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Introduction
As COVID-19 spreads, governments are asking their citizens to socially distance them- selves, at least until we find a better solution. In many cases, where jobs cannot be performed from home, this leads to workers not receiving income for an uncertain amount of time. This is a problem for relatively poor households that cannot endure these income-less periods, making the crisis worse in poor countries. In this paper, we compare the impact of COVID-19 in countries with different levels of income.

We build on 1 (henceforth ERT), who combine the SIR epidemiological model by 2 with a standard macroeconomic model. Individuals can be susceptible to contracting the disease, infected, recovered, or dead. Recovered individuals cannot get re-infected.11 Rates of contagion depend on the actions of individuals: an increase in labor participation or in consumption increases the spread of the disease. In equilibrium, susceptible individuals endogenously substitute consumption for leisure to minimize the risk of contagion.
The problem is that in low-income countries, consumption is not easily substituted for leisure. To model this, we modify ERT by introducing a subsistence level of consumption. Being close to the subsistence level increases the marginal utility of consumption. As a result, hours worked react less to the risk of infection or to social distancing policies.

An additional problem in low-income countries is that there are fewer jobs that can be performed at home. 3 find a positive relationship between GDP per capita and the share of jobs that can be performed from home. To address this, we assume that a fraction of individuals can work in each country without increasing their risk of contagion. A third problem, related to the transition from infection to death, is that the number of hospital beds per capita is decreasing in income, as evidenced by 4. Counteracting these effects, the fact that populations are relatively younger in lower income countries reduces the probability of death.
We find that without government intervention, there is less self isolation in countries with lower income per capita, increasing the peak of infections more where income is low. Quantitatively, a 1% increase in income per capita reduces the peak of infections by 326 people per million. This does not translate into a lower death rate. While the point estimate suggests that a 1% increase in income lowers the death rate by 2 people per million, this is not statistically significant. Macroeconomic effects are milder in poor countries: a 1% increase in income increases the drop in consumption relative to steady state by 0.03%

We next introduce social distancing as in ERT. This involves a tax on consumption that is rebated back to consumers. It makes consumption expensive relative to leisure, so consumers work and consume less, which effectively amounts to social distancing. This tax is determined by maximizing the present value of the utility of individuals. While the levels of infections and deaths drop following this policy, their effect is larger in richer economies, having almost no impact on inequality. The inequality in recessions increases to almost 0.05% larger recession per percentage point increase in GDP per capita. This stems from taxes being higher in high income economies.
Almost half of the inequality in infections is due to the possibilities to work from home. Ignoring the level of subsistence consumption would lead to the false conclusion that inequal- ity in infections is 10% lower than what it actually is. The fact that there is no inequality in deaths is a combination of more people infected in low-income countries, and them being younger, and therefore more likely to survive. In fact, using the age distribution of the U.S. in all countries greatly increases the inequality in deaths rates. In this case, an increase in GDP per capita of 1% increases the death rate by over 15 people per million, significant at the 1% level.

To verify whether the model implications have any empirical validity, we turn to Google mobility data, which tracks GPS cellphone usage at various locations including the work- place. Mobility around the workplace dropped significantly more in high income countries, especially when compared to the drop in other locations, such as grocery stores and transit
stations. Relative to the drop in the other locations included in the Google database, an increase in income of 1% reduces traffic around workplaces by 7%. These results are in line with 5, who finds that lockdown policies were highly effective in rich neighborhoods in Santiago, Chile, but had no significant effects on lower income neighborhoods.
This begs the question: is there a better policy to implement in developing countries? The first policy to encourage would be to allow workers to work from home, but this would be too hard to enforce and would probably involve deep re-structurings that take time. Alternatively, a loan, paired with imports, addresses the problem of subsistence consumption. In practice, a country like China could lend money to Mexico, which Mexico would in turn use to finance imports from China. This would help both Mexico and China. It would provide a boost to income in Mexico, so individuals would reduce hours worked without sacrificing consumption. It would help China by boosting demand, which is particularly relevant in a world where China seems to be recovering faster than other countries. The potential gains by the lender are beyond the scope of this paper.

Loans are more powerful in improving both epidemiological and macroeconomic outcomes than the optimal social distancing policy. Loans reduce the peak of infections, deaths, and recession for all countries. Loans also reduce the unequal effects of COVID-19: the reduction in infections are decreasing in income, and the reduction in the peak of the recession are increasing in income. Finally, the cost of these loans is much smaller in low-income countries. The present value of the optimal loan would be of $84 per person in Ecuador, versus $4,959 in Ireland. In the U.S. the present value of this loan is equal to $4,371, considerably larger than the stimulus of roughly $1,000 per person. However, this comparison is not straightforward, since we are abstracting from other policies contained within the CARES act, such as unemployment insurance (see 6, 7for an analysis of the effects of unemployment insurance). The closest paper to ours is 4, who explore the different effects we should expect among countries of different income. The main difference with them is that we calibrate the economy to many individual countries, while they compare a representative developed country with arepresentative developing country, with similar conclusions in terms of infections being higher in the developing country, and recessions milder. My conclusions, on the other hand, stem from comparing all countries we have information for. The different exercises also lead to several modeling assumptions. In particular, 4 feature a greater level of heterogeneity across populations, with a share of individuals that consume hand to mouth. Doing so in this paper would be impractical, since it would add an extra layer of complications that would be very hard to calibrate,  since  this share is not available for the countries in my sample. Another area where we depart from them (and from 8), is in the way to incorporate the additional risk introduced by older populations. They introduce a new set of older individuals, with their own discount, contagion and death probabilities, while we directly incorporate it in the probability of becoming critically ill. It makes sense for them to introduce them the way they model the economy, with heterogeneous agents that have exogenous income processes. With homogeneous agents and deterministic incomes, introducing a new type of older individuals would not change the results.

This paper is related to a number of recent papers incorporating the SIR model to macroeconomics.
9 introduces the model and discusses a number of applications. 10 and 11 use versions of this model to infer an optimal lockdown and testing policies. While we abstract from lockdown policies, these are very effective, especially when combined with testing, as several papers have recently found (see 12–14 among others). A proper analysis of these containment policies across countries would greatly complement this paper.

15 extend it to incorporate skilled and unskilled workers to explore the containment policy in India. 16 adapt the model to study how different sectors react, finding that sectors with lower rate of contagion in consumption expand at the expense of sectors with higher rates. This substitutability reduces the economic and epidemiologic effects of the pandemic. The fact that we abstract from this possibility implies that my effects are larger than the actual ones. However, the relative effects across countries should be similar. 17 find that the pandemic increases the probability of default in low-income countries, which matters in my case given that the alternative policy suggested includes a loan. However, their findings concern existing loans, and, similar to my findings, they show that low-income countries can greatly benefit from fresh loans.
This paper is organized as follows. Section 2 presents the observations that motivate the differences across countries. Section 3 introduces the model and characterizes the equi- librium. Section 4 calibrates it. Section 5 presents the main results. Section 6 provides a measure of empirical validation to my results. Section 7 introduces a loan, and section 8 concludes.

1 Data
This paper models how differences in subsistence consumption, opportunities to work from home, healthcare systems, and the age of a population influence the effects of COVID- 19 across countries. To that end, this section shows how these characteristics vary across countries.
Figure 1 shows the cost of living in different countries, as estimated by The Economist Intelligence Unit (EIU). GDP per capita is from the Groningen Growth and Development Centre (GGDC). Clearly, richer countries have higher living costs. The slope of a fitted line across countries implies that an increase in GDP per capita of 1% increases the cost of living by about a quarter of a percent. Thus, relative to income, the cost of living is larger in poorer countries, putting additional pressure on these when hit by COVID-19. 18 and 19 describe this dataset in detail.

2 estimate the fraction of jobs that can be done from home, finding a positive association with income. Figure 2 shows this.
Figure 3 shows the number of beds per 10,000 people across countries. The World Health Organization (WHO) provides the number of hospital beds, not intensive care units (ICU) beds. We assume that ICU beds are proportional to hospital beds, in the same proportion as in the U.S., where there are ICU beds to cover 0.042 percent of the population, as in 8. The figure shows that richer countries have more hospital beds per person.

Figure 1: Cost of Living Across countries (EIU).

The last statistic in this section is the fraction of the population older than 64, shown in Figure 4. Data comes from the World Development Indicators (WDI). Richer populations are also relatively older. This relaxes the effects of COVID-19 in poor countries.
These data suggest that there are reasons for which this disease may be worse in low-income countries because of higher living costs relative to income, less jobs that can be done from home, and lower hospital capacity. On the other hand, the fact that these countries are relatively younger implies milder consequences. To explore the importance of each effect, the next section develops a model incorporating all these features.

3    The Model
The model mixes a macroeconomic model with an epidemiological model. We start describing the former and then introduce the epidemiological aspects. While there are many countries in the analysis, each country is a closed economy. Thus, we do not differentiate across countries and clarify which parameters change across countries in section 4.

Figure 2: Percentage of jobs that can be done from home (3).

3.1    The Macroeconomic Model

Time runs t = 0, 1, 2,.., ∞. There is a continuum of agents at time 0 with measure 1, with preferences

where β  ∈ (0, 1) is the discount factor, ct  ≥ 0 is consumption in period t and 0 ≤ nt  ≤ n¯ is hours worked. One of the main departures from ERT is in the definition of the within period utility function. This is

Figure 3: Hospital beds per 10,000 people (WHO).

Individuals cannot borrow or save. This greatly simplifies the analysis, and it is unlikely that relaxing this assumption would bring additional realism. In any case, the ability to save is  lower in low-income countries, so adding savings would likely amplify the differences across countries.
There is a representative firm with technology Ct = ANt, where Ct ≥ 0 is output in period t, A ≥ 0 is productivity, and Nt ≥ 0 is labor demand. This stand-in firm operates under perfect competition. While this seems a reasonable assumption, 20 show that, when investment is added to the model, an industrial organization with monopolists works better in accounting for the behavior of investment. Since this work abstracts from investment, we maintain the assumption of perfect competition. Lastly, feasibility implies ct = Ct and nt = Nt.

3.2    The Epidemiological Model

The epidemiological side is based on 2. The population is divided into four groups: susceptible (not yet exposed to the disease), infected (contracted the disease), recovered (survived the disease and acquired immunity), and deceased (died from the disease). The fractions of people in these four groups are denoted by St, It, Rt and Dt, respectively. The labor productivity is 1 for S and R individuals, ϕ < 1 for I individuals, and 0 for D individuals. The productivity of I individuals is lower than 1 to reflect the fact that a fraction of individuals are symptomatic and cannot work, making their productivity 0 and reducing the aggregate productivity of the group.

Figure 4: Fraction of the population over 65 (WDI).

Every period, I individuals can become critically ill with probability η, in which case they can die, recover, go back to being infected but not critical, or remain critical. Technically, becoming critically ill is an i.i.d. shock to the pool of infected individuals. It proxies for how exposed a population is. Given that COVID-19 is more likely to kill relatively older people, countries with older populations have higher η. Critically ill do not work or consume,2 and their utility is normalized to uc.3
Susceptible individuals can become infected in three ways. First, they can meet people while purchasing consumption goods and services with probability

This depends on a constant πsc, the measure of infected, non-critical individuals (1 −  η)It, how much they consume Cit relative to the steady state Crss, and how much susceptible individuals consume Cst relative to the steady state. We depart from ERT in assuming that consumption relative to steady state matters in determining this probability, while they  assume that only consumption matters. None of their results would be affected by this as- sumption: only the value of πsc would change. When dealing with several countries with different levels of consumption, consumption relative to steady state should be used. In- tuitively, in low-income countries, individuals might have smaller cars or may go to the supermarket on foot, which results in them making fewer purchases per trip, so by normal- izing consumption to the steady state level, we are capturing the number of trips to the supermarket more precisely, and therefore the number of interactions while shopping.

A second way to contract the disease is by working. The more the hours worked, the more likely a susceptible individual contracts the disease. However, some jobs can be easily performed at home, so not all increases in hours worked increase the probability of contagion. Let 0 ≤ χ ≤ 1 denote the fraction of jobs that can be performed from home. Then the probability of contracting the disease at work is πsnNst((1 − η)ItNit)(1 − χ), where Nst is hours worked by a susceptible individual and Nit by an infected one. ERT do not incorporate χ into the analysis. A third way in which individuals can contract the disease is randomly. This probability is πsr(1 − η)It. The total mass of new infections in period t is

The law of motion for susceptible individuals is St+1 = St −Tt. Infected individuals can recover with probability πr. The probability of death depends on the number of ICU beds available. If this exceeds the number of critically ill, a patient dies with probability πd. If the number of beds available is lower than the number of critically infected, the beds are randomly allocated among the critically ill, as in 4. Not having assigned a bed increases the death probability to τπd, where τ  > 1.  Denote the probability of death by π˜d (I ) and the number of beds by B, then

This implies that the law of motion for infected people is It+1  = It + Tt −(πr + π˜d (It ))It , the law of motion for recoveries is Rt+1 = Rt + πrIt, and the law of motion for deaths is Dt+1 = Dt +πd min{ηIt, B}+max{τπd(ηIt −B), 0}. Population evolves as Lt+1 = L0 −Dt+1.

3.3    The Social Distancing Policy

We follow ERT in introducing a consumption tax µt to proxy for social distancing, re- bating the proceeds back to consumers. This makes consumption relatively more expensive, so individuals substitute away from consumption and into leisure. The budget constraint of individuals is

(1 + µt)ct = wtϕtnt + Γt,

where Γt = µt(StCst + It(1 − η)Cit + RtCrt) (implying a zero fiscal deficit each period) and the price of the consumption good is normalized to 1. The wage rate per efficiency unit is wt, and ϕ is the number of efficiency units per hour worked.

3.4    Equilibrium

At time 0, there is  a measure  I0  = ε  > 0 of infected individuals.  This implies  S0  = 1 − ε,  R0 = 0 and D0 = 0. The laws of motion depend on the behavior of each type of individual.

Susceptibles: The maximization problem of susceptible individuals is

Note that susceptible people determine their probability of contagion pt. Working more, or consuming more, increases this probability. They take this into account when optimizing.

Infected. Infected individuals can be critical or non-critical. If critical, their consump- tion is exogenous, and uses up resources normalized to 0. Since the probability of being critical is η, their maximization problem is Ui,t  = ηUc   + (1i,t −η)Unc, wheri,et
U  c i,t= uc  + β[(1 −πr  − π˜d (It+1 ))Ui,t+1  + πrUr,t+1],  and

Unc = max u(c, n) + β [(1 −πr  − π˜d (It+1 ))Ui,t+1  + πrUr,t+1]  s.t.  (1 + µt)c = wtϕn + Γt.i,tc,n

and uc is the value of the utility of a hospitalized individual. Notice here that Ud,t+1 = 0, so that the cost of death is foregone utility of life. Through some algebra, this value function becomes

Ui,t  = max ηuc  + (1 − η)u(c, n) + β[(1 −πr  − ηπ˜d (It+1 ))Ui,t+1  + πrUr,t+1]c,n
s.t. (1 + µt)c = wtϕn + Γt.

This specification makes it clear that the actual rate of death for an infected individual is ηπ˜d (It+1 ).  The behavior of this group produces the externality: since they are already infected, they are more likely to go to work and consume, increasing the rate of contagion. The social distancing policy µ corrects for this. The next proposition shows how this works:

Proposition 1. The effect of the social distancing policy µ is decreasing in the ratio c¯/A.
Proof. See Appendix A.

The proposition shows that the ratio c¯/A is key to determine the effect of the social distancing policy µ on hours worked. The higher this ratio, the lower the response. This implies that ignoring subsistence consumption would amplify the effect of the social distancing policy, predicting a success of the policy that is not likely to take place.

Recovered. The maximization problem of recovered individuals is
Ur,t = max u(c, n) + βUr,t+1 s.t. (1 + µt)c = wtn + Γt.c,n

Market clearing. The labor and consumption markets clear. This implies

Nt = StNst + (1 −η)ItNit + RtNrt, ANt = StCst + (1 −η)ItCit + RtCrt.

3.5    Equilibrium Characterization

Before moving on to the quantitative results, it is worth describing the qualitative prop- erties of the equilibrium. Figure 5 shows how the crisis unfolds.4 The scenarios portrayed are the decentralized equilibrium and the optimal social distancing policy. The top panels focus on the epidemiological consequences. In this example, without any explicit policy, the rate of infections peak at about 6.67% of the population in week 32, and the total death rate is 0.35%. Adding the optimal policy reduces the peak of infections to 6.34% in week 32 and the death rate to 0.35%. The bottom panel shows the economic effects. At maximum impact absent any government policy, consumption by susceptible individuals falls by 11% relative to its steady state level, and that of those infected by 16%. This is mainly driven by the reduction in hours worked by susceptible people, in an effort to prevent contagion. Infected people increase their labor supply by 4.5%. This has two main reasons. The first is that these individuals are already infected, so the preventative motive no longer applies. The second is a wealth effect: the reduction in productivity lowers their income, which drives them to work more. Notice that there is also a substitution effect that goes the other way: the reduction in wages makes leisure relatively cheaper. Along similar lines, recovered individuals, who cannot contract the disease at work, do not change their behavior relative to the steady state.

The optimal policy amplifies the recession, with a maximum drop in consumption by susceptibles of 15%, and their hours at work dropping by 16%. The infected drop their consumption by 21% and hours worked by 2.7%, both at their peak contraction. By making consumption more expensive, the hours worked by all individuals drops, even those infected, reducing labor supply and hence output.

Figure 5: Equilibrium with and without optimal social distancing

Figure 6 shows the optimal policy. It involves very large tax rates at the onset of the disease, of up to 17% by week 30, and then a slow convergence to 0. The strong initial response is similar to what 21 find when solving for an optimal policy of a planner that minimizes the number of deaths subject to costs associated to output loss.

4    Calibration

We follow ERT in the calibration, except for the additional parameters we introduce. We start by describing the data sets used. Next, we describe how we calibrate the parameters that are common to all countries, which, with the exception of the share of infected house- holds with critical conditions, replicates the strategy in ERT, and we finally describe the country specific parameters. Appendix Appendix B lists the countries in the sample.

4.1    Parameters Common to all Countries
One period is a week. The mortality rate πd comes from the South Korean Ministry of  Health and Welfare from March 16, 2020. These estimates are reliable because, as of late March, South Korea had the world’s highest per capita test rates for COVID-19 (22). Excluding people aged 70 and over, because their labor-force participation rates is very low, the average mortality rate is 0.4 percent. Excluding people aged 75 and over, the mortality rate is 0.7 percent. Based on these estimates, we target a mortality rate equal to 0.5 percent. As in Atkeson (2020), it takes on average 18 days to either recover or die from the infection. Recall that the recovery probability is πr, and the death rate is ηπd. The calibration for η is described in section 4.2. Given this value, and since the model is weekly, set πr+ηπd = 7/18. A 0.5 percent mortality rate for infected people implies ηπd = 7/18 × 0.005.5 The parameters πsc, πsn and πsr come from contagion rates in other respiratory diseases. In the case of influenza, 23 argue that 30 percent of transmissions occur in the household, 33 percent in the general community, and 37 percent in school or the workplace.

Using data from the Bureau of Labor Statistics 2018 Time Use Survey, ERT estimate that 48 percent of time spent on general community activities relates to consumption. Thus, 16 percent (=0.33 × 0.48) of infections come from consumption. Related to work, ERT estimate that 46 percent of transmissions come from the workplace. Since 37 percent of transmissions occur in schools and workplaces, 17 percent of transmissions are related to work (0.37 × 0.46).
This implies the following equations must hold:

*5 This holds when the hospital capacity does not bind. We make this assumption because it amplifies the calibration. Incorporating the dates when hospital capacity binds barely change any calibration estimate.

where N is hours worked in steady state. In addition, 60 percent of the population either recovers or dies from the infection. This follows an article that cites Angela Merkel’s estimates.6 The resulting values are πsc = 8.7 × 10−8, πsn = 1 × 10−4 and πsr = 0.51.
The measure of individuals initially infected is ε = 0.001. We set β = 0.961/52  so that the value of life is $9.5 million in 2018 Dollars (see ERT). We set ϕ = 0.8 as in ERT, to reflect the fact that 80% of COVID-19 carriers are asymptomatic according to the China Center for Disease Control and Prevention. We set τ, the probability of dying if not assigned an ICU bed, to 2, as in 4. We normalize the within period utility of being critically ill to uc = 0.7.

Parameters Specific to Each Country

The parameters that are calibrated individually for each country are A, θ, c¯, χ, η, and B. We set these to match the GDP per capita in each country, the weekly hours worked, the relative cost of living, the fraction of jobs that can be performed from home, the fraction of the population younger than 15 and older than 65 and their death rates, and the number of hospital beds available. GDP per capita and weekly hours worked come from the Total Economy Database produced by the GGDC. We use 2018 data. Relative cost of living is from the EIU. The fraction of jobs that can be performed from home is from 3. The composition of the population by age comes from the WDI. Hospital beds come from the WHO.
We set the subsistence level of consumption in the U.S. equal to 30% of income, following the rule of thumb for how much a household should spend on rent. This is conservative in the sense that rent is not the only subsistence consumption item, so this is a lower bound.

For the remaining countries, we set c¯ = P × c¯U S , where P is an index of the cost of living in each country, and c¯U S   is the subsistence consumption level in the U.S.We set η to reflect the higher death probability of old people, and the different rates of old people in different countries. To represent the different age distribution across countries, we use the share of population younger than 15 and older than 65 reported by the WDI. To impute the different death rates of older populations, we rely on 24, who compute the death rate by age group of critically ill patients, along with the rate of symptomatic patients that need hospitalization. Specifically, the WDI reports the share of people older than 65, and younger than 15. Ferguson reports the share of symptomatic patients that get hospitalized, the share of those that are critical, and the share that die, in the U.S., in age groups of 10 years, that is, from 0 to 9, 10 to 19,. ..,  70 to 79,  and more than 80.  To determine the  value of η, we first compute the simple average death rate for individuals between 0 and 14, 15 to 64. The death rate for those under 15 is the average of the death rate of those between 0- 9, and 10-19. The rate for those between 15 and 64 is the average death rate of those  between 10-19, 20-29,..., 60-69. The rate for those older than 64 averages the rates for the groups 50-69, 70-79, and 80 and older. The resulting rates are 0.01%, 1.06%, and 11.47%, respectively. Next, we use the fraction of the population in each group as weights to compute a weighted average of these death rates.

To compute the number of ICU beds in each country, we rely on data by the WHO. The problem with these data is that they do not distinguish between a normal hospital bed and an ICU bed. To work around this, we follow 4 and assume that the number of ICU beds is proportional to the number of beds. We set the number of ICU beds in the U.S. as in 8 to 0.042 percent of the population, and the number of ICU beds in each country as Bi = 0.00042 × B˜i / B˜ U S for each country i, where B˜ i is the number of total hospital beds in country i.

Table 1 shows the parameters that are common to all countries, and Table 2 shows the parameters for each country.

*6 “Merkel Gives Germans a Hard Truth About the Corona Virus,” New York Times, March 11, 2020. 7 Changing this so that critically ill have the same utility level as non-critically ill infected individuals as very minimal effects on the optimal policy or the optimal loans in section 7.

Table 1: Parameter values common to all countries.

5    Results

This section presents the main results. The decentralized equilibrium has µt = 0, and the optimal social distancing policy computes the sequence of µt that maximizes the sum ofthe welfare of all individuals, that is,

max S0Us0 + I0Ui0 + R0Ur0
{µt}

5.1    The Decentralized Equilibrium

To represent the problem of the spread of the virus, we focus on the rate of infections at its peak. This is more meaningful than the total number of infections, because infections are worse when they are concentrated in time. They make the externality problem worse, and they put more pressure on hospital capacity. Figure 7 shows the peak of the infections rate across countries, along with a fitted line using least squares. The slope of the line fitting the data has a coefficient of −0.0326, suggesting that an increase in GDP per capita of 1% reduces the infections peak by 326 infections per million people. This is significant at the 1% level.

Figure 7: Peak of Infections

In the case of deaths, we focus on total (accumulated) deaths. The slope of the OLS fit is−0.000226, suggesting that an increase in GDP per capita of 1% reduces the number of deaths per million people by 2. However, the estimate is not significant. This is in line with death rates not being higher in low-income countries. 25 document that, until May 2020, only 21% of COVID related deaths came from low-income countries, when these countries hold 85% of the world population.
A 1% increase in income increases the trough of consumption relative to steady state, meaning that richer countries suffer larger recessions. The elasticity is 0.034, so that an increase in income of 1% deepens the recession by 0.03%. These numbers are shown in the first row of Table 3.
Table 4, columns 3 to 5, shows the actual estimated number of infections at the peak, deaths, and consumption trough for each country.

5.2    Optimal Policy

The second row in Table 3 shows the inequality under the optimal social distancing policy. Introducing an optimal social distancing policy reduces the peak of infection rates in all countries, but it exacerbates the inequality to a reduction in infections of 326 people per million per percent increase in income. The reason for this is that the policy is “tougher” on countries with higher income. Figure 8 shows the relation between the sum of taxes collected in time relative to income in each country. The OLS fit has a slope of 0.79, significant at the 5% level, meaning that an increase in income of 1% increases the tax collected relative to income by 0.81 percentage points. Note that this is taxes added throughout all periods, with no discounting. Adding a discount rate equal to β does not affect these estimates.
Columns 6 to 8 shows the deaths, infections, and consumption trough across countries under the optimal social distancing policy.

Figure 8: Sum of optimal taxes collected relative to income across time.

5.3    Decomposing the Effects

To understand the effect of each one of the features introduced in the model on inequality, this section performs counterfactuals where we change these features one at a time. This reveals what lies behind the large inequalities in infection rates, and the lack of inequality in deaths. Table 3 reports shows all the numbers.
Most of the inequality in infections stems from the ability to work at home or not. In fact, if all countries had the same possibilities as the U.S., an increase in GDP per capita of 1% would reduce the infection rates by 180 per million. Compared to the decentralized equilibrium, this is a reduction of 45%. The change in the consumption trough is very mild. Abstracting from the subsistence level of consumption would undermine the unequal effects of COVID-19. Setting c¯ = 0, one would conclude that the elasticity of infections with respect to income is of 293 per million, almost 10% lower than what it actually is. Different hospital capacities do not affect infection rates or consumption change with income. There is a reduction in the point estimate of inequality in death rates, but still this is not significant.

The lack of inequality in death rates is a combination of a younger population in low-income countries, pushing death rates down, and higher infection rates, pushing them up. To see this, assuming the population of the U.S. in all countries would greatly amplify the inequality in deaths, as shown in Table 3, to 15 additional deaths per million people per percentage point drop in income. This supports the conclusions in 25, who argue that the reduced death toll in low- income countries is due to a younger population. The last counterfactual exercise shows that not taking into account differences in living costs would dramatically increase the inequality to an elasticity of infections to income of 450 people per million, and the elasticity of recessions to 0.06. Inequality in deaths would become significant at the 10% level. This is because lower income countries usually have lower living costs.

Table 3: Decomposing the effects of income on different outcomes. The dependent variable is the log of GDP per capita. The coefficient shows the increase in the peak of infections and death rates per million people in columns 1 and 2, and the increase in consumption trough relative to steady state in column 3. Standard errors in parentheses. ∗ and ∗∗∗ indicates significant at the 10% and 1% level, respectively.

6    Empirical Validation

This section evaluates one key implication that can be verified empirically. The model predicts that individuals in rich countries are more likely to stay away from their workplace. To test this in the data, we turn to the Google Mobility Dataset (26) paired with GDP per capita. Appendix C lists the countries in the sample.
Google tracks and reports how traffic has changed relative to a benchmark date pre- COVID-19 in different locations, including workplaces. 27 already find that non-pharmaceutical interventions are effective in limiting mobility in all except the lowest income countries, pro- viding some evidence in favor of my predictions. In this section, we go further in the empirical analysis and test whether there is a continuous relationship between income per capita and the reduction in mobility.
To study the change in traffic around location j in country i, we regress:

yij   = α0j  + α1j  log(GDPpci) + εij,    (1)

where GDPpci is GDP per capita in country i, and yij is percentage change in traffic in country i around location j = work, groceries and pharmacy, parks, transit stations, retail and recreational, and residential. The estimate for yi,j is a simple average of each yi,j,t, where t stands for day over the period 2/15/2020 through 8/17/2020. Table 5, row 1 column 1, shows the results. Specifically, an increase in GDP per capita of 1% reduces traffic around the workplace by almost 4%. Appendix D shows the results of regressing the traffic around each location on GDP per capita. An interesting observation is that income reduces traffic around non-workplace locations by less than around workplace locations. In the case of parks and grocery stores, an increase in income increases traffic.
A valid criticism is that the error term could be correlated with GDP per capita. For example, people in lower income countries could be less obedient of government mandates. To address this, we model the error term as εij = ϵi + νij, which assumes that the part correlated with income is common to all locations, and then run the difference equation:

∆yi  = ζ0  + ζ1  log(GDPpci) + ε˜i ,    (2)

where ∆yi  = yij  − yij′, ζ0  = α0j  − α0j′, ζ1  = α1j  − α1j′ and ε˜i  = νij  − νij′ for some pair j  ̸=   j′.

In practice, we compute the difference between traffic around workplaces (j) and the simple average of traffic around all other locations (j′) except residential.8 Row 2 in Table 5 shows the results become even stronger.
A second criticism is that the higher work mobility in low-income countries may be due to the different seasons. South America and Oceania are in the summer during the benchmark8.
We exclude residential because an increase of traffic around these locations is expected under social distancing.  Notwithstanding, we also included this with a negative sign and found, which is in January, so benchmarks can be artificially low because people go on holidays. To explore this, column 2 excludes South American countries, column 3 excludes both South American and Oceanic countries, and column 4 excludes all countries south of the Equator, which adds some African countries as well.9 The results are similar.
One last concern is that the results are driven by the behavior of those countries in the lowest income group, as defined by 27. The authors show that these are the only countries that, absent non-pharmaceutical innovations, do not reduce their traffic around the workplace. To test whether this is the case, column 5 in Table 5 excludes these countries. The results remain qualitatively unchanged.

7    An Alternative Policy

Given the lack of success of the “laissez-faire” or the social distancing policy, this section investigates whether an alternative policy could work better. We study a loan extended to finance imports at a low interest rate. It is important to highlight that this loan would not only benefit  the recipient country, but also the lending country, if it gets to export the goods. We do not model these benefits, but one can understand that a country like China, by extending loans to low-income countries, could also export to these places. Since China is apparently recovering faster than other countries, this seems to be a reasonable policy.
The loan considered is a two-year loan at a 5% interest rate. Recipients can only start paying it as of month 6.10 The loan is determined by maximizing the sum of the utility of individuals in each country, in the same way the optimal policy is determined.

Table 6 shows the effect of loans on each country’s rate of infections, deaths, and con- sumption trough. Comparing it with Table 4 one can note that loans are more effective at reducing the peak of infections, deaths, and recession for all countries. Moreover, the unequal effects of loans reduce the inequality both in infections and recession.
Table 7 shows 9These countries are Angola, Mozambique, Tanzania, Zambia, and Zimbabwe.10 Otherwise, countries would front-load payments, increasing working hours early on this. Row 1 shows that an increase in income of 1% reduces the number of infections by 305 people per million. This is considerably lower than the 326 in the decentralized equi- librium. The point estimate for deaths barely moves. The loan is very effective at reducing the inequality in the recession. Compared to the decentralized equilibrium, where a 1% increase in GDP per capita deepens the recession by 0.03%, with loans these differences are of 0.014%, a reduction of about 60%. The reduction with respect to the optimal taxes is even larger, of over 70%. Thus, the loan reduces overall inequality: the lower the income, the larger the reduction in infections, and the higher the income, the larger the reduction in the recession. Rows 2 and 3 reproduce the inequality under the decentralized equilibrium and the one under the optimal policy, respectively.

Figure 9 illustrates these effects for infections. The solid blue line is the fit in the decen- tralized equilibrium. The dashed red line uses the optimal social distancing policy in each country, and the dotted green line uses optimal loans. The dots represent each country under each scenario, by color. It stands out how much the line flattens for loans when compared to both the decentralized and optimal allocations. While the slopes are not significantly differ- ent from each other (probably due to the low number of observations), the flattening of the loans curve highlights how far a loan can go to reduce the unequal effects of COVID-19. It also shows how the line with the optimal policy is steeper than the decentralized equilibrium, which implies deeper inequalities. Figure 10 shows that loans are the best tool in reducing the inequality in recession. The slopes are significantly different in the case of consumption. Not only are loans relatively more effective in low-income countries, they are also cheaper.
Their present value ranges from $84 in Ecuador to $4,959 in Ireland. The slope of the line associating the size of the (log of) the loan to the (log of) income is significant and equal to 1.2, implying that when income increases by 1%, the loan requested increases by 1.2%.

Figure 9: The success of loans in lowering the unequal effects on infections.

8    Conclusion

Covid-19 is currently hitting all countries, regardless of income. The best action so far to avoid infection has been to socially distance oneself. If working from home is not possible, this means enduring potentially long periods of time with no income. This is a problem in all countries, but especially in low-income ones, where citizens cannot remain under lockdowns for long periods of time. As a result, we find that infections are worse in lower income countries. The fact that populations are relatively younger in low-income countries implies that this does not translate into more deaths. Recessions are milder in lower income countries, because of the milder reaction of hours worked.

Google mobility data shows that lower income countries reduced traffic around the work- place less than high income ones, consistent with my results. It is not that low-income countries are less careful: their mobility around parks and grocery stores has been reduced by more than in high income countries. The problem is that low-income individuals cannot sustain long periods with no income.

Figure 10: The success of loans in reducing the unequal effects on the recession.

An alternative policy that has larger desirable effects on low-income countries is the extension of a loan at relatively low interest rates to finance a trade deficit, to be offset in the future. Loans would be more successful at lowering the rate of infections relative to the optimal policy, particularly for low-income countries. Similarly, they are better at reducing the peak of the recession, particularly for high income countries. Since, absent any policy, infection rates are higher in low-income countries and the recession is deeper in high income ones, loans reduce the inequality in both of these dimensions.

Table 4: Estimates on Infections, Death, and the speed of transmission in different countries under different policies.

Table 5: Google Mobility data across income levels. The dependent variable is average percentage drop in traffic around workplaces relative to a pre-pandemic benchmark in row 1, and the average percentage drop in traffic around workplaces minus the average percentage drop in traffic around all other locations except residential in row 2. The dependent variable is the log of GDP per capita. Standard errors in parentheses.
∗∗∗ indicates significant at the 1% level. Source: 26.

Table 6: Infections and Death with loans.

Table 7: Effects of Loans with changes in income and effects relative to the decentralized equilibrium. In row 1, the dependent variable is the log of GDP per capita. The coefficient shows the increase in the peak of infections and death rates per million people in columns 1 and 2, and the increase in consumption trough relative to steady state in column 3. Rows 2 and 3 replicate these elasticities for the decentralized and optimal tax cases, respectively. Standard errors in parentheses. ∗∗∗ indicates significant at the 1% level.

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Appendix A    Proof of Proposition 1

The first order conditions of the infected individuals are

where λbit is the Lagrange multiplier. Combining equations (Appendix A.1) and (Appendix A.2), obtain

Applying the implicit function theorem,

This expression is positive. Since the whole derivative is negative, this implies that the larger the ratio c¯/A, the lower the reaction of hours worked to the social distancing policy. In the limit, as c¯/A → 0 because either A is too large or c¯ too small, the economy behaves as if there is no subsistence consumption level. In general, in low-income countries this ratio is higher than in high income countries as we find in section 4, so the hours supplied by infected individuals are less reactive to social distancing policies.

Appendix B    Countries included in the Analysis

Table Appendix B.1 specifies the countries that result from the intersection of these five databases. Out of these countries, we eliminate 5 countries based on the fact that, given the targeted productivity, hours worked, and cost of living, the subsistence level of consumption is higher than the consumption when infected. These countries are Bangladesh, Brazil, Cambodia, Pakistan, and the Philippines.

Table Appendix B.1: Countries in initial sample

Appendix C    Countries in Empirical Validation

Table Appendix C.1: Countries used for empirical validation. ∗ African countries south of the Equator, † low-income countries.

Appendix D    Additional Regression Estimates from Google Mobility Data

Reduction in traffic around different locations as a function of income per capita. Standard errors in parentheses. ∗ p <.1, ∗∗ p <.05, ∗∗∗ p <.01