Social security and longevity risk: An analysis of couples

• Published date: 01 June 2022
• Author: Erin Cottle Hunt,Frank N. Caliendo
• Date: 01 June 2022
• DOI: http://doi.org/10.1111/jpet.12564

Received: 22 March 2021

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Accepted: 8 December 2021

DOI: 10.1111/jpet.12564

ORIGINAL ARTICLE

Social security and longevity risk: An analysis

of couples

Erin Cottle Hunt

1

|Frank N. Caliendo

2

1

Department of Economics, Lafayette

College, Easton, Pennsylvania, USA

2

Department of Economics and Finance,

Utah State University, Logan, Utah, USA

Correspondence

Erin Cottle Hunt, Department of

Economics, Lafayette College, Easton,

PA, USA.

Email: cottle.erin@gmail.com and

cottlee@lafayette.edu

Abstract

To help manage longevity risk, Social Security pays

three types of benefits to retirees: retirement bene-

fits as a life annuity, spousal benefits until the death

of the primary earner, and survivor benefits after the

death of primary earner. How effective is Social

Security at insuring couples against the joint long-

evity risks that they face? We take a public finance

approach to this important question by comparing a

Laissez Faire economy to a variety of different public

insurance structures including the First Best, the

Second Best, and US Social Security. We find that

the welfare gains to couples from participating in the

US Social Security system are large, and the survivor

benefit feature is the key to this result while the

spousal benefit provides very little efficiency gains.

In fact, the optimal mixture of spousal and survivor

benefits (i.e., the Second Best) improves ex ante

efficiency by providing a larger payment to widows

and a smaller spousal benefit than the current US

system. We obtain these results using a theoretical

model of couples who have full information about

gender‐specific longevity risks and solve a dynamic

stochastic (regime‐switching) problem to optimally

hedge these risks.

J Public Econ Theory. 2022;24:547–579. wileyonlinelibrary.com/journal/jpet © 2021 Wiley Periodicals LLC

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1|INTRODUCTION

Social Security pays benefits to retirees as a life annuity, and in the absence of competitive

annuity markets, this feature is commonly understood to provide welfare gains by allowing

individuals to pool their longevity risk. Such risk sharing is referred to as Social Security's

longevity insurance role.

When evaluating Social Security's longevity insurance role, the typical starting point is a

life‐cycle model of single individuals. Of course, modeling singles rather than couples keeps the

analysis clean and tractable, and many important economic lessons can be learned at this level

of abstraction. However, the US Social Security system has two important features relating to

couples: spousal benefits and survivor benefits. First, if both individuals are alive, then a spouse

can collect benefits equal to the larger of their own benefits or half of their spouse's benefits.

For example, if a husband's average earnings exceeds that of the wife's, then he collects benefits

based on his own earning history while she collects benefits equal to the larger of her own

benefits based on her earning history or half of her husband's benefits. Second, Social Security

provides benefits to the surviving spouse. For example, if a husband passes away first, then the

widow will collect the larger of his benefit or her benefit for the remainder of her life.

In this paper, we evaluate Social Security's longevity insurance role from the perspective of

a couple. We develop a life‐cycle consumption/saving model of a husband and wife, and we

solve the couple's optimization problem recursively. We first consider the contingent problems

of the widow and widower upon the death of their spouse, and we solve these problems to

obtain the continuation value of asset holdings at each possible date of death of the spouse.

Moving back to the beginning of the life cycle, we then embed these continuation values into

the initial problem of a couple who must form a consumption and saving plan that optimally

hedges the joint longevity risks that they face. We work in continuous time and we derive an

analytical solution to this dynamic stochastic control problem.

1

We take a public finance approach to the problem by characterizing and comparing the

couple's consumption, saving, and welfare across a variety of scenarios, including a Laissez

Faire economy with no government, an economy with ex ante efficient (First Best) insurance,

an economy with US Social Security, and an economy with various permutations to US Social

Security including removing some of its features as well as reconfiguring the program to reach

the Second Best welfare level.

Our baseline analysis focuses on a married, single‐earner household consisting of a working

male with a shorter life expectancy than the female spouse who does not participate in the

labor force. Of course, the prevalence of dual‐earner households in America has changed

dramatically over the last half century, rising from a small minority to a significant majority

(Fisher & Johnson, 2019), and we also consider a dual‐earner couple with wage parity between

husband and wife as an alternative bookend assumption. Survivor benefits and spousal benefits

are redundant features for dual‐earner couples who earn the same wage. That is, a dual‐earner

couple would not use the spousal or survivor benefit if both spouses earn the same wage—

instead both spouses would claim identical retirement benefits based on their identical earn-

ings history. In contrast, these marriage‐related features of Social Security are especially

1

We take into consideration gender‐specific longevity risk, since women in the US have a longer life expectancy than

men. As such, we focus our analysis on a male–female couple. The modeling framework we develop can also

accommodate male‐male or female–female couples.

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relevant (and would always be claimed) for single‐earner couples and so we select this parti-

cular family structure for our baseline analysis.

We evaluate the effectiveness of Social Security in providing longevity insurance in a setting

that is designed to allow Social Security the greatest possible chance to improve welfare. The

couple in our model is unable to insure their longevity risk (no annuity markets) and does not

adjust their joint labor supply. Their only avenue of self‐insurance is through precautionary

savings. These assumptions create room for a public, Second Best option to improve ex ante

welfare.

Yet, even in this setting, we find that the spousal benefit is not very useful to single‐earner

couples. This is an important result because it is an expensive feature to finance. In contrast,

eliminating the survivor benefit makes single‐earner couples much worse off. In fact, the

couple would be better off fending for themselves in Laissez Faire without Social Security than

participating in a program with only retirement and spousal benefits and no survivor benefits.

If the goal is to help single‐earner couples insure their joint longevity risk, then the current

Social Security system could improve the ex ante wellbeing of single‐earner couples even more

if it were revised to pay larger survivor benefits and smaller spousal benefits, holding taxes and

retirement benefits fixed. To the extent that policy makers wish to better protect widows who

did not work, increasing the survivor benefit by shrinking the spousal benefit is a budget‐

neutral way to achieve that goal.

2

Finally, while dual‐earner couples do benefit from the

annuitization feature of Social Security, their welfare gains are significantly smaller than those

accruing to single‐earner couples.

A few authors have expanded the seminal longevity risk model from Yaari (1965) to include

an analysis of couples. Hurd (1999) studies the joint optimization problem facing couples and

our theoretical analysis is similar, though we focus specifically on the welfare effects of Social

Security. Likewise, Kotlikoff and Spivak (1981) examine the degree to which couples may

naturally hedge their longevity risk through cooperative optimization of their joint resources

and by naming the other as the sole beneficiary of their joint wealth. Our analysis incorporates

these features, and it goes a step further in seeking to understand the importance of Social

Security in providing additional longevity insurance beyond what is naturally found through

self‐insurance within the family.

Brown and Poterba (2000) calculate the welfare gains to couples who purchase annuities

from competitive private markets and find that the welfare gains accruing to couples tend to be

smaller than for singles. Although our technical treatment of couples is similar, they calculate

the welfare gains from access to competitive annuities on top of Social Security, while we study

the welfare effects of Social Security when competitive annuity markets are missing.

3

2

To focus on Social Security's longevity insurance role, we shut down other potential roles: households do not vary by

earning type so there is no redistributive role for Social Security, and households optimize their resources with full

information about the risks that they face, so there is no role for Social Security to rescue irrational savers. Also, the

public and private rates of interest on the storage of wealth are equal (set to zero for simplicity), so there are no

dynamic (in)efficiencies associated with our welfare results. All welfare gains are therefore strictly the result of

households sharing their longevity risk through Social Security.

3

One limitation in our study is the absence of life insurance markets. In reality a couple can purchase life insurance

against the untimely death of a spouse, and holding at least some life insurance is common, especially among married

households (Chambers et al., 2003). However, most of the poverty experienced by surviving women tends to be the

result of inadequate life insurance coverage according to Bernheim et al. (2003), and notwithstanding relatively high

participation rates in life insurance markets, the aggregate welfare gains associated with such participation appear to be

quite small, even if insurance is actuarially fair, according to Chambers et al. (2003). Given that a lack of sufficient

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