The Influence of Sellers on Contract Choice: Evidence from Flood Insurance

• Date: 01 June 2020
• Author: Marc A. Ragin,Benjamin L. Collier
• Published date: 01 June 2020
• DOI: http://doi.org/10.1111/jori.12280

©2019 The Journal of Risk and Insurance (2019).

DOI: 10.1111/jori.12280

The Influence of Sellers on Contract Choice:

Evidence from Flood Insurance

Benjamin L. Collier

Marc A. Ragin

Abstract

We examine the ability of insurers to influence the coverage limit decisions

of 180,000 households in the National Flood Insurance Program. In this pro-

gram, private insurers sell identical flood contracts at identical rates and bear

no risk of paying claims. About 12 percent of new policyholders overinsure,

selecting a coverage limit that exceeds their home’s estimated replacement

cost. Overinsuring is expensive relative to expected loss, making it difficult

to explain with standard decision-making models. The rate of overinsuring

differs substantially across insurers, ranging from zero to one-third of new

policies. Insurer effects on the likelihood of overinsuring are statistically sig-

nificant after controlling for the policyholder’s characteristics. Additionally,

some insurers seem to encourage households to overinsure in percentage

terms (e.g., buy 110 percent of replacement cost) while others encourage

rounding up in dollars (e.g., to the next $10,000). Wefind that insurers’ distri-

bution systems and commission rates influence whether their policyholders

overinsure.

Introduction

We examine whether insurers influence the contract choices of their policyholders.

Economists model insurance decisions as a function of a consumer’s risk exposure

and risk preferences (e.g., Arrow, 1974; Cohen and Einav, 2007). For many insurance

decisions, however, the consumer has incomplete information and must rely on the

seller to understand the risk and the insurance contract. Thus, a consumer’s contract

decisions may depend on what its insurer recommends. Investigating potential seller

effects in an insurance setting, however, often involves empirical challenges due to

We thank David Eckles, Jed Frees, Rob Hoyt, Kenneth Klein, Joan Schmit, Roxane Steinacker,

Justin Sydnor, and seminar participants at University of Wisconsin-Madison, Temple Univer-

sity, the American Risk and Insurance Association, and the Southern Risk and Insurance As-

sociation for helpful comments. We also thank Jianing Yao and Juan Zhang for their research

assistance.

Benjamin L. Collier is at the Department of Risk, Insurance, and Healthcare Management,

Temple University. he can be contacted via e-mail: collier@temple.edu. Marc A. Ragin is at

the Department of Insurance, Legal Studies, and Real Estate, University of Georgia. He can be

contacted via e-mail: mragin@uga.edu

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differences between insurers (e.g., credit rating) and the product features that they

offer (e.g., coverage terms and pricing).

In this study,we examine a market setting that overcomes these empirical challenges—

private insurers who sell residential flood insurance policies in the National Flood

Insurance Program (NFIP). The U.S. federal government sets all terms of the insurance

contract (e.g., premium rating, coverage options) and bears all claims risk. The NFIP

incentivizes private insurers to sell these policies via commissions on the premium

paid. Thus, the contracts in our study are identical in every sense except for the seller—

an ideal setting to examine the ability of sellers to influence households’ contract

choices.

Our analyses focus on overinsuring, where consumers select a flood insurance cover-

age limit that is larger than their home’s estimated replacement cost. About 12 percent

of new policyholders overinsure. The replacement cost is the cost to rebuild the home

with materials of like kind and quality, and is estimated by the seller at the time of

purchase.1A household might overinsure for several reasons, which we discuss be-

low. In our setting where insurers sell identical products, standard economic theory

suggests that the selected coverage limit should not depend on the insurer. Yet, we

observe that overinsuring differs substantially across insurers.Figure 1 is a motivating

illustration. It shows the distribution of selected coverage limits (relative to estimated

replacement cost) for new policyholders of three large participating insurers. A ratio

of one indicates full coverage, while a ratio above (below) one denotes overinsuring

(underinsuring). The policyholders of Insurer A tend to purchase full coverage, and

they never overinsure. The policyholders of Insurer B often overinsure, with more

than 30 percent of policyholders purchasing excess coverage. Insurer C’s policyhold-

ers are the most likely to partially insure (about 40 percent), though approximately 15

percent overinsure.

Under an assumption of fully-informed consumers, overinsuring is difficult to explain

with standard models of decision making (e.g., expected utility theory or prospect

theory). The cost to overinsure appears large relative to the expected loss. Out of

nearly 180,000 policies in our sample, assessed damages are greater than estimated

replacement cost only 40 times—a rate of 0.02 percent. Six of these 40 policies with

excess damage were overinsured. The mean amount of excess damage for the 40

policies is $6,872. This results in an expected loss per household of $1.53. Overinsuring

households pay an average of $71.07 in additional premium for excess coverage, which

1Throughout the article, we refer to the seller’s estimate of the cost at this point as the home’s

“replacement cost.” Insurers use software to estimate replacementcost for the customer based

on claims data and a home’s characteristics (e.g., size, location, and construction materials).

Insurers are required to report the home’s replacement cost to the NFIP for the policies that

we study.The NFIP instructs sellers to use “normal company practice” to provide the home’s

estimated replacement cost to the policyholder when the flood insurance contract is origi-

nated (NFIP, 2006, p. 4–175). Deriving an accurate estimate of the home’s replacement cost is

instrumental to the property insurance industry.

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The Influence of Sellers on Contract Choice: Evidence from Flood Insurance 3

Figure 1

Policyholder Coverage Limits for Three Insurers

Note: Figure shows the distribution of selected building coverage limits (relative to estimated

replacement cost) of new policyholders for three large insurersin the National Flood Insurance

Program.We selected these three insurers for purposes of illustration. A ratio equal to 1 indicates

full coverage, while a ratio greater than (less than) 1 indicates overinsurance (underinsurance).

The policyholders of Insurer A tend to fully insure (i.e., choose a coverage limit equal to their

home’s replacement cost) and never overinsure. In contrast, more than 30 percentof Insurer B’s

policyholders overinsure. Finally, about 40 percent of the policyholders of Insurer C partially

insure and approximately 15 percent overinsure.

is 4,645 percent of the expected loss. Paying such a large risk premium implies triple-

digit levels of relative risk aversion.2

2A back-of-the-envelope calculation for a representative household in our data indicates that

overinsuring would requirea coefficient of relative risk aversion of at least 117. For this calcula-

tion, we assume that the representative household has initial wealth of the mean replacement

cost for overinsuring households ($146,380), a 0.02 percent probabilityof $6,872 possible excess

damage, and must pay a $71.07 premium to cover this risk. This household is assumed to be an

expected utility maximizer with constant relative risk aversion, 1/(1 −)x(1−)with x>0. We

identify the minimum relative risk aversion for which the expected utility of overinsuring ex-

ceeds that of fully-insuring. A =117 is consistent with recent researchshowing the difficulty

of explaining households’ insurance decisions with expected utility.For example, households’

homeowners deductibles (Sydnor, 2010) and their decision to fully insure rather than par-

tially insure in the NFIP (Collier et al., 2017) each require triple-digit relative risk aversion.

We conduct a similar calculation for cumulative prospect theory, using a reference point of

no losses and no premiums paid and the parameters given by Tversky and Kahneman (1992).

While Sydnor (2010) and Collier et al. (2017) find that cumulative prospect theory can explain

households’ deductible and coverage limits, we find that it cannot explain overinsuring for

our representative household using this approach.

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