ECONOMIC ANALYSIS OF SOCIAL SECURITY SURVIVORS INSURANCE

• Published date: 01 November 2018
• Date: 01 November 2018
• DOI: http://doi.org/10.1111/iere.12329
• Author: Yue Li

INTERNATIONAL ECONOMIC REVIEW

Vol. 59, No. 4, November 2018 DOI: 10.1111/iere.12329

ECONOMIC ANALYSIS OF SOCIAL SECURITY SURVIVORS INSURANCE∗

BYYUE LI1

University at Albany, SUNY, U.S.A.

This article develops a heterogeneous agents model to analyze the effects of Social Security survivors insur-

ance. The model features a negative mortality–income gradient, asymmetric information of individual mortality

rates, and a warm-glow bequest motive that varies by age and family structure. The model matches life-cycle

changes in life insurance coverage and generates advantageous selection in the insurance market. For male

agents, reducing survivors benefits for dependent children generates welfare losses, whereas reducing survivors

benefits for aged spouses produces welfare gains. The opposing welfare results are explained by differences in

the timing of benefits and in the funding cost.

1. INTRODUCTION

The Social Security trust fund is expected to be depleted in 2035, and major changes in the

Social Security program are anticipated to resolve its long-term solvency issue (Social Secu-

rity Administration, 2015a). There is large and expanding literature that uses heterogeneous

agents models to study Social Security Old-Age Insurance (OAI) reforms, but considerably

less attention has been given to Social Security survivors insurance, which comprises 13% of

total benefit outlays in 2014.2In particular, none of the previous analyses of survivors insurance

have used a framework where mortality rates and the probability of receiving survivors benefits

are decreasing with income (Kitagawa and Hauser, 1973; Duleep, 1986; Deaton and Paxson,

2001; Cristia, 2009; Chetty et al., 2016).3To fill the gap in the literature, this article extends the

Bewley–Huggett–Aiyagari framework to include a negative income–mortality gradient and the

opportunity to purchase life insurance and uses it to study the long-term effects of reducing

survivors benefits.

The model assumes that male agents make decisions for the household and derive a warm-

glow utility from leaving bequests.4The baseline bequest motive is allowed to vary by age and

across four types of family structures: single men without children, single men with children,

married men without children, and married men with children. In response to changes in

∗Manuscript received July 2015; revised July 2017.

1This article was previously circulated under the title “Economic Analysis of Social Security Survivors Benefits

for Dependent Children.” I thank three referees and editor Dirk Krueger for their valuable comments. I also thank

John Bailey Jones, Daniele Coen-Pirani, Marla Ripoll, Betty Daniel, Michael Sattinger, Laurence Ales, John Duffy,

Sewon Hur, Alejandro Badel, Satyajit Chatterjee, Pablo D’Erasmo, Jeremy Greenwood, Soojin Kim, Fabian Lange,

Samuel Myers, and Kim Ruhl for helpful discussions, and the participants in University of Pittsburgh Macroeconomic

Seminars, the 88th Annual Meetings of Western Economic Association International, and the 2015 Fall Midwest Macro

Conference. All remaining errors are mine. Please address correspondence to: Yue Li, Department of Economics,

University at Albany, SUNY, 1400 Washington Ave., Albany, NY 12222, U.S.A. Phone: 518-442-4738. Fax: 518-442-

4736. E-mail: yli49@albany.edu.

2In 2014, the total benefit outlays of the Social Security program were $848.4 billion, among which $19.2 billion was

paid to surviving children and $93.2 billion was paid to surviving aged spouses.

3For example, see Chambers et al. (2011), Hong and R´

ıos-Rull (2012), Kaygusuz (2015), and Bethencourt and

S´

anchez-Marcos (2016).

4The demand for life insurance is derived from a warm-glow bequest motive instead of a household joint decision,

because I want to capture the empirical finding that many individuals, especially young fathers, do not hold sufficient

life insurance to protect survivors from consumption drops upon their death (Auerbach and Kotlikoff, 1987, 1991; Hurd

and Wise, 1996; Bernheim et al., 2003a, 2003b).

2043

C

(2018) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

2044 LI

survivors benefits, agents can adjust their holdings of life insurance and risk-free assets to reach

the desired amount of bequests. The insurance firm observes an imperfect measure of individual

mortality risks and offers a one-sided long-term life insurance contract with a fixed uniform unit

price for all agents with the same risk measure. Consistent with findings of Cawley and Philipson

(1999) and McCarthy and Mitchell (2010), the model generates advantageous selection in the

life insurance market: Conditional on observed risk factors, insured agents have a lower average

mortality rate than the uninsured. This is because bequests are luxury goods, and agents with

lower mortality rates have higher income and are more likely to purchase life insurance to

increase the size of (potential) bequests. Under the alternative assumption that bequests are

normal goods, there is adverse selection in the insurance market.

To understand the economic implications of providing survivors insurance, I implement two

counterfactual experiments that separately reduce survivors benefits for dependent children

(SBDC) and survivors benefits for aged spouses (SBAS) by 23%, the projected reduction in

Social Security benefits in 2035 when the trust fund is depleted (Social Security Administration,

2015a). In these experiments, labor tax rates and insurance unit prices are adjusted, respectively,

to balance the government budget and to satisfy the zero-profit condition of the insurance firm.

The model suggests that reducing SBDC causes a 0.03% increase in consumption, a 2.38%

increase in insurance premium expenditures, a 0.25% decrease in bequests left by deceased

agents, a 0.04% increase in risk-free assets, and a 5.29% increase in insurance face values. The

change in premium expenditures is different from the change in insurance face values, because

the unit price varies substantially across agents. Reducing SBAS causes a 0.45% increase in

consumption, a 0.63% increase in premium expenditures, a 0.41% fall in bequests left by

deceased agents, a 1.46% increase in risk-free assets, and a 1.96% fall in insurance face values.

Reducing SBAS has a much larger impact on most aggregate variables mainly because the

funding cost for SBAS is 10 times as large as the funding cost for SBDC.

Turning to welfare, reducing SBDC generates a welfare loss equivalent to a 0.28% reduction

in lifetime consumption. The magnitude of the welfare loss falls with respect to permanent

income, indicating that low-income agents who have high mortality rates and high marginal

utilities of consumption lose more from reducing SBDC than high-income agents. In addition,

reducing SBDC reallocates resources away from young agents and from agents with children,

both of whom tend to have a high marginal utility of consumption. Under the veil of ignorance,

the benefits from redistribution outweigh the cost of funding SBDC. Conversely, reducing SBAS

generates a welfare gain equivalent to a 0.40% increase in lifetime consumption, with agents

of different permanent income levels benefiting from the experiment to a similar extent. The

opposing welfare implications of reducing SBDC and reducing SBAS are robust to alternative

assumptions about the behavior of life insurance firms and alternative specifications of the

bequest motive. This is because a new generation always discounts heavily the value of insurance

obtained later in life under the SBAS program but discounts little the value of insurance obtained

earlier in life under the SBDC program, and because the funding cost for SBAS is always much

greater than the funding cost for SBDC.

This article complements three strands of existing research. The first strand is the structural

analysis of Social Security reforms.5Within this literature, Chambers et al. (2011) and Hong and

R´

ıos-Rull (2012) are the two other papers that consider survivors benefits in a framework that

includes the life insurance market: Hong and R´

ıos-Rull (2012) evaluate the effect of eliminating

SBAS; Chambers et al. (2011) study the effect of simultaneously eliminating SBDC and SBAS.

This article differs from the previous literature by studying a setting where (i) mortality rates

decline with income, (ii) insurance firms have imperfect information about individual mortality

rates, and (iii) the amount of survivors benefits varies by the agent’s income and by the age of

survivors.

The second strand studies the demand for life insurance using two alternative approaches.

The first approach specifies a bequest preference independent of life insurance holdings

5see Feldstein and Liebman (2002) for a review.