Efficient policy interventions in an epidemic

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Abstract

In the context of an epidemic, a society is forced to face a system of externalities in consumption and in production. Command economy interventions can support efficient allocations at the cost of severe information requirements. Competitive markets for infection rights (alternatively, Pigouvian taxes) can guarantee efficiency without requiring direct policy interventions on socio-economic activities. We demonstrate that this is the case also with moral hazard, when the infections cannot be associated to the specific activities which originated them. Finally, we extend the analysis to situations where governments have only incomplete information regarding the values of the parameters of the infection or of firms’ production.

Introduction

A society hit by an epidemic is forced to face a complex system of externalities in consumption and in production. The epidemic diffuses by social contacts between agents, which are an essential by-product of production and consumption-leisure activities. Rational agents and profit maximizing firms, in this society, will take into account the individual costs of the infections generated by their choices but will not internalize the externalities of their actions. As a consequence, firms will over-produce, agents will over-consume, and in turn infections will be more widely spread.

Policy interventions will generally be necessary to design efficient mechanisms to limit infections while allowing for some economic activity. In the course of the SARS-Cov-2 epidemic the most frequently adopted non-pharmaceutical policy interventions were partial lockdowns; that is, command economy interventions directly restricting firms and agents’ behavior, selecting which firms produce how much and which agents are allowed to engage in social interaction activities and how much so. In several instances, different socio-economic activities have been ranked in terms of their infectiousness and their opening staggered.

But command economy interventions are not the only possible mechanism to implement efficient allocations in general, nor are the mechanism with minimal information requirement to be implemented. As for other types of externalities, e.g., pollution, markets for the rights to externality-producing activities, or alternatively, Pigouvian taxes, can be set-up which induce agents and firms to consume and produce efficiently. The cost of infection rights or the Pigouvian taxes induce individuals and firms to limit the kinds of activities that are more likely to produce infections. 1

An efficient Pigouvian mechanism requires firms to pay a tax proportional to the infections occurring in the workplace and, similarly, agents to pay a tax proportional to the infections occurring in the context of their consumption-leisure activities. Alternatively, this mechanism can be implemented via a system of taxes on the socio-economic activities which give rise to infections. In practice, taxes on firms’ production and on individual agents’ consumption-leisure activities might in fact be easier to implement than taxes directly on infections. In this case, efficient tax rates depend on the potential to spread infections and thus would be higher on firms whose production process requires close contact between workers for prolonged periods, e.g., on manufacturing firms with large assembly lines; or for firms whose abatement costs are higher, like firms relatively concentrated in dense cities whose workers, e.g., are likely to use public transportation. Tax rates would be lower instead on firms who rely more on remote working, e.g., on firms in the service, technology, and education sectors. Similarly, consumption-leisure activities like large concerts and sport events would be subject to higher tax rates. Furthermore, the tax system should include rebates based on the abatement measures that are introduced in the context of production and consumption-leisure activities, such as, e.g., mandatory testing, distancing, and use of face masks.

In this paper we study the design of these alternative mechanisms, say markets for infection rights or Pigouvian taxes, in the context of a simple model of a society hit by an epidemic. We determine the conditions under which these mechanisms decentralize efficient allocations in this environment. We also characterize the properties of these mechanisms. In particular, we characterize the equilibrium prices of infection rights or, equivalently, the optimal Pigouvian taxes on economic activities.

We study in detail the information requirements for the implementation of such mechanisms. We demonstrate that efficiency can be attained even when infections cannot be associated to the activities which generated them; that is, to the production choices of specific firms or to the social interaction activities of specific consumers. In this environment, the limited information on the source of the infection generates a problem of moral hazard in teams. Nonetheless, we show that the decentralization of the efficient allocation via markets for infection rights does not require this fine degree of observability at the individual level, only the observation of the average infection rate suffices. Finally, we extend the analysis to situations where governments have only incomplete information regarding the values of the parameters of the infection process or of firms’ production processes. In this case efficiency cannot be attained and we compare the welfare properties of i) setting the quantity of infection rights to be traded, ii) setting their prices or taxes; iii) command economy interventions.

A few very recent papers have introduced rational, optimizing agents in the framework of epidemiological models, highlighting the importance of individual behavior in response to policy interventions and the trade-offs between health and economic costs; see e.g., Acemoglu et al. (2020); Alvarez et al., 2020, Argente et al., 2020 Atkeson (2020); Bisin and Moro, 2020, Eichenbaum et al., 2020 Farboodi et al., 2020, Toxvaerd, 2020. In particular, Rowthorn and Toxvaerd (2020) provide a theoretical analysis of taxes and subsidies which decentralize efficient allocations in an epidemiological model of the dynamics of an infection. Kaplan et al. (2020) provide a quantitative analysis of the distributional effects of taxes on production and consumption activities that generate infections. Also, Bethune and Korinek (2020) provide a quantitative assessment of the individual and social cost of infections. The novelty of our analysis relative to this work consists in our emphasis on the characterization of the informational requirements of measures that do not rely on the direct control of some individual choices but rather on the design of additional markets (or taxes) which can induce agents to internalize the social costs of their behavior.

Extensive previous work along these lines has concentrated on other externalities, notably pollution; see for instance, Dales (1968) and Van den Bergh (2002). The case of the externalities arising in an epidemic is distinct from those typically considered in analyses of pollution rights in that i) infections occur in and affect both the production and the consumption-leisure side of the economy; hence prices of rights or taxes implementing efficient allocations need to be designed to affect both the production choices determining the supply of goods and the consumption-leisure choices which influence the demand for various kinds of goods; and ii) infections have direct and immediate negative effects, in terms of labor lost and disease, on both firms and agents, who then partially internalize the negative consequences of their behavior even with no markets for rights nor Pigouvian taxes. As a consequence, for instance, we show the Pigouvian taxes on firms are designed so that they internalize the additional marginal benefits of infection abatement measures (beyond those on firms’ output level), such as the lower costs for the public health system and the higher utility of workers’ due to their improved health status. Similarly for the tax levied on each consumer, which reflects the additional costs - in terms of output loss and health expenses - of the consumer getting infected because of his/her social interaction choices, as well as the costs induced by the transmission of his/her own infection to other agents. Especially when allowing for heterogeneity in technologies and consumers, the characterization of these taxes offers novel and interesting insights, as it must reflect the variety of effects resulting from the rich web of interactions between the different kinds of production and the consumption-leisure choices of different individuals.2

The abstract nature of the paper does not lend itself easily to the evaluation of specific public health policy proposals, besides suggesting the general consideration of economic incentives, via taxes and markets for rights, alongside direct interventions, via e.g., selective lockdowns. It is noteworthy that an efficient system of Pigouvian taxes would include (i) subsidies on abatement measures in firms and on the use of protective equipment, like masks, and protective behavior, like social distancing, testing, vaccination, that limit infections and their spread; (ii) taxes on production and consumption-leisure activities; as well as (iii) lump-sum transfers to all agents and firms, to rebate to them the cost of those externalities that are non pecuniary (as, for instance, the disutility of getting infected).

Importantly, we consider an environment where firms are required to provide full insurance of workers in the labor market, in that they receive full wages independently of whether they are healthy or infected (and hence do not work). This induces firms to internalize the costs of infections occurring in the workplace, given by losses of productivity, but also to bear these costs for the infections that are instead the result of workers’ social interaction choices. The combination of these taxes, subsidies, and transfers might then configure, for instance, a labor market where firms’ abatement measures include leaving a fraction of the workers at home - thereby limiting infection and saving on taxes - without consequences on the workers’ budget constraint. The most interesting implications in terms of public health policy proposals obtain when we allow for heterogeneity in the firms’ and the agents’ characteristics. In that case we find that the same tax rate on infections at work applies to all types of firms, no matter how important their sector is in the production system, nor how different is the cost of reducing these infections for the different firms3. In contrast, to control the infections generated by the agents’ consumption-leisure activities it does not suffice to impose a common tax on individuals for the infections generated by such activities; personalized taxes are needed, to reflect the differences in health treatment costs and in wealth across agents, as well as in the levels of centrality or influence of consumers in the system of social interactions in the society.

Section snippets

Economy

We describe a simple abstract society hit by an epidemic.

Agents. The society is populated by H ex-ante identical (representative) agents and F identical (representative) firms. Each agent supplies labor inelastically and receives utility from consumption of a private good c and from his/her level l of social interaction activities. The agent can be infected at work or while interacting socially. Let Il denote the probability he/she is infected with his/her social interaction activities. We

Market implementation of the efficient allocation

In this section we show how the efficient allocation can be implemented via markets, designed to induce firms to produce, and consumers to choose social interaction activities, efficiently.

We shall discuss several different implementation mechanism, but it is convenient to set markets for infection rights as the benchmark.

Informational requirements for efficiency

In this section we argue that markets for infection rights (and hence Pigouvian taxes) are generally superior to command economy interventions, in that they require less information to be implemented. To this end, we study the informational requirements necessary to achieve efficiency in a society hit by an epidemic. We compare the informational requirements necessary for command economy interventions with those necessary to implement markets for infection rights. We also compare the relative

Conclusions

In this paper we study the role of markets for infection rights or, equivalently, Pigouvian taxes in an epidemic. In these conclusions we mention and briefly discuss several possible extensions of interest.

First of all, it is of interest to explicitly account for the dynamics of the epidemic, e.g., by integrating an epidemiological model into the analysis. In a dynamic environment the abatement decisions by firms and consumption-leisure choices of consumers affect not only current but also

Declaration of Competing Interest

None.

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    We wish to thank Ben Moll, Flavio Toxvaerd and GianLuca Violante for helpful discussions. We are also grateful to the Co-Editor, Joseph Shapiro, and three anonymous referees for very helpful comments.

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