Saving lives during the COVID-19 pandemic: The benefits of the first Swiss lockdown

Gatti, Nicolò; Retali, Beatrice Article Saving lives during the COVID-19 pandemic: The benefits of the first Swiss lockdown Swiss Journal of Economics and Statistics Provided in Cooperation with: Swiss Society of Economics and Statistics, Zurich Suggested Citation: Gatti, Nicolò; Retali, Beatrice (2021) : Saving lives during the COVID-19 pandemic: The benefits of the first Swiss lockdown, Swiss Journal of Economics and Statistics, ISSN 2235-6282, Springer, Heidelberg, Vol. 157, Iss. 1, pp. 1-21, https://doi.org/10.1186/s41937-021-00072-2 This Version is available at: https://hdl.handle.net/10419/259768 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Swiss Journa l o f Economics and Statistics Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 https://doi.org/10.1186/s41937-021-00072-2 ORIGINAL ARTICLE Open Access Saving lives during the COVID-19 pandemic: the benefits of the first Swiss lockdown Nicolò Gatti*and Beatrice Retali Abstract The implementation of a lockdown to control the spread of the COVID-19 pandemic has led to a strong economic and political debate in several countries. This makes it crucial to shed light on the actual benefits of such kind of policy. To this purpose, we focus on the Swiss lockdown during the first wave of COVID-19 infections and estimate the number of potentially saved lives. To predict the number of deaths in the absence of any restrictive measure, we develop a novel age-structured SIRDC model which accounts for age-specific endogenous behavioral responses and for seasonal patterns in the spread of the virus. Including the additional fatalities which would have materialized because of the shortage of healthcare resources, our estimates suggest that the lockdown prevented more than 11,200 deaths between March and the beginning of September 2020. Keywords: COVID-19, Lockdown, Saved lives, SIRDC model, SIR model, Behavioral responses JEL Classification: I18; D91; H12 1 Introduction Since the end of 2019, all countries in the world have experienced a rapid spread of the COVID-19 epidemic, which has required the fast development of appropriate policy responses to face the increasing number of infections, hospitalizations, and deaths. The majority of governments have therefore introduced different types of measures to reduce contacts among people. Such interventions have included bans on public events and gatherings of people and closures of national and regional borders, as well as school closures and the interruption of all non-essential business activities. These policies have been at the center of a heated debate, mainly due to their high economic and social costs. Alockdownmayhavesubstantialnegativeeffectson economic activities, leading to business disruption, job losses, and earnings reductions. Recent surveys reveal that *Correspondence: [email protected] Institute of Economics (IdEP), Università della Svizzera Italiana, via G. Buffi 13, CH-6900 Lugano, Switzerland at least 42% of young people experienced a deterioration of their career prospects and serious income losses (ILO, 2020). Such detrimental consequences in terms of learning outcomes and disposable income are also reverberated in lower levels of well-being and worse mental health conditions (OECD, 2020b; Cutler and Summers, 2020). The aim of this paper is to evaluate the number of lives which a lockdown can potentially save. Given the economic costs implied by this policy, a reliable estimate of its benefits is crucial to understand whether its adoption is actually optimal (Gros, 2020). In order to address our research question, we focus on the lockdown implemented in Switzerland in response to the first wave of COVID-19 infections. To the best of our knowledge, the existing literature has not provided yet an estimate of the lives saved by the Swiss lockdown in spring 2020. Taking advantage of a unique dataset about the universe of individuals who tested positive for the disease, we estimate the number of potentially saved lives by developing a novel SIRDC model, which allows to predict the daily amount of infections, hospitalizations and © The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 2 of 21 deaths for different age groups in the absence of lockdown. In particular, our model accounts for seasonal patterns characterizing the transmissibility of the virus (Atkeson, 2021) and includes age-specific endogenous behavioral responses (Cochrane, 2020). More specifically, we assume that not only individuals respond to changes in the death rate of their age group, but they are also altruistic and care about the well-being of other subjects. A basic SIR model, instead, would lead to overstate the impact of the policy right because it does not consider that citizens spontaneously reduce their contacts even in the absence of government interventions. To obtain a reliable estimate of saved lives, we also take into account potential overflow deaths due to hospital overcrowding. This is particularly relevant if we consider that the impossibility of providing proper hospital treatments, especially in intensive care units (ICU), results in a higher mortality risk also for younger subjects. Our SIRDC model suggests that the absence of any policy intervention in Switzerland would have resulted into approximately 11,500 deaths by September 1, plus 1500 additional casualties due to the lack of available beds in intensive care units. Relying on a basic SIR model, instead, we would have predicted roughly 65,000 deaths, plus 62,000 fatalities due to the limited availability of healthcare resources. Such estimates would be in line with the simulations performed by the Imperial College COVID- 19 Response Team. Neglecting hospital overcrowding, behavioral responses and seasonality, indeed, Flaxman et al. (2020) conclude that Switzerland would have reached 54,000 deaths by May 4. Our basic SIR model would deliver higher estimates only because we consider a time horizon which goes beyond May 4 and reaches the end of May, when the contagion fades out. Our work is related to a growing literature concerning the impact of restrictive measures which limit the spread of an epidemic, especially after the outbreak of COVID-19. For instance, Zhang et al. (2020) show that contacts among people were reduced by more than seven times in China thanks to physical distancing policies, while Fang et al. (2020) document that the lockdown in Wuhan reduced the number of potential infections by almost 65%. Some studies have also attempted an evaluation of the monetary benefits associated to the lives saved by the lockdown (e.g., Greenstone and Nigam, 2020; Thunström et al., 2020). However, these analyses often rely on simulations based on early limited data (Verity et al., 2020). This work contributes to the current literature about the COVID-19 pandemic from both a methodological and an empirical point of view. First, we develop a novel agestructured SIRDC model that accounts for seasonal patterns and age-specific endogenous behavioral responses, including both an egoistic and an altruistic component. Second, we provide an estimate of the severity of COVID- 19 based on rich data concerning the entire period of the first wave of infections in Switzerland. Third, to the best of our knowledge, this is the first estimate of the number of lives saved by the first Swiss lockdown in spring 2020. The rest of the paper is organized as follows. Section 2 introduces the Swiss context and the policies implemented during the first wave of the COVID-19 pandemic, between March and the beginning of September. Section 3 describes the data. Section 4presents our model and the estimates of the potential number of deaths in the absence of containment measures. Section 5focuses on overflow deaths due to hospital overcrowding. Section 6concludes. 2 Background After the outbreak of the COVID-19 epidemic in China and in several European countries, at the end of February 2020 Switzerland started facing the spread of the virus, with an increasing number of infections. As a consequence, massive public health non-pharmaceutical interventions became the only viable strategy to limit the contagion. Switzerland is a Confederation made up of 26 independent and sovereign cantons, so interventions can be planned and implemented both at national and cantonal levels. Indeed, some restrictive measures were already introduced, canceling several public events, on February 26 in the cantons at the border with Italy and France, where the first COVID-19 cases were reported1.Meanwhile, the first containment measure adopted at the national level by the federal government on February 28 was the banning of any event involving more than 1000 participants. However, because of the rapidly increasing number of infections throughout the country, the Swiss federal government intervened with more stringent measures. In particular, on March 17, schools and non-essential economic activities were closed, while gatherings of more than five people were forbidden starting from March 20. Nevertheless, differently from other countries like Italy, Switzerland did not opt for a strict lockdown, with the general requirement to stay at home. Although economic losses were expected to be severe also in a country with a high GDP per capita (World Bank, 2020)andHuman Development Index score (United Nations, 2020), the the Federal Council (2020)aimedat avoiding an unsustainable burden in terms of infections and lost lives. Such concern was particularly reasonable considering that the Swiss population has increasingly aged over the last decades and more than 20% of people are older than 65, hence far more likely to develop serious 1The first official COVID-19 case in Switzerland was reported on February 25 in Ticino, the most southern canton at the border with Italy. Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 3 of 21 illnesses or eventually die from COVID-19. In light of the constrained availability of healthcare facilities, moreover, it was necessary to prevent a scenario in which access to life-saving treatments would have been denied to patients in need. After reaching a peak during the first half of April, the number of infections and, consequently, deaths started to exhibit a decreasing pattern. As a result, lockdown measures were progressively loosened. On April 27, several shops opened again, while schools restarted on May 11 and the activities in the majority of offices and facilities could take place again from June 8. 3Data Our analysis is based on individual-level data released by the Federal Office of Public Health (FOPH) about the universe of individuals who tested positive for COVID-19 in Switzerland between February 24 and May 15, during the first wave of the epidemic2.Foreachpositivecaseina specific Swiss canton on a certain day, this dataset contains information about age and gender, as well as the date of the onset of the first symptoms. Furthermore, these data also report whether and when an individual was hospitalized, specifying if intensive care was required and providing the exact days on which the patient entered and left the intensive care unit. Finally, we know whether and when the person eventually died. Table 1summarizes these data. In spite of relevant testing efforts, however, during the first wave of the pandemic, asymptomatic cases were largely undetected. Because of the limited availability of resources, only people with severe symptoms were tested. This is the reason why we derive information about seroprevalence from the study conducted in Geneva by Stringhini et al. (2020). In this way, it is possible to understand the extent to which younger subjects, who tend to be under-represented in the official data, were actually affected by the spread of the disease. These data are complemented by the yearly cantonal statistics provided by the Federal Statistical Office about the resident population and the weekly number of deaths by age. As we will discuss in Section 4, we also exploit the Value of Statistical Life (VSL) to model the age-specific individual behavioral responses. The average VSL for the Swiss population is derived from the estimates released by the Federal Office for Spatial Development (2019)3. To obtain an age-specific VSL4, we rescale the estimates 2In addition, we exploit the number of deaths in each age group by the first week of September. 3The most updated value refers to year 2017 and amounts to 6.7 million Swiss Francs. More information about the Swiss VSL is provided by Ecoplan (2016). 4The VSL should exhibit a hump-shaped relationship with age (Aldy and Viscusi, 2008). Indeed, the VSL reflects not only life expectancy, but also other age-dependent characteristics such as education and career prospects. Hence, after increasing with age, the VSL starts declining when the individual turns approximately 30. obtained by Murphy and Topel (2006)intheUSAby means of the Swiss average value. As far as the healthcare supply in Switzerland is concerned, we rely on several sources. The Organization for Economic Cooperation and Development (OECD) provides indicators about the number of total and acute care hospital beds per 1000 inhabitants, and the latest statistics available for Switzerland are for year 2018 (OECD, 2020a). We also refer to Rhodes et al. (2012), whoestimatedthenumberofintensivecarebedsinseveral European countries including Switzerland, expressing them as a percentage of total acute care beds. Besides, we rely on the information released by the Swiss Society of Intensive Care Medicine about the percentage of healthcare resources which could be exclusively allocated to COVID-19 patients. In order to derive the number of daily available beds, finally, we need statistics about the average length of stay in hospital and intensive care for COVID-19 patients. To this purpose, we exploit the FOPH dataset to compute the average number of days spent in ICU by these patients. In the case of individuals who were hospitalized but did not enter ICU, instead, FOPH data provide only the day of entrance, so we take advantage of the statistics available in Pellaud et al. (2020) about hospitalizations related to COVID-19 in Fribourg. To estimate the number of overflow deaths due to hospital overcrowding, we finally need information about the mortality rates associated with being admittedtoorrejectedfromhospitalorICU.WhileFOPH data allow to compute mortality rates for COVID- 19 patients who received appropriate care, the corresponding estimates for rejected individuals will be taken from the literature (Greenstone and Nigam, 2020; Rojas, 2020), since Switzerland never faced the problem of overcrowded hospitals during the first wave of the pandemic. 4 An estimate of potential direct deaths The present section describes our estimates of the potential number of avoided direct deaths thanks to containment measures in Switzerland. The term “direct” refers to the fact that these estimates do not include the additional potential deaths due to hospital overcrowding, which will be computed in the next section. We now proceed with the following steps. First, we focus on the initial phase of the epidemic, when the growth of infections was not influenced yet by any restriction, to determine the parameters which allow to predict the subsequent spread of the contagion in a counterfactual scenario without mitigation policies. Second, we develop a novel SIRDC model to estimate the potential number of infections and the corresponding deaths between March and the beginning of September. To this purpose, we use an Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 4 of 21 Table 1 Descriptive statistics by age group (by May 15) Age groups 0–9 10–19 20–29 30–39 40–49 50–64 65–79 80+ Total Panel A: positive cases Number of cases 153 862 3801 4106 4768 8318 4393 4059 30460 Share of total cases 0.50% 2.83% 12.48% 13.48% 15.65% 27.31% 14.42% 13.33% 100% Share of women 47.02% 58.58% 59.73% 57.20% 57.19% 50.29% 44.81% 60.70% 54.30% Panel B: hospitalizations and ICU Hospitalizations 26 33 110 136 258 866 1275 1187 3891 Hospitalizations/cases 16.99% 3.83% 2.89% 3.31% 5.41% 10.41% 29.02% 29.24% 12.77% ICU 1 1 5 15 27 132 239 78 498 ICU/cases 0.65% 0.12% 0.13% 0.36% 0.57% 1.59% 5.44% 1.92% 1.63% Average days in ICU – – – 4.33 10.50 16.25 11.41 8.66 11.30 Panel C: deaths Numberofdeaths00054714031112 1,595 Deaths/cases 0.00% 0.00% 0.00% 0.12% 0.08% 0.85% 9.17% 27.39% 5.24% Share of women 0.00% 0.00% 0.00% 40.00% 25.00% 25.35% 31.27% 47.48% 42.32% Note: This table summarizes the individual-level data released by the Federal Office of Public Health, which cover the period between February 24 and May 15, 2020. Panel A displays the number of officially reported positive cases, as well as the share of total cases in each age group and the share of women. Panel B shows the number of patients requiring hospitalization or intensive care in each age group, also expressed as a share of the total number of cases in the corresponding age group. In case of access to intensive care units, the data even report the exact dates of entry and exit, allowing to compute the average length of stay. Finally, panel C displays the number of COVID-related deaths in each age group, indicating the corresponding case fatality rate and the share of total fatalities occurred among women age-specific imputed infection fatality rate derived from the data5. However, before proceeding with our analysis, we need to address a preliminary issue, which requires an adjustment of the data. Indeed, older people, who are more likely to exhibit severe symptoms, tend to be over-represented among positive cases, while younger (and often asymptomatic) individuals are systematically under-reported. Therefore, the total number of predicted infections in the counterfactual scenario cannot be attributed to the different age groups on the basis of the shares retrieved from the original data. To circumvent this issue, we exploit the results obtained by Stringhini et al. (2020) from the seroprevalence tests conducted in Geneva. They not only estimate the overall seroprevalence in the population in each of the 5 weeks between April 6 and May 9, but they also 5In order to check the robustness of our results, we also estimate the age-specific infection fatality rate of COVID-19 using an alternative approach based on a Bayesian model. See Appendix 3for more details. compute how the relative risk varies depending on age. After computing the average value of seroprevalence over the 5 weeks, using the number of observations in each week as a weight, we exploit the specific relative risks to obtain the shares of people belonging to different age groups who have been actually infected in Geneva. At this point, for each age group, we compute the ratio between the actual share of infected people in Geneva and the corresponding share of infected individuals in our data. Such ratio represents an age group-specific factor kameasuring the extent to which each age group in the canton of Geneva is under-represented in the data (see Table 2). Since testing criteria in Switzerland are defined centrally by the FOPH, it is reasonable to assume that the factor kacomputed for Geneva can be applied to all the other cantons. Hence, after multiplying the number of reported cases in each age group by the corresponding adjustment factor ka, the issue of over- or under-representation of different groups is overcome (Table 3). Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 5 of 21 Table 2 Adjustment factors Age Estimated Adjustment seroprevalence factor ka 0–9 0.02808 44.908633 10–19 0.07546 30.858332 20–49 0.08774 7.7625095 50–64 0.06931 5.0841335 65+ 0.04387 3.0066347 Note: This table reports the values of seroprevalence in different age groups inferred from the results of Stringhini et al. (2020) and the coefficients which should be multiplied by the official number of reported positive cases to predict the actual number of infections 4.1 Estimating R0during the early stage of the epidemic As a first step, we estimate the basic reproduction number (R0) of the disease, which reveals the number of individuals who are infected by a single positive person during the initial phase of the epidemic6, when the population consists almost exclusively of susceptible individuals and the cumulative number of cases grows exponentially until some containment measures are introduced (Muggeo et al., 2020; Daddi and Giavalisco, 2020; Massad et al., 2005). The starting date of the epidemic is identified as the first day when an incidence of at least 20 cases of COVID- 19 per 100,000 people is registered after the adjustment described above. The duration of the initial phase, before the materialization of any effect due to containment measures, is computed by estimating when the linear growth of the logarithm of the cumulative number of infections changes slope. In practice, we estimate a hockey stick regression model that allows to identify the breakpoint date at which the slope of this linear relationship changes7, as also displayed in Fig. 1: log (E[Yt])=β0+β1t(1) where Ytis the cumulative number of infections at day t=1, 2, ..., n, after we have normalized the first day of the epidemic as day 1. Table 4reportsthebreakpointdatesestimatedbothfor Switzerland and its seven macro-regions. Since the federal lockdown was announced on March 16, its effects are expected to be observed at most 10 days later, considering that the incubation period for COVID-19 amounts to 5 days and other 4.5 days pass on average between the onset of the first symptoms and the test. This timing is exactly reflected in our estimates, with an anticipated effect in French cantons and in Ticino, where some restrictions were introduced earlier. 6If R0=1, the number of infected people remains constant; if R0<1,the number of infected people decreases; if R0>1, the number of infected people increases. 7If the cumulative number of infections grows exponentially during the early stage of the epidemic, the log of the cumulative number of infections exhibits a linear growth over time. In light of these results, it is finally possible to compute the value of R0using the following equation (Massad et al., 2005; Daddi and Giavalisco, 2020): Yb=Y1∗e(R0−1)γ t(2) Here, Ybis the cumulative number of infections on the breakpoint date, Y1is the cumulative number of infections on the first day, while γrepresents the resolving rate, so that 1 γis the average infectious period during which an individual can transmit the virus to others. Such period can be expected to be similar to the incubation period and, indeed, according to Almeshal et al. (2020), it amounts to 5.8 days. Exploiting this value, we derive the estimates of R0reported in Table 4. Given that the basic reproduction number R0is defined as the product between the contact rate βand the average infectious period 1/γ ,we can finally retrieve the value of β, which captures how the infection is transferred. Table 4reveals the existence of remarkable differences across Swiss regions in the intensity of the spread of the epidemic, which can also be explained by cultural heterogeneity (Mazzonna, 2020). A separate analysis of regions, however, would not allow to take into account the possibility that the contagion also spreads from one region to another, an aspect of key importance in a country where the degree of mobility is extremely high. Hence, in order to avoid underestimating the potential effects of lockdown measures, in the following sections of the paper we will rely on the number of infections, hospitalizations and deaths estimated at the national level. 4.2 Imputed infection fatality rates The most widely used measure for the severity of a disease is the infection fatality rate (IFR), which indicates the proportion of deaths among all infected individuals, including those who are asymptomatic or undiagnosed. After adjusting the data in light of seroprevalence results, we can actually estimate the whole number of cases in each age group. Hence, by taking the ratio between the number of reported deaths and the number of cases within each age group, we obtain an age group-specific imputed infection fatality rate IFRafor COVID-198.Theseestimates will now be exploited to fit our model and derive the potential number of direct deaths in the absence of restrictive measures. 4.3 Direct deaths in the absence of restrictions 4.3.1 An age-structured SIRDC model with endogenous behaviors The values of R0and βdetermined above can be now exploited to fit a model which allows to simulate the 8The value of IFRais null if no deaths are reported for age group a .The youngest individual who officially died from COVID-19 in Switzerland by May 15 is aged 31. Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 6 of 21 Table 3 Descriptive statistics by age group after adjusting the data (by May 15) Age groups 0–9 10–19 20–29 30–39 40–49 50–64 65–79 80+ Total Panel A: positive cases Number of cases 6871 26507 29366 31733 36911 42203 13181 12189 198961 Share of total cases 3.45% 13.32% 14.76% 15.95% 18.55% 21.21% 6.63% 6.13% 100% Panel B: hospitalizations and ICU Hospitalizations 26 33 110 136 258 866 1275 1187 3891 Hospitalizations/cases 0.38% 0.12% 0.37% 0.43% 0.70% 2.05% 9.67% 9.74% 1.96% ICU 1 1 5 15 27 132 239 78 498 ICU/cases 0.01% 0.00% 0.02% 0.05% 0.07% 0.31% 1.81% 0.64% 0.25% Average days in ICU – – – 4.33 10.50 16.25 11.41 8.66 11.30 Panel C: deaths Number of deaths 0 0 0 5 4 71 403 1112 1,595 Deaths/cases 0.00% 0.00% 0.00% 0.02% 0.01% 0.17% 3.06% 9.12% 0.80% Share of women 0.00% 0.00% 0.00% 40.00% 25.00% 25.35% 31.27% 47.48% 42.32% Note: This table summarizes the dataset which combines the individual-level data released by the Federal Office of Public Health (February 25–May 15, 2020)andthe seroprevalence results inferred from Stringhini et al. (2020). Panel A displays the number of estimated positive cases, as well as the share of total cases attributed to each age group. Panel B shows the number of patients requiring hospitalization or intensive care in each age group, also expressed as a share of the total number of cases in the corresponding age group. In case of access to intensive care units, the data even report the exact dates of entry and exit, allowing to compute the average length of stay. Finally, panel C displays the number of COVID-related deaths in each age group, indicating the corresponding imputed infection fatality rate and the share of total fatalities occurred among women spread of the COVID-19 epidemic in Switzerland in the absence of any mitigation policy. In particular, our aim is to improve the estimates which could be derived from a basic SIR model (see Appendix 1) by considering a more realistic counterfactual scenario in which people tend to reduce spontaneously their contacts also in the absence of any government intervention. Furthermore, following Atkeson (2021), we are also including in the model an additional component which accounts for seasonal variation in the spread of the virus. Indeed, as documented by the epidemiological literature (e.g., Park et al., 2020), the transmissibility of the virus changes during the year, reaching a peak towards the end of January. As far as the time horizon of our predictions is concerned, we focus on the 180 days between March 5 and September 1. Indeed, the present analysis is meant to estimate the benefits associated to the lockdown implemented in response to the first wave of infections. Moreover, such focus allows us to avoid a potential bias in our estimates arising from factors which changed after summer and led to the insurgence of the second wave of infections. However, Appendix 4also reports the results of our model when the time horizon is not restricted and we consider the entire period over which infections and deaths would occur. We start from a simple SIRDC model (Villaverde and Jones, 2020), in which individuals can be in one of five possible states: Susceptible (S), Infectious (I), Resolving (R), Dead (D), and reCovered (C). Since we are interested in estimating how the number of potential infections and deaths varies with age, we distinguish eight age groups9. Excluding vital dynamics (i.e., neglecting births and deaths that are unrelated to the epidemic, see Rowthorn and Maciejowski, 2020) and taking into account that the contagion may spread also across age groups, the model is described by the following system of five ordinary differential equations: 9To implement this model, we have followed Deforche (2020), but identifying eight different age groups rather than only two. See Appendix 1for more details. Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 7 of 21 Fig. 1 (Log) number of cumulative positive cases. Note: This figure shows the evolution over time of the logarithm of the cumulative number of infections after March 5. The number of cases represented here is the one obtained after adjusting the official number of reported cases in light of the seroprevalence estimates by Stringhini et al. (2020). The change in the slope which occurs around the 20th day reflects the end of an exponential growth of cases thanks to the implementation of restrictive measures in the country dSa dt =− β08 a=1Ia 8 a=1Na ∗Sa(3) dIa dt =β08 a=1Ia 8 a=1Na ∗Sa−γIa(4) dRa dt =γIa−θRa(5) dDa dt =δaθRa(6) dCa dt =(1−δa)θRa(7) with aindicating one of the eight age groups, a∈ {1, ..., 8}.Narepresents the total population belonging to a given age group, while Nrepresents the total population, which does not vary over time since vital dynamics are here neglected. The number of subjects in each compartment varies over time, but the stock across the five states remains constant: 8  a=1 Sa(t)+ 8  a=1 Ia(t)+ 8  a=1 Ra(t)+ 8  a=1 Da(t) + 8  a=1 Ca(t)= 8  a=1 Na(t)=N(t)=N The rate at which susceptible individuals in each age cohort abecome infectious is β08 a=1Ia 8 a=1Na ∗Sa=β0IS N.Hence, it depends on the share of infectious subjects in the total population, on the value of the contact rate β0, which mirrors the speed of the transmission of the disease, and on the amount of individuals who are still susceptible. Infectiousness resolves at rate γ. Once individuals are no longer in the state in which they can infect others, they move to the resolving state. In each period t, then, a constant fraction of individuals (θ) in every considered age group leaves the resolving compartment, ending in one of the two final stages: either dead (with probability δa) or recovered (with probability (1−δa))10.Theselasttwostatesarepermanent, that is, once in them, people can no longer change compartment. We set β0=0.3596 and γ=0.1724, while δaindicates age-specific mortality rates11. Finally, we set θ=0.1. This value reflects the 1 θ=10 days which on average an individual spends with the disease before it resolves. The system of differential equations can be recursively estimated to predict the daily number of people in each compartment. Since the analysis is performed at the national level, the initial conditions are represented by the individuals in each age group and compartment on March 10Note that this dynamics collapses to that of a basic SIR model if we aggregate Ra,Da,andCa. 11Age-specific mortality rates are the imputed IFRs described in Section 4.2. Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 8 of 21 Table 4 Estimates of R0during the early phase of the epidemic Region Starting date Breakpoint date R0β Lake Geneva 6 March 23 March 2.2939 0.3955 Espace Mittelland 6 March 26 March 1.9005 0.3277 Northwestern Switzerland 5 March 25 March 1.9528 0.3367 Zurich 8 March 24 March 2.1808 0.3760 Eastern Switzerland 7 March 24 March 2.0553 0.3544 Central Switzerland 5 March 25 March 1.8601 0.3207 Ticino 3 March 22 March 2.1577 0.3720 Switzerland 5 March 24 March 2.0859 0.3596 Note: This table reports the estimated length of the early phase of the epidemic—characterized by an exponential growth of cases—and the corresponding basic reproduction number R0in the main Swiss regions. The starting date is conventionally fixed when an incidence of at least 20 cases per 100,000 individuals is reached. The breakpoint date corresponds to a change in the growth rate of the cumulative number of cases due to containment measures (see Fig. 1). The value of βis retrieved by multiplying R0and γ 5(seeAppendix2). More in detail, the initial number of susceptible people in each age group is the number of individuals who had not been infected by March 5. Since the infectious period 1/γ is assumed to be 5.8 days on average, the initial number of infectious individuals is represented by the number of new infections occurred during the 5.8 days before March 512. The initial number of people in the resolving state is given by all the subjects who were infected previously13. Only one person aged 72 had officially died from COVID-19 before March 5, while no subjects had recovered yet on this date. Finally, dividing these values by the total population, we obtain the shares of individuals who initially belong to each age group and compartment14. At this point, following Cochrane (2020), we introduce in this framework an endogenous behavioral response common to all age groups. In other words, we suppose that when individuals start getting infected and dying, the contact rate βbecomes lower, as people try to avoid thedisease.Hence,wemodelthebehavioralresponseas a function of the current death rate, according to the following equation: log(βt)=log(β0)−αD Dt N(8) where Dt=8 a=1Da,tand N=8 a=1Na. We calibrate αDas in Cochrane (2020). Using Eq. 8, we assign values to β0,βtand Dtto obtain the parameter αD, which measures people’s sensitivity to changes in the death rates. β0is the baseline contact rate (β0= 0.3596), while βtis the lowest value of βwhich is observed. 12The initial number of infectious individuals on March 5 includes the infections registered between March 1 and March 5, plus 80% of the infections occurred on February 29. 13Hence, individuals infected before February 28, plus 20% of those infected on February 29. 14The adjustment based on seroprevalence results described before is meant to obtain reliable values at this stage of the analysis, avoiding an over-representation of older individuals. Thus, the calculations based on our data reveal that βt= 0.17315. The peak in the variation of the daily number of deaths in Switzerland is 25 deaths, so Dt=25. Finally, Nis the total Swiss population in 2020. We recover αD= 108, 697.16. However, we know that there is striking heterogeneity in mortality rates across age groups. If people’s behavior is affected by their perceived personal risk, behavioral responses could greatly vary by age and imposing a common differential equation for βcould be an unrealistic assumption. Thus, we adapt the behavioral differential equation to introduce age-specific responses. We model the behavioral response of each age group as a function of both the death rate for that particular age group and a fraction of the death rates registered for the other age groups (introducing both an egoistic and an altruistic component). First of all, we assume that individuals care to the maximum possible level (=1) to the death rate of people belonging to their own age group, so we keep a one-to- one relationship between dβa dt and dDa dt . Second, we assume that individuals are, at least partially, altruistic, and adjust their behavior also in response to changes in the death rates of other age groups. However, they weight other people’s well-being less than their own, with an altruism factor equal to 0.27 (Long and Krause, 2017). Third, we assume that people do not give the same importance to the death rates of all the other age cohorts, but rather they adopt a societal perspective. In other words, individuals give more weight to the death rates of those age groups that have a higher VSL. Therefore, if we consider the perspective of age cohorts 0–9, 10–19, 30–39, 40–49, 50–64, 65–79, and 80+, and we normalize their VSL by giving value 1 to the highest VSL (i.e., that of the age group 20–29), we obtain 15We recovered the lowest observed value for βfrom R0t. Indeed, we first estimate the daily value for R0t, and we recover the corresponding βtfrom the relationship R0t=βt γ Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 15 of 21 Fig. 4 SIR model. Note: This figure plots the evolution of the daily shares of individuals in each compartment according to the predictions of a basic SIR model IFR discussed in Section 4.2 by estimating the severity of the disease with an alternative methodology. More specifically, we follow the approach proposed by Rinaldi and Paradisi (2020), which relies on the use of administrative data concerning death counts and demographic information. A potential concern regarding the imputed IFR reported in Table 6, indeed, is represented by the fact that official data about COVID-19 cases may misrepresent the actual number of deaths related to the spread of the virus. FOPH deaths data may present a downward bias because people might die at home (because of COVID-19) or in other Table 9 Initial values—SIR model Susceptibles Infectious Recovered S1,0 =871031 8603899 I1,0 =90 8603899 R1,0 =90 8603899 S2,0 =843844 8603899 I2,0 =242 8603899 R2,0 =6 8603899 S3,0 =1044880 8603899 I3,0 =197 8603899 R3,0 =83 8603899 S4,0 =1228592 8603899 I4,0 =334 8603899 R4,0 =62 8603899 S5,0 =1197959 8603899 I5,0 =246 8603899 R5,0 =35 8603899 S6,0 =1809807 8603899 I6,0 =323 8603899 R6,0 =27 8603899 S7,0 =1152211 8603899 I7,0 =69 8603899 R7,0 =12 8603899 S8,0 =453792 8603899 I8,0 =36 8603899 R8,0 =0 8603899 Note: This table reports the shares of individuals in each compartment of the SIR model on March 5 Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 16 of 21 Table 10 Initial values—SIRDC model Susceptibles Infectious Resolving Dead Recovered S1,0 =871031 8603899 I1,0 =90 8603899 R1,0 =90 8603899 D1,0 =0 8603899 C1,0 =0 8603899 S2,0 =843844 8603899 I2,0 =242 8603899 R2,0 =6 8603899 D2,0 =0 8603899 C2,0 =0 8603899 S3,0 =1044880 8603899 I3,0 =197 8603899 R3,0 =83 8603899 D3,0 =0 8603899 C3,0 =0 8603899 S4,0 =1228592 8603899 I4,0 =334 8603899 R4,0 =62 8603899 D4,0 =0 8603899 C4,0 =0 8603899 S5,0 =1197959 8603899 I5,0 =246 8603899 R5,0 =35 8603899 D5,0 =0 8603899 C5,0 =0 8603899 S6,0 =1809807 8603899 I6,0 =323 8603899 R6,0 =27 8603899 D6,0 =0 8603899 C6,0 =0 8603899 S7,0 =1152211 8603899 I7,0 =69 8603899 R7,0 =11 8603899 D7,0 =1 8603899 C7,0 =0 8603899 S8,0 =453792 8603899 I8,0 =36 8603899 R8,0 =0 8603899 D8,0 =0 8603899 C8,0 =0 8603899 Note: This table reports the shares of individuals in each compartment of the SIRDC model on March 5 non-medical facilities, and remain untested. This situation can be present if individuals decide not to go to the hospital, or they are not in a position to go. At the same time, official COVID-19 deaths data can present an upward bias since a fraction of those who died because of the pandemic were already severely ill individuals, who might have died over the following few weeks or months without the virus. Thus, COVID-19 has simply slightly anticipated their death. In the attempt to correct for these biases, we use weekly administrative data about the deaths recorded between 2000 and 202021 by the Federal Statistical Office, which also provides demographic information at the cantonal level22. We then elaborate these data to identify eight age groups (0–9; 10–19; 20–29; 30–39; 40–49; 50–64; 65–79; 80+) in the seven major Swiss regions (Lake Geneva, Espace Mittelland, North-West Switzerland, Zurich Region, Eastern Switzerland, Central Switzerland, and Ticino). Exploiting such information, we build a Bayesian model which fits age-stratified mortality and demographic data for the seven regions between 2000 and 2020 over the weeks 11–19, namely those characterized by the COVID- 19 outbreak. Specifically, starting from a simple standard binomial mortality mode, we assume that deaths are binomially distributed and in weeks affected by COVID-19 the baseline lethality rate is augmented by a factor that indicates the interaction between the IFR and the infection rate of COVID-19. Furthermore, we assume that mortality is not correlated between different age groups. The model is described with the following binomial equations: 21Data provide information about gender, age group (5 years bin), and cantonal residence. 22Data provide information on the total population, by gender and age. Di,a,y∼Binomial(δa,Ni,a,y)for y∈{2000, ..., 2019} (20) Di,a,2020 ∼Binomial(δa+δCovid a∗θi,Ni,a,2020) (21) where idenotes the macro-region, ythe year, and aone of the eight age groups (0–9; 10–19; 20–29; 30–39; 40–49; 50–64; 65–79; 80+). Di,a,yand Ni,a,yare, respectively, the total deaths and population in macro-region i,yeary,and age range a. The baseline lethality rates δaareassumedtobeconstant across macro-regions and years, but can vary across age groups. Before 2020, the infection fatality rates δCovid a are assumed to be equal to zero, while in 2020, they are heterogenous across age ranges and fixed in the other dimensions. Finally, the infection rates θiare regionspecific but constant across age groups. The identifying assumption is that in the absence of the COVID-19 outbreak, the weekly deaths recorded in 2020 would have been the same on average as the ones in the previous 20 years. We provide visual evidence (Fig. 5) about the extent to which this assumption is satisfied. Indeed, over the first 10 weeks of 2020, excess mortality (calculated as the number of deaths in 2020 versus the average value of deaths over the years between 2000 and 2019) is substantially null. However, we cannot check whether the composition of the typologies of deaths changes over time and particularly in 2020, given that statistics on the causes of deaths are not available. Using Markov Chain Monte Carlo procedures, we estimate an overall infection fatality rate for COVID-19 of 1.087123% (95% confidence interval 0.2899833%), with striking heterogeneity across age groups (see Table 11). As required with a Bayesian model, we specify priors for all the parameters we are interested in monitoring, i.e., δa,δCovid a,θi. We choose uninformative priors for all Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 17 of 21 Fig. 5 Excess mortality 2020 vs. mean 2000–2019. Note: This figure plots the weekly difference between the death counts in 2020 and the corresponding mean computed over the years between 2000 and 2019. During the first 10 weeks of 2020, excess mortality is approximately zero in expectation, while during the phase of the pandemic outbreak (weeks 11–19), excess mortality becomes significantly positive parameters: δa∼Uniform[ 0, 0.1] (22) δCovid a∼Uniform[ 0, 0.3] (23) θi∼Uniform[ 0, 0.2] (24) To derive point estimates and respective 95% confidence intervals for the parameters of interest, we employ a Markov Chain Monte Carlo procedure that allows us to calculate the median and the confidence intervals of the posterior distributions of δa,δCovid a,andθi, using as model Table 11 Infection fatality rates by age group Age groups Median Confidence interval 0–9 0.00016 (0.0000056–0.00110) 10–19 0.00023 (0.0000089–0.00130) 20–29 0.00014 (0.0000045–0.00094) 30–39 0.00019 (0.0000064–0.00120) 40–49 0.00023 (0.0000078–0.00150) 50–64 0.00023 (0.0000076–0.00160) 65–79 0.01300 (0.0031–0.03000) 80+ 0.17000 (0.047–0.29000) Note: This table reports the age group-specific infection fatality rates computed by means of the Bayesian approach, as well as the corresponding confidence intervals Eqs. (6)and(7)23. We draw 100,000 samples from the joint posterior distribution and use 50 independent chains. The burn in interval is fixed at 20,000, and the thinning interval is 30. Convergence is checked (and satisfied) visually with Gelman-Rubin diagnostic. Our estimates are robust to the definitions of alternative distributions of the priors. Table 12 shows our estimates of the potential number of direct deaths in the absence of restrictive measures (both for SIR and SIRDC models), when we use the infection fatality rates estimated through this Bayesian approach. As previously mentioned, this approach leads to higher infection fatality rates, which result in more potential direct deaths, also among younger age groups. It is worth underlining here that such differences in the infection fatality rates are also reverberated in the slight discrepancies between the number of cases predicted by the SIRDC model reported in Tables 6and 12. According to our SIRDC model, indeed, individual behavioral responses depend on the number of daily deaths. Hence, changes in the fatality rate imply differences in the intensity of reduction of the contact rate βaand in the number of predicted infections. 23The likelihood function is composed of 5 equations for each combination macro-region—age group, for a total of 21 ∗7∗8=1176 equations Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 18 of 21 Table 12 Direct deaths (infections until September 1) SIR model SIRDC model Age Pop Cases IFRaDeaths Cases IFRaDeaths 0–9 871,211 712,403 0.016% 114 159,980 0.016% 26 10–19 844,092 690,167 0.023% 159 154,907 0.023% 36 20–29 1,045,160 854,592 0.014% 120 191,341 0.014% 27 30–39 1,228,988 1,004,847 0.019% 191 225,456 0.019% 43 40–49 1,198,240 979,793 0.023% 225 219,719 0.023% 51 50–64 1,810,157 1,480,214 0.023% 340 331,345 0.023% 76 65–79 1,152,223 942,376 1.300% 12,251 181,062 1.300% 2354 80+ 453,828 371,150 17.00% 63,095 51,367 17.00% 8732 Total 8,603,899 7,035,542 76,495 1,515,177 11,345 Note: This table reports the number of direct deaths predicted according to both a basic SIR model and our SIRDC model accounting for seasonality and endogenous behavioral responses. For each model, the table displays the estimated number of infections in each age group and the corresponding number of direct fatalities, as well as the Bayesian infection fatality rate used for the computation Since an alternative infection fatality rate leads to a different number of predicted infections, in Table 13,we report the corresponding overflow deaths due to the lack of available beds in intensive care units. Appendix 4: Results from the SIRDC model without restrictions on the time horizon This Appendix reports the estimates derived from our SIRDC model accounting for seasonality and endogenous behavioral responses when we consider the entire time horizon until the contagion finally fades out and we do not restrict our attention only on the first 6 months after the beginning of the pandemic, before the outbreak of the second wave of infections. Figure 6shows that the model predicts also a second peak of infections after 200 days. The dynamics stabilizes after approximately 500 days, when 40% of Swiss individuals have been infected. Tables 14 and 15 report the corresponding number of direct and overflow deaths by age group. In the absence of restrictions on the time horizon, our model would predict roughly 28,500 fatalities, more than twice the value over the first 6 months (see Tables 6 and 7). Table 13 Overflow deaths (infections until September 1) SIR model SIRDC model Age Hospital ICU Total Hospital ICU Total 0–9 772 256 1,028 0 18 18 10–19 140 57 197 0 4 4 20–29 799 194 993 0 14 14 30–39 967 669 1636 0 47 47 40–49 1549 889 2438 0 63 63 50–64 2856 4743 7599 0 333 333 65–79 16,083 17,888 33,971 0 1032 1032 80+ 10,729 3680 14,409 0 138 138 Total 33,895 28,376 62,271 0 1649 1649 Note: This table reports the number of overflow deaths due to the shortage of healthcare facilities predicted according to both a basic SIR model and our SIRDCmodel accounting for seasonality and endogenous behavioral responses. For each model, the table displays separately the number of overflow deaths which can be attributed to the lack of, respectively, hospital (but not ICU) and ICU beds Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 19 of 21 Fig. 6 SIRDC model–time horizon: 1000 days. Note: This figure plots the evolution of the daily shares of individuals in each compartment according to the predictions of our SIRDC model in the absence of restrictions on the time horizon Table 14 Direct deaths—SIRDC model Age Cases IFRaDeaths 0–9 381,119 0.0000% 0 10–19 369,223 0.0000% 0 20–29 456,055 0.0000% 0 30–39 536,458 0.0158% 85 40–49 523,409 0.0108% 57 50–64 764,014 0.1682% 1285 65–79 360,673 3.0574% 11,027 80+ 142,946 9.1148% 13,029 Total 3,533,897 25,483 Note: This table reports the total number of direct deaths predicted by our SIRDC model accounting for seasonality and behavioral responses. The table displays the estimated number of infections in each age group and the corresponding number of direct fatalities, as well as the imputed infection fatality rate used for the computation Table 15 Overflow deaths—SIRDC model Age Hospital ICU Total 0–9 0 40 40 10–19 0 9 9 20–29 0 30 30 30–39 0 104 104 40–49 0 138 138 50–64 0 703 703 65–79 0 1775 1775 80+ 0 368 368 Total 0 3167 3167 Note: This table reports the total number of overflow deaths due to the shortage of healthcare facilities predicted by our SIRDC model accounting for seasonality and behavioral responses. The table displays separately the number of deaths which can be attributed to the lack of, respectively, hospital (but not ICU) and ICU beds Gatti and Retali Swiss Journal of Economics and Statistics (2021) 157:4 Page 20 of 21 Abbreviations COVID-19: Coronavirus disease 2019; FOPH: Federal Office of Public Health; GDP: Gross Domestic Product; ICU: Intensive care unit; IFR: Infection fatality rate; OECD: Organization for Economic Cooperation and Development; SIR: Susceptible-Infectious-Recovered; SIRDC: Susceptible-Infectious-Resolving-Dead-reCovered; VSL: Value of Statistical Life Acknowledgements We thank the Federal Office of Public Health for providing the data and we are grateful to Prof. Fabrizio Mazzonna for his precious supervision and invaluable support. We also thank Christian Althaus, Marius Brülhart, Paolo Campli, Sara Rellstab, and the participants to the USI Brown Bag Seminars for valuable feedbacks. The views expressed in this paper are clearly those of the authors and not necessarily those of the FOPH. Authors’ contributions The authors jointly developed the idea, conducted the data analysis, interpreted the results, and were major contributors in writing the manuscript. Both authors proof-read and approved the final manuscript. Funding This research was not supported by any external funding. Availability of data and materials The individual data used in this paper have been provided by the Federal Office of Public Health for the purpose of academic research. Such data are not publicly available to preserve patients’ anonymity, as the detailed personal information could potentially allow to identify specific subjects. The syntax used to analyze the data and derive the estimates is available from the authors upon request. Declarations Competing interests The authors declare that they have no competing interests. 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