Smbliq C 082 Significant Effects Covid 19 Leisure Hospitality Small Business Revenue 2021 09 27

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In this brief research report published 27 September 2021 in Frontiers in Public Health (doi 10.3389/fpubh.2021.753508), Zhou Lu, Yunfeng Shang and Linchuang Zhu study daily seasonally adjusted data on net revenues and openings of small businesses in the U.S. accommodation, food services, leisure and hospitality sectors from January 10, 2020 to June 24, 2021. Using the Dorta-Sanchez bootstrap unit-root test for a random walk with drift, they find that the COVID-19 crisis significantly affected the revenues and openings of small leisure and hospitality firms. They report that the result holds at the national level and across 51 states.

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BRIEF RESEARCH REPORT
published: 27 September 2021
doi: 10.3389/fpubh.2021.753508

The Significant Effects of the
COVID-19 on Leisure and Hospitality
Sectors: Evidence From the Small
Businesses in the United States
Zhou Lu 1 , Yunfeng Shang 2* and Linchuang Zhu 1
1
School of Economics, Tianjin Univesity of Commerce, Tianjin, China, 2 School of Hospitality Administration, Zhejiang Yuexiu
University, Shaoxing, China

This paper uses the daily seasonally-adjusted data for net revenues and openings of
small businesses in the accommodation, food services, leisure, and hospitality sectors
in the United States from January 10, 2020, to June 24, 2021. The results from the
Dorta-Sanchez bootstrap unit-root test for a random walk with drift show that the
COVID-19 crisis has significantly affected revenues and openings of small leisure and
hospitality firms. Moreover, the results remain valid when the data for the national level
Edited by: and 51 states are considered.
Giray Gozgor,
Istanbul Medeniyet University, Turkey Keywords: COVID-19 shocks, leisure and hospitality, accommodation and food services, small businesses,
bootstrap unit-root test for a random walk with drift
Reviewed by:
Yuhua Song,
Zhejiang University, China
Jianmin Sun, INTRODUCTION
Nanjing University of Posts and
Telecommunications, China The COVID-19 pandemic is one of the largest pandemics in the industrialized world. It has
*Correspondence:
significantly affected all sectors almost in all countries. Since the new type of coronavirus is more
Yunfeng Shang lethal and easily contagious than the common flu, governments have had to take many measures
yfshang1985@163.com to slow the spread of the virus (1). Governments have imposed lockdowns, including closures of
accommodation and hospitality facilities, leisure activities, restaurants, and show businesses (2, 3).
Specialty section: Governments have also implemented several restrictions on domestic mobility and international
This article was submitted to travel during the COVID-19 era (4), and this issue has negatively affected the tourism sector (5).
Health Economics, The precautionary measures and the widespread use of COVID-19 vaccines have caused significant
a section of the journal changes in small business revenues and openings (6).
Frontiers in Public Health
Understanding the stochastic properties of small business revenues and openings is also essential
Received: 04 August 2021 for macroeconomic variables, such as business cycles, employment, inflation expectations, job
Accepted: 30 August 2021 openings, and wages (7–9). At this stage, if small-business indicators do not follow a stationary
Published: 27 September 2021
process, this issue indicates an external shock (i.e., the COVID-19 pandemic) that has significantly
Citation: affected small businesses in the related sector and entrepreneurship behaviors. The evidence of
Lu Z, Shang Y and Zhu L (2021) The
rejecting the stationarity of the business indicators means the significant changes of business cycles
Significant Effects of the COVID-19 on
Leisure and Hospitality Sectors:
(10). Significant changes in business indicators can also affect employment, inflation expectations,
Evidence From the Small Businesses job openings, and wages.
in the United States. Previous papers show the significant effects of uncertainty shocks (e.g., financial crises, natural
Front. Public Health 9:753508. disasters, political instability, terrorist attacks) on accommodation, food services, leisure and
doi: 10.3389/fpubh.2021.753508 hospitality sectors in the United States (11). There are also previous papers to examine the effects

Frontiers in Public Health | www.frontiersin.org 1 September 2021 | Volume 9 | Article 753508
Lu et al. COVID-19 and Leisure-Hospitality Sectors

of the COVID-19 crisis on small businesses in the United States. accommodation, food services, leisure and hospitality sectors
For example, Bartik et al. (12) use the survey data from 5,800 in the United States from January 10, 2020, to June 24,
small firms in the United States from March 28, 2020, to 2021. At this stage, we consider the data at the national
April 4, 2020. The authors find the significant impact of the and state levels. For this purpose, we utilize the bootstrap
COVID-19 crisis on small businesses, particularly financially unit-root test for a random walk with the drift of Dorta
fragile firms. The impact quickly transmits (within a few weeks), and Sanchez (16). The bootstrapped critical values decrease
and firm closure is negatively related to the expectations, which the size distortions following the bootstrap procedure in
are heterogeneous based on the length of the COVID-19 crisis. Park (17).
The authors also compare the effectiveness of loan reliefs To the best of our knowledge, this paper provides the
with grants-based stimulus programs. Fairlie and Fossen (13) first empirical evidence using the daily seasonally-adjusted
observe that sales losses in California during the 2020Q2 were data for net revenues and openings of small businesses in
greatest in accommodations, arts, entertainment, recreation, and Chetty et al. (6) for accommodation, food services, leisure,
restaurants. Huang et al. (14) find that business closures cause and hospitality sectors in the United States. For this purpose,
around 30% decline to the non-salaried workers’ employment we aim to examine the dynamics of small businesses in the
in entertainment, food, hospitality, and leisure sectors in the leisure and hospitality sector in the United States during the
United States between March 2020 and April 2020. Khan et al. COVID-19 period. Moreover, we utilize the Dorta-Sanchez
(15) use the leisure sector employment data in the United States bootstrap unit-root test for a random walk with drift to
from February 1, 2020, to July 31, 2020. The authors find that address poor sample size in small business data. Therefore,
museums, performing arts, and sports have been the worst- we aim to reduce the shortcomings of traditional unit-root
affected businesses during the COVID-19 era. tests. As a result, we find that the COVID-19 crisis has
Given this backdrop, this paper analyzes the validity significantly affected the revenues and openings of small leisure
of the hypothesis of whether the COVID-19 crisis has and hospitality firms in the United States. Moreover, this result
significantly affected revenues and openings of businesses in the is valid when the data for the national level and 51 states
accommodation, food services, leisure, and hospitality sectors are considered.
in the United States. Our main hypothesis is to reject the The remainder of the study is organized as follows.
stationarity of the revenues and openings of small leisure and Section 2 clarifies the details of the dataset and the
hospitality firms. To test the main hypothesis, we consider Dorta-Sanchez bootstrap unit-root test methodology.
the daily seasonally-adjusted data, introduced by Chetty et Section 3 presents the empirical results. Section
al. (6), for net revenues and openings of small businesses in 4 concludes.

FIGURE 1 | Small businesses net revenues: leisure and hospitality sector (national level, % of change). Source: https://tracktherecovery.org/ proposed by Chetty
et al. (6).

Frontiers in Public Health | www.frontiersin.org 2 September 2021 | Volume 9 | Article 753508
Lu et al. COVID-19 and Leisure-Hospitality Sectors

DATASET AND TEST METHODOLOGY The null hypothesis of the Dorta-Sanchez unit-root test is as
followsHo : δ = 0 The model can be defined as follows:
Dataset
This paper uses the seasonally-adjusted data for net revenues and
openings of small businesses in accommodation, food services, p
X
leisure and hospitality sectors in the United States from January 1yt = α + δyt−1 + β1yt−i + εt (1)
10, 2020, to June 24, 2021. The frequency of the data is daily, and i=1
the sample is based on the data availability. Note the first case of
the COVID-19 in the United States is recorded on January 20, εt is the independent and identically distributed (iid) error term.
2020. Therefore, our dataset captures the COVID-19 era. Both The fitted regression can be written as follows:
series are defined as the relative change between the given date
and the average from January 4, 2020, to January 31, 2020. These
p
series are proposed by Chetty et al. (6) at https://tracktherecovery. X
1yt = α + β1yt−i + εt (2)
org/, and the data are provided by Womply (a private-sector firm
i=1
in the United States). The dataset in Chetty et al. (6) has been used
by various empirical papers related to the COVID-19 pandemic Park (17) shows that resampling the restricted model in Eq. (2)
[see, e.g., (18, 19)]. will be better than the unrestricted model in Eq. (1). Following
According to the data in Figure 1, as of June 24, 2021, net the findings in Park (17), estimated residuals (ε̂t ) based on the
small businesses revenues in the leisure and hospitality sector in bootstrap sample sizes can be calculated. The new residuals ()
the United States reduced by 47.3% compared to January 2020. with the bootstrap method can be written as such:

Dorta-Sanchez Bootstrap Unit-Root Test
n
!
Methodology ε̂t −
1X
ε̂i (3)
We utilize the bootstrap unit-root test for a random walk with n
i=1
drift introduced by Dorta and Sanchez (16). The Dorta-Sanchez
unit-root test corrects the possible bias in the data generation t = 1;...; n
process (DGP) that corresponds to a random walk with a non- For each bootstrap sample (yt∗ ), the fitted regressions can be
zero drift for small and medium sample sizes. For example, written as such:
Hylleberg and Mizon (20) show the poor sample size in the
Augmented Dickey-Fuller (ADF) test in the small number of
observations. Hamilton (21) suggests the ordinary least squares p
X
(OLS) estimation with the standard t and F distributions to 1yt∗ = α ∗ + δ ∗ yt−1
∗
+ βi∗ 1yt−i
∗
+ vt (4)
decrease the sample bias. Park (17) uses the ADF unit-root test for i=1
autoregressive (AR) unit-root models with bootstrapped critical
values to address possible sample bias. At this stage, Dorta and The original sample based on fitted regression is as follows:
Sanchez (16) calculate the bootstrapped critical values for the
unit-root test methodology of Park (17). Poor sample size can p
also be an issue in our case, given that there are sub-periods in
X
1yt = µ + δyt−1 + βi 1yt−i + εt (5)
the sample during the COVID-19 period (See Figure 1). i=1

TABLE 1 | Results of the bootstrap unit-root test for a random walk with drift (small businesses revenues and openings in different sectors, national level).

Small Businesses Revenues (Leisure and Hospitality)
Criteria & (Lag) Test Stat. Prob. 5% CVs HL (Days)
AIC (1) −2.479 (0.092) −2.799 –
Small Businesses Revenues (Accommodation and Food Services)
Criteria & (Lag) Test Stat. Prob. 5% CVs HL (Days)
AIC (1) −2.458 (0.093) −2.783 –
Small Businesses Openings (Leisure and Hospitality)
Criteria & (Lag) Test Stat. Prob. 5% CVs HL (Days)
AIC (1) −2.299 (0.090) −2.566 –
Small Businesses Openings (Accommodation and Food Services)
Criteria & (Lag) Test Stat. Prob. 5% CVs HL (Days)
AIC (1) −2.258 (0.066) −2.420 –

CVs: Bootstrapped Critical Values. The CVs are obtained by 500 bootstrap replicates with 530 observations. For details, refer to Dorta and Sanchez (16). The optimal number of lags
is selected by the AIC. Null hypothesis: random walk with drift; Alternative hypothesis: series are stationary.

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Lu et al. COVID-19 and Leisure-Hospitality Sectors

TABLE 2 | Results of the bootstrap unit-root test for a random walk with drift TABLE 2 | Continued
(small businesses revenues, leisure and hospitality).
State Test stat. Prob. 5% CVs HL (Days)
State Test stat. Prob. 5% CVs HL (Days)
WI −1.938 (0.334) −2.911 –
AL −2.188 (0.238) −2.911 – WY −1.954 (0.340) −3.028 –
AK −2.849** (0.032) −2.849 64
CV: Bootstrapped Critical Value. The CVs are obtained by 500 bootstrap replicates with
AZ −2.673 (0.076) −2.833 –
530 observations. For details, refer to Dorta and Sanchez (16). The optimal number of
AR −2.044 (0.300) −2.885 – lags is selected by the AIC. Null hypothesis: random walk with drift; Alternative hypothesis:
CA −2.533 (0.060) −2.559 – series are stationary. **p < 0.01.
CO −2.461 (0.106) −2.806 –
CT −2.532 (0.088) −2.713 –
DE −2.465 (0.118) −2.961 – The t statistic for δ is calculated, compared to the bootstrapped
DC −2.324 (0.144) −2.483 – critical values, which are defined above. If the t statistic is lower
FL −2.562 (0.116) −3.099 – than the bootstrapped critical values, the unit root hypothesis
GA −2.006 (0.216) −2.714 – will be rejected. Furthermore, the p-values on comparing
HI −2.320 (0.136) −2.831 – bootstrapped critical values and t statistics are also provided (16).
ID −1.943 (0.346) −3.023 – Finally, the optimal number of lags is also determined by the
IL −2.237 (0.140) −2.801 – Akaike Information Criteria (AIC).
IN −2.407 (0.102) −2.838 – If we obtain stationary series, we can calculate the Half-life
IA −1.850 (0.398) −2.886 – (HL) values to detect how many days COVID-19 shocks survive.
KS −2.327 (0.158) −2.899 – We calculate the HL values, as such:
KY −2.181 (0.260) −3.006 –
LA −2.402 (0.112) −2.786 –
ME −2.360 (0.150) −2.835 – Half − life = ln(0.5) / ln(ρ) (6)
MD −2.023 (0.200) −2.769 –
MA −2.573 (0.068) −2.668 – In Equation 6, ρ is the AR coefficient in AR (1) process Yt =
MI −2.040 (0.194) −2.850 – ρYt−1 + εt .
MN −2.267 (0.195) −2.888 –
MS −2.045 (0.190) −2.669 –
EMPIRICAL RESULTS
MO −2.144 (0.316) −3.038 –
MT −1.698 (0.608) −3.121 – Table 1 reports the findings of the bootstrap unit-root test for a
NE −1.874 (0.344) −2.856 – random walk with drift proposed by Dorta and Sanchez (16) at
NV −1.772 (0.540) −3.192 – the national level for small businesses revenues and openings of
NH −2.213 (0.234) −2.929 – two sectors: (i) leisure and hospitality and (ii) accommodation
NJ −2.541 (0.060) −2.602 – and food services. The results indicate that small businesses
NM −1.979 (0.184) −2.691 – revenues and openings in two sectors follow the random walk
NY −2.417 (0.064) −2.506 – with drift process. In other words, the stationarity of the small
NC −2.366 (0.160) −2.878 – business indicators is rejected. Moreover, these results are robust
ND −2.268 (0.194) −2.871 – to different lag selection criteria.
OH −2.426 (0.148) −2.856 – Tables 2, 3 report the bootstrap unit-root test results for a
OK −2.110 (0.206) −2.795 – random walk with drift proposed by Dorta and Sanchez (16)
OR −2.443 (0.134) −2.757 – for the state level for small businesses’ revenues and openings
PA −2.446 (0.092) −2.777 – for leisure and hospitality. The results of the Dorta-Sanchez test
RI −2.346 (0.108) −2.717 – in Table 2 show that nearly all small businesses revenues series
SC −2.113 (0.228) −2.812 – follow the random walk with drift process. The only exception
SD −2.103 (0.276) −2.892 – is observed in Alaska, and the HL of the COVID-19 shock is
TN −2.016 (0.386) −2.965 – 64 days.
TX −2.393 (0.096) −2.659 – Similarly, the results of the Dorta-Sanchez test in Table 3
UT −2.705 (0.078) −2.851 – indicate that nearly all small businesses openings series follow
VT −2.418 (0.110) −2.801 – the random walk with drift process. Again, the only exception
VA −2.239 (0.120) −2.668 – is observed in Alaska, and the HL of the COVID-19 shock is
WA −2.235 (0.252) −3.023 – 92 days.
WV −2.368 (0.138) −2.736 – In short, we observe that the COVID-19 crisis has significantly
affected small businesses’ revenues and openings in the
(Continued) United States. Moreover, this evidence is valid when we consider

Frontiers in Public Health | www.frontiersin.org 4 September 2021 | Volume 9 | Article 753508
Lu et al. COVID-19 and Leisure-Hospitality Sectors

TABLE 3 | Results of the bootstrap unit-root test for a random walk with drift TABLE 3 | Continued
(small businesses openings, leisure and hospitality).
State Test stat. Prob. 5% CVs HL (Days)
State Test stat. Prob. 5% CVs HL (Days)
WI −2.384 (0.102) −2.690 –
AL −2.303 (0.102) −2.619 – WY −1.876 (0.252) −2.755 –
AK −2.613** (0.030) −2.411 92
CV: Bootstrapped Critical Values. The CVs are obtained by 500 bootstrap replicates with
AZ −2.182 (0.120) −2.619 –
530 observations. For details, refer to Dorta and Sanchez (16). The optimal number of
AR −2.110 (0.212) −2.885 – lags is selected by the AIC. Null hypothesis: random walk with drift; Alternative hypothesis:
CA −2.367 (0.064) −2.524 – series are stationary. **p < 0.01.
CO −2.379 (0.108) −2.716 –
CT −2.244 (0.096) −2.574 –
DE −2.167 (0.123) −2.452 – the data at the national and state levels. Regarding the COVID-
DC −2.213 (0.088) −2.450 – 19 era, our results align with the previous results of Bartik et al.
FL −2.353 (0.086) −2.474 – (12, 14, 15) in the United States. Furthermore, we have enhanced
GA −1.906 (0.118) −2.291 – these results by using the daily data with the recent unit-root test.
HI −2.285 (0.112) −2.703 –
ID −1.730 (0.310) −2.698 –
IL −2.272 (0.110) −2.703 –
IN −2.263 (0.112) −2.544 – CONCLUSION
IA −1.972 (0.226) −2.913 –
This paper uses the dataset in Chetty et al. (6) at https://
KS −2.282 (0.098) −2.731 –
tracktherecovery.org/. It focuses on the small businesses’
KY −2.401 (0.096) −2.829 –
revenues and openings in accommodation, food services, leisure
LA −2.289 (0.128) −2.690 –
and hospitality sectors in the United States. We consider the daily
ME −2.453 (0.084) −2.676 –
data from January 10, 2020, to June 24, 2021. We utilize the recent
MD −2.107 (0.108) −2.497 –
bootstrap unit-root test for a random walk with drift proposed
MA −2.202 (0.062) −2.338 –
by Dorta and Sanchez (16). We observe that the COVID-19
MI −2.292 (0.078) −2.513 –
crisis has significantly affected the revenues and openings of small
MN −2.181 (0.140) −2.863 –
leisure and hospitality firms in the United States. The findings are
MS −2.441 (0.124) −2.683 –
valid when we use data for the national level and 51 states.
MO −2.060 (0.196) −2.717 – Regarding policy implications, the findings show that
MT −1.762 (0.260) −2.633 – an external shock, such as the COVID-19 pandemic, has
NE −1.377 (0.378) −2.845 – permanently affected the revenues and the openings of leisure
NV −2.665 (0.075) −2.879 – and hospitality firms in the United States. Leisure and hospitality
NH −2.477 (0.080) −2.806 – firms in all states have performed relatively weak during the
NJ −2.356 (0.0600) −2.449 – COVID-19 era. Rejecting the stationarity in the small business
NM −1.998 (0.128) −2.361 – indicators of leisure and hospitality is a strong signal of the
NY −2.417 (0.054) −2.462 – business cycles during the COVID-19 era. The significant change
NC −2.565 (0.067) −2.689 – during the COVID-19 can be related to declining demand for
ND −2.134 (0.158) −2.733 – leisure and hospitality services due to the lockdowns or other
OH −2.227 (0.130) −2.780 – limitations on mobility. There are also supply chains problems
OK −2.041 (0.168) −2.697 – and restrictions on the supply side of leisure and hospitality firms
OR −2.263 (0.132) −2.887 – due to the COVID-19 pandemic.
PA −2.317 (0.116) −2.808 – Our results are consistent with the idea that the COVID-19
RI −2.226 (0.132) −2.714 – pandemic has not affected coastal and inland areas differently.
SC −1.878 (0.138) −2.558 – In other words, we find that the COVID-19 pandemic has
SD −1.552 (0.276) −2.703 – significantly affected the leisure and hospitality firms in all
TN −2.367 (0.092) −2.624 – states. At this stage, implications for supporting struggling small
TX −2.158 (0.093) −2.455 – business firms are important to mitigate the devastating effects
UT −2.234 (0.130) −2.854 – of the COVID-19 crisis. For instance, the American Rescue
VT −2.185 (0.180) −2.794 – Plan in March 2021 provides credit expansion, direct capital
VA −1.938 (0.138) −2.492 – injection, and tax reliefs to boost business activities, including
WA −2.267 (0.130) −2.723 – the leisure and hospitality sector. Finally, future papers can
WV −2.221 (0.110) −2.715 – focus on the other sectors to examine whether the COVID-19
has disproportionately affected small businesses across the
(Continued) United States.

Frontiers in Public Health | www.frontiersin.org 5 September 2021 | Volume 9 | Article 753508
Lu et al. COVID-19 and Leisure-Hospitality Sectors

DATA AVAILABILITY STATEMENT writing the paper. All authors contributed to the article and
approved the submitted version.
Publicly available datasets were analyzed in this study. This data
can be found here: https://tracktherecovery.org/. FUNDING
The authors acknowledge the funding from the Philosophy
AUTHOR CONTRIBUTIONS & Social Science Fund of Tianjin City, China. Award #:
TJYJ20-012 (Prompting the Market Power of Tianjin City’s
ZL: empirical analyses, writing the paper, and supervision. YS: E-commerce Firms in Belt & Road Countries: A Home Market
methodology and writing the paper. LZ: data collection and Effect Approach).

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