Prevention incentives in long‐term insurance contracts

• Author: Renaud Bourlès
• Date: 01 September 2017
• DOI: http://doi.org/10.1111/jems.12196
• Published date: 01 September 2017

Received: 8 October 2015 Revised: 8 November2016 Accepted: 20 November 2016

DOI: 10.1111/jems.12196

ORIGINAL ARTICLE

Prevention incentives in long-term insurance contracts

Renaud Bourlès

Centrale Marseille (Aix-Marseille School of

Economics), CNRS & EHESS, Marseille,

France (Email: renaud.bourles@centrale-

marseille.fr)

Abstract

Long-term insurance contracts are widespread, particularly in public health and the

labor market. Such contracts typically involve monthly or annual premia which are

related to the insured’s risk profile. A given profile may change, based on observed

outcomes which depend on the insured’s prevention efforts. The aim of this paper is

to analyze the latter relationship. In a two-period optimal insurance contract in which

the insured’s risk profile is partly governed by her effort on prevention, we find that

both the insured’s risk aversion and prudence play a crucial role. If absolute prudence

is greater than twice absolute risk aversion, moral hazard justifies setting a higher pre-

mium in the first period but also greater premium discrimination in the second period.

This result provides insights on the trade-offs between long-term insurance and the

incentives arising from risk classification, as well as between inter- and intragenera-

tional insurance.

1INTRODUCTION

Long-term insurance contracts are common, notably in public health and the labor market (e.g., unemployment insurance). One

of their main features is the adjustment of premia in response to observed outcomes and the consequent evolutionof r isk profiles.

The aim of this paper is to analyze the effect of this on an insured’s preventive efforts.

The topic of risk classification (i.e., the use of observable characteristics to pool together individuals with similar risk expo-

sure) has received significant attention in the literature (see Crocker & Snow, 2013, for a survey). Being analogous to price

discrimination, it has raised equity issues (see, e.g., Dionne & Rothschild, 2014) that have recently been tackled by regulators.1

The allocative efficiency resulting from information acquisition by insurance companies has also been explored (see Bond &

Crocker, 1991; or Polborn, Hoy, & Sadanand, 2006).

In long-term insurance, however, risk classification is not only a response to hidden knowledge or adverse selection; it also

relates to moral hazard, shaping incentives for prevention that can impact the insured’s future risk profile. Accordingly, we

study here optimal long-term insurance contracts under moral hazard, focusing on the evolution of premia and the impact of

classification risk.

We do so using a two-period model of dynamic insurance with change in risk exposure during the life cycle. In the first

period, agents are identically exposed to a risk and can invest in prevention. In the second period, agents can either be of

high-risk or low-risk type. Prevention effort in the first period has the effect of lowering the probability of being high-risk

(that is, the probability of having a high probability of falling ill, in the case of health insurance2) in the second period.

The author thanks the editor and two anonymous referees for suggestions that substantiallyimproved the paper and Dominique Henriet for his constant help.

He is also grateful to Francis Bloch, Louis Eeckhoudt, and Bernard Sinclair-Desgagné for valuable comments and encouragement; and to Marjorie Sweetko

for English language revision. Special thanks are also due to, without implicating, Mohamed Belhaj, Bruno Decreuse, Pierre Picard, Jean-Charles Rochet,

Hubert Stahn, Bruno Ventelou, participants of the Journées de Microéconomie Appliquée (Dijon, France), the ECORE summer school (Brussels, Belgium), the

ARIA meeting (Providence, RI, USA),t he EEA meeting(Barcelona, Spain), and t he EGRIE meeting(Bergen, Norway), and seminar participants at GREQAM

(Marseille, France), THEMA (Cergy-Pontoise, France), and CES (Paris, France) for helpful discussions.

J Econ Manage Strat. 2017;26:661–674. © 2017 WileyPeriodicals, Inc. 661wileyonlinelibrary.com/journal/jems