metadata: authors: 0: author: Ma,Lin
1: author: Shapira,Gil
2: author: De Walque,Damien B. C. M.
3: author: Do,Quy-Toan
4: author: Friedman,Jed
5: author: Levchenko,Andrei A.
count: World
docna: 0: docna: The Intergenerational Mortality Tradeoff of
            COVID-19 Lockdown Policies
docty: Policy Research Working Paper
subtopic: Law and Justice Institutions,Early Child and Children's Health,Reproductive Health,Health Care Services Industry,Labor Markets
teratopic: Law and Development,Health, Nutrition and Population,Industry,Social Protections and Labor
abstracts: cdata!: In lower-income countries, the economic
            contractions that accompany lockdowns to contain the spread
            of COVID-19  can increase child mortality, counteracting the
            mortality reductions achieved by the lockdown. To formalize
            and quantify this effect, this paper builds a
            macro-susceptible-infected-recovered model that features
            heterogeneous agents and a country-group-specific
            relationship between economic downturns and child mortality,
            and calibrate it to data for 85 countries across all income
            levels. The findings show that in low-income countries, a
            lockdown can potentially lead to 1.76 children's lives
            lost due to the economic contraction per COVID-19 fatality
            averted. The ratio stands at 0.59 and 0.06 in lower-middle
            and upper-middle income countries, respectively. As a
            result, in some countries lockdowns can actually produce net
            increases in mortality. In contrast, the optimal lockdown
            that maximizes the present value of aggregate social welfare
            is shorter and milder in poorer countries than in rich ones,
            and never produces a net mortality increase.
repnme: repnme: The Intergenerational Mortality Tradeoff of
            COVID-19 Lockdown Policies
display_title: The Intergenerational Mortality
            Tradeoff of COVID-19 Lockdown Policies
listing_relative_url: /research/2021/05/33116866/intergenerational-mortality-tradeoff-covid-19-lockdown-policies
topicv3: Infant and Child Mortality m1326544 1446,Labor Supply m1504055 2751,Mortality m1504365 3661,Health m1504661 3480,Coronavirus (COVID-19) m1939478 4828
publishtoextweb_dt: 2021-05-27T00:00:00Z
dois: 10.1596/1813-9450-9677
historic_topic: Law and Development,Health, Nutrition and Population,Industry,Social Protections and Labor
origu: DECRG: Human Development (DECHD)
no_of_pages: 70
author_keys: 0: author_key: 964001
1: author_key: 687876
2: author_key: 433894
3: author_key: 669320
4: author_key: 1132316
model_extractions: Policy Research Working Paper 9677 The Intergenerational Mortality Tradeoff of COVID-19 Lockdown Policies _Lin Ma_ _Gil Shapira Damien de Walque Quy-Toan Do Jed Friedman Andrei A. Levchenko_ Development Economics Development Research Group May 2021
Policy Research Working Paper 9677

# **Abstract**

In lower-income countries, the economic contractions that accompany lockdowns to contain the spread of COVID-19 can increase child mortality, counteracting the mortality reductions achieved by the lockdown. To formalize and quantify this effect, this paper builds a macro-susceptible-infected-recovered model that features heterogeneous agents and a country-group-specific relationship between economic downturns and child mortality, and calibrate it to data for 85 countries across all income levels. The findings show that in low-income countries, a lockdown can potentially lead to 1.76 children’s lives lost due to the economic contraction per COVID-19 fatality averted. The ratio stands at 0.59 and 0.06 in lower-middle and upper-middle income countries, respectively. As a result, in some countries lockdowns can actually produce net increases in mortality. In contrast, the optimal lockdown that maximizes the present value of aggregate social welfare is shorter and milder in poorer countries than in rich ones, and never produces a net mortality increase.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at gshapira@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# The Intergenerational Mortality Tradeoff of COVID-19 Lockdown Policies<sup>_∗_</sup>

Lin Ma, Gil Shapira, Damien de Walque, Quy-Toan Do, Jed Friedman, and Andrei A. Levchenko<sup>_†_</sup>

**Keywords:** COVID-19, child mortality, lockdown, SIR-macro.

**JEL Classification:** _I18_ , _I15_

Originally published in the Policy Research Working Paper Series on _May 2021._ This version is updated on _November 2021._ To obtain the originally published version, please email prwp@worldbank.org.

> _∗_ We are grateful to the editor (Jes ́us Fern ́andez-Villaverde), three anonymous referees, Mohamed Abdel Jelil, Daron Acemoglu, Jishnu Das, Shanta Devarajan, Xavier Devictor, Rema Hanna, Aaditya Mattoo, Mushfiq Mobarak and Nina Yamanis for helpful comments.

> _†_ Ma: Singapore Management University (linma@smu.edu.sg); Shapira: World Bank (gshapira@worldbank.org); de Walque: World Bank (ddewalque@worldbank.org); Do: World Bank (qdo@worldbank.org); Friedman: World Bank (jfriedman@worldbank.org); Levchenko: University of Michigan, NBER, and CEPR (alev@umich.edu).
# **1 Introduction**

Governments across the world introduced unprecedented lockdown policies in an attempt to contain the spread of COVID-19. Unsurprisingly, a debate soon erupted on what type of lockdowns were warranted and whether the benefits of such policies justify the accompanying dramatic economic contractions. Embracing utilitarianism, economists, among others, focused on the tradeoff between the lives saved by a lockdown and its economic costs (Hall et al., 2020; Kim and Loayza, 2021). On the other hand, both proponents of deontological ethics and critics of the statistical value of life recused a policy analytic approach that involves the monetary valuation of life (Singer and Plant, 2020; Viscusi and Aldy, 2003; Slovic and Peters, 2006). This paper casts a new light on this debate by uncovering and quantifying an intergenerational mortality tradeoff inherent to pandemic mitigation: the disease and the lockdown policies affect the mortality of younger and older individuals differentially.

In the early days of the pandemic, evidence emerged that the COVID-19 mortality risk increases substantially with age (Verity et al., 2020). On the other hand, empirical evidence has shown that infant and child mortality in low- and middle-income countries is countercyclical (Pritchett and Summers, 1996; Bhalotra, 2010; Baird et al., 2011; Cruces et al., 2012; Friedman and Schady, 2013). This implies that lockdown policies in developing countries can lead to an increase in infant and child mortality due to the consequent economic contraction.<sup>1</sup> Thus, pandemic mitigation policies in low-income settings not only forgo economic well-being to save lives but also embed a between one life and another.

This paper quantitatively evaluates this tradeoff in a Susceptible-Infected-Recovered (SIR)-macro model (e.g. Eichenbaum et al., 2021) augmented with two main features. First, a lockdown can potentially increase child mortality by inducing an economic contraction. The main innovation of our paper is to model and quantify this effect. We estimate countrygroup-specific semi-elasticities of child mortality with respect to aggregate income by applying the methodology of Baird et al. (2011) to microdata from 83 countries, and use the resulting estimates in our quantitative model. Second, we relax the representative agent

> 1Indeed, policy discussions and the public health literature have sounded the alarm on the negative impacts of the COVID-19 pandemic on children, especially in developing countries (Roberton et al., 2020; Swinnen and McDermott, eds, 2020; Kotlar et al., 2021; Shapira et al., 2021a).

1
assumption of most SIR-macro models and allow for three types of agents that differ by age: the children, the working adults, and the elderly (as in Acemoglu et al., 2020).

Infection is assumed to spread through work- and consumption-related activities, as well as community and intra-household interactions. Adults are the only ones supplying labor, trading consumption off against the risk to themselves and their family members of contracting COVID-19. A decentralized equilibrium features excess supply of labor since individuals do not internalize the social cost of being infected, which consists of an increased probability of infection for all susceptible individuals as well as a higher infection fatality rate due to limited hospital capacity. A lockdown, which we model as an income tax, reduces labor supply in order to reduce COVID-19 transmission. A lockdown can lower mortality by either containing the virus or by “flattening the curve,” that is slowing the virus’ spread such that demand for COVID-19 treatment does not exceed health system capacity. However, the reduction in labor supply and consequent consumption losses increase child mortality in low- and middle-income country settings.

We calibrate the model to 85 countries across all income groups. Low-, middle-, and high-income countries differ along several relevant dimensions. First, economic contractions raise child mortality in poorer countries, but not in rich ones. We estimate that a percent decrease in per capita GDP can increase under-5 mortality by up to 0.15 deaths per 1,000 children in the poorest countries. Second, poorer countries have a higher ratio of children to elderly. Since the survival of the former is put at risk by an economic downturn while the latter are most vulnerable to dying from COVID-19, a lockdown in lower-income countries leads to more recession-induced deaths per COVID-19 fatality averted, _ceteris paribus_ . Third, a smaller share of social contacts are in the context of work- or consumption-related activities in developing countries compared to developed ones. The preponderance of communityrelated transmission in low-income countries renders government-mandated lockdowns comparatively less effective at reducing the spread of infections. Finally, low health care capacity in poorer countries lowers the efficacy of a lockdown through a “flattening the curve” channel as hospitals are quickly overwhelmed.

To highlight the consequences of these country differences, we subject each of the 85 countries in our sample to a uniform _reference_ lockdown that lasts 7 weeks. The duration 2
and the strength of the reference lockdown is chosen based on experiences in seven European countries in the start of the pandemic (Flaxman et al., 2020).<sup>2</sup> We then compare the economic and mortality outcomes in the reference lockdown to a scenario without any government intervention.

Our main quantitative result is that there is substantial variation in health outcomes across countries following the reference lockdown. In our model, the lockdown led to an average of 1.76 child deaths for every COVID-19 fatality averted in low-income countries. The ratio falls to .59 and .06 in the case of lower-middle and upper-middle income countries, respectively. By assumption, there is no mortality tradeoff in high-income countries. As a result, lockdowns lower the total mortality by 6.2 percent in the richest countries, but _raise_ total mortality by 2.6 percent in the poorest ones. The main country characteristics driving the heterogeneity in health outcomes are (i) the semi-elasticities of child mortality with respect to GDP and (ii) demography, as poorer countries are also younger countries.

Finally, we consider a utilitarian approach to designing lockdown policies, in which the social planner trades off COVID-19 deaths averted against loss of life due to reduced GDP and the loss of consumption. The optimal lockdown varies across countries, as marginal costs and benefits are heterogeneous. Poor countries with younger populations generally feature shorter and milder optimal lockdowns, as the governments take into account the impacts on child mortality. Thus, the optimal lockdown significantly reduces the share of the population infected in the rich countries but not in the poorer ones. In the end, the child mortality impact is smaller as well: among the poorest countries, the optimal lockdown would lead to only 0.32 child deaths for every COVID-19 fatality averted.

Our findings hold general lessons for pandemic mitigation, past and future. Empirical evidence has shown repeatedly that in lower- and middle-income countries, infant and child

> 2We take the perspective of the initial months of the COVID-19 pandemic when governments were first confronted with designing pandemic responses in the absence of effective vaccines or therapeutics. We implement only non-pharmaceutical interventions because in the event of a new but similar pandemic, the same tradeoffs will be relevant as new vaccines and/or therapeutics would most likely not be immediately available. According to the Oxford Blavatnik COVID-19 Government Response Tracker, every single one of the 175 countries that it covers imposed at least some lockdown policy. Lockdown severity was remarkably similar across countries at different levels of development. On a scale of 0 to 100, the mean Oxford–Blavatnik lockdown stringency index was 79 in the low-income countries, and 78 in the high-income countries. (These averages are as of April 2020, the most globally synchronized phase of the lockdown. We use the World Bank classification of countries into income groups.)

3
mortality rises more in economic downturns than mortality of other age groups. Thus, the intergenerational tradeoff is a generic feature of the policy options in these countries: lockdowns will always adversely affect children disproportionately. The impact of lockdowns on children’s mortality would then need to be compared to the mortality profile of the disease itself. Evidence suggests that these differ across epidemics. To take some of the most prominent examples, the 1918-1919 influenza pandemic was characterized by an age shift with most excess deaths occurring among young adults (ages 15-44) and fewer excess deaths occurring among those over 65 (Olson et al., 2005; Andreasen et al., 2008). The Ebola case fatality rates for young children under 5 and for elders over 75 are both approximately 80 percent higher than for prime-age adults (Garske et al., 2017). During the 2003 SARS outbreak, the case fatality rate was estimated to be an order of magnitude higher for patients in China over 60 years of age than those under 40 years (25 percent vs 2 percent) (Jia et al., 2009). A similar age gradient was observed in Hong Kong during the same outbreak (Karlberg et al., 2004). Thus, the exact nature of the intergenerational mortality tradeoff will differ across pandemics in a way that is quantifiable within the framework developed here.

Our paper complements the burgeoning body of work on the macroeconomic impact of the COVID-19 pandemic (see, among others, Atkeson, 2020; Alvarez et al., 2021; Barrot et al., 2021; Baqaee and Farhi, 2020, 2021; Bonadio et al., 2021; Glover et al., 2020; Kaplan et al., 2020; Krueger et al., 2021). Most closely related are Eichenbaum et al. (2021), who develop an SIR-macro model, and Acemoglu et al. (2020), who model population heterogeneity by age. We customize these macro frameworks to developing countries. Our analysis shares the developing country focus with Alon et al. (2020), Barnett-Howell and Mobarak (2020), Loayza (2020), or Ravallion (2020b) who also point out differences between rich and poor countries in the benefits and costs of a lockdown and ultimately come to the same conclusion that the tradeoffs are different and country-specific. Our analysis highlights and more importantly quantifies a distinct mechanism, whereby a lockdown potentially increases child mortality in poorer countries.<sup>3</sup> Other work that has surmised the potential toll for infant and

> 3One underlying mechanism by which a lockdown increases child mortality is through deteriorating food security and was posited by Ravallion (2020a).

4
child health as a consequence of the COVID-19 pandemic includes Roberton et al. (2020), who use a health care seeking and supply model, and posit reductions in care seeking and available quality of care. In contrast, our approach uses the data on past contractions to calibrate the under-5 mortality semi-elasticity with respect to the economic shock.

The rest of the paper is structured as follows. Section 2 lays out the quantitative framework. Section 3 details the calibration, and 4 presents the quantitative results. Section 5 concludes. The Appendix contains additional details on theory, quantification, and robustness.

# **2 Quantitative Framework**

This section builds a macro-SIR framework along the lines of Eichenbaum et al. (2021) with the added feature that households comprise several members in different age groups (Acemoglu et al., 2020). Our key innovations are (i) to model income shocks as a source of mortality not related to COVID-19; and (ii) to calibrate the model to 85 countries with different underlying characteristics.

## **2.1 Economic Environment**

We consider a discrete and infinite time horizon model, _t_ = 0 _,_ 1 _, · · · , ∞_ , and a continuum of households indexed by _j ∈_ [0 _,_ 1]. A model time period corresponds to one week. The measure of households is normalized to 1 in the initial period. Households are formed by individuals differentiated by age group _m ∈{_ 1 _,_ 2 _,_ 3 _}_ to which they belong. Type _m_ = 1 individuals are children ages 0-14, type _m_ = 2 are working prime-age adults ages 15-59 and _m_ = 3 household members are the elderly aged 60 and over. Denote by _l_<sup>_m_</sup> the mass of individuals of age group _m_ so that<sup>�3</sup> _m_ =1<sup>_lm_= 1.Weomitcountryindicesintheexposition</sup> to streamline notation, but the quantitative analysis uses country-specific values for many of the parameters.

5
Household _j_ evaluates its lifetime utility according to: where _β_ is the discount factor. The instantaneous utility function takes the form where ̄ _cjt_ is aggregate consumption of household _j_ in period _t_ , and _njt_ is the amount of labor it supplies.

Household consumption _c_ ̄ _jt_ aggregates individual consumption _cjt_ ( _m_ ) of all members of the household: where _σ_ is the elasticity of substitution.

**COVID-19 SIR states** COVID-19-related health status is relevant for both disease transmission and economic behavior. Each individual can be in one of four states: susceptible ( _S_ ), infected ( _I_ ), recovered ( _R_ ), or deceased ( _D_ ). One feature of our model is that death can be due to either COVID-19 or another cause. We thus index each household state with integer _k ∈{_ 1 _, ...,_ 64 _}_ , which uniquely identifies a triplet _{ζ_ (1) _, ζ_ (2) _, ζ_ (3) _}_ , where _ζ_ ( _m_ ) _∈{S, I, R, D}_ indicates the health status of individual _m_ . Appendix Table B.1 reports the list of possible household states.<sup>4</sup>

**Labor supply, lockdown policy, and government budget** In our model, only the prime-age adult ( _m_ = 2) household members supply labor.<sup>5</sup> They are paid a wage _wt_ , which

> 4Note that to reduce the dimensionality of the state space, we make the assumption that within households, all members in the same age group are in the same state. We thus do not allow two children (or adults or elderly) to be in two different states. While this assumption may be unrealistic at the household level, this simplification does not affect the analysis at the aggregate level.

> 5While some fraction of children under 15 indeed work in the poorest countries, the prevalence of child labor has been declining over time and is now relatively low. In addition, the majority of children who are working do so as contributing family members (and thus likely within their household) and/or in agriculture.

6
the government can tax at rate _μt_ . As in Eichenbaum et al. (2021), the tax rate _μt_ will be the instrument by which the policy maker implements a lockdown.<sup>6</sup> Tax revenues are then remitted to households in a lump-sum manner. The budget constraint of household _j_ is: where _cjt_ is total household consumption expenditure. Household income on the right-handside of (4) consists of after-tax labor income and the government transfer Γ _jt_ . If the working adult is infected ( **I** _jt_ (2) = 1), the effective labor supply falls by a fraction _φ ≤_ 1. After the death of the working adult ( **D** _jt_ (2) = 1), household _j_ lives off government transfers.

The amount Γ _jt_ transferred to households is determined by the government’s budget constraint, i.e.

where Γ<sup> ̄</sup> _t_ is some exogenous development assistance revenue.

**Firms** There is a unit measure of competitive firms that produce consumption goods _Ct_ using the aggregate labor input _Nt_ :

International Labour Office and United Nations Children’s Fund (2021, p. 74) reports that worldwide, 9.7% of children 5-11, and 9.3% of children 12-14 are engaged in child labor, often less than full-time. The highest percentages are in Africa (22.1% age 5-11; 23.5% age 12-14) and especially sub-Saharan Africa (24.7% age 5-11; 25.8% age 12-14). In all other world regions, these fractions are below 10%. While the percentages remain high in Africa, the study reports that 82.6% of children aged 5-11 and 74.5% of children 12-14 who engaged in child labor are “contributing family workers.” Similarly, 76.6% of children aged 5-11 and 75.8% of children 12-14 engaged in child labor are working in agriculture. Thus, the large majority of children engaged in child labor are either contributing family workers and/or working in agriculture. In both cases, the labor takes place within the household or in agricultural fields, and there would not be a disease transmission benefit from work-related social distancing.

> 6We interpret lockdown policies broadly to include multiple forms of containment, such as encouraging social distancing, restricting public events, school and border closures, and so on. As will become clear below, in the calibration the lockdown policy will also lower community transmission.

7
Firms choose total labor input to maximize their profit, Π _t_ : In equilibrium, goods and labor market clearing conditions are thus

# **2.2 Mortality and Disease Transmission**

We incorporate a modified SIR model to our macroeconomic framework. In our model there are three types of mortality risks: (i) economic distress risk, (ii) a COVID-19-related risk, and (iii) an exogenous baseline risk.

**Economic distress and baseline mortalities** An individual in age group _m_ faces increased mortality during an economic contraction. A contraction is a downward deviation � from baseline consumption _cj_ , defined as the level that would be achieved at time _t_ = 0 in the absence of a labor tax ( _μ_ = 0). Thus, for household _j_ , a contraction takes place when faced with a positive labor tax or in the case of death of the working adult. In addition, in each period _t_ an individual draws an exogenous age-group specific baseline death shock with probability _π_  ̄ _n_ ( _m_ ).

The economic distress mortality cum baseline mortality probability is: where _ν_ ( _m_ ) is the elasticity of economic distress-related mortality with respect to the fluctuations in consumption. Importantly, in our quantification _ν_ ( _m_ ) will vary by country income level: it will be positive in poorer countries and decreasing in the income level. In rich countries economic distress-related mortality elasticity _ν_ ( _m_ ) will be 0. In the quantification, 8
_ν_ ( _m_ ) will be positive only for children ( _m_ = 1).

**COVID-related mortality** The infection status of an individual of age group _m_ in household _j_ at time _t_ is denoted **I** _jt_ ( _m_ ) _∈{_ 0 _,_ 1 _}._ Thus, the mass of infected individuals at time _t_ is given by

Conditional on contracting COVID-19, the probability of death from the infection takes the following form: where _πd_<sup>_m_is a baseline infection fatality rate and</sup><sup>_κm_(</sup><sup>_._) captures the dependence of mortality</sup> on the total infection rate. The function _κ_<sup>_m_</sup> ( _._ ) reflects the possibility that a larger epidemic will lead to higher mortality due to saturation of key health services such as ICU beds, oxygen ventilators, etc. (Yang et al., 2020).

In each period, the probability _πdjt_ ( _m_ ) that an individual _j_ will die combines both COVID-19 and non-COVID-19 mortality risks. We make the assumption that the economic distress and COVID-19 mortality probabilities are orthogonal to each other in the cross-section of households. In that case, the death probability of a person of type _m_ in household _j_ becomes: This equation states the probability of death for an infected individual, thus implicitly conditioning on an applicable household state _k_ (that is, _k_ being one in which household member _m_ is currently infected). To streamline notation, in this equation as well as in (9) and (11), we suppress the conditioning on an applicable _k_ .

9
**Lockdown policies and COVID-19 disease dynamics** Adapting the model of Eichenbaum et al. (2021), we assume that the transmission of the infection occurs through four channels: (i) the labor channel, whereby the infection spreads through workplace interactions, (ii) the consumption channel, which comprises contacts occurring while shopping for goods, (iii) the community channel, which represents all other interactions of individuals across households, and (iv) the within-household channel, to account for higher exposure of individuals who share a residence with an infected individual.

A lockdown policy, therefore, will affect transmission likelihood through these same channels. As a tax on labor income, a lockdown reduces individual labor supply and consequently also household consumption. Both lead to a decrease in infection rates. We further allow a lockdown policy to mitigate community-related transmission with a semi-elasticity of _ξ_ . This captures restrictions on social gatherings that affect community spread. We do not directly model decisions related to such gatherings and instead account for the impact of lockdowns on community spread via the parameter _ξ_ .

The probability that a susceptible individual _m_ in household _j_ will get infected in period _t_ is given by: The first line of (11) describes the infection probability of the working adult. The four terms reflect transmission through consumption, labor supply, the community, and within the household, respectively. Consumption and labor supply transmissions are a function of the aggregate consumption and labor supply of the infected individuals in period _t CIt_ and _NIt_ , which equal: Community transmission, on the other hand, is a function of the total number of infected 10
people, _It_ , as defined above. Finally, for within-household transmission, **I** _jt_ , equals to one if any member of the household _j_ is infected, and zero otherwise. The second line of equation (11) applies to the children and the elderly, who will only be infected through the community or within-household transmission channels, since they do not work and are assumed not to get exposed through consumption-related activities.

The total number of newly infected individuals _Tt_ is thus given by: where **S** _jt_ ( _m_ ) is an indicator function that takes the value of 1 when member _m_ of household _j_ is susceptible, and 0 otherwise. The number of susceptible individuals, _St_ , evolves according to In period _t_ , all infected individuals will receive the “recovery” shock. With probability _πrt_ ( _m_ ), the member recovers, with probability _πdt_ ( _m_ ) s/he dies, and with probability _πit_ ( _m_ ) s/he stays infected. Note that _πrt_ ( _m_ ) + _πdt_ ( _m_ ) + _πit_ ( _m_ ) = 1. The number of infected individuals thus evolves according to: which consists of previously infected people who remain so for one additional period and newly infected individuals.

# **2.3 Household Optimization**

We now turn to household optimization, subject to the aggregate state of the economy as summarized by Θ _t_ = _{CIt, NIt, It}_ and government policy _μt_ . We first note that all the households in state _k_ face the same maximization problem and make the same decision. As a result, we use the subscript _k_ instead of _j_ to indicate the variables for a household in state 11
_k_ .

**Consumption and labor supply** Before solving the dynamic problem, we first solve the within-period problem through backward induction by expressing household instantaneous utility as only a function of labor supply and then optimizing accordingly.

As we abstract from saving and risk sharing across households, the solution to the consumption problem is static and is characterized by the binding budget constraint (4) for household _k_ . In light of this observation, we can re-write the probability of death specified in equation (10), _πdkt_ ( _m_ ), as a function of labor supply: where _ckt_ depends on _nkt_ through (4), and is a function of the infection state of the working adult. Similarly, the probability of a susceptible adult contracting COVID-19 can also be re-expressed as a function of labor supply: Lastly, the standard property of CES aggregation implies that we can also re-write the flow utility function as a function of labor supply: in which the individual level consumption is equal to and where once again the dependence of _ckt_ on _nkt_ takes the form of (4). Combining the two 12
and simplifying:

**Dynamic optimization** With the solution of the consumption problem in hand, we can turn to the dynamic problem of a household in state _k_ . The Bellman equation for household in state _k_ can be written

subject to the transition probabilities from state _k_ to _k_<sup>_′_</sup> , _ρkk′_ ( _·_ ), that depend on the aggregate state of the economy Θ _t_ .

The first-order condition determines optimal labor supply _nkt_ : We can then write the optimal labor decision as where Λ _kt_ = _β_<sup>�</sup><sup>_K_</sup> _k_<sup>_′_</sup> =1 _∂n∂_<sup>_ρkk′_(</sup><sup>_nkt|_Θ</sup><sup>_t_)</sup><sup>_Uk′,t_+1(Θ</sup><sup>_t_+1).</sup>

First, note that in the absence of capital accumulation, households’ labor decisions will only affect a subset of the transition probabilities, _ρkk′_ . Labor supply only affects the probability of infection of the working age adults and the non-COVID mortality rate of children (since we assume that excess mortality from an economic contraction only affects children). All the other mortality rates, infection rates, and recovery rates follow a process that is not influenced by the decision of atomistic agents but depend on the aggregate state Θ _t_ . We thus state the following result (proof available in the Appendix): 13
**Lemma 1: First-order conditions** The first-order condition for the household in state _k_ , period _t_ is:

where _λ_<sup>_k_</sup> _πI_<sup>istheLagrangianmultiplierontheinfectionprobability,</sup><sup>_πIkt_(2):</sup> and _λ_<sup>_k_</sup> _πd_<sup>istheLagrangianmultiplierforthenon-COVIDchildmortalityrate,</sup><sup>_πdkt_(1):</sup>

# ■

For households without a susceptible prime-age adult, _λ_<sup>_k_</sup> _πI_<sup>=0asthetermsinsidethe</sup> curly bracket in equation (22) are equal to zero. Similarly, _λ_<sup>_k_</sup> _πd_<sup>=0forhouseholdswithout</sup> a child as the terms inside the curly bracket in equation (23) are equal to zero.

The first-order condition captures the tradeoff between the static optimization (i.e. today’s consumption vs. leisure) and the health risk of increased exposure through consumption and work. Lemma 1 describes the heterogeneity in households’ responses to the pandemic, as a function of their demographic composition and the health status of their members. On the one hand, labor decisions have no dynamic implications when no prime-age adult is susceptible. On the other hand, incentives to increase (decrease) labor supply depend on whether there are children (susceptible elderly people) in the household.

**Equilibrium** An equilibrium of the economy in period _t_ is defined by a vector of labor supply decisions _{nkt}k∈{_ 1 _,...,K}_ such that _nkt_ is a solution to (18) for some given Θ _t_ +1, and Θ _t_ +1 is in turn determined by transition probabilities (10) and (11). To solve for the equilibrium, therefore, we propose the following algorithm:

14
**Solution algorithm** Take the policy vector, _μt_ , as given. Start with a guess of _nkt_ for all _k_ = 1 _, . . . , K_ and _t_ = 1 _, . . . , T_ .

1. Given the initial conditions, simulate the model forward from _t_ = 1 to _T_ to generate _St, It, Rt_ , and _Dt_ , as well as all the transition probabilities.

2. Infer _Ukt_ for every _k_ via the following steps. The details are discussed in the appendix.

- (a) Compute the post-pandemic steady state values of _Uk_ for all _k_ .

- (b) Compute backwards from the post-pandemic state _T_ to 1 for all the _Ukt_ .

3. Infer _λπdk_<sup>_,t_and</sup><sup>_λπ_</sup> _I_<sup>_k,t_fromthefirst-orderconditionsof</sup><sup>_πdkt_(1)and</sup><sup>_πIkt_(2),conditional</sup> on _Ukt_ .

4. Infer _nkt_ from the first-order conditions of _nkt_ . Iterate on _nkt_ until convergence.

# **2.4 Discussion**

Before moving on to the calibration and quantification, we discuss some features of our theoretical framework.

**Non-COVID-19 mortality** In our framework economic downturns affect the mortality of only children, and only in the poorer countries. This combination of assumptions appears the most realistic in light of available empirical evidence. The hypothesis that mortality will rise in economic downturns goes back to at least Brenner (1979), who emphasized the impact of adverse economic shocks on lower access to health services and harmful behaviors driven by stress. While Brenner (1979)’s analysis was applied to developed countries in the first half of the 20th century, there is now broad consensus that today adult mortality in high-income countries is if anything pro-cyclical (e.g. Ruhm, 2000; Stevens et al., 2015) due to a variety of reasons including a reduction in harmful behaviors in recessions and business cycle effects on health care staffing quality.

On the other hand, mortality patterns in low- and middle-income countries are typically found to be counter-cyclical, especially for vulnerable groups such as infants and young 15
children. Ferreira and Schady (2009) propose a conceptual framework in which an increase in infant/child mortality is driven by increased food insecurity and reduced access to (or demand for) essential health services (including preventive services such as vaccination), and review the available literature. Baird et al. (2011) document that indeed, downward deviations in GDP from trend increase child mortality in a sample of 1.7 million births in 59 countries. The food security/nutrition channel does appear to be important - not only is child mortality counter-cyclical, but so is child wasting and other measured nutritional outcomes (Headey and Ruel, 2020).

There is an emerging body of empirical evidence that food insecurity and access to healthcare services have worsened during this pandemic period (e.g. Egger et al., 2021; Shapira et al., 2021b). Osendarp et al. (2021), for example, project between 47,000 to 283,000 additional child deaths in 2020-2022 due to increases in child wasting and declines in nutrition intervention coverage in 118 low- and middle-income countries.

The survival of other vulnerable groups could also be impacted by income shocks. Unfortunately, there is very little existing evidence on economic contractions and mortality in non-child populations. Cutler et al. (2002) show higher elderly mortality during economic crises in Mexico, Khvan et al. (2020) show a similar relation in Russia, and Hone et al. (2019) find a generalized increase in adult mortality in Brazil.<sup>7</sup> We are not aware of a data source that would allow us to estimate the impact of economic downturns on elderly mortality in a systematic way across countries in the same way we estimated it for children. We rely on standardized Demographic and Health Surveys for child health measures as vital statistics in low- and lower-middle-income countries are unreliable.

Allowing for a mortality increase among non-children due to lockdowns would only increase the ratio between the non-COVID-19 deaths caused by the lockdowns and the number of COVID-19 deaths averted, conditional on a given lockdown severity. However, we would expect the overall impact via the elderly mortality rates to be much smaller. One reason is that, as we highlight below, adults above 60 account for a small proportion of the population in developing countries.

> 7These three studies are from middle-income countries with relatively reliable vital statistics data, a rarity in lower income countries. These results are of course in contrast to the literature from wealthy countries that finds recessions to lower mortality rates at adult ages.

16
**Consumption** In our framework, the child’s consumption depends only on the total income of the household. It could be that in an economic downturn, the consumption of young children falls by even more than average household consumption for various reasons such as the household privileging the consumption of the main earner. Unfortunately, we cannot incorporate this possibility directly because there is no sufficiently reliable data to inform within-household consumption differences over the business cycle.

In addition, it may be that children’s consumption involves components outside of the household, such as school meals. This would be relevant to our application if lockdown measures such as school closures also reduce children’s access to consumption resources outside of the household. However, according to available estimates (e.g. Baird et al., 2011), mortality sensitivity to income shocks sharply decreases with the age of the child. In fact, most of the mortality is concentrated among infants and toddlers and declines in our data as children get older. Because the youngest children largely remain inside the household, it is appropriate to model their consumption as only driven by household income, as school closures will not directly affect the food intake of these children. In both cases, if one believes that children’s consumption falls more than proportionally to household consumption during economic downturns, our approach is conservative and allowing for this possibility would only quantitatively strengthen our main point.

**Health system oversaturation** Our framework models the pandemic’s impact on child mortality through the negative income shock, which can include changes in the utilization of health services as experienced historically during non-pandemic economic downturns. However, the pandemic may impact non-COVID-19 child mortality through changes in availability or utilization of health services in unique ways. Indeed, if health system oversaturation due to treating COVID-19 patients reduces the coverage of life-saving services for children, then _ceteris paribus_ child mortality would increase in the absence of a lockdown. This would reduce the ratio between excess child deaths and COVID-19 mortality averted by a given lockdown policy. On the other hand, there is suggestive evidence that lockdowns themselves might also reduce utilization of essential health services. In Nigeria, for example, a third of women surveyed during exit interviews after receiving reproductive and maternal health

17
services reported not being able to access such services at some point since the start of the pandemic, with the most cited reasons being mobility restriction and increased cost of public transportation during the lockdowns (Balogun et al., 2021). In a study of 18 lowand middle-income countries, Ahmed et al. (2021) find a correlation between monthly reductions in health service utilization and stringency of mobility restrictions, even controlling for the monthly COVID-19 burden. If lockdowns reduce coverage of life-saving health services, then we would be under-estimating the ratio between excess child deaths and COVID-19 mortality averted by a given lockdown. As for reduced demand for services out of fear of contracting the disease in health facilities, it may happen independent of whether lockdowns are imposed. In sum, it is not clear whether non-COVID-19 mortality due to reduced health service utilization (or reduced service quality) would be higher with lockdowns or with health system congestion.

**State capacity** In our framework, the lockdown is successfully implemented by the government. One may be worried that if a particular country does not have the state capacity to enforce a lockdown, then our quantification is of limited policy relevance to that country. This is a general critique of policy analysis in low-state-capacity environments. Nonetheless, our conclusions are still relevant for countries with sufficient state capacity to enforce lockdowns. Judging from the widespread use of lockdowns in countries across all levels of development, governments at least believed that their policies would have some effect. There are also journalistic accounts that low-income country governments deployed police to enforce lockdowns.<sup>8</sup>

The substantial GDP contractions in 2020 are suggestive evidence that lockdowns had consequences in even the poorest countries. While real GDP data are annual and thus will have imperfect overlap with lockdowns, more high-frequency data sources also point to large contractions in economic activity during lockdowns. Aminjonov et al. (2021) analyze mobility data from Android smartphones to document widespread mobility declines in every

> 8See, e.g., India: https://www.reuters.com/world/india/police-enforce-lockdown-indias-nagpurinfections-surge-2021-03-12/, https://www.aljazeera.com/news/2021/4/21/for-indias-poor-lockdownpolicing-adds-to-pandemic-hardships; and Africa: https://www.dw.com/en/covid-19-security-forces-inafrica-brutalizing-civilians-under-lockdown/a-53192163, https://www.aljazeera.com/news/2020/4/28/unraises-alarm-about-police-brutality-in-covid-19-lockdowns.

18
– major region of the world more so in Latin America or the Middle East than in Asia. The largest declines occurred in the first three pandemic months and the subsequent recovery has been only partial. Using local area poverty estimates, the paper finds high lockdown stringency significantly reduced mobility even in high-poverty areas, although to a lesser degree than in low-poverty areas. Google Mobility Trends data also show substantial reductions in workplace visits during the first months of the pandemic in all sub-Saharan African countries where data are available. These mobility reductions happened during periods of stringent lockdowns. On April 15th, for example, the number of visitors to workplaces were 50-75% lower than the pre-pandemic level in Uganda, South Africa, Botswana, Namibia and Zimbabwe, and 25-50% lower in in Kenya, Tanzania, Angola, Gabon, Nigeria, Ghana, Guinea-Bissau, and Senegal.<sup>9</sup> Even if there were pronounced economic downturns related to the pandemic, it may still be that low-income country lockdown policies were comparatively ineffective, and the reductions in economic activity came purely from private behavioral responses. Emerging evidence suggests, however, that lockdowns did have some effect. Beyer et al. (2021) exploit differential timing and severity of lockdown measures across 600+ Indian districts and a difference-in-differences estimator to show that more severe lockdown restrictions curtailed economic activity substantially at the district level, relative to localities with less severe restrictions. Thus, it appears that lockdown policy interventions did have a direct effect on economic activity in India.<sup>10</sup> Finally, we note that throughout our analysis, there continues to be community transmission that is not entirely eliminated by the lockdown, and we calibrate community transmission to be higher in developing countries. This feature of our quantification could be thought of as one means to capture lower state capacity in poorer countries.

> 9The data are here: https://ourworldindata.org/covid-google-mobility-trends.

> 10Ultimately it may never be possible in the data to cleanly separate the impact of enforcement of lockdown restrictions _per se_ from private behavioral responses, if – plausibly – agents have imperfect information. When households do not perfectly observe the exact COVID-19 prevalence in their area and do not perfectly know the associated risks, a lockdown imposed by a policymaker signals to the households that the outbreak is severe, and thus induces a belief update and a greater private behavioral response. The signal value of a lockdown means that a policy may have a marginal effect (relative to no policy) even in environments with low state capacity to enforce lockdowns.

19
**Government transfers and the wealth effect on labor supply** In our model, the government rebates the lockdown-tax income back to households lump sum. This assumption can be thought of as a stand-in for the transfer programs that governments put in place jointly with the lockdowns. In principle there may be a wealth effect from these government transfers on labor supply. If the wealth effect is large, the labor supply response to the lockdown could be sensitive to the adopted assumption on government transfers. First note, however, that available empirical evidence suggests that there is little to no change in adult labor supply as a result of cash transfer program receipt in low- and middle-income countries (see Baird et al., 2018, for a review of the literature). Second, in our model, the functional form for preferences rules out a substantial wealth effect on labor supply, and thus the shape of the labor supply response to the lockdown is not sensitive to the assumption we put on the transfers. This is because our preferences are GHH (Greenwood et al., 1988). The GHH preferences feature a zero wealth effect on labor when the labor supply decision is purely static. In our framework the labor supply decision is not purely static because today’s labor input affects transition probabilities across the different future family infection states _k_<sup>_′_</sup> . Quantitatively, however, this is not a large effect: the labor supply response to the lockdown labor tax _μ_ is virtually identical whether the labor tax revenue is rebated as a lump-sum to the households, or removed from circulation.<sup>11</sup>

**Schooling** The impact of school closings on transmission is captured by the assumption of lower community transmission during the lockdown, governed in the model by the semielasticity _ξ_ . While we could not find a disciplined way to make _ξ_ country-specific, available data suggest that school closures were quite broad-based across countries of all income levels. UNESCO reports that in the beginning of April 2020, for example, there were more than 139 country-wide school closures. Moreover, most of the countries in Latin America and South Asia had longer school closures than most European countries.<sup>12</sup>

> 11Details available upon request.

> 12See en.unesco.org/covid19/educationresponse#schoolclosures.

20
# **3 Data and Calibration**

The strength and duration of a lockdown are critical aspects of our quantitative analysis. Our _reference_ lockdown policy attempts to mimic what had been observed in the first weeks of the pandemic. It is henceforth defined by three parameters: its starting time, length, and severity. To calibrate these parameters alongside transmission rate parameters, we proceed in two steps. In the first step, we calibrate the transmission parameters _πI_ 1,... _πI_ 4 to match the relative importance of the different transmission modes and the overall predicted infection rate in an unmitigated spread scenario. In the second step, we calibrate the effect of lockdown severity on community transmission _ξ_ , alongside the strength of the reference lockdown _μ_ ̄, to jointly match the decline in GDP and the reproduction number _R_ 0 as estimated by Flaxman et al. (2020) for European countries early in the pandemic.

## **3.1 Infection and Mortality Parameter Calibration**

The within-household transmission parameter, _πI_ 4, is taken from a meta-analysis of household transmission estimates from different settings. Lei et al. (2020) estimate the secondary infection rate in the household to be 0.27.<sup>13</sup> To discipline the three other transmission parameters, we jointly match three moments. The first moment is the proportion of the population that would get infected in each country in the absence of any mitigating policy. We use projections reported by Walker et al. (2020) that use country- and age-specific contact patterns to simulate health impacts of COVID-19 in 202 countries. They develop an SIR model incorporating the age distribution of each country. Employing a basic reproduction number ( _R_ 0) of 3.0, they project that about 90 percent

> 13Household living conditions in poor and rich countries differ, and thus it would have been desirable to calibrate country-group-specific within-household transmission rates. Unfortunately, we are not aware of any systematic studies on country heterogeneity in within-household transmission. The value in Lei et al. (2020) is based on various settings, including several estimates from China. A recent paper based on data for Norway (Telle et al., 2021) finds a secondary attack rate (SAR) of 0.24 when the index case is a parent or a child under 6, and a SAR of 0.14 when the index case is an older child. It is thus reassuring that the rates for Norway are similar to those for China, two countries at different levels of development (and with different levels of housing area per resident). There is a feature of our calibration that accommodates the notion that slums or other high-density living arrangements can lead to higher transmission rates. Namely, we calibrate substantially higher community transmission rates in lower- and middle-income countries compared to wealthier ones. This difference can be thought of as capturing the prevalence of high-density living such as slum areas.

21
of the population would ultimately either recover from infection or die in an unmitigated epidemic scenario in lower- and middle-income countries. The unmitigated epidemiological model in Walker et al. (2020) assumes no behavioral response to the pandemic. For consistency, we assume that households continue to supply labor and consume at the same levels as in the pre-pandemic steady state in this stage of the calibration exercise. This assumption is relaxed in the following steps of the calibration.

The other two moments used for the calibration of the transmission parameters are the shares of infections occurring through work- and consumption-related activities. As most of the world’s population lives in urban areas, we chose to use data reported by JohnstoneRobertson et al. (2011) on locations of contacts in a South African township community.<sup>14</sup> The authors define close contacts as those involving physical contact or a two-way conversation with three or more words. They find that 6.2 percent of close contacts occur in workplaces, while 3.5 percent occur in shops or local bars and therefore can be thought of as related to consumption. Another 8.9 percent of close contacts take place during transport and could theoretically be linked to either labor or consumption. We assume that half of the transport contacts is related to labor and half to consumption. This implies that 10.6 percent of close contacts are related to work and 8 percent to consumption. For high-income countries, we use the rates employed by Eichenbaum et al. (2021) for the US. Based on an analysis of the Bureau of Labor and Statistics 2018 Time Use Survey data and contact patterns reported in Ferguson et al. (2006) and Lee et al. (2010), they conclude that 16 percent of transmissions are related to consumption and 17 percent to work.

# **3.2 Reference Lockdown and Community Transmission Parameter**

Conditional on the transmission parameters calibrated above, we calibrate the reference lockdown policy, and the parameter determining the relationship between lockdown strength and reduction in community transmission, _ξ_ .

> 14We reviewed the public health literature on social contacts in low- and middle-income countries and found no nationally representative study. Most of the studies focus on age-specific contacts and only a handful of studies categorized interpersonal contacts in a manner that permitted direct mapping into consumption and labor components.

22
A country starts to impose the reference lockdown when the infected population reaches 2.6%. This rate is based on the COVID-19 prevalence at the time of the first lockdown in the Italian municipality of Vo, the site of the first COVID-19-related death detected in Italy (Lavezzo et al., 2020). In our calibration, the countries start to impose the reference lockdown policy between week 9 and 13, with an average start date at week 11.

The length of the reference lockdown policy is based on Flaxman et al. (2020) that estimates the impacts of non-pharmaceutical interventions in 11 European countries during the first months of the pandemic.<sup>15</sup> We drop the four countries that only imposed mild or no lockdown policies (Denmark, Norway, Sweden, and Switzerland) and work with the remaining seven countries.<sup>16</sup> We compute the lockdown length for each country based on the difference between the reported lockdown date and the end of the sample period in Flaxman et al. (2020). The lockdown policies range between 43 to 54 days, with an average of 7 weeks, which we use as the length of the reference lockdown. The strength of the lockdown was inferred from the GDP decline in the first two quarters of the year 2020. As explained later in this section, we calibrate _θ_ = 1, which implies that a lockdown policy of _μ_ ̄ reduces aggregate ̄ labor supply and GDP by _μ_ . Therefore, an _x_ -day lockdown reduces the two-quarter GDP by _xμ/_ ̄ 180, from which one can infer _μ_ ̄, conditional on the length of the lockdown calibrated ̄ above and the observed decline in GDP. For example, the inferred _μ_ in Germany with a 6 _._ 68 percent decline in GDP and a 43-day lockdown is 0.0668*180/43 = 0.2796. We repeat the calculation for all seven countries and find that the strength of the lockdown policy to be between 28% and 46%. The average across the seven countries is 38%, which we use as _μ_ ̄ for the reference policy.

Given the country-specific _μ_ ̄ and lockdown length in these 7 countries, we can then compute _ξ_ , the elasticity of community transmission with respect to lockdown, for each of these countries. To do this, we simulate the model and target the post-lockdown _R_ 0 of 0.66 as reported in Flaxman et al. (2020) for the sample countries. The corresponding _R_ 0 at period _t_

> 15Out of the five non-pharmaceutical interventions studied in Flaxman et al. (2020), we focus on “lockdowns” to quantify the reference lockdown. Note that the “lockdown” in our model should be interpreted broadly to include the other four forms of intervention policies in Flaxman et al. (2020), such as social distancing, self-isolation, school closure, and restricting public events.

> 16The four countries with mild or no lockdown policies lead to corner solutions in the calibration of _ξ_ , as explained below. The remaining 7 countries are Austria, Belgium, Britain, France, Germany, Italy, and Spain.

23
in our model is computed as<sup>_T_</sup> _π_<sup>_t−_</sup> _rt_<sup>1</sup> +<sup>_<u>/I</u>_</sup> _π_<sup>_t_</sup> _dt_<sup>_−_1, where</sup><sup>_πrt_and</sup><sup>_πdt_are the population-weighted average</sup> recovery and mortality rates in period _t_ . We take the _R_ 0 at the period after the lockdown policy ends, as the counter-part of the post-lockdown reproduction number in Flaxman et al. (2020).<sup>17</sup> The resulting _ξ_ ranges between 1.9 to 3.5 among the 7 countries with an interior solution, and we take the average of 2.32 to apply to all the 85 countries in the full sample.<sup>18</sup>

# **3.3 Mortality Rates**

We look to two distinct literatures to calibrate our mortality parameters.

**COVID-19 mortality** Walker et al. (2020) projects hospitalization and mortality rates per age group that are in turn based on findings from China reported by Verity et al. (2020).<sup>19</sup> Conditional on infection, the average projected hospitalization and mortality rates in lowand middle-income countries are listed in Appendix Table B.2. In the calibration of the model, we use country-specific rates as countries have different age distributions within the broader age groups defined in our model.

For severe cases of COVID-19 infection, hospitalization offers treatments such as oxygen

> 17We have computed the _R_ 0 for all the countries in the sample using our calibrated model. The postlockdown _R_ 0 is similar across countries and is close to those reported for the European countries in Flaxman et al. (2020). The average _R_ 0 among the 85 countries one week after the reference lockdown is 0.57. In comparison, the same statistic among the 11 European countries in Flaxman et al. (2020) is 0.66. Given that the _R_ 0 estimates in Flaxman et al. (2020) is our calibration target, the consistency among 85 countries provides some reassurance, but not external validation. Our estimates are also broadly consistent with the _R_ 0’s reported in the economics literature, such as Atkeson et al. (2020) and Fern ́andez-Villaverde and Jones (2020). While our estimated _R_ 0 is not directly comparable to the _R_ 0 reported in the papers above - the main difference is that the _R_ 0’s in our paper are computed based on simulated data assuming a 7-week reference lockdown while the _R_ 0’s reported in these two papers are based on the actual data where the strength and length of the lockdown policies vary - the general consistency is reassuring. For example, the average _R_ 0 reported in Fern ́andez-Villaverde and Jones (2020) in May 2020, a period immediately after the first wave of lockdown policies in the world, is 0.86. Atkeson et al. (2020) shows that after the initial outbreak, the estimated _R_ 0 usually hovers around 1.0. Figure 1 in Atkeson et al. (2020) shows that _R_ 0 usually first drops below 1.0 at around 50 days after the initial outbreak, before increasing again to hover around 1.0. The dip in _R_ 0 is probably due to the lockdown policies implemented immediately after the outbreak.

> 18A corner solution in this step occurs for the four countries that we have dropped (Denmark, Sweden Switzerland, and Norway). If the country imposes a mild lockdown, the implied _μ_  ̄ for this country will be low, which makes it impossible to reach the target _R_ 0 even with _ξ_ = _∞_ .

> 19Infection fatality rates calculated with data from China might not be generalizable to other countries because of factors such as prevalence of comorbidities and quality of health services (Ghisolfi et al., 2020; Demombynes, 2020). More recent meta-analyses found mortality rates in line with those reported by Verity et al. (2020) (Levin et al., 2020; Meyerowitz-Katz and Merone, 2020). It is important to note, however, that these analyses overwhelmingly rely on studies from high-income countries.

24
therapy for patients with respiratory failure. Therefore, it is believed that when hospital care cannot be accessed, the case fatality rate (CFR) for a COVID-19 infection is higher. We assume that the COVID-related mortality is elevated by a factor of 3 for those patients who are in need of hospitalization but cannot receive it.<sup>20</sup> We denote by _πb_ ( _m_ ) the probability an individual of group _m_ requires hospitalization, conditional on being infected. The share of individuals in need of hospital beds at time _t_ , _Bt_ , is given by We assume that hospital bed allocation is random among those in need. Denoting by _h_ the number of hospital beds, the probability that an infected individual dies at period _t_ is given by As in Atkeson (2020) and Eichenbaum et al. (2021), we assume that it takes an average of 18 days from infection to either recover or die. To obtain weekly mortality probabilities, we multiply the rates obtained from Walker et al. (2020) by 7/18.<sup>21</sup> The number of hospital beds in each country is obtained from the World Bank’s World Development Indicators. It should be noted that the indicator is not measured frequently,

> 20For example, Yang et al. (2020) find that the CFR by the middle of February 2020 within the city of Wuhan, China, the presumed outbreak location of origin for COVID-19, was substantially higher (5.25 percent) than in regions outside Wuhan but within the same province (1.41 percent) and in regions outside the province (0.15 percent). While the CFRs within and outside Wuhan should vary for several reasons, including availability of testing, a key factor was the initial demand for hospital beds exceeded the supply.

> 21It has been noted that the Eichenbaum et al. (2021) SIR-macro model misses on the timing of COVID19 deaths for the US. Unfortunately, there is no practical way to assess whether our model reproduces the relative timings of the economic downturn vs. COVID-19 deaths in our sample of countries. The first basic issue is that our exercise does not model _actual_ lockdowns that occurred in these 85 countries. Rather, we impose the same lockdown parameters on all countries and compare the cross-country differences in outcomes. Second, a systematic comparison of our model’s predictions to actual lockdown outcomes would be complicated by the large heterogeneity among countries in the timing of the appearance of the virus and the timing of the policy responses. In addition, seasonality in transmission rates might play a role. Unfortunately, there is no parsimonious way to incorporate seasonality into our analysis, because we have 85 countries on all continents and climactic zones, and seasonality in transmission rates likely varies substantially across countries. Heterogeneous seasonality would further complicate any potential comparison between the data and our model’s predicted timing of economic downturn and death rates.

25
particularly in lower-income countries. We use the most recent measurement reported for each country. In our sample, the average number of hospital beds per 1,000 people is 0.6, 1.6, 3, and 4.15 in low-, lower-middle, upper-middle, and high-income countries, respectively.

**Non-COVID-19 mortality** Baseline mortality rates _π_  ̄ _n_ 1, _π_  ̄ _n_ 2 and _π_  ̄ _n_ 3 are computed from country-specific life table data obtained from the Global Health Observatory Data Repository of the World Health organization.<sup>22</sup>

In terms of elevated mortality due to shortfalls in aggregate income, several papers have estimated the relation between economic shocks and infant or young child mortality (Baird et al., 2011; Bhalotra, 2010; Cruces et al., 2012; Friedman and Schady, 2013; Maruthappu et al., 2017). For low and middle-income countries, the population groups most vulnerable to declines in aggregate income are young children and, perhaps, the elderly (Cutler et al., 2002). We focus on mortality impacts among children under-5 as this population group has been the most extensively studied. We estimate the effect of short-term aggregate income shocks on mortality following the methodology of Baird et al. (2011). We use data on GDP per capita from the World Development Indicators. The values are adjusted for purchasing power parity, corresponding to 2011 US dollars. Data on infant and child mortality are taken from retrospective birth histories as reported in the Demographic and Health Surveys (DHS) conducted in 83 low- and middle-income countries between 1985 and 2017. The combined sample is of 5.2 million births in low- and middle-income countries. We run regressions of the following form: where _Dict_ is a binary indicator that takes the value 1 if child _i_ in country _c_ died in year _t_ , log GDP is the natural logarithm of per capita GDP, _fc_ ( _t_ ) is a country-specific flexible time trend, _δc_ is the country fixed effect, and _εict_ is the error term. Standard errors are clustered at the country level.

We run the regression separately for countries of different income levels, as classified by the World Bank 2020 income groups. The main result is that a 1 percent decrease in per capita GDP is associated with a 0.15 increase in under-5 mortality per 1,000 children in low-

> 22who.int/gho/data

26
income countries. The semi-elasticity is 0.10 and 0.03 for lower- and upper-middle-income countries, respectively. We assume that under-5 mortality is not impacted by income shocks in high-income countries. Unlike the results from low- and middle-income countries, studies analyzing data from the United Stated find mortality to be pro-cyclical (Ruhm, 2000; Dehejia and Lleras-Muney, 2004).

To map the estimated semi-elasticities into our calibration, we define _s_ 0 _−_ 5 to be the share of children under five years old in the total number of children of ages 0 to 15. The semi-elasticity of child mortality with respect to consumption is given by where _βg_ represents the regression coefficients for low-, lower-middle- and upper-middleincome countries. _ν_ (1) equals zero in high income countries.

It is important to note that we convert the annual semi-elasticity estimate into weekly frequency in the quantification, to match the period definition in the model. Unfortunately, we are unable to estimate the mortality semi-elasticity at a shorter frequency due to data – limitations the national accounts data for many developing countries are only available annually. However, we believe the underlying relationship operates at a shorter frequency than annual for several reasons. Baird et al. (2011) find that only contemporaneous GDP deviations are correlated with mortality likelihood even though a large share of the infants in the estimating dataset experienced the majority of the in-utero period in the lagged year and an equal share of infants experienced the majority of their first year of life in the leading year. Moreover, the authors find that the coefficients on economic conditions in utero and after the first month of life are both small and insignificant. By contrast, the coefficient on per capita GDP in the first month is large, significant, and very close in magnitude to the main effect reported in the paper. These results underscore that it is the economic conditions around birth (say the last months of pregnancy and the first months of life) that matter most for infant survival during economic contractions. As 47 percent of under-5 mortality in 2019 occurred in the neo-natal period, it appears clear that the actual frequency through which 27
economic contraction affects child survival is shorter than an annual frequency.<sup>23</sup> The empirical estimate of the mortality semi-elasticity with respect to GDP downturns will be mapped in the model to the increased mortality from lower consumption. However, the estimated coefficient may capture other mechanisms, such as lower availability or utilization of health services. Unfortunately, there is insufficient health system capacity time series data to isolate this effect empirically. The available health capacity data would be _de facto_ absorbed by the country fixed effects in estimation. Going further, we tested for heterogeneous semi-elasticities when stratifying by hospital capacity and found no statistically significant differences in the semi-elasticity estimates across countries with different levels of hospital capacity.

Further we believe it unlikely that the health capacity channel is an important one for the magnitude of the semi-elasticity estimate. This is because the semi-elasticity is estimated on past (pre-pandemic) data on “regular” economic downturns, rather than those brough on by pandemics. In a regular economic downturn, there is less reason to believe that the recession in and of itself leads the health system capacity to be overrun. To the extent that lower utilization of health services is responsible for part of the child mortality response in regular recessions, it is likely due to lower demand for health services by the households suffering negative income shocks, rather than sharp reductions in availability.

# **3.4 Demographic and Economic Parameters**

Country-specific age distributions are obtained from the 2020 World Population Prospects.<sup>24</sup> The age distribution is used to compute _s_ 0 _−_ 5, which is then used to rescale the semi-elasticity of under-5 mortality to the age group 0 - 15 using the formula in the previous section. In addition, we use the age distribution of the three age groups to compute the masses of the different age groups within the household ( _l_<sup>1</sup> _, l_<sup>2</sup> _, l_<sup>3</sup> ) in each country.

> The weekly discount factor equals to _β_ = 0 _._ 96<sup>1</sup><sup>_/_52</sup> to reflect an annual risk-free rate of 4 percent. We assume that at _t_ = 0, _ε_ = 0 _._ 1 percent of population is infected. We set

> 23Source: WHO fact sheet, https://www.who.int/news-room/fact-sheets/detail/newborns-reducingmortality

> 24population.un.org/wpp

28
_φ_ = 0 _._ 8 so that an infected working adult is only 80 percent effective in supplying labor. This is equivalent to assuming that 80 percent of the infected prime-age population is either asymptomatic or experiences a mild case.<sup>25</sup> We set _θ_ to 1 so that the steady state labor supply in the pre-pandemic world is normalized to 1 in all countries.

The parameter _σ_ governs the elasticity of substitution between household members. We – set it to 3, so that the loss of a non-productive household member the children or the elderly – with mass _l_<sup>_m_</sup> reduces the instantaneous utility, _u_ ( _·_ ), by a proportion _l_<sup>_m_</sup> in steady state. Appendix A.3 provides the details of the derivation.

The values of Γ<sup> ̄</sup> _t_ are calibrated based on the Atlas of Social Protection Indicators of Resilience and Equity (ASPIRE) data set. In the dataset, 1.55 percent of GDP was spent on social assistance programs on average. We assume that Γ<sup> ̄</sup> _t_ is constant across the entire simulation, and calibrate it to be 1.55 percent of GDP in every country.

Table 1 summarizes all the parameters of the model and indicates the data sources used to calibrate them. Appendix Table B.3 lists the countries in the sample. Appendix Tables B.4 and B.5 list all the country-specific parameters for each country.

# **4 Results**

To quantitatively illustrate how the same policy might lead to different mortality outcomes across countries, we compare two scenarios. The first scenario traces economic and diseaserelated behavior without any government intervention. The second scenario involves the reference lockdown as described above, where a labor tax of 38 percent is imposed for a seven-week period once the rate of infection prevalence reaches 2.6 percent. While the reference lockdown is picked to mimic policies adopted during the early months of the pandemic, it is not designed to capture all the complexities of mobility and social gathering restrictions imposed by various countries. Rather, the results below aim at highlighting the large heterogeneity in outcomes following the adoption of the same policy rule.

> 25This corresponds to media reports on the results of an unpublished sero-prevalence study conducted in New York in April 2020 (nytimes.com/2020/04/23/nyregion/coronavirus-antibodies-test-ny.html). Li et al. (2020) and Stringhini et al. (2020) report even higher rates of asymptomatic cases in China and Switzerland.

29
|Source/Target<br>Note<br>share of transmission due to consumption-related activities<br>consumption-related activity transmission<br>share of infection due to work-related activities<br>work-related transmission<br>proportion of infected population<br>community-based infection<br>Lei et al. (2020)<br>within-household infection<br>post-lockdown _R_0 in<br>impact of lockdown on<br>Flaxman et al. (2020), 7-country sample<br>community transmission<br>population infection rate of 2.6%<br>start date of the reference lockdown<br>lockdown length from<br>length of the reference lockdown<br>Flaxman et al. (2020), 7-country sample<br>GDP decline in 2020Q1-Q2 in<br>strength of the reference lockdown<br>the 7 countries from Flaxman et al. (2020)<br>semi-elasticity of child mortality w.r.t. income<br>Authors’ estimation using DHS data<br>low-income countries<br>Authors’ estimation using DHS data<br>lower-middle income countries<br>Authors’ estimation using DHS data<br>upper-middle income countries<br>Assumed based on literature<br>high-income countries<br>Walker et al. (2020)<br>COVID-19 mortality, type-_m_<br>Walker et al. (2020)<br>probability of hospitalization, type-_m_<br>World Development Indicators<br>number of hospital beds per 1000 people<br>WHO Global Health Repository<br>non-COVID mortality, type-_m_<br>World Population Prospects, 2020<br>mass of type-_m_<br>annual risk-free rate of 4 percent<br>weekly discount factor<br>Eichenbaum et al. (2021)<br>initial infected population<br>Eichenbaum et al. (2021)<br>efciency loss due to infection<br>steady-state labor supply = 1<br>disutility from labor supply<br>loss of type-_m_ reduces _u_(_·_) by _lm_<br>elasticity of substitution between household members<br>ASPIRE dataset<br>external transfer payment|the calibrated parameters discussed in the main text. Country-specifc parameters are presented in the appendix.|
|---|---|
|Value<br>country-specifc<br>country-specifc<br>country-specifc<br>0.27<br>2.32<br>country-specifc<br>7<br>38%<br>0.15<br>0.10<br>0.03<br>0.00<br>country-specifc<br>country-specifc<br>country-specifc<br>country-specifc<br>country-specifc<br>0_._961_/_52<br>0.1%<br>0.8<br>1.0<br>3.0<br>1.55% of GDP|te: This table lists|
|Name<br>_πI_1<br>_πI_2<br>_πI_3<br>_πI_4<br>_ξ_<br>-<br>-<br> ̄_μ_<br>_νj_(1)<br>_πd_(_m_)<br>_πb_(_m_)<br>_k_<br> ̄_πn_(_m_)<br>_l_(_m_)<br>_β_<br>_ε_<br>_φ_<br>_θ_<br>_σ_<br> ̄Γ_t_|No|

30
# **4.1 Lockdowns and Total Mortality**

Figure 1 plots the reduction in adult COVID-19-related mortality as a result of the reference government-imposed lockdown. The figure depicts excess adult mortality in the first year of the pandemic under the reference lockdown, relative to excess adult mortality in the noaction scenario. In both pandemic scenarios, excess adult mortality is the difference between the number of adult deaths and the number of adult deaths had the economy not experienced a COVID-19 outbreak.<sup>26</sup> Overall, a single seven-week lockdown will reduce adult mortality from COVID-19 by less than 9 percent in all countries. The figure also shows that the efficacy of the reference lockdown at averting mortality is correlated with per capita income. In low-income countries, an average of 3.5 percent of COVID-19-related deaths are averted, in comparison to an average of 6.2 percent in high-income countries.<sup>27</sup> Several factors drive this pattern. First, wealthier countries’ populations have a larger share of adults over 60, the group most at risk of dying from COVID-19. Second, because of greater hospital capacity in wealthier countries, a slowed pace of the virus’ spread is more likely to translate into higher survival probabilities. Lastly, greater shares of transmission in high-income countries occur through labor and consumption-related contacts. Therefore, the reduced economic activity in these countries has a bigger impact on the virus transmission relative to countries where a larger share of transmissions occurs through community contacts.

**Lockdowns and the mortality tradeoff** Panel (a) of Figure 2 illustrates the intergenerational mortality tradeoff that is the focus of this paper. As in Figure 1, on the horizontal axis is log per capita income. The vertical axis represents the number of children’s lives lost during the first year of the pandemic per COVID-19 fatality averted by the reference lockdown. There is a pronounced negative relationship between this indicator and income.

> 26This calculation of excess mortality represents a minor underestimation of COVID-19 mortality. A share of adults who are simulated to die from COVID-19 might also receive a non-COVID-19 mortality shock in the simulation of the no-COVID-19 scenario. These deaths will not count towards the excess mortality calculation.

> 27The lockdown slows the virus’ spread but over a full-year horizon the effect on the total share of the population ever infected is small in many countries. On average, the number of _cases_ averted by the reference lockdown is around 2 percent of the country’s total population. Appendix Figure B.1 plots the reduction in total infections as a fraction of population against per capita income. The reference lockdown is more effective at averting cases in the high-income countries: it prevents 2.8% of the population in high-income countries from getting infected, but only 1.8% in low-income countries.

31
<!-- Start of picture text --> 0.98 Reduction in Adult Mortality Rate by the Lockdown<br>ekAZ Average:<br>*MDG LIC: 0.965<br>0.97 *®MNG LMC: 0.957<br>.<br>sogNEReee SAGO UMC: 0.945<br>0.96 DI apRbreawhes oy NAM, coun” 0.938<br>*@CAF oni RAWE abet<br>*CHN<br>0.95 eKH J MEX . FRAY<br>i ea *ARG fusA<br>oR*®MAR- ®ZAFON *JPNEU*@BEL<br>0.94 *vNM oAUSPEReIRQOL®THAN PAN<br>0.93 eBGR *GRB *Bbi6BR<br>scEO oop eDNREHE<br>*NOR<br>0.92<br>*BIH<br>0.91<br>5 6 7 8 9 10 11 12<br>Ln(Per Capita GDP)<br><!-- End of picture text -->
<!-- Start of picture text --> 3 Expected number of children lives lost per COVID-19 fatality averted<br>Average:<br>*UGA LIC: 1.758<br>2.5 aHER LMC: 0.585<br>“zou”‘ UMC:HIC: 0.0610.000<br>2}<br>. *]ZA<br>"Yes<br>15 ficoenwA\BEN*ZMB eAGO<br>1 SR<br>°ZWE<br>*MNG<br>nerd<br>0.5 . * egy<br>°sane PHIRN, nal<br>oVAMP*SIRBRO<br>0 OOO= BNUAZ 3 ERGO<br>5 6 7 8 9 10 11 12<br>Ln(Per Capita GDP)<br><!-- End of picture text --> <!-- Start of picture text --> Reduction in Total Mortality Rate by the Lockdown<br>0.1 Average:<br>0.08 LIC: -0.02614 BIH<br>. LMC: 0.02037 NOR<br>UMC: 0.05191 GEO .acR e@gRB* BBMGBRONCHE<br>0.06 HIC: 0.06189 oVNM oseOPER.HAL5 RpePAN®ARG “beUSA<br>0.04 Py sgmrlag rear<br>#1 AOsIDNayaBWYA<br>oni@PHELKABLR *BHR<br>0.02 nel!° HSNKGZPAK ®EGYeMNG NaI ®KAZ<br>0 ad°ZWE<br>eRWhe<br>omP®Z etza<br>-0.02 e4hGO Nye °AGO<br>-0.04 eppiNER BFA<br>-0.06 *UGA<br>5 6 7 8 9 10 11 12<br>Ln(Per Capita GDP)<br><!-- End of picture text -->
# **4.2 Understanding the Intergenerational Mortality Tradeoffs**

The previous section illustrated the large variation in outcomes across countries following the reference lockdown. This section investigates the contributions of various country characteristics to the spread of the infection and subsequent mortality, both COVID-19-related and not.

## **4.2.1 Lockdown and the dynamics of the COVID-19 pandemic**

To illustrate further what drives cross-country differences in outcomes, we present a more detailed analysis from four countries at different stages of economic development. We purposefully selected one country from each income group: Uganda (low income), Pakistan (lower-middle income), South Africa (upper-middle income), and the US (high income). These different income levels dictate how consumption shortfalls due to lockdown policies would affect child mortality. The selected countries also differ substantially along other dimensions that determine the effect of lockdown policies, such as the population age distribution and health system capacity. Forty-six percent of the Ugandan population is under the age of 15 while only 3 percent are 60 years or older. In Pakistan (South Africa), 34 (29) percent of the population are under 15 and 7 (9) percent are 60 or older. The US has the oldest population out of the four countries, with only 18 percent under 15 and 23 percent over 60. Uganda and Pakistan have only 0.5 and 0.6 hospital beds per 1,000 people to contrast with rates in South Africa and the United States of 2.8 and 2.9, respectively.

Column (a) of Figure 3 displays the aggregate labor supply during the first year of the pandemic as a fraction of the no-pandemic steady-state labor supply. The blue line represents labor supply without any government intervention and the red line represents the reference lockdown. Without a lockdown, there would be only small declines in labor supply during the weeks with the highest current infection rates (depicted in Panel (c) of the figure, solid blue line). This drop is entirely due to households limiting their own labor supply to lower COVID-19 transmission risks to their own members. Relative to the other countries, the drop in labor supply is largest in the United States given its substantially larger share of older adults in the population. However, even in the United States the max of the labor decline 34
in the no-action scenario is less than 5 percent. This muted response reflects the sizeable externality associated with pandemics, i.e. households consider the tradeoff between their members’ mortality risk and income loss but not the impact their exposure could have on the further spread of the virus in the population. Under the lockdown scenario, there will be a uniform reduction of 38 percent in labor supply during the weeks in which the labor tax will be in effect. Then there are subsequent additional small reductions in labor supply when active infections reach their highest rates. As in the no-action scenario, the subsequent reduction in labor supply is largest in the US but never exceeds 5 percent.

Columns (b) and (c) of Figure 3 illustrate how the lockdown policy affects virus transmission in the different countries. As can be seen in column (b), the reference lockdown will have only a negligible impact on the share of the population ever-infected by the end of the pandemic’s first year. Instead, the lockdown slows the pace of transmission and displaces the peak infectivity period to later in the year. Overall, this policy slows the spread of the virus more effectively in wealthier countries. The infection rate peaks in Uganda and Pakistan before it does in South Africa and the US. The primary reason for that is that the share of working-age adults in the total population is larger in the wealthier countries and, hence, the reduced economic activity has a larger impact on transmission rates in South Africa and the US than it does in the other two countries.

Column (d) of Figure 3 depicts the cumulative all-cause child and adult mortality in the reference lockdown scenario, relative to the cumulative mortality in the no-lockdown scenario. In the three low- and middle-income countries, lockdown policies increase child mortality. This increase in child mortality is entirely due to the impact of the economic contraction induced by the lockdown. Given the high sensitivity of survival rates to income fluctuations in low-income countries, the largest increase in child mortality is in Uganda. In the United States, however, the lockdown policy reduces child mortality. Here this reduction is entirely due to reduced COVID-19 child mortality, albeit from a low reference level.

With respect to adults, the reference lockdown temporarily reduces mortality in all countries. However, by the end of the first year of the epidemic, the lockdown will have a small effect on the cumulative adult mortality, as already shown in Figure 1. As highlighted above, the lockdown slows the spread of the virus by a number of weeks but has only a minor impact 35
<!-- Start of picture text --> a Infected Population<br>0908 t 7 --—s—-- ]]<br>07 ! |<br>- !1 |<br>08 1 ]<br>os I<br>03 1 ]<br>0.2 a<br>on0 0 10207 ceNo= _=Referenceaction Lockdown |<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> 03 + Infection———RateNo action7 Cr<br>02s —_=Reference Lockdown |<br>oo myIN |<br>oas nl<br>oa yo\<br>\<br>0.05 \ |<br>° 0 FT a = a x = a a)<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> hos Aggregate Labor Supply7 7<br>=_——1 +<br>0.95 1 I<br>a09 rot<br>oa 1<br>075 rot1<br>o7 t 1<br>06s 1—o No action<br>06 = _=Reference Lockdown!<br>0 Fr, i a a<br>Weeks<br><!-- End of picture text --> <!-- Start of picture text --> ae Death<br>1as 4<br>at<br>1051 = = |}<br>0.95 \ ‘<br>09 \ ;7 |<br>oe \ 1<br>08 ‘ j<br>o7so7 0 Fr vfs 7 i a a FeWo=<)chiaren action |<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> 1 Infected PopulationPs<br>09 Pie<br>os ‘ 4<br>o7 ! |<br>os !<br>os 1! |<br>o4 !<br>03 t 4<br>oz /<br>on -’ No action |<br>° 0 1020 Weeksrr)= _=Reference Lockdown<br><!-- End of picture text -->

<!-- Start of picture text -->
1.05 A‘s9regjate Labor Supplply<br>i<br>0.95 1 1 ]<br>0.9 toytoy ]<br>os oy ;<br>os ty |<br>075 I<br>06so706 0 1tyry..Fe 1i i WeeksNo= _=Reference actiona - Lockdown a)]|<br><!-- End of picture text -->

<!-- Start of picture text --> 12 r r Deathr + r<br>1<br>1 SSS<br>09 \\ t ‘<br>\ 1<br>08 \ 1<br>on 1,\ 7of =aNohcats action<br>060 Fe rw i Weeksa a ee children a)<br><!-- End of picture text --> <!-- Start of picture text --> 03 Infection Rate<br>No action<br>0.25 —_= Reference Lockdown’<br>02 an*<br>oas. ryry<br>i"<br>on \\<br>0.0 \ \<br>° 0 Fe Weeksi, ‘ rr)<br><!-- End of picture text --> <!-- Start of picture text --> 09 Infected Population—<br>oa ‘ca |<br>o7 t<br>06 !<br>os !<br>oa '! ]J<br>03 / ]<br>92 / ]<br>01 li“ "—No action |<br>0 ° 1020 300-4050—_=Reference Lockdown<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> hos Aggregate Labor Supply<br>‘ is<br>09 oy<br>09 roy<br>os oy<br>oa 1toyy<br>075 roy<br>o7 1<br>0.65 ty ——No action<br>06 0 ily= i = =Referencea, a Lockdown: a)<br>Weeks<br><!-- End of picture text --> <!-- Start of picture text --> 02s Infection Rate<br>No= = Reference action Lockdown!<br>02<br>0.15 aN<br>1!<br>on 1 \<br>\<br>0.05 ‘<br>\<br>° 0 Fe a a,‘cr . er )<br>Weeks<br><!-- End of picture text --> <!-- Start of picture text --> hos . Death .<br>:<br>\ , a<br>0.95 \ ? |<br>\ /<br>oaso9 \\ t1 ]|<br>0.75oa \‘7of7 / (—HoadJa ho action<br>07 ° Fr i a a [=e children<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> 09 Infected PopulationPs<br>al<br>0.8 , ]<br>0706 !v<br>os ! |<br>oa03 /111 ]]<br>02 v ]<br>oa 7 (No action J<br>0 0 1020 ce= _=Reference Lockdown<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> 0.25 Infection Rate<br>No action<br>= _=Reference Lockdown, |<br>02<br>’ON<br>oas \ |<br>1I \<br>on \\ 4<br>0.05 \\ |<br>.<br>oO 0 Fe a a . )<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> hos Aggregate Labor Supply<br>. :<br>1 WSs' =<br>os io<br>09 I !<br>os to<br>08 rot<br>075 1ot1 ot<br>o7 rot<br>0.65 iol — No action<br>06 0 FC,1_t= i = a _=Reference Lockdown!<br>Weeks<br><!-- End of picture text --> <!-- Start of picture text --> 1 Death<br>a<br>0.95 \ ‘ va 4<br>0.8509 ‘1 !? |<br>os 1 |<br>0.75 \1 t<br>06s07os 11\ !!I J]<br>oss v/ [==tioaction) |<br>Os: 0 Fr 7 i a a Fe chiaren<br>Weeks<br><!-- End of picture text -->
the slowdown in the virus spread causes a bigger improvement in survival rates.

Linking back to the results presented in Figure 2, in the poorest country of the four, Uganda, the total mortality in the lockdown scenario is _higher_ than the no-action mortality rate by the end of the year. That is, the number of children who die from the GDP decline is greater than the number of COVID-19 deaths averted by the lockdown. In Pakistan, the excess child mortality is just slightly smaller than the modest adult mortality reduction achieved by the lockdown. In South Africa and the US, the lockdown achieved positive although small reductions in total deaths.

# **4.2.2 Decomposing the heterogeneity in policy impact**

This subsection presents counterfactual simulations designed to isolate various contributing mechanisms and gauge their influence on the overall cross-country variation in lockdown impacts.

**Population age distribution** In the first simulation, we impose the same age distribution on all countries, equal to the unweighted average age distribution among the 85 sample countries. Figure 4(a) plots the number of children’s lives lost per COVID-19 fatality averted by the reference lockdown in this counterfactual (y-axis) against the baseline. Relative to the results presented in Figure 2(a), the ratios are substantially lower when equalizing the age distribution across countries. The counterfactual death ratio is below the 45-degree line and below 0.5 for all countries. This suggests that the variation in the age distribution plays a crucial role in determining how the lockdowns affect overall mortality and the number of child deaths per COVID-19 fatality averted. Had the poorer countries had fewer children per adult, the number of child deaths per COVID-19 fatality averted would have been much lower

**Country income** In the second exercise, we keep the age structure of each country as in the data but assign all countries the same per capita income and therefore the same semielasticity of child mortality with respect to income. The income level in each country in this example is the geometric average of per capita incomes in the sample, corresponding to a

37
<!-- Start of picture text --> 3 Expected number of children lives lost per COVID-19 fatality averted .<br>2B Yo<br>va<br>E “<br>0.5 Yo oMDG SHER<br>yu YONG . éERRSureGaawa SBE Sua<br>Z ozweetr AGAB<br>oe<br>0 0.5 1 1.5 2 2.5 3<br>Baseline<br><!-- End of picture text --> <!-- Start of picture text --> 4 Expected number of children lives lost per COVID-19oUGA fatality averted<br>3.5<br>oNER<br>> oBDI “Oo<br>3622.35 Mill, oBFArai<br>a 2 cage”<br>[2 4<br>a THE<br>E SBRN omoc<br>215 ETH<br>5 aN<br>1 a<br>4<br>0.5 Z<br>ope Rc<br>os<br>0 0.5 1 1.5 2 2.5 3 3.5 4<br>Baseline<br><!-- End of picture text --> <!-- Start of picture text --> 3 Expected number of children lives lost per COVID-19 fatality averted .<br>oy Yo<br>_ va<br>£ “o<br>0.5 wa<br>Y vo . . UGA<br>Zz 6 ozwegih ope GEC BBA ONER<br>0<br>0 0.5 1 1.5 2 2.5 3<br>Baseline<br><!-- End of picture text --> <!-- Start of picture text --> 3 Expected number of children lives lost per COVID-19 fatality avertedTA<br>OGM<br>2.5 ra<br> ONER<br>e BE!<br>&cg 2 Techoe) 2aha2<br>515 cEBBIGO<br>o “<br>f “ oMDG<br>c oRBAR<br>5 ra ze<br>= 1 ene RWA<br>ONRIG<br>oPAK<br>0.5 ogbtPoez<br>RMD OEGY<br>os<br>0 0.5 1 1.5 2 2.5 3<br>Baseline<br><!-- End of picture text -->
relationship between income shortfalls and child mortality in poorer countries.

**Hospital capacity** In the next counterfactual, we impose the US hospital capacity on all countries. Figure 4(c) shows that the ratio of children’s lives lost per COVID-19 fatality averted increases for most low-income countries in this counterfactual. The reason is that with larger health systems, there are fewer COVID-19 fatalities under both the no-intervention and lockdown policies, leading to a smaller number of COVID-19 fatalities averted by the lockdown. It should be noted that in this simulation, the health system capacity only affects COVID-19-related mortality. Improved health system capacity may also reduce non-COVID-related mortality and improve child survival resilience to income shocks, but these channels are not incorporated in our model. **COVID-19 transmission shares by activity** Finally, Figure 4(d) depicts a counterfactual in which transmission probabilities in all the countries are calibrated such that the share of transmission through each channel is similar to the U.S. As explained above, the spread of COVID-19 in high-income countries is more reliant on work- and consumption-related activities, while it is more dependent on community transmission in developing countries. Therefore, the reference lockdown is more effective in slowing transmission in high-income countries, even though the reduction in aggregate labor supply induced by the policy is identical in all countries. Attributing the US transmission parameters to all countries leads to only small declines in the ratio of children’s lives lost per COVID-19 fatality averted in poorer countries. This is because the change in transmission probabilities affects the distribution of infections among the different age groups regardless of whether a lockdown is imposed. Because only working-age adults both supply labor and conduct consumption-related activities in our model, increasing the weight of these channels implies that a larger share of the initial infections would be among this group. Therefore, at the time the reference lockdown is imposed, a smaller share of the elderly are infected, and fewer deaths would be averted by the lockdown. This increases the mortality ratio and explains why changing the transmission probabilities could increase the mortality ratio for some countries or only produce a moderate reduction in others.

39
**Oaxaca-Blinder decomposition** One way to assess the relative importance of the various mechanisms considered is to split all sample countries according to a binary distinction of low- vs high-income, and then conduct an Oaxaca-Blinder decomposition including all factors explored individually above. This exercise is described in Appendix Section C and summarized in Appendix Table C.1. Three mechanisms absorb most of the cross-country variation in the number of children’s lives lost per COVID-19 fatality averted (these findings hold for the reference lockdown as well as the optimal lockdown discussed below). The most influential factor is the semi-elasticity of child mortality to the economic contraction, which accounts for 80 percent of the explained variation across the two country groups. The share of the population under 15 years of age is also a significant factor, accounting for 29 percent of the variation. These two factors “explain” more than 100 percent of the variation across countries since other considered factors decrease the cross-country variation in the ratio of child deaths to averted COVID-19 deaths. The most significant factor that decreases this variation is the community transmission parameter. When community-based transmission constitutes a larger share of total COVID-19 disease transmission, any lockdown policy will be less effective in averting COVID-19 mortality, resulting in higher ratios of child deaths to COVID-19 deaths averted. These three factors are the only significant factors in the decomposition exercise. Other factors such as the share of the population 60 years or older, hospital capacity, or the work- and consumption- related transmission parameters are not especially influential in explaining the observed variation in the tradeoff between child- and COVID-19-mortality.

# **4.3 An Optimal Lockdown Policy**

To conclude our discussion, we consider alternative lockdown policies that explicitly weigh COVID-19-related mortality against welfare more generally.

40
# **4.3.1 Definitions and mortality differences**

We define an _optimal_ lockdown policy as a labor tax sequence _{μt}_ that maximizes the present value of aggregate social welfare, i.e.

As such, the objective function now captures the tradeoff between COVID-19 deaths and both increased infant mortality and the welfare loss due to reduced consumption. As this problem does not yield a straightforward optimality condition, we use global maximization methods to search for the optimal lockdown policy.

Figure 5 depicts the ratio of child deaths per adult death averted by the optimal lockdown. Compared to the rates under the reference lockdown (Figure 2(a)), the ratio of child to adult mortality under the optimal policy is substantially lower. The ratio for all countries is below 0.7 and Uganda is the only country with a ratio above 0.5. Thus, in contrast to the reference lockdown calibrated to mimic policies implemented by European governments in the first few months of the pandemic, the optimal lockdown never leads to a net mortality increase.

Figure 6 demonstrates how the optimal lockdown policies vary across the four selected countries. Relative to the reference lockdown, the labor contraction in the optimal lockdown is smaller but starts earlier and lasts longer in all four countries. Column (a) of the figure also highlights the substantial differences in the length and severity of the optimal lockdowns among countries. There is a negative relation between a country’s income level and the drop in labor supply under the optimal policy. Relative to the poorer countries, the lockdown in the US is be more severe as it has no impact on child mortality and is more effective in reducing transmission. In the US, lockdown measures will be applied during the whole duration of the first year of the pandemic and the labor supply will decline by more than 25 percent when the current infection rate peaks. At the other extreme, Uganda would introduce lockdown measures only in the first half of the year and labor supply never drops below 90 percent of the pre-pandemic steady state.

As seen in column (b) of Figure 6, the optimal lockdown policy substantially reduces the share of the population that ever gets infected in South Africa and the US but not in 41
<!-- Start of picture text --> 0.7 Expected number of children lives lost per COVID-19 fatality averted<br>Average:<br>LIC: 0.319<br>0.6 *UGA LMC: 0.126<br>UMC: 0.016<br>HIC: 0.000<br>0.5<br>@NER<br>0.4 *#MOZ<br>*TZA<br>*BDI<br>0.3 eM eet<br>eTaQvA *AGO<br>*GMDG *BERENIP<br>0.2 a<br>*NPle@ak eLAO®*MNG<br>O41. *KHM ®EGY<br>evn RAD<br>@1OB NEE WA<br>5 6 7 8 9 10 11 12<br>Ln(Per Capita GDP)<br><!-- End of picture text -->
<!-- Start of picture text --> 1 Infected Populatireputation<br>oo SSS SSE<br>oe éoy<br>on fou<br>/<br>06os fogfot<br>o4os02 /;fp hdfi;iyfiIoyot No action<br>on fe = =Reference Lockdown<br>°° 10 - 20 30=== Optimal40 Lockdown50 60<br>Weeks<br><!-- End of picture text --> <!-- Start of picture text --> 03 InfectionNoRate action<br>0.25 =====Fixed OptimalLockdown Lockdown | 7<br>02 IN 4<br>i! \<br>on het ]<br>0.05oa \anan\,\ oN ||<br>\<br>° 0 10 20 30SON= 40 50 60<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text -->
1.05, Aggregate Labor Supply<br>1<br>0.95 Tah, . T 7<br>1b<br>8 tot<br>os} 4 |<br>os ot<br>ons it! ;<br>07 to No action<br>os06 0 ro10— 20 30 =====Fixed Optimal40 LockdownLockdown)50 60<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> M2 peath<br>1as-<br>1.05<br>if = >=<br>0.95 Wooo<br>09 \ ‘<br>oe08 \\ niU/ NeAdit action (ees<br>ons a =o cilren tre<br>x |= Children (optimal)<br>°75 10 20 30 40 50 60<br>Weeks<br><!-- End of picture text -->

<!-- Start of picture text --> 2 Infected Population<br>09oa laia LS7SSS<br>on A 1<br>os ;<br>os / I<br>* | 1<br>!<br>03 !<br>92 ’ No action<br>oa -7 — =Reference Lockdown<br>°,0 10 20 Weeks30=== Optimal40 Lockdown50 60<br><!-- End of picture text -->

<!-- Start of picture text -->
1.05, - Aggregate Labor Supply, -<br>cos1 = tfse<br>09 tad1 ylyd<br>08s toy<br>oe ty<br>ors07 114oy<br>toy No action<br>os ty = =Fixed Lockdown<br>06 o -e10 20 Weeks30 === Optimal40 Lockdown)30 60<br><!-- End of picture text -->

<!-- Start of picture text --> 03 Infection Rate<br>025 ‘===No= =Fixed ptimalaction Lockdown Lockdown<br>a<br>02 my<br>ry<br>os 4<br>\<br>oa \\<br>os ON<br>‘. \<br>° 0 10 20 Ss,Weeks30 ne 40 50 60<br><!-- End of picture text --> <!-- Start of picture text --> 12 Death<br>u<br>2 f——————cose >.<br>Woe c<br>09 1 v<br>\ ‘<br>os , Ne eadaction<br>on 1 of "hats tae)<br>, / er cainoon)<br>of 10 wa20 Weeks30 |=40 Children (optimal)50 60<br><!-- End of picture text -->

<!-- Start of picture text --> 09 Infected Populati— -7<br>oson aaane<br>fu<br>06os /J/ !1<br>04 ii 11<br>03 i)<br>02 A vy<br>on [f - 7 |—=No"= =Reference Lockdown action<br>°° 10 20 Weeks30=== Optimal40 Lockdown50 60<br><!-- End of picture text -->

<!-- Start of picture text --> 025 InfectionNoRate action<br>02 =====Fixed OptimalLockdownLockdown) |<br>oas 1, \ ]<br>, *<br>oa " \ J<br>,‘. ON<br>os \ \ |<br>f NOONON<br>° 0 10 20 Weeks30 sw40— 50 60<br><!-- End of picture text -->

<!-- Start of picture text --> 10s Aggregate Labor Supply<br>0951 ee ees lia<br>Mor<br>08s09 my1\y+ edsy7<br>0758 oyi]<br>ty<br>on 1<br>os I 1 No= =Fixed action Lockdown<br>06 0 10ly 20 Weeks30 === Optimal40 Lockdown!50 60<br><!-- End of picture text --> <!-- Start of picture text --> 208 ’ : peath. ’ ,<br>1 = =<br>‘ sie<br>0.9509 asnay aifae<br>ee |<br>0.85 \ t<br>os \ 1<br>\ Uy [——=No action<br>O75 \ou, Adultser cain (fixea)<br>N [=a childrenoon) (optimal)<br>°75 10 20 Weeks30 40 50 60<br><!-- End of picture text -->

<!-- Start of picture text --> 09 Infected Populati‘opuation<br>os , < ==><br>0706: Vea _—<br>os a<br>o4 /fuft<br>0.302 //fa7<br>oa°° 10 [pe[fos20 Weeks30“No=====Reference Optimal action40i LockdownLockdown50 60<br><!-- End of picture text --> <!-- Start of picture text --> 0.25 Infection Rate<br>No= =Fixedaction Lockdown<br>02 === Optimal Lockdown) |<br>r<br>oas 1 \ |<br>oa Poy\ |<br>\<br>cos \ |<br>° 0 10 20 Weekssy30“.SAN40——50 60<br><!-- End of picture text -->

<!-- Start of picture text --> tos Aggregate Labor Supply<br>1 rs<br>TIN<br>oes09 4s‘ ! SeerPa-oe<br>oss ml 7P<br>08 1\t' \ - va<br>075 1 Ke<br>on io<br>os06 0 10tot1! 20 Weeks30“===No= =FixedOptimal40 action Lockdown Lockdown50 60<br><!-- End of picture text --> <!-- Start of picture text --> : Death<br>N_ee<br>0.95 \ >= ia<br>0.8509 \‘\1 T, 4 7 _<br>os \\ le -<br>075o7 \rv!vie<br>0.65 1 11 —"o acon<br>oss06°%5 10 \20\ 7 / Weeks30 Adultsomaus|=40 Children (optimal) chicren optima50(fixea) trea 60<br><!-- End of picture text -->
consumption and total fertility data from the World Development Indicators. In our sample of 85 countries, the average value of children is around 37% of household utility.<sup>28</sup> The value of children as a fraction of household utility in our model is computed as where _u_ ( _·_ ) is the pre-pandemic steady-state level of utility of a household in state _k_ ; _k_ = 1 is the state in which all the members are alive, and _k_ = 4 is the state in which the children are deceased (see Appendix Table B.1 for the list of household states). This exercise yields _σ_ = 2 _._ 5.

Finally, we could assess sensitivity by treating _σ_ as a free parameter. Appendix Table B.6 compares the basic results from using the baseline _σ_ , the fertility literature-based _σ_ , as well as a wider range of _σ_ ’s from 1 to 5. As expected, a lower _σ_ implies that both the reference and the optimal lockdowns lead to fewer children’s lives lost per COVID-19 fatality averted (top panel). This is because a lower _σ_ implies a stronger private labor supply response, making the government-imposed lockdown less needed (bottom panel). Qualitatively the results are unchanged. Even with _σ_ very close to 1, there is a substantial number of children’s lives lost per COVID-19 fatality averted in the lower-income countries.<sup>29</sup>

**Simple adjustments to the reference lockdown** While the optimal lockdown involves a high-dimensional global optimization problem, an interesting question is whether governments could have done better than the reference lockdown by varying either the duration or the onset timing of the reference lockdown. Appendix Table B.7 investigates this. It summarizes our key statistic, the ratio of children’s deaths per adult COVID-19 fatality averted under alternative reference lockdown scenarios. The middle panel shows what happens when

> 28We abstract from the distinction between skilled and unskilled children in Doepke (2004) and compute the value of children as a fraction of household utility as 0 _._ 132 _∗_<sup>_√_</sup> _<u>n/</u>_ (<sup>_√_</sup> _<u>c</u>_ +0 _._ 132 _∗_<sup>_√_</sup> _<u>n</u>_ <u>), where</u> _n_ is the number of children and _c_ is consumption. We approximate the number of children using the total fertility rate and consumption using the per capita consumption in WDI.

> 29 We cannot lower _σ_ below 1 because as often happens in similar CES settings, the model is not continuous at _σ_ = 1. Instead it’s a hyperbola. Values of _σ <_ 1 have some perverse implications, as they imply that household members’ consumptions are complements. In this environment losing a family member actually _raises_ household utility conditional on the same level of consumption expenditure – the mirror image of the “love for variety” effect.

44
we lengthen the reference lockdown by between 2 and 8 weeks. If anything, for the lowerincome countries, the mortality ratio rises under longer lockdowns, as longer lockdowns have a disproportionately larger effect on child mortality relative to adult lives saved.

On the other hand, delaying the lockdown onset lowers the mortality ratio substantially, putting it firmly below 1. Evidently, delaying the lockdown is beneficial. Looking closer, it appears that the fall in the mortality ratio is driven entirely by the number of adult lives saved. The second and third columns of the table report the number of children’s deaths and the number of adult lives saved in each alternative scenario, normalized by the number of deaths in the baseline reference lockdown. Delaying the lockdown by 2 to 8 weeks hardly changes the number of child deaths. This is not surprising, as the child mortality comes from the economic downturn engineered by the lockdown, and so it doesn’t matter very much whether the economic downturn occurs now or 8 weeks from now. However, the third column shows that delaying the lockdown leads to many more adult lives saved, compared to the baseline lockdown onset, due to a flattening of the epidemic peak which renders health system constraints less binding. Overall, the results do not change qualitatively. There is a substantial number of children’s lives lost per COVID-19 fatality averted in low-income countries in all hypothetical scenarios.

# **5 Conclusion**

At the start of the COVID-19 pandemic, countries around the world imposed lockdown measures similar in severity. Our analysis, however, suggests that optimal policies substantially differ, depending on the vulnerability of child survival to income shocks, countries’ demographic characteristics, and patterns of social contacts. The reason is that economic contractions in low- and middle-income countries increase child mortality, and policy responses to the pandemic contributed to declines in national income in much of the world. This paper highlights and then quantifies this relatively neglected consequence of lockdowns purely in terms of inter-generational mortality tradeoffs, thereby informing country-specific assessments of the costs and benefits of lockdowns as policies to fight a pandemic.

Since our main objective is the formulation of a new tradeoff, we abstracted from other 45
channels through which lockdowns might affect health outcomes. Importantly, the impacts of such channels might differ across countries, hence generating heterogeneity in how they affect the choice of lockdown policies. Concerns have been raised that the lockdowns, and the income declines associated with them, would negatively affect health outcomes through deterioration in mental health and increased engagement in violent and criminal behaviors. While an increase in domestic violence has been documented in some contexts (Leslie and Wilson, 2020; Bullinger et al., 2021), findings on outcomes such as suicide rates (CalderonAnyosa and Kaufman, 2021; John et al., 2020; Sinyor et al., 2021) and homicides (CalderonAnyosa and Kaufman, 2021; Boman and Gallupe, 2020) have been mixed. On the other hand, lockdowns have been shown to reduce road accidents (Calderon-Anyosa and Kaufman, 2021; Saladi ́e et al., 2020) and limit transmission of other non-COVID infectious diseases (Soo et al., 2020; Olsen et al., 2020). The simulations in our paper should, therefore, not be a source of definitive policy prescriptions, but rather a quantification of the importance of an inter-generational tradeoff that had been largely overlooked in both academic and policy fora.

An important lesson from this analysis, which holds beyond the COVID-19 pandemic, is that non-pharmaceutical interventions to prevent infectious disease spread will likely affect subgroups of the population in an adverse manner and will do so in a context-specific way. This implies that additional targeted policy instruments could be used to alleviate the downside distributional effects. In our setting, targeted income transfers to households with young children and pregnant mothers are examples of mitigating policies that can be adopted during lockdowns. Given the positive externality that epidemic containment policies have on the rest of the world (in part because of the lower likelihood of the emergence of novel and possibly more lethal variants), there is a rationale for these aforementioned mitigating instruments to be financed through development assistance to low-income countries.

46