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Nber Working Paper Series Vaccine Hesitancy NBER WORKING PAPER SERIES VACCINE HESITANCY, PASSPORTS AND THE DEMAND FOR VACCINATION Joshua S. Gans Working Paper 29075 http://www.nber.org/papers/w29075 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 July 2021 Thanks to Ajay Agrawal, Avi Goldfarb and Richard Holden for helpful discussions. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2021 by Joshua S. Gans. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Vaccine Hesitancy, Passports and the Demand for Vaccination Joshua S. Gans NBER Working Paper No. 29075 July 2021 JEL No. I12,I18 ABSTRACT Vaccine hesitancy is modelled as an endogenous decision within a behavioural SIR model with endogenous agent activity. It is shown that policy interventions that directly target costs associated with vaccine adoption may counter vaccine hesitancy while those that manipulate the utility of unvaccinated agents will either lead to the same or lower rates of vaccine adoption. This latter effect arises with vaccine passports whose effects are mitigated in equilibrium by reductions in viral/disease prevalence that themselves reduce the demand for vaccination. Joshua S. Gans Rotman School of Management University of Toronto 105 St. George Street Toronto ON M5S 3E6 CANADA and NBER [email protected] 1 Introduction Vaccine hesitancy, whereby individuals elect not to be vaccinated, has been a long-standing issue in public health. During the Covid-19 pandemic, such factors have meant that the adoption of vaccines has been short of what might generate lasting herd immunity in many populations. This has led to the creation of incentives to stimulate adoption, education campaigns to provide information on vaccine safety and calls for vaccine passports. One factor that has been documented to counter vaccine hesitancy has been the preva- lence of the relevant virus/disease itself. Oster (2018) found that an outbreak in a county in the year prior led to a 28 percent increase in childhood vaccinations. This raises an interest- ing question: If vaccine adoption reduces prevalence, does that very adoption drive observed vaccine hesitancy? And if there is an endogenous behavioural effect, does this change the impact of proposed policies to counter hesitancy? This paper examines this issue. In so doing, vaccine adoption is endogenously driven by prevalence and vice versa. In addition, the underlying model is a behavioural epidemiolog- ical model where individuals can take costly social distancing actions to manage their own infection risk if they remain unvaccinated. The simple model presented here demonstrates that this can have a significant impact on the efficacy of various interventions to counter hesitancy. Blanket incentives/education for vaccination involve infra-marginal effects that are costly which limit their desirability as a means of encouraging vaccination. More crit- ically, it is demonstrated that vaccine passports are ineffective (in this model, completely ineffective) at improving vaccination rates and may reduce them as the restrictions imposed by passports reduce prevalence. This implies that while vaccine passports (or credentials) may be useful in assuring others that someone has a lower risk of being infectious, they are unlikely to be useful as a punitive tool to counter vaccine hesitancy. The literature on the economics of vaccines has proven more subtle than the textbook treatments of vaccination would suggest. These often state that vaccine adoption is, liter- ally, a textbook example of a positive externality and so requires government intervention to encourage adoption and reduce free-riding. But as Francis (1997) demonstrated, when em- bodied within an epidemiological model of viral spread, those externalities do not necessarily manifest themselves in terms of socially suboptimal vaccinations. Indeed, he shows that with homogeneous agents and a perfect vaccination but for their personal cost of vaccination, the decentralised and socially optimal vaccination outcomes coincide.1 This paper builds on Francis (1997) and present a model with his underlying structure 1Chen and Toxvaerd (2014) demonstrate that when agents are heterogeneous and vaccination is imper- fect, this equivalence not longer holds. See also Gersovitz (2003) and Toxvaerd and Rowthorn (2020). 2 of homogeneous agents but for vaccination costs and the introduction of a perfectly effec- tive vaccine. But as policies such as vaccine passports involve costly restrictions on agent activity, a behavioural model is built where agents endogenously choose their activity/social distancing (using a similar structure to Toxvaerd (2020) but with discrete time).2 Auld and Toxvaerd (2021) present preliminary evidence that vaccinations did impact on people's social activity in the Covid-19 pandemic. The focus here is not on the social optimality of any policies per se but their impact on total vaccination take-up. The paper proceeds as follows. First, the standard susceptible-infected-recovered (or SIR) model is presented followed by its behavioural analog. Second, vaccines are introduced and the equilibrium with both endogenous activity and vaccine adoption is analysed. To resolve technical issues associated with non-stationarity, the analytical shortcut outlined in Gans (2020b) is utilised. Finally, various policies are explored and their impact on vaccination rates is characterised. A final section concludes with a list of the paper's obvious shortcomings in the hope of infecting someone to overcome them. 2 The Standard SIR Model Let fS(t);I(t);R(t)g denote the shares (and levels) of the population (normalised to be of size 1 over a continuum of agents) who are either susceptible to the virus, infected with the virus or removed (i.e., recovered or dead) from the virus at time t ≥ 0. It is assumed that time is discrete. In the SIR model, these variables are assumed to evolve according to the following dynamic equations: S(t + 1) − S(t) = −βS(t)I(t) I(t + 1) − I(t) = (βS(t) − γ)I(t) R(t + 1) − R(t) = γI(t) Here γ is the probability that an infected person will be removed in any given period while β is the probability that a susceptible person will become infected by an infected person in a given period. Observe that the number of infections in the population will be falling (i.e., β β I(t+1) < I(t)) if γ S(t) < 1 and will be rising (i.e., I(t+1) > I(t)) if γ S(t) > 1. The LHS of β these inequalities is the effective reproduction number, Rt. Since S(0) ≈ 1, then R0 = γ . R0 2Talam`asand Vohra (2020) also show that behavioural effects can impact on vaccination by changing the network of interactions { similar in spirit to Kremer (1996). However, their focus is on whether imperfect vaccines may create increased prevalence rather than on vaccine adoption per se which is costless in their model. 3 is the basic reproduction number which has the interpretation as the total expected number of infections one infectious person will create over the life of their infection. Vaccination is a way of moving people from the susceptible to the recovered population segments. It is assumed here that vaccination is perfect. Of key interest in this model is the herd immunity threshold that is reached when S(t) becomes low enough, through either acquired or vaccinated immunity, so that Rt < 1. This threshold, for 1 − S(t) is 1 − 1 . A goal of many vaccination programs is to ensure that the total of the recovered R0 and vaccinated shares exceeds this threshold allowing the pandemic to abate without any further interventions.3 3 The Behavioural SIR Model The fact that the standard SIR model lacked behavioural elements has not been lost on epidemiologists. In particular, it has been recognised that people might observe current prevalence (that is, I(t)) and modify their own behaviour so as to reduce infection risk. However, the mathematical epidemiologists have typically taken what economists would call a `reduced-form' approach to this. For instance, they might posit a variable, x 2 [0; 1], that is a filter reducing the impact of β on new infections. That variable is then assumed to be a decreasing function of I(t); e.g., x(I(t)).4 3.1 Literature Review Work in economics to include behavioural elements in models of epidemics started in earnest with the study of the spread of AIDS; e.g., Philipson and Posner (1993), Geoffard and Philip- son (1996), Kremer (1996) and empirically by Greenwood et al. (2019). The pioneering treatment that first introduced forward-looking, rational economic agents into epidemiolog- ical models was provided by Gersovitz and Hammer (2004). They explored the different effects that prevention versus a treatment might have on the dynamics of epidemics. In doing this, they were able to clarify the externalities that may be present and the efficacy of various forms of interventions (including taxes and subsidies) to improve social welfare. The literature is now extensive and has been reviewed by Philipson (2000) and Gersovitz (2011) and, more recently, Gans (2020b) and McAdams (2021). The models of Toxvaerd (2020) 3This is not to say that further vaccination beyond this threshold may be worthwhile as infections and health costs can continue thereafter. See Gans (2020c) for a discussion. 4See for example, Eksin et al. (2019) who also explore assumptions where x(I(t);R(t)) is decreasing in both variables, that they argue is a model of `long-term awareness' in contrast to `short-term awareness' where x is a function of I(t) alone.
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