian Gaussian Gaussian Gaussian Gaussian Gaussian Gaussian
Correlation: exchangeable exchangeable exchangeable exchangeable exchangeable exchangeable exchangeable
Wald chi2(13) 142 *** 0 461 *** 0 394 *** 0 428 *** 0 1241 *** 0 1819 *** 0 2603 *** 0
Scale
parameter: 0.00 0.01 0.02 0.02 0.06 0.08 0.08
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Figures
Figure 1
Trend of WFH, COVID severity, Unemployment, March 21-July 28, 2020
Figure 2
Marginal Effect of the End of SHO on WFH based on Model (4)
Figure 3
WFH Rate Effects on Small Business’ Cash Flow, Based on Models (12)-(15)
Figure 4
WFH Effects on Small Business’ Operating Revenue Increase, Based on Model (16)
Figure 5
WFH Rate Effects on Small Business’ Temporary Closure, Based on Model (17)
Figure 6
WFH Rate Effects on Small Business’ Disruption in Supply Chain, Based on Model (18)
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