Yes, No, Perhaps? Premium Risk and Guaranteed Renewable Insurance Contracts With Heterogeneous Incomplete Private Information

• Author: Andreas Richter,Petra Steinorth,Richard Peter
• Published date: 01 June 2016
• DOI: http://doi.org/10.1111/jori.12064
• Date: 01 June 2016

©2015 The Journal of Risk and Insurance. Vol.83, No. 2, 363–385 (2016).

DOI: 10.1111/jori.12064

Yes, No, Perhaps? Premium Risk and Guaranteed

Renewable Insurance Contracts With

Heterogeneous Incomplete Private Information

Richard Peter

Andreas Richter

Petra Steinorth

Abstract

The article shows that heterogeneous incomplete private information can ex-

plain the limited existence of guaranteed renewable health insurance (GR)

contracts in an otherwise frictionless markets. We derive a unique equilib-

rium that can be of the form that either only a portion of the population

or none will cover themselves against premium risk with a GR contract.

Increased risk aversion, increased premium risk, and first-order stochastic

improvements of the distribution of private information increase the like-

lihood of positive take-up. In case GR contracts are in demand, increased

risk aversion and first-order stochastic improvements of the distribution of

private information lead to more individuals purchasing the GR contract.

Introduction

Premium risk plays an important role in repeated, long-term, or any other future

insurance contracts. Premium risk refers to the uncertainty of the future insurance

premium due to the evolution of individual risk factors.1It has mostly been discussed

Richard Peter is at the Institute for Risk Management and Insurance, Ludwig-Maximilians-

Universitaet Munich. Peter can be contacted via e-mail: peter@bwl.lmu.de. Andreas Richter is at

the Institute for Risk Management and Insurance, Ludwig-Maximilians-Universitaet Munich.

Richter can be contacted via e-mail: richter@bwl.lmu.de. Petra Steinorth is at the School of

Risk Management, Insurance and Actuarial Science, St. John’s University. Steinorth can be

contacted via e-mail: steinorp@stjohns.edu. The authors thank Mike Hoy, James Ligon, Harris

Schlesinger, and Paul Thistle for their helpful comments on earlier versions of this article.

We also thank participants at the Rosen-MacCahan-Huebner Seminar at the Wharton School,

the 2nd World Risk and Insurance Economics Congress (WRIEC), the University of Nevada,

Florida State University, Georgia State University, the University of Alabama, the University

of Wisconsin and the 2011Risk Theory Society Annual Meeting for valuable comments, which

led to significant improvements. Two anonymous referees and the co-editor of the JRI also

provided very thoughtful comments. Any remaining errors are, of course, our own.

1In this sense, the literature also speaks of classification or reclassification risk. As we focus on

the resulting uncertainty of the future insurance premiumwe stick to the term “premium risk”

throughout the article.

363

364 The Journal of Risk and Insurance

as related to health insurance although forms of (implicit) protection against premium

risk are also observed for long-term care insurance or life insurance. One reasonmight

be that medical expenses are extremely heterogeneous. Strictly speaking, premium

risk refers to differences in expected costs. Pauly and Herring (2007) investigate the

individual health insurance market and find that high-risk individuals (with above-

median expected medical expenses) had approximately four times higher expected

expenses than low-risk individuals (with below-median expected medical expenses).

At the same time, we do not observe that private insurance markets succeed to cover

the majority of individuals in the United States. Starting in 2014, the Patient Protection

and Affordable Care Act forces insurers to give up individual underwriting nearly

completely2as markets obviously failed to provide a comprehensive protection of

premium risk. Our article addresses the question of why this is the case and shows

that the distribution of information among individuals can lead to scenarios where a

substantial part of the population does not cover their premium risk.

Cochrane (1995) and Pauly,Kunreuther, and Hirth (1995) discuss ways of addressing

premium risk in health insurance contracts. They both argue that a prepayment for

the premium risk either explicitly in the form of premium risk insurance (PRI) or

implicitly within guaranteed renewable long-term health insurance (GR) contracts

implies that all individuals are completely covered against premium risk. Besides

GR contracts as suggested by Pauly, Kunreuther, and Hirth and stand-alone PRI as

discussed by Cochrane, community rating could remedy the premium risk problem

(see Kifmann, 2000, 2001). These three ways of addressing premium risk differ in

several dimensions. To implement stand-alone PRI, risk types must be observable

and contractible, which is not easily satisfied. GR contracts, however, create a lock-

in problem as individuals choose insurers early in life and might find it difficult to

switch later in life because they would lose the prepayment. Furthermore, borrowing

constraints and high levels of impatience could render GR contracts and stand-alone

PRI unattractive (Frick, 1998). With community rating it might be hard to ensure

efficient provisionof medical services and to accommodate heterogeneous preferences

over medical care. Consequently, there is no dominant solution.

There are several examples where premium risk is insured by front-loading in guar-

anteed renewable long-term insurance contracts sold in private insurance markets as

life insurance (Hendel and Lizzeri, 2003) and long-term care contracts. In these two

markets, early purchases mitigate severe premium risk problems. However, other

insurance contracts expose individuals to significant premium risk in the future such

as, for example, car insurance contracts and, unfortunately, most individual health

insurance contracts in the United States.3Reasons discussed in the literature for the

limited premium risk protection are divergent expectations of future loss severity,

2Acceptable underwriting factors will be age, family size, geographic area, and, restricted to a

1:1.5 ratio, tobacco use (see Sec. 2705 of the Patient Protection and Affordable Care Act).

3Before the Patient Protection and Affordable Care Act stopped this practice, contracts were

annual and insurance companies were allowed not to renew contracts of indivduals who

became severely sick.