The Cost of Legal Restrictions on Experience Rating

• Published date: 01 March 2020
• Author: Darcy Steeg Morris,Joshua C. Teitelbaum,Francesca Molinari,Levon Barseghyan
• DOI: http://doi.org/10.1111/jels.12242
• Date: 01 March 2020

Journal of Empirical Legal Studies

Volume 17, Issue 1, 38–70, March 2020

The Cost of Legal Restrictions on

Experience Rating

Levon Barseghyan, Francesca Molinari, Darcy Steeg Morris, and

Joshua C. Teitelbaum*

We investigate the cost of legal restrictions on experience rating in auto and home insur-

ance. The cost is an opportunity cost as experience rating can mitigate the problems asso-

ciated with unobserved heterogeneity in claim risk, including mispriced coverage and

resulting demand distortions. We assess this cost through a counterfactual analysis in

which we explore how risk predictions, premiums, and demand in home insurance and

two lines of auto insurance would respond to unrestricted multiline experience rating.

Using claims data from a large sample of households, we first estimate the variance-

covariance matrix of unobserved heterogeneity in claim risk. We then show that condition-

ing on claims experience leads to material refinements of predicted claim rates. Last, we

assess how households’ demand for coverage would respond to multiline experience rat-

ing. We find that the demand response would be large.

I. Introduction

In many insurance markets, there are variables that affect an insured’s claim risk but are

not observable by the insurer.

1

In other words, there is unobserved heterogeneity in

claim risk. The problem with unobserved heterogeneity in claim risk is that it can lead to

mispriced insurance, which in turn can impair the efficient operation of insurance mar-

kets, including by distorting the demand for insurance coverage.

*Address correspondence to Joshua C. Teitelbaum, Georgetown University Law Center, 600 New Jersey Ave. NW,

Washington, DC 20001; email: jct48@law.georgetown.edu. Barseghyan is Professor of Economics, Cornell Univer-

sity; Molinari is H. T. Warshow and Robert Irving Warshow Professor of Economics and Professor of Statistics, Cor-

nell University; Morris is Research Mathematical Statistician, Center for Statistical Research and Methodology,

U.S. Census Bureau; Teitelbaum is Agnes N. Williams Research Professor and Professor of Law, Georgetown Uni-

versity Law Center.

We thank the editor and the referees for their helpful comments and feedback. We acknowledge financial sup-

port from National Science Foundation Grant SES-1031136. Molinari also acknowledges financial support from

NSF Grant SES-0922330. This article is released to inform interested parties of research and to encourage discus-

sion. The views expressed are those of the authors and not necessarily those of the U.S. Census Bureau.

1

Alternatively, there may be variables that are observable by the insurer but that the insurer is prohibited from

using when it underwrites or rates the insured’s policy (Salanie´ 1997; Avraham et al. 2014).

38

In theory, an insurer can mitigate these problems through experience rating. The

logic is straightforward. Even if there is unobserved heterogeneity in claim risk at the

time the insurer underwrites and rates an insured’s policy, the insurer subsequently

receives signals about the insured’s latent risk type. In particular, the insurer observes the

insured’s claims experience. By conditioning on the insured’s claims experience, the

insurer can refine its initial prediction about the insured’s claim risk, which is based

solely on observables. The insurer can then use its refined prediction to adjust—or expe-

rience rate—the insured’s premium to better reflect her true claim risk.

2

In practice, however, U.S. law frequently imposes restrictions on an insurer’s ability

to engage in experience rating.

3

An example from federal law is the Affordable Care

Act’s community rating provisions, which forbid experience rating of premiums for heath

insurance coverage offered in the individual or small-group market.

4

A state law example

is New York’s Insurance Law, which forbids experience rating of premiums for auto com-

prehensive or home insurance coverage and also prohibits using auto comprehensive

claims to experience rate premiums in any other line of insurance coverage.

5

In this article, we empirically investigate the cost of legal restrictions on experience

rating in the context of auto and home insurance. The cost is an opportunity cost. As

noted above, experience rating has the potential to mitigate the problems associated with

unobserved heterogeneity in claim risk. When the law imposes restrictions on experience

rating, insurers lose the opportunity to fully utilize their insureds’ claims experience to

refine their risk predictions and adjust their premiums to better reflect the true risks. We

assess this opportunity cost through a counterfactual analysis in which we explore how

risk predictions, premiums, and demand in two lines of auto coverage and one line of

home coverage would respond to unrestricted experience rating within and across the

three lines of coverage.

Our data comprise an unbalanced panel of 62,425 households that purchased auto

and home policies from a single insurance company between 1998 and 2006. Among

other things, the data record the number of claims filed by each household in three lines

of coverage: auto collision, auto comprehensive, and home all perils. In addition, the

data contain detailed information about the households and their auto and home

policies.

2

Experience rating is not to be confused with classification rating. Under classification rating, an insured’s pre-

mium is based on the collective loss experience of all insureds in the insured’s risk class. Under experience rating,

by contrast, an insured’s premium is adjusted based on her individual loss experience.

3

Advocates for legal restrictions on experience rating (and other forms of risk classification) generally rely on argu-

ments from equity (distributional and deontological) (e.g., Abraham 1985; Avraham et al. 2014). For instance, they

argue that such restrictions promote access to insurance for high-risk, low-income insureds (e.g., Meier 1991;

Thiery & Van Schoubroeck 2006; Thomas 2007; Dionne & Rothschild 2014). That said, many consider efficiency

questions as well (e.g., Abraham 1985; Avraham et al. 2014; Dionne & Rothschild 2014; Abraham &

Chiappori 2015).

4

See Patient Protection and Affordable Care Act § 2701, 42 U.S.C. § 300gg (2018).

5

See N.Y. Ins. Law § 2334 (2018); N.Y. Comp. Codes R. & Regis. tit. 11, §§ 161.8, 169.1 (2018).

Cost of Legal Restrictions on Experience Rating 39

Our analysis proceeds in three steps. First, we use the data to estimate the variance-

covariance matrix Σof unobserved heterogeneity in claim risk and to generate the house-

holds’ predicted claim rates based on observables. We model households’ claim counts

using a Poisson mixture model with correlated random effects. To estimate the model,

we take a moments-based approach that uses generalized estimating equations based on

marginal moments (Morris 2012). Unlike the standard approach—maximum likelihood

estimation of a parametric mixture of Poisson distributions—our estimation approach is

semi-parametric and unconstrained with respect to the parameters of the mixing distribu-

tion (Pinquet 2013). Among other things, the estimates reveal that unobserved heteroge-

neity in claim risk is positively correlated across lines of coverage.

Next, we demonstrate the value of the information contained in ^

Σ—and, by implica-

tion, the value of the signals provided by the households’ claims histories—by showing that

conditioning on claims experience leads to material refinements of the households’

predicted claim rates. For instance, we find that (1) among households with downward

revisions, their predicted claim rates decrease on average by 7 percent in auto collision,

13 percent in auto comprehensive, and 14 percent in home, and (2) among households

with upward revisions, their predicted claim rates increase on average by 10 percent in

auto collision, 23 percent in auto comprehensive, and 28 percent in home. We also dem-

onstrate the incremental value of conditioning across lines of coverage (in addition to con-

ditioning within lines of coverage).

Finally, we investigate the extent to which the households’ demand for coverage, as

captured by their deductible choices, wouldrespond to experience rating within and across

lines of coverage (i.e., uniline and multiline experience rating). In so doing, we obtain a

lower bound on the potential for unpriced heterogeneity in claim risk to distort demand.

Our experience rating scheme is a simple bonus-malus system under which changes in pre-

miums are proportional to changes in predicted claim risk. We model households’ deduct-

ible choices according to standard expected utility theory. After calibrating the model with

the risk aversion estimate reported by Barseghyan et al. (2013), we use the model to gener-

ate deductible choices for the households in our data assuming first that premiums are not

experience rated and then that they are experience rated. We find that there would be

large responses to experience rating. In particular, we find that the fraction of households

that would change deductibles if premiumswere experience rated is 7 percent in auto colli-

sion, 21 percent in auto comprehensive, and 15 percent in home, resulting in average

changes in coverage of $247, $178, and $347,respectively, among policies with a change.

The article proceeds as follows. Section II discusses the related literature. Section III

describes our data. Section IV presents the model and explains our estimation approach. Sec-

tions V–VIIcontain the three steps of ouranalysis. Section VIII offers concluding remarks.

II. Related Literature

The article contributes to two literatures. The first is the literature on experience rat-

ing in insurance markets. For surveys, see, for example, Pinquet (2000, 2013) and

40 Barseghyan et al.