Optimal Vaccine Subsidies for Endemic and Epidemic Diseases Matthew Goodkin-Gold, Michael Kremer, Christopher M

WORKING PAPER · NO. 2020-162 Optimal Vaccine Subsidies for Endemic and Epidemic Diseases Matthew Goodkin-Gold, Michael Kremer, Christopher M. Snyder, and Heidi L. Williams NOVEMBER 2020 5757 S. University Ave. Chicago, IL 60637 Main: 773.702.5599 bfi.uchicago.edu OPTIMAL VACCINE SUBSIDIES FOR ENDEMIC AND EPIDEMIC DISEASES Matthew Goodkin-Gold Michael Kremer Christopher M. Snyder Heidi L. Williams The authors are grateful for helpful comments from Witold Więcek and seminar participants in the Harvard Economics Department, Yale School of Medicine, the “Infectious Diseases in Poor Countries and the Social Sciences” conference at Cornell University, the DIMACS “Game Theoretic Approaches to Epidemiology and Ecology” workshop at Rutgers University, the “Economics of the Pharmaceutical Industry” roundtable at the Federal Trade Commission’s Bureau of Economics, the U.S. National Institutes of Health “Models of Infectious Disease Agent” study group at the Hutchinson Cancer Research Center in Seattle, the American Economic Association “Economics of Infectious Disease” session, and the Health and Pandemics (HELP!) Economics Working Group “Covid-19 and Vaccines” workshop. Maya Durvasula, Nishi Jain, Amrita Misha, Frank Schilbach, and Alfian Tjandra provided excellent research assistance. Williams gratefully acknowledges financial support from NIA grant number T32- AG000186 to the NBER. © 2020 by Matthew Goodkin-Gold, Michael Kremer, Christopher M. Snyder, and Heidi L. Williams. 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. Optimal Vaccine Subsidies for Endemic and Epidemic Diseases Matthew Goodkin-Gold, Michael Kremer, Christopher M. Snyder, and Heidi L. Williams November 2020 JEL No. D4,I18,L11,L65,O31 ABSTRACT Vaccines exert a positive externality, reducing spread of disease from the consumer to others, providing a rationale for subsidies. We study how optimal subsidies vary with disease characteristics by integrating a standard epidemiological model into a vaccine market with rational economic agents. In the steady-state equilibrium for an endemic disease, across market structures ranging from competition to monopoly, the marginal externality and optimal subsidy are non-monotonic in disease infectiousness, peaking for diseases that spread quickly but not so quickly as to drive all consumers to become vaccinated. Motivated by the Covid-19 pandemic, we adapt the analysis to study a vaccine campaign introduced at a point in time against an emerging epidemic. While the nonmonotonic pattern of the optimal subsidy persists, new findings emerge. Universal vaccination with a perfectly effective vaccine becomes a viable firm strategy: the marginal consumer is still willing to pay since those infected before vaccine rollout remain a source of transmission. We derive a simple condition under which vaccination exhibits increasing social returns, providing an argument for concentrating a capacity-constrained campaign in few regions. We discuss a variety of extensions and calibrations of the results to vaccines and other mitigation measures targeting existing diseases. Matthew Goodkin-Gold Christopher M. Snyder Department of Economics Department of Economics Harvard University Dartmouth College Littauer Center 301 Rockefeller Hall 1805 Cambridge Street Hanover, NH 03755 Cambridge, MA 02138 and NBER United States [email protected] [email protected] Heidi L. Williams Michael Kremer Department of Economics University of Chicago Stanford University Kenneth C. Griffin Department of Economics 579 Serra Mall 1126 E. 59th St. Office 323 Chicago, IL 60637 Stanford, CA 94305 and NBER and NBER [email protected] [email protected] 1. Introduction Technologies that help prevent infectious diseases such as vaccines, condoms, and mosquito nets can generate positive health externalities. While standard economic models provide a justification for public subsidies of such preventive technologies, existing models provide little guidance on the appropriate magnitude of these subsidies. This gap in understanding makes it difficult for economists to provide guidance—even at a conceptual level—on both the optimal level of government subsidies for infectious disease control and the ways in which the level of such subsidies should vary across diseases. Furthermore, most existing work by economists has been oriented toward endemic diseases and policies which play out over years or decades such as vaccination campaigns to eradicate polio or circumcision to reduce the spread of HIV. However, the Covid-19 pandemic has underscored the urgency of understanding short-run policy responses to the epidemics that can result from the emergence of novel diseases or from localized outbreaks of otherwise dormant diseases such as Ebola or MERS. To address these questions, we construct a tractable model integrating epidemiological and economic considerations. For concreteness, the discussion is focused on the market for a vaccine, but the analysis applies to any technology (circumcision, bed nets, social distancing) preventing consumers from contracting a disease. Consumers and producers base their economic decisions on rational expectations of disease dynamics based on a susceptible-infected-recovered (SIR) model standard in the epidemiology literature. Section 2 adopts a long-run perspective suited to an endemic disease. Consistent with this perspective, we incorporate population turnover into the SIR model and analyze the steady-state equilibrium of the vaccine market. Section 3 shifts to a short-run perspective of a vaccine campaign introduced at a single point in time into an SIR epidemic without population turnover. Absent preventive measures, such an epidemic can rapidly peak before ulti- mately burning out, leaving some untouched. Consumers in the short-run analysis make vaccination decisions based on their probability of being infected before the disease burns out, while consumers in the long-run analysis base their decisions on the probability of infection in the steady state. For a continuum of market structures—including perfect competition, monopoly, and Cournot competition nesting these extremes—the long-run analysis generates a closed-form solution for the marginal vaccine externality in steady-state equilibrium as a function of estimable parameters including disease infectiveness, recovery rate, vaccine cost, and efficacy. A key finding is that this marginal externality is nonmonotonic in the disease’s basic reproductive ratio R0, a widely used measure of infectiveness. For sufficiently low values of R0 (technically, R0 ≤ 1), the disease dies 1 out in the steady state even without a vaccine, so there is no vaccine market and no marginal externality. For sufficiently high values of R0, vaccinating a given consumer does not provide much protection to others since they are almost certain to contract the disease from another source any- way. To be sure, a consumer’s vaccination provides a substantial social benefit when R0 is extremely high, but most of that benefit is internalized by the consumer themselves. The marginal externality on others is greatest not for extreme but for intermediate values of R0. The optimal vaccine subsidy (minimum subsidy needed to obtain the first-best quantity) is likewise nonmonotonic in R0. Hold- ing constant disease burden (the product of prevalence and harm), our results suggest that the best candidates for vaccine subsides are rarer but more serious diseases. Our crude calibrations suggest that optimal subsidies may be very large relative to current lev- els in the case of competitively supplied products. For example, the external benefit from using circumcision to prevent HIV in developing countries could justify subsidies of more than $1,000, while programs studied to date paid participants no more than $15 beyond procedure costs. For products produced by a monopoly selling directly to consumers, a per-dose subsidy may not always be a viable policy option since the minimum subsidy achieving the first best can be enormous: in our measles calibration, for example, fifteen times the harm from actually having the disease. Given plausible values for the social cost of public funds, such subsidies would be prohibitively expensive. Bulk purchase of the optimal quantity coupled with subsidized distribution may be a cheaper route to the first best. Moving from the long-run to the short-run analysis, the latter is technically more difficult because equilibrium variables no longer have closed-form expressions, requiring the Lambert W function to express analytically. Still, we are able to recover the result from the long-run analysis that the marginal externality and optimal subsidy are nonmonotonic in R0 for market structures ranging from perfect competition, to Cournot, to monopoly. The featured calibration of the short-run analysis is to the Covid-19 pandemic. A major point of departure between the long- and short-run analyses regards the viability of universal vaccination as a business strategy. In the long-run analysis, a perfectly effective vaccine would never be universally purchased if sold at a positive price because, with all other consumers protected, the marginal consumer obtains no private benefit. A number of previous game-theoretic analyses of vaccine uptake make exactly this point (Geoffard and Phillipson 1997, May 2000, Bauch and Earn 2004). In our short-run analysis, however,

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