An Economic Framework for Vaccine Prioritization
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This document presents an economic framework for the allocation of vaccines, focusing on socially optimal mechanisms that integrate both prices and priorities during the COVID-19 pandemic. It outlines various models that consider individual preferences, health benefits, socio-economic externalities, and ethical concerns while optimizing vaccine distribution. Key findings indicate that the optimal allocation strategy varies based on group characteristics and the interplay between market and free allocation methods.
![An Economic Framework for Vaccine Prioritization
Mohammad Akbarpour Eric Budish Piotr Dworczak Scott Duke Kominers
Graduate School of Business, Booth School of Business Department of Economics, Harvard Business School,
Stanford University University of Chicago Northwestern University, and FAME | GRAPE and NBER
Motivation
What should guide the allocation of scarce re-
sources in a society?
• Classical economic answer: prices
• (Some) Ethicists: access to essential goods
and services should be based on need, not
ability to pay; prices should not be used in
some contexts (Sandel, Satz, etc.)
This debate played out in the context of allocating
vaccines during the Covid-19 pandemic.
What we do
A market-design approach to socially optimal alloca-
tion of Covid-19 vaccines:
• specification of social and individual preferences
over vaccination;
• strategic environment with agents
– having private information,
– making endogenous choices about what
actions to take absent receiving a vaccine;
• incorporating ethical and equity concerns, as
well as externalities;
• endowing the designer with an arbitrary infor-
mation structure, but also
• allowing the designer to use prices to screen for
unobservable characteristics.
Key insight: Dichotomy between prices versus pri-
orities is artificial; the optimal mechanism combines
prices and priorites.
Model #1
• Designer controls the allocation of vaccines (that become
available gradually over time) to a unit mass of agents.
• Prior to receiving a vaccine, each agent takes a binary
decision a ∈ {Safe, Risky}.
• Each agent is characterized by five parameters:
– v: the private socio-economic benefit of
choosing a = Risky relative to a = Safe, not
including Covid-related risk;
– h: the private health benefit of choosing
a = Safe relative to a = Risky;
– vex: the socio-economic externality gener-
ated by the agent choosing a = Risky relative
to a = Safe, not including Covid-related risk;
– hex: the health externality generated by the
agent choosing a = Safe relative to a = Risky;
– λ: a social welfare weight.
Model #3
• Each agent observes (at least) their private
benefits v and h.
• Designer does not directly observe which
action was taken, and does not observe any
of the agents’ characteristics (including the
welfare weights).
• Designer does observe one of finitely many
labels i ∈ I for each agent, and knows the
distribution of characteristics.
Most important equation:
Vi(r) = Λi(r)
1 − Gi(r)
gi(r)
| {z }
weighted utility
+ α
r −
1 − Gi(r)
gi(r)
| {z }
revenue
+ E [Tex|i, r]
| {z }
externality
.
Model #4
• Tex is the externality generated by vaccinat-
ing the agent; if v and h are independent of
vex and hex conditional on i:
E[Tex|i, r] = vi
ex · P(a = Safe|i, r)]+
+hi
ex · P(a = Risky|i, r),
where vi
ex = E[vex|i] and hi
ex = E[hex|i].
• Λi(r) is the expected welfare weight:
Λi(τ) = E[λ|i, r ≥ τ].
Model #2
• Payoff of agent vaccinated at time t, enjoying
the benefits of vaccination for a fraction δ(t) of
the duration of the pandemic:
δ(t) [v + h]
| {z }
post-vacc.
+(1 − δ(t)) [max{v, h}]
| {z }
pre-vacc.
− p
• Willingness to pay (WTP) is r = min{v, h}.
• Designer’s payoff (where α ≥ 0):
1Safe(λ(δ(t)v − p) + δ(t)vex)+
+1Risky(λ(δ(t)h − p) + δ(t)hex) + αp.
Derivation of Optimal Mechanism Illustrative Example
Fig.1. Across-group allocation. Fig.2. An example of optimal mechanism when prices can (right panel) or cannot (left panel) be used with three groups
Results
Result 1
Suppose prices cannot be used (random al-
location within each group). It is optimal to
vaccinate groups sequentially according to
V i = E[Vi(r)| i].
Result 2
It is optimal to use (within group i)
• market allocation, when Vi(r) is ↗
• free allocation, when Vi(r) is ↘
Results cnd.
Result 3
Suppose that A(0) ≥ µi (mass of agents in
group i). Then, it is optimal for all agents
in group i to receive a vaccine immediately
and for free if
min
x
E[Vi(r)| r ≤ x] ≥ max
j̸=i, x
E[Vj(r)| r ≥ x].
Results cnd.2
Result 4
Suppose that it is optimal to use a market al-
location within group j and a free allocation
within group i. If Vj(r̄j) V i Vj(rj), then
it is optimal to start vaccinating agents in group
i first, then to vaccinate all agents in group j,
and then to vaccinate the remaining agents in
group i.
Acknowledgements
The authors thank Susan Athey, Péter Biró, Ezekiel Emanuel, Simon Finster, Navid Ghaffarzadegan, Romans Pancs, Parag Pathak,
Canice Prendergast, Hazhir Rahmandad, Tayfun Sönmez, Alex Tabarrok, Nikhil Vellodi, and numerous seminar and conference audiences
for insightful conversations and comments, as well as Joanna Krysta and Xiaoyun Qiu for excellent research assistance.](https://image.slidesharecdn.com/vaccinepaperposter-220728163721-aacd6552/85/An-Economic-Framework-for-Vaccine-Prioritization-1-320.jpg)
An Economic Framework for Vaccine Prioritization
- 1. An Economic Framework for Vaccine Prioritization Mohammad Akbarpour Eric Budish Piotr Dworczak Scott Duke Kominers Graduate School of Business, Booth School of Business Department of Economics, Harvard Business School, Stanford University University of Chicago Northwestern University, and FAME | GRAPE and NBER Motivation What should guide the allocation of scarce re- sources in a society? • Classical economic answer: prices • (Some) Ethicists: access to essential goods and services should be based on need, not ability to pay; prices should not be used in some contexts (Sandel, Satz, etc.) This debate played out in the context of allocating vaccines during the Covid-19 pandemic. What we do A market-design approach to socially optimal alloca- tion of Covid-19 vaccines: • specification of social and individual preferences over vaccination; • strategic environment with agents – having private information, – making endogenous choices about what actions to take absent receiving a vaccine; • incorporating ethical and equity concerns, as well as externalities; • endowing the designer with an arbitrary infor- mation structure, but also • allowing the designer to use prices to screen for unobservable characteristics. Key insight: Dichotomy between prices versus pri- orities is artificial; the optimal mechanism combines prices and priorites. Model #1 • Designer controls the allocation of vaccines (that become available gradually over time) to a unit mass of agents. • Prior to receiving a vaccine, each agent takes a binary decision a ∈ {Safe, Risky}. • Each agent is characterized by five parameters: – v: the private socio-economic benefit of choosing a = Risky relative to a = Safe, not including Covid-related risk; – h: the private health benefit of choosing a = Safe relative to a = Risky; – vex: the socio-economic externality gener- ated by the agent choosing a = Risky relative to a = Safe, not including Covid-related risk; – hex: the health externality generated by the agent choosing a = Safe relative to a = Risky; – λ: a social welfare weight. Model #3 • Each agent observes (at least) their private benefits v and h. • Designer does not directly observe which action was taken, and does not observe any of the agents’ characteristics (including the welfare weights). • Designer does observe one of finitely many labels i ∈ I for each agent, and knows the distribution of characteristics. Most important equation: Vi(r) = Λi(r) 1 − Gi(r) gi(r) | {z } weighted utility + α r − 1 − Gi(r) gi(r) | {z } revenue + E [Tex|i, r] | {z } externality . Model #4 • Tex is the externality generated by vaccinat- ing the agent; if v and h are independent of vex and hex conditional on i: E[Tex|i, r] = vi ex · P(a = Safe|i, r)]+ +hi ex · P(a = Risky|i, r), where vi ex = E[vex|i] and hi ex = E[hex|i]. • Λi(r) is the expected welfare weight: Λi(τ) = E[λ|i, r ≥ τ]. Model #2 • Payoff of agent vaccinated at time t, enjoying the benefits of vaccination for a fraction δ(t) of the duration of the pandemic: δ(t) [v + h] | {z } post-vacc. +(1 − δ(t)) [max{v, h}] | {z } pre-vacc. − p • Willingness to pay (WTP) is r = min{v, h}. • Designer’s payoff (where α ≥ 0): 1Safe(λ(δ(t)v − p) + δ(t)vex)+ +1Risky(λ(δ(t)h − p) + δ(t)hex) + αp. Derivation of Optimal Mechanism Illustrative Example Fig.1. Across-group allocation. Fig.2. An example of optimal mechanism when prices can (right panel) or cannot (left panel) be used with three groups Results Result 1 Suppose prices cannot be used (random al- location within each group). It is optimal to vaccinate groups sequentially according to V i = E[Vi(r)| i]. Result 2 It is optimal to use (within group i) • market allocation, when Vi(r) is ↗ • free allocation, when Vi(r) is ↘ Results cnd. Result 3 Suppose that A(0) ≥ µi (mass of agents in group i). Then, it is optimal for all agents in group i to receive a vaccine immediately and for free if min x E[Vi(r)| r ≤ x] ≥ max j̸=i, x E[Vj(r)| r ≥ x]. Results cnd.2 Result 4 Suppose that it is optimal to use a market al- location within group j and a free allocation within group i. If Vj(r̄j) V i Vj(rj), then it is optimal to start vaccinating agents in group i first, then to vaccinate all agents in group j, and then to vaccinate the remaining agents in group i. Acknowledgements The authors thank Susan Athey, Péter Biró, Ezekiel Emanuel, Simon Finster, Navid Ghaffarzadegan, Romans Pancs, Parag Pathak, Canice Prendergast, Hazhir Rahmandad, Tayfun Sönmez, Alex Tabarrok, Nikhil Vellodi, and numerous seminar and conference audiences for insightful conversations and comments, as well as Joanna Krysta and Xiaoyun Qiu for excellent research assistance.