Recession and recovery from the pandemic — Hunt, Zhang and Zhang, Research in Globalization

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An article in Research in Globalization 6 (2023) 100117, Recession and recovery from the pandemic, by Lester C. Hunt, Anqi Zhang and Shuonan Zhang. The abstract states that the authors develop an SIR-macroeconomic model with virus detection and inequality to study COVID-19 economic and health consequences. It reports a two-way relationship between the pandemic recession and inequality, which exacerbate each other, and states that accurate and extensive testing could break that vicious circle and could be a better alternative to lockdown for the life-or-economy trade-off.

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Hunt, Lester C.; Zhang, Anqi; Zhang, Shuonan

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Recession and recovery from the pandemic

Research in Globalization

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Suggested Citation: Hunt, Lester C.; Zhang, Anqi; Zhang, Shuonan (2023) : Recession and recovery
from the pandemic, Research in Globalization, ISSN 2590-051X, Elsevier, Amsterdam, Vol. 6, pp.
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https://doi.org/10.1016/j.resglo.2023.100117

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Research in Globalization 6 (2023) 100117

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Research in Globalization
journal homepage: www.sciencedirect.com/journal/research-in-globalization

Recession and recovery from the pandemic
Lester C. Hunt a, Anqi Zhang b, Shuonan Zhang c, *
a
University of Portsmouth, School of Accounting, Economics and Finance, Portsmouth PO1 2UP, UK
b
Fudan University, Institute of Belt and Road & Global Governance, Shanghai 200433, China
c
University of Southampton, Business School, Southampton SO17 1BJ, UK

A R T I C L E I N F O A B S T R A C T

Keyword: We develop an SIR-macroeconomic model with virus detection and inequality to study their implications for
COVID-19 economic and health consequences during a pandemic crisis. We find a two-way relationship between the
SIR-macro model pandemic recession and inequality that exacerbate each other although such a vicious circle could be broken by
Testing
accurate and extensive testing. This mitigation effect can be improved given complementary arrangements such
Inequality
as social protection. The extensive virus detection could not only be a better alternative intervention to lock-
down to break the “life-or-economy” trade-off, but also prevent the economy to be permanently damaged if
there is reinfection.

1. Introduction To facilitate this, we build a Susceptible-Infectious-Recovered-macro
(SIR-macro) model to analyse the recession and recovery of the
The COVID-19 pandemic crisis generated far-reaching impacts on pandemic crisis. Consistent with other modelling of feedbacks between
both public health and the economy. One year after the outbreak of the an epidemic and economic activities (Chari, Kirpalani, & Phelan, 2021;
pandemic, more than 520 million people had been infected with millions Eichenbaum et al., 2021; Farboodi, Jarosch, & Shimer, 2021), our model
of people dead. Moreover, the economic losses are unprecedently severe features both epidemiological and economic blocks with endogenous
with many economies suffering their largest slump in economic growth feedbacks between the two parts.
since World War Two. Moreover, the adverse effects of the COVID-19 In this paper, we augment this approach in several ways. In the
pandemic show a heterogeneous pattern that depends on the financial macroeconomic parts, we classify household inequality by financial
vulnerability of households (see Goldin & Muggah (2020) among others) status. The wealthy not only earn a wage or salary but they also obtain
with the poor tending to be more exposed to the pandemic than the rich. dividends given their ownership of firms. On the contrary, the poor have
Since the COVID-19 pandemic crisis is not an economic crisis alone, to rely on a wage or salary for living and hence their income is more
analysing the impacts of the pandemic requires a unified framework exposed than the wealthy, especially in quarantine. Such a classification
combining both epidemic dynamics and economic decisions. An essen of households is consistent with data showing that the majority of net
tial question is what factors determine the recession and recovery from wealth is held by the top half of households in the US and the EU (e.g. the
the COVID-19 pandemic? The goal in this paper is to understand the wealthy in the model, see Fig. 16 and 17 in Appendix B). Compared with
question by focusing on the interaction between an economic factor SIR-macro models including more sophisticated wealth distributions, we
(inequality) and pharmaceutical interventions1 (testing and quaran provide a parsimonious way to approach inequality, the solution of
tine). Moreover, we seek to understand the role of virus detection in the which does not require nontrivial computational techniques (Debortoli
dynamics of the pandemic crisis. This effect was not well-recognized, & Gali, 2018) thus there is no need to keep track of the distribution of
especially in the early outbreak of the pandemic. wealth in the presence of pandemic evolution. Furthermore, for the

* Corresponding author.
E-mail address: shuonan.zhang@soton.ac.uk (S. Zhang).
1
There are other important factors which are addressed in the literature (Baker, Farrokhnia, Meyer, & Pagel, 2020; Carroll, Crawley, & Slacalek, 2020; Coibion
et al., 2020; Eichenbaum, Rebelo, & Trabandt, 2021; Elenev et al., 2020; Faria-e Castro, 2021; Ganong, Noel, & Vavra, 2020). In terms of the economic sides, fiscal
stimulus and loose monetary policies are adopted to support the survival of firms and households. For pharmaceutical factors, vaccination and treatment are
important to end the widespread of the virus. Some non-pharmaceutical factors, such as social distancing and the use of face masks, are important to buy time for the
arrival of pharmaceutical measures.

https://doi.org/10.1016/j.resglo.2023.100117

Available online 10 February 2023
2590-051X/© 2023 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

epidemiological block, we incorporate virus testing, and for infected dynamics. An efficient and high level of detection rate could lead to a V-
people, we distinguish between those detected and those undetected. shaped recovery while an inaccurate and low level of detection rate
The virus detection can identify undetected people who are infected and could relatively delay the recovery and lead it to be U-shaped. The re
will enter quarantine. Compared with other macroeconomic models covery speed could be further delayed due to the presence of income
with testing, such as Aum, Lee, and Shin (2021) and Eichenbaum, inequality. An L-shaped recovery is likely when reinfection becomes
Rebelo, and Trabandt (2022), we isolate the effect of testing and that of possible and there is no sufficient pharmaceutical and non-
social protection. Accounting for this important difference provides pharmaceutical interventions, e.g., detection and vaccination, to deal
valuable insights highlighting the ambiguous implications of virus with this situation.
detection for the poor in the early outbreak of the pandemic. Detection is The rest of the paper is organized as follows. Section 2 provides some
useful since it helps to cut down the transmission path of the virus. motivational evidence followed by Section 3 that outlines the model
However, the livelihood of the poor entering quarantine would signifi with virus detection and inequality. Section 4 describes our parameter
cantly deteriorate in the absence of social protection. The combination calibrations. In Section 5, we present our quantitative analysis, followed
of the epidemiological and economic aspects enables us to investigate by Section 6 which relaxes some of the assumptions used in the model to
the interaction of the virus detection and the inequality, to further shed check the robustness of our key findings and conduct further analysis.
light on the magnitude of the recession and shapes of recovery of the Section 7 concludes with comments.
pandemic crisis.
Our model delivers important findings in several aspects. Firstly, we 2. Motivational Evidence
find that the pandemic crisis has heterogeneous effects on households
with the poor being more affected due to their vulnerable income po In this section, we provide empirical evidence to motivate the
sition. In turn, the presence of inequality exacerbates the pandemic model’s mechanism, particularly focusing on the relationship between
recession and also leads to a sluggish recovery. Secondly, the adverse economic growth and inequality or virus detection in the COVID-19
impacts of the pandemic crisis on both health and economic sides could pandemic period.
be significantly mitigated by extensive testing at the aggregate level. The
virus detection can reduce infection probability, which further encour
ages people to consume and work. Such an effect for the wealthy could 2.1. Inequality and growth
be more apparent, compared with the poor. For the latter, they would
enjoy benefits from the testing given complementary policies such as In this subsection, we examine the role of the pandemic in the
social protection policies which ensure their livelihood in quarantine. inequality-growth relationship. To this end, we first apply cross-
Thirdly, testing and quarantine is an effective intervention tool to sectional data in 2020 based on the World Development Indicators2 to
break the “life-or-economy” trade-off, induced by a lock-down. This explore the inequality-growth relationship after the pandemic following
finding implies that extensive testing could be an alternative tool to the model specification below.
combat the pandemic crisis, and stresses the importance of medical Growthi = α0 + α1 Inequalityi + α2 Xi + ∊i (1)
preparedness in the early outbreak of the COVID-19 pandemic. And
fourthly, we find that testing and quarantine is beneficial if reinfection is where Growthi denotes economic growth for country i, measured by
possible. The presence of reinfection is likely to undermine the economy either GDP growth or GDP per capita growth rate, Inequalityi represents
permanently. Comparing the two types of households, the poor would be the inequality for the country i. Here we measure inequality by the Gini
more affected by the loss of immunity or virus mutation. To deal with coefficient and the wealth share of the top 10% respectively. The
this situation, extensive testing could shield the economy from irre inequality literature distinguishes between different types of inequality
versible damage and prevent worsened inequality. but mainly focuses on income inequality, primarily measured by the
This paper is related to the rapidly growing literature on the impli Gini coefficient. Besides income inequality, wealth concentration is
cations of an epidemic, in particular, the interaction between the another important measure (Piketty, 2014) also considered. Following
COVID-19 pandemic and the economy (Eichenbaum et al., 2021; Far Keister and Moller (2000);De Nardi (2004);Zucman (2019), we adopt
boodi et al., 2021; Hall et al., 2020). In the literature, the epidemio the wealth share of the top 10% as another measure of inequality as
logical evolution is integrated into economic models to address the robustness check.
overall economic and health consequences simultaneously. Departing It should be noted that the association between inequality and
from them, we study these consequences at both the aggregate and the growth is not meant to imply a causal relationship. Intuitively, income
individual levels. Another strand of literature analyses the dynamic of or wealth inequality is less affected by external shocks, compared to
income and/or wealth inequality during the pandemic crisis (Adams- economic growth. The well-recognized determinants of income
Prassl, Boneva, Golin, & Rauh, 2020; Alon, Kim, & Lagakos, 2020; inequality include demographic features, labour quality, trade policies
Glover, Heathcote, & Krueger, 2020; Kaplan et al., 2020; Stantcheva, and other institutional aspects (Perugini & Martino, 2008; Tridico,
2022). Furthermore, since the pandemic crisis is not triggered by eco 2018), all of which are not easily changed by the pandemic. Therefore,
nomic factors, some papers investigate the driving factors of the we regard inequality as the dependent variable to empirically verify the
pandemic recession (Baqaee & Farhi, 2020; Brinca et al., 2020; Guer negative relationship between inequality and economic growth. More
rieri, Lorenzoni, & Straub, 2020). In terms of policy interventions, the over, the aim of empirical analysis is to highlight the relationship as part
pandemic crisis has also spurred the evaluation of the effects of non- of the motivation for our theoretical model rather than identifying
economic policies, such as pharmaceutical and non-pharmaceutical causality, although any casual identification or test would be interesting
policies, on fighting the pandemic crisis (Acemoglu, Chernozhukov, & for future research.
Werning, 2020; Alvarez, Argente, & Lippi, 2020; Berger, Herkenhoff, & Following Barro (1996), Xi is a set of control variables including
Huang, 2020; Brotherhood, Kircher, Santos, & Tertilt, 2020; Chari et al., population (logged), CPI (2010 = 100), lagged GDP growth rate, lagged
2021; Eichenbaum et al., 2022; Krueger, Uhlig, & Xie, 2022). health expenditure (share of GDP), government spending (share of
We contribute to the literature by developing a simple SIR-macro GDP), household consumption (share of GDP), and employment (share
model with virus detection and inequality. We argue that accounting of all population over 15). ∊i denotes regression errors. The detailed
for the interaction between detection and inequality provides important
insights into the pandemic recession, and address some potential chal
lenges for the recovery. In particular, we show that the virus detection 2
The 2020 cross-section sample includes 92 countries for which we could
and quarantine is an important element determining the recovery obtain data for the Gini coefficient.

2
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Table 1
Inequality-Growth relationship in the pandemic.
Variable 2020 Cross Section 2001–2020 Panel

Income Inequality Wealth Inequality Income Inequality Wealth Inequality

GDP GDP per capita GDP growth GDP per capita GDP growth GDP per capita GDP GDP per capita
growth growth growth growth growth growth
(i) (ii) (iii) (iv) (v) (vi) (vii) (viii)

Inequality − 0.107* − 0.00141** − 0.119* − 0.00104# 0.0425 0.000263 0.00843 0.000222
(0.0591) (0.000559) (0.0679) (0.000671) (0.0264) (0.000266) (0.0292) (0.000287)
Inequality*Pandemic − 0.0657* − 0.000568# − 0.00610 0.0000666
(0.0362) (0.000364) (0.0445) (0.000437)
Pandemic − 5.497*** − 0.0551*** − 7.199** − 0.0824***
(1.408) (0.0142) (2.813) (0.0277)
pop 0.441 0.749** 1.928* − 1.826**
(0.307) (0.294) (1.032) (0.903)
cpi − 0.00155 − 0.0000144 − 0.000722 − 0.00000475 − 0.00342*** − 0.0000345*** − 0.000996 − 0.0000167**
(0.00205) (0.0000195) (0.00131) (0.0000130) (0.00101) (0.0000101) (0.000825) (0.00000813)
l.gdpg 0.00598 − 0.00125 0.0567 0.000243 0.111*** 0.00107*** 0.165*** 0.00137***
(0.275) (0.00261) (0.198) (0.00198) (0.0189) (0.000191) (0.0201) (0.000198)
l.health exp − 0.322 − 0.000814 − 0.713** − 0.00379 − 0.121 − 0.00128 − 0.116 − 0.000729
(0.321) (0.00301) (0.278) (0.00277) (0.130) (0.00130) (0.149) (0.00146)
gov − 0.244** − 0.00315*** − 0.118 − 0.00230** 0.0391 0.000452* − 0.0471* − 0.000267
(0.121) (0.00107) (0.107) (0.00102) (0.0247) (0.000249) (0.0263) (0.000259)
con − 0.0477 − 0.000519 − 0.0934*** − 0.000972*** − 0.0916*** − 0.000978*** − 0.126*** − 0.00116***
(0.0415) (0.000394) (0.0351) (0.000350) (0.0136) (0.000137) (0.0148) (0.000146)
employ 0.0853 0.000386 0.0742* 0.000545 0.157*** 0.000965*** 0.124*** 0.00100***
(0.0606) (0.000578) (0.0398) (0.000398) (0.0305) (0.000299) (0.0328) (0.000323)
Obs 92 92 117 117 2477 2477 2521 2514
R2 0.232 0.2033 0.2697 0.183 0.5146 0.4847 0.4762 0.4595

Note: robust standard errors are reported in parentheses; *** p < 0.01, ** p < 0.05, * p < 0.1, # p = 0.15. All variables are defined in Table 4 in Appendix B.

descriptions of the variables are given in Table 4 in Appendix B.
Table 2
Second, the inequality-growth relationship is further investigated by
Testing-Growth relationship in the pandemic.
employing a fixed-effect (FE) panel data model from 2001 to 2020 in
order to compare the inequality-growth relationship in general and that Variables Full (v) 2020Q1-Q2 (vi) 2020Q3-2021Q4 (vii)

specifically in the COVID-19 pandemic period. We therefore treat 2020 Test 0.470* 0.335 0.432*
as the pandemic year and interact it with the Gini coefficient and esti (0.256) (0.854) (0.237)
pop 0.0128** 0.000891 0.0141***
mate the following specification (2).
(0.0054) (0.0165) (0.00523)
Growthit = α0 + α1 Inequalityit + α2 Pandemicit + α3 Inequalityit cpi 0.114*** 0.158 0.0926***
(0.0278) (0.118) (0.0257)
∗ Pandemicit + α4 Xit + α5 Yi + α6 Zt + ∊it (2) con − 0.864 − 4.559 − 0.273
(0.958) (2.694) (0.907)
where Pandemicit is a dummy variable (=1 if in the year 2020), capturing gov 2.390** 4.509 2.169**
(1.085) (2.823) (1.029)
the effect of the pandemic, Xit is the same control variable matrix as in inv − 1.376 − 0.903 − 1.712*
Eq. (1) and Yi represents the country fixed effects and Zt represent the (1.032) (2.917) (0.969)
year fixed effects3. Importantly, the estimate of coefficient α3 captures l.gdpg − 0.342*** 0.480 − 0.424***
the inequality-growth relationship in the pandemic period. (0.0716) (0.431) (0.0656)
l.gdp − 0.0275** 0.00593 − 0.0295**
Table 1 reports the estimated relationships between inequality and
(0.0120) (0.0331) (0.0114)
economic growth. Columns (i) and (ii) show results based on (1), and Obs 164 22 142
columns (iii) and (iv) show results based on (2). The results show that in R2 0.8129 0.7476 0.7009
the cross-sectional model (1) the coefficient of Inequality is negative and
Note: the dependent variable is GDP growth. Others are the same as above.
significant, suggesting a negative inequality-growth relationship during
the pandemic. Moreover, overall GDP growth is more affected by
inequality compared to the GDP per capita growth, although the pop shaped inequality–growth relationship. Halter, Oechslin, and Zwei
ulation is controlled. These findings are further confirmed by the panel müller (2014) find that the long-run (or total) effect of higher inequality
data model (2) which shows that the estimated coefficient for the tends to be negative on growth. In our analysis, although our aim is not
interaction term Inequalityit ∗ Pandemicit is negative and significant, re-examining the inequality-growth relationship, we find that such a
suggesting that the growth rate is lower in the pandemic year for a relation can be negative, which is shaped by the pandemic.4
country with a higher level of inequality. Interestingly, the estimated
coefficient of Inequality is positive and insignificant in the columns (iii) 2.2. Testing and growth
and (iv), suggesting that inequality is more likely to be a drag on growth
in the pandemic rather than in normal times. Based on different In this subsection, we examine the test-growth relationship. As the
frameworks, the literature suggest different relationships between
inequality and growth. Banerjee and Duflo (2003) suggest an inverted U-
4
Regarding the control variables, CPI, lagged health expenditure, govern
ment and household consumption have negative relationships with economic
growth, while population, lagged GDP growth and employment positively
3
Note that Pandemicit is a special term of yearly FE. relate to economic growth.

3
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

pandemic spreads in short periods and testing policies changes rapidly, Table 3
yearly data is insufficient and might be inappropriate. Given the relative Calibrated parameters.
data availability advantage of OECD countries, we focus on the quarterly Parameters Description Value
panel data based on OECD countries to estimate the relationship be
πr recovery prob 0.3873
tween COVID-19 testing and economic growth. The testing data is from πd decease prob 0.0016
European Centre for Disease Prevention and Control (ECDC). We explore P0 initial population 1
the testing-growth relationship after the pandemic using the following t0 initial infected people 0.001
specification: πu detection prob [0,0.6]
β discount factor 0.9992
Growthit = α0 + α1 Testit + α2 Xit + α3 Yi + α4 Zt + ∊it (3) λ price mark-up 1.2
H ss labour hour 30
A ss productivity 24.4872
where Test it represents COVID-19 testing rate per 100,000 people from
χ ss share of wealthy people 0.5
2020Q1, when the pandemic started, to 2021Q4 in 24 OECD countries,
and Xit is a set of control variables including population, CPI, lagged
GDP growth rate, government spending, and household consumption. be shown in Section 6.1, such extensions do not qualitatively change our
Table 2 presents the estimation results based on specification (3). findings, and hence we exploit simplicity of the benchmark model to
The full sample results shown in column (v) show that the estimated Test provide our major explanations.
coefficient is positive and significant at 10% level, suggesting a positive
relationship between testing and growth. We further consider that many 3.1. Firm
countries implemented job retention schemes after the outbreak of the
pandemic. Effects of such schemes may affect the testing-growth rela The representative monopolistic firm use labour Nt to produce
tionship, which could be captured by the full sample regressions. output Yt based on the following production function
Moreover, as Fig. 18 in Appendix B suggests, potentially the relation
Yt = AN t (4)
ships differed over the sample period if split after the first two quarters
of 2020 given that the implementation of such schemes took time and f
were very limited in the first two quarters of 2020. Hence, we conduct where A is the productivity of labour. The profit π t for the representative
sub-sample regressions, splitting the sample at 2020Q3 and the results firm is
are given in columns (vi) and (vii) of Table 2. This shows that although πft = pt Yt − mct Yt = pt AN t − wt Nt (5)
the estimated Test coefficient is positive over both periods it is only
statistically significant in the later stage of the pandemic, implying that Optimal price setting implies that the price is equal to a mark-up λ times
testing alone may not have been effective to combat the pandemic the marginal cost mct .
recession.
The motivational evidence in the sub-sections above provides pt = λmct (6)
empirical support to the main mechanism of our model detailed below.
where λ is the price mark-up. The marginal cost and the firm profit are
In particular, the empirical results are consistent with the model pre
dictions that, a higher degree of inequality exacerbates the economic mct =
wt
(7)
loss in the pandemic periods, which could be mitigated by extensive A
testing provided by other rescue schemes. ( ) ( )
Πft = λ − 1 mct Yt = λ − 1 wt Nt (8)
3. The Model
3.2. Epidemic transition
We build an SIR-Macro model with heterogeneous agents. There are
two types of households with different equity holding: “wealthy” and We incorporate epidemiology dynamics that models the transition of
“poor”. The wealthy households are owners of firms and hence enjoy the health status of households. The population can be divided into four
dividend payment as extra income. The poor households rely only on categories: susceptible (people who have not yet been exposed to the
wages as income. disease), infected (people who contracted the disease), recovered (people
In terms of the epidemic block of the model, we incorporate testing of who survived the disease and acquired immunity), and deceased (people
infected people in a conventional SIR model (Kermack & McKendrick, who died from the disease). The fractions of people in these four groups
1927). By doing so, we distinguish between detected and undetected are denoted by St , It , Rt and Dt , respectively. The number of newly
infectious people with the former entering quarantine and hence being infected people is denoted by Tt . Within the It category, we further
no longer be infectious. distinguish between detected and undetected infections. The former refers
Eichenbaum et al. (2021) implies that households are aware of their to infected people who are also tested, diagnosed, and under quarantine
health states in the absence of testing while Eichenbaum et al. (2022) while the latter refers to infected people who are not tested and free from
assume that households are unaware of their health states unless they quarantine. Specifically, undetected people may be asymptomatic6 or
get tested. Taking these studies as distinct ways to treat health infor show mild symptoms which are hard to distinguish from other disease,
mation, our model lies between the two treatments. In addition to such as seasonal flu.7 We label these two sub-categories as Idt and Iut
testing, we consider that households may use their limited information respectively.
to conjecture their health states5 when making consumption and Following Eichenbaum et al. (2021), susceptible people can become
working decisions. Such an assumption is further relaxed by developing infected through three ways: purchasing consumption goods, meeting at
two extensions in the model. In one extension, we consider that only a work, and random meeting with contagious people or materials.
fraction of households can conjecture their health states. In the other The total number of newly infected people is given by:
extension, we further consider that testing has wider coverage. As will

6
Long et al. (2020) find that asymptomatic patients may account 20% of
infected people.
5 7
For example, those who have close contacts with infected people are likely In the early outbreak of the COVID-19, many infected people could not be
to suspect that they are infected. tested.

4
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 1. The evolution of the epidemic.

Fig. 2. Impacts on consumption and hours.

( )( ) ( )( )
Tt = π1 St Cst I ut Ciu + π2 St N st I ut N iu + π 3 St I ut Rt+1 = Rt + πr It (14)
⏟̅̅̅̅̅̅̅̅̅̅̅ ⏞⏞̅̅̅̅̅̅̅̅̅̅̅t ⏟due to consumption ⏟̅̅̅̅̅̅̅̅̅̅̅̅⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅⏟
t
due to working

(9) Dt+1 = Dt + πd It (15)
where π1 , π2 , and π3 are parameters governing the magnitude of each
Popt+1 = Popt − πd It (16)
source of infection. Comparing with Eichenbaum et al. (2020, ?), we
assume that only undetected people are infectious. detected people enter where π r , πu and π d denote probability of recovery, detection and
quarantine and hence they would not be infectious. decease respectively. Note that the increase of πu may capture larger
The evolution of each category of people are given by: coverage of testing as in Eichenbaum et al. (2022) and more accurate
St+1 = St − Tt (10) testing.

( )
I ut+1 = I ut + Tt − πr + πd + πu I ut (11) 3.3. Households
( )
I dt+1 = I dt + πu I ut − πr + πd I dt (12) We classify households by health and income conditions. The
potentially healthy status is defined in Section 3.2. In terms of the in
It = I dt + I ut (13) come status, a fraction χ of households are wealthy while the remaining

5
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 3. Impacts of different detection rates.

Fig. 4. Impacts on consumption and hours: with inequality.

1 − χ are poor. Both types of households enjoy wage incomes but only ( )
θ( i,j )2
wealthy people are owner of firms and hence obtain firm profits. The u ci,j
t , n i,j
t = lnci,j
t − n (17)
poor may be also interpreted as the working classes and the wealthy 2 t
people as entrepreneurs.
ci,j i,j f
t = wt nt + 1π t (18)
Next, we describe the optimization problems for each type of agent.
The upper index i(i = s,iu,r) denotes the health status and j(j = w,p) i,j i,j
denotes the income status. The utility function (Eichenbaum et al., where ct and nt denote consumption and hours worked respectively. 1
f
2021) and the budget constraint for a type-i,j person is is an indicator variable equal to one if the household is wealthy. π t is
profits per head or dividend payments.

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L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 5. Implications of inequality for consumption loss. Note: This figure shows the relationship between 1-year aggregate consumption loss and degree of inequality.

Susceptible people The lifetime utility of representative susceptible S +Iu +R
(18). Θt = Stt +Itt +Rtt is an adjustment factor, due to the presence of testing
people is and quarantine. It captures the fact that wealthy people in the infected
U s,j
( s,j s,j ) [( )
+ β 1 − τt U s,j iu,j
]
(19) detected category earn dividend payment but do not work to produce
t = u ct , nt t+1 + τt U t+1
output. Since Iut < It ,Θt < 1. If there is no testing and quarantine, Iut = It
where τt is the infection probability and Θt = 1. We obtain the standard first order conditions as in other
( ) ( ) macroeconomic models.
τt = π1 cst I ut Ciut + π2 nst I ut N iut + π3 I ut (20) Infected undetected people The lifetime utility of infected unde
tected people is
Optimization yields ( ) [( ) ]
( ) U iu,j
t = u ciu,j iu,j
t , nt + β 1 − πu − πr − πd U iu,j id,j r,j
t+1 + π u U t+1 + π r U t+1 (24)
1
= λ s,j
t + β π I u iu
C
1 t t U s,j
t+1 − U iu,j
t+1 , j = w, p (21)
cs,j
t Optimization yields
( )
θns,p s,p u s,p
iu
t = λt wt − βπ 2 I t N t U t+1 − U t+1
iu,p
(22) 1
= λiu,j j = w, p (25)
t ,
ciu,j
t
( )
θns,w = λs,w
t AΘt − βπ u iu
2It Nt U s,w
t+1 − U iu,w
t+1 (23)
(26)
t
θniu,p
t = λiu,p
t wt

where λst is the Lagrange multiplier associated with the budget constraint

Fig. 6. Impacts of different detection rates: with inequality.

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L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 7. Consumption loss and detection. Note: This figure shows relationships between 1-year averaged consumption loss and detection for aggregate case, sus
ceptible people, wealthy people and poor people.

θniu,w
t = λiu,w
t AΘt (27) the goods and the labour market clear.

Infected detected people The lifetime utility of infected detected St Cst + I ut Ciu d id r
t + I t Ct + Rt C t = AN t (33)
people is
( ) [( ) ] St N st + I ut N iu r
t + Rt N t = Nt (34)
U id,j
t = u cid,j id,j
t , nt + β 1 − πr − πd U id,j r,j
t+1 + π r U t+1 (28)
( ) i,r
Cit = χ ci,w
t + 1 − χ ct , i = s, iu, id, r (35)
Detected people enter quarantine immediately after detection and they
would stop working (Eichenbaum et al., 2022). Hence their wage in N it = χ ni,w
( ) i,r
(36)
t + 1 − χ nt , i = s, iu, id, r
come becomes zero. In this case, the rich consume profit income while
the consumption of the poor becomes zero. This might be an extreme
4. Calibration
assumption but it allows us to highlight different degrees of vulnera
bility of households to the pandemic crisis. Moreover, this assumption is
Table 3 reports the calibrated parameter values used for the quan
consistent with the data used in our calibration below, which shows that
titative analysis. Each period corresponds to a week.
the share of wealth held by the bottom half of households (i.e., the poor
In terms of the parameter values related to pandemic evolution, we
in the model) is very small and they rely on wage income for living. In
closely follow the approach used in Eichenbaum et al. (2021) for cali
Section 5.3, we relax this assumption and allow households to receive
bration, except for the detection rate π u which is not present in the
social protection. Comparatively, the model in Eichenbaum et al. (2022)
literature. As suggested by Atkeson (2020), it takes 18 days to recover or
implies that detected people receive consumption through government
die from infection. Hence, we set π r + πd =7/18. For the mortality rate,
transfers. Our model separates the wage income from government
Eichenbaum et al. (2021) set it as 0.5% based on the US data but given
transfers thus allowing us to focus on the effect of detection alone in our
that the EU mortality rate is slightly lower than the US counterpart, we
benchmark model.
set the mortality rate as 0.4%. This implies πd is 0.004∗7/18. Following a
Recovered people The lifetime utility of is recovered people8 is
general pattern of an epidemic that 37% of virus transmission is related
( r,j r,j )
U r,j
t = u ct , nt + βU r,j
t+1 (29) to working, 16% of transmission is related to consumption (Eichenbaum
et al., 2021), the infection parameters π1 , π2 , π 3 are calibrated as
Optimization yields 7.8408 ∗ 10− 8 , 1.2442 ∗ 10− 4 , and 0.3902, respectively.
The discount factor is calibrated as 0.961/52 on a weekly basis
1
= λr,j
t , j = w, p (30) (Krueger et al., 2022). The steady state labour hour H and productivity A
cr,j
t
are set as 30 and 24.4872 respectively to match the weekly working
hour and income data based on the Europe from the Eurostat database.
θnr,p r,p
t = λ t wt (31)
The share of wealthy household χ is set as 0.5, consistent with the fact
θnr,w = λr,w (32) that more than 96% of net wealth is held by top 50% of wealth per
t AΘt
centiles in the Europe9. Finally, the price mark-up λ is calibrated as 1.2
t

(Schmöller & Spitzer, 2020).
3.4. Equilibrium
5. SIR-Macro Model Results
In equilibrium, each household optimizes their decisions and both
We start the analysis for the benchmark case where household

8
The recovery probability may also depend on the financial condition of
household. To keep traceability of the model, we do not include this type of
9
heterogeneity. Source: The World Inequality Database, https://wid.world/data/

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Fig. 8. Consumption loss and detection: with social protection. Note: This figure shows relationships between 1-year averaged consumption loss and detection for
aggregate case and poor people.

Fig. 9. Impacts on consumption and hours: lock-down v.s. testing.

incomes are equal. In such a case, the focus is on the implications of the Turning to the economic sides, Fig. 2 shows that the presence of
detection on both the health and economic aspects. Then we present detection could also mitigate the magnitude of the pandemic recession.
results based on the extended model with heterogeneous income and In such a case, the decline of aggregate consumption and labour hours
compare with the benchmark results. Through the comparison we are dampened (see blue lines in Fig. 2). Comparing the three categories
emphasize the roles of inequality in the pandemic recession and how the of households, the recovered people are the least affected, followed by
inequality is interacted with virus detection. susceptible, while infected people are the most affected. The latter result
is due to the reason that quarantined people (after detection) could not
5.1. Implications of the detection work and hence their consumption would be also limited.
Fig. 3 plots the impacts of the pandemic of different detection rates
Fig. 1 and 2 respectively display the population dynamics and eco on consumption (left panels), hours (middle panels), and health out
nomic impacts following the outbreak of the pandemic. For the illus comes (right panels). Fig. 3 shows that the impact on both the economy
tration purpose, we set the detection rate as 5%. We use a relatively low and health suffer the most without any testing (illustrated by the dashed
detection rate with the consideration that testing could be difficult and pink lines) and even with testing but a small detection rate of 2.5% (the
inaccurate at the beginning of the pandemic outbreak. In spite of this, a full blue lines), the magnitude of the recession, and the impact on
more comprehensive investigation is presented later. infection and mortality are only slightly smaller. With a higher detection
Compared with the case without detection as in Eichenbaum et al. rate of 10% (the green lines) the magnitude of the recession, and the
(2021), there is a decrease in the amount of people in the infected and impact on infection, and mortality is reduced with the largest loss of
death categories. This finding is not surprising since the detected people aggregate consumption being 1.5%. with an even higher detection rates
would enter quarantine and hence the transmission probability would of 25% and 50%, the impacts of the pandemic on both the economy and
be cut down. household health becomes very limited (the red and yellow lines) with a

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L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 10. The evolution of the epidemic: lock-down v.s. testing.

very different evolution of the economy and health impacts. In the cases After establishing the implications of the inequality, we further
with high detection rates, the economy rebounds quickly as the trans investigate its interaction with detection to further shed light on the
mission path of the pandemic is quickly cut down – a V-shaped recovery. pandemic crisis. To this end, the same experiment as in Fig. 3 is per
For the cases with low detection rates, they lead to sluggish containment formed but based on the heterogeneous income model. The results are
of the pandemic and the influence on the economy is prolonged. shown in Fig. 6. Contrast to the economic impacts as in Fig. 3, the
Consequently, not only the magnitude of the recession is more sizeable, magnitude of the recession does not show a monotonic decreasing
but also the recovery is relatively slow, leading to an U-shaped recovery. relationship with detection rates when inequality is present. Instead, the
relationship is found to be nonlinear. For relatively low detection rates
(e.g., 2.5% and 5%), the magnitude of the recession increases with
5.2. The presence of inequality detection. While the relationship turns to be decreasing when detection
rates become high (e.g., 25% and 50%). These findings imply a U-shaped
In this section, we relax the homogeneous income assumption and relationship between detection and magnitude of recession. Such a
allow a fraction of households, the wealthy, to obtain all firm dividends. finding is confirmed in Fig. 7.
Fig. 4 reports the impacts of the pandemic on the economy. Essentially, Fig. 7 shows U-shaped relationships between the detec
The upper panels of Fig. 4 compare the economic dynamics at the tion rate and 1-year averaged consumption loss at the aggregate level,
aggregate level between the benchmark and the inequality cases. This for the susceptible category and poor people. On the contrary, the
shows significant differences in the response of aggregate consumption relationship for wealthy people is negative. The relationship at the
and hours. The presence of income heterogeneity significantly exacer aggregate level (blue curves) is driven by the relationship between
bates the recession, leading to a larger magnitude of loss and slow detection and poor people. As assumed by the model, the poor will lose
recovery. all income after detected as infection. On one hand, increasing the test
Moving attention to the middle panels of Fig. 4, they show that the rate would reduce transmission probability, which encourages working
susceptible category is the most affected due to the presence of the and consumption, leading to less significant recession (labelled as Effect
inequality. Compared with Fig. 2, the largest loss of susceptible house One). On the other hand, higher test rates add pressure for the poor in
holds could be near 30%, four times larger as in the benchmark case. the fear of being detected and losing all incomes. Hence, they also try to
While we are cautious in interpreting the quantitative results, the size avoid virus transmission by cutting down consumption and working
able difference indeed suggests a significant role of the inequality in (labelled as Effect Two). To see Effect two, we borrow the equilibrium
exacerbating the recession. conditions of poor people (37) and (38) for explanations.
The lower panels of Fig. 4 show consumption and hours for house ( ) [( ) ]
holds classified by different wealthy levels. The impacts on the rich are U iu,p
t = u ciu,p iu,p
t , nt + β 1 − πu − πr − πd U iu,p r,p
t+1 + π r U t+1 (37)
similar to the benchmark level, both of which are comparatively lower ( )
than those on the poor. Since the poor only have one source of income in 1 s,p u iu
s,p = λt + βπ 1 I t C t U s,p iu,p
t+1 − U t+1 (38)
the model, it is not surprising that they are vulnerable to the pandemic ct
crisis.
According to Eq. (37), the increase of detection rate πu decreases lifetime
To further explore the implication of income heterogeneity, we
utility for the poor if they are infected. Given others as constant, the
investigate a relationship between inequality and the magnitude of the
recession. Fig. 5 plots the relationship between (in-) equality and 1-year utility gap Us,p iu,p
t+1 − Ut+1 would be broadened. With this consideration, the

loss of aggregate consumption. A larger (smaller) value on the horizontal susceptible poor people could reduce consumption, as implied by Eq.
axis denotes a larger degree of (in-) equality and less (more) significant (38).
income heterogeneity. Specifically, the figure shows a positive rela The two counteracting forces play quantitatively different roles at
tionship between the magnitude of the recession and the degree of different detection levels. Our results imply that increasing the testing
inequality. This result further corroborates the finding that the presence rate thus reducing the transmission probability and encouraging work
of inequality exacerbates the pandemic recession. Moreover, these re and consumption, i.e., Effect One, would be relatively more powerful
sults are consistent with the motivational empirical evidence presented when the detection rate becomes high. Wealthy people have an alter
in Section 2 (see Table 1) regarding the inequality-growth relationship native source of income so that even under quarantine, they can still
in the pandemic crisis. earn dividends owing to their firm ownership. Hence, the role played by

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L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 11. Evolution of the economy and epidemic: alternative models. Note: The fraction of households aware of their health states ω is set as 0.2 for illustration
purpose. Results in this figure are robust to different value of ω.

Effect Two may not overweight Effect One. On the contrary, Effect Two relative low level is not effective to combat the pandemic crisis. In the
can be more powerful for the poor as they would lose all income under next Section, we consider a complementary arrangement which could
quarantine. Overall, the wealthy benefit more from detection than the mitigate the sided effects of low detection and deliver monotonic
poor for the economic side. Despite the asymmetric economic impacts of beneficial effect of detection as suggested by column (i) and (iii) in
detection, its effects on health outcomes are positive for both groups of Table 2.
people - Fig. 6 and Fig. 3 suggest that the health outcomes do not show a
notable difference. 5.3. Roles of social protection
Given that the low-detection region is likely to be coincident with the
initial outbreak of the pandemic, the heterogeneous implications of the Section 5.2 establishes nonlinear impacts of detection for the poor
detection is also consistent with the motivational evidence presented in due to their financial vulnerability. In this subsection, an extended case
Section 2 (Table 2). Due to the presence of inequality, detection alone at that quarantined people are protected by the social security system is

Fig. 12. Consumption loss: alternative models. Note: The same as above.

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L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 13. Impacts on consumption and hours: with reinfection.

considered. Even if they cannot work after detection, they can obtain ( )
government transfers which are used for consumption. We assume that 1 + μt ci,j i,j f
t = wt nt + 1π t + Γt (39)
the transfer amount is equal to the income of recovered people
f where μt captures the containment rate, modelled as a tax on con
(Eichenbaum et al., 2022). In this case, cid,p = cr,p
t , and ct
id,w
= cr,p
t + πt .
t sumption, analogous to Farhi and Werning (2014). The proceeds due to
Such an extended case is consistent with income support or short-time
the containment are rebated lump sum to all agents Γt . Following
working programs implemented in many European countries (ECB,
Eichenbaum et al. (2021), an optimal containment rate can be obtained
2020).10 The aim of this subsection is to explore the implication of
by maximizing social welfare U0 –a weighted average of the lifetime
detection in the presence of support programs rather than evaluating
utility of different people U0 = S0 Us0 + Iiu iu
0 U0 .
effectiveness of these programs.
Fig. 9 shows the evolution of consumption and hours at the aggregate
We highlight relationships between the detection rate and con
level, and consumption for susceptible and infected people. With 20% of
sumption loss for the aggregate case and poor people in Fig. 8. There are
detection rate, the economy is strongly hit by the pandemic crisis at the
2 important differences after accounting for the social protection for
beginning but recover quickly. If the detection rate becomes 5%, the
detected people. First, the relationships are likely to be monotonic and
recession is more significant and the recovery becomes more sluggish,
negative with social protection, implying that the livelihood for the poor
despite a smaller initial response. In another case with lock-down but no
under quarantine would no longer be a major threat. Second, the pres
detection, the evolution of the aggregate economy is similar to the low-
ence of social protection also dampens the magnitude of the recession
test case.
given others as constant. For instance, at 20% of detection rate, the 1-
In terms of the health outcomes, Fig. 10 shows the evolution of
year aggregate consumption loss is 0.3% in Fig. 8 while that loss is 4%
people in different healthy categories. Not surprisingly, the relatively
in the absence of the social protection (see Fig. 7). Finally, our finding is
high detection rate leads to the least infection and death. Comparing the
consistent with literature showing that government interventions could
low-test case with the lock-down, we find that the testing, even at the
reduce inequality (Stantcheva, 2022).
relatively low level, could lead to fewer people being infected and dead.
Moreover, Fig. 9 and 10 together suggest an interesting finding. Between
5.4. Lock-down v.s. testing
testing and lock-down leading to the similar aggregate economic per
formance in the pandemic crisis, the case with testing could be more
During the pandemic crisis, many countries implemented contain
effective in containment of the virus transmission, thereby leading to
ment policies such as lock-downs to prevent the transmission of the
better health outcomes. We therefore interpret the testing case as smart
Covid-19. In this section, we compare the effects of the lock-down with
quarantining with specific targets while the lock-down as massive
testing. In particular, we compare the evolution of the epidemic in three
quarantine. In this sense, the former measure is not surprisingly seen to
cases: (1) a lock-down as described in Eichenbaum et al. (2021) without
be a more efficient tool to fight the pandemic crisis.
detection, (2) relatively low detection rate (5%) without lock-down, and
(3) relatively high detection rate (20%) without lock-down.
6. Further Analysis
With the containment policy, the budget constraint for a type-i,j
person becomes
In this section, we conduct further analysis by relaxing some as
sumptions. Section 6.1 investigates robustness of our key findings by
developing two extended models which are more realistic or fit the later
stage of a pandemic crisis. Whereas, Section 6.2 investigates how re
10
For example, the UK implemented a COVID-19 job retention scheme or infections affect a pandemic crisis.
furlough scheme in 2020. The scheme is a type of wage subsidy program aiming
to support employees who are on furlough to receive some grants. The gov
ernment is the major payer for this scheme.

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Fig. 14. Consumption loss and immunity loss rate. Note: This figure shows relationships between 4-year averaged consumption loss and immunity loss rate for
aggregate case, susceptible people, wealthy people and poor people. For each case, we further classify it by a relatively low detection rate (10%, red lines) and a
relatively high detection rate (20%, green lines).

Fig. 15. Consumption loss and detection: with reinfection. Note: This figure shows relationships between 4-year averaged aggregate consumption loss and detection
rate. We include four cases in the figure: no-reinfection, a relatively low immunity loss rate (2%), a relatively high immunity loss rate (10%), and the relatively high
immunity loss rate with vaccine.

6.1. Extended models with partial awareness of infection and wider ( )
1
testing = λ s,j
t + β π 1 ωI u iu
C
t t U s,j
t+1 − U iu,j
t+1 , j = w, p (41)
cs,j
t

In the main analysis, we assume that households can conjecture their ( s,p )
health state. In this section we relax this assumption by considering that θns,p s,p u iu iu,p
t = λt wt − βπ 2 μI t N t U t+1 − U t+1 (42)
only a fraction ω of households have sufficient information to do so. This ( s,w )
would change the utility of susceptible people as follows: θns,w
t = λs,w u iu iu,w
t AΘt − βπ 2 μI t N t U t+1 − U t+1 (43)
Susceptible people (S)
( ) [( ) ( ) s,j ] After differentiating awareness of infection among households, the
U t = u cs,j
s,j s,j
t , nt + β 1 − τt U s,j iu,j
t+1 + ωτt U t+1 + 1 − ω τt U t+1 (40) model implies that virus detection only applies to existing infected un
detected Iut . This implication might not be realistic and we further
Eq. (40) implies that 1 − ω fraction of infected undetected people are develop the model such that detection also applies to the newly infected
unaware of their infection and hence, they believe that they still enjoy Tt . The utility function of the susceptible becomes
utility as susceptible. ωτt can be interpreted as subjective infection Susceptible people (S)
probability, in a the spirit of Eichenbaum et al. (2022). The optimal ( s,j s,j ) [{( ) ( ) [ iu,j ( ) s,j ]}
conditions change as follows: U s,j
t =u ct ,nt +β 1− τt U s,j id,j
t+1 + π u τt U t+1 + 1− π u τt μU t+1 + 1− μ U t+1

(44)

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L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 16. Net wealth in the US: comparing the top and bottom 50%. Source: the Distributional Financial Accounts.

The optimal conditions change as follows: CoV-2 starts to decrease within 2–3 months after infection (e.g., Long
[ ( ) ( )( )] et al. (2020)). The duration of the immunity might be shorter than other
1 s,j u iu s,j id,j s,j iu,j SARS-CoV or MERS-CoV. Furthermore, some recovered people got
= λ + β π I C π U − U + μ 1 − π U − U , j
infection again though this probability is low. Moreover, we observed
t 1 t t u t+1 t+1 u t+1 t+1
cs,j
t

= w, p frequent mutations of SARS-CoV-2, such as the Delta and the Omicron
(45) variants. All these facts and findings call for investigation of implications
of the pandemic when reinfection is possible. Hence, we relax the no-
θns,p s,p u s,j
iu
[ ( id,j
U s,j
) ( )( iu,j
)]
(46) reinfection assumption in this subsection. By doing so, we attempt to
t = λt wt − βπ 2 I t N t π u U t+1 − U t+1 + μ 1 − π u t+1 − U t+1
analyse the implication of the pandemic crisis for the recession and
θns,w = λs,w u iu
[ ( s,j id,j
) ( )( s,j
U t+1 − U iu,j
)] subsequent recovery in this extended case. In the mid-to-long run of an
t AΘt − βπ 2 I t N t π u U t+1 − U t+1 + μ 1 − π u
epidemic, vaccine might be developed and it is essential to keep people’s
t t+1

(47)
immunity. Hence, we also incorporate vaccine in the model to investi
In the second extended model, the evolution of infected categories be gate its implications when reinfection is possible.
comes Taking into account the immunity lost and vaccine, the evolution of
( ) ( ) susceptible and recovered people become as follows
I ut+1 = I ut + 1 − πu Tt − πr + π d + π u I ut (48)
St+1 = (1 − δv )St − Tt + πs Rt (50)
( )
I dt+1 = I dt + πu Tt + π u
uIt − πr + πd I dt (49)
Rt+1 = Rt (1 − πs ) + π r It + δv St (51)
Compared to Eqs. (11) and (12), (48) and (49) imply a wider and faster where πs and δv denote the immunity loss rate and vaccination rate,
detection system so that infected people might be detected immediately respectively. Eq. (50) and (51) suggest that each period a fraction of
after infection. Such a situation is likely to correspond to a relatively recovered people becomes susceptible, and in the meanwhile a fraction
later stage of an epidemic when testing capacity is sufficiently large and of susceptible people enter recovery category after vaccinated. The
testing procedure is swift. Since our major focus is the early outbreak of presence of the immunity lost and vaccine will also change lifetime
an epidemic, we use the extended models in this subsection as further utility for recovered and susceptible people, respectively.
analysis. Recovered (R)
Fig. 11 and 12 compare the benchmark findings with the two ( ) [( ) ]
extended cases regarding evolution of the economy and epidemic, and θ
max U rt = lncrt − nrt + β 1 − πs U rt+1 + πs U st+1 (52)
consumption loss. Overall, Fig. 11 and 12 confirm our key findings based r r
ct ,nt 2
on the benchmark model regarding (a) the two-way negative relation
Susceptible people (S)
ship between inequality and pandemic recession, and (b) the heteroge
( s,j s,j ) [( )( ) ( ) iu,j ]
neous implications of detection. U s,j
t = u ct , nt + β 1 − δv 1 − τt U s,j v v r,j
t+1 + 1 − δ τt U t+1 + δ U t+1 (53)

To begin with, we set πs at 5%, implying that on average recovered
6.2. An attempt to relax no-reinfection assumption people may significantly lose antibodies about 5 months after recovery.
Note that this ratio may not be a rigorous value and it is mainly served as
In the model, we assume that recovered people have sufficient im illustration purpose. The weekly vaccination rate δv is set at 0 if t < 52,
munity so that they would not be affected again. If the majority of people and 1/52 if t > 52, implying that it takes one year for vaccine to be
obtains immunity, either through vaccination or recovery after infec discovered and another one year for a person to get vaccine on average
tion, the spread of the pandemic would be unlikely, implying that herd (Eichenbaum et al., 2020).
immunity occurs. However, it remains questionable if the no-reinfection Fig. 13 shows the evolution of the economy in this extended case. It
assumption holds. Medical research finds that the antibody of SARS-

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L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 17. Net wealth in the EU: comparing the top and bottom 50%. Source: the World Inequality Database (WID).

shows that the pandemic could permanently affect the economy, leading might not be long-lasting or weakened, e.g., due to potential mutation of
to irreversible damage – a L-shaped recovery. For example, the aggre the virus, efficient and swift tests could be useful.
gate consumption would be about 15% less than the pre-crisis level for
one year after the pandemic outbreak, contrast to the benchmark case 7. Conclusion
where consumption starts to recover to the pre-crisis level at that time.
Nevertheless, the presence of vaccine could still save the economy, The COVID-19 pandemic raised challenges for the economics re
leading it back to the pre-crisis situation. The lower panels of Fig. 13 searchers to address both the economic and health consequences of the
further shows that the impacts on households with different wealth crisis, resulting in the publication of studies addressing the interaction
levels also differ; the poor household is more affected. In spite of this between the epidemic and the economy. This paper further that litera
difference, both types of households would suffer from permanent loss of ture by addressing an additional set of important implications of the
consumption. The rationale is that the virus would exist with people in pandemic crisis, and shedding light on the recession and recovery of the
the long-run who have to permanently reduce consumption and working crisis. Although this study is motivated by the COVID-19, we take it as an
to avoid being infected. On the contrary, the presence of vaccine would example to shed light on how to promptly respond to a general
benefit both groups of households to limit the impact of the virus. epidemic. To study the economic and health consequences of an
We further investigate relationships between the magnitude of the epidemic, we develop a SIR-macro model with virus detection and in
consumption loss and immunity loss rate, as depicted in Fig. 14. Since come inequality for households. Essentially, we find a two-way rela
the reinfection is more likely to affect long-run dynamics of the tionship between the pandemic recession and inequality, both of which
pandemic recession as shown in Fig. 13, we show 4-year averaged can exacerbate one another. We show that such a vicious circle could be
consumption loss rather than the 1-year loss in Fig. 14. In general, this broken by accurate and extensive testing. In order to maximize the
figure shows positive relationships between the speed of losing the im benefits of the virus detection, especially for the poor, some comple
munity and magnitude of consumption loss. Comparatively, the re mentary arrangements such as social protection should be provided.
lationships are much steeper when the detection rate is relatively low. In These policies are important for the containment of the virus in the early
particular, the most pronounced impacts are found from the poor, outbreak of the pandemic when testing capacity and accuracy were low.
indicating that they are more likely to suffer from the immunity loss Our framework provides important insights based on a simple model,
issue than the rich. The decision of economic activities for the poor could highlighting several fundamental forces of the pandemic crisis. Further
be the most sensitive to the strength of antibody. On the contrary, the research could therefore enhance our framework by incorporating some
relationships become insensitive when the detection rate is relatively important real-world factors such as considering the role of monetary
high. Therefore, the presence of reinfection might exacerbate inequality and fiscal policies in the dynamic of inequality during the pandemic
in the pandemic recession given the relatively low detection rate. recession. In our model, income and wealthy inequality are two sides of
However, accurate and extensive testing could be helpful to deal with the same coin. One may distinguish them to further investigate hetero
the reinfection issue, to prevent deep recessions and enlarged inequality. geneous implications of an epidemic. Regarding the health part of the
Finally, we investigate how the testing may interact with the im model, different arrangements of testing could be explored, such as that
munity loss issue. Fig. 15 shows that high detection rates could signifi provided by private companies and testing decisions could be endoge
cantly mitigate the adverse effects due to the reinfection. For example, nous choices of households. Moreover, it is important to consider sector
the gap between the red dash line and the blue solid line in Fig. 15 be heterogeneity and study the supply-sided implications to further identify
comes negligible with high detection rates. Moreover, the presence of the long-run effects of the COVID-19 pandemic.
the vaccine shifts the consumption loss upward, indicating that the
vaccine is another important force to rescue the economy. Interestingly, Declaration of Competing Interest
the effect of the vaccine becomes larger (i.e., the gap between the green
dot line and the orange dash dot line) with a higher detection rate. This The authors declare that they have no known competing financial
finding implies a complementary role of detection to the vaccine in interests or personal relationships that could have appeared to influence
rescue. For example, in an extreme case that even if effects of the vaccine the work reported in this paper.

15
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Fig. 18. Testing and growth.

Appendix A. Equilibrium Conditions

.
( )( ) ( )( )
Tt = π1 St Cst I ut Ciu
t + π2 St N st I ut N iu
t + π3 St I ut (A1)

St+1 = St − Tt (A2)
( )
I ut+1 = I ut + Tt − πr + πd + πu I ut (A3)
( )
I dt+1 = I dt + πu I ut − πr + πd I dt (A4)

It = I dt + I ut (A5)

Rt+1 = Rt − πr It (A6)

Dt+1 = Dt + πd It (A7)

Popt+1 = Popt + πd It (A8)
( s,p s,p ) [( ) ]
U s,p
t = u ct , nt + β 1 − τt U s,p iu,p
t+1 + τt U t+1 (A9)
( ) [( ) ]
U s,w
t = u cs,w s,w
t , nt + β 1 − τt U s,w iu,w
t+1 + τt U t+1 (A10)
( ) [( ) ]
U iu,p
t = u ciu,p iu,p
t , nt + β 1 − π u − πr − π d U iu,p id,p r,p
t+1 + π u U t+1 + π r U t+1 (A11)
( ) [( ) ]
U iu,w
t = u ciu,w
t , niu,w
t + β 1 − πu − πr − πd U iu,w id,w r,w
t+1 + π u U t+1 + π r U t+1 (A12)
( ) [( ) ]
U id,p
t = u cid,p id,p
t , nt + β 1 − πr − πd U id,p r,p
t+1 + π r U t+1 (A13)

16
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

Table 4
Data used in the empirical analysis.
Variables Description Source

Growth GDP Growth WDI,
OECD
GDP per capita Growth WDI
Gini Gini index WDI,
SWIID
Test Weekly testing rate per 100000 people ECDC
pop Population, total (logged) WDI
cpi Consumer price index (2010 = 100) WDI,
OECD
gov General government final consumption expenditure (% WDI,
of GDP) OECD
con Households and NPISHs final consumption expenditure WDI,
(% of GDP) OECD
inv Gross capital formation (% of GDP) WDI,
OECD
health_exp Domestic general government health expenditure (% of WDI
GDP)
employ Employment to population ratio, 15+, total (%) WDI
(modeled ILO estimate)

Note: WDI represents World Development Indicators, OECD represents OECD
quarterly national account database, SWIID represents the Standardized World
Income Inequality Database, and ECDC represents European Centre for Disease
Prevention and Control COVID-19 datasets. Yearly data of controls are obtained
from WDI, while quarterly data are from OECD. The missing value of Gini is
interpolated according to the previous data and other development Indicators.
Test data are aggregated from weekly to quarterly frequency.

( ) [( ) ]
U id,w
t = u cid,w
t , nid,w
t + β 1 − πr − πd U id,w r,w
t+1 + π r U t+1 (A14)
( r,p r,p )
U r,p
t = u ct , nt + βU r,p
t+1 (A15)
( )
U r,w
t = u cr,w r,w
t , nt + βU r,w
t+1 (A16)
( )
1 s,p u iu
s,p = λt + βπ 1 I t Ct U s,p iu,p
t+1 − U t+1 (A17)
ct
( )
1 s,w u iu
s,w = λt + βπ 1 I t C t U s,w iu,w
t+1 − U t+1 (A18)
ct
( s,p )
θns,p s,p u iu iu,p
t = λt wt − βπ 2 I t N t U t+1 − U t+1 (A19)
( )
θns,w
t = λs,w u s,w
iu
t AΘt − βπ 2 I t N t U t+1 − U t+1
iu,w
(A20)

wt
θniu,p
t = (A21)
ciu,p
t

AΘt
θniu,w
t = (A22)
ciu,w
t

nid,p
t =0 (A23)

nid,w
t =0 (A24)

cid,p
t =0 (A25)

γ− 1
cid,w
t = AN t Θt (A26)
γ
wt
θnr,p
t = (A27)
cr,p
t

At Θt
θnr,w = (A28)
t
cr,w
t

St Cst + IU t Ciu id r
t + IDt Ct + Rt C t = AN t (A29)

St N st + IU t N iu r
t + Rt N t = N t (A30)
( )
Cit = χ ci,w
t + 1 − χ ci,r
t , i = s, iu, id, r (A31)

17
L.C. Hunt et al. Research in Globalization 6 (2023) 100117

( ) i,r
N it = χ ni,w
t + 1 − χ nt , i = s, iu, id, r (A32)

Appendix B. Data

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