Insurance Fraud in a Rothschild–Stiglitz World

• Author: M. Martin Boyer,Richard Peter
• Date: 01 March 2020
• DOI: http://doi.org/10.1111/jori.12264
• Published date: 01 March 2020

©2018 The Journal of Risk and Insurance. Vol.XX, No. XX, 1–26 (2018).

DOI: 10.1111/jori.12264

Insurance Fraud in a Rothschild–Stiglitz World

M. Martin Boyer

Richard Peter

Abstract

In this article, we model a competitive insurance market where policyhold-

ers privately have information about their probability of accident ex ante and

know the state of the world ex post. Wecombine costly state verification with-

out commitment and arguments from insurance contracting under adverse

selection to characterize the resulting allocations. Insurance fraud convexi-

fies the insurer’s zero expected profit condition, which can lead to complete

unraveling with low risks dropping out of the market. The standard case,

however, involves rationing of low risks, which raises their probability of

fraud and their success rate when committing it. As a result, adverse selec-

tion increases fraud in the economy. We also show that cross-subsidization

from low risks to high risks mitigates the fraud externality.Our results high-

light that adverse selection and insurance fraud interact in nontrivial ways

and have the potential to aggravate each other.

Introduction

Insurance fraud is an ongoing problem in the insurance industry. In the United States,

the Federal Bureau of Investigation estimates the annual cost of insurance fraud at

$40 billion, whereas the Coalition Against Insurance Fraud estimates that “at least $80

billion in fraudulent claims are made annually in the U.S. . .. (in) all lines of insurance.

It’s also a conservative figure because much insurance fraud goes undetected and un-

reported.”1Typesof fraud include build-up (exaggerating the loss amount), planned

M. Martin Boyer holds the Power Corporation of Canada Chair in the Department of Fi-

nance, HEC Montr´

eal (Universit´

e de Montr´

eal). Boyer can be contacted via e-mail: mar-

tin.boyer@hec.ca. Richard Peter is at the Department of Finance, University of Iowa. Peter

can be contacted via e-mail: richard-peter@uiowa.edu. Wethank Wanda Mimra, Pierre Picard,

J¨

org Schiller, and Faith Neale for their comments on a previous iteration of this article, as well

as the journal’s referees. Boyer would also like to thank Andreas Richter, Johannes Jaspersen,

and the entire team of researchersat the Munich Risk and Insurance Center for their hospitality.

This research benefited from the financial support of the Social Sciences and Humanities Re-

search Council of Canada (Grant #435-2016-1109), and of the Retirement and Savings Institute

(ire.hec.ca) at HEC Montr´

eal. The continuing support of CIRANO is also acknowledged.

1See https://www.fbi.gov/stats-services/publications/insurance-fraudfor the FBI figure and

http://www.insurancefraud.org/the-impact-of-insurance-fraud.htmfor that of the Coalition

Against Insurance Fraud.

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fraud (reporting a loss when none happened), lying on the policy application, and

lying on the amount invested in mitigation. Dionne et al. (1993) report that fraudulent

claims amount to at least 13 percent of all claims, and the Insurance Fraud Council es-

timates that between $5.6 and $7.7 billion were paid in excess in 2012 because of fraud-

ulent or build-up claims, representing between 13 and 17 percent of all claims paid.2

In this article, we extend the economic analysis of insurance fraud by considering

that policyholders have private information about their probability of accident ex ante

and the state of the world ex post, thereby providing the first joint analysis of adverse

selection and insurance fraud. We combine costly state verification without commit-

ment and arguments from insurance contracting under asymmetric information to

gain new insights into the effects of both types of frictions on insurance market out-

comes. Ex post moral hazard convexifies the insurer’s zero expected profit constraint,

which makes more than full coverage optimal when risk types are known. This can

help explain the existence of replacement-cost endorsements (see Dionne and Gagn´

e,

2001) and a preference for low deductibles (see Sydnor, 2010). Indifference curves

in premium/indemnity space are increasing, concave, and satisfy single crossing so

that the possibility of fraud does not alter the qualitative properties of insurance mar-

ket outcomes under adverse selection. The Rothschild–Stiglitz allocation entails no

distortion of the high-risk contract whereas low risks are shut out of the market or ra-

tioned, depending on the severity of the high-risk incentive compatibility constraint.

If they are rationed, the total amount of fraud rises in the economy. We also con-

sider cross-subsidized contracts to address those cases where the Rothschild–Stiglitz

contracts fail to be an equilibrium or are inefficient, and find that cross-subsidization

reduces the total amount of fraud in the economy. A numerical example illustrates

that adverse selection and insurance fraud interact nontrivially and can aggravate or

alleviate each other in terms of social welfare.

Existing research on insurance fraud assumes that accident probabilities are common

knowledge. It is natural to apply Townsend’s(1979) costly state verification approach

to insurance fraud. The optimal insurance contract stipulates a no-auditing region

where a fixed payment is made to the insured, and an auditing region where all

claims are audited and coverage is provided as full insurance less a deductible (see

also the standard debt contract of Gale and Hellwig, 1985). Mookherjee and Png (1989)

and Bond and Crocker (1997) show that truth telling can be achieved using stochastic

audits, which is Pareto superior to Townsend’sapproach for being more cost effective.3

Tennyson (2002) and Miyazaki (2009) explain the presence of insurance fraud by the

fact that some policyholders feel justified to pad claims (see also Dean, 2004). Tennyson

(1997) finds that the build-up of insurance claims is related to the social acceptability

of exaggerating claims, one’s personal attitude toward dishonesty (see Boyer, 2007,

for a model), and the perception of the inherent integrity of insurance institutions.

The traditional mechanism design literature has concentrated on problems where it

is optimal for all players to tell the truth, which requires the principal to commit

2See http://www.insurancefraud.org/downloads/InsuranceResearchCouncil02-15.pdf.

3Tennyson and Salsas-Forn (2002) find evidence that insurers audit rationally and that audits

are effective in deterring and detecting fraud.

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