Why do life insurance policyholders lapse? The roles of income, health, and bequest motive shocks

• Published date: 01 December 2021
• Author: Hanming Fang,Edward Kung
• Date: 01 December 2021
• DOI: http://doi.org/10.1111/jori.12332

Received: 10 August 2020

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Revised: 26 October 2020

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Accepted: 1 November 2020

DOI: 10.1111/jori.12332

ORIGINAL ARTICLE

Why do life insurance policyholders lapse?

The roles of income, health, and bequest

motive shocks

Hanming Fang

1,2,3

|Edward Kung

4

1

Department of Economics, University of

Pennsylvania, Philadelphia,

Pennsylvania, USA

2

School of Entrepreneurship and

Management, ShanghaiTech University,

Shanghai, China

3

The National Bureau of Economic

Research, Cambridge,

Massachusetts, USA

4

Department of Economics, California

State University at Northridge,

Northridge, California, USA

Correspondence

Hanming Fang, Department of

Economics, University of Pennsylvania,

133 S. 36th St., Philadelphia,

PA 19104, USA.

Email: hanming.fang@econ.upenn.edu

Funding information

National Science Foundation,

Grant/Award Number: SES‐0844845

Abstract

We present and empirically implement a dynamic

discrete choice model of life insurance decisions to

assess the importance of various factors in explaining

life insurance lapsation. We estimate a model using

information on life insurance holdings from the Health

and Retirement Study. Counterfactual simulations

using the estimates of our model suggest that a large

fraction of life insurance lapsations are driven by

idiosyncratic shocks, uncorrelated with health, income,

and bequest motives, particularly when policyholders

are relatively young. As the remaining policyholders

get older, however, the role of such independent and

identically distributed (i.i.d.) shocks gets smaller, and

more of their lapsation is driven by income, health, or

bequest motive shocks. As anticipated, income and

health shocks are relatively more important than

bequest motive shocks in explaining lapsation when

policyholders are young, with bequest motive shocks

playing a more important role as we age.

KEYWORDS

life insurance lapsations, sequential Monte Carlo method

JEL CLASSIFICATION

G22, L11

J Risk Insur. 2021;88:937–970. wileyonlinelibrary.com/journal/JORI

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937

© 2020 American Risk and Insurance Association

1|INTRODUCTION

The life insurance market is large and important. According to Life Insurance Marketing

and Research Association International (LIMRA International), 78% of American families

owned some type of life insurance in 2004. By the end of 2008, the total number of

individual life insurance policies in force in the United States stood at about 156 million;

and the total individual policy face amount in force reached over 10 trillion dollars (see

American Council of Life Insurers, 2009, pp. 63–74).

1.1 |Life insurance market

There are two main types of traditional individual life insurance products, term life in-

suranceandwholelifeinsurance.

1

A term life insurance policy covers a person for a

specific duration at a fixed or variable premium for each year. If the person dies during the

coverage period, the life insurance company pays the face amount of the policy to his/her

beneficiaries, provided that the premium payment has never lapsed. The most popular type

of term life insurance has a fixed premium during the coverage period and is called level

term life insurance. A whole life insurance policy, on the other hand, covers a person's

entire life, usually at a fixed premium. In the United States at year‐end 2008, 54% of all life

insurance policies in force were Term Life insurance. Of the new individual life insurance

policies purchased in 2008, 43%, or 4 million policies, were term insurance, totaling $1.3

trillion,or73%,oftheindividuallifefaceamount issued (see American Council of Life

Insurers, 2009,pp.63–74). Besides the difference in the period of coverage, term and whole

life insurance policies also differ in the amount of cash surrender value (CSV) received if

the policyholder surrenders the policy to the insurance company before the end of the

coverage period. For term life insurance, the CSV is zero; for whole life insurance, the CSV

is typically positive and prespecified to depend on the length of time that the policyholder

has owned the policy. One important feature of the CSV on whole life policies relevant to

our discussions below is that by government regulation, CSVs do not depend on the health

status of the policyholder when surrendering the policy.

2

1.2 |Lapsation

Lapsation is an important phenomenon in life insurance markets. Both LIMRA and the Society

of Actuaries consider a policy to lapse if its premium is not paid by the end of a specified time

(often called the grace period).

3

According to LIMRA (2009, p. 11), the life insurance industry

calculates the annualized lapsation rate as follows:

1

The whole life insurance has several variations such as universal life (UL), variable life (VL), and variable‐universal

life (VUL). Universal life allows flexible premiums subject to certain minimums and maximums. For variable life, the

death benefit varies with the performance of a portfolio of investments chosen by the policyholder. Variable‐universal

life combines the flexible premium options of UL with the varied investment option of VL (see Gilbert & Schultz, 1994).

2

The life insurance industry typically thinks of the CSV from the whole life insurance as a form of tax‐advantaged

investment instrument (see Gilbert & Schultz, 1994).

3

This implies that if a policyholder surrenders his/her policy for cash surrender value, it is also considered as a

lapsation.

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FANG AND KUNG

A

nnualized policy lapse rate = 100 × Number of policies lapsed during the year

Number of policies exposed to lapse during the year

.

The number of policies exposed to lapse is based on the length of time the policy is exposed to

the risk of lapsation during the year. Termination of policies due to death, maturity, or con-

version is not included in the number of policies lapsing and contributes to the exposure for

only the fraction of the policy year they were in force. Table 1provides the lapsation rates of

individual life insurance policies, calculated according to the above formula, both according to

face amount and the number of policies for the period of 1998–2008. Of course, the lapsation

rates also differ significantly by the age of the policies. For example, LIMRA (2009, p. 18)

showed that the lapsation rates are about 2%–4% per year for policies that have been in force for

more than 11 years in 2004–2005.

1.3 |Reasons for lapsation have important welfare implications

Our interest in the empirical question of why life insurance policyholders lapse their policies is

motivated by recent research on the effects of lapsation in life insurance and life settlements

markets. It is well known that life insurance pricing is supported by lapsation but recent work

has highlighted the fact that the reasons for lapsation have important welfare consequences.

For example, Gottlieb and Smetters (2020) note that the efficiency implications of lapsation

depend on whether policyholders lapse due to forgetfulness or income shocks, and also on

whether these shocks are anticipated or unanticipated. Daily et al. (2008) and Fang and Kung

(2010b,2020) also showed that the efficiency implications of the growing secondary market for

life insurance depends crucially on whether lapses are driven by loss in bequest motive or other

factors. They showed that if policyholders' lapsation is driven only by the loss of bequest

motives, then consumer welfare is unambiguously lower with a secondary market than

without, but if lapsation is driven by income or liquidity shocks, then a life settlement market

may potentially improve consumer welfare.

4

To understand why the reasons for lapsation matters, it is important to remember that life

insurance premiums are front‐loaded, meaning in the early part of the policy period, the pre-

mium payments exceed the actuarially fair value of the risk insured, but in the later part of the

policy period, the premium payments are lower than the actuarially fair value. As a result,

policyholders who lapse after holding the policy for some time give up value, which the life

insurance company pockets as a profit. Due to competition, these so‐called lapsation profits are

factored into thepricing of the life insurance policyto start with (Gilbert & Schultz, 1994), and so

policyholders who lapse end up cross‐subsidizing policyholders who do not. The welfare im-

plications of this cross‐subsidization depend on the marginal utility of income of lapsers relative

to entire pool (since everyone benefits from lower pricing), and it therefore depends on the

reasons for lapsation. If lapsation happens mainly for idiosyncratic reasons, such as a loss in

4

Related, Fang and Wu (2020) showed that when policyholders are overconfident about the strength of their bequest

motive at the time of purchasing their life insurance policy, they will underestimate their probability of lapsation, and

end up being exploited by the life insurance by purchasing “too much”risk reclassification insurance. A life settlements

market can potentially improve consumer welfare by imposing a limit on the extent to which primary insurers can

exploit overconfident consumers.

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