Social distancing in macrodynamic models

Posted on October 28, 2020

During the COVID-19 pandemic, policymakers have often relied on epidemiology models to track the spread of the outbreak. However, such models lack the necessary tools to account for individual behaviour potentially influencing the dynamics of the pandemic. This column integrates individual economic decision-making and voluntary social distancing into these models. It argues that voluntary social distancing is important for both flattening the infection curve and minimising economic damage. Although government-enforced social distancing is much more effective in flattening the curve, it comes at a higher cost to the economy.
At the time of writing – about ten months after the COVID-19 virus was first reported in Wuhan, China, in December 2019 – more than 28.68 million people are infected with COVID-19 worldwide, more than 920,000 have died, and the pandemic shows no signs of slowing down. However, many countries have already relaxed the strict lockdown measures implemented during the early stages of the epidemic in order to ease the pressure on the economy.
Accordingly, controlling the spread of the infection has mainly been left to individual choices. While policymakers often rely on existing epidemiology models to track the spread of the virus, such models do not have the necessary tools to account for individual behaviour which might potentially influence the dynamics of the pandemic.
Recently, many economists have developed models integrating individual decision-making into the canonical epidemiology models, with examples including the work by Makris (2020), Eichenbaum et al. (2020), Krueger et al. (2020), and Toxvaerd (2020). My recent work (Getachew 2020) is part of these efforts and provides an alternative framework to the SIR (Susceptible-Infected-Recovered) epidemiology model integrated into the standard economic dynamic model through voluntary social distancing.
SIR models classify the population into three categories: susceptible, infectious, and recovered. The number of new cases is the contact rate multiplied by the number of interactions between infectious and susceptible people. Each new case makes the infectious group larger and the susceptible group smaller, whereas the size of the infectious group falls as people get better and join the recovered group (see Box 2 in Baldwin and di Mauro 2020).
In my paper, I modify the SIR model to include economic agents that derive utility from consumption and leisure. The agents also derive utility from social closeness such as hugging, kissing, and shaking hands of their loved ones. However, this could expose the susceptible individuals in the population to the virus. Infected people work less time, due to sickness, and hence lose labour income. They could also die from the infection. However, if they recover, they resume their normal life. Infected and recovered individuals tend to practice minimum social distancing, which is zero. While the latter develop immunity, the former have nothing to lose.
The mechanism used to integrate individual behaviour into the SIR models does not depend on individuals’ consumption, work, or leisure activities, but on infection-averse susceptible individuals who have a taste for non-pecuniary social closeness. This is in contrast to the work of Eichenbaum et al. (2020) and Krueger et al. (2020), who attach susceptible individuals’ consumption and labour activities to the contact rate in their SIR model to increases their likelihood of being infected.
The reason for separating social distancing from individual consumption and leisure activities is that two individuals could choose a similar bundle of consumption goods or leisure time but may practice different social distancing. In their leisure choice, for instance, one person may go out to a beach for three hours and the other may stay at home watching The Wolf of Wall Street. Both of these individuals spend the same time in leisure, but while one is practicing social distancing, the other is not.
In my model, the optimal amount of an individual’s social distancing is proportional to the welfare loss the individual incurs if she is infected. It increases in the individual’s psychological discount factor but it decreases in the probability of her likelihood of developing immunity. I also find that treatment and vaccination, if they are available, positively influence aggregate welfare but through different mechanisms. Treatment increases aggregate welfare by increasing individuals’ likelihood of recovering quickly.
Vaccinations, in contrast, move individuals out of the susceptible pool from the outset, allowing them to avoid costly (in terms of welfare loss) social distancing.
Vaccination has a relatively strong influence on the dynamics of the epidemic and consequently on the economy. One of the numerical analysis shows that a 0.06% vaccination rate per period (similar to vaccinating 0.2 million susceptible individuals per week) could lead to herd immunity after only 2% of the population is infected. Without a vaccination, 73% of the population has to be infected to achieve herd immunity.
Laissez-faire social distancing
The numerical analysis shows that voluntary social distancing is important for delaying and flattening the infection curve and minimising the economic damage from the outbreak. Figure 1 shows that it delays the peak period by about 20 periods (weeks), and flattens the curve at the peak by about 10 percentage points from the baseline case of no social distancing. The decrease in the infection and fatality rates increases labour supply. As a result, aggregate income and consumption increase, which in turn raises aggregate welfare.
Timing also matters. During the early periods, when the infection and fatality rates are low, the difference in the macroeconomic variables between practicing and not practicing social distancing is small. This changes once the pandemic gains momentum, as more people get infected and hence lose their labour income due to sickness and death. At the peak of the epidemic, there is a 20 percentage point difference in aggregate income between practicing and not practicing social distancing and there is a permanent 5 percentage point difference between the two after herd immunity is achieved (Figure 2).
Government-enforced social distancing
Almost all governments have instituted some sort of lockdown policies (which are often difficult to measure) to control the spread of COVID-19. In computing the lockdown rate for a real economy, I first assume that the government lockdown rate is proportional to the unemployment rate during the pandemic period. Individuals who are most likely to lose their jobs are those who work in industries that are severely affected by the lockdown, such as hotels and tourism. Due to this and to the fact that the main purpose of a lockdown is to cut down the number of susceptible individuals, I assume that individuals who are out of work are also out of the susceptible compartment.
In general, government-enforced social distancing or lockdown is found to be highly effective in flattening the infection curve. With a 0.5% lockdown rate (which roughly reflects the US lockdown rate), at the peak of the epidemic, only 0.74% of susceptible individuals are infected and 2.43% of them die. A scenario without any policy leads to 11.43% of susceptible individuals becoming infected and 17% of them dying (Figure 3). However, the lockdown has also had a strong negative impact on the macroeconomy, due to losses in aggregate labour income. The numerical simulations show that aggregate income and welfare have reduced by 46 and 75 percentage points, respectively.
The timing of an intervention is important. When comparing a stricter (α=0.005) to a less strict lockdown rate (α=0.001), the former leads to a relatively higher welfare loss in the early stages of the epidemic (Figure 4). However, at the peak of infections, it leads to a relatively lower welfare loss since some of the welfare loss is offset by the life- and job-savings effects of the lockdown.
Voluntary social distancing may not be the single most effective way of controlling the spread of the COVID-19 outbreak. Nevertheless, it has the desirable (albeit moderate) effects of delaying and flattening the infection curve while minimising the economic damage from the outbreak. In contrast, government-enforced social distancing is highly effective in flattening the infection curve but it comes at a great cost to the economy. The model and the analysis imply that the recent government lockdowns might have saved lives but they might have also led to significant job losses and, consequently, a loss in aggregate labour income.
New empirical evidence seems to support these findings. According to the Bureau of Economic Analysis, real GDP in the US decreased at an annual rate of 31.7% in the second quarter of 2020; Singapore’s economy shrunk by 41.2% while South Africa saw its economy shrink by an annualised 51% in the same quarter. Thus, when such trade-offs are present, policymakers may need to act more judiciously. Particularly, the timing of their intervention could be crucial, both in terms of saving lives and mitigating the economic damage.
Baldwin, R and B Weder di Mauro (2020a), Economics in the Time of COVID-19, a eBook, CEPR Press.
Eichenbaum, M S, S Rebelo and M Trabandt (2020), “The macroeconomics of epidemics”, NBER Working Paper.
Getachew, Y (2020), Optimal social distancing in SIR based macroeconomic models, Covid Economics 40: 115–163.
Krueger, D, H Uhlig and T Xie (2020), Macroeconomic dynamics and reallocation in an epidemic,” Covid Economics 5: 22–55.
Toxvaerd, F (2020), Equilibrium social distancing”, Covid Economics 15: 110 – 133.
This article was originally published in VoxEU. Read the original article.
- Author Yoseph Getachew

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