Dynamic Moral Hazard: A Longitudinal Examination of Automobile Insurance in Canada

• Author: Jean‐Philippe Boucher,Wei Zhang,Peng Shi
• Date: 01 December 2018
• Published date: 01 December 2018
• DOI: http://doi.org/10.1111/jori.12172

©2016 The Journal of Risk and Insurance (2016).

DOI: 10.1111/jori.12172

Dynamic Moral Hazard: A Longitudinal

Examination of Automobile Insurance in Canada

Peng Shi

Wei Zhang

Jean-Philippe Boucher

Abstract

This article examines moral hazard in the context of dynamic contracting

in automobile insurance. Economic theory shows that experience rating of

insurers results in state dependence of driving behavior under moral haz-

ard. The empirical analysis is performed using a longitudinal data set from

a Canadian automobile insurer. We employ dynamic nonlinear panel data

models to distinguish the structural and spurious state dependence, and thus

moral hazard and selection on unobservables. As a measure of the riskiness

of driving, we consider the frequency,the number,as well as the cost of claims

for the policyholder. We find that the state dependence in claim cost reflects

both structural and spurious relationships, supporting the moral hazard hy-

pothesis. However, the state dependence in claim occurrenceis solely due to

unobserved heterogeneity.

Introduction

There is a vast literature in contract theory that addresses information asymmetry

where one party possesses more information than the counterparty in an economic

transaction. Historically, insurance has been a particularly promising field for study-

ing contract design and for investigating asymmetric information both theoretically

and empirically (see Dionne, Fombaron, and Doherty, 2013, for a recent review). Two

distinct forms are adverse selection and moral hazard.The former predicts the positive

relation between policyholders’ risk and demand for insurance, and the latter con-

cerns policyholders’ behavior change due to the incentives provided in an insurance

contract.

Peng Shi is at the Wisconsin School of Business, University of Wisconsin-Madison. Shi can be

contacted via e-mail: pshi@bus.wisc.edu. WeiZhang is at the Department of Economics, North-

ern Illinois University. Zhang can be contacted via e-mail: wzhang1@niu.edu. Jean-Philippe

Boucher is at the D´

epartement de Math´

ematiques, Universit´

eduQu

´

ebec `

a Montr´

eal. Boucher

can be contacted via e-mail: boucher.jean-philippe@uqam.ca. We thank Editor Keith Crocker

and two anonymous reviewers for their valuable comments. Shi also acknowledges the support

by the Center of Actuarial Excellence (CAE) Research Grant from the Society of Actuaries and

the Fall Research Competition from the University of Wisconsin-Madison.

1

2The Journal of Risk and Insurance

In this study,we aim to investigate information asymmetry in the context of dynamic

contracting in automobile insurance, especially the effect of moral hazard on policy-

holders’ driving behavior. After decades-long predominance of theoretical work in

contract theory, empirical studies on contracts are attracting more attention recently,

with a fair amount of work focusing on testing for the existence of private information

in automobile insurance markets. Grounded on the theoretical prediction set forth by

Rothschild and Stiglitz (1976), Stiglitz (1977), and Wilson (1977), the majority of the

existing literature has resorted to the conditional correlation test for the identifica-

tion of residual asymmetric information by examining the risk–coverage relationship

within a risk class (see Cohen and Siegelman, 2010). The evidence is mixed. Using

cross-sectional data in a static context, some studies find positive residual correla-

tion, including Puelz and Snow (1994), Cohen (2005), Kim et al. (2009), Shi and Valdez

(2011), and Shi, Zhang, and Valdez (2012), while others do not, for example, Chiappori

and Salani´

e (2000) and Dionne, Gouri´

eroux, and Vanasse (2001).

The conditional correlation approach is easy to implement; however, it is subject to

the criticism of not being able to disentangle the effects of adverse selection and moral

hazard. Addressing this issue, some recent studies have devoted attention to the iden-

tification of moral hazard from adverse selection using dynamic insurance data. The

first efforts are due to Abbring et al. (2003) and Abbring, Chiappori, and Pinquet

(2003), where the authors show that moral hazard can be distinguished from selec-

tion on unobservables from the dynamics in claims. Specifically, experience rating

implies negative dependence in claim intensity under moral hazard. This prediction

was then tested using data in the French market and little evidence of moral hazard

was found. More recently, Abbring, Chiappori, and Zavadil (2008) extend the test by

differentiating the ex ante and ex post moral hazard, and with additional structural

assumptions, they detect moral hazard in the Netherlands. Instead of looking into

dynamics of claims, Dionne et al. (2011) examine the demerit points in the public

automobile insurance market in the Quebec and also find evidence of moral hazard.

Using a unique longitudinal survey data where both reported and unreported acci-

dents are observed, Dionne, Michaud, and Dahchour (2013) are able to distinguish

dynamic moral hazard from asymmetric learning in the French automobile insurance

market. Recent evidence of asymmetric learning in automobile insurance markets also

includes Cohen (2012) and Shi and Zhang (2014). Note that the learning problem in

Dionne, Michaud, and Dahchour (2013) is between the insured and the insurer where

the insured learns on his risk by observing accidents, while in Cohen (2012) and Shi

and Zhang (2014) the learning problem is between insurance companies about the

insured.

The current study is more in line with Abbring, Chiappori, and Pinquet (2003) in

that we test the existence of moral hazard by investigating the state dependence of

driving behavior using dynamic insurance data. Toemphasize our departure from the

literature, we conduct our investigation in an insurance system that features a very

different merit rating system. In the above studies, experienced rating takes the form

ofabonus–malus system or a no-claims discount, where premium adjustments follow

a clearly set schedule based on a policyholder’s claim history. And this premiumsetup

is known to policyholders and the information is commonly shared among insurers.

In contrast, we examine the market in the Ontario province of Canada. Similar to the

United States, while experience rating is employed in this market, there is no explicit