The benefits and costs of U.S. employer COVID‐19 vaccine mandates

In 2021, the Biden Administration issued mandates requiring COVID‐19 vaccinations for U.S. federal employees and contractors and for some healthcare and private sector workers. These mandates have been challenged in court; some have been halted or delayed. However, their costs and benefits have not been rigorously appraised. This study helps fill that gap. We estimate the direct costs and health‐related benefits that would have accrued if these vaccination requirements had been implemented as intended. Compared with the January 2022 vaccination rates, we find that the mandates could have led to 15 million additional vaccinated individuals, increasing the overall proportion of the fully vaccinated U.S. population from 64% to 68%. The associated net benefits depend on the subsequent evolution of the pandemic—information unavailable ex ante to analysts or policymakers. In scenarios involving the emergence of a novel, more transmissible variant, against which vaccination and previous infection offer moderate protection, the estimated net benefits are potentially large. They reach almost $20,000 per additional vaccinated individual, with more than 20,000 total deaths averted over the 6‐month period assessed. In scenarios involving a fading pandemic, existing vaccination‐acquired or infection‐acquired immunity provides sufficient protection, and the mandates’ benefits are unlikely to exceed their costs. Thus, mandates may be most useful when the consequences of inaction are catastrophic. However, we do not compare the effects of mandates with alternative policies for increasing vaccination rates or for promoting other protective measures, which may receive stronger public support and be less likely to be overturned by litigation.


INTRODUCTION
The emergence of COVID-19 in the United States has been a massive health shock with enormous economic and social implications, precipitating numerous public and private adjustments at the individual and population levels, including biomedical and non-biomedical responses (e.g., development of medical prevention and treatment options, economic lockdowns, and masking requirements).Vaccination has been central to many of these efforts throughout the pandemic, with large public and private investments made into the rapid development, testing, production, and distribution of COVID-19 vaccines (Bloom, Cadarette, Ferranna, Hyer, et al., 2021).Substantial effort has also been devoted to encouraging vaccine uptake.In this study, we explore one such effort: the issuance of employer vaccination mandates by the U.S. federal government.We estimate the potential direct costs and health-related benefits of four mandates issued in September and November 2021, assuming they had been implemented as initially planned.Our results provide insights into the possible consequences of other mandates issued by firms, state or local governments, and national governments around the world.Our results also provide a basis for comparing the effects of mandates to the effects of other policies, offering insights into the relative merits of implementing different policies alone or in combination.
The U.S. Food and Drug Administration granted the first emergency use authorization for a COVID-19 vaccine on December 11, 2020, and all U.S. adults were eligible to be vaccinated by April 19, 2021(HHS, 2022a).From the inception of public immunization efforts, the vaccination rate among adults grew steeply until mid-summer 2021, at which point it slowed notably (CDC, 2022a).As of May 2022, 66.4% of the overall U.S. population was fully vaccinated, about eight percentage points less than the average for highincome countries at 74.7% (Mathieu et al., 2021).Relative to high vaccination coverage, weak coverage translates to higher rates of COVID-19 infection, hospitalization, and mortality; increases the likelihood of a surge of infections overwhelming the health system; potentially allows the proliferation of new, possibly more dangerous variants; increases reliance on economically and socially costly nonpharmaceutical interventions (such as limiting capacity in indoor spaces or more extensive lockdowns); and threatens economic productivity and output (Bloom, Cadarette, & Ferranna, 2021).
Many organizations and government agencies have issued mandates requiring employee vaccination against COVID-19 to address concerns about worker health, virus transmission, operational efficiency, and the broader economic and social consequences of infection.In this study, we focus on four of these mandates issued within the United States.The first is a presidential executive order requiring vaccination of federal executive agency employees (Biden, 2021a).The second is an executive order requiring that federal contracts and subcontracts include safeguards against the spread of COVID-19 (Biden, 2021b;SFWTF, 2021).The third is a regulation issued by the Occupational Safety and Health Administration (OSHA) in the U.S. Department of Labor, applicable to private sector firms with 100 or more employees (OSHA, 2021a).The fourth is a regulation issued by the Centers for Medicare and Medicaid Services (CMS) in the U.S. Department of Health and Human Services (HHS), requiring vaccination of Medicare and Medicaid providers and suppliers (CMS, 2021).
Although these mandates have been subject to legal challenges and some have been halted or delayed, rigorous appraisal of their benefits and costs accompanied neither the decisions to implement them nor the efforts to terminate them.The objective of this study is to help fill that gap.We estimate the gain in the number of individuals fully vaccinated due to the mandates, the costs associated with these additional vaccinations, the population-wide health benefits in terms of reduced COVID-19 cases and deaths, and the monetary value of these benefits, considering a range of possible pandemic paths.
Our analysis suggests that the overall net benefits of the mandates depend on the state of the pandemic at the time the mandates take effect.In particular, if a more transmissible variant (i.e., similar to Omicron) emerges, for which vaccines and previous infection are less protective, the net benefits of issuing mandates skyrocket.If not, exist-ing vaccination-acquired or infection-acquired immunity may provide sufficient protection, and the net benefits of mandates decrease substantially.We do not address whether the net benefits of mandates are greater or less than the net benefits of other policies designed to encourage increased vaccination or other protective measures.
The study is structured as follows.Section 2 provides background information on the mandates under investigation.Section 3 lays out the methodology for calculating the net benefits of the mandates, including use of a simulation model to estimate averted illnesses and deaths and their economic value.Section 4 discusses the results.Section 5 concludes, highlighting the implications for both policy and future research.

BACKGROUND
The four mandates we address were issued in two waves.
The two executive orders, covering federal employees and contractors, were published in September 2021.The two regulations, covering private sector employees and healthcare workers, were published in November 2021.The original deadlines by which covered employees were required to be fully vaccinated varied across the mandates.1Each mandate has been challenged in court, delaying or preventing full implementation.The results of this litigation vary depending on the legal authority for the mandate, the basis for the challenge, the views of the court that considered the challenge, and other factors.As of April 2022, the mandates for federal employees and for healthcare workers remained in place, although some challenges continued to be heard, while mandates for federal contractors and private sector employees were blocked.However, by the time these two mandates were blocked, the vaccination requirements had been incorporated into several federal contracts and subcontracts, and many private sector employers had made significant progress on their implementation plans.Hence, these requirements may have had some effect despite their termination.Table 1 summarizes the status of each mandate.
While all four mandates allow exemptions from the vaccination requirements due to medical conditions or religious beliefs as required by law, only the OSHA regulation for private sector firms provides additional flexibility.While encouraging mandatory vaccination, OSHA allows employers to adopt policies that permit regular COVID-19 testing and wearing a face covering while at work as an alternative.
Although benefit-cost analysis is well established and widely used to inform policy decisions in the United States and elsewhere, these mandates were issued without a full understanding of their likely impacts due to the desire to act quickly.Benefit-cost analysis is not required for executive orders.It would normally be required for major regulations such as the OSHA and CMS mandates (Clinton, 1993; U.S. Office of Management and Budget, 2003), but analysis was limited due to these regulations' emergency nature.A feasibility analysis that focused on the costs to employers over a 6-month period accompanied the OSHA mandate (OSHA, 2021a), and estimates of a broader range of costs imposed on society at large over the first year of implementation accompanied the CMS mandate (CMS, 2021). 2 While both agencies provide some information on the number of people potentially affected by these regulations, they do not estimate the total value of the resulting benefits.This means that little information is available on the impacts of the executive orders, and that it is not possible to determine the extent to which the benefits of the OSHA and CMS mandates were likely to exceed their costs based on the agency analyses alone.We build on these analyses to provide a more comprehensive understanding of the impacts of the vaccination requirements.

DATA AND METHODS
Our approach follows the standard benefit-cost analysis framework, as described in the HHS (2016) Guidelines for Regulatory Impact Analysis and elsewhere.It includes three major steps, as illustrated in Figure 1 and discussed in more detail in the sections that follow.First, we estimate the expected increase in the number of vaccinated individuals attributable to the mandates.This step involves estimating the number of employees covered by the mandates, their vaccination rates in the absence of the mandates, and the effect of the mandates on these rates.Second, we simulate the change in the number of COVID-19 nonfatal cases and deaths attributable to the change in vaccination rates using a standard compartmental epidemiological model.This model is illustrated in more detail in Figure 2 in the next section.Calibration of the model requires estimating several parameters; the most important relate to the characteristics of the vaccine itself (its effectiveness and duration), the initial condition of the population (e.g., the proportion susceptible, infectious, or recovered), and the reproduction number (the infectiousness of the virus, given infection-and vaccination-acquired immunity and other measures to control its spread).Finally, we estimate the monetary value of the benefits of averting illnesses and deaths and compare these benefits to the direct costs of vaccination.The benefit values include individual willingness to pay to reduce the risk of illness and death and the associated reduction in medical costs paid by insurers or other third parties.The direct costs include those associated with administering the vaccination as well as employee time losses associated with getting vaccinated and adverse reactions.
Our viewpoint is ex ante, that is, before the mandates were implemented.In particular, we regard the future course of the pandemic from the time of implementation as uncertain.We estimate the potential health impacts of the mandates Abbreviations: S, susceptible; E, exposed; I, infectious; H, hospitalized; R, recovered; D, dead; P, vaccinated and protected; S V , vaccinated and susceptible; E V , vaccinated and exposed; I V , vaccinated and infectious; H V , vaccinated and hospitalized; R V , vaccinated and recovered;  V , waning rate of vaccination-acquired immunity;  S , waning rate of infection-acquired immunity;  E , rate of transition out of exposed state;  I , rate of transition out of infectious state;  H , rate of transition out of hospitalization state; , infection rate; h, hospitalization rate; , hospitalization fatality rate; v, vaccination rate; , vaccine effectiveness at reducing infection; , vaccine effectiveness at reducing severe disease.
under several pandemic trajectories that vary according to differences in the infectiousness of the dominant variant and in the effectiveness of vaccination-and infection-acquired immunity.
In the simulation exercises, we begin our modeling on February 1, 2022, after the original deadlines for full vaccination of current employees under all four mandates.The choice of date is primarily for convenience, as explained subsequently.We consider impacts over a 6-month period, given evidence that protection against severe disease remains high for at least 6 months after full vaccination (Andrews, Tessier, et al., 2022).
We first describe the epidemiological model and its application to the mandates and discuss the calibration of the main parameters. 3Then, we describe the approach for estimating the value of the associated benefits and costs.

Epidemiological model
To estimate the potential health impacts of the mandates, we use a susceptible, exposed, infectious, recovered epidemiological model-an approach often used to predict the evolution of the pandemic (e.g., IHME, 2021). 4We adopt an age-stratified model because age affects the intensity of social interactions (Prem et al., 2021), susceptibility to SARS-CoV-2 infection (Davies et al., 2020;Goldstein et al., 2021), and risk of severe disease and death from COVID-19 (O'Driscoll et al., 2021).
Figure 2 represents the model schematically.Time is measured in days and is denoted by t.The U.S. population is partitioned into five age groups (0−17, 18−49, 50−64, 65−74, and 75+), with N i denoting the number of individuals in age group i.Individuals are categorized as susceptible (S), exposed (E), infectious (I), hospitalized (H), recovered (R), dead (D), vaccinated and protected (P), vaccinated and susceptible (S V ), vaccinated and exposed (E V ), vaccinated and infectious (I V ), vaccinated and hospitalized (H V ), or vaccinated and recovered (R V ).The model assumes that the disease is transmitted with some probability when a susceptible individual comes into contact with an infectious one.The newly infected individual moves to an exposed compartment before becoming infectious.Most of those infected experience no or mild symptoms and recover after a short period, and a small proportion develop more serious health conditions that may require hospitalization and may lead to death.Infection-acquired immunity wanes over time, and recovered individuals move back to the susceptible compartment.Similarly, as discussed in more detail below, vaccinationacquired immunity wanes over time.Thus, the model reflects the possibility that an individual may be infected more than once.
overburdening of the healthcare system prevent individuals from seeking care for other (potentially fatal) conditions.
Transition across compartments is described by the following set of equations, where dots denote derivatives with respect to time: The terms  E ,  I , and  H represent, respectively, the rates of removal from the exposed, infectious, and hospitalized compartments, while  S and  V are the rates at which infection-acquired immunity and vaccination-acquired immunity wane over time.The parameter h i represents the age-specific hospitalization rate, and  i is the agespecific hospitalization-fatality rate.The term v it denotes the proportion of individuals who are newly vaccinated in period t.
The variable  it represents the infection rate and equals where  it is the susceptibility to transmission, that is, the probability of transmission given contact with an infectious person; c ij is the prepandemic number of contacts between an individual of age group i and an individual of age group j; and is the probability that the member of age group j is infectious.The parameter  it depends on the characteristics of the virus variant and on the presence of nonpharmaceutical interventions or changes in individuals' behavior (e.g., the use of masks or adherence to social and physical distancing practices).For a given set of contacts c ij ,  it can be adjusted to match any effective reproductive number  t for the virus.We assume that vaccination may affect the risk of infection, the risk of severe disease or death, or a combination of those endpoints (Peiris & Leung, 2020).In each period, a fraction  ∈ [0, 1] of newly vaccinated individuals is 100% protected against the risk of infection and moves to the vaccinated and protected compartment P. The remaining fraction of the newly vaccinated, 1-, is not protected against the risk of infection and moves to the vaccinated and susceptible compartment S V .Vaccinated susceptible individuals face the same risk of infection  it as unvaccinated ones.However, if infected, they have a smaller probability of suffering from severe disease (here proxied by hospitalization) than unvaccinated people.Let  ∈ [0, 1] denote the effectiveness of the vaccine at preventing severe disease or death conditional on being infected.Thus, if  = 1, none of the vaccinated individuals get infected.If  < 1, some vaccinated individuals get infected after meeting an infectious person; however, if  = 1, none of them suffers severe disease.
The vaccine's effectiveness wanes over time, and vaccinated individuals move back to the susceptible compartment S. 5 To simplify, we assume that, with the exception of individuals in the hospitalized state, anyone can be vaccinated independently of their health status. 6Vaccination confers both direct and indirect protection: Vaccinated individuals are less likely to be infected, and they are less likely to develop serious health conditions if they are infected.In addition, by reducing the probability of being infected and hence infectious, their vaccination benefits other members of the population.
We also distinguish nonfatal cases based on symptom severity because the economic value of illness varies by severity.We consider four disease severity categories: asymptomatic cases, mild cases, severe cases, and critical cases (Robinson, Eber, et al., 2021;Robinson et al., 2022).We assume that mild cases do not require hospitalization, severe cases are hospitalized but not admitted to the intensive care unit (ICU), and critical cases are admitted to the ICU.
The employer vaccine mandates increase the number of individuals who are fully vaccinated against COVID-19.We assume that individuals vaccinated because of the mandates reach full vaccination status at t = 0 (the beginning of the simulation).Thus, mandates only affect the initial number of individuals who are vaccinated.All other parameters are independent of whether vaccine mandates have been introduced.We interpret the period t = 0 as shortly after full vaccination is required under all four mandates (in the simulation, we assume this date to be February 1, 2022). 7By increasing the stock of individuals who are vaccinated at the beginning of the simulation, the mandates affect the evolution of the pandemic, in particular the number of COVID-19 cases and deaths that will occur in the simulated period among the entire population.

Calibration of the epidemiological model
This section discusses the most important parametric assumptions.Appendix A in Supplement 1 includes details on the calibration of the remaining parameters.Here, we focus on the characteristics of the vaccines, assumptions about the initial conditions in the epidemiological model, and the reproduction number.

Vaccination
The COVID-19 vaccines available in the United States when the mandates were implemented have been very effective (90%−100%) against severe disease and death with respect to all known virus variants as of spring 2022.In contrast, effectiveness against infection varies considerably across variants: Effectiveness against infection with the Delta variant is about 90% in the early weeks after full vaccination (Andrews, Stowe, et al., 2022;Lopez Bernal et al., 2021;Tartof et al., 2021), while effectiveness against infection with the Omicron variant is substantially lower (65%−75% in the first weeks after the second dose) and wanes at a faster pace (Andrews, Stowe, et al., 2022).In the simulations, we assume the vaccine is 95% effective at preventing severe disease (here proxied by hospitalization) for all age groups.To account for ex ante uncertainty about the characteristics of the dominant variant, we vary the effectiveness of the vaccine at preventing infection from 90% to 20% (with 90% representing the Delta variant that was dominant when the mandates were issued and 20% representing a hypothetical variant for which vaccines are not very effective).
The durations of both infection-and vaccination-acquired immunity are not definitively known, although evidence exists of immune memory several months after infection or 7 For simplicity, we assume all reach full vaccination status at the beginning of the simulation rather than at various times over the 2-to 4-month period from mandate publication to the implementation deadline.In the sensitivity analysis, we vary the share of the population that is susceptible at t = 0.This can be interpreted as starting the simulation at a date other than February 1.
vaccination (Atmar et al., 2022;Dan et al., 2021;De Giorgi et al., 2021;Lyke et al., 2022).Additionally, infection with one variant confers protection against other variants to some extent (Harvey et al., 2021;Planas et al., 2021), although cross-protection against the Omicron variant appears to be considerably reduced (Ferguson et al., 2021;McCallum et al., 2022).To simplify, we assume that both infection-acquired and vaccination-acquired immunity have the same mean duration, and we set this equal to 6 months.As a consequence, after a period of 6 months (on average), previously infected individuals are susceptible to re-infection, and successfully vaccinated individuals lose their protection and can be infected.
We do not model the receipt of booster doses, consistent with the focus of the mandates on initial vaccination.As previously explained, we assume that the only difference between the with-mandates and without-mandates scenarios concerns the proportion of individuals who are fully vaccinated at the beginning of the simulation.We assume additional vaccinations will be minimal during the simulation period and set v it = 0, for all i, t > 0. Our model allows us to vary the parameter values to test the extent to which infection-acquired immunity and vaccination-acquired immunity substantially limit the spread of COVID-19 throughout the population, as the population approaches what is often referred to as the "herd immunity" threshold (Desai & Majumder, 2020).

Initial conditions
The epidemiological model requires specifying the proportion of the population that is in each compartment at t = 0.
For the sake of simplicity, we set E i0 = I i0 and H i0 = h i I i0 .
In addition, we assume that no exposed, infectious, or hospitalized individuals are present among any who are vaccinated.
We set the population share with active infection at t = 0 equal to 0.5%.To simplify, we assume that the distribution of active infections across age groups is the same as the distribution of population across age groups.
According to estimates from the Centers for Disease Control and Prevention (CDC) of infection-induced seroprevalence antibodies, by the end of January 2022, about 43% of the population had been infected with SARS-CoV-2 (31% by the end of November 2021, before the spread of the Omicron variant) (CDC, 2022b).Seroprevalence rates are considerably higher for children and younger adults than for older individuals (58% in the 0−17 age group vs. 23% in the 65+ age group by the end of January 2022, and 42% in the 0−17 age group vs. 17% in the 65+ age group by the end of November 2021).This is likely due to differences in vaccination rates and contact patterns among age groups.
Even though about 40% of the population has infectioninduced seroprevalence antibodies, not everyone in this group is necessarily immune to reinfection, either because of waning immunity over time or because their antibodies do not protect against a new variant.Thus, we vary the percentage of the population that is in the recovered state from 10% to 40% depending on the characteristics of the dominant variant (with 10% representing a hypothetical new variant for which past infection provides little protection).This percentage determines the overall number of vaccinated or unvaccinated individuals who are in the recovered state.We use the aforementioned CDC data to determine the distribution of recovered individuals by age group and vaccination status (see Appendix A in Supplement 1).
Because the increase in vaccination attributable to the mandates, ΔVax, occurs only among susceptible and recovered individuals, the age-specific initial number of exposed, infected, and hospitalized individuals in the with-mandates scenario is the same as in the without-mandates one.We assume that the distribution of additional vaccinated individuals across the susceptible and recovered compartments is proportional to the initial distribution in the without-mandates scenario, that is,

Reproduction number
The effective reproduction number represents the degree of infectiousness of the virus given the population level of natural immunity and the presence of vaccination or other policies to control the virus' spread (e.g., physical distancing requirements or school and business closures).The more infectious the virus variant, or the less effective the control policies, the larger the reproduction number.In the simulation, we vary the initial reproduction number from one to five to capture different transmissibility levels.A reproduction number equal to one represents a situation in which the pandemic reaches a steady state; each infected person infects one other.
A reproduction number equal to five represents a situation in which the pandemic is rapidly intensifying, perhaps due to the emergence of a new, more transmissible variant for which existing vaccines and control measures are less effective at preventing contagion.Appendix A in Supplement 1 provides details on the computation of the reproduction number.

Economic values
To estimate the net benefits of the mandates, we rely on the conventional benefit-cost analysis framework, as described in the HHS (2016) Guidelines for Regulatory Impact Analysis and elsewhere.We compare conditions without the mandates to conditions with the mandates, estimate the benefits associated with reducing the risk of incurring both fatal and nonfatal cases of COVID-19, and compare those benefits with the direct costs associated with the additional vaccinations.
For fatal cases, consistent with the benefit-cost analysis framework, we rely on estimates of the value per statistical life (VSL) to value a change in the risk of death from the perspective of the affected individual.VSL is derived from the rate at which individuals are willing to trade small changes in their own income for small changes in their own risk of death within a defined period. 8This individual willingness to pay presumably includes any reduction in earnings and averted costs associated with the risk reductions as well as the value of continuing to experience the joys of life itself for a longer time period.
In the benchmark case, we assume that the value of preventing a COVID-19 death is equal to the central population-average VSL estimate recommended by HHS: $11.4 million in 2020 US$ and at 2020 income levels (HHS, 2021).The effects of personal characteristics (such as age) and risk characteristics (such as dread) on VSL are uncertain and may be counterbalancing (Hammitt, 2020;Robinson, Eber, et al., 2021;Robinson, Sullivan, et al., 2021 ).We test the effects of applying higher and lower VSL estimates to reflect uncertainty in the underlying empirical studies.We apply a low value of $5.3 million and a high value of $17.4 million based on the HHS (2021) Guidelines.
We likewise value nonfatal cases based on estimates of the willingness of those affected to exchange their own money for a change in their own risk.This willingness to pay captures both the intrinsic value of being in better health and the averted out-of-pocket costs of medical treatment and lost work and leisure time.Because estimates of willingness to pay are not available for COVID-19 cases of varying severity, we approximate these values using the approach recommended in the HHS ( 2016) Guidelines.This approach involves estimating the increase in quality-adjusted life years (QALYs) associated with averting nonfatal cases of illness and multiplying these gains by a constant monetary value per QALY.We use estimates of QALY gains per nonfatal COVID-19 case averted by age and disease severity based on Robinson, Eber, et al. (2021) and Robinson et al. (2022), who estimate the change in QALYs based on conditions similar to COVID-19 cases of differing severity.We value these gains using a constant value per QALY derived from a populationaverage VSL estimate. 9Assuming a 3% discount rate, the value per QALY ranges from $270,000 (if the VSL is $5.3 million) to $880,000 (if the VSL is $17.4 million), with the central estimate equal to $580,000 (if the VSL is $11.4 million) (HHS, 2021).
We do not assign a value to reducing the risk of an asymptomatic case. 10While asymptomatic individuals may need to quarantine if they receive a positive test result, they also benefit from an increase in immunity without experiencing the adverse health effects initially associated with illness.The value of these impacts and the extent to which they 8 For example, if an individual is willing to pay $1000 to reduce their risk of death by one-in-10,000 in a given year, that willingness to pay can be converted into a VSL of $10,000,000 by dividing by the risk change.This does not mean that the individual can or will pay $10,000,000 to guarantee their own survival.At a population level, if each individual in a group of 10,000 is willing to pay $1000 out of their own income for a 1-in-10,000 reduction in their own risk of death over a defined time period, in the aggregate they would be willing to pay $10,000,000 to avert one expected death over that time. 9The constant value per QALY is equal to the VSL divided by the present value of quality-adjusted life expectancy, calculated at the average age of the individuals included in the studies that underlie the VSL estimates.See HHS (2016,2021)  are counterbalancing is difficult to ascertain.In addition, the long-term impacts of asymptomatic COVID-19 are largely unknown or uncertain (Boyton & Altmann, 2021).Thus, we exclude averted asymptomatic cases from our benefit calculations.
In addition to the value of preventing a death or a case of illness from the perspective of the affected individual, we include costs that would be borne by other members of society.Specifically, we include the costs of outpatient and inpatient medical treatment borne largely by private or government insurers.To estimate these costs, we rely on research on COVID-19 medical costs for fee-for-service Medicare patients (Tsai et al., 2021), which provides detail on the average costs for different types of inpatient and outpatient care.To extrapolate these costs to other insurers and age groups, we multiply by an adjustment factor based on data on average hospitalization costs across insurers (Avalere Health, 2020).11Further, we assume that not all symptomatic mild cases will seek care.Based on estimates of the proportion of symptomatic cases that are reported (CDC, 2021), we assume 29% of mild cases incur outpatient medical costs (such as testing or provider office visits).12These estimates do not include medical costs incurred after the initial acute COVID-19 episode, which may be substantial especially for those with more severe acute disease and those who develop long COVID.
Table 2 summarizes the overall values of averting fatal and nonfatal cases of illness, including estimates of individual willingness to pay and insured medical costs.Appendix B in Supplement 1 provides additional details.
The direct costs of the mandates include those associated with the vaccine itself and its administration as well as associated time losses.We assume two doses per vaccinated individual, given that more than 97% of the U.S. population has chosen one of the available two-dose options (the Pfizer-BioNTech or Moderna vaccine) (CDC, 2022c).Based on CMS (2021), we assume a cost of $40 per dose for the vaccine and its administration plus $50 in staff time to plan and arrange for vaccination, for a total of $130 per additional vaccinated individual.
In addition, we include two types of time losses that accrue to the employee.The first is time spent getting the vaccine, which we assume is 1 hour per dose or 2 hours total, including scheduling, transportation, and wait time.The second is the time lost to adverse reactions.OSHA (2021a) estimates that these reactions lead to 0.36 days of administrative leave per vaccinated individual across both doses on average.We apply this rate to all waking hours (16 hours) to represent the loss in leisure, unpaid (household) labor, and paid work for a loss of 5.76 hours on average.Thus, the time loss per additional vaccinated employee totals 7.76 hours.
The value of changes in time use depends on the extent to which the change is pleasurable or unpleasurable and on the extent to which the time would otherwise be used for paid work or other activities (Baxter et al., 2017).For simplicity, we value these time losses at the U.S. average hourly wage rate of $27.07 as of May 2020, as reported by the U.S. Bureau of Labor Statistics (2021).The overall value of time losses thus averages $210 per vaccinated individual.Adding these losses to the costs of administering the vaccine itself, the total cost per vaccinated individual is $340.Note that these estimates include direct costs only; as discussed later, we do not estimate likely additional economic consequences of the vaccination requirements-some of which may be positive and some negative.

NET BENEFITS OF EMPLOYER VACCINE MANDATES
To determine the potential net benefits of these four U.S. employer vaccination mandates, we compare the benefits of averting COVID-19 cases and deaths to the costs of increased vaccination.We simulate disease dynamics over a 6-month period (from February 1, 2022 to July 31, 2022), without and with the mandates, estimating the potential health impacts of the mandates under several pandemic trajectories.
In the following, we first discuss the increase in the number of fully vaccinated adults potentially attributable to the mandates.We then present our estimates of the health impacts of the mandates and the total costs and benefits.

Increase in vaccinated workers
Evaluating the impacts of the mandates requires estimating the number of people likely to be vaccinated without the mandates over the period assessed for comparison.Although research on other COVID-19 vaccine mandates finds that they spur increased vaccination rates (Karaivanov et al., 2022;Oliu-Barton et al., 2022), the size of the effect varies depending on the share of the population already vaccinated, the degree to which individuals and organizations comply with the requirements, the details of the requirements and the allowed exemptions, and the pandemic trajectory (Mills & Rüttenauer, 2022).In the absence of the U.S. employer mandates, additional people would likely still become vaccinated, for example because of concerns about the emergence of a more dangerous variant, the implementation of vaccine mandates at the local or firm level, or requirements to be vaccinated to participate in certain activities (such as attending a concert) or visit certain venues (such as some restaurants).In addition, social norms may play an important role.As more people become vaccinated, vaccine hesitancy may decrease.We estimate that the U.S. employer mandates covered 86.7 million workers, based on federal workforce data from the U.S. Office of Personnel Management (OPM, 2021), healthcare worker data from CMS (2021), and federal contractor and private sector employer data reported by OSHA (2021a, 2021b) (see Appendix B in Supplement 1 for estimated age distribution).Most (85%) of the covered workers were subject to the private sector employer mandate.
In the without-mandates scenario, we assume that vaccination rates among non-healthcare workers, including federal employees, federal contractors, and private sector employees, are equal to population-level rates.Vaccination rates among healthcare workers are typically higher, although significant disparities in vaccine uptake exist among those who work in different health care settings (CMS, 2021;Farah et al., 2022;OSHA, 2021a).Based on reports of vaccination coverage among hospital-based healthcare personnel (Reses et al., 2021), we estimate that healthcare workers were about 12% more likely to be vaccinated than the rest of the working-age population when the mandates were announced; we assume that this relationship persists under the without-mandates scenario. 13As of October 2021 (i.e., around the time the mandates were announced), about 64% of the U.S. workingage population (18−64) was fully vaccinated (CDC, 2022a).This is likely an underestimate of the vaccination rates that could have been expected by the time the mandates were fully in effect.Thus, we use the age-specific vaccination rates observed on January 31, 2022, as the "benchmark" estimate of the rates for non-healthcare workers in the withoutmandates scenario, with the 12% upward adjustment in the case of Medicare and Medicaid providers and suppliers.We recognize that observed rates as of January 31, 2022 include 13 According to Reses et al. (2021), by mid-September 2021, 30% of hospital-based healthcare workers were not vaccinated, compared with 37.6% of the general workingage population.Thus, 70 62.4 ≃ 1.12.some vaccinations attributable to the mandates, but expect the effect of the mandates was small given that (as noted earlier) all had been subject to challenges and the largest (the OSHA regulation) had been withdrawn. 14e rely on research reported in OSHA (2021a) and CMS (2021) to determine the additional number of federal contractors, private sector employees, and healthcare workers that will be vaccinated under the with-mandates scenario (see Appendix C in Supplement 1).We use OSHA estimates for both private sector employees and federal contractors, given uncertainty about the extent to which individual firms will be covered by the OSHA regulation or by the contractor executive order.Based on estimates of vaccine confidence, religious and medical exemptions, the coverage of existing state-or firm-level mandates, and the extent to which firms will allow testing in lieu of vaccination, OSHA projects that 89.4% of all covered workers will be vaccinated under the mandate. 15CMS projects that 98.9% of healthcare workers will be vaccinated under its mandate, based on the impact of previous state and organizational COVID-19 vaccination requirements for these workers.For federal workers, we rely on vaccination rates provided by the White House in December 2021, according to which 92.5% of covered federal employees were estimated to have received at least one COVID-19 vaccination dose as of December 8, 2021 (White House, 2021).We stratify these overall projections by age group by assuming that the age-specific increase in vaccination is proportional to the proportion of unvaccinated individuals in the without-mandates scenario. 16n total, we estimate the mandates will increase the vaccination rate among covered employees by 18.2 percentage points, or about 15.8 million individuals.When added to the estimated number of adults vaccinated nationally as of January 31, 2022, overall coverage increases from 74.7% to 79.4% of the U.S. population aged 18 and older and from 64% to 68% of the overall U.S. population.Most of this increase is attributable to the OSHA mandate for private sector employees, which covers a much larger population than the other mandates.Table 3 summarizes the overall number of vaccinated employees with and without mandates by employee category.Appendix B in Supplement 1 reports the percentage of vaccinated individuals by age group in the without-mandates and with-mandates scenarios.

Health impacts
As discussed earlier, we estimate the number of COVID-19 cases of differing severities and deaths averted due to  F I G U R E 3 Deaths averted (in thousands) and corresponding net benefits (in $ billions) with the mandates as a function of the reproduction number (y-axis) and of the proportion of the population with vaccination-acquired or infection-acquired immunity (x-axis).
Note: "Low" immunity corresponds to 20% vaccine effectiveness against infection and 10% of the population protected against re-infection because of past infection."High" immunity corresponds to 90% vaccine effectiveness against infection and 40% of the population protected against re-infection because of past infection.
the increase in the number of individuals fully vaccinated over a 6-month period.Because the future path of the pandemic was perhaps the most significant uncertainty at the time the mandates were issued, we vary associated parameters to illustrate the effects of this uncertainty.We vary the reproduction number from one to five, vaccine effectiveness against infection from 20% to 90%, and the share of the population with infection-acquired immunity from 10% to 40%. Figure 3 (left panel) and Appendix Figure B1 in Supplement 1 summarize the simulation results in terms of, respectively, deaths and cases of illness averted as a function of the reproduction number (y-axis) and of the proportion of the population with either infection-acquired or vaccinationacquired immunity (x-axis).The proportion of the population with immunity depends on the effectiveness  of the vaccine and on the proportion of the population in the recovered states at the beginning of the simulation, R 0 .We vary these variables linearly and simultaneously from their respective lower bounds to their respective upper bounds.Thus, the "low" immunity case corresponds to  = 20% and R 0 = 10%, while the "high" immunity case corresponds to  = 90% and R 0 = 40%.The middle point in the x-axis corresponds to  = 55% and R 0 = 25%, and so on.The number of deaths averted goes from a few dozen, if the reproduction number is low and the share with immunity is high, to more than 20,000 if the variant is very infectious and the share of the population with immunity is low.The number of total cases averted ranges from a few hundred to 5 million.
To highlight the importance of uncertainty in the pandemic trajectory on the net benefits of the mandates, we consider two illustrative pandemic paths from among the ranges considered above.The first path assumes that at the beginning of the simulation, the pandemic will soon fade toward an endemic state.A large share of the population has infection-or vaccination-acquired immunity (R 0 = 35%,  = 80%, and  0 = 2); only a small surge of infections occurs before new cases rapidly diminish, and as a result the health benefits of the mandates are limited.The second path assumes that at the beginning of the simulation period, a new variant emerges that is more infectious and for which  existing vaccines and past infection are less protective (e.g., an Omicron-type variant; R 0 = 15%,  = 40%, and  0 = 3).Note that the scenario with a declining infection rate (i.e., a low reproduction number, combined with a high proportion of infection-acquired immune individuals and high vaccine effectiveness) is consistent with reaching herd immunity, while the scenario with a growing pandemic (i.e., a high reproduction number, a low proportion of infection-acquired immune individuals and low vaccine effectiveness) is a situation in which herd immunity has not been reached.17Figure 4 depicts the number of active infections over time without the mandates for the two illustrative scenarios.
In contrast to the fading pandemic, the emergence of a new variant leads to a large surge of infections, and the health benefits of the mandates are substantial.Table 4 reports the number of cases and deaths averted by age group for each pandemic scenario over the 6-month simulation period.Overall, with a fading pandemic, only a few hundred deaths are prevented, while with the emergence of a new variant, 19,000 deaths are avoided.Table 4 also reports the number of additional vaccinations by age group.In absolute terms, most of the health benefits accrue to individuals in the 50−64 age group due to their relatively high risk of severe illness and death from COVID-19 and the estimated increase in vaccination uptake in this group with the mandates.Although relatively few additional vaccinations occur among individuals in the 65-74 age group (given that many in this age range are no longer employed), these individuals accrue a large reduction in mortality risk, especially in the presence of a more dangerous variant.Non-working-age populations (0−17 and 75+) benefit from the mandates as well, due to the indirect protection conferred by a higher vaccination rate in the population.

Net benefits
Figure 3, right panel, shows the net benefits of the mandates (in billions of dollars) as a function of the reproduction number and of the proportion of the population with infection-acquired or vaccination-acquired immunity, using our central estimates of benefit values from Table 2 and estimated costs of $340 per additional vaccinated individual.Nonfatal illnesses dominate the number of averted cases, which are mostly asymptomatic or relatively mild.The value per death averted is an order of magnitude greater than the value for even the most critical nonfatal case.Thus, a close correlation exists between the number of deaths averted and the size of the net benefits.The pandemic trajectory substantially affects net benefits, suggesting that the timing of the mandates relative to this path is an important determinant of the results.However, this timing is particularly difficult to predict for a relatively unfamiliar virus such as SARS-CoV-2.If, by the time the mandates are fully enforced, the reproduction number is low and the share of the population with vaccination-or infectionacquired immunity is high, few cases and deaths are averted, and the mandates yield very small, and possibly negative, net benefits.By contrast, if a new viral strain emerges that is more transmissible (i.e., has a high reproduction number) and for which existing immunity is not very protective, then the net benefits from the mandates are substantial (about $300 billion from Figure 3).A simple back-of-the-envelope calculation using the central VSL estimate suggests that if the per-person cost of vaccination is $340 and we ignore nonfatal cases, the mandates would need to prevent at least 470 deaths to break even (i.e., to yield zero net benefits).If the per-capita cost doubles (to $680), the breakeven point is 941 deaths.
Table 5 summarizes the net benefits for the two illustrative pandemic scenarios.With a fading pandemic, net benefits are negative.They reach $241.6 billion with a new, more dangerous variant.Table 5 also highlights the sensitivity of net benefits to the high and low VSL estimates discussed earlier and tests the effects of increasing vaccination costs to account for potential unforeseen factors.Not surprisingly, with the threat of a new variant, the net benefits of the mandates are substantial, regardless of which cost and benefit values are adopted (see also Appendix Figure B2 in Supplement 1).
Because COVID-19 deaths occur disproportionally among older adults, some previous analyses of lockdowns, social distancing, and other policies (e.g., Greenstone & Nigam, 2020) have adjusted VSL for age and ignored other potentially counterbalancing factors.As discussed in Robinson, Sullivan, et al. (2021), the relationship between age and VSL is uncertain.Robinson et al. find that alternative approaches to adjusting for age lead to average VSL estimates that are 42% and 78% of the central estimate, given the distribution of COVID-19 deaths throughout the U.S. population.Thus, our low value for VSL (which is 46% of our central estimate) leads to results that resemble the effects of using lower estimates to adjust VSL solely for age.
In the previous sections, we explore the effects of uncertainty in the pandemic pathway and in the benefit and cost values.Several other model parameters are also subject to significant uncertainty.Table 6 reports the results of additional sensitivity tests.In particular, we focus on the withoutmandates population-wide vaccination rates, the vaccination rates among children, the effectiveness of the vaccine, and the duration of immunity.Our estimate of vaccine uptake due to the mandates (15.8 million additional vaccinated individuals) depends in part on the assumptions about vaccination rates in the without-mandates scenario.If vaccination rates without mandates were lower (e.g., if we used the rates observed in October 2021 rather than those observed in January 2022), but we use the same approach to estimate the change in rates due to the mandates, the associated increase in vaccinated individuals is 21 million.Under this scenario, estimated benefits would substantially increase even if no new variant emerges.When predicting the without-mandates vaccination rates, the largest uncertainty concerns vaccination uptake among young children because they became eligible only in the fall of 2021 (HHS, 2022a).Although the mandates do not directly affect children, the rates at which they are vaccinated affects the spread of infection throughout the population under each scenario.However, assuming lower vaccination rates among children (i.e., the rates observed in October 2021) does not substantially affect the estimated net benefits of the mandates.
Throughout the analysis, we assume that vaccines are very effective at preventing severe disease independently of the dominant variant.If the vaccines do not confer additional protection against severe disease ( = 0), that is, if protection against severe disease were reduced to the same level as protection against infection, net benefits would increase.This results from nonlinearities in the epidemiological model and in particular from the result that, compared with a scenario with  > 0, when  = 0 the number of deaths increases faster with low vaccination rates (without-mandates scenario) than with higher overall vaccination rates (with-mandates scenario).Paradoxically, this suggests that the benefits of increasing vaccination rates through mandates are larger with a vaccine that is less effective at inducing direct protection against death.Finally, we test the importance of our assumption that mean duration of immunity is six months.If vaccination-and infection-acquired immunity wanes after three months, the net benefits of the mandates are larger in the case of a fading pandemic due mostly to the increase in the number of deaths averted.Due to the chosen time horizon (six months), the simulations capture only one wave of infections.If the duration of immunity shortens, a larger wave of infections occurs because more people are likely to have lost their immunity.Consequently, the potential benefits of increasing the number of vaccinated individuals increase for the period studied.In contrast, in the presence of a new variant, the benefits of the mandates decrease.Thus, the correlation between timing of the infection wave and duration of immunity matters.

DISCUSSION AND CONCLUSIONS
This study investigates the COVID-19-related health benefits and direct costs of four employer vaccination mandates issued by the U.S. federal government in September-November 2021 as if they had been implemented as intended.Our analysis suggests that the benefits exceed the direct costs under various assumptions regarding the pandemic trajectory, except under a scenario in which the mandates are implemented when the pandemic is fading.The net benefits are particularly large in the presence of a new variant that is more infectious and for which vaccines and previous infection are less effective at preventing contagion.Thus, the main benefit of the mandates may be to prevent the potential catastrophic consequences that a new variant could pose.
Based on the results in Figure 3, we estimate that the gross benefits of the mandates range from $10 to more than $20,000 per additional vaccinated person, depending on the status of the pandemic.Most of the benefits accrue to the newly vaccinated individuals via the direct protection vaccination provides.However, the mandates also confer indirect protection to individuals not covered by the mandates (e.g., children and older adults) by reducing transmission.
Herd immunity is a common rationale for increasing vaccinations: Once a sufficiently large proportion of the population is immunized, the rate of new infections declines and the effective reproduction number falls below one, leading the pandemic to begin to wane.In our analysis, the fading pandemic represents a scenario in which herd immunity is reached.The growing pandemic corresponds to a situation in which herd immunity has not been achieved.Our simulations show that the net benefits of the vaccine mandates are very small (perhaps negative) under the former scenario, while they are substantial under the latter scenario.By increasing the number of individuals who are vaccinated, the likelihood of reaching the herd immunity threshold increases.However, the emergence of new variants for which previous vaccinations and infections are less protective has made this threshold difficult to reach in the case of COVID-19.
Our analysis has several limitations.Most importantly from a policy perspective, we do not compare the effects of the mandates with other strategies to encourage vaccinations or to provide other types of protection.The primary difference between mandates and other vaccine promotion efforts is that mandates require rather than encourage vaccination.As such, they likely spur faster and perhaps greater increases in vaccination rates.However, as ongoing litigation illustrates, mandates may also increase social discord and raise issues about government use of coercive tactics.In addition, the mandates may provoke resentment and distrust of the vaccines and the government.Our analysis does not account for these concerns, which likely counterbalance the positive benefits of mandates to an unknown extent.
We also do not compare vaccination policies with other protective measures such as masking, testing, social distancing, ventilation and filtration, or activity limitations (including lockdowns).Such policies may be useful substitutes or supplements to vaccination requirements.More work is needed to assess the costs and benefits of these policies so they can be compared with the impacts of vaccination mandates or promotion efforts.
One challenge in assessing policies to promote vaccination and other types of protection is that differences in analytic approach can obscure or exaggerate differences in impacts.Applying consistent analytic methods and assumptions across a suite of policy options aids in determining the most desirable combination of actions.Our methodology, including the epidemiological model and the benefit-cost analysis framework, can be adapted for use in determining the net benefits of other pandemic-related interventions to promote comparability.
Another challenge is the need to inform policy decisions at a time when limited data are available to estimate several parameter values.While we use sensitivity analysis to examine the effects of key uncertainties, we know relatively little about the likelihood that each parameter estimate is reasonably accurate.As ongoing data collection and analysis yield new findings, many of the assumptions and estimates in our modeling can be refined.For example, new survey and other data are becoming available that will support more sophisticated modeling of the effects of mandates on vaccination rates, including consideration of variation by age, occupation, and geographic location.In addition, our benefit values are derived from research on other similar illnesses and causes of death.As more research becomes available that directly addresses the effects of COVID-19, these values can be refined.Emerging research will also allow analysts to estimate the likelihood of long COVID and the economic value of averting its effects.Finally, many parameters of the epidemiological model can be updated as new data become available on inputs such as the degree and duration of vaccinationacquired and infection-acquired immunity, the effectiveness of vaccines against new variants, the likelihood of mortality among the unvaccinated, and so forth.
More generally, our estimates likely understate the net benefits of the mandates given that we limit the analysis to a 6-month time frame and consider a limited set of effects.Additional benefits of increased vaccination may include reduced public and private expenditures on outbreak containment and response, lower likelihood that other variants will emerge, increased resources available to treat other health conditions, and improved mental health.Increased vaccination rates may also improve educational outcomes by permitting schools to stay open, spur economic activity and growth by reducing business closures and increasing consumer confidence and demand, and improve social wellbeing by decreasing isolation (Bloom, Cadarette, & Ferranna, 2021).
In addition to highlighting the need to assess other policies and a broader range of effects within the COVID-19 context, our analysis highlights the need to assess alternative policies for addressing pandemics well in advance.Once a virus reaches pandemic proportions, the need to act quickly leaves little time for careful assessment.Case studies of the effects of alternative policies for addressing hypothetical pandemics with differing characteristics would promote improved decision-making in times of crisis.In addition, developing models that can be used to address likely pandemic pathways in the face of substantial uncertainty seems essential.

F
I G U R E 2 Diagram of the susceptible, exposed, infectious, recovered (SEIR) model.

Note:
Vaccinated employees as a percentage of covered employees are reported in parentheses.Source: Authors' calculations based on OPM (2021), OSHA (2021a, 2021b), CMS (2021) for the number of covered employees; CDC (2022c), Reses et al. (2021) for the number of vaccinated employees without mandates; OSHA (2021a), CMS (2021), White House (2021) for the number of vaccinated employees with mandates.
for more details.10Asymptomaticrates vary by age group and range from 33% to 34% for older adults to 60% for children (see Supplement 1 Appendix A).Value per illness and death averted (2020 US$) For nonfatal cases, the exhibit provides the minimum and maximum estimates across age groups.Appendix B in Supplement 1 provides age-specific values for individual willingness to pay and insured medical costs.The monetary values reflect a 3% discount rate and 2020 income levels based on HHS (2021).
Projected change in the number of vaccinated employees TA B L E 3

TA B L E 4
Number of cases and deaths averted by age group in two illustrative pandemic scenarios