Voluntary Contributions to a Mutual Insurance Pool

• Author: JONATHAN VAKSMANN,MARIE CLAIRE VILLEVAL,LOUIS LÉVY‐GARBOUA,CLAUDE MONTMARQUETTE
• Date: 01 February 2017
• Published date: 01 February 2017
• DOI: http://doi.org/10.1111/jpet.12181

VOLUNTARY CONTRIBUTIONS TO A MUTUAL INSURANCE POOL

LOUIS L ´

EVY-GARBOUA

Universit´

e Paris 1 - Panth´

eon Sorbonne

CLAUDE MONTMARQUETTE

Universit´

e de Montr´

eal

JONATHAN VAKSMANN

Universit´

e du Maine

MARIE CLAIRE VILLEVAL

Universit´

edeLyon

Abstract

We study mutual-aid games in which individuals choose to contribute to

an informal mutual insurance pool. Individual coverage is determined

by the aggregate level of contributions and a sharing rule. We analyze

theoretically and experimentally the (ex ante) efficiency of equal and

contribution-based coverage. The equal coverage mechanism leads to

a unique no-insurance equilibrium while contribution-based coverage

develops multiple equilibria and improves efficiency. Experimentally,

the latter treatment reduces the amount of transfers from high contrib-

utors to low contributors and generates a “dual interior equilibrium.”

That dual equilibrium is consistent with the co-existence of different

prior norms which correspond to notable equilibria derived in the the-

ory. This results in asymmetric outcomes with a majority of high con-

tributors less than fully reimbursing the global losses and a significant

Louis L´

evy-Garboua, Universit´

eParis1-Panth

´

eon Sorbonne, Paris School of Economics, Centre

d’´

Economie de la Sorbonne, 106-112 Bd de l’Hˆ

opital, 75647 Paris Cedex 13, France; and Cirano,

Montreal, Canada (Louis.Levy-Garboua@univ-paris1.fr). Claude Montmarquette, CIRANO and

Universit´

edeMontr

´

eal, 2020 rue University, Montreal (Quebec), Canada, H3A 2A5 (Claude.

Montmarquette@cirano.qc.ca). Jonathan Vaksmann, GAINS-TEPP, Universit ´

e du Maine, Facult´

ede

Droit et des Sciences ´

Economiques, Avenue O. Messiaen, 72085 Le Mans Cedex 9, France; and Centre

d’´

Economie de la Sorbonne, Universit´

eParis1-Panth

´

eon Sorbonne (jonathan.vaksmann@univ-

lemans.fr). Marie Claire Villeval, Universit´

e de Lyon, CNRS, GATE 93, chemin des Mouilles, F-69130-

Ecully, France; IZA, Bonn, Germany; Department of Public Finance, University of Innsbruck, Austria

(villeval@gate.cnrs.fr).

We thank Romain Zeiliger for programming the experiment presented in this paper and Nathalie

Viennot for research assistance. Financial support from the Government of Qu´

ebec and the French

Agence Nationale de la Recherche (Inter-SHS program, Convention 04 5 675/50.0520) is gratefully

acknowledged. This research was performed within the framework of the LABEX CORTEX (ANR-11-

LABX-0042) of Universit´

e de Lyon, within the program Investissements d’Avenir (ANR-11-IDEX-007)

operated by the French National Research Agency (ANR). Referees’ comments and suggestions were

very useful in revising the paper. The usual disclaimer applies.

Received March 6, 2013; Accepted September 4, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 19 (1), 2017, pp. 198–218.

198

Voluntary Contributions 199

minority of low contributors less than fully defecting. Such behavioral

heterogeneity may be attributed to risk attitudes (risk tolerance vs risk

aversion) which is natural in a risky context.

1. Introduction

In spite of the prevalence of assistance and universal insurance in a growing number of

countries, the economic theory of insurance tends to ignore the fact that one’s cover-

age against insurable risk will often not depend solely on one’s own contributions. In

this paper, we wish to examine cases in which individual coverage against risk is deter-

mined by the aggregate level of voluntary contributions in a group and a sharing rule.

We designate this type of insurance scheme as “voluntary mutual aid.” We envision mu-

tual aid here as a unifying concept that can be useful for analyzing various institutions.

Mutual-aid pools offer insurance to members of a specified group, typically sharing a

common characteristic. The homogeneity of members facilitates the full coverage of

independent random losses at fair price and enhances solidarity among members and

their willingness to contribute to the pool. To illustrate this point, Schwindt and Vining

(1998) motivate their proposal for a mutual insurance pool for transplant organs by

the incentive it provides to donate. Group members are free to join and contribute and

they redistribute resources between themselves according to a sharing rule. All mem-

bers are impartially treated and resources are divided between them according to needs

or participation: those who need or participate most are helped most. Mutual-aid orga-

nizations have existed at least since the medieval craft guilds.1Important contemporary

examples of voluntary mutual-aid pool are “climate clubs” of adherents to international

climate policy agreements (Nordhaus, 2015) that offer some kind of mutual insurance

against differential climate change damages and trade unions that provide unionized

workers with protection against employment hazards. However, trade unions and cli-

mate clubs are perfect illustrations of the problem raised by the group’s heterogeneity

to voluntary mutual-aid pools. Workers who didn’t unionize and countries who didn’t

sign the agreement may still benefit from the contributions of unionized workers or

cooperative countries. Thus, a conflict arises between insurance motives and incentives,

which needs to be resolved. For illustration, going back to the proposal of a mutual

insurance pool for transplant organs, Howard (2007) remarks that the pool derives its

efficiency by linking very explicitly the willingness to donate and the ability to benefit

from transplantation and by punishing free riders: persons who refuse to donate but

would gladly accept organs from others.

In contrast with formal mutual insurance schemes in which paying a premium is

contractual, compulsory and excludable,2voluntary contributions and indemnities to

a mutual-aid pool constitute an informal insurance scheme with no contract, no legal

1Friendly Societies were found throughout Europe in the 18th and 19th centuries. During the Great

Depression, the American “fraternity societies” and the English “workers clubs” provided their members

with health insurance. (Almost) complete consumption insurance in small communities (Townsend,

1994) and in large societies (Mace, 1991; Cochrane, 1991; Schulhofer-Wohl, 2011) reveals an efficient

implicit structure of mutual insurance in those groups. Anecdotally, we have been aware of the example

of students contributing to a fund used to reimburse contraveners who have been fined for fare dodging

in public transportation.

2In Barigozzi et al. (2013), mutualization corresponds to participating policies in which policyholders

jointly hold the residual claims on the common pool. Policyholders share the aggregate risk and, af-

ter an initial contribution, contribute whatever amount is needed yearly to meet the losses insured by

the pool (on participating policies. See also Doherty and Dionne, 1993; Smith and Stutzer, 1990, 1995;