The efficiency of voluntary risk classification in insurance markets

• Published date: 01 June 2021
• Author: Keith J. Crocker,Nan Zhu
• Date: 01 June 2021
• DOI: http://doi.org/10.1111/jori.12326

J Risk Insur. 2021;88:325–350. wileyonlinelibrary.com/journal/JORI

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325

Received: 11 June 2019

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Accepted: 12 August 2020

DOI: 10.1111/jori.12326

ORIGINAL ARTICLE

The efficiency of voluntary risk classification

in insurance markets

Keith J. Crocker|Nan Zhu

Risk Management Department,

Pennsylvania State University,

University Park, Pennsylvania

Correspondence

Nan Zhu, Risk Management Department,

Pennsylvania State University, 303 Business

Building, University Park, PA 16802.

Email: nanzhu@psu.edu

Abstract

It has been established that categorical discrimination

based on observable characteristics such as gender, age,

or ethnicity enhances efficiency. We consider a different

form of risk classification when there exists a costless

yet imperfectly informative test of risk type, with the

test outcome unknown to the agents ex ante. We show

that a voluntary risk classification in which agents are

given the option to take the test always increases effi-

ciency compared with no risk classification. Moreover,

voluntary risk classification also Pareto dominates a

regime of compulsory risk classification in which all

agents are required to take the test.

KEYWORDS

adverse selection, efficiency, risk classification

1|INTRODUCTION

When insurers face customers who have private information about their propensities for suf-

fering insurable losses, the resulting problem of adverse selection is widely understood to have

pernicious effects on insurance markets. A common response by insurers is to engage in risk

classification, a process in which the contracts offered to each customer are conditioned on

observable characteristics of the customer that are known to be correlated with the individual's

underlying risk. Employed in this fashion, risk classification may be viewed as a tool insurers

use against privately informed consumers to mitigate their informational disadvantage. In

contrast to the traditional approach in which insurers make the decision to engage in risk

classification, there has recently been a move in some settings to permit the insured individual

to choose whether or not to be classified. This paper develops a model of voluntary classification

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© 2020 American Risk and Insurance Association

and demonstrates that, by increasing the dimensionality of the screening space, such classifi-

cation always is welfare enhancing. Given that voluntary classification is desirable, one might

conjecture it would be even better to require those who would prefer not to be classified to take

the test as well. Such a conjecture would be false, as we find that voluntary classification is

always preferred to a regime of compulsory classification in which all customers are required to

take the classification test.

The use of risk classification by insurers on the basis of immutable customer characteristics that

are both costlessly observable and imperfectly correlated with underlying risk, such as sex, age, or

race, is first examined by Hoy (1982). Using an equilibrium analysis, he concludes that the effect of

risk classification depends on the particular equilibrium concept employed and that there may be

winners as well as losers, so that the net effect of permitting such classification is ambiguous.

1

In

contrast, Crocker and Snow (1986) examine costless but imperfect categorization in the context of

an efficiency analysis and demonstrate that to permit such classification would shift the utility

possibilities frontier outward, resulting in Pareto improvements. Bond and Crocker (1991)examine

the use of risk classification by insurers on the basis of observable consumer choices that either

directly cause higher risk, such as smoking and heart disease, or that simply have a correlation with

risk, such as students with good grades who tend to be more careful drivers. They find that the

insurers can harness the consumption choices made by consumers to design more efficient con-

tracts in the insurance market. Finally, Rothschild (2011) examines the case of risk categorization

on the basis of immutable characteristics that are costly to observe and concludes that to prohibit

such classification would be inefficient.

2

The common threads in this received literature on risk

classification are that the decision to categorize is made by the insurer, so the insured has no say in

the matter, and that the characteristics upon which the classification is based, such as gender, age,

or ethnicity, are observable to everyone ex ante. Put differently, the insured faces no uncertainty

regarding the outcome of the classification test.

3

In recent years, voluntary classification has become increasingly common in the context of

automobile insurance. Perhaps the best known example is the “Snapshot”program offered by

Progressive in which drivers may opt to install a telematic device in their car that, for 6 months, will

track several parameters (such as hard braking) of driving behavior.

4

Drivers that are determined by

the insurer to be “good”are given a discount that remains even after the device is removed, and

those who are determined to be “bad”may see rate increases in some states. Similar usage‐based

1

The equilibrium concepts employed by Hoy (1982) utilize what is termed “Wilson foresight”in which firms

restrain from offering contracts that, while initially profitable given the contracts currently offered by other

firms, would become unprofitable were other contracts in the market that were rendered unprofitable by their offering

withdrawn. In the discussion that follows in this footnote, we will refer to the classification category with the lower

proportion of high risks as the “

G

group”and the category with the higher proportion of high risks as the “

B

group,”

which is consistent with our usage later in the paper. Using the Wilson (1977) E2 equilibrium, Hoy (1982) shows that if

the pre‐and post‐classification equilibrium allocations were pooling, then both risk types in the

G

group

would be better off and those in the

B

group would be worse off as a result of the classification. If the pre‐classification

equilibrium allocations were pooling and the post‐classification allocations entailed separation for those in the

B

group but pooling for those in group

G

, then the former would be worse off and the latter better off as a result of the

classification. Finally, if the pre‐classification equilibrium were to entail separation and the post‐classification equili-

brium were to result in pooling in the

G

group and separation in the

B

group, the former would be better off, and the

latter no worse off, as a result of the classification. Similar ambiguous welfare results are also obtained by Hoy (1982)

using the Miyazaki (1977)–Wilson (1977)–Spence (1978) equilibrium concept.

2

Specifically, Rothschild (2011) demonstrates that the government can design and implement a partial social insurance

policy that provides insurers with the incentive to engage in costly categorization only when it is socially efficient to

do so.

3

See Dionne and Rothschild (2014) for a recent survey of research on the efficiency effects of insurance risk classification.

4

For details of the program, see https://www.progressive.com/auto/discounts/snapshot/.

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