mathematics
Article
Explosivity and Time-Varying Granger Causality: Evidence
from the Bubble Contagion Effect of COVID-19-Induced
Uncertainty on Manufacturing Job Postings in the United States
Festus Victor Bekun 1,2,* , Abdulkareem Alhassan 3,*, Ilhan Ozturk 4,5,6,* and Obadiah Jonathan Gimba 3
1 Faculty of Economics Administrative and Social Sciences, Department of International Logistics and
Transportation, Istanbul Gelisim University, Istanbul 34310, Turkey
2 Adnan Kassar School of Business, Department of Economics, Lebanese American University,
Beirut 11022801, Lebanon
3 Department of Economics, Federal University of Lafia, Lafia 950101, Nigeria
4 College of Business Administration, University of Sharjah, Sharjah 27272, United Arab Emirates
5 Faculty of Economics, Adminis-Trative and Social Sciences, Nisantasi University, Istanbul 25370, Turkey
6 Department of Medical Research, China Medical University Hospital, China Medical University,
Taichung 40402, Taiwan
* Correspondence: fbekun@gelisim.edu.tr (F.V.B.); a.alhassan@socsci.fulafia.edu.ng (A.A.);
iozturk@sharjah.ac.ae (I.O.)
Abstract: This study evaluates the explosive behavior and Granger causality episodes in manufactur-
ing job postings in the United States (JOBPUS) and COVID-19-induced uncertainty (COVIDEMV).
This study applied the novel unit root tests with explosive behavior, and the novel time-varying
Granger causality test for a sample period ranging from 1 January 2020 to 29 July 2022. Further,
Citation: Bekun, F.V.; Alhassan, A.;
this study used date stamping to identify the subperiods of the explosive behavior and causality.
Ozturk, I.; Gimba, O.J. Explosivity
The findings revealed that JOBPUS exhibits explosive behavior, with several episodes of exuberance
and Time-Varying Granger Causality:
Evidence from the Bubble Contagion (bubbles) across the sample period while COVIDEMV does not exhibit explosivity during the pe-
Effect of COVID-19-Induced riod. However, the results of the causality provide evidence of bidirectional causality, with several
Uncertainty on Manufacturing Job episodes between the variables. Moreover, the episodes of the explosivity and causality coincide with
Postings in the United States. significant episodes in the history of the COVID-19 pandemic worldwide and in the United States
Mathematics 2022, 10, 4780. particularly, such as the date when United States recorded a COVID-19-related death toll of over
https://doi.org/10.3390/ 100,000 people for the first time, after the presidential election, after Halloween celebrations, after the
math10244780 discovery and administration of COVID-19 vaccines as well as the discovery of the Delta and the
Academic Editor: María del Omicron variants of COVID-19. Therefore, the time-series characteristics of JOBPUS and its causal
Carmen Valls Martínez nexus with COVIDEMV largely depend on the intensity of the instability caused by the pandemics.
Hence, explosivity and time-varying causal behavior should necessarily be accounted for when
Received: 3 October 2022
modelling the job market conditions in the United States, particularly during pandemic-related crises.
Accepted: 5 December 2022
Published: 15 December 2022
Keywords: explosivity; COVID-19; manufacturing job; time-varying Granger causality; United State
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in MSC: 91B39; 91B84
published maps and institutional affil-
iations.
1. Introduction
The COVID-19 pandemic came with much uncertainty that altered numerous eco-
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland. nomic projections. The uncertainty has affected many sectors of the US economy, with keen
This article is an open access article interest from policy makers. To contribute to this discourse, this study focuses on the nexus
distributed under the terms and between COVID-19-induced uncertainty and manufacturing job postings in the United
conditions of the Creative Commons States. The manufacturing job market has become vulnerable during the pandemic. This is
Attribution (CC BY) license (https:// evident through the reduction in job advertisements and direct feedback from the sector
creativecommons.org/licenses/by/ demonstrated through permanent dismissal, temporary termination of employment, and a
4.0/). decline in hours of work and pay.
Mathematics 2022, 10, 4780. https://doi.org/10.3390/math10244780 https://www.mdpi.com/journal/mathematics
Mathematics 2022, 10, 4780 2 of 17
COVID-19 has caused unemployment across the world including Europe, where Italy,
Spain and the United Kingdom were considered the worst affected [1]. However, with
approximately 1,069,757 deaths—16.2% of total COVID-19 deaths worldwide—the United
States is the worst hit in terms of COVID-19 deaths [2,3]. Further, the US lost more work
hours during the COVID-19 pandemic than the 28 European Countries combined [4]. Fur-
ther, global value chains were adversely affected in the US [5]. In addition, the devastating
effects of previous economic crises such as the 1930s Great Depression and 2007 Global
Financial Crisis emanated from the US and spread to the rest of the world. Thus, economic
crises and job market distortions in the US are of great relevance worldwide. Therefore, this
study focuses on the dynamic nexus between COVID-19-related uncertainty and manufac-
turing job postings in the United States. Meanwhile, data for manufacturing job postings
reflect labor demand for new workers. Consequently, they are a manifestation of the overall
economy. Since its debut, the economic impact of the COVID-19 pandemic has attracted
enormous policy and research attention. Many studies have considered the effect of the
pandemic on labor market conditions worldwide. The initial strand of literature focused on
the scale and magnitude of the impact of the pandemic [6,7]. For instance, it is estimated
that 305 million full-time jobs were lost across the world in the second quarter of 2020 [8].
It was also reported that the US economy lost approximately 22.1 million jobs in March
2020 [9]. Albert et al. [10] examined how the COVID-19 pandemic affected employment
dynamics across states and sectors of the US. The study found that employment in mining,
construction, and manufacturing fell by 12.1%, representing 2.6 million jobs, and the service
sector fell by 15.1%, representing 19.8 million jobs.
Two channels are responsible for the decrease in manufacturing activities in the US
during the pandemic. These channels are classified into the domestic channel through the
lockdown and other restrictions imposed to curtail the spread of the virus, which invariably
dampened demand and reduced supply across industries. Further, there is the international
factor through the reliance of local production on foreign raw materials and other inputs.
The manufacturing sector in the US largely depends on raw materials from other countries;
if those countries experience severe lockdown, this will stop the flow of inputs and hinder
the production process.
Moreover, the literature on COVID-19 and labor market dynamics is vast. For instance,
the authors of [11], using data from Emsi on online job postings during the pandemic in the
US, found that the overall job posting for the economy decreased by 16%. Decomposing
it to different sectors shows a 56% decline in oil and gas; a 40% drop in oil and gas; a
40% fall in the service sector; and the manufacturing sector had a weekly drop of 10%
between March and April 2020. Similarly, the study in [12] evaluates the impact of the
COVID-19 pandemic on labor market in Canada. The resultant effect of the pandemic is
evident in the increase in unemployment from 5.6% in the first quarter of 2020 to 13.7% in
the second quarter. Specifically, the employment narration for medium food manufacturing
as it relates to food and vegetables shows a decline for a short period. However, the decline
was more severe in seafood. Further, fluctuations in employment in the agricultural food
supply chain have been moderate. Overall, the GDP plummet by approximately 11.1% in
the second quarter. Cho et al. [13] utilize individual-level data and examine the impact of
the COVID-19 pandemic on employment across US metropolitan areas using the difference-
in-difference regression estimation. The study discovered that job losses were higher in
large metropolitan areas but in non-metropolitan areas, the impact was less. These findings
support the fact that most large manufacturing and business enterprises are located in large
metropolitan areas, hence experiencing more job losses during the pandemic. Further, the
rate of job losses spiked is attributed to firms changing their behavior to cope with the rules
of mitigating the spread of the virus [14].
However, the COVID-19 pandemic occurs in different episodes ranging from pre-
lockdown, complete lockdown, discovery of vaccines, administration of vaccines and
easing of lockdown and movement restrictions. Although these episodes are capable of
changing the causal nexus between the pandemic and job market conditions, the extant
Mathematics 2022, 10, 4780 3 of 17
literature on the COVID-19-labor market nexus did not consider this important feature
of the relationship. It is imperative, therefore, to capture these episodes and identify
exuberance in the causal nexus between the COVID-19 pandemic and job market conditions,
especially in the US.
Therefore, this study evaluates the explosive behavior and Granger causality episodes
in manufacturing job postings in the United States (JOBPUS) and COVID-19-induced
uncertainty (COVIDEMV). This study provides answers to some fundamental questions
in this regard. First, does the COVID-19-induced uncertainty and manufacturing job
posting exhibit explosive behavior during the COVID-19 pandemic? Second, does the
COVID-19-induced uncertainty have a causal effect on manufacturing job postings? Third,
to what extent does the uncertainty associated with the pandemic prove contagious to
manufacturing job postings? Forth, does the causality vary based on the episodes of the
pandemic? Hence, this study contributes to the literature on COVID-19 uncertainty and
labor market outcomes in the following ways: first, this study examine how the US reacts
to the pandemic-induced uncertainty as it affects manufacturing job postings. Secondly,
this study employs the novel COVID-19 uncertainty index conceived by [15], which is
composed of the daily number of newspaper articles bearing keywords such as pandemic,
virus, lockdown, coronavirus, and epidemic. Thirdly, the estimation techniques used, unit
root tests with explosive behavior and the time-varying causality enable us to identify
episodes of explosive behavior and causality, as well as to discover if a peculiar causality
exists between COVID-19 uncertainty and manufacturing job postings. This is important
for the predictability of the job market dynamics in the United States, as it enables policy
makers to make appropriate policy decisions about labor market fluctuations induced by
the COVID-19 pandemic. This also has the advantage of allowing the identification of
distinct periods where the COVID-19 uncertainty–manufacturing job posting causal relation
is explosive. In addition, this study provides a basis for the accounting of explosivity
(explosive behavior) and the instability of the causal nexus in the modelling of the job
market conditions in the United States, particularly during pandemic-related crises. Many
studies ([16–21]) have used Granger causality to evaluate the dynamic nexus between
macroeconomic fundamentals, but none of them used time-varying Granger causality to
examine the relationship between job postings in the United States and COVID-19-induced
uncertainty considered in this study. Further, the previous studies failed to consider
different episodes of causality among the variables. Meanwhile, the Granger causality
varies with different sample periods and instability [8].
Although the nexus between COVID-19 and job market conditions attracted many
scholars, the issue of explosivity and time-varying causality between the pandemic and
the job market conditions have not been considered in the literature. Thus, this study fills
the research gap by examining the explosive behavior and Granger causality episodes
in manufacturing job postings in the United States (JOBPUS) and COVID-19-induced
uncertainty.
The remaining parts of this paper include Section 2, materials and method, the results
in Section 3, the discussion in Sections 4 and 5, which entails the conclusion.
2. Materials and Methods
The methodology of this study involves the following two steps: (1) unit root tests with
the explosive behavior of the series and (2) calculating time-varying Granger causality as
discussed below. The main advantage of these methods over others techniques is that the
techniques used is this study involve the use of lag-augmented VAR (LA-VAR), which does
not require the variables to be stationary—it can provide valid estimates with non-stationary
series, and can solve the problem of non-linearity and multiple structural breaks, which
diminishes the discriminatory power of extant unit root tests and Granger causality tests,
especially when a period of instability, such as the COVID-19 period, is considered [22–24].
These desirable properties make the methods used in this study the most appropriate for
this study. The methods can also detect exuberances emanating from difference sources
Mathematics 2022, 10, 4780 4 of 17
including the explosive behavior-induced fluctuation of the macroeconomic variables under
consideration [25]. Due to these desirable features of the methods, several studies [26–33]
have used them to evaluate the relationship and characteristics of numerous time-series
variables. However, the disadvantage is that the techniques do not perform well for short
series, and do not provide the graph for more than 600 observations [23,34,35].
2.1. Test for Explosivity
The econometric procedure in this study started with the identification of the explosive
behavior of the variables because the sample period is a period of instability, crisis, and
distress due to the COVID-19 pandemic. The methods rely on the theoretical framework
provided by [34,36], and the empirical findings of [37]. Thus, this study used the estimation
procedure in [37] for testing the unit root with explosive behavior to identify crises in the
series. The procedure was based on the recursive rolling window developed by [38], which
is more efficient, especially in the presence of bubbles over the sample period. The test can
be conducted for observations ranging from r0 to 1, with recommended r0 = r0 = 0.01+ √1.8 ,T
where T is the total number of observations in the data (sample length). Assuming r
is the interested observation, the authors of [36] estimate the Augmented Dickey–Fuller
(ADF) accordingly by backward expanding the sample sequence. Suppose the start and
the end points of the sample are r1 and r2, respectively, ADF
r2
r1 will be the calculated as the
ADF statistic from the sample. Following [37], the following ADF regression equation is
estimated for the test.
p
∆yt = αr1,r2 + βr1,r2 y + ∑ ∅jt−1 r1,r2 ∆yt−j + εt (1)
j=1
where yt represents the time series of interest at time t (daily manufacturing job postings,
and the daily infectious disease equity market volatility index (EMVID) used to measure
COVIDEMV). The ∆ is the lag operator, p denotes the maximum number of lags of the
dependent variable; r1, and r2 symbolize the starting and ending points considered for
the estimation, respectively; εt denotes the stochastic error term. The null and alternative
hypothesis are as follows.
Null hypothesis (H0): βr1,r2 = 0 (there is unit root)
Alternative hypothesis (H1): βr1,r2 > 0 (explosive behavior)
Based on this framework, the study in [34] calculates two statistics. The first is the
right-tailed ADF statistic, which is based on the full sample (r1 = 0, r2 = 1) and denoted by
ADF10 , The second statistic is the right-tailed supremum t-statistic of the forward recursive
window, which is symbolized by SADFr20 and expressed in Equation (2) as follows.
SADF(r0) = sup ADF
r2
0 (2)
r2e[r0,1]
However, the authors of [36] submit that the forward recursive approach is efficient in
identifying the first bubble but cannot identify the subsequent episodes of explosive behavior
when there are several bubbles. Hence, the authors of [36] developed the generalized supremum
ADF (GSADF), which allows varying the start point to point r1, with a range (0, r2 − r0), and
varying the end point, ranging from r0 to 1. The GSADF is mathematically expressed in
Equation (3) as follows.
GSADF(r0) = sup ADF
r2
r1 (3)
r2e[r0, 1]
r1e[0, r2 − r0]
To identify episodes of explosive behavior, the authors recommended the backward
expanding SADF statistic, which allows a varying starting point r1, with a range (0, r2 − r0),
Mathematics 2022, 10, 4780 5 of 17
and fixed ending point of all samples on the interested observation, such that r = r2. The
backward expanding SADF statistic is defined as:
BSADFr2 (r0) = sup ADF
r2
r1 (4)
r1e[0, r2−r0]
These statistics are compared with critical values and bootstrap critical values com-
puted by [38,39] to evaluate the explosivity of US manufacturing job postings and the
COVIDEMV time series considered in this study.
2.2. The Time-Varying Granger Causality Test
This study further employs the time-varying Granger causality test to evaluate the
causal relationship between daily manufacturing job postings and daily EMVID used to
measure COVIDEMV. Time-varying Granger causality involves three test procedures—
forward-expanding [21], rolling and the recursive rolling window, also known as the
evolving procedure developed by the authors of [36] and practicalized by the authors
of [39,40]. In this study, all three procedures are estimated together, adopting the corrective
bootstrap algorithm process described in the following steps.
Step 1: Estimation begins with a bivariate vector autoregressive —VAR(1) model
specified in matrix form as[fol]lows[: ]
y (1)
[ ] [ ]
1t θ= 11
0 y1, t−1 ε1t
y2t (2) (2)
+ (5)
θ y11 θ21 2,t−1 ε2t
The y1t and y2t represent COVIDEMV and manufacturing job postings, respectively.
The coefficients are represented by (1)θ11 and
(1), with their estimates symbolized by (1)θ21 θ̂11 and
(1)
θ̂21 , respectively. The residuals are ε1t and ε2t while e1t and e2t denote the estimated residu-
als, respectively. The null hypothesis is that there is no causality from y1t (manufacturing
job postings) to y2t (manufacturing job postings), and from y2t to y1t in the first and second
step, respectively. This study focused on the causal relationship between COVIDEMV
and manufacturing job postings because COVID-19 is an exogenous phenomenon (global
health challenge), which is not caused by job market dynamics. Thus, the first part of the
null hypothesis suffices in the current study.
Step 2: The second step involves the generation of the bootstrap sample. Let Tb = τ0 + τ[b −]1
denote the sample size of the bootstrapped data series, where τ0 = [Tr0 ] and τb = Trb .
Hence, the bootstrap samp[le is]gen[erated as fo]l[lows. ] [ ]
yb (1)1t θ̂ 0 y
b b
= 11 1,t−1
e1t
yb (2) (2) yb
+ (6)
2t θ̂ θ̂ 2,t−1 e
b
11 21 2t
The eb1t and e
b
2t are drawn from the estimated residuals e and e2t with replacement,
while the yb11 = y11 and y
b
21 = y21 are used to obtain the initial values of the bootstrap series.
Step 3: In the third step, the yb(1t and y
b
2t (bo)otstrap series) are used to compute thesequences of the three test statistics {viz. } ( )τ0+τ { }b−1 τ0+τb−1
Theforward-expandingwindow: (T{b b1,t } ; the)rollingwindow Tt−τ +1 ;t=τ 00 t=τ0τ0+τb−1
and the recursive evolving window Tbt (τ0) . The forward and the rolling win-t=τ0
dow algorithm are based on Wald statistics while the recursive algorithm is made up of
supremum norm of a set of Wald statistics for each observation considered. Therefore, the
maximum values of each of the test statistics are expressed as follows.
The forward-expanding window [21]:
Mb1,t = Max T
b
1,t (7)
te[τ0,τ0+τb−1]
Mathematics 2022, 10, 4780 6 of 17
The rolling window
Mbt−τ +1, t = Max T
b
t−τ +1 (8)0 te[τ 00,τ0+τb−1]
The recursive window [39–44]: { }
Mbt (τ0) = Max T
b
− t
(τ0) (9)
te[τ0,τ0+τb 1]
The supremum norm of the sequence of the supremum norm Wald test is symbolized
by Mbt (τ0).
Step 4: This step involves the repetition of the above steps up to a total of b = 1, . . . . . . B
times.
Step 5: This is the last step, which entails the computation of the critical values (90%,
95%, and 99%) for the forward-expanding and rolling-window procedures, and Wald
statistics as the corresponding 90th 95th and 99th percentiles of the bootstrap statistics
estimated in step 4.
The procedure is implemented in this study with the use of the tvgc command in
STATA. The estimates are used to evaluate the causal nexus between COVIDEMV and
manufacturing job postings in the United States.
2.3. Data
The data for the two variables (COVIDEMV and manufacturing job postings) con-
sidered in this study are daily data starting from 1 February 2020 to 28 May 2022. The
period is chosen to capture the period of the novel COVID-19 pandemic. COVIDEMV is
measured by the daily infectious disease equity market volatility tracker index (EMVID)
computed by [15]. The EMVID is constructed from news-based uncertainty by counting
infectious disease -related keywords such as pandemic, flu, disease, and coronavirus from
approximately 300 newspapers in the United States. The index computed is normalized by
the total number of articles submitted to the newspapers each day.
The COVID-19 pandemic disrupted production and led to the loss of jobs in the
manufacturing sector globally, and the United States was amongst the countries that
experienced the most severe contraction in its economy. Thus, this study used daily job
postings (advertisement) in the US manufacturing sector during the COVID-19 pandemic.
The data on job postings were sourced from the real-time intelligence (RTI) from Chumura
Economics & Analytics, which is updated daily. The data were obtained from a collection of
online job advertisements of over 15,000 sources (companies). Job postings were analyzed
and grouped into different categories including occupations, job titles, skill requirements,
locations, wages, and education levels. The RTI job postings data have been considered
good and comprehensive indicators of the overall labor market conditions in the United
States, and are strongly correlated (approximately 0.8 correlation coefficient) with data
on total employment developed by the Bureau of Labor Statistics [41]. Although job
advertisements are not a perfect substitute for employment and wages, they signal the
labor market conditions in a timely manner, which was especially true during the COVID-19
pandemic, when the labor market experienced rapid changes in employment and wages.
3. Results
3.1. Statistical Properties
Table 1 presents the statistical properties of daily manufacturing job postings (JOBPUS)
and daily EMVID used to measure COVID-19-induced uncertainty (COVIDEMV). The
standard deviations of both JOBPUS (47.499) and COVIDEMV (13.117) are large (greater
than 2), indicating that both experienced substantial fluctuations during the period con-
sidered. The minimum and maximum statistics and the percentile also revealed a wide
range of variations in the series. The skewness indicates that JOBPUS is negatively skewed,
while COVIDEMV is positively skewed. The kurtosis of JOBPUS is less than 3, while
Mathematics 2022, 10, x FOR PEER REVIEW 7 of 18 
 
3. Results 
3.1. Statistical Properties 
Table 1 presents the statistical properties of daily manufacturing job postings 
(JOBPUS) and daily EMVID used to measure COVID-19-induced uncertainty 
(COVIDEMV). The standard deviations of both JOBPUS (47.499) and COVIDEMV 
(13.117) are large (greater than 2), indicating that both experienced substantial fluctuations 
Mathematics 2022, 10, 4780 during the period considered. The minimum and maximum statistics and the perce7notfil1e7 
also revealed a wide range of variations in the series. The skewness indicates that JOBPUS 
is negatively skewed, while COVIDEMV is positively skewed. The kurtosis of JOBPUS is 
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This study first applied the SADF and the GSADF tests to the explosivity of daily
manufacturing job postings, and COVIDEMV for the full sample. This current study further
 tested the hypothesis that the series has a unit root against the alternative hypothesis that
the variables exhibit explosive behavior over the period considered using the default
settings of the radf command in STATA. Table 2 contains the results of the tests for the
unit root and explosive behavior of the two variables considered in this study. The results
contain the statistics alongside right-tailed critical values for the 10%, 5%, and 1% levels of
significance [38]. From Table 2, the SADF and the GSADF statistical estimates of JOBPUS
for the full sample are 1.328, and 4.6593, respectively. The SADF statistic is greater than the
Mathematics 2022, 10, 4780 8 of 17
critical values at a 10% level of significance while the GSADF statistic exceeds the right-
tailed tabulated critical values with a 99% confidence level. This provides clear evidence
for the rejection of the null hypothesis. Thus, JOBPUS exhibits explosive behavior during
the COVID-19 pandemic.
Table 2. Results of unit root tests with explosive behavior.
Variables US Manufacturing Job Postings(JOBPUS) COVIDEMV
Statistics ADF0 SADF GSADF ADF0 SADF GSADF
Full sample
Test −0.947 1.328 * 4.6593 *** −11.369 *** −1.711 ** −1.711
Critical values
10% −0.427 1.284 2.0742 −0.4269 1.2835 2.0742
5% −0.057 1.581 2.2924 −0.057 1.5812 2.2924
1% 0.6084 2.096 2.743 0.6084 2.0959 2.743
First 600 observations
Test 0.3973 1.3284 * 3.1183 *** −9.0507 *** −1.0252 −1.0252
Critical values
10% −0.3903 1.2435 1.9873 −0.3842 1.2435 1.9873
5% −0.0327 1.525 2.237 −0.0146 1.525 2.237
1% 0.6068 2.0712 2.6413 0.6392 2.0712 2.6413
Last 600 observations
Test −2.4216 *** 1.2759 * 4.6593 *** −13.344 *** −5.282 *** −2.4536 **
Critical values
10% −0.3842 1.2435 1.9873 −0.3842 1.2435 1.9873
5% −0.0146 1.525 2.237 −0.0146 1.525 2.237
1% 0.6392 2.0712 2.6413 0.6392 2.0712 2.6413
Note *, **, and *** denote the 10%, 5%, and 1% levels of significance, respectively.
For COVIDEMV, the SADF and GSADF statistics are less than the right-tailed tabulated
critical values for a 90% confidence level. Thus, there is not enough statistical evidence
to reject the null hypothesis. It is observed that COVIDEMV does not exhibit explosive
behavior during the period considered. The result of the BSADF statistic with 199 bootstrap
replications in Table 3 and that of the subsamples of last 600 and first 600 observations
in Table 2 revealed the same conclusion that JOBPUS exhibits explosive behavior while
COVIDEMV does not. In other words, there is evidence of bubbles in the JOBPUS data for
the sample period.
Table 3. Results of BSADF unit root tests with explosive behavior.
Variables Manufacturing Job Postings (JOBPUS) COVIDEMV
Statistics ADF0 BSADF GSADF ADF0 SADF GSADF
Test −0.947 1.328 * 4.6593 *** −11.37 *** −1.711 ** −1.711
RTMC90 −0.622 3.098 5.0148 −0.202 1.235 2.3901
RTMC95 −0.517 3.245 5.088 −0.16 1.3972 3.2432
RTMC99 −0.365 3.367 5.2611 0.2487 1.5973 3.4508
Critical
values
10% −0.427 1.284 2.0742 −0.427 1.2835 2.0742
5% −0.057 1.581 2.2924 −0.057 1.5812 2.2924
1% 0.6084 2.096 2.743 0.6084 2.0959 2.743
Note RTMC: right-tailed Monte-Carlo critical values for the 90th, 95th, 99th percentiles. *, **, and *** denote the
10%, 5%, and 1% levels of significance, respectively.
Mathematics 2022, 10, 4780 9 of 17
Furthermore, the changes in the explosive behavior of the variables were examined by
date stamping the sequence of the SADF and BSADF statistics, as presented in Figures 2
and 3 for JOBPUS and COVIDEMV, respectively. The plots compared the SADF and
BSADF statistics with the right-tailed tabulated critical values for the 10% and 5% levels of
significance. From Figure 3, there is no single episode of explosive behavior for COVIDEMV
because the SADF and BSADF statistics are below the critical values throughout the period.
For JOBPUS, Figure 2 displays several subperiods of explosive behavior (exuberance).
Therefore, this study identified several episodes of bubbles (crisis) for JOBPUS across the
sample period. This is indicated by the portions of the plot where the SADF and BSADF
statistics exceed the critical values. The subperiods reflect important timelines in the history
of COVID-19 worldwide and in the United States particularly. The timelines include when
Mathematics 2022, 10, x FOR PEER REtVhIeEWC OVID-19 deaths in the US exceeded 100,000 for the first time in 28 May 2020, 1a0s owf e1l8l 
 as after the presidential election and after Halloween celebrations (November 2020), which
resulted in a significant spike in COVID-19 cases and deaths in the country.
 
Figure 2. Date stamping the explosive behavior of US manufacturing job postings during COVID-
1F9ig (u1 rJean2.uDarayt e20st2a0m–2p9in Jgultyh e20e2x2p)l.o sive behavior of US manufacturing job postings during COVID-19
(1 January 2020–29 July 2022).
 
Maatthheemmaattiiccss 22002222,, 1100,, 4x7 F8O0 R PEER REVIEW 111 0ooff 1187 
 
 
FFiigguurree 33.. DDaattee ssttaammppiinngg tthhee eexxpplloossiivvee bbeehhaavviioorr ooff CCOOVVIIDDEEMMVV.  
3..2.. Tiime--Varyiing Granger Causalliitty—Fullll Samplle Anallysiis 
The resulltt iinn TTaabbllee 44 isi sththe eesetsimtimataetse bsabsaesde dono tnheth feulflu slalmsapmlep olebtoaibnteadin ferdomfr othme tshue-
psurepmreummu mnonromrsm osfo tfhteh seesqeuqeunecnec eofo tfhteh eWWaaldld tetesst tsstatatitsistitcicss ooff tthhee ffoorrwaarrd--expanding and 
rolling window algorithms,, as welll as the supremum norm of the Wald statistics of the 
recursive evolving algorithm. Thee sttattiissttiiccss arre the results of the time-varying Granger 
causality test, which was used to evaluate the causal nexus between COVIDEMV and 
manufacturing jjoobb ppoosstitninggss inin thteh eUUninteitde dStSateaste. sT.hTe hesetiemstaimtesa toefs thofe thereteh tresetst—esths—e ftohre-
wfoarwrda-redx-peaxnpdaindgi,n tgh,e trhoellrinogll ianngda tnhde trheecurresciuvres ievveolevvinolgv iwnigndwoiwnds—owasr—e raerpeorretepdo ritne dcoiln-
ucomlunm 1n, 21,, a2n, dan 3d, 3re, srpesepcteicvteivlye.l yT. hTeh esetsimtimataetse saraer erorobbuusts ttoto hheeteterroosscceeddaassttiicciittyy aand tthe ffiirst 
diifference (d = 1) was used because tthe resulltt of tthe uniitt roott ttestt shows tthatt JOBPUS iis 
iinttegrratted tto an oorrddeerro offo onnee. .T Thheen nuullllh hyyppooththeseissisf ofrorth tehete tsetsits itsh tahtatth tehreries inso neov eidveidnceencoef 
oGfr aGnrgaenrgcear ucsaaulsitayliatyt  aant yanpyo ipnotiint tihne twheh wolheoslaem spamlepbleet wbeetewnemena nmuafnacutfuarcitnugrijnogb jpoobs ptionsgts-
(inJOgsB P(JUOSB)PaUnSd) CanOdV CIDOEVMIDVE(MCOV V(CIDOEVMIDVE).MTVhu). sT, hthues,a tlhteer nalatteirvneahtiyvpeo htyhpesoitshiensiPsa ine Pl aAneisl 
Ath aist tChOatV CIDOEVMIDVEGMrVan Ggrearncgaeurs ecasu(GseCs )(GJOCB)P JOUSBPwUhSil ewthhieler tehvee rrseeveisrsper eiss epnrteesdenintePda inne Pl aBnaesl 
Bth aesa tlhteer nalatteirvneahtiyvpeo hthypesoitsh. esis. 
 
Mathematics 2022, 10, 4780 11 of 17
Table 4. Time-varying Granger causality between COVIDEMV and US manufacturing job postings
(JOBPUS).
(1) (2) (3)
Test Statistics Max_Wald_ Max_Wald Max_Wald
Forward Expanding Rolling Recursive Evolving
8.299 * 22.522 *** 22.524 ***
GC (7.818) (7.613) (8.256)Panel A: COVIDEMV→ JOBPUS [9.187] [8.868] [9.593]
{12.429} {12.361} {12.429}
13.673 ** 44.985 *** 46.997 ***
GC (7.493) (7.563) (7.892)Panel B: JOBPUS→ COVIDEMV [8.919] [9.724] [9.724]
{14.184} {13.417} {14.184}
Note: TVGC is time-varying Granger causality. The estimation used default (199) bootstrap replications. ( ), [ ], and
{ } denote the 90th, 95th and 99th percentiles of test statistics, respectively, while *, ** and *** denote the statistical
significance of the test at the 90th, 95th and 99th percentiles, respectively.
The maximal Wald statistics of all three algorithms show that the null hypothesis
that COVIDEMV does not Granger cause job postings at any point in the entire sample
is rejected at the 90% significance level for the forward-expanding window and at the
99% significance level for the rolling window and recursive evolving window, respectively.
This is indicated by the robust test statistics—maximal Wald statistics—which are greater
than the percentiles of the test statistics. Thus, job market conditions in the United States,
represented by manufacturing job postings, Granger caused COVIDEMV at some points in
the period considered in this study. In short, COVIDEMV affects manufacturing job market
conditions in the United States.
This study further tested the null hypothesis that job postings (JOBPUS) does not
Granger cause COVIDEMV (COVIDEMV) and presented the estimates in Panel B. The
results indicate the rejection of the null hypothesis for all three test statistics. The estimates
of the forward-expanding (13.673), rolling (44.985), and the recursive evolving (46.997) are
greater than the percentile of test statistics at the 95th and 99th percentiles, respectively.
This suggests the rejection of the null hypothesis and revealed that job postings (JOBPUS)
Granger caused COVIDEMV at some points in the sample period. This means that the
dynamics of COVIDEMV can be predicted by the job market. Put differently, the job market
conditions contribute to the uncertainty induced by the COVID-19 pandemic over the
period considered.
Therefore, the results of the time-varying Granger causality test indicate a bidirectional
causality between COVIDEMV and manufacturing job postings (JOBPUS) in the United
States. The results reveal a causal effect running from the job market to COVIDEMV, and
vice versa. However, the greater the test statistics, the greater the effect of the variables. So,
the estimates show that Panel B contains higher values of the test statistics than Panel A.
This demonstrates that the effect of job postings (JOBPUS) on COVIDEMV is less than the
effect of COVIDEMV on job postings (JOBPUS). The causality running from COVIDEMV
to job postings (JOBPUS) is greater than the causality running from job postings (JOBPUS)
to COVIDEMV.
3.3. Date Stamping
Time-varying Granger causality shows the evidence of bidirectional causality between
job postings (JOBPUS) and COVIDEMV. Thus, the current study further date stamps the
causality to examine how the causal relationship between the variables changes during
the sample period. This is achieved by plotting the sequence of the test statistics of the
forward, rolling, and recursive evolving algorithms. The sequence of the test statistics is
plotted alongside the 90th and 95th percentiles of the empirical distribution to examine the
statistical significance of the statistics at any point in time. Causality is said to occur when
the sequence of the statistics is greater than the 90th or 95th percentiles. Concerning the
Mathematics 2022, 10, 4780 12 of 17
causality running from job postings (JOBPUS) to COVIDEMV presented in Figure 4, all
three algorithms (forward, rolling, and recursive evolving) established clear evidence of an
unstable causal relationship between the two variables. In other words, the result reveals a
number of causal episodes, and periods of non-causality during the sample period. For
instance, in Figure 5, Panel A, the forward window shows 3–20 March 2021, 29 April 2021–
15 May 2021, 1 June 2021, 10–14 July 2021 and 28 January 2022–30 March 2022 as the five
episodes of Granger causality running from COVIDEMV to JOBUS. For the rolling window
algorithm, four (4) episodes of causality are identified—25–28 January 2021; 11 February
2021–21 March 2021; 16 September 2021; and 12–13 May 2022. The recursive evolving
algorithm also stamped 28–29 January 2021, 8 February 2021–4 June 2021, 16–20 September
2021 and 5 March 2022–22 July 2022 as the periods when COVIDEMV Granger caused
JOBUS during the sampled period.
Moreover, the forward window in Panel A of Figure 5 shows two episodes of causality
running from job postings (JOBPUS) to COVIDEMV. The first occurs between 15 November
2020 and 21 November 2020 while the second started in January 9, and continued to the
end of the sample in 29 July 2022. Similarly, the recursive evolving algorithm displayed
in Panel C of Figure 5 revealed up to five (5) episodes in which JOBUS Granger caused
COVIDEMV. The first lasted for two days each (28–29 May 2020) and the second occurred
between 16 November 2020 and 28 November 2020. The third episode also lasted for two
days (19–20 March 2021) while the fourth causal episode started on 22 April 2021 and
ended on 27 April 2021. The final episode was observed between September 26, 2021, and
6 October 2021. In the case of the recursive evolving, 28 May 2020–13 June 2020 marked the
first episode of Granger causality from JOBUS to COVIDEMV while the second and the
third episodes covered 15 November 2020–5 December 2020 and 19 March 2021–27 April
2021, respectively. The last episode started on 27 September 2021, to the end of the sample
(29 July 2022). These show that there are many other periods within the sample when
the two variables do not Granger cause each other. That is, there are periods during
which the neutrality of the variables is established. Thus, the Granger causality during
the COVID-19 pandemic is unstable and requires date stamping to identify the periods of
causal relationship between the variables.
It is important to note that these episodes of the causal nexus between the variables
coincide with critical timelines in the history of the COVID-19 pandemic worldwide and in
the United States particularly. For example, 28 May 2020, which is identified as the first
episode of causality between JOBUS and COVIDEMV, is the date on which the United
States recorded a death toll of over 100,000 people for the first time during the COVID-19
pandemic. Further, the United States experienced a spike in COVID-19 cases and deaths
in November 2020, which was when the presidential election took place and again on
15 November 2020, which marked two weeks after Halloween celebrations. By December
2020–January 2021, after the discovery of COVID-19 vaccines and when the vaccination
program was started, and thus the period marked the end of the second episodes of
causality between the variables. However, conspiracy about the efficacy of the AstraZeneca
Vaccines and strict restrictions started on 18 March 2021, which is stamped as the third
episode of the Granger causality. Finally, the discovery of the Delta and the Omicron
variants of the COVID-19 could explain the resurgence of the causal nexus between the
variables, which lasted to the end of the sample considered in this study. Therefore, the
dates identified by the date stamping of the Granger causality between job manufacturing
job postings in the United States (JOBPUS) and COVIDEMV have empirical backing in
the significant timelines in the history of the COVID-19 pandemic in the United States
and worldwide.
MaMthaetmheamtiactsic2s0 22022,21,0 1,04,7 x8 F0OR PEER REVIEW 14 1o3f o1f8 17
 
 
Figure 4. Date stamping the causality behavior between COVIDEMV and manufacturing job post-
Fiinggusr ebe4t.wDeaetne 1s tJaamnupainryg 2th0e20c aaunsda l2i9ty Jubleyh 2a0v2io2r. between COVIDEMV and manufacturing job postings
between 1 January 2020 and 29 July 2022.
 
MaMthaetmheamtiactsic2s0 22022,21,0 1,04,7 x8 0FOR PEER REVIEW 15 1o4f o1f81 7
 
 
FFigiguurere 55. . DDaattee ssttaammppiinngg tthhee ccaauussaalliittyy bbeehhaavvioior rrruunnnniningg frforomm mmananuufafcatcutruinrign gjojbo bpopsotisntignsg stot o
COVIDEMV between 1 January 2020 and 29 July 2022. 
COVIDEMV between 1 January 2020 and 29 July 2022.
 
Mathematics 2022, 10, 4780 15 of 17
4. Discussion
This study evaluated the explosive behavior and Granger causality episodes in manu-
facturing job postings in the United States and COVIDEMV. This study applied the novel
SADF and GSADF unit root tests with explosive behavior, and the novel time-varying
Granger causality test for a sample period ranging from 1 January 2020 to 29 July 2022—
during the COVID-19 pandemic. This study also examined the presence of explosivity and
causality between the variables. Further, this study used date stamping to identify the
subperiods of the explosive behavior and causality. The findings revealed that manufactur-
ing job postings in the United States exhibit explosive behavior, with several episodes of
exuberance (bubbles) across the sample period. On the other hand, COVIDEMV does not
exhibit explosivity during the period.
However, the results of the causality provide evidence of bidirectional causality be-
tween job postings and COVIDEMV. The findings further revealed several episodes of
causality running from each variable to the other. These findings support the submis-
sion of [44] who provided evidence of significant temporal variations in the causal nexus
between the United States industrial production, income and money supply. Similarly,
the study in [25] identified temporal instability in the oil and gas market by detecting
common periods of explosivity and bilateral causality between oil prices and gas prices
during the COVID-19 pandemic. Similarly, the findings of this study are in tandem with
the submission of [27,28], the authors of which argued that the adverse effect of COVID-
19-induced uncertainty on the overall economy, and the tourism and hospitality sector
in the US, varies by subsample periods, and the causal nexus exhibits temporal instabil-
ity. Thus, explosivity (explosive behavior) and the instability of time-series variables are
important features that must be captured in examining the causal relationship between
macroeconomic variables [39,44].
The findings of this study are plausible because the episodes of the exuberance (ex-
plosivity) and causality coincide with significant episodes in the history of the COVID-19
pandemic worldwide and in the United States particularly. This occurs during periods
such as May 2020, which marks when United States recorded a COVID-19-related death
toll of over 100,000 people for the first time during the COVID-19 pandemic. Further
episodes reflect when the United States experienced a spike in COVID-19 cases and deaths
in November 2020 due to the presidential election and after Halloween celebrations, with
substantially increases in COVID-19 cases across the United States.
In addition, after the discovery of the COVID-19 vaccines and after the vaccination
program was started, as well as after the conspiracy about the efficacy of the vaccines
spread and strict restrictions are periods that are also equally reflected in our findings.
Finally, the discovery of the Delta and the Omicron variants of the COVID-19 dictates the
explosion of the causal nexus between the variables which lasted to the end of the sample.
Therefore, the dates identified by the date stamping of the Granger causality between
job manufacturing job postings in the United States (JOBPUS) and COVIDEMV provided
interesting empirical insights concerning the job market conditions in the United States
during the COVID-19 pandemic.
5. Conclusions
This study applied novel unit root tests with explosive behavior and the novel time-
varying Granger causality test for a sample period ranging from 1 January 2020 to 29 July
2022. Further, this study used date stamping to identify subperiods of the explosive
behavior and causality. This study revealed that manufacturing job postings in the United
States exhibit explosive behavior, with several episodes of exuberance (bubbles) across the
sample period while COVID-19-induced uncertainty does not exhibit explosivity during
the period. However, the results of the causality provide evidence of bidirectional causality,
with several episodes between the variables.
Therefore, the time-series characteristics of the manufacturing job market conditions
and its causal nexus with COVIDEMV largely depend on the intensity of the distress, crisis
Mathematics 2022, 10, 4780 16 of 17
and instability caused by the pandemics. Hence, explosivity (explosive behavior) and the
instability of the causal nexus should be accounted for when modelling the job market
conditions in the United States, particularly during pandemic-related crises.
However, the limitation of this study is the use of only the US job market for this
study. Further studies can consider a panel of countries or conduct a comparative analyses
of the nexus between COVID-19-induced uncertainty and labor market conditions across
the world.
Author Contributions: Conceptualization, A.A.; methodology, A.A.; software, A.A.; validation,
F.V.B.; formal analysis, A.A. and F.V.B.; investigation, F.V.B. resources, I.O.; data curation, O.J.G.;
writing—original draft preparation, A.A., F.V.B., O.J.G. and I.O. writing—review and editing, F.V.B.;
visualization, I.O.; supervision, I.O. All authors have read and agreed to the published version of
the manuscript.
Funding: This research did not receive any specific grant from funding agencies in the public,
commercial, or not-for-profit sectors.
Data Availability Statement: Data for this study on EPU were sourced from http://www.policyun
certainty.com/ (accessed on 3 October 2022) We obtained the data on the natural gas price and crude
oil price from the British Petroleum (BP) Statistical Review of World Energy.
Acknowledgments: The authors’ gratitude is extended to the prospective editor(s) and reviewers for
their time.
Conflicts of Interest: We declare that there are no potential conflicts of interest in the current study
in any form.
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