Sunk Costs and Screening: Two‐Part Tariffs in Life Insurance

• Published date: 01 September 2020
• Date: 01 September 2020
• Author: Robert E. Hoyt,Krzysztof Ostaszewski,James M. Carson,Cameron M. Ellis
• DOI: http://doi.org/10.1111/jori.12283

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

DOI: 10.1111/jori.12283

Sunk Costs and Screening: Two-Part Tariffs in Life

Insurance

James M. Carson

Cameron M. Ellis

Robert E. Hoyt

Krzysztof Ostaszewski

Abstract

We develop a model of insurance pricing under heterogeneous lapse rates

with asymmetric information about lapse likelihood within the context of

an optional two-part tariff as a screening device for future policyholder be-

havior. We then test for consumer self-selection using policy-level data on

life insurance backdating. We exploit randomness in the initial tariff size to

separately identify the selection and sunk cost effects of backdating on lapse

proclivity.We find that consumers who are less likely to lapse self-select into

the two-part tariff pricing structure and we also document consumer behav-

ior consistent with sunk cost fallacy.

Introduction

There are large, upfront, fixed costs to writing a life insurance policy. Both agent

commission and direct underwriting costs (e.g., fees for physicals and blood tests) are

almost fully borne by insurers a few years into contracts that may last upwards of

30 years. Because of these upfront costs, insurers can actually lose money on policies

when the consumer lapses early into the contract, even if no death benefit is ever paid

James M. Carson is at the Terry College of Business, The University of Georgia. Carson can be

contacted via e-mail: jcarson@uga.edu. CameronM. Ellis is at the Fox School of Business, Temple

University,630 Alter Hall, 1801 Liacouras Walk, Philadelphia, PA 19122. Ellis can be contacted

via e-mail: cameron.ellis@temple.edu. Robert E. Hoyt is at the Terry College of Business, The

University of Georgia.Hoyt can be contacted via e-mail: rhoyt@uga.edu. Krzysztof Ostaszewski

is at Illinois State University. Ostaszewski can be contacted via e-mail: krzysio@ilstu.edu. The

authors are grateful to Scott Atkinson, Richard Butler,David Eckles, Julio Garin, Irina Gemmo,

Josh Kinsler, Alexander Muermann, Lars Powell, Thomas Quon, David Russell, Ian Schmutte,

Art Snow, John Turner, Bill Vogt, Juan Zhang, and seminar participants at meetings of the

WorldRisk and Insurance Economics Congress (Munich August, 2015), the Southern Risk and

Insurance Association (New Orleans November, 2015), the CEAR/MRIC Behavioral Insur-

ance Workshop(Munich December, 2016), the Allied Social Science Association—ARIA Session

(Philadelphia December,2017), Cal State Fullerton, the University of Georgia, the University of

Nebraska, and St. John’s University as well as two anonymous referees for helpful comments.

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out. Thus, to properly price contracts, insurers must estimate lapse risks. However,

because consumers may have knowledge about their relative lapse likelihood that

the insurer does not observe, asymmetric information arises and room for a screening

mechanism exists.

In this article, we develop a model of life insurance pricing under heterogeneous

lapse behavior with asymmetric information about lapse likelihood. We establish

the existence of a separating equilibrium under a menu of contracts containing an

optional two-part tariff. We then show the consumer’s choice serves as a screening

device for private information on lapse likelihood. Using detailed, policy-level data

on life insurance backdating as an example of our proposed optional two-part tariff,

we empirically test our model’s prediction of consumer self-selection. We use a con-

trol function approach to separately identify selection effects from potential sunk cost

fallacy.We find that consumers who choose to take part in the two-part tariff by back-

dating their policies are less likely to lapse, due to both self-selection and sunk costs.

Lapse rates in life insurance are substantial. Between 1991 and 2010, $29.7 trillion of

new individual life insurance coverage was issued in the United States. During this

same time period, $24 trillion of coverage lapsed. In a given year, for every term life

policy that ends in death or term maturation, 36 policies lapse due to nonpayment of

premiums (Purushotham, 2006). Eighty-eight percent of whole life insurance policies

never pay a death benefit (Gottlieb and Smetters, 2016). There are several theories on

why consumers lapse on their polices. This literature is well-developed and can be

condensed into: preference shocks, income shocks, policy replacement, and nonex-

pected utility explanations.

Preference shocks refer to a number of situations wherethe private value of the life in-

surance contract has changed (Fang and Kung, 2010; Liebenberg, Carson, and Dumm,

2012; Fei, Fluet, and Schlesinger, 2015).1Examples include: divorce, death of a spouse

or child, children becoming self-sufficient, increase in spousal income, etc. Income

shocks refer to consumers experiencing a negative shock to income and thereby hav-

ing insufficient funds to pay premiums. The effect of an income shock on lapse rates

is stronger in whole life insurance due to the higher premiums and presence of a

surrender value. This is referred to in the literature as the emergencyfund hypothesis

(Linton, 1932; Outreville, 1990; Kuo, Tsai,and Chen, 2003). The aptly named policy re-

placement hypothesis refers to consumers who lapse on one policy because they find

what they believe to be a better one (Outreville, 1990; Carson and Forster, 2000). The

interest rate hypothesis is a specific case of the policy replacement hypothesis where

the driver of better available policies is a change in expectations of future interest

rates (Schott, 1971; Pesando, 1974; Kuo, Tsai, and Chen, 2003).2The final category of

research on lapse rates focuses on nonexpected utility models of consumer behavior

1This reason for lapsing generally only covers negative shocks to the insurance value of the

policy. Positive shocks to preferences are typically subsumed by the policy replacement cate-

gory.

2Because insurance premiums are collected, and invested, long before benefits are paid out,

expectations about interest rates play an important part in the determination of premium

rates.

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