The current COVID-19 pandemic has been causing significant economic and public health turmoil throughout most of the world. Governments quickly mandated various forms of social distancing to ‘flatten the curve’ and thereby save lives compared to the deaths predicted by epidemiological models (e.g. Ferguson et al. 2020). Individuals will also voluntarily change behaviour to protect themselves.
Economic models are good tools to understand such individual behavioural change and to evaluate government policies,1 and an exponentially growing number of economic papers already study different aspects of the disease.2
Despite being a global shock, this pandemic has several unique characteristics: older individuals are more likely to die from the disease, distinct sectors of the economy are affected differently by lockdowns, and some individuals know they are infected and some do not, rendering testing important.3
In a recent working paper (Brotherhood et al. 2020), we build a choice-theoretic heterogeneous-agent equilibrium model to study the importance of age-specific policies and testing in the context of the COVID-19 pandemic. We build on Greenwood et al. (2019), who developed a quantitative model for the HIV/AIDS epidemic and add ingredients specific to the current disease.4 With the calibrated model, we analyse policies such as confinement, testing, quarantining, and selective mixing across age groups.
An economic model of the COVID-19 epidemic
Underlying our quantitative assessment is a basic SIR epidemiological model into which we embed behavioural choices and age heterogeneity, as well as imperfect information about infection status. Individuals in the model can be either healthy, have mild symptoms (which could be due to COVID-19 or the common cold/flu), or known to be infected. Of those infected, some develop serious symptoms, others recover, and some eventually die. We add testing to the model, which tells those who are unsure whether they are infected with COVID-19.
Individuals consume three goods: regular consumption, a composite leisure good, and leisure at home. Individuals allocate their time between working (outside the home), social activities (outside), and leisure inside the home. The infection risk increases with time outside the house (both work and leisure time), so the higher the infection risk is, the more people will voluntarily reduce their work and outside leisure hours. However, leisure at home (such as reading a book or resting) is no perfect substitute for leisure outside the house (such as bars, fitness centre).
The model features two age groups: young and old. The young are less likely to develop serious symptoms and die from COVID-19 than the old. Only the young can work, while the old get a fixed retirement income. Thus, the old naturally spend less time outside the house, even when the COVID-19 infection risk is zero.
The model features a negative externality: spending more time outside increases not only one’s own risk (which people will rationally take into account when choosing their time allocation), but it also increases the risk that they will infect others down the road. This externality is made worse by the information problem and the age heterogeneity in death rates.
The underlying epidemiological model also features a hidden ‘positive’ externality in the presence of heterogeneous agents: the disease dies out once enough people are infected, i.e. once herd immunity is reached. When the young engage in riskier behaviour, they reduce the time until herd immunity is reached.
The parameters of the model are calibrated using data describing individual’s time use and mobile-phone mobility, as well as epidemiological aspects of the disease. Different counterfactuals are performed in order to assess the importance of behaviour and the impact of a plethora of policies.
The importance of behaviour
Our baseline results refer to a world in which the COVID-19 epidemic develops without any mitigation policy. As individuals are rational, they change their behaviour in response to the risk of contracting the disease. Figure 1 illustrates this change in behaviour.
Figure 1 Time spent at home and number of infected with no mitigation policy (baseline) vs epidemiological model
Focus on the left panel: the dashed lines correspond to time spent at home by the young and the old in a pure SIR model without behavioural change, whereas the solid lines are the counterparts for our full model. Note that, as the disease progresses (right panel), agents become more careful and spend more time at home. This is especially true for the old who have a higher likelihood of dying.
This preventive behaviour leads to a flattening of the curve of the disease (Figure 1, right panel). Fewer people get infected and fewer people die compared to a world with no behavioural change (Figure 2). Just as the change in behaviour, the decrease in the death toll is particularly pronounced among the old.
Figure 2 Changes in GDP and deaths in with behaviour change (baseline) and without (epidemiological model)
On the other hand, as the young spend more time at home, they cut their labour supply. This is reflected by a lower level of output. At the peak of the disease, GDP falls by 20%. In the first year of the epidemic, GDP is 3% lower compared to the epidemiological scenario that features no changes in labour supply. The equilibrium features a positive externality: if the young take more risks, all else equal, in the long run fewer elderly and fewer people in total die.
Policy analysis
Consider now the implementation of two policies: a shelter-at-home order and a test-and-quarantine policy.5 We examine the shelter-at-home order first. Suppose the policy lasts for 26 weeks and requires individuals to reduce their time outside their houses by 90% compared to the no-disease world (Figure 3, left panel).
Figure 3 Time spent at home and no. of infected with shelter-at-home order vs epidemiological model
Such a policy can supress the development of the disease for quite a while (Figure 3, right panel). Even though the policy is in place for 26 weeks, the peak of the disease comes after 56 weeks. Indeed, during the first year of the epidemic, less than 0.01% of the population die.
If a vaccine or cure is found within this timeframe, this will be a successful policy. If that is not the case, however, the long-run death toll is very similar to the world without any policy (Figure 4); only the timing is changed.
Figure 4 Changes in GDP and deaths with behaviour change only (baseline) vs with shelter-at-home order vs test-and-quarantine policy
Requiring all individuals to stay at home for such a long period will substantially cut the labour supply of the young. GDP thus falls considerably in the first year (Figure 4).
An alternative policy would be to shelter only the old, who do not work and are more affected by the disease. Such a policy (not shown) would substantially decrease the death toll among the old while the young develop herd immunity.
In this scenario, however, the old are required to stay at home more than they would have chosen: their welfare declines substantially, as externalities among the old are small and they warrant little additional intervention.
We could also consider a policy that shelters the young, as for them the externality is larger. However, this policy leads to more deaths in the long run, since it is easier to reach herd immunity through the more numerous young rather than the old.
Finally, consider a test-and-quarantine policy. For this we assume 50% of the population who are unsure whether they have the disease are tested every week. If the test is positive, they are required to quarantine themselves for 90% more time, as long as the disease lasts. This policy would substantially decrease the number of infected and deaths without much effect on GDP.
Note that such a policy requires a substantial number of tests to be performed: at the peak of the disease, 2.9% of the population would have to be tested every week (just under 10 million tests per week in the US alone).
Policies that involve quarantines require infected agents to stay longer at home, even if this is against their best interest. However, this can be a welfare-improving policy due to the negative externalities of infections. Indeed, we find that the welfare for both young and old populations is higher with quarantine policies in place, even though they may be required to quarantine themselves if they are unfected.
Conclusions
Heterogeneity by age is an important factor in the COVID-19 pandemic. Older individuals have a much higher risk of dying from the virus. Further, since older individuals typically do not participate in the labour market, the economic impact of lockdown is lower for the old than for the young. Thus, public policy measures may differentiate by age.
We find that sheltering the old more saves many lives by the end of the first year and hence may be considered a good policy, assuming a vaccine will be available by then. However, we also show that the old do not like this policy.
References
Baldwin, Richard, and Beatrice Weder di Mauro (2020), Economics in the Time of COVID-19, VoxEU.org Book, CEPR Press.
Bethune, Zachary, and Anton Korinek (2020), “COVID-19 infection externalities: Pursuing herd immunity versus containment?”, COVID Economics, Vetted and Real-Time Papers, 11.
Brotherhood, Luiz, Philipp Kircher, Cezar Santos and Michèle Tertilt (2020), “An economic model of the COVID-19 epidemic: The importance of testing and age-specific policies”, CEPR Discussion Paper 14695.
Chan, Tat, Barton Hamilton and Nicholas Papageorge (2016), “Health, risky behavior and the value of medical innovation for infectious disease”, Review of Economic Studies 83(3): 1737–55.
Ferguson, Neil M, Daniel Laydon, Gemma Nedjati-Gilani et al. (2020), “Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand”, Imperial College COVID-19 Response Team, 16 March.
Galeotti, Andrea, Paolo Surico and Jakub Steiner (2020), “The value of testing”, VoxEU.org, 23 April.
Greenwood, Jeremy, Philipp Kircher, Cezar Santos and Michèle Tertilt (2019), “An equilibrium model of the African HIV/AIDS epidemic”, Econometrica 87(4): 1081–113.
Heathcote, Jonathan, Andrew Glover, Dirk Krueger and Victor Rios-Rull (2020), “Health vs. wealth: On the distributional effects of controlling a pandemic”, VoxEU.org, 26 April.
Keppo, Juusi, Elena Quercioli, Marianna Kudlyak, Lones Smith and Andrea Wilson (2020), “The behavioral SIR model, with applications to the swine flu and COVID-19 pandemics”, technical report, work in progress.
Kremer, Michael (1996), “Integrating behavioral choice into epidemiological models of AIDS”, The Quarterly Journal of Economics 111(2): 549–73.
Quercioli, Elena, and Lones Smith (2006), “Contagious matching games”, mimeo.
Scott, Andrew and Jonathan David Old (2020), “The interaction between COVID-19 and an aging society”, VoxEU.org, 27 April.
Toxvaerd, Flavio (2019), “Rational disinhibition and externalities in prevention”, International Economic Review 60(4): 1737–55.
Endnotes
1 A seminal theory paper that added behaviour to epidemiological models was Kremer (1996). See also Quercioli and Smith (2006) and Toxvaerd (2019).
2 See the Annex for a review of the recent literature and Baldwin and Weder di Mauro (2020) for a collection of essays debating diverse economic facets of the pandemic.
3 These issues are discussed in several related VoxEU columns. Heathcote et al. (2020) discuss heterogeneity during this pandemic; Scott and Old (2020) discuss the importance of age; Bethune and Korinek (2020) analyse externalities and lockdowns; and Galeotti et al. (2020) examine testing.
4 For other quantitative papers of the economics of infectious diseases, see Chan et al. (2016) and Keppo et al. (2020).
5 Many more policies are explored in Brotherhood et al. (2020).
Annex: Literature review
Our project contributes to the literature that combines epidemiological models in the tradition of Kermack and McKendrick (1927) with equilibrium behavioral choice. Theory work on this has long pointed out the negative externality of too little prevention by self-interested agents that do not internalize the costs of transmission to others; see, e.g., Kremer (1996) for SI models, Quercioli and Smith (2006) and Chen (2011) for SIR models, and more recently Toxvaerd (2019).1 This literature has mostly abstracted from externalities between heterogeneous groups, though Kremer (1996) shows that an increased engagement of people who have a higher proclivity for prevention can lead to disappearance of a disease (in the context of HIV/AIDS) by suppressing the aggregate reproductive number among active people.2 This result hinges on their transmission function where more engagements by low activity people reduces infection rates for others. This is not present in our transmission function for Covid, where more activity by others always increases the infection rate. While our model has heterogeneity in prevention (as the old do not work), the main driver for the positive externality mentioned earlier is the difference in death rates.
Among the early quantitative economic models of disease transmission, Greenwood et al. (2013, 2019) develop a heterogeneous-agent choice-theoretic equilibrium model for the HIV/AIDS epidemic and use it to analyze different mitigation policies. Within this framework, Greenwood et al. (2017) explore particular channels of selective mixing by relationship type, while Greenwood et al. (2013) allow for incomplete information in infection status. In these works, the behavioral response of agents is crucial for the results of different policies. Chan, Hamilton, and Papageorge (2016) argue in a structurally estimated model that behavioral adjustments quantitatively matter for the valuation of medical innovations. Keppo et al. (2020)’s agenda expands Quercioli and Smith (2006) to a calibrated homogeneous-agent epidemiological model and argues that a substantial behavioral elasticity is necessary to match the Swine Flu and, now, the Covid-19 epidemic.
In the great influx of recent economics papers studying different aspects of the Covid-19 epidemic some papers look for optimal containment policies that trade off economic well-being of living individuals versus lost lives. Alvarez, Argente, and Lippi (2020) solve an optimal control problem to find the optimal containment policy in the presence of the Covid-19. Unlike our model, there is no behavioral response in their analysis. Eichenbaum, Rebelo, and Trabandt (2020a) solve computationally for the optimal containment policy in a model that does feature agents’ optimization. Garobaldi, Moen, and Pissarides (2020) characterize theoretically the discrete-time equilibrium and planning problem with a more general matching function and show in a calibration that the equilibrium attains the lowest level of herd immunity. Farboodi, Jarosch, and Shimer (2020) and McAdams (2020) provide the theoretical differential equations in continuous time, and the former calibrates an immediate, mild and long-lasting policy. Unlike our work, these models so far feature homogeneous agents and no age heterogeneity, and agents either have perfect information or no information whether they are currently infected.3 This reduces the control variable of the policy maker to a single one, but omits considerations of across-group externalities and improvements through testing, which are qualitatively and quantitatively important in our analysis. The sheer number of policy variables in our model (how much to test, to shelter-at-home for the healthy, to quarantine if infected, for the young or old) as well as the fact that some costs are outside the model (e.g., the cost of extending testing capacity) complicates the search for the optimal policy. This version of the paper therefore aims to inform about the effects of stylized representations of the most common intervention policies; the optimal time-variant mix remains to be computed.
Some recent papers also take into account the potential uncertainty about one’s infection status and the role for testing, e.g. Berger, Herkenhoff, and Mongey (2020). von Thadden (2020) explicitly introduces asymptomatic infections, leading to a role for testing. Piguillem and Shi (2020) solve an optimal control problem to find the best testing policy in an SIR model without behavior. Eichenbaum, Rebelo, and Trabandt (2020b) account also for behavioral adjustments like in our paper, though in their setting infected individuals become more reckless if tested which makes testing optimal only when combined with quarantines. Neither paper considers individuals with different ages (and, consequently, different risk groups). In our model individual optimization makes the infected more cautious if tested (because of partial altruism), the others less cautious because the environment gets safer, and these reactions are heterogeneous by age and shape the response to testing.
Our paper features a key heterogeneity across individuals: different ages and, hence, different risk groups. Other papers have also explored heterogeneity across different dimensions. Kaplan, Moll, and Violante (2020) focus on the different effects of the epidemic across agents that are heterogeneous regarding their occupation and their asset holdings. They do not model different age groups as we do. Glover et al. (2020) have different age groups in their model and they solve for the optimal containment policy within a parametric class and compare them to the age-preferred policy. Acemoglu et al. (2020) characterize the optimal frontier between GDP and lives lost through an unrestricted lock-down policy. They highlight large improvements by targeting the elderly separate from the working-age population, while they find little benefits for age-specific policies within the working age population. Favero, Ichino, and Rustichini (2020) allow for rich age and sector specific transmissions and analyze the effect of stylized policies to end the lockdown in Italy. Gollier (2020a,b) discuss which age group should/will carry the burden of the disease. Except for Acemoglu at al (2020) these papers do not consider uncertainty about the infection status nor testing. These papers on age dependency assume that individual behavior is affected by policy only, and otherwise fixed. They usually trade off lost production vs lives-saved, which tends to imply a low cost to confinement of the elderly who do not produce and whose main cost of lockdown is lost access to services and leisure. Our model predicts a strong decline in transmission to the elderly even without policy as they protect themselves especially during the peak, and further confinement of just the old tends to lower their welfare. Another difference is that we assess the effectiveness of specific policy instruments which is of course different from finding the optimal policy abstracting from implementation. In this sense the two approaches are very complimentary as results on optimal policy could be used to assess how close our specific policy instruments get the economy to the frontier.
Fernández-Villaverde and Jones (2020) analyze possible reopening scenarios in a SIRD model of many countries and cities. While there are no explicit economic choices, behavioral adjustments are captured through an exogenous contact function which changes over time as the disease spreads.
On a more empirical side Kuhn and Bayer (2020) propose the differences in the interaction between old and young as a possible explanation for the cross-country differences in death rates across countries. Reducing the spread through separation of old and young, e.g., through different times for shopping, has also been part of the current debate.4 We take up this idea about selective mixing as part of the policy analysis where we plan to analyze the effects of separating the old and the young more.
Finally, even though we analyze the impact of the epidemic and different policies on output, we do not focus on macroeconomic stabilization policies. This is the focus of some recent papers, such as Faria-e-Castro (2020) and Guerrieri et al. (2020) for example.
References for the annex
Acemoglu, Daron, Azarakhsh Malekian and Asu Ozdaglar (2016), “Network security and contagion”, Jounal of Economic Theory, 166: 536-585.
Acemoglu, Daron, Victor Chernozhukov, Ivan Werning, and Michael D. Whinston (2020), “A multi-risk SIR model with optimally targeted lockdown”, NBER working paper 27102.
Alvarez, Fernando, David Argente, and Francesco Lippi (2020) “A Simple Planning Problem for COVID-19 Lockdown”, Working paper.
Berger, David W, Kyle F Herkenhoff, and Simon Mongey (2020), “An SEIR Infectious Disease Model with Testing and Conditional Quarantine”, Working paper 26901, National Bureau of Economic Research.
Chen, Frederick (2012), “A Mathematical Analysis of Public Avoidance Behavior During Epidemics Using Game Theory”, Journal of Theoretical Biology, 302: 18-28.
Chen, F., M. Jiang, S. Rabidoux and S. Robinson (2011), "Public Avoidance and Epidemics: Insights from an Economic Model", Journal of Theoretical Biology, 278: 107-119.
Eichenbaum, Martin S, Sergio Rebelo, and Mathias Trabandt (2020a), “The Macroeconomics of Epidemics,” Working paper 26882, National Bureau of Economic Research.
Eichenbaum, Martin S, Sergio Rebelo, and Mathias Trabandt (2020b), “The Macroeconomics of Testing and Quarantining”, Working paper.
Farboodi, Maryam, Gregor Jarosch, and Robert Shimer (2020), “Internal and External Effects of Social Distancing in a Pandemic”, Working paper.
Faria-e-Castro, Miguel (2020), “Fiscal Policy during a Pandemic,” Working paper.
Favero, Carlo, Andrea Ichino, and Aldo Rustichini (2020), “Restarting the economy while saving lives under COVID-19”, Technical Report 3580606, SSRN.
Fernández-Villaverde, Jesús, and Charles I. Jones (2020), “Estimating and Simulating a SIRD Model of COVID-19 for Many Countries, States, and Cities”, Unpublished Manuscript, Stanford University.
Galeotti, Andrea, and Brian R. Rogers (2012), “Immunization and Group Structure”, American Economic Journal-Microeconomics, 5(2): 1-32. 5 (2): 1–32.
Galeotti, Andrea, and Brian R. Rogers (2015), “Diffusion and protection across a random graph”, Network Science 3:361–376.
Garibaldi, Pietro, Espen R. Moen, and Christopher A. Pissarides (2020), “Modelling contacts and transitions in the SIR epidemics model”, COVID Economics, Vetted and Real-Time Papers, 5 (April): 1–20.
Glover, Andrew, Jonathan Heathcote, Dirk Krueger, and Jose-Victor Rios-Rull (2020), “Health versus Wealth: On the Distributional Effects of Controlling a Pandemic”, Working paper.
Gollier, Christian (2020a), “Cost-benefit analysis of age-specific deconfinement strategies”, Working Paper.
Gollier, Christian (2020b), “If the objective is herd immunity, on whom should it be built?”, Working Paper.
Greenwood, Jeremy, Philipp Kircher, Cezar Santos, and Michèle Tertilt (2013), “An Equilibrium Model of the African HIV/AIDS Epidemic”, Working paper 18953, National Bureau of Economic Research.
Greenwood, Jeremy, Philipp Kircher, Cezar Santos, and Michèle Tertilt (2017), “The Role of Marriage in Fighting HIV: A Quantitative Evaluation for Malawi”, American Economic Review 117 (5): 158–162 (May).
Guerrieri, Veronica, Guido Lorenzoni, Ludwig Straub, and Ivan Werning (2020), “Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages?”, Working paper.
Kapicka, Marek, and Peter Rupert (2020), “Labor Markets during Pandemics”, Working paper.
Kaplan, Greg, Benjamin Moll, and Gianluca Violante (2020), “Pandemics Ac-cording to HANK”, Working paper.
Kermack, W. O. and A. G. McKendrick (1927), “A Contribution to the Mathematical Theory of Epidemics”, Proceedings of the Royal Society A, 115(772): 700-721.
Kuhn, Moritz, and Christian Bayer (2020), “Intergenerational ties and case fatality rates: A cross-country analysis”, Technical Report DP14519, CEPR.
McAdams, David (2020), “Nash SIR: An Economic-Epidemiological Model of Strategic Behavior During a Viral Epidemic”, Working paper.
Piguillem, Facundo, and Liyan Shi (2020), “The Optimal COVID-19 Quarantine and Testing Policies”, Working paper.
Reluga, T. (2010), “Game Theory of social distancing in response to an epidemic”, PLoS Computational Biology. 6, e1000793.
Rowthorn, Robert and Falvio Toxvaerd (2012), “The Optimal Control of Infectious Diseases via Prevention and Treatment”, CEPR Discussion paper No. DP8925.
von Thadden, Elu (2020), “A simple, non-recursive model of the spread of COVID-19 with applications to policy”, COVID Economics, Vetted and Real-Time Papers, 10 (April).
Endnotes to the annex
1 Chen (2012) highlights that this negative externality is present if the contact rate of meeting others is increasing in other people’s activity, which is the current specification in all applied papers discussed in this review. Reluga (2010) shows that for a constant contact rate the decentralized equilibrium and the planner’s solution coincide, similar to a point in Garibaldi, Moen, and Pissarides (2020). Chen et al (2011) analyze a game with adaptive expectations rather than a rational expectations Nash equilibrium. Rowthorn and Toxvaerd (2012) consider prevention efforts in a model with decentralized decision-making.
2 See also Galeotti and Rogers (2012) who consider two identical populations but with non-random mixing patterns and shows that government immunization efforts depend on the mixing pattern. Galeotti and Rogers (2015) consider protection efforts in a network model where individuals differ with respect to their degree. This links to a large literature on protection in networks of which some can be reinterpreted in a disease context, see e.g. Acemoglu at al (2020).
3 This also holds for Kapicka and Rupert (2020) who model the interaction between the pandemic and individual choices through a labor search model. Farboodi, Jarosch, and Shimer (2020) have heterogeneity in death risk as an extension to be done.
4 Different shopping times feature in many countries. For the UK, see for example the article “These are the supermarket opening times for the elderly: when Tesco, Aldi, Sainsbury’s and more are open just for over-70s during lockdown” in the Edinburgh Evening News, April 23rd 2020.
