are life insurance holdings related to financial vulnerabilities?

ARE LIFE INSURANCE HOLDINGS RELATED TOFINANCIAL VULNERABILITIES?

B. DOUGLAS BERNHEIM, KATHERINE GRACE CARMAN, JAGADEESH GOKHALE, andLAURENCE J. KOTLIKOFF*

Using the 1995 Survey of Consumer Finances and an elaborate life-cycle model, wequantify the potential financial impact of each individual's death on his or her survivorsand measure the degree to which life insurance moderates these consequences. Lifeinsurance is essentially uncorrelated with financial vulnerability at every stage of thelife cycle. As a result, the impact of insurance among at-risk households is modest, andsubstantial uninsured vulnerabilities are widespread, particularly among youngercouples. We also identify a systematic gender bias: For any given level of financialvulnerability, couples provide significantly more protection for wives than for husbands.(JEL D10, G22)

I. INTRODUCTION

The purpose of this article is to examine lifeinsurance holdings and financial vulnerabil-ities among couples over the life cycle. Twoseparate concerns motivate our analysis. First,there are reasons to suspect that life insurancecoverage is poorly correlated with underlyingfinancial vulnerabilities. A well-known insur-ance industry adage holds that life insurance issold and not bought. Alternatively, householdsmay purchase long-term policies relativelyearly in life and subsequently fail to adjust cov-erage appropriately because of inertia or otherpsychological considerations. Second, house-holds that purchase little or no life insurancemay leave either or both spouses at risk of ser-ious financial consequences.

With respect to the first concern, the avail-able evidence is limited. Using a sample of olderworkersdrawnfromthe1992waveoftheHealthand Retirement Study (HRS), Bernheim et al.(2003) documented a startling mismatchbetween life insurance holdings and underly-ing vulnerabilities (defined as the decline inliving standard that a survivor would experi-ence in the absence of insurance). In particular,they found virtually no correlation betweenthese two variables. However, because the HRSfocuses on individuals approachingretirement,this finding did not permit them to distinguishbetween the two hypotheses mentioned in theprevious paragraph.

The second concern has received consider-ably more attention. One branch of the liter-ature examines the experience of widows.Holden et al. (1986) and Hurd and Wise(1989) documented sharp declines in livingstandards and increases in poverty rates(from 9% to 35%) among women whose hus-bands actually passed away. A second branchof the literature projects the consequences ofwidowhood for married individuals. Analyz-ing data gathered during the 1960s from house-holds in middle age through early retirement,

ABBREVIATIONS

HRS: Health and Retirement Study

OECD: Organisation for Economic Co-operation

and Development

OLS: Ordinary Least Squares

SCF: Survey of Consumer Finances

*We are grateful to the National Institute of Agingprovided financial support. Economic Security Planner(ESPlanner) is used in this study with the permission ofEconomic Security Planning, Inc.

Bernheim: Professor, Department of Economics, StanfordUniversity, Stanford, CA 94305-6072 and NationalBureau of Economic Research. Phone 650-725-8732,Fax 650-725-570, E-mail [email protected]

Carman: Postdoctoral Fellow, Center for Basic Researchin the Social Sciences, Harvard University,Cambridge, MA 02138. Phone 617-495-5365.

Gokhale: Senior Economic Advisor, Federal ReserveBank of Cleveland, P.O. Box 6387, Cleveland, OH44101-1387. Phone 216-579-2970, Fax 216-579-3050,E-mail [email protected]

Kotlikoff: Professor, Boston University, Department ofEconomics, 270 Bay State Rd., Boston, MA 02215.Phone 617-353-4002, Fax 617-353-4001, [email protected]

531

Economic Inquiry(ISSN 0095-2583) DOI: 10.1093/ei/cbg026Vol. 41, No. 4, October 2003, 531±554 # Western Economic Association International

Auerbach and Kotlikoff (1987; 1991a; 1991b)found that roughly one-third of wives andsecondary earners would have seen their livingstandards decline by 25% or more had theirspouses died. Bernheim et al. (2003) adopteda similar approach but used more recent, high-quality data, more accurate estimates of surviv-al±contingent income streams, and a moreelaborate life-cycle simulation model. Theydocumented significant underlying vulnerabil-ities among older working couples; ignoringlife insurance, one-third of secondary earnerswould have experienced significant (20% orgreater) declines in living standards had theirspouses died in 1992, whereas one-fifth wouldhave experienced severe declines (40% orgreater). More important, only one in threehouseholds in these at-risk populations heldsufficient life insurance to avert significant orsevere financial consequences. Though pri-mary earners (typically husbands) were lessfrequently at risk for significant or severe con-sequences, they generally had much less pro-tection (insurance on the secondary earner'slife) for any given level of risk exposure. Nota-bly, none of the studies mentioned examineduninsured exposures among younger house-holds. This is a significant omission, becauseyounger couples generally have more contin-gent income to protect and hence greaterunderlying vulnerabilities.

In the current study, we reexamine both setsof issues using data obtained from the 1995wave of the Survey of Consumer Finances(SCF). Relative to the HRS (studied byBernheim et al., 2003), the primary advantageof the SCF is that it includes adult respondentsof all ages. Consequently, we extend the exist-ing literature by examining financial vulner-abilities and life insurance coverage at allstages of the life cycle. This permits us toprovide the first available evidence concern-ing uninsured financial vulnerabilities amongyoung households, as well as to distinguishbetween the two alternative explanations forthe absence of a correlation between financialvulnerabilities and insurance holdings men-tionedÐthat insurance bears little relation toneeds at the time of purchase and that house-holds purchase long-term contracts with ini-tially appropriate insurance coverage but failto adjust this coverage through time as theircircumstances change.

Because the SCF data are in some waysless comprehensive than the HRS data, this

extension comes at a cost. Most notably,matching Social Security earnings historiesare not available for the SCF sample. In addi-tion, certain measurement problems (e.g.,the likelihood that a nonworking widow orwidower will enter the labor force or the poten-tial for remarriage) are more severe for youngerhouseholds than for older households. Never-theless, because the SCF does contain informa-tion on many important factors that determinefinancial vulnerabilities, it is reasonable to inferthat measured and actual financial vulnerabil-ities are correlated. If households respond togreater financial vulnerabilities by purchasingmore insurance, one would still expect toobserve a correlation between measured vul-nerabilities and insurance holdings.

In practice, we find that aside from scaleeffects associated with the level of income,the correlation between financial vulnerabil-ities and life insurance holdings is essentiallyzero throughout the entire life cycle. This find-ing is consistent with the hypothesis that lifeinsurance bears little relation to needs at thetimeof purchase; however, it tends to refute thehypothesis that households purchase long-term contracts with initially appropriate insur-ance coverage but fail to adjust this coveragethrough time as their circumstances change.

We also find that uninsured vulnerabilitiesareconsiderablygreateramongyoungercouplesthan among older couples. Nearly two-thirdsof secondary earners between the ages of 22and 39 have significant uninsured financialvulnerabilities (projected reductions in livingstandards exceeding 20%), and nearly one-third have severe uninsured vulnerabilities(projected reductions exceeding 40%). More-over, for this age group, only one in five house-holdswithat-risk secondaryearners (thosewhowould experience significant or severe declinesin living standard on the death of their spouse,ignoring insurance) held sufficient life insur-ance to avert significant or severe financialconsequences. For the entire sample, in theabsence of life insurance, 56% of secondaryearners and 6% of primary earners would haveexperienced significant or severe declines inliving standard on the death of a spouse. Actuallife insurance holdings reduce these figures to,respectively, 42% and 5%. Thus, the overallimpact of life insurance holdings on financialvulnerabilities among at-risk households ismodest. Roughly two-thirds of poverty amongsurviving women and more than one-third of

532 ECONOMIC INQUIRY

poverty among surviving men resulted from afailure to ensure survivors of an undiminishedliving standard through insurance.

Whereas our analysis of the correlationbetween vulnerabilities and insurance holdingsonlyrequires us toassume that there isa reason-ably strong correlation between actual andmeasured vulnerabilities, our findings concern-ing the prevalence of financial vulnerabilitiesrely more heavily on the accuracy of computedvulnerabilities. In light of the limitations of theSCF and the associated measurement prob-lems, we therefore examine the robustness ofthe findings summarized in the preceding para-graphs with respect to a variety of alternativeassumptions and imputations.

Finally, we find evidence of a significantgender bias in life insurance holdings. Specif-ically, for any given level of financial vulner-abilities, couples provide significantly moreprotection for wives than for husbands. Forexample, couples with severely at-risk wiveson average hold $166,628 of life insurance,whereas couples with severely at-risk husbandson average hold only 15% of this amount($24,827). Life insurance reduced the averageimpact of a husband's death on the living stand-ard of a severely at-risk wife from a 65.5%decline to a 47.6% decline. In contrast, lifeinsurance reduced the average impact of awife's death on the living standard of a severelyat-risk husband by a much smaller amount,from a 68.4% decline to a 64.1% decline. It isunlikely that these results are attributable tomeasurement problems. If anything, our anal-ysis understates the true gender differential byoverstating the vulnerabilities of nonworkingspouses relative to working spouses.1

The article proceeds as follows. Section IIdiscusses methods, section III describes thedata, section IV presents basic results, section Vprovides sensitivity analysis, and section VIconcludes.

II. A STRATEGY FOR MEASURING FINANCIALVULNERABILITIES

Following Bernheim et al. (2003), we adopta concrete and easily understood yardstick forquantifying financial vulnerabilities: the per-centage decline in an individual's sustainable

living standard that would result from aspouse's death.2 The use of this yardstick per-mits us to make apples-to-apples comparisonsof vulnerabilities across households and inves-tigate correlations between vulnerabilities andinsurance coverage. We also compare actuallife insurance holdings to a natural benchmark,defined as the level of coverage required toensure survivors of no change in their sustain-able living standard. It is worth emphasizingthat we do not regard this benchmark as a de-finitive standard of adequacy or rationality.Rational decision makers may elect to pur-chase either higher or lower levels of insurance.However, when combined with other evidenceon household objectives, comparisons with thebenchmark potentially shed light on the ade-quacy of life insurance coverage.

Concepts

We clarify our strategy for measuring finan-cial vulnerabilities through an example. Imag-ine that a husband and wife each live for atmost two years (equivalently, they are withintwo years of maximum life span). Both are aliveinitially, but either may die before the secondyear. The household's well-being depends onconsumption in each year and survival contin-gency. As will be discussed further, we allow forthe possibility that some ongoing expendituresare either exogenous or determined early in lifeby `̀ sticky'' choices. We refer to these expend-itures as fixed consumption and to residualspending as `̀ variable consumption.'' Let y1denote initial assets plus first period earningsnet of fixed consumption, and let y2s denotesecond period earnings net of fixed consump-tion in state s�W,H,B, where the stateidentifies survivors (wife, W, husband, H, orboth, B). The couple divides first-periodresources between variable consumption, c1,saving, A, and insurance premiums, piLi,i�H,W, where Li represents the second-period payment to i if his or her spouse dies,and pi denotes the associated price per dollar ofcoverage.AssetsA earn the rate of return r. Thecouple faces the following constraints: c1�y1ÿAÿ pWLWÿ pHLH, c2B� y2B�A(1� r),

1. Our base-case calculations assume that an indivi-dual does not increase hours worked in the labor forceafter the death of his or her spouse.

2. To calculate this decline, we make use of an elaboratelife-cycle model. The model is embodied in financial plan-ning software, Economic Security Planner (ESPlanner).Economic Security Planning, Inc., provides free copies ofthesoftwareforacademicresearch.Foradditional informa-tion, consult www.ESPlanner.com

BERNHEIM ET AL.: LIFE INSURANCE AND FINANCIAL VULNERABILITY 533

and c2i� y2i�A(1� r)�Li for i�W,H,where c2i denotes second period variable con-sumption in state i (for the moment, we ignorenonnegativity restrictions on life insuranceand assets). Defining pB� (1� r)ÿ1ÿ pwÿ pH,these equations imply

c1 � pBcB � pW cW � pHcH�1�� y1 � pByB � pW yW � pHyH � Y :

We equate living standard with per capitavariable consumption adjusted for family com-position. To determine each individual's livingstandard when both are alive, we divide vari-able consumption by a factor 2a. We assumethat 0<a� 1; the second inequality reflectseconomies of scale associated with shared liv-ing expenses. To maintain a living standardthat is constant across time and states of nature(in other words, one that is undiminished if andwhen either spouse dies), the couple must spend2aC dollars in every period and state whereboth are alive for every C dollars in any statewhere only one survives. From (1), it is appar-ent that the household's highest sustainableliving standard is

c� � Y=�2a�1� pB� � �pW � pH ��:�2�

The couple can guarantee that spouse j 's deathwill not diminish i's living standard from itshighest sustainable level, c�, by purchasing alife insurance policy with face value Li

� �(c� ÿ y2i)� (y2Bÿ 2ac�).3

We measure underlying financial vulner-abilities by comparing an individual's highestsustainable living standard, c�, with ci

n�y2i�A(1� r), which represents the living stan-dard he or she would enjoy if widowed, ignor-ing life insurance. We define the variableIMPACT (ignoring insurance) as ([ci

n/c�]ÿ 1)�100, i�W,H. This is a measure of the percentby which the survivor's living standard would(with no insurance protection) fall short of orexceed the couple's highest sustainable livingstandard. Similarly, we measure uninsuredfinancial vulnerabilities by comparing c� withci

a� y2i�A(1� r)�Lia, which represents the

living standard that the individual would actu-

ally enjoy if widowed, based on actual lifeinsurance coverage, Li

a. We define the variableIMPACT (actual ) as ([ci

a/c�]ÿ 1)� 100. This isa measure of the percent by which the survi-vor's living standard would (given actual levelsof coverage) fall short of or exceed the couple'shighest sustainable living standard. TheIMPACT variables are based on a concreteand easily understood yardstick for quantify-ing the consequences of a spouse's death.4 Wealso compare actual household life insuranceholdings, La

H � LaW , with the benchmark level,

L�H � L�W .For the preceding example, we implicitly

assumed that individuals could borrow at therate r and issue survival-contingent claims atthe prices pH and pW. As a practical matter,households encounter liquidity constraints.They are also typically unable or at least veryreluctant to purchase negative quantities of lifeinsurance (buy annuities).5 In solving for eachhousehold's highest sustainable living stand-ard, we take these restrictions into account,smoothing consumption to the greatest extentpossible.6

When the life insurance constraint binds, thebenchmark living standard for a survivor, ci

�

(where i�H or W ), may be greater than thebenchmark living standard for the couplewhileboth spouses are still alive, cB

�. This observationraises the following practical issue: When cal-culating IMPACT, should we set c� � ci

�, orc� � cB

�? Were we to use cB�, actual IMPACT

would be positive not only for householdsthat depart from the benchmark by purchasingadditional insurance (Li

a>Li�) but also for con-

strainedhouseholds that conform to thebench-markbypurchasingno insurance (Li

a�Li�� 0).

3. In the special case in which the household hasLeontief preferences (defined over per capita adjustedexpenditures), this is also the utility maximizing outcome.

4. Note that when actual life insurance is below thebenchmark, the intact couple saves on insurance premiums,so its actual consumption exceeds c�. Hence, the IMPACTvariables understate the change in living standard that anindividual experiences on a spouse's death. However,because life insurance premiums typically account for asmall fraction of expenditures, the degree of understate-ment is small.

5. A nonnegativity constraint for life insurance pur-chases is equivalent to the restriction that life annuitiesare not available for purchase at the margin. For furtherdiscussion, see Yaari (1965), Kotlikoff and Spivak (1981),and Bernheim (1987).

6. Formally, one can think of the outcome that weidentify as the limit of the solutions to a series of utilitymaximization problems in which the intertemporal elasti-city of substitution approaches zero. In the limit (theLeontief case), the household is actually indifferent withrespect to the distribution of consumption across any yearsin which its living standard exceeds the minimum level.


In contrast, the use of ci� implies that actual

IMPACT is positive when Lia>Li

� and zerowhen Li

a�Li�� 0. Because we wish to use

actual IMPACT as a measure of the extentto which a household deviates from theconsumption-smoothed benchmark, we selectci� rather than cB

�. As a result, the value ofIMPACT ignoring insurance is always non-positive (even though, absent insurance, thesurvivor's material living standard might actu-ally increase on his or her spouse's death), andit equals zero whenever the correspondingbenchmark insurance level, Li

�, is zero.

Implementation

We actually evaluate each household'sfinancial vulnerabilities using a more elaborateand realistic life-cycle model. As mentionedpreviously, the model is embedded in a finan-cial planning software program, EconomicSecurity Planner (ESPlanner). Although acomplete description of the model would beprohibitively lengthy, it is important to sum-marize some key features.

For our base-case calculations, we assumethat each individual lives to a maximum ageof 95. We include children as members of thehousehold through age 18. We representhousehold scale economies as follows: anexpenditure of (N� bK)aC, when there areN adults and K children in the household pro-vides the same standard of living for eachhousehold member as does an expenditure ofCwhen there is only one adult in the household(this generalizes the adjustment factor used inour simple illustration). The coefficient b is achild±adult equivalency factor; we set it equalto 0.5.7 The exponent a captures economiesof scale in shared living. We set it equal to0.678, which implies that a two-adult house-hold must spend 1.6 times as much as a one-adult household to achieve the same livingstandard.8

Insurance needs depend on differences insurvival-contingent income streams. Con-sequently, a careful and thorough treatmentof the Social Security system is essential. Incalculating benefits for retirement, survivors,parents, children, spouses, and dependentchildren, the model accounts for eligibilityrules, early retirement reductions, delayedretirement credits, benefit recomputation, thelegislated phased increase in the normal retire-ment age, the earnings test, restrictions on max-imum family benefits, the wage indexation ofaverage indexed monthly earnings, and theprice indexation of benefits once received.

Various characteristics of the tax system,such as rate structure and the treatment of mar-ried couples, can alter insurance needs by influ-encing the distribution of after-tax incomeacross the various survival contingencies. Con-sequently, a careful treatment of taxation isalso critical. The model calculates federaland state income and payroll taxes for eachyear in each survival contingency.9 It incor-porates a wide range of provisions, includingfederal deductions and exemptions, the deci-sion to itemize deductions, the taxation ofSocial Security benefits, the earned incometax credit, the child tax credit, the phase-outat higher income levels of itemized deductions,and the indexation of tax brackets to the con-sumer price index. In computing federal deduc-tions, it determines whether the sum of stateincome taxes, mortgage interest payments, andproperty taxes is large enough to justify item-ization. Contributions to tax-favored retire-ment savings accounts are excluded fromtaxable income, and withdrawals are included.Though the model determines total savingsimultaneously with life insurance, tax-favoredsaving is specified exogenously.

Choices concerning housing may also affectlife insurance needs. Unlike many other ex-penditures, housing outlays are not easilysmoothed. It is difficult to scale mortgage,property tax, and insurance payments up anddown with other expenditures. Cost and incon-venience discourage many households frommoving or refinancing mortgages; others formpsychological attachments to their homes andresist changing residences prior to death (Ventiand Wise, 2001). Moreover, few households

7. Our child±adult equivalency factor is that used bythe Organisation for Economic Co-operation and Devel-opment (OECD) (see Ringen, 1991). Nelson's (1992) worksuggests a smaller value, but she considers total householdexpenditures, whereas our child±adult equivalency factorapplies only to nonhousing consumption expenditure;for our base-case results, we treat housing expenditureas inflexible. It appears from Nelson's work that ahigher equivalency factor is appropriate for nonhousingexpenditures.

8. The OECD uses a value of 0.7 for a (see Ringen,1991). Williams et al. (1998) consider values of 0.5 for botha and b.

9. The SCF does not contain data on the state of resi-dency. Therefore, we assume all households reside inMassachusetts.


access the equity in their homes through refi-nancing or reverse annuity mortgages (Caplin,2001). Consequently, for our base-case calcu-lations we treat housing as fixed consumption.In effect, we assume that couples and survivorsremain in the same home until death and diewith home equity intact. Formally, we subtracthousing expenses from income off the top,itemizing mortgage interest and propertytaxes as deductions for federal income tax pur-poses when it is optimal to do so, prior tosmoothing variable consumption.

Several potentially important factors areomitted from our analysis. We do not modeluncertainty concerning future income andnondiscretionary expenses (e.g., medical care).Because small groups of individuals can sharerisks to some extent, the adverse effect of uncer-tainty on living standard is probably greater forwidows and widowers than for couples. Forthis reason, our analysis tends to understateinsurance needs. We also neglect the possibilitythat an individual might remarry after aspouse's death. The extent to which remarriagemitigates the financial consequences of aspouse's death depends on one's view of themarriage market (see Lundberg, 1999, for adiscussion). Although relatively few elderlyindividuals remarry after the death of a spouse(see Bernheim et al., 2003), remarriage is morecommon among younger households.

Table 1 summarizes some illustrative lifeinsurance calculations.10 We begin with acouple consisting of a 40-year-old man earning$45,000 per year and a 38-year-old womanearning $25,000 per year. The man intends toretire at age 64, the woman at age 63. They havetwo children, ages 5 and 7. The net value of theirnonhousing assets is $50,000; in addition, theyown a $150,000 home and have an unpaidmortgage balance of $120,000. They expecttheir real earnings to grow at the rate of 1%per year until retirement. They also expect toearn a real after-tax return of 3% on their non-housing investments. According to our model,this couple must purchase $285,922 in terminsurance on the husband's life, and no insur-ance on the wife's life, to ensure each potentialsurvivor of an undiminished living standard.The remainder of the table illustrates the sen-sitivity of insurance needs to changes in various

household characteristics and economic para-meters. As one would expect, benchmark lifeinsurance falls with age and with the earningsof the insured spouse; it rises with the additionof a child, with an increase in the rate of earn-ings growth, and with a reduction in the realinterest rate (these last two changes increase thepresent discounted value of future human capi-tal). There is one surprising finding: bench-mark insurance also rises with the removal ofone child. This result is attributable to the asso-ciated changes in Social Security survivorbenefits, which are quantitatively importantfor the hypothesized family. For an otherwiseidentical family with high income (for whichSocial Security survivor benefits are less impor-tant), benchmark insurance rises monotoni-cally with the number of children.

Interpretation

We do not regard any single measure offinancial vulnerability as ideal. Though elab-orate, the life-cycle model used in our analysisis still an abstraction, and we have imperfectinformation concerning the economic circum-stances of each household (see the appendix).Nor do we regard the benchmark level of lifeinsurance as an objective standard of adequacy

TABLE 1

Sample Life Insurance Benchmarks

InsuranceBenchmarkfor Husband

InsuranceBenchmark

for Wife

Base case 285,922 0

�Age (50,48) 127,455 0

±Age (30,28) 607,446 0

�Husband's earnings ($60K) 382,239 0

±Husband's earnings ($30K) 187,457 32,581

�Wife's earnings ($40K) 225,430 52,606

±Wife's earnings ($20) 282,246 0

�Child (age 9) 298,016 0

±Child (only the 5-year-old) 295,732 0

�Earnings growth (2%) 327,984 0

±Earnings growth (0%) 240,957 0

�Real interest rate (5%) 210,364 0

±Real interest rate (1%) 409,454 0

Notes: Assumptions for base case: age of husband: 40,age of wife: 38, husband's employee earnings: $45,000,wife's employee earnings: $25,000, husband's retirementage: 64, wife's retirement age: 63, number of children: 2,age of children: 5 and 7, nonhousing net wealth: $50,000,primary home value: $150,000, mortgage balance:$120,000, earnings growth: 1%, real interest rate: 3%.

10. For additional examples and for comparisonswith recommendations generated by Quicken FinancialPlanner, see Gokhale et al. (2001).


or rationality. Optimal insurance coveragedepends on a variety of considerations, includ-ing (but not limited to) the manner in whichmarginal utilities vary across survival states,the weights that households attach to thewell-being of each family member, degrees ofrisk aversion, and load factors (more generally,the degree to which the industry departs fromactuarially fairpricing).Consequently, it ispos-sible to rationalize a wide range of behaviors.

Nevertheless, the absence of a significantcorrelation between life insurance and finan-cial vulnerabilities (measured by benchmarklife insurance) would be difficult to reconcilewith theories of rational financial behavior.Even if a household places less weight on thewell-being of a particular spouse, and even if itmust pay actuarially unfair rates, it shouldstill obtain greater insurance protection whenthe spouse in question is exposed to moresevere financial consequences. To explain theabsence of a correlation, one would need tobelieve either that our measure of benchmarklife insurance is largely unrelated to underlyingvulnerabilities, or that marginal utilities vary ina way that just offsets the differences in meas-ured vulnerabilities. Both possibilities strike usas improbable.

Evidence of widespread and substantialuninsured vulnerabilities (as measured byactual IMPACT or by the divergence of actualinsurance from the benchmark) are also moredifficult to rationalize than it might at firstappear. Most potential explanations presup-pose that households deliberately choose dif-ferent living standards for survivors. Yet thispremise is inconsistent with preliminary find-ings from a financial planning case study atBoston University involving nearly 500 sub-jects. Each of these individuals constructed acomprehensive financial plan using the samefinancial planning software employed in thecurrent study. Participants hoped to benefitfrom these sessions and therefore had strongincentives to provide accurate information.Though the software permits users to specifydifferent living standards for intact couples andeach potential survivor, the vast majority ofsubjects selected the same living standard foreach contingency.11 Though it is perfectly ra-tional for individuals to have other objectives,

it is irrational for individuals with these objec-tives to purchase coverage that diverges signif-icantly from our benchmark (assuming, ofcourse, that the benchmark is derived from amodel that correctly depicts all importantaspects of the household's opportunity set).

III. DATA

The 1995 wave of the SCF was fieldedbetween June and December 1995. It surveyedover 4,000 households (2,874 married couples,1,425 single individuals), with oversamplingof the wealthy. The data cover demographics,income, wealth, debt and credit, pensions,attitudes about financial matters, the natureof various transactions with various types offinancial institutions, housing, real estate, busi-nesses, vehicles, health and life insurance, cur-rent and past employment, current SocialSecurity benefits, inheritances, charitable con-tributions, education, and retirement plans.The architects of the SCF data files imputedmissing information, supplying five `̀ impli-cates'' for each household.12 We use the firstimplicate.

Our final sample consists of 1,033 couples.We excluded couples for the following reasons:(1) a spouse was self-employed or owned andactively managed a business (67% of excludedobservations); (2) a spouse was temporarilyunemployed(11%); (3)neitherspousehadregu-lar earnings as an employee (54%); (4) laborearnings were defined in terms of a unitother than time worked, for example by thepiece (0.7%); (5) mortgage information wasinconsistent (7.4%); (6) property taxes weregreater than 5% of the value of the home(2.6%); (7) a spouse was over the age of 85(1.6%); or (8) the couple's reported incomeand other economic resources were insufficientto support its reported fixed expenditures(3.3%) (note that some households fell intomore than one category).

Accurate measurement of life insurance cov-erage is, of course, particularly critical for ouranalysis. Fortunately, the SCF data match upreasonably well with other sources of informa-tion concerning this variable. In Table 2, wemake some comparisons between statisticson life insurance coverage (including all indi-vidual and group policies) drawn from the SCF

11. Even with risk aversion, such choices are reason-able if load factors are low. For evidence on load factors inthe context of life annuities, see Mitchell et al. (1999).

12. Kennickell (1991) provides a description of theimputation procedure.


and from a survey fielded by the Life InsuranceMarketing Research Organization, an author-itative industry source. Generally, the figuresare quite close. Certainly, there is no indicationthat the SCF understates life insurance cover-age. It is, of course, possible that householdsunderreported certain forms of insurance (e.g.,employer-provided policies) in both surveys.As an additional check on the validity of thedata, we computed the aggregate amount ofin-force life insurance implied by the SCF sur-vey responses and compared this with totalin-force life insurance reported by the industry(obtained from the American Council on LifeInsurance, 1999). Because the latter figure isderived directly from company records, it ispresumably reliable. The SCF survey data ac-counts for roughly 81% of aggregate in-forcelife insurance ($9.52 trillion out of $11.70 tril-lion). Because some life insurance policies areowned by companies, trusts, and foreign indi-viduals rather than by U.S. households, theSCF figure appears to be in the right ballpark.

An important limitation of the SCF is that itcontains information only on the total amountof life insurance held by each household, andnot on the division of this insurance betweenspouses. In contrast to Bernheim et al. (2003)(who treated an individual spouse as the unit ofanalysis throughout), we therefore focus inmuch of our analysis on household aggregates.However, for some purposes, we also imputethe fraction of insurance held to protect eachspouse. The imputation is based on a regressionequation explaining the fraction of a couple'stotal life insurance held on the life of the hus-band as a function of the age of each spouse, the

husband's earnings, the husband's share of thecouple's total nonasset income, family size, andthe husband's share of the couple's total bench-mark life insurance, estimated using data fromthe 1992 HRS.

IV. RESULTS

Analysis of Household Insurance Holdings

We begin with an analysis of householdinsurance holdings. For the results in this sec-tion, it is not necessary to impute the fraction ofa household's insurance held to protect eachspouse.

Table 3 provides a variety of summary sta-tistics, including some simple information oninsurance coverage. According to figures inpanel A, the average benchmark level of lifeinsurance for a household exceeded actuallife insurance holdings by a wide margin(more than two to one for the mean, and nearlythree to one for the median). One might beinclined to conclude that on average, life insur-ance addresses between one-third to one-halfof underlying exposures. However, this conclu-sion is premature. Underlying financial expo-sures vary dramatically across households.From an inspection of averages (Table 3), onecannot determine whether the distribution ofinsuranceholdingsmatchesupwiththedistribu-tion of exposures. As we will see, the averagesmask a startling mismatch between vulnerabil-ities and insurance holdings.

Table 4 provides a first glimpse at the rela-tion between benchmark insurance and actualinsurance across households. In panel A, we

TABLE 2

Validation of the SCF Life Insurance Data

Percent Covered (All Life Insurance) Mean Coverage (All Life Insurance)

LIMRA SCF LIMRA SCF

All households 78 85 132,304 163,973

Ages 18±24 47 51 92,222 96,438

Ages 25±34 75 80 149,476 159,916

Ages 35±44 85 87 202,150 203,759

Ages 45±54 83 92 159,569 200,058

Ages 55±64 83 86 96,567 105,441

65 and older 77 87 27,156 39,692

Note: Life Insurance Marketing Research Association (LIMRA) figures are based on a 1992 survey (see AmericanCouncil of Life Insurance, 1994), with mean coverage adjusted to 1995 dollars.


group households into four categories based onthe benchmark insurance level (aggregatedover spouses). As indicated in the second col-umn, similar fractions of the data sample fallinto each of these groups. The figures in thethird column suggest that there is practicallyno relationship between benchmark insuranceand the likelihood of holding some insurance.In this sense, the decision to obtain insur-ance appears to be uncorrelated with under-lying vulnerabilities. The fourth and fifthcolumns permit comparisons between the med-ians of benchmark insurance and actual insur-ance (in each case, household aggregates) foreach of the four groups. There is perhaps asmall correlation across groups between insur-ance purchases and the benchmark. A similarconclusionfollowsfromacomparisonofmeans(columns six and seven), though the averagelevel of actual insurance for those with nounderlying vulnerabilities (benchmark insur-ance of zero) is anomalously large.

Though there is some indication that bench-mark insurance is mildly correlated with actualinsurance, the proper interpretation of this cor-relation is unclear. From panel A of Table 4, itis apparent that differences in the median andmean levels of actual insurance across groupscorrespond reasonably closely to differences inmedian household income (second to last col-umn). Consider the alternative hypothesis thathouseholds with more income mechanicallyacquire more insurance without much deliber-ate consideration of vulnerabilities and needs.It is reasonable to entertain this possibilitybecause many employers automatically pro-vide life insurance equal to some multiple ofsalary, and because life insurance agents fre-quently base recommendations on simplerules of thumb involving multiples of earnings.This hypothesis would account for the positivecorrelation between benchmark and actualinsurance levels among those for whom thebenchmark is positive. Moreover, it would

TABLE 3

Descriptive Statistics

Mean Median

Panel A: Household-Level Variables

Nonhousing net wealth 1,641,724 45,250

Primary home ownership 0.76 1

Primary home value 160,551 85,000

Household nonasset income 125,779 52,300

Total household life insurance, actual 206,022 71,000

Total household life insurance, benchmark 443,444 205,058

Number of children 0.97 1

Husband Wife Primary Earner Secondary Earner

Mean Median Mean Median Mean Median Mean Median

Panel B: Individual-Level Variables

Age 44 43 42 41 43 43 42 41

Nonwhite 0.172 0

Gender 0 0 1 1 0.220 0 0.780 1

College degree 0.404 0 0.375 0 0.422 0 0.356 0

Pension coverage 0.716 1 0.538 1 0.750 1 0.504 1

Nonasset income 85,292 34,200 18,606 14,160 87,916 36,000 15,983 12,480

Imputed life ins. 166,215 54,391 39,806 14,685 160,539 47,597 45,483 15,598

Benchmark life ins. 405,916 149,535 37,528 0 415,229 168,224 28,214 0

D liv. std., ignore ins. (%) ÿ5.66 0.00 ÿ28.6 ÿ21.5 ÿ3.77 0.00 ÿ30.5 ÿ24.6

D liv. std., imputed (%) ÿ2.40 0.66 ÿ16.3 ÿ7.75 ÿ0.16 0.87 ÿ18.5 ÿ13.3

Notes: Imputed and benchmark life insurance refer to insurance on the life of the individual listed at the top of thecolumn. Changes in living standard (D liv. std.) for the spouse listed at the top of each column depend on insurance onthe life of the other spouse.


TABLE 4

Characteristics of Households with Different Levels of Benchmark Insurance

BenchmarkHouseholdInsurance

Fraction ofHouseholds (%)

PercentInsured

MedianBenchmarkInsurance

Median ActualInsurance

MeanBenchmarkInsurance

Mean ActualInsurance

MedianHouseholdEarnings

MedianAverage Age

of Couple

Panel A: Insurance Levels (Household Aggregates)

$0 21.2 83.1 0 68,000 0 215,174 65,000 56

$1ÿ199,999 28.4 81.2 97,972 39,000 99,073 106,499 35,360 46

$200,000ÿ449,999 25.8 82.8 309,668 100,000 313,821 174,565 50,000 38

$450,000 or more 24.6 83.5 674,480 100,000 1,359,286 346,001 62,220 31

Ratio of BenchmarkHousehold Insuranceto Household Earnings

Fraction ofHouseholds

(%)PercentInsured

Median Ratioof BenchmarkInsurance toHouseholdEarnings

Median Ratio ofActual Insurance

to HouseholdEarnings

Mean Ratioof BenchmarkInsurance toHouseholdEarnings

Mean Ratio ofActual Insurance

to HouseholdEarnings

MedianHouseholdEarnings

Median AverageAge of Couple

Panel B: Ratios of Insurance to Earnings (Household Aggregates)

0 21.2 83.1 0 0.96 0 2.53 65,000 56

0 to 3.99 26.8 87.0 2.07 1.37 2.08 2.09 54,000 47

4 to 7.99 24.9 89.9 5.59 1.91 5.69 2.84 54,789 39

8 or more 27.1 71.1 12.57 1.09 15.03 2.86 37,901 30

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explain the otherwise anomalously high levelsof insurance holdings among those for whobenchmark insurance is zero (and who alsotend to have higher incomes).

Panel B of Table 4 contains the same infor-mation as panel A, except that insuranceholdings (again, household aggregates) areexpressed as ratios to household earnings.This serves as a rough control for earnings,and permits us to evaluate the extent of therelationship between benchmark and actuallevels of insurance that exists independentlyof the mechanical `̀ income effect'' hypo-thesized in the preceding paragraph. Onceagain, we divide the sample into four groupsof roughly equal sizes (as indicated in the sec-ond column). Though the percent insured risesslightly with the ratio of benchmark insuranceto earnings across the first three groups, it islowest for the most vulnerable group (thosewith ratios of benchmark insurance to earningsin excess of 8). Moreover, regardless of whetherone looks at medians (columns four and five) ormeans (columns six and seven), the correlationacross groups between the ratio of benchmarkinsurance to earnings and the ratio of actualinsurance to earnings is weak at best. Theseobservations suggests that the small correla-tion between benchmark and actual insurancelevels noted in our discussion of panel Aresults from an income effect and not fromdeliberate evaluation of other factors affectingvulnerabilities.

Table 5 summarizes the relationship be-tween benchmark and actual levels of life insur-ance (household aggregates) through somesimple univariate regression models. Panel Apresents results based on levels of life insur-ance, and panel B examines ratios of life insur-ance to earnings. In each panel, we estimate theequation of interest using three different meth-ods: Ordinary least squares (OLS), tobit (tocheck for potential biases arising from the siz-able fraction of households who hold no insur-ance), and median regression (to check forsensitivity to outliers). In addition, we also esti-mate a probit model explaining the likelihoodthat a household's actual insurance holdingsare strictly positive.

In panel A, we find that a $1 increase inthe benchmark tends to coincide with a 22-cent increase in actual insurance holdingsfor the household. For each of the three meth-ods employed, we estimate this coefficientwith considerable precision. Households with

higher levels of benchmark insurance are alsomore likely to hold strictly positive insurance,but the difference is not statistically significant.In panel B we find that the correlations noted inpanel A result almost entirely from systematicdifferences in income. The ratio of benchmarkinsurance to earnings is almost completelyunrelated to the ratio of actual insurance toearnings and is in fact negatively related tothe likelihood of holding insurance.

The logic of examining simple univariateregressions is that benchmark insurance func-tions as a sufficient statistic for the full range offactorsÐages of spouses, number of children,division of earnings between spouses, and soforthÐthat determine underlying vulnerabil-ities. Certainly, it would not be sensible tocontrol for all of the factors affecting vulner-abilities, because this would leave no residualvariation in benchmark insurance fromwhich to identify the covariation with actualinsurance.

There are, however, valid reasons to investi-gate the correlation between benchmarkand actual levels of insurance conditional ona subset of the factors that determine vulner-abilities. As mentioned at the outset, Bernheimetal. (2003) previouslydocumented theabsence

TABLE 5

Regression Results, Actual LifeInsurance versus Benchmark LifeInsurance, Household Aggregates

Constant Benchmark

Panel A: Level of Actual Household Insurance

OLS 109,294.5(10,904.63)

0.2181(0.0029)

Tobit 61,187.04(12,799.07)

0.2187(0.0033)

Median regression 20,275.87(11,529.65)

0.2202(0.0453)

Probit (probability scaled, usingbenchmark insurance/105)

0.0010(0.0021)

Panel B: Ratio of Life Insurance to Earnings

OLS 2.432(0.2598)

0.024(0.0275)

Tobit 1.911(0.3057)

ÿ 0.042(0.0341)

Median regression 1.487(0.1316)

ÿ 0.026(0.0091)

Probit (probability scaled) ÿ 0.0093(0.0015)

Note: Standard errors are given in parentheses.


of a correlation between insurance holdingsand vulnerabilities among older workers.One of our primary objectives is to distinguishbetween two alternative explanations for thispattern: that insurance purchases are largelyuncorrelated with vulnerabilities, or thathouseholds purchase long-term policiesbased on vulnerabilities relatively early in lifebut subsequently fail to adjust coverage appro-priately because of inertia or other psycho-logical considerations. To accomplish thisobjective, we must study the relationshipbetween life insurance and underlying vulner-abilities conditional on age.

The final column of panels A and B inTable 4 provide a separate reason to controlfor age. Note that both the absolute value ofbenchmark insurance and the ratio of thebenchmark to household earnings declinesharply with the couple's average age (definedas the average of the husband's and wife'sages). This stands to reason, because youngerindividuals generally have more future humancapital to protect. Now consider the followingtwo-part hypothesis: (1) Young individualstend to procrastinate with respect to decisionsconcerning life insurance, and (2) when theyfinally obtain insurance, the amount purchasedis closely related to vulnerabilities. Becauseyounger households have greater vulnerabil-ities, the first portion of the hypothesis wouldtend to create a negative correlation betweeninsurance holdings and underlying vulnerabil-ities. In principle, this could obscure the posi-tive correlation implied by the second portionof the hypothesis.

Table 6 contains various regressions inwhich we control for the effects of age. Ineach case, the dependent variable is the ratioof actual life insurance (household aggregate)to household earnings.13 There are two sepa-rate sets of results. For the first four regres-sions, we include linear and quadratic termsin the couple's average age (already defined),as well as an interaction term between age andthe ratio of benchmark life insurance (house-hold aggregate) to household earnings. Theinteraction term permits us to investigate

the hypothesis that the correlation betweeninsurance holdings and vulnerabilities changeswith age. If households initially purchaseappropriate levels of insurance but subse-quently fail to adjust their holdings as circum-stances change, we would expect to obtain apositive coefficient for the benchmark insur-ance term and a negative coefficient for theinteraction term. For the last four regressionsin Table 6, we adopt a more flexible functionalspecification. In particular, we divide the popu-lation into five age groups and control bothfor age-group dummies and for interactionsbetween these dummies and the benchmarkinsurance±to-earnings ratio. This is equivalentto estimating a separate univariate regressionfor each age group. At the bottom of the table,we report test statistics for two hypotheses. Thefirst is that there is no relation between actualinsurance and benchmark insurance at any age.The second is that the relation between actualinsurance and benchmark insurance does notchange systematically with age.

In the first three specifications of Table 6,the coefficient of the benchmark insurance±to-earnings ratio is small, slightly negative,and statistically insignificant, whereas theinsurance±age interaction term is indistin-guishable from zero. This implies that thereis essentially no relationship between actualinsurance and benchmark insurance at anyage. The test statistics at the bottom of thetable confirm this impression. For the fourthspecification (a probit model), the coefficient ofthe benchmark insurance±to-earnings ratio isnegative and marginally significant, and thecoefficient of the interaction term is positivebut insignificant. One rejects the hypothesisthat vulnerabilities (as measured by bench-mark insurance) have no effect on the likeli-hood of holding insurance at any age, but thedirection of the effect is counterintuitive: Theprobit coefficients imply that the likelihood ofholding insurance is negatively correlated withbenchmark insurance for households under100 years of age.

Regression results based on a more flexiblefunctional specification tell a similar story. Theage-specific benchmark insurance coefficientsare generally small, frequently negative, andalmost always insignificant. For the OLS andtobit specifications, one cannot reject the jointhypothesis that there is no significant correla-tion between benchmark insurance and actualinsurance at any age. In every specification, we

13. Scaling the insurance variables by earnings is, ofcourse, a perfect control for earnings only if the earningselasticity of insurance purchases is unity. When an earningsvariable (either levels or logs) is added to the list of expla-natory variables for any specification in Table 5, the resultschange relatively little.


TABLE 6

Additional Regression Results, Actual Life Insurance versus Benchmark Life Insurance, Household Aggregates

OLS Tobit Median Reg. Probit OLS Tobit Median Reg. Probit

Benchmark insurance to household income ÿ0.0485(0.1057)

ÿ0.1923(0.1355)

ÿ0.0524(0.0337)

ÿ0.0102(0.0059)

Average age of couple 0.0540(0.1390)

0.1374(0.1701)

0.0854(0.0507)

0.0195(0.0077)

Average age of couple squared ÿ0.0012(0.0013)

ÿ0.0023(0.0017)

ÿ0.0012(0.0005)

ÿ0.0002(0.0001)

Benchmark insurance to incomeinteracted with age

ÿ0.0009(0.0034)

0.0034(0.0042)

0.0009(0.0012)

0.0001(0.0002)

Age < 22 (group 1) 0.15054(3.8696)

ÿ1.7201(5.1116)

0.00(1.7100)

0.1367(0.2005)

Age 22±40 (group 2) 3.4352(0.5222)

3.1355(0.6250)

2.2503(0.2103)

0.2959(0.0295)

Age 41±55 (group 3) 2.2872(0.4705)

1.8239(0.5415)

1.5278(0.2209)

0.3293(0.0305)

Age 56±70 (group 4) 1.6729(0.5756)

0.7231(0.6674)

0.6167(0.1167)

0.2340(0.0330)

Age 71� (group 5) 0.7924(1.4840)

ÿ1.2351(1.7915)

0.2759(0.1381)

0.1109(0.0750)

Benchmark insurance to earnings ratiointeracted with age group 1

0.0458(0.1213)

ÿ0.0405(0.1706)

0.00(0.0814)

ÿ0.0077(0.0069)


ÿ0.0306(0.0408)

ÿ0.1098(0.0510)

ÿ0.0556(0.0128)

ÿ0.0091(0.0222)


0.0738(0.1261)

0.0400(0.1464)

0.0362(0.0779)

ÿ0.0083(0.0076)


ÿ0.0066(0.2239)

ÿ0.0052(0.2575)

0.0348(0.0632)

0.0003(0.0131)


ÿ0.0368(0.7363)

0.2251(0.8592)

0.0750(0.1057)

0.0389(0.0443)

Constant 2.7713(3.43)

0.8826(4.19)

0.3540(1.3460)

p-value for tests

No relationship between actual andbenchmark at any age

0.840 0.184 0.123 0.009 0.958 0.435 0.002 0.001

The relationship between actual andbenchmark is the same at all ages

0.793 0.420 0.456 0.598 0.925 0.864 0.287 0.794

Note: Standard errors are given in parentheses.

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fail to reject the hypothesis that this correlationdoes not vary significantly with age.

Analysis of Vulnerabilities for IndividualSpouses

We turn next to an individual-specific analy-sis of financial vulnerabilities. This requires usto impute the fraction of a household's insur-ance held to protect each spouse, as describedin section III.

It is useful to begin once again with sum-mary statistics. Panel B of Table 3 indicatesthat the average level of insurance actuallyheld on the lives of husbands and primary earn-ers diverged sharply from the average bench-mark, whereas the average level of insuranceactually held on the lives of wives and second-aryearnerswasquiteclosetotheaveragebench-mark. This implies that on average, wives andsecondary earners faced substantial uninsuredvulnerabilities, whereas husbands and primaryearners did not.

In the second-to-last line of panel B (D liv.std., ignore ins.), we tabulate means and med-ians for IMPACT calculated as if each house-hold held no life insurance. This variablemeasures underlying financial exposure.With-out insurance, the average living standards forsurviving husbands, wives, primary earners,and secondary earners would have been,respectively, 5.7%, 28.6%, 3.8%, and 30.5%below their benchmark levels. Because the cor-respondingmedians for husbands and primaryearners are zero, we can infer that more thanhalf of these individuals were not at risk of areduction in sustainable living standard. Like-wise, because the corresponding median livingstandard reductions for wives and secondaryearners were 21.5% and 24.6%, respectively,we conclude that more than half of theseindividuals confronted significant underlyingvulnerabilities.

In the final line of panel B (D liv. std., impu-ted), we tabulate means and medians forIMPACT based on imputed insurance hold-ings. This variable measures uninsured finan-cial exposure. Life insurance reduced the meanvalue of IMPACT by roughly 40% for wivesand secondary earners. The decline in the me-dian value of IMPACT for secondary earnersis a bit larger, whereas the proportional declinein median IMPACT for wives is closer to two-thirds. For husbands and primary earners, lifeinsurancehada relativelyminor absolute effect

on mean and median IMPACT, but the aver-age underlying vulnerabilities were small forthese groups to begin with.

As before, the averages in Table 3 obscurethe mismatch between vulnerabilities andinsurance holdings. Table 7 provides furtherinformation on the distributions of theIMPACT variables. As discussed previously,ignoring insurance, IMPACT is never strictlygreater than zero. This reflects the fact that wehave imposedanonnegativity constraint on lifeinsurance purchases. An individual's livingstandard may rise on a spouse's death; how-ever, without life insurance, it cannot exceedthe living standard that the he or she wouldenjoy as a survivor assuming implementationof the (constrained) benchmark financial plan.Note also that actual IMPACT is exactly equalto zero for a substantial fraction of the popula-tion.Generally, these are individuals forwhomactual and (model-generated) benchmarklevels of insurance protection are both zero.

From Table 7, it is again evident that insur-ance holdings match up rather poorly withfinancial vulnerabilities. Overall, 36.8% ofwives, 64.1% of husbands, 32.0% of secondaryearners, and 68.8% of primary earners hadstrictly positive life insurance protectiondespite the fact that they would have experi-enced increases in living standards on thedeaths of their spouses (in Table 7, thosewith actual IMPACT greater than zero). Insur-ance reduced the fraction of individuals at riskfor severe financial consequences (defined as adecline in living standard of 40% or greater)from 31.0% to 19.3% for wives, from 32.5%to 20.6% for secondary earners, from 3.5%to 2.9% for husbands, and from 1.9% to1.6% for primary earners. Similarly, insurancereduced the fraction of individuals at risk forsignificant financial consequences (defined asa decline in living standard of 20% or greater)from 51.9% to 37.9% for wives, from 55.9%to 41.7% for secondary earners, from10.0% to8.5% for husbands, and from 6.0% to 4.7%for primary earners. Roughly speaking, only15% to 25% of households with significantfinancial exposures held sufficient life insur-ance to avert significant consequences forsurvivors.

Table 8 provides further information on theextent to which insurance mitigates financialvulnerabilities. We subdivide the populationbased on underlying financial exposure, meas-ured by the value of IMPACT, ignoring


insurance. For each subgroup, we then calcu-late the means of both IMPACT variables, aswell as thepercentageofhouseholdsholdingnolife insurance, andaverages for benchmark andactual insurance.

We draw three conclusions from Table 8.First, life insurance had, at best, a moderateimpact on financial exposures among the at-risk population. For example, among severelyat-risk wives, insurance reduced the averageconsequences of a spouse's death (meanIMPACT ) by only 27% (17.9 percentagepoints), from ÿ65.5% to ÿ47.6%. This is afar cry from the one-half overall reduction inmean IMPACT for wives noted in Table 3. Forthis same group, households would haveneeded to hold an average of $630,079 intotal life insurance to ensure both the husbandandwife of anundiminished living standard. Infact, on average, they held only one-quarter ofthis amount ($166,628). This implies an even

larger discrepancy (more than $460,000) thanthe overall difference ( just under $240,000)noted in Table 3.

Second, for a fixed level of financial expos-ure, households were more inclined to protectwomen than men. For example, amongseverely at-risk husbands, insurance reducedthe average consequences of the wife's death(mean IMPACT ) by only 6% (4.3 percentagepoints), from ÿ68.4% to ÿ64.1%. This con-trasts sharply with the corresponding figuresfor wives, already noted. One might questionthe reliability of this finding on the groundsthat we have imputed the division of insurancebetween spouses based on patterns in theHRS.However, the gender difference is plainly notan artifact of the imputation procedure. Forexample, couples with severely at-risk wiveson average held in total $190,388 of life insur-ance (versus $166,628 imputed to the protec-tion of the wife), whereas couples with severely

TABLE 7

Distribution of Changes (%) in Living Standard for Surviving Spouses

Surviving Spouses are

Wives Husbands

IMPACT Ignoring Insurance Imputed Insurance Ignoring insurance Imputed Insurance

Panel A: Husbands and Wives

<ÿ40% 30.98 19.26 3.48 2.90

ÿ40% to ÿ20% 20.91 18.68 6.49 5.61

ÿ20% to 0% 19.36 19.94 17.42 15.10

0% 28.75 5.32 72.60 12.29

0% to 20% Ð 31.85 Ð 63.12

20% to 40% Ð 3.39 Ð 0.68

> 40% Ð 1.55 Ð 0.29

Observations 1,033 1,033 1,033 1,033

Surviving Spouses Are

Secondary earners Primary earners

IMPACT Ignoring Insurance Imputed Insurance Ignoring Insurance Imputed Insurance

Panel B: Primary and Secondary Earners

<ÿ40% 32.53 20.62 1.94 1.55

ÿ40 to ÿ20% 23.33 21.10 4.07 3.19

ÿ20% to 0% 20.52 22.17 16.26 12.88

0% 23.62 4.07 77.73 13.55

0% to 20% Ð 27.49 Ð 67.47

20% to 40% Ð 3.00 Ð 1.06

> 40% Ð 1.55 Ð 0.29

Observations 1,033 1,033 1,033 1,033


at-risk husbands on average held in total onlyone-third of this amount ($62,689 versus$24,827 imputed to the protection of thehusband).

Third, the likelihood of holding insurancebears little if any relation to underlying vulner-abilities, as measured by IMPACT (ignoringinsurance). Indeed, the fraction of couples with-out life insurance is generally largest for thosewith severe financial exposures (IMPACTignoring insurance less than ÿ40%).

Thus far we have measured the con-sequences of a spouse's death in terms of theproportional change in sustainable living stan-dard. For many individuals, the potentialfinancial consequences of a spouse's deathare also severe in absolute terms. With maximalconsumption smoothing (benchmark insur-ance), sustainable consumption for 3.58% ofsurviving wives and 2.61% of surviving hus-bands would fall below the 1995 povertythresholds published by the U.S. CensusBureau. Taking into account actual levels ofinsurance coverage, poverty rates would havebeen 10.45% among surviving wives and 4.16%among surviving husbands. These findingsimply that 66% (6.87 of 10.45 percentagepoints) of poverty among surviving women

and 37% (1.55 out of 4.16 percentage points)of poverty among surviving men resulted froma failure to ensure survivors of an undiminishedliving standard through insurance. Ignoringinsurance, poverty rates would have been13.17% among surviving wives and 4.26%among surviving husbands. Consequently,insurance eliminated only 28% of the avoidablepoverty among surviving widows (2.72 out of9.59 percentage points) and only 6% of theavoidable poverty among surviving men (0.1out of 1.63 percentage points).

Results for Population Subgroups

Table 9 provides disaggregated results. Forvarious population subgroups, we report theratio of actual-to±benchmark life insurancecalculated two ways (meanto mean and medianto median). These figures pertain to the entirehousehold and therefore do not rely on theimputed division of insurance betweenspouses. For primary and secondary earners,we also report the percentage of each sub-group with severe and significant exposuresbased on IMPACT with actual insurance(`̀ frequency''), as well as the fractional reduc-tion in these exposures resulting from actual

TABLE 8

Effect of Life Insurance on Changes in Living Standards for Surviving Spouses by Level ofVulnerability

Mean IMPACT Insurance Holdings

SurvivingSpouses Are

Range for IMPACT,Ignoring Insurance

IgnoringInsurance (%)

ImputedInsurance (%)

PercentUninsured

MeanBenchmark

MeanActual

Wives <ÿ40% ÿ65.5 ÿ47.6 22.8 630,079 166,628

ÿ40% to ÿ20% ÿ30.1 ÿ17.2 14.8 908.146 265,210

ÿ20% to 0% ÿ10.3 1.68 10.5 107,633 133,122

0% 0.0 6.14 18.2 0 116,059

Husbands <ÿ40% ÿ68.4 ÿ64.1 22.2 291,568 24,827

ÿ40% to ÿ20% ÿ27.1 ÿ23.4 22.4 210,961 23,056

ÿ20% to 0% ÿ8.7 ÿ4.4 18.3 78,528 37,625

0% 0.0 2.9 16.7 0 42,545

Secondary earners <ÿ40% ÿ65.8 ÿ49.1 22.3 614,989 159,234

ÿ40% to ÿ20% ÿ29.8 ÿ18.2 14.9 830,155 236,420

ÿ20% to 0% ÿ10.3 ÿ0.3 13.2 104,850 116,975

0% 0.0 6.9 16.8 0 125,237

Primary earners <ÿ40% ÿ66.4 ÿ53.2 30.0 274,272 35,598

ÿ40% to ÿ20% ÿ26.8 ÿ21.5 26.2 243,488 44,115

ÿ20% to 0% ÿ8.6 ÿ3.1 15.5 79,962 51,181

0% 0.0 2.9 17.2 0 44,609


TABLE 9

Life Insurance Coverage and Financial Consequences for Surviving Spouses: Selected Population Subgroups

Ratio of Actual-to-Benchmark Insurance

(Household Totals)

Consequences for Secondary Earners Consequences for Primary Earners

Severe (>40%) Significant (>20%) Severe (>40%) Significant (>20%)

Mean-to-Mean

Median-to-Median

Frequency(%)

FractionAddressed

Frequency(%)

FractionAddressed

Frequency(%)

FractionAddressed

Frequency(%)

FractionAddressed

Full sample 0.465 0.346 20.6 0.366 41.7 0.254 1.55 0.201 4.74 0.210

HH earnings < $15K 0.145 0.041 46.2 0.143 53.9 0.159 5.13 0.080 5.13 0.000

HH earnings $15±45K 0.333 0.116 30.1 0.246 51.6 0.161 2.73 0.080 7.65 0.125

HH earnings $45±100K 0.465 0.381 15.0 0.481 40.0 0.292 0.65 0.000 3.91 0.308

HH earnings> $100K 0.522 1.62 9.52 0.555 22.0 0.449 0.60 0.000 0.60 0.496

Dual earners 0.508 0.345 17.1 0.385 41.9 0.273 1.69 0.214 5.99 0.250

Single earners 0.428 0.491 26.7 0.290 41.4 0.217 1.31 0.510 2.62 0.090

Earnings diff. 1-1 to 2-1 0.503 0.384 9.07 0.426 35.5 0.300 2.59 0.167 9.07 0.238

Earnings diff. over 4-1 0.440 0.364 28.0 0.344 43.6 0.219 1.02 0.171 2.04 0.093

Age of survivor < 22 0.056 0.000 60.0 0.000 90.0 0.000 0.00 0.000 9.09 0.000

Age of survivor 22±39 0.276 0.196 31.1 0.344 62.6 0.203 1.67 0.301 6.70 0.200

Age of survivor 40±55 0.825 0.813 11.9 0.500 27.6 0.320 0.71 0.245 2.12 0.000

Age of survivor 56±70 2.57 NA* 7.64 0.293 13.4 0.298 0.67 0.000 2.01 0.250

Age of survivor > 71 16.8 NA* 8.82 0.000 11.8 0.197 16.7 0.000 26.7 0.000

No children 0.605 0.538 19.2 0.286 37.2 0.200 1.98 0.168 6.14 0.162

One or more child 0.411 0.349 22.0 0.280 46.0 0.290 1.14 0.070 3.41 0.281

Whites 0.463 0.403 20.1 0.389 40.9 0.266 1.17 0.287 4.21 0.217

Nonwhites 0.483 0.150 23.0 0.256 45.5 0.198 3.37 0.000 7.30 0.188

Note: *Median benchmark insurance is zero for these groups.

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insurance holdings (`̀ fraction addressed''),14 ineach instance using the imputed division ofinsurance (results for husbands and wives,not reported in the table, are similar).

Uninsured financial vulnerabilities weremore common among low-income households,couples with disparate earnings, relativelyyoung households, couples with dependentchildren, and nonwhites. Thus, factors thatare highly correlated with underlying vulner-abilities (particularly earnings disparities, age,and children) are also highly correlated withuninsured vulnerabilities. This finding is, ofcourse, implied by the poor correlation be-tween vulnerabilities and insurance holdings.

According to Table 9, conditional on theexistence of a significant or severe vulnera-bility, households with lower incomes, greaterincome disparities between spouses, no chil-dren, and nonwhites are less likely to moderatethe financial consequences of a spouse's deaththrough life insurance (see the column labeledFraction Addressed). The relationship betweenage and the conditional likelihood of addres-sing a significant or severe vulnerability washump-shaped, with a peak in the 40±55-yearage range. Households were generally lesslikely to address vulnerabilities for primaryearners. Note that a low proclivity to addressexposures can coincide either with high (as inthe case of lower-income households) or low(as in the case of older individuals and primaryearners) levels of underlying vulnerability.

When one compares households of similarages, our results are quite close to those derivedfrom the HRS data in Bernheim et al. (2003).15

For example, we find that 13.4% of secondaryearners between the ages of 56 and 70 havesignificant uninsured vulnerabilities, whereas7.6% have severe uninsured vulnerabilities; thecomparable figures in Bernheim et al. (2003)for 60- to 69-year-old survivors are 14.1%and 8.9%. Moreover, the data exhibit thesame qualitative patterns with respect to themagnitudes of vulnerabilities, as well as with

respect to the propensity to address vulnerabil-ities, across household categories.

It is important to reiterate that data limita-tions precluded previous studies from sheddinglight on the insurance holdings of youngerhouseholds. Consequently, our findings con-cerning age are particularly noteworthy.According to Table 9, for 22- to 39-year-olds, household life insurance holdings aver-aged only 27.6% of the benchmark, comparedwith 82.5% for 40- to 55-year-olds. Nearly two-thirds of secondary earners between the ages of22 and 39 have significant financial vulnerabil-ities (projected reductions in living standardsexceeding 20%), and nearly one-third havesevere vulnerabilities (projected reductionsexceeding 40%). Moreover, for this agegroup, only one in five households with at-risk secondary earners (those who wouldexperience significant or severe declines in liv-ing standard on the death of their spouse,ignoring insurance) held sufficient life insur-ance to avert significant or severe financialconsequences.

V. ROBUSTNESS

Given the limitations of the SCF data, it isimportant to examine the extent to which mea-sured vulnerabilities are sensitive to changes inkey assumptions and parameters. We sum-marize a variety of alternative calculations inTable 10. As in Table 9, we report household-level ratios of actual to benchmark life insur-ance, as well as the fractions of primary andsecondary earners with severe and significantuninsured exposures. For purposes of compar-ison, we reproduce our base-case results in thefirst line of the table.

Changes in the real interest rate, baselinewage growth rate, and maximum lifespanhave relatively little effect on the fractions ofspouses with severe and significant vulnerabil-ities.16 In each case, this reflects the opposingeffects of offsetting forces. With higher interestrates, a given level of life insurance cover-age generates higher real income. However,because survivors are typically more dependenton long-duration life annuities than intactcouples, the present discounted value of theirresources tends to decline by a larger propor-tion when the rate of return rises. For older

14. Formally, fraction addressed� [(Frequency giveninsurance� 0) ± (Frequency given actual insurance)]/(Frequency given insurance� 0).

15. The age-adjusted frequencies of severe and signific-ant uninsured financial exposures reported here and inBernheim et al. (2003) are lower than Auerbach and Kotlik-off 's (1987; 1991a; 1991b) estimates. Possible explanationsfor the disparity include increases in female labor forceparticipation since the 1960s, changes in patterns of insur-ance coverage, and methodological differences.

16. For our base case, we assume that the inflation rateand real interest rate are both 3%.


TABLE 10

Frequency of Severe and Significant Financial Consequences for Surviving Spouses: Robustness (Full Sample)

Ratio of Actual-to-Benchmark Insurance(Household Totals)

Consequences for Secondary Earners(Imputed Insurance) (%)

Consequences for Primary Earners(Imputed Insurance) (%)

Mean-to-Mean Median-to-Median Severe (>40%) Significant (>20%) Severe (>40%) Significant (>20%)

Base case 0.465 0.346 20.6 41.7 1.55 4.74

Real interest rate� 1% 0.333 0.239 23.9 44.2 1.92 5.19

Real interest rate� 5% 0.610 0.462 19.3 38.5 1.35 4.15

Baseline wage growth rate� 0% 0.537 0.401 19.8 40.0 1.65 4.55

Baseline wage growth rate� 2% 0.403 0.306 22.6 42.9 1.45 5.14

Maximum lifespan� 85 0.473 0.352 20.5 41.2 1.45 4.66

Consumption growth rate� 1% 0.484 0.366 20.2 39.9 1.45 4.17

Consumption growth rate� ±1% 0.450 0.342 21.1 42.5 1.55 5.02

No ecs. of shared living (a� 1) 0.877 1.14 14.7 26.2 0.77 1.84

Survivor receives 50% pension benefits 0.435 0.300 22.3 45.3 1.65 4.84

Housing completely fungible 0.552 0.513 10.8 28.3 0.38 2.00

Survivor downsizes house by 30% 0.503 0.422 18.5 36.9 1.16 4.07

Survivors fully employed 0.533 0.569 11.5 29.6 1.45 4.65

All life insurance assigned to the primary earner 0.465 0.346 19.9 38.8 1.94 6.00

Wealth reduced by 20% 0.446 0.337 21.3 43.1 1.54 4.73

Wealth increased by 20% 0.484 0.357 20.2 40.9 1.45 4.45

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workers, the rate of wage growth is relativelyunimportant because it affects comparativelyfew years of earnings. Moreover, although agiven rate of growth produces a larger absoluteincrease in earnings for primary earners, sec-ondary earners tend to be younger and there-fore benefit from higher growth over a longertime frame. A reduction in maximum lifespanreduces the resources that a survivor needs toachieve a given living standard but increasesthe living standard that the intact couple canachieve from available resources.

The consumption growth rate refers tosteepness of the sustainable living standardtrajectory. For our base case, we computethe highest living standard that is sustainablethroughout life in all contingencies; this corres-ponds to a consumption growth rate of zero.For sufficiently patient (impatient) house-holds, it may be more natural to constructbenchmarks based on a rising (falling) livingstandard trajectory. The proportional effectsof a change in the consumption growth rateon the resource needs of survivors and intactcouples are approximately equal. Our resultsare therefore robust with respect to changes inthis parameter.

The frequencies of exposure to significantand severe financial consequences are notice-ably lower in the absence of household scaleeconomies (an extreme and somewhat implaus-ible assumption). It is somewhat higher whenwe reduce the rate of pension survivor benefitsfrom 100% to 50%, but the change is muchsmaller than that reported in Bernheim et al.(2003). The discrepancy is presumably attrib-utable to differences between the age distribu-tions of the SCF and HRS samples. Foryounger households, pension survivor benefitsmake less of a difference both because theyare further in the future and thus more heavilydiscounted and because younger workershave not yet accumulated substantial pensionentitlements.

As mentioned previously, our base-caseassumptions concerning housing are consistentwith empirical evidence indicating that indi-viduals avoid changing residences (increasinglyso as they age) and that they resist using hous-ing equity to finance ordinary living expenses.However, because some widows do move, weexamine sensitivity to two alternative assump-tions. For the first, we adopt the extreme posi-tion that housing consumption is completelyand continuously flexible and that housing

equity is a perfect substitute for other formsof wealth. For the second alternative, weadopt an intermediate position: A survivordownsizes the couple's primary residence by30%, but thereafter avoids using housingequity to finance ordinary living expenses.17

Though the first alternative dramaticallyreduces the estimated frequencies of indi-viduals at risk of severe or significant financialconsequences, the effect of the second (and, wethink, more plausible) alternative is relativelysmall.

As in Bernheim et al. (2003), our base-casecalculations assume that survivors do not altertheir labor force participation. Because non-working wives approaching retirement agehave limited employment options subsequentto their husbands' deaths, this assumption wasappropriate for the HRS sample. It is some-what more problematic for the younger house-holds included in the SCF. Conceivably, somecouples may hold apparently low levels ofinsurance on a primary earner because, inthe event of his or her death, they expect thesurviving spouse to find full-time employment.We note, however, that this explanation isinconsistent with a finding reported in sectionIV: Fixing the level of underlying vulnerability,couples are less likely to obtain insurancefor the protection of primary earners (and hus-bands) than for secondary earners (and wives).Because primary earners are already (in mostcases) fully employed, secondary earners havegreater latitude to increase labor force partici-pation. Consequently, for a given level ofvulnerability, one would expect to observegreater protection of primary earners, whichis not the case.

To evaluate the sensitivity of our results withrespect to possible changes in labor force par-ticipation, we consider an extreme alternativeassumption: All survivors, whether out ofthe labor force or employed part-time, shift tofull-time employment. We impute full-timeearnings based on regressions of earnings ondemographic characteristics, estimated separ-ately for fully employed men and women. Asurvivor's contingent earnings are set equal

17. In this exercise, we assume that the financing for thenew house is the same as the continuation financing for theold house. Consequently, on a spouse's death, the decline inhome equity equals the reduction in the value of the home,and there is an offsetting increase in nonhousing assets;mortgage payments are unchanged, but other housingexpenses fall by 30%.


tothemaximumof imputedearningsandactualearnings. Due to familiar sample selectionproblems, this procedure tends to overstatepotential earnings for nonworkers; it thereforeunderstates survivors' financial vulnerabilities.As indicated in Table 10, the estimated fre-quencies of financial vulnerability are reason-ably sensitive to this alternative assumption.This contrasts with the findings of Bernheimet al. (2003). The difference is not particularlysurprising, because the ability to alter laborsupply is more important for younger workers.Note, however, that substantial uninsured vul-nerabilities are reasonably widespread evenwith this extreme alternative assumption.This, too, is not surprising, given the high levelsof vulnerabilities among dual-earner house-holds noted in Table 9.

Not surprisingly, this alternative assump-tion concerning conditional changes in laborforce participation has a larger impact onmeasured vulnerabilities among youngerhouseholds. It does not, however, reverse thequalitative conclusions that uninsured vulner-abilities decline with age, or that substantialuninsured vulnerabilities are widespreadamong young households. In particular, theratio of means for actual to benchmark house-hold insurance is 0.314 for 22- to 39 yearolds, 0.975 for 40- to 55-year-olds, 2.76 for56- to 70-year-olds, and 16.8 for those over70; the corresponding ratio of medians is0.235 for 22- to 39-year-olds, 1.45 for 40- to55-year-olds, and not defined for older house-holds (because the median benchmark is zero).Moreover, the fraction of secondary earnerswith severe (significant) vulnerabilities is15.5% (42.9%) for 22- to 39-year-olds, 7.7%(19.6%) for 40- to 55-year-olds, 5.1% (12.1%)for 56- to 70-year-olds, and 8.8% (11.8%) forthose over 70.

In principle, shifts in nonlabor incomemight also cushion the financial impact of aspouse's death. Our analysis makes no allow-ance for this possibility. Presumably, the mostimportant source of potential support is assist-ance from relatives. Bernheim et al. (2003)report that between the first two waves of theHRS, only 6.2% of new widows received anyassistance of this type. Between the secondand third waves, the figure was 7.5%; andbetween the third and fourth waves, it wasonly 2.5%. In addition, support may havebeen modest or temporary in many of thesecases. Consequently, there is little evidence

that external support payments are significantin practice. Although the HRS only providesinformation on older widows, we conjecturethat these figures are lower for young widows(except perhaps where young children arepresent).

As emphasized in section III, the SCF col-lects information only on total life insurancefor each household and not on the proportionsattributable to each spouse. Our base-caseresults apportion this insurance using theimputation method described previously. Ifin some cases these imputations falsely implythat insurance is held to protect spouses whoare not financially vulnerable, then our calcu-lations will overstate uninsured vulnerabilitiesfor at-risk individuals. To examine the poten-tial significance of imputation error, we con-sider an extreme alternative assumption: Alllife insurance is held to protect the secondaryearner (who is, in general, considerably morevulnerable). As indicated in Table 10, theeffects on our results are minimal. This is notsurprising for two reasons: Total household lifeinsurance is typically small relative to bench-mark insurance, and, in any case, our imputa-tions attribute most life insurance to theprimary earner.

If important economic variables are meas-ured with error, our calculations may overstatethe thickness of the upper and lower tails of thedistribution of IMPACT, thereby exaggeratingthe frequencies of significant and severe finan-cial vulnerabilities. Measures of householdassets tend to be particularly noisy. However,as illustrated in the final two rows of Table 10,our findings are not sensitive to moderatechanges in the values of wealth (a 20% increaseor decrease).

As mentioned in section II, we have ignoredthe possibility that remarriage might cushionthe impact of a spouse's death. Bernheimet al. (2003) report that remarriage occurswith low frequency among the HRS sample,but it is probably more common for theyounger households included in the SCF.Because it is difficult to model the con-sequences of remarriage, we did not conductpertinent sensitivity analysis. Consequently,we cannot rule out the possibility that low levelsof insurance among young households areattributable to the expectation that a survivorwill benefit financially from remarriage. How-ever, this hypothesis strikes us as odd. Evenyoung individuals must consider the risk that


they may be unable or unwilling to remarry, thevalue of retaining the option not to remarry,and the effect of financial status on remarriageprospects.

Although our measures of uninsured finan-cial vulnerabilities are sensitive to certain criti-cal assumptions, it is important to emphasizethat the poor correlation between coverage andvulnerability is robust. From Table 10, we seethat the change in the estimated incidence ofvulnerability is largest when we assume thatthere are no economies of shared living, thathousing expenditures are completely flexible,or that all survivors work full time. However,for all of these alternative scenarios, regres-sions analogous to those reported in section IVcontinue to indicate that households withgreater vulnerabilities (measured by bench-mark insurance) typically have no more cover-age on average, at any age, than those withgreater vulnerabilities.

VI. CONCLUSIONS

Using the 1995 SCF and an elaborate life-cycle model, we have quantified the potentialfinancial impact of each individual's death onhis or her survivors, and we have measured thedegree to which life insurance moderates theseconsequences. We have found that life insur-ance is essentially uncorrelated with financialvulnerability at every stage of the life cycle. Thisfinding is consistent with the hypothesis thatlife insurance bears little relation to needs at thetime of purchase; however, it tends to refute thehypothesis that households purchase long-term contracts with initially appropriate insur-ance coverage but fail to adjust this coverageover time as their circumstances change.

The impact of insurance among at-riskhouseholds is modest, and substantial unin-sured vulnerabilities are widespread, particu-larly among younger couples. Nearly two-thirdsof secondary earners between the ages of 22and 39 have significant financial vulnerabil-ities (projected reductions in living standardsexceeding 20%), and nearly one-third havesevere vulnerabilities (projected reductionsexceeding 40%). Moreover, only one in fiveof these at-risk households held sufficient lifeinsurance to avert significant or severe finan-cial consequences. Combining all age groups,56% of secondary earners and 6% of primaryearners would have experienced significant or

severe declines in living standard on the deathof a spouse in the absence of life insurance.Actual life insurance holdings reduce thesefigures to, respectively, 42% and 5%. Thus,the overall impact of life insurance holdingson financial vulnerabilities among at-riskhouseholds is modest. Roughly two-thirdsof poverty among surviving women andmore than one-third of poverty among surviv-ing men results from a failure to ensure survi-vors of an undiminished living standardthrough insurance.

We have also provided evidence of a signi-ficant gender bias in life insurance holdings.Specifically, for any given level of financial vul-nerabilities, couples provide significantly moreprotection for wives than for husbands. Forexample, couples with severely at-risk wiveson average hold $166,628 of life insurance,whereas couples with severely at-risk husbandson average hold only 15% of this amount($24,827).

APPENDIX: DATA IMPUTATION

Nonasset Income

Our calculations require data on each spouse's past andfuture covered earnings as well as future total (covered anduncovered) earnings. We assume that all earnings are cov-ered. For respondents who were working at the survey date,we have 1995 self-reported labor earnings. To impute pastand future earnings we use a model that assumes that thecross-section age-earnings profile for fully employed work-ers remains constant through time. We allow real wages forall ages to grow over time, using the historic Social Securityreal wage growth for past years and a 1% overall real wagegrowth factor for future years. (In our robustness analysis,was also look at a 0% and 2% overall real wage growthfactor for future years.) In estimating past earnings weassume that the first year of employment is the maximumof 1951 and the year the person was age 22.18 Households inwhich one of the spouses was temporarily not working, asopposed to out of the labor force, were dropped from oursample.

The SCF provides information on other kinds of non-asset income. We treat some of these income sources, suchas veteran's benefits, Social Security, disability income,welfare, child support, and regular help from friends orrelatives, as nontaxable. Except for Social Security disabil-ity income and child support, we assume these incomestreams continue, with full adjustments for inflation, untilthe respondent's death. Social Security disability income isassumed to end at age 62, when the recipient becomes eli-gible for Social Security retirement benefits. We dividechild support received by the number of children to obtain

18. For workers who were under age 22 in 1995, weassume that 1995 was their first year of employment.


child support per child and assume it is received until thechild in question reaches age 18.19 We treat other kinds ofspecial receipts, such as income from trust funds and roy-alties, as taxable. We assume they will be received for 10years beyond the survey date and that the payments will beconstant in nominal terms. Relatively few respondentsreceive these kinds of income flows, and the amounts aregenerally small relative to average earnings. We assumethat SCF respondents retire at their stated intended agesof retirement or age 70, whichever is smaller. For those whofail to say when they will retire, we use age 65.

Pension Plans, Retirement Accounts, and SocialSecurity

The SCF provides information on nominal benefitscurrently received from defined benefit pension plans aswell as expected nominal benefits for future pension reci-pients. We assume that all pensions are indexed to inflationand that a surviving spouse would receive 100% of themonthly benefit or lump-sum distribution. We furtherassume that employer-sponsored defined contributionplans and all private retirement accounts (IRAs andKeoghs) provide for tax-deductible contributions andtax-deferred accumulation. Contributions in all futureyears up to age 59 are set equal, in real terms, to contribu-tions in the survey year. If total contributions are greaterthan the legal limits ($30,000 or 25% of income), contribu-tions are truncated. The proportion given by the employerremains constant. Any contributions (by the employee orthe employer) over the legal limit are included in employeenondeductible and tax-favored contributions.

The SCF contains information on IRA account bal-ances but not annual contributions. We impute contribu-tions based on tobit regressions from the ConsumerExpenditure Survey. Contributions are calculated as afunction of marital status, work status, age, earnings,and family size.

Ifan individual isalreadyreceivingSocialSecuritybene-fits, we assume that benefits have already started. Other-wise, we impute the initial age of benefit receipt as follows.If the individual is still working, we assumethat benefits willstart at his or her projected retirement age (but not earlierthan age 62). If the individual is retired, we use the reportedstart date for those currently receiving benefits; for thosenot yet receiving benefits, we assume benefits will start atage 62 for those currently under 62, and at the current agefor those over 62. In all cases, the initial age of benefitreceipt is between 62 and 70. For respondents currentlyreceiving Social Security disability benefits, we assumethat they switch to retirement benefits at age 62.

Our calculations also require information on the age atwhich individuals begin to receive private pension benefits.For those not yet receiving benefits, we use the age at whichthe individual expects benefits to begin as reported in theSCF.

Individuals with previous marriages lasting morethan 10 years and ending in divorce or separation andindividuals with previous marriages lasting more than 9

months and ending in the spouse's death are eligible toreceive Social Security benefits based on the earnings his-tory of their prior spouse. This presents a problem becausewe do not have any information about prior spouses. Weassume that all such individuals receive benefits based oneither their own earnings history or that of their currentspouse.

Housing

Our calculations require information on a variety ofspecific housing expenditures, including mortgages,home insurance premiums, property taxes, and other recur-ring expenses. Association fees, homeowner or condo/co-op/townhouse association fees, and rent on the site forhouseholds owning and living in mobile homes areadded to home insurance premiums to form recurringhouse expenditures. When one owns part of a farm, oneis classified as a homeowner. The rent paid is then alsoadded to the insurance premium. The SCF does not containinformation on home insurance premiums. We imputedannual home insurance premiums by multiplying thehome value by 0.0025.

If the mortgage payment (minus property taxes andinsurance premium if respondent states these are includedin their payments) is negative then the observation isdropped. If the annual property tax is greater than 5% ofthe home value, the observation is dropped.

With regard to mortgages, the SCF reports the balanceremaining, the number of years remaining, the interest rate,and the payment. To ensure consistency, we imputed thebalance remaining on the mortgage based on the yearsremaining and the interest rate and payment.

In some instances, rental payments reported in the sam-ple include heat and electricity expenses; in such cases,respondents were not asked separately about these utilitypayments. We apportionthereportednumber into separatecomponents by assuming that the ratio of rent to utilities isthe same for these respondents as the average ratio com-puted from the HRS. If rent includes all utilities, rent is setto 0.77 * rent. If rent includes some utilities, rent is set to0.89 * rent. We have no information on utility expenditureif it is not included in rent. The SCF does not include anyinformation concerning property taxes paid on secondhomes. We assume that this property is taxed at thesame rate as the primary home. Finally, we set monthlyrental payments equal to zero for the few respondents whoreport that they live in a house or apartment that theyneither rent nor own.

In addition, for our base case we assume that all house-holds plan to remain in the same house before and afterretirement. One test of robustness allows widows andwidowers to move to smaller homes. For this case weassume that the move to homes that are 70% of the sizeof their previous homes.

Other Variables

For confidentiality reasons, the SCF does not report therespondent's date or month of birth or state of residency.We assume that each respondent was born on June 15.For the purposes of computing state taxes, we useMassachusetts law. We set the maximum age of life to95 for all individuals. Many households have adult childrenliving with them. For the purposes of this project, onlychildren age 18 or under are included.

19. The SCF reports only the sum of child support andspousal support. However, we confine our attention tocouples, 98% of which are married. Because spousal sup-port generally ends on remarriage (and also declines some-what on average when individuals become unmarriedpartners), we can safely assume that the entire reportedamount is child support.


We assume for all respondents a fixed amount forfuneral expenses, which is set equal to the median of thereported expenses ($5,000) for HRS spouses who actuallydied in 1991 (90 observations). The HRS reports informa-tion on actual funeral expenses and legal fees of deceasedspouses. We set intended bequests equal to zero.

The SCF allows mortgages to end with a balloon pay-ment. When there is a balloon payment, we assume thatthey refinance for the amount of the balloon payment witha 15-year mortgage (8% interest rate). There is no space inESPlanner for future mortgages, so these are included inspecial expenditures. Interest payments on the first homeare included in deductible special expenditures. Paymentson the balance are included in nondeductible special expen-ditures. Nondeductible special expenditures also includechild support or alimony payment and support to otherfamily members. These are assumed to be paid in the cur-rent year and the next four years (a total of five years).

As a measure of a household's net worth, we use totalnonhousing assets minus total nonhousing liabilities. Totalnonhousing assets include checking and saving accounts,money market funds, certificates of deposit, governmentsaving bonds, T bills, stocks, mutual funds, investmenttrusts, business equity, bonds, bond funds, real estateother than primary and vacation homes, the cash valueof life insurance policies, and some miscellaneous items.Total nonhousing liabilities include personal loans, studentloans, credit card balances, car loans, installment loans,and other nonhousing debt. Housing debt (mortgagesand equity lines of credit) are considered separately. Weassume that apart from mortgages and other outstandinghousing debt, households cannot borrow against futureincome. For our base case, we use a 3% rate of inflationand a 3% real pretax rate of return.

We assume respondents' borrowing limit is set equalto zero.

The expected change in living standard after retirementor in case of death of one partner is set equal to zero.

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are life insurance holdings related to financial vulnerabilities?

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