Inequality in Comprehensive Wealth

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Inequality in Comprehensive Wealth Hannah Landel, David Love, Paul A. Smith 2026-007 Please cite this paper as: Landel, Hannah, David Love, and Paul A. Smith (2026). “Inequality in Comprehensive Wealth,” Finance and Economics Discussion Series 2026-007. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2026.007. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Inequality in Comprehensive Wealth HannahLandel* DavidLove† PaulA.Smith‡ January21,2026 Abstract Wecreateanannualizedmeasureofcomprehensivehouseholdwealthusingthe1998–2022 wavesoftheHealthandRetirementStudyandexamineheterogeneityinretirementresources across households, cohorts, and time. We augment traditional net worth with the actuarial present values of expected future payment streams from labor-market earnings, Social Security, defined-benefit pensions, annuities, life insurance, and government transfers. We then calculate an annualized measure of that lump sum by converting it into an actuarially fair jointlifeannuitythatwecallannualizedcomprehensivewealth(ACW).WefindthatthemedianACWincreasesthroughoutretirement,indicatingthatthemedianhouseholdisspending down its total resources more slowly than its joint life expectancy is shortening. In addition, wedocumentconsiderableheterogeneityinthelevelsandtrajectoriesofACWacrosscohorts, educationgroups,andrace. Notably,wefindthatthepatternofrisingACWislargelydriven bycollege-educatedandWhitehouseholds. OthergroupsshowrelativelyflatordecliningtrajectoriesofACWafterretirement. WefurtherexploretheheterogeneityofACWwiththehelp of recentered influence function regressions. We show that inequality in ACW is associated withhigherhousehold-specificratesofreturn,highereducation,andgreaterconcentrationsof single-headedandBlackandHispanichouseholds. Keywords: saving,wealthaccumulation,cohorteffects,retirement,inequality JELClassification: D14,J26,J11,D91,I24,J15,J14,E21 *FederalReserveBoard.Email:hannah.n.landel@frb.gov. †DepartmentofEconomics,WilliamsCollege.Email:dlove@williams.edu. ‡FederalReserveBoard.Email:paul.smith@frb.gov. 1

1 Introduction The past half century has seen a dramatic change in the way that households prepare for retirement. While earlier generations relied on a combination of Social Security, employer-based defined-benefit(DB)pensions,andpersonalsaving,theriseofindividualretirementaccountsand 401(k)-type plans has made retirement security more dependent on household decisions about savingandassetallocationthroughouttheirworkinglives,aswellasmovementsinfinancialand housing markets. As a result, the Baby Boomers have arrived at retirement with a very different set of resources than their parents. In addition, the experiences of different households within thesegenerationshavevariedsystematicallywitheducation,earnings,anddemographiccharacteristics. Moreover,asthecompositionofretirementwealthhaschanged,thetrajectoryofwealth afterretirementhasalsoevolvedacrossandwithincohorts.1 This paper uses a panel of households from the 1998–2022 waves of the Health and RetirementStudy(HRS)toexplorehowthesedevelopmentshaveaffectedhouseholds’abilitytofinance consumption after retirement.2 We develop a broad measure of household wealth that includes the actuarial present values of expected future flows from labor-market earnings, Social Security, DB pensions, annuities, life insurance, and transfer payments. Following Love et al. (2009), wethenconverttheseestimatesofcomprehensivewealthintoannualizedamountsbyimagining thathouseholdsweretopurchaseafairlypricedjoint-lifeannuitywiththeirtotalresources. This annualizedmeasure,whichwecallannualizedcomprehensivewealth(ACW),isanalogoustothe classicmeasureofpermanentincome,andinheritsthesameconnectiontothelife-cycletheoryof consumption. Themostdirectadvantageoflookingatannualizedwealth,asopposedtototalwealth,isthat itallowsustomoremeaningfullycomparetheresourcesofhouseholdsofdifferentagesandsizes. Because we have a panel of households, our measure also provides a direct indicator of whether a household’s ability to finance annual consumption is rising or falling as it ages. Conventional measures of net worth may decline as a household draws down resources in retirement, but this does not tell us whether the rate of drawdown is fast or slow relative to life expectancy. If our annualized measure is declining with age, however, it suggests that households are less able to 1Wolff(2025a)showsthatthesechangeshaveledtoa”seismicshift”intheagedistributionofwealth.Inparticular, the Baby Boom generation experienced a rapid increase in wealth relative to other cohorts due to a combination of higherstockholdingandhome-ownershiprates. 2TheHRSisanongoingbiennialpanelsurveyofU.S.householdsoverage50,sponsoredbytheNationalInstitute onAging(grantnumberNIAU01AG009740)andconductedbytheUniversityofMichigan. Weprovidemoredetails onouruseoftheHRSbelow. 2

support the same level of consumption as they age. Conversely, if ACW is rising with age, it suggests that households are spending down resources more slowly than their life expectancies areshortening. Ourfocusondifferencesacrosscohortsismadepossiblebytherelativelylongpanelofhousehold data in the HRS. Our panel includes retirement-age households from cohorts born from the start of the 20th century through the mid-1960s. The sample period also includes some tumultuous movements in financial and housing markets, including the dot-com crash in 2001, the Great Recession of 2008-2009, and the COVID pandemic starting in 2020. These rich data allow ustoexaminehowthetrajectoryofretirementresourcescomparesacrossandwithingenerations, and to understand the differential impact of economic shocks on different cohorts and groups of householdswithincohorts. Ourpapermakesthreemaincontributions. First, relativetoLoveetal.(2009), whichfocused on the 1998–2006 waves of the HRS, we extend the length of the panel substantially, allowing us to trace the evolution of ACW across multiple cohorts and a time horizon that includes major economic events such as the Great Recession and the COVID pandemic. Second, we document several new facts about the level and the distribution of household resources in retirement. Like Loveetal.(2009),wefindthatmedianACWriseswithage,indicatingthatthemedianhousehold drawsdownwealthmoreslowlythanitslifeexpectancyisshortening,incontrasttowhatasimple life-cycle model would suggest.3 We show that this pattern holds at the median for younger cohortsaswellasoldercohorts. However,wealsoshowthattheupwardtrajectoriesinACWare drivenbycollege-educatedandWhitehouseholds,whileothergroupshaveflatorslightlydeclining trajectories of ACW with age. We also show that inequality in ACW increases as households age,whichweattributetodifferencesinportfolioexposuresandgrowingheterogeneityinbequest motives and out-of-pocket medical expenses. Looking across generations, we find that younger cohorts have arrived at retirement with greater average resources than their elders, especially in theformoffinancialwealthandexpectedlaborearnings. A third contribution is that we provide new evidence on the role of household-specific asset returns in shaping the distribution of resources in retirement. By estimating household-specific real rates of return on equities, fixed-income assets, and housing, we find that heterogeneity in returns is likely an important driver of cross-sectional inequality in ACW. Using recentered in- 3By “simple,” we mean a life-cycle model without frictions in the housing market, precautionary motives in retirement, bequestmotives, oruncertainlongevityormedicalexpenses. Aricherlife-cyclemodelthatincludesthese featurescanproduceincreasingannualizedwealthprofilessuchasthoseweobserve. 3

fluence function (RIF) regressions, we show that differences in household returns are strongly associated with increases in the Gini coefficient and the 90–10 ratio, and positively (though imprecisely)associatedwithotherdistributionalmeasures,suchasthetop-10percentshareandthe Theil index. We conclude that inequality in ACW is not only a function of differences in lifetime earnings, savingbehavior, financialsophistication, lifeexpectancy, andbequestmotives, butalso afunctionofhoweconomy-widefluctuationsinassetreturnsdifferentiallyaffecttheportfoliosof individualhouseholds. In focusing on the inequality of retirement resources, we are building on a large body of research examining the determinants of wealth during the working life, as well as patterns of drawdown in retirement. For example, previous research has shown that life-cycle models that include transfer programs, health expenses, and precautionary motives have been successful at broadly matching the wealth distribution in the U.S. (Hubbard et al., 1994; Engen et al., 1999), whileScholzetal.(2006)showedthatanaugmentedlifecyclemodelcanalsopredictwealthlevelsonahousehold-by-householdbasis. Anotherstrandofresearchhasinvestigatedthefactorsaffectingtheevolutionofhouseholdresourcesafterretirement,includingbequestmotives(Hurd,1987;Dynanetal.,2002;Laitner,2002) andtherealizationofkeyuncertainvariablessuchaslongevity,health,andout-of-pocketmedical costs (Poterba et al., 2011; De Nardi et al., 2016; Palumbo, 1999; De Nardi et al., 2006; De Nardi et al., 2010a, 2025). Other key factors include the role of housing (Poterba et al., 2011, 2015) and the extent of annuitization (Inkmann et al., 2011; Lockwood, 2012; Peijnenburg et al., 2016). We find that these factors are also important for determining the level, trajectory, and heterogeneity ofannualizedcomprehensivewealthafterretirement. Ourfocusonamorecomprehensivemeasureofretirementwealthbuildsonaseriesofstudies thathaveaugmentedtraditionalmeasuresofnetworthtoincludepresentvaluesofSocialSecurity and other annuitized streams of payments (Gustman et al., 1997; Gustman and Steinmeier, 1998; Weller and Wolff, 2005; Love et al., 2008, 2009; Poterba et al., 2011, 2015, 2018; Jacobs et al., 2020; Wolff,2024;Llanesetal.,2025). ThesestudieshavedocumentedtheimportanceofSocialSecurity tothewealthofmostretiredhouseholds,aswellastheimportanceoftheongoingtransitionfrom traditionaldefined-benefitpensionstodefined-contributionplanssuchas401(k)s. Arelatedlineofresearchstudiestheevolutionofretirementwealthacrosscohortsanditsdistributionalimplications. LusardiandMitchell(2007)documenttherolesofplanningandfinancial literacyforBabyBoomers’retirementsecurity. BosworthandBurke(2021)examinecohort-specific 4

growth in retirement wealth using the HRS. And Ke´zdi et al. (2020), Sabelhaus and Volz (2022), and Bauluz and Meyer (2024) investigate the determinants of widening cohort inequality. Our paper contributes to this literature by analyzing cohort differences in annualized comprehensive wealth,bothatthestartofretirementandthroughoutthepost-retirementperiod. Finally, our analysis connects to an emerging literature on the role of household-specific asset returns in shaping inequality. Fagereng et al. (2019) find that heterogeneity in asset returns is large and persistent across households, and Kuhn et al. (2020) link differences in equity exposure to the rise of U.S. wealth inequality over a long sample period. Relatedly, Wolff (2025b) finds that wealthier households earn systematically higher returns on housing and other real estate,suggestingthatreturnsmaydifferbothbecauseofdifferentportfolioweightsandbecauseof differentrealizedreturns.4 Methodologically,wedrawontherecenteredinfluencefunction(RIF) framework of Firpo et al. (2009), which has been used to study wage inequality (Lemieux, 2008; Dube,2019),behavioralaspectsofwealthinequality(Cobb-Clarketal.,2016),and,mostrecently, theimpactoftheCOVIDpandemiconincomeinequality(AngelovandWaldenstro¨m,2023). We usetheRIFapproachtoestimatetheimpactofhousehold-levelreturnsonseveralstandardmeasuresofinequality,includingtheGinicoefficient,the90-10ratio,thetop10-percentshare,andthe Theilindex. Takenasawhole,ourresultsprovidenewevidenceoftheextentanddeterminantsofinequality in retirement resources among U.S. households. We find stark differences in ACW by cohort, education group, and race, and find that these differences become more pronounced with age in retirement. Intheremainderofthepaper,wedescribeinmoredetailourmeasureofannualizedcomprehensivewealth,investigatetheagetrajectoriesofannualizedcomprehensivewealthacrossdemographic groups, and explore how various measures of inequality are related to household-level heterogeneityinassetreturns. 2 Annualized comprehensive wealth in the HRS We construct our measure of annualized comprehensive wealth using data from the 1998–2022 waves of the Health and Retirement Study (HRS). The HRS began in 1992 as a panel survey of about12,500householdsaged51–61. In1998,theHRSexpandedtoabout21,000households,rep- 4Ouranalysisdoesnotallowfordifferencesonrealizedreturns,conditionalonportfolioshares,butthiswouldbe aninterestinglineoffutureresearch. 5

resenting all non-institutionalized U.S. households aged 51 and older. Since then, the HRS has re-interviewed these households every two years, and has refreshed the panel with new householdsaged51–56everysixyears(addingnewhouseholdsin1998,2004,2010,2016,and2022). For muchof theanalysis, we usethe RANDHRS longitudinalfile, which hasconsistent variable names across surveys and imputations for some income and wealth variables.5 We supplementthiswiththeRANDFATfiles,whichprovidemoreinformationonpensionplans,annuities, Social Security, and life insurance. We convert all dollar values into year-2022 dollars using the CPI-U. Ourunitofanalysisisthehousehold,whichconsistsofasurveyrespondentandoftenaspouse or partner.6 In some cases, respondents report that they do not know the exact value of some financialvariables,suchasaccountbalancesin401(k)-typeplans. Inthesecases,theHRSprovides aseriesofunfoldingbracketquestionsthatallowstherespondenttoreportthatabalanceiswithin aspecifiedrange. Wherepossible,weusetheunfoldingbracketstructuretoimputevalues.7 2.1 ComprehensiveWealth We construct a measure we call comprehensive wealth (CW) as a broad measure of household resources. Comprehensive wealth starts with a conventional measure of net worth, which is the value of all financial assets (including defined-contribution pension plans) and nonfinancial assets such as housing and vehicles, less any debt. To make our measure more comprehensive, wethenaddintheactuarialpresentvaluesofexpectedfuturepaymentstreamsfromlaborearnings,SocialSecuritybenefits,defined-benefitpensions,annuities,lifeinsurance,andgovernment transferprogramssuchasSupplementalSecurityIncomeandveteransbenefits.8 5Specifically, we use the RAND HRS longitudinal file for some measures of assets, income, demographics, and expectations(includingfinancialassetslikestocksandbondsandnon-financialassetslikehouses,vehicles,andbusinesses),governmenttransfers,andwages,aswellashouseholdcharacteristicvariables. 6The HRS interviews each person in the household, regardless of which individual was selected for the survey. Typically, one respondent is designated as the financial respondent, and we use their responses for household-level financialquestions. Forrespondent-levelfinancialquestions,weusebothrespondents’answers,andthensumtothe householdlevel. 7Specifically, we use the unfolding brackets to impute missing values from the RAND FAT files, since variables fromthelongitudinalfilehavealreadybeenimputedasneededbyRAND.Toimputeusingtheunfoldingbrackets, wedrawrandomlyfromthevalueswithintherangespecifiedbytherespondent. Iftherespondentspecifiesarange withnomaximumvalue,wedrawrandomlyfromthedistributionofnon-missingvalueswithintherangespecifiedby therespondent. WeuseregressionstoimputevaluesforexpectedSocialSecurityin1998and2000,becauseunfolding bracketquestionswerenotaskedinthoseyears. 8Thisapproachfollowspreviousstudiesthathaveincludedinwealththeexpectedpresentvaluesoffuturepayments,includingGustmanetal.(1997),GustmanandSteinmeier(1998),GustmanandSteinmeier(2000),Gustmanetal. (2010),Jacobsetal.(2020),Llanesetal.(2025),Loveetal.(2008),Loveetal.(2009),Poterbaetal.(2011),WellerandWolff (2005),andWolff(2024). 6

To do this in a standardized way, we make a number of assumptions. For households with a working respondent or spouse under age 65, we include the present value of their current selfreportedlaborearnings,projectedthroughage65.9 Forhouseholdsreportingcurrentorexpected Social Security benefits, we use the self-reported benefit amount, top-coded at the maximum amount reported by the Social Security Administration.10 For households reporting life insurancepolicies thatlistthe spouseasa beneficiary, weinclude theactuarialexpectedvalue ofsuch policies. ForhouseholdsreportingoneormoreDBpensionplan,weincludethepresentvalueof allpaymentsfromsuchplans.11 The details of the computation of actuarial present values depend on the structure of each payment (e.g., when it begins, how long it lasts, whether it is contingent on states of the world, whetheritincludesspousalbenefitsorcost-of-livingadjustments). Butingeneral,thecalculation isafunctionoftheamountofeachpayment,thehouseholdmembers’survivalprobabilities,and discountrates. Asanillustration,considerthecalculationforatwo-personhouseholdwitharespondentaged a and a spouse aged a . For the purposes of the calculation, we assume no one will survive h s beyondage119.12 Thenthemaximumnumberofperiodsofreceiptofaflowoffuturepayments to the household will be T ≡ 119−min{a ,a }. We use p to denote the probability that the h s h,t respondent (or head) is alive at age a +t, conditional on being alive at a , and p to denote the h h s,t probabilitythatthespouseisaliveatage a +t,conditionalonbeingaliveat a .13 s s For a future date t years ahead, the household can be in one of three states: both members arealive(whichwedenoteasstate B),onlytheheadisalive(state H),oronlythespouseisalive (state S). We use X ,X , and X to denote the payment to the household at time t in each B,t H,t S,t 9Ofcourse,retirementagesareendogenouslydeterminedbyhouseholds,butthismethodprovidesastandardized waytocomparethehumancapitalofdifferentworkinghouseholds. 10To do this, we use the ”Benefit Examples For Workers With Maximum-Taxable Earnings” available at www.ssa.gov/oact/cola/examplemax.html. 11Priorto2012,theHRSaskedaboutDBandDCpensionplansseparately.Beginningin2012,theHRSaskedabout allofarespondent’spensionplanstogether. WhiletheHRSdidaskrespondentstoclassifyeachplanasDBorDC, weusethevaluesreportedforspecificquestionstoindicatetheplantype. Inparticular, wecategorizeasDCplans anyplanforwhichtherespondentprovidesaplausiblenumericalvalueinresponsetothequestion”Howmuchisin theplanaccountnow?”. WecategorizeasaDBplananyplanforwhichtherespondentprovidesaplausiblevaluefor ”Howmucharethepaymentspermonthoryear?.”Ifrespondentsreportplausiblevaluesforbothquestions,weuse theself-reportedplantypeandthesurvey’sinternalplan-consistencyvariabletoclassifytheplan. Becausewecould substantiallyover-estimatewealthifwemisclassifiedaDCplanasDB,weerronthesideofcautionbyonlyclassifying aplanasDBifthetypeandconsistencyquestionsareinagreementthataplanisDB;otherwiseweclassifyitasDC. 12Asdescribedbelow,wewillapplysurvivalprobabilitiesfromtheSocialSecuritylifetables,sowearenotassuming thateveryonewilllivetoage119,onlythatnoonecouldlivelongerthanthat. 13WeconstructthesesurvivalprobabilitiesbasedontheSocialSecurity2013periodactuariallifetable,asreported inthe2016TrusteesReport. 7

state. (These payments can depend on the state, for example, through spousal benefits.) Given a constantdiscountrater(nominalorreal,dependingonthenatureofthepayment),14 wecompute theactuarialpresentvalueas: PV = ∑ T X B,t p h,t p s,t +X H,t p h,t (1−p s,t )+X S,t p s,t (1−p h,t ) . (1) (1+r)t t=0 The present value formula in (1) can accommodate different types of payments. For Social Security,asanexample,whenbothmembersarealive,benefitsX arethesumofthetwobenefits, B,t including any spousal benefits (individuals can receive the maximum of their own benefits and 50% of their spouse’s benefit). After the death of a spouse, the survivor receives the maximum of their two individual benefits. As another example, consider a DB pension benefit amount B that includes a survivor benefit equal to κB. In this case, X = B, X = B, X = κB. As B,t H,t S,t a final example, we can compute the present value of remaining wage income for a household in which one member is working and under 65 and the other is not. In this case, for example, X = X = w(1+g)t−1 until retirement, and X = 0, where w is the current labor income B,t H,t S,t amount,and gistheassumedrealgrowthrateinwages.15 We use this method to compute the present values of all future payments expected for each household.16 For each household, we define comprehensive wealth as the sum of the present values of all expected future payment streams and the values of conventional financial and nonfinancialassets. Table 1 presents summary statistics characterizing comprehensive wealth for our full sample (about 168,000 observations, pooling all panel years 1998–2022), with the components ranked in descendingorderbytheircontributiontoaveragecomprehensivewealth. Thefirstcolumnreports theshareofhouseholdswithnon-zerovaluesofeachcomponent(forexample,93%ofhousehold report current or expected Social Security benefits,17 while only 16% report current transfer paymentssuchasSupplementalSecurityIncome). Poolingacrossallpanelyears,wefindanaveragecomprehensivewealthofabout$1.65million (in 2022 dollars). The largest components are non-financial wealth (e.g., housing), making up 23 14Wesetinflationtobe2percenteachyear,andwesetthenominalinterestratetobe4.5percenteachyear. 15Weassumearealwagegrowthrateof1%,whichisbroadlyconsistentwithlong-runestimatesofrealearnings growth. UsingBLSdataonaveragehourlyearningsandtheCPI-U,wefindthatrealwagesgrewatabout0.7%per yearover1998–2022. 16Webasetheexpectationoneachhousehold’scurrentstate;e.g.,weprojectforwardearningsandtransferpayments forhouseholdscurrentlyreceivingthose,butwedonotmodeltheprobabilityofahouseholdbeginningtoreceivesuch paymentsiftheydonotcurrentlydoso. 17TypicallythehouseholdsnotexpectingSocialSecuritybenefitsarestateandlocalgovernmentemployees. 8

Table1: ComponentsofComprehensiveWealth AvgatptilesofCW Component %positive Average %ofAvg 25th 50th 75th (thous2022$) (thous2022$) Non-financial 90 382 23 94 225 403 PVSocialSecurity 93 344 21 217 343 466 PVEarnings 49 296 18 48 148 420 Retirementaccounts 56 233 14 15 91 293 Financial 71 185 11 21 80 192 PVDBpensions 36 150 9 23 83 218 PVAnnuities&lifeinsurance 34 46 3 4 21 53 PVTransferpayments 16 22 1 17 26 28 Comprehensivewealth 100 1658 100 439 1018 2072 Observations 162,003 Notes:Thetablereportssummarystatisticsforthecomponentsofcomprehensivewealth,usingtheHRS householdweights.Datacomefromthe1998–2022wavesoftheHRS.Thefinalthreecolumnsofthetable reportthemeansofeachcomponentforhouseholdswithintwopercentagepointsofthe25th,50th,and 75thpercentilesofcomprehensivewealth. percentofaveragecomprehensivewealth,thevalueoffutureSocialSecuritybenefits,makingup 21percent,andthevalueoffutureearningsthroughage65,makingup18percent. To show how comprehensive wealth and its components vary across the distribution, we reportthecomponentsofaveragecomprehensivewealthwithintwo-percentage-pointbandsaround the25th,50th,and75thpercentilesofcomprehensivewealth.18 Wefindsubstantialheterogeneity, with a median comprehensive wealth of about $1 million, significantly less than the average of $1.65 million. We also find that the 75th percentile of comprehensive wealth ($2.1 million) is 4.7 times larger than the 25th percentile ($436,000). At the 25th percentile, Social Security is by far thedominantcomponentofcomprehensivewealth,makingupabouthalfofthetotal. Atthe75th percentile, by contrast, Social Security makes up less than a quarter of the total, though it is still thelargestsinglecomponent. TheseresultsillustratehowimportantSocialSecurityistomostUS households, and especially those lower in the wealth distribution. They also indicate how much Social Security helps to reduce wealth inequality—without it, the ratio of comprehensive wealth atthe75thpercentiletoitsvalueatthe25thpercentilewouldrisefrom4.7to7.3.19 TheresultsalsounderscorethecontributiontoinequalityofthetransitionfromtraditionalDB pensions to retirement accounts. The 75-25 ratio of the average retirement account is about 19.5, 18Weusethisapproachtotakeadvantageofthefactthattheaverageofthecomponentswilladduptotheaverage ofthetotalwithineachband. 19Thisisjustanillustrativecalculation,nottakingintoaccountthegeneral-equilibriumeffectsofremovingSocial Securityonhouseholdsavingsbehavior. 9

while for DB pension wealth the ratio is 9.8. While these ratios reflect variation along both the intensivemargin(accountbalancesorbenefitlevels)andtheextensivemargin(participation),the results suggest that the shift from DB plans to retirement accounts is associated with increasing wealthinequalityovertime. 2.2 AnnualizedComprehensiveWealth To facilitate the comparison of comprehensive wealth across households of different ages and sizes,weconvertthevaluesofcomprehensivewealthintoanexpectedlifetime-annualequivalent by imagining that a household were to use the entire value of CW to purchase an actuarially fair joint-life annuity with survivor’s benefits. This measure, which we call annualized comprehensive wealth (ACW), illustrates how much consumption could be financed annually for the rest of the household’sexpectedlifetime. Forthiscalculation,weassumethatthepriceofsuchanannuityisgivenby: P = ∑ T ϕp h,t p s,t +p h,t (1−p s,t )+p s,t (1−p h,t ) , (2) (1+r)t t=0 where p and p are defined as before as the age-dependent t-period-ahead survival probabilh,t s,t ities of the head and spouse, r is the real interest rate, and ϕ is a household economy of scale parameter.20 Intuitively, the price of the annuity can be thought of as the actuarial present value ofreceivingtheequivalentof1unitofresourcesperhouseholdmemberfortherestoflife. Witha price of P for each unit of the annuity, we can convert comprehensive wealth into an annualized equivalentbydividingbytheannuityprice: CW ACW = . (3) P The main advantage of looking at annualized comprehensive wealth, as opposed to comprehensive wealth or conventional measures of net worth, is that it expresses total household resources in a way that accounts for differences in household composition and expected longevity. Inthesamewaythatpermanentincomeprovidesameasureofsustainableconsumption,annualizedcomprehensivewealthoffersawaytothinkaboutthesustainableannualuseoftotalavailable householdresourcesduringretirement(e.g.,forconsumptionorbequests). 20Inpractice,wesetϕ=1.67,whichisconsistentwithtypicalvaluesofhouseholdequivalencescales(seeBuhmann etal.(1988)andDeatonandPaxson(1998)). 10

A caveat about the measure is that, if taken literally, it implicitly assumes that all sources of wealtharefungibleandliquid. Householdswithalargeshareoftheirwealthheldinhousing,for example, may not be able to convert that wealth into regular annual consumption, given imperfectionsinreversemortgagemarketsthatlimittheabilitytoextracthomeequityatactuariallyfair prices. Similarly,householdsaregenerallyunabletoborrowagainstthefuturevaluesofSocialSecuritybenefits, annuities, or transferpayments. Nevertheless, annualized comprehensivewealth provides a useful conceptual basis for comparing the level of retirement resources across cohorts anddemographicgroups,andforexamininghowtheseresourcesevolveovertime. Table 2 presents summary statistics of annualized comprehensive wealth for our full sample (poolingallpanelyears),withthecomponentsrankedbytheircontributiontoaverageACW. Table2: ComponentsofAnnualizedComprehensiveWealth AvgatptilesofACW Component %positive Average %ofAvg 25th 50th 75th (thous2022$) (thous2022$) Non-financial 90 25 26 6 14 26 PVSocialSecurity 93 19 20 17 21 23 PVEarnings 49 13 14 4 11 19 Retirementaccounts 56 13 14 1 5 17 Financial 71 14 14 1 4 12 PVDBpensions 36 9 9 1 5 14 PVAnnuities&lifeinsurance 34 3 3 0 1 2 PVTransferpayments 16 1 1 1 2 1 AnnualizedComp. Wealth(ACW) 100 97 100 32 62 114 Observations 162,003 Notes: Thetablereportssummarystatisticsforthecomponentsofannualizedcomprehensivewealth, using theHRShouseholdweights. Datacomefromthe1998–2022wavesoftheHRS.Thefinalthreecolumnsofthe tablereportthemeansofeachcomponentforhouseholdswithintwopercentagepointsofthe25th,50th,and 75thpercentilesofannualizedcomprehensivewealth. Poolingacrosspanelyears,wefindanaverageACWofabout$96,000(in2022dollars),meaning that on average, households in the sample have the resources to finance about that much consumptionperyearfortherestoftheirlives. ThemedianvalueofACWissignificantlyless,at about $62,000, and the 25th percentile is about $32,000, with more than half of that coming from SocialSecurity. Notably,atthemedianACW,SocialSecuritycontributesaboutathirdofthetotal, while retirement accounts contribute about 8 percent, indicating that, in this sample, retirement accountsdonotaccountforamajorportionofretirementresourcesforthemedianhousehold.21 21Thetwoarealittlecloseratthe75thpercentileofACW,withSocialSecurityaccountingforabout20percentand retirementaccountsaccountingforabout15percent. 11

3 The trajectory of annualized comprehensive wealth A key advantage of a panel such as the HRS is that we can use the data to study how household wealth evolves as households age through retirement, which we call the trajectory of household wealth. Thelengthofthepanel,spanning1998to2022,allowsustodistinguishcohorteffectsand age effects by, for example, comparing wealth across different cohorts when they are at the same age. 3.1 ACWbyageandcohort WebeginbylookingatcohortdifferencesinaverageACWanditscomponentsaroundthestartof retirement. Figure1showsthelevelandcompositionofaverageACWforhouseholdsaged61–70 across three different cohorts: the Silent and Older generation (born 1945 and earlier), the early Baby Boomers (born 1946–1954), and the late Baby Boomers (born 1955–1964).22 For this figure, weselecthouseholdsaged61-70toillustrateresourcesavailablerelativelyearlyinretirement,and for now we focus on the mean (rather than median) to show how the components add up to the total. The figure illustrates a number of findings about our measure of ACW. First, for all three cohorts, the average household can finance between $75,000 and $100,000 of consumption per year (in 2022 dollars) over their expected lifetimes.23 Looking across cohorts, we see that younger cohorts are arriving at retirement with more resources, on average, than their elders. And looking at the components of wealth for the youngest vs. oldest cohorts, we see a shift from annuitizedwealthtofinancialwealth,likelyreflectinginparttheshiftfromdefined-benefittodefinedcontributionpensionplans. Wealsoseeagrowingshareofwealthfromearnings,likelyindicating ahigherlabor-marketattachmentforyoungercohorts.24 WhileFigure1focusesonearlyretirees(aged61-70),Figure2expandstheanalysistoinclude all of our observed age ranges. For all three cohorts, we see that average ACW generally rises withagethroughoutretirement, apatternconsistentwithLoveetal.(2009). Lookingatthecomponents,weseethatexpectedearningsmakeupasubstantialshareofACWamongtheyoungest 22ThesecohortdefinitionsarebasedonthoseusedbythePewResearchCenter(2019).Giventheirrelativesizes,for thisanalysiswecombinetheSilentGeneration(1928–1945)andtheGreatestGeneration(before1928),andwesplitthe BabyBoomgeneration(born1946–1964)intotwogroups. 23AsshowninTable2,averageACWacrossthefullsampleis$96,000,withthemediansignificantlylessat$62,000. 24Recallthatthismeasureincludesexpectedfutureearningsuptoage65forhouseholdswithcurrentearnings,and issettozeroforrespondentsunderage65withoutearningsandforallrespondentsoverage65. 12

Silent & Older (b. 1945 and before) Early Boomers (b. 1946−1954) Late Boomers (b. 1955−1964) 0 25 50 75 100 Thousands of year−2022 dollars Wealth Category: annuitized housing financial other wage Figure1: Averageannualizedcomprehensivewealth(ACW)atage61-70,bycohort Notes: AnnuitizedwealthincludesDBpensions, SocialSecurity, annuities, andtransfers. Retirementaccountsareincludedinfinancialwealth. ”Other”includeslifeinsurance,vehicles,andbusinesses. ”Wage” isthePVofexpectedearningsthroughage65.Datacomefromthe1998–2022wavesoftheHRS. age ranges, falling off sharply (by construction) after age 65. But as the earnings component declines rapidly, overall ACW continues to increase due to the growth of the housing and financial wealth components. This pattern of rising ACW with age indicates that, on average, households are spending down their resources more slowly than their life expectancy is shortening. From the perspective of a life-cycle model, this would be most consistent with a model accounting for precautionarybehaviorinthecontextofuncertainlifetimesormedicalexpenses(Palumbo,1999; Poterbaetal.,2011;DeNardietal.,2016),orbequestmotives(Dynanetal.,2002;Laitner,2002). 3.2 ACWbyeducationandrace Figure 3 shows how ACW for households in early retirement (age 61–70) varies by education and race/ethnicity. For each race/ethnicity group (Hispanic, Non-Hispanic, Black, and White), thepanelsshowthecomponentsofaverageACWforthreemutuallyexclusiveeducationgroups: those without a high school degree, high school graduates, and college graduates.25 There is a very steep ACW gradient by education, across all the race and ethnicity groups. Households with less than a high school degree have less than a third as much ACW as college graduates, and high school graduates have about half as much. This illustrates the very important role of 25The race and ethnicity groups are defined by the self-reported race and ethnicity of the household head. The ”Hispanic”and”NotHispanic”categoriescanincludehouseholdsofanyrace.Thus,thefourrace/ethnicitycategories showninFigure3arenotmutuallyexclusive. 13

51−55 56−60 61−65 66−70 71−75 76−80 81−85 86−90 >90 0 50 100 150 Thousands of year−2022 dollars egA Silent and Older Cohort 51−55 56−60 61−65 66−70 71−75 76−80 0 50 100 150 Thousands of year−2022 dollars egA Early Boomer Cohort 51−55 56−60 61−65 66−70 0 50 100 150 Thousands of year−2022 dollars egA Late Boomer Cohort Wealth Category: annuitized housing financial other wage Figure2: Averageannualizedcomprehensivewealth(ACW)byageandcohort Notes: AnnuitizedwealthincludesDBpensions, SocialSecurity, annuities, andtransfers. Retirementaccountsareincludedinfinancialwealth. ”Other”includeslifeinsurance,vehicles,andbusinesses. ”Wage” isthePVofexpectedearningsthroughage65.Datacomefromthe1998–2022wavesoftheHRS. education in determining lifetime earnings, as well as financial literacy, survival expectations, and intergenerational transfers via bequests. Looking at the components, we see that annuitized wealth(whichincludesSocialSecurity)makesupthebulkofACWforhouseholdswithoutahighschooldegree,whilehousingandfinancialwealthmakeupthebulkofACWforcollege-educated households. Thedifferencesacrossraceandethnicitygroupsarealsostark. Householdswithheadsidentifying as Black or Hispanic hold between half and three-quarters the annual resources of those headed by heads identifying as White or non-Hispanic. For example, college-educated Black householdshaveaverageACWofaround$80,000peryear,whilecollege-educatedWhitehouseholds have over $150,000. These differences in the average levels of ACW by race and ethnicity reflect different earnings experiences, homeownership rates, retirement plan participation, and intergenerational wealth transfers (Bhutta et al., 2020). Looking at the components, we see that White households have substantially higher financial wealth than Black households. Regardless of the cause, the ACW levels in the figure indicate that retirement preparation varies greatly by 14

Hispanic Not Hispanic <High <High School School High High School School College College 0 50 100 150 0 50 100 150 Thousands of year−2022 dollars Thousands of year−2022 dollars Black White <High <High School School High High School School College College 0 50 100 150 0 50 100 150 Thousands of year−2022 dollars Thousands of year−2022 dollars Wealth Category: annuitized housing financial other wage Figure3: Averageannualizedcomprehensivewealth(ACW)byeducationandrace/ethnicity Notes: Race/ethnicitygroupsarenotmutuallyexclusive. AnnuitizedwealthincludesDBpensions,Social Security,annuities,andtransfers. Retirementaccountsareincludedinfinancialwealth. ”Other”includes lifeinsurance,vehicles,andbusinesses. ”Wage”isthePVofexpectedearningsthroughage65. Datacome fromthe1998–2022wavesoftheHRS. 15

botheducationandrace/ethnicity.26 3.3 TheTrajectoryofMedianACW We have focused on average levels of ACW in order to examine how the components add to the total. But as noted, average values are significantly larger than median values, due to skewness inboththelifetimeearningsdistributionandthewealthdistribution. Thusthetypicalhousehold experiencemaybebettercapturedbycomparingthemedianlevelsofACW. Figure 4 illustrates the trajectories of median ACW by age for the three different cohorts. All three cohorts show declining median ACW at younger ages, followed by rising ACW at higher ages. Butnotethatwhilethechartcontrolsforcohorteffectsbyshowingthreeseparatelines,each lineisstillacombinationofageeffectsandyeareffects. Inotherwords,thesepatternsaredriven by both the dynamics of household aging (”age effects”) and other time-varying effects such as changing returns to housing and equity markets (”year effects”). This is particularly important in this sample due to the financial crisis and economic downturn after 2008 that significantly reduced the market values of housing and equity, mechanically reducing ACW at whatever age a householdiswhenthosemarketcorrectionsoccurred. 70 65 60 51−55 56−60 61−65 66−70 71−75 76−80 81−85 86−90 >90 Age srallod 2202−raey fo sdnasuohT Cohort Silent & Older (b. 1945 and before) Early Boomers (b. 1946−1954) Late Boomers (b. 1955−1964) Figure4: Medianannualizedcomprehensivewealth(ACW)byageandcohort Notes: ThefigureshowsmedianACWbyfive-yearagebucketfortheSilentandoldergeneration, Early Boomers,andLateBoomers. Therecessionbandsindicatetheagebucketscoveringthe25thto75thpercentilesofageforeachcohortduringtheyears2008-2012.Datacomefromthe1998–2022wavesoftheHRS. 26Notethatourpresent-valuecalculationsandannualizingfactorsuseSocialSecuritylifetablesthatdonotaccount for differential mortality by education or race. Accounting for higher mortality rates among less educated groups, Blacks,andHispanics(Brown,2000)wouldaffectthedifferencesshowninthisfigure. 16

We will control for these effects more formally later in the paper, but for the purposes of this figure,wesimplyindicatetheapproximateagerangeeachcohortwasinduringtheGreatRecession. To do this, we highlight color-coded recession bands indicating, for each cohort, which age ranges were covered by the years 2008–2012.27 We see that the younger two cohorts experience fallingACWconcurrentlywiththeGreatRecession,whichisnotsurprising. Butwealsoseethat the oldest cohort experiences falling ACW from ages 51–70 even before the Great Recession, and thatACWrisesforthiscohortduringtheGreatRecession, likelyduetolessexposuretohousing andfinancialmarkets. To explore this further, we also examine the trajectories of ACW by year, shown in Figure 5. This figure shows the differences across cohorts in how each experienced the Great Recession. The Silent and Older generation was aged 63 and above during the years 2008–2012, while the Early Boomers were 54–66 and the Late Boomers were 51–57. We see that the two younger cohorts experienced fairly substantial drops in ACW during the Great Recession years, with the EarlyBoomerssubsequentlyrecoveringmuchofthelossandtheLateBoomersonlypartiallyrecovering. TheSilentandOldergeneration,incontrast,experiencedaquitemodestdropinACW during the recession years, followed by a steep increase, consistent with the fairly rapid rise in ACWshownatlateragesinFigure2. 70 60 50 1998 2002 2006 2010 2014 2018 2022 Year srallod 2202−raey fo sdnasuohT Cohort Silent & Older (b. 1945 and before) Early Boomers (b. 1946−1954) Late Boomers (b. 1955−1964) Figure5: Medianannualizedcomprehensivewealth(ACW)byageandcohort Notes:ThefigureshowsmedianACWbyyearfortheSilentandoldergeneration,EarlyBoomers,andLate Boomers. Therecessionbandindicatestheyears2008-2012. Datacomefromthe1998–2022wavesofthe HRS. The trajectory of ACW also varies by wealth. Figure 6 displays the median levels of ACW 27Becausethereisadistributionofagesforeachyear,eachrecessionbandcoversthe25thto75thpercentileofages. 17

for three wealth brackets: the top 10% of the distribution, the middle 40%, and the bottom 10%. Median ACW rises dramatically with age for the top wealth bracket, particularly at the oldest ages, indicating that comprehensive wealth for this group becomes increasingly large relative to remaining life expectancy. The age profile for the middle 40% is much flatter but still upward slopingattheoldestages,whiletheprofileforthebottom10%ofACWisessentiallyflatatalow level. Wedonotseemuchdifferenceacrosscohorts. 1000 Top 10% 750 500 250 Middle 40% Bottom 10% 0 51−5556−6061−6566−7071−7576−8081−8586−90 >90 Age srallod 2202−raey fo sdnasuohT Cohort Silent & Older (b. 1945 and before) Early Boomers (b. 1946−1954) Late Boomers (b. 1955−1964) Figure6: MedianACWbycohortandwealthbracket. Notes: ThefigureplotsmedianACWbyagefortheSilent&Oldergeneration, EarlyBoomers, andLate Boomers,disaggregatedbywealthbracket.Datacomefromthe1998–2022wavesoftheHRS. NextwelookathowtheagetrajectoriesofmedianACWvarybyeducationandcohort. Figure 7showsthattherearelargedifferencesinthelevelsofmedianACWbyeducationgroupacrossall cohorts. Median ACW for households with a college degree is over $100,000 and generally rises with age in retirement. By contrast, it is about $60,000 for households with a high-school degree and$25,000forthosewithoutahigh-schooldegree,withbothofthesegroupsshowinglessofan upwardtrajectorywithage. Lookingacrosscohorts,weseethatthetrajectoriesofmedianACWarelargelysimilar,except that college graduates in the Early Boomer cohort (born 1946–1954) saw their ACW begin to rise at a younger age than the Silent and Older generation (born before 1946). While there could be a variety of explanations for the gap, it may be partially due to the rise in the college wage premiumafter1980(GoldinandKatz,2007),whichwouldhaveincreasedthelifetimeearningsof the more recent generations of college graduates, as well as generally favorable returns in equity andhousingmarketsforthiscohort. 18

College 120 High School 80 <High School 40 51−55 61−65 71−75 81−85 >90 Age srallod 2202−raey fo sdnasuohT Cohort: Silent & Older (b. 1945 and before) Early Boomers (b. 1946−1954) Late Boomers (b. 1955−1964) Figure7: MedianACWbycohortandeducation Notes: The figure plots median ACW by five-year age bucket for the Silent & Older generation, Early Boomers,andLateBoomers,disaggregatedbyeducationgroup. Figure 8 shows how these age trajectories vary by cohort across race and ethnicity groups. Again we see that the level differences in ACW are substantial, with Black households holding significantlylessACWthanWhitehouseholdsacrossretirementages. Further,thesegapsdonot diminishwithmorerecentcohorts;ifanything,theyappeartobelargerforyoungercohorts,with White and non-Hispanic households showing a much faster rise in ACW. In addition, the age trajectories of median ACW also differ by race and ethnicity, particularly at older ages. While medianACWforWhitehouseholdsincreasesafterage70, itfallsnotablyforBlackandHispanic membersoftheSilentandOldergeneration(thoughnotfortheEarlyBoomers). Thisshowsthat the rising trajectory of annual retirement resources that we observed at the median is not shared acrossallgroups. Again,however,notethattheseprofilesreflectbothcohortandageeffects. The oldesthouseholdsinoursampleaccumulatedwealthinadifferentenvironmentthanmembersof younger generations. As a result, these age trajectories reflect both the accumulation patterns of aginghouseholdswithinagivencohort,aswellasdifferencesacrosscohorts. 3.4 Returns Thelevelsandtrajectoriesofannualizedcomprehensivewealthreflectbothactivesaving/spending decisionsandhousehold-specificrealizationsofreturnsonfinancialwealthandhousing. Householdsthatholdgreaterconcentrationsofhousingandfinancialassetstendtoshowlargergrowth in wealth over time, though of course they are also more exposed to market corrections. And 19

80 White 60 40 Black 20 51−55 61−65 71−75 81−85 >90 Age srallod 2202−raey fo sdnasuohT 80 Not Hispanic 60 40 Hispanic 20 51−55 61−65 71−75 81−85 >90 Age srallod 2202−raey fo sdnasuohT Silent & Older Early Boomers Late Boomers Cohort: (b. 1945 and before) (b. 1946−1954) (b. 1955−1964) Figure8: MedianACWbycohortandraceandethnicity Notes: ThefigureplotsmedianACWbyagebucketfortheSilent&Oldergeneration,EarlyBoomers,and LateBoomers, disaggregatedbyraceandethnicity(BlackandWhite; HispanicandNotHispanic). Data comefromthe1998–2022wavesoftheHRS. importantly, households who participate less in financial markets, or who hold relatively little housingwealth,willnotseelargechangesinannualizedwealthinresponsetoeitherincreasesor decreasesinassetprices. In order to examine the role of asset returns in shaping patterns of annualized wealth, we constructhousehold-specificestimatesofrealratesofreturnonassets. Forsimplicity,wefocuson equities,fixed-incomeassets,andhousingwealth. Letαi denotehouseholdi’sshareofasset jas j,t afractionofcomprehensivewealth(equivalently,annualizedcomprehensivewealth)inperiod t. Lettingr denotetherealreturnonasset jinperiodt,wecanwritethehousehold-specificreturn, j,t ri as: t n ri = ∑ αi r . (4) t j,t j,t j=1 Thatis,thehousehold-specificrateofreturnisaweightedsumofthereturnsonthehousehold’s assets,wheretheweightscorrespondtotheportfolioshares. To compute household-level estimates of rates of return, we apply data on real returns on equities(usingtheS&P500),corporatebonds(Moody’sBaacorporatebondyield),Treasuries(10year),andhousing(Case-Shiller)toeachHRShousehold’sportfolio.28 Wecalculatetwo-yearreal 28We use the estimates available on Aswath Damodaran’s website: https://pages.stern.nyu.edu/~adamodar/ New_Home_Page/home.htm. 20

returns for each asset type, then construct the household-specific returns according to the equation above. To implement this with the data available in the HRS, we compute the equity share for a household as the sum of directly held equities, equities held in mutual funds, and equities heldinretirementaccounts,dividedbycomprehensivewealth.29 Forfixed-incomeassets,wesum directly held bonds and fixed-income assets held in retirement accounts, and divide by comprehensivewealth.30 Finally,wedefinethehousingshareofwealthashomeequity(themarketvalue ofthehomelessmortgagedebt),dividedbycomprehensivewealth. Figure9showshowtheaveragehouseholdratesofreturndifferacrossthedistributionofannualized comprehensive wealth in our sample. In general, we see that market movements lead todifferentaverageratesofreturnacrosshouseholds,reflectingdifferencesinportfoliocomposition.31 Households with higher ACW tend to hold more financial wealth, increasing the importance of financial market fluctuations (including the dot-com bust in 2000, the Global Financial Crisis in 2008, and the Covid pandemic). Households with lower ACW were less exposed to financialmarkets,thoughtheystillexperienceddeclinesduringthefinancialcrisisduetotherelative importance of housing in their portfolios. Overall, the fluctuations in average returns both across groups, and within groups over time, suggest that household-level asset returns play an importantroleinshapingtheevolutionofinequalityinACW. Figure10showshowhousehold-specificreturnsdifferbytheeducationofthehouseholdhead. Prior to the Global Financial Crisis, the average returns across education groups moved fairly closely together (though with higher volatility for college educated households, due to more financial wealth). Following the Financial Crisis, there is a much wider gap in household-level returns by education group, with higher education groups earning substantially higher returns from 2010 to 2020. The divergence reflects the higher exposure to equity markets within higher education groups, which translated into large differences in average returns in the wake of the longrun-upinequitiesfollowingtheFinancialCrisis. Wealsolookatdifferencesinaveragehouseholdreturnsbyraceandethnicity. Returnsacross race and ethnicity groups move fairly closely together before 2008, after which the household returns for White households begin to outpace those for the other groups. This again reflects 29WhiletheHRSasksaboutthepercentofIRAsheldinstocks,itdoesnotincludequestionsabouttheequityshare of DC plans. For this calculation, we assume that 65% of retirement account balances are invested in U.S. equities. AccordingtoEBRIBriefNo. 606,about71%of401(k)assetsareinvestedinequities(CopelandandBass,2024). Since theequityallocationinIRAsiscloserto55%(InvestmentCompanyInstitute,2024),wechoosetheintermediatevalue of65%ofretirementassetsforthiscalculation. 30Forthiscalculation,weassumethatbondsarecomposedof50%10-yearTreasuriesand50%Baacorporatebonds. 31Appendixfigure18showstheACWportfoliocompositionsbywealthbracket,education,andrace/ethnicity. 21

nruteR dlohesuoH laeR egarevA 51. 1. 50. 0 50.- 1998 2002 2006 2010 2014 2018 2022 Year Bottom 10% 40–60% Top 10% Whole sample Figure9: HouseholdreturnsbyACWgroup Notes: Thefiguredepictstheaveragerealhouseholdreturnforeachsurveyyearinthe1998–2022waves oftheHRSforthebottom10percentofhouseholds,themiddle40–60percent,thetop10percent,andthe sampleasawhole. nruteR dlohesuoH laeR egarevA 1. 50. 0 50.- 1998 2002 2006 2010 2014 2018 2022 Year < High school High school College Whole sample Figure10: Householdreturnsbyeducation Notes:Thefiguredepictstheaveragerealhouseholdreturnforeachsurveyyearinthe1998–2022wavesof theHRSforhouseholdswhoseheadshadlessthanahighschooldegree,ahighschooldegree,acollege degree,andforthesampleasawhole. 22

differences in equity exposure by race and ethnicity. In the wake of the Global Financial Crisis, non-Whiteandlesswell-educatedhouseholdsdisproportionatelyexitedthestockmarket(Zhou, 2020), which meant that these households missed the historic increase in asset prices in the followingdecade. nruteR dlohesuoH laeR egarevA 60. 40. 20. 0 20.- 40.- 1998 2002 2006 2010 2014 2018 2022 Year White Black Hispanic Whole sample Figure11: Householdreturnsbyrace Notes:Thefiguredepictstheaveragerealhouseholdreturnforeachsurveyyearinthe1998–2022wavesof theHRSforhouseholdswithWhite,Hispanic,andBlackhouseholdheads. 3.5 Regression-basedACWprofiles As described above, for the sample as a whole, ACW appears to increase with age throughout retirement, indicating that the median household is spending down its total wealth more slowly than its life expectancy would suggest. The life cycle model provides a number of reasons why we might expect such a trajectory. Bequest motives (De Nardi, 2004; Hurd, 1989) and uncertain longevity, combined with imperfect annuity markets, provide an incentive to self-insure against the risk of outliving one’s resources (Davidoff et al., 2005; Yaari, 1965). In addition, imperfect reverse mortgage markets mean that some families will hold on to their homes until they either needtomoveintoassistedlivingfacilitiesordownsize(NakajimaandTelyukova,2020;Ventiand Wise, 2004). Finally, uncertain out-of-pocket medical expenses, which tend to rise with age, may causehouseholdstobuildupaprecautionarybufferofresources(Palumbo,1999;DeNardietal., 23

2010b). Theseconsiderationsnaturallyraisethequestionofhowmuchoftheobservedagepattern inACWreflectsdifferencesinobservablelife-cyclecharacteristics. We explore this question using two complementary approaches. First, we estimate quantile fixed-effects regressions that allow us to construct age profiles of median ACW, conditioning on householdfixedeffectsandtime-varyinghouseholdcharacteristics. Wethenturntoasequenceof OLSfixed-effectsregressionswithlayeredblocksofcontrols, whichshowhowtheestimatedage profiles change as we control for life-cycle variables such as portfolio composition, expectations, andhouseholdcomposition. SummarystatisticsforourregressionsamplearereportedinTable3. Life-cyclevariablesofinterestthatcouldaffectsavingincentivesandthusACWincludethehousehold’ssubjectiveprobabilitiesofleavingbequestsofmorethan$10,000,$100,000,and$500,000,thesubjectiveprobability ofneedingtomovetoanursinghomeinthenextfiveyears, thehousehold’sout-of-pocketmedical expenses, household composition, and the household’s survival expectations relative to the lifetable.32 Inaddition,wealsoincludecontrolsforportfoliocompositionandhousehold-specific assetreturns. Inconstructingtheregression-basedageprofiles,weestimatemedianregressionsoflogACW withhouseholdfixedeffectsandyeareffects. Specifically,weestimateregressionsoftheform ln(ACW ) = α + ∑ β 1{AgeBin = a}×1{G = g}+X ′ γ+δ , (5) it i ag it i it t a,g where ACW denotes annualized comprehensive wealth for household i in year t, and α is the it i household-specificfixedeffect. ThesummationtermallowseachgroupG tohaveitsownageproi file. Depending on the specification, G represents education (less than high school, high school, i college),race(White,Black,Other),orethnicity(Hispanic,non-Hispanic). ThevectorX includes it controls for characteristics observable in the HRS data that are related to the life-cycle considerations mentioned above, including bequest expectations, inheritance expectations, subjective life expectancy(relativetoactuarialexpectations),andout-of-pocketmedicalexpenditures. Theδ are t yeardummiesincludedtocaptureaggregatetimeeffects,suchaseconomy-widechangesinasset returns. These regressions are estimated at the median, so that the coefficient estimates describe 32TheHRSaskseachrespondentabouttheirsubjectiveoddsofsurvivingtoageA,whereAisdeterminedbytheir currentage: 85iftheyareunder65, andthenaslidingscale(80iftheyare65-69, 85iftheyare70-74, 90iftheyare 75-79,95iftheyare80-84,and100iftheyare85-89). Thesubjectiveoddsarethenexpressedasaratiototheimplied probabilityfromalifetablebasedontherespondent’sageandsex. 24

Table3: SummaryStatistics Mean StdDev Min Max ln(ACW) 10.85 1.01 -1.94 17.19 Age 68.11 10.98 26 109 Black 0.19 0.39 0 1 Hispanic 0.11 0.32 0 1 White 0.73 0.44 0 1 LessthanHighSchool 0.22 0.42 0 1 Highschool 0.54 0.50 0 1 College 0.24 0.42 0 1 P(Bequest>$10K) 0.61 0.41 0 1 P(Bequest>$100K) 0.39 0.41 0 1 P(Bequest>$500K) 0.14 0.28 0 1 P(nursinghome) 0.08 0.17 0 1 Lifeexpectancyratio 1.25 1.82 0 49.63 ln(medicalexpenses) 6.95 2.93 0 14.69 Householdassetreturn 0.02 0.05 -0.22 0.49 FinancialACWshare 0.15 0.21 0 1 NonfinancialACWshare 0.21 0.22 0 1 Householdsize 2.16 1.27 1 19 Married 0.45 0.50 0 1 Pre-Boomer 0.66 0.48 0 1 Boomer 0.26 0.44 0 1 Post-Boomer 0.08 0.28 0 1 Observations 162,003 Notes:Thetablereports(weighted)summarystatisticsforthevariablesusedintheregressions.”P(Bequest<$10k”,”P(Bequest<$100k”,and”P(Bequest<$500k”areself reportedprobabilitiesofleavingbequestsofthoseamounts.”P(nursinghome)”isthe self-reportedprobabilityofenteringanursinghomeinthenext5years. ”ln(medical expenses)”isthenaturallogofout-of-pocketmedicalexpensesplus1. ”Household assetreturn”reflectshousehold-specificportfolioweightsofstocks,bonds,andhousing,alongwiththeirrespectiveaggregatereturns.”Pre-Boomer”indicateshouseholds withaheadbornbefore1948,”Boomers”indicatethosewithaheadborn1948–1965, and”Post-Boomers”arethosewithaheadbornafter1965. Datacomefromthe1998– 2022wavesoftheHRS. effectsontheconditionalmedianofln(ACW).33 Using the estimated coefficients on the age dummies, we construct median age profiles of ACW, conditional on the household fixed effect, year effects, and observable characteristics for differentgroups. Figure12showsthepredictedtrajectoryofmedianACWforthefullsample. We find a a slight decrease in ACW around the start of retirement, followed by a steepening rise at older ages. Median ACW increases by around 17% from age 61–65 to age 81–90. The increasing growthratetowardtheendoflifeisnotable,suggestingthatthetypicalhouseholddoesnotdraw downitsresourcesintandemwiththedeclineinlifeexpectancies. 33Themodelsareestimatedusingthefixed-effectsquantileregressionestimatorofMachadoandSantosSilva(2019) andimplementedusingStata’sxtqregcommand. Inconstructingthefiguresbelow, thepredictedvaluesfromeach modelarere-centeredsothatthefittedmedianlog(ACW)valuesforeachgroupequaltheobservedmediansatages 51–60. 25

90 80 70 60 50 )sdnasuoht( WCA naidem detciderP 51–60 61–65 66–70 71–75 76–80 81–90 Age Figure12: PredictedtrajectoryofmedianACW Notes: The figure plots the age trajectory of ACW using the marginal estimates of a set of age dummies fromaquantilefixedeffectsregressionthatincludescontrolsforbequestexpectations,inheritanceexpectations,subjectivelifeexpectancy(relativetoactuarialexpectations),out-of-pocketmedicalexpenditures, householdfixedeffects,andyeareffects.Datacomefromthe1998–2022wavesoftheHRS. Nextwelookathowthesetrajectoriesvarybyeducation,race,andethnicity. Figure13shows the predicted trajectories of ACW by our three education groups. In addition to the substantial differencesinthelevelsofACWacrossgroups,wealsoseenotabledifferencesinthetrajectories. In particular, households with a college degree see a steeper rise in ACW than those with high schooldegrees,andthosewithoutahighschooldegreestayflatatarelativelylowlevel. Therearesimilardifferencesinthetrajectoriesbyraceandethnicity. Figure14showsthepredictedmedianACWtrajectoriesforhouseholdswithWhiteandBlackheads, respectively. While medianACWrisessteadilythroughoutretirementforWhitehouseholds,themediantrajectoryis essentially flat for Black households, suggesting widening inequality by race as households age. AscanbeseeninFigure15,Hispanichouseholdsaccumulateannualresourcesmoreslowlywith agecomparedtonon-Hispanichouseholds,butbothgroupsgenerallyrisethroughoutretirement. In comparing the median age profiles of ACW by race and ethnicity, the most notable difference is in the overall level of annual resources. What factors help explain the gap in ACW by race and ethnicity? While it is difficult to identify causal factors, we can attempt to explain the differencesbylookingattherolesofdifferencesinobservablesvs. differencesinreturnsonthose observables,similartothetraditionalOaxaca-Blinderdecomposition. Inparticular,weimplement amedianOaxaca–Blinderdecompositionbasedonrecenteredinfluencefunction(RIF)regressions, 26

usingthemethodofFirpoetal.(2018).34 Table4reportstheresults,showingthedecompositionofdifferencesinmedianACWbyrace andethnicity. Atthemedian,logACWis0.76logpointslowerforBlackthanforWhitehouseholds and 0.98 log points lower for Hispanic than for White households. These gaps imply that White median ACW is roughly twice that of Black households (exp(0.76) = 2.14) and about 2.7 times that of Hispanic households (exp(0.976) = 2.65). In both comparisons, the majority of the gap is accountedforbydifferencesinobservablecharacteristics,ratherthandifferencesincoefficients. Themostimportantcharacteristicsinexplainingthegapshavealsobeenhighlightedinpreviouslife-cyclestudiesofsaving. Educationservesasa(noisy)proxyforlifetimeearnings. Bequest expectations provide both a motive for wealth accumulation and help identify households with higher-than-average total wealth. Household returns account for 10–12% of the explained portionofthegap,suggestingthatasubstantialportionofthedifferenceinannualizedwealthcomes from differences in portfolio composition (which determine returns). For both comparisons, outof-pocket costs explain a similar portion of the gap as household returns. Finally, differences in marital status appear to be important in explaining the Black-White gap, but not the Hispanic- Whitegap. Table 4: Median Oaxaca–Blinder (RIF) Decomposition of ACW by Race and Ethnicity Black–White Hispanic–White Estimate Std.Error Estimate Std.Error Totalgap 0.763 0.021 0.976 0.029 Explained 0.545 0.018 0.641 0.028 Education 0.082 0.008 0.171 0.022 Bequestexpectations 0.280 0.012 0.325 0.018 Householdreturns 0.057 0.004 0.054 0.006 OOPmedicalspending 0.052 0.006 0.075 0.010 Married 0.067 0.007 0.008 0.003 Othercontrols 0.000 0.000 0.000 0.000 Unexplained 0.236 0.017 0.385 0.023 Interaction -0.019 0.013 -0.051 0.022 Notes: Thetabledecomposesdifferencesinannualizedcomprehensivewealth(ACW)byrace andethnicity,followingFirpoetal.(2009). Thismethodpartitionsthegapintheunconditional medianoflogACWintoan“explained”component,capturingdifferencesinobservables,and an “unexplained” component, capturing differences in coefficients. “Other controls” include age,agesquared,cohort,expectedinheritance,subjectivelife-expectancyratios,householdsize, andyearfixedeffects.Standarderrorsareclusteredatthehouseholdlevel,andallestimatesare weightedusingHRSsamplingweights.Datacomefromthe1998–2022wavesoftheHRS. Taken together, these results indicate that ACW tends to rise with age for many households, 34Firpoetal.(2018)developamethodofusingrecenteredinfluenceregressionstoextendtheOaxaca–Blinderdecompositiontootherdistributionalmeasures,includingtheunconditionalmedian. 27

150 100 50 0 )sdnasuoht( WCA naidem detciderP 51–60 61–65 66–70 71–75 76–80 81–90 Age College High school Less than HS Figure13: TrajectoryofmedianACW,byeducation Notes: The figure plots the age trajectory of ACW using the marginal estimates of a set of age dummies interactedwitheducationcategoriesfromaquantilefixedeffectsregressionthatincludescontrolsforbequestexpectations,inheritanceexpectations,subjectivelifeexpectancy(relativetoactuarialexpectations), out-of-pocketmedicalexpenditures, householdfixedeffects, andyeareffects. Datacomefromthe1998– 2022wavesoftheHRS. 100 80 60 40 20 )sdnasuoht( WCA naidem detciderP 51–60 61–65 66–70 71–75 76–80 81–90 Age White Black Figure14: TrajectoryofmedianACW,byrace Notes: The figure plots the age trajectory of ACW using the marginal estimates of a set of age dummies interacted with race categories from a quantile fixed effects regression that includes controls for bequest expectations, inheritance expectations, subjective life expectancy (relative to actuarial expectations), and out-of-pocketmedicalexpenditures.Datacomefromthe1998–2022wavesoftheHRS. 28

80 60 40 20 )sdnasuoht( WCA naidem detciderP 51–60 61–65 66–70 71–75 76–80 81–90 Age Hispanic Non-Hispanic Figure15: TrajectoryofmedianACW,byethnicity Notes: The figure plots the age trajectory of ACW using the marginal estimates of a set of age dummies interactedwithethnicitycategoriesfromaquantilefixedeffectsregressionthatincludescontrolsforbequest expectations,inheritanceexpectations,subjectivelifeexpectancy(relativetoactuarialexpectations),out-ofpocket medical expenditures, household fixed effects, and year effects. Data come from the 1998–2022 wavesoftheHRS. and that this pattern is especially pronounced for college-educated and White households. Further, these age patterns emerge even after controlling for time-varying household characteristics andyearfixedeffectsintheregressions. Toexplorefurtherhowtheseagepatternsvarywithobservablehouseholdcharacteristics,we estimateaseriesofOLSfixedeffectregressionsoflogACWthatsequentiallyaddblocksofhouseholdcharacteristics. Table5reportstheresultsfromthese“layered”regressionsoflogACW,each of which includes household and year fixed effects and a common set of age dummies. Column (1)includesonlytheagedummies. Column(2)addsafinancialblockconsistingofthehouseholdspecificreturn,logout-of-pocketmedicalcosts,andthefinancialandnonfinancialsharesofACW. Column (3) adds an expectations block that includes the probabilities of leaving bequests of differentsizes,thelifeexpectancyratio,andtheprobabilityofenteringanursinghome. Column(4) addshouseholdsizeandanindicatorofmarital-status. The age coefficients in column (1) show that ACW tends to increase with age, which is consistent with the median profiles above. Adding the financial variables in column (2) leaves the ageestimatespracticallyunchanged,despitethefactthatallofthesevariablesarestatisticallysignificant. The household-specific return, log medical costs, and the financial share of ACW are all stronglyandpositivelyassociatedwithACW.Thecoefficientestimateonthenonfinancialshareis 29

negative and statistically significant, which may seem surprising in light of the slow drawdown of housing wealth. This result likely reflects the fact that the fixed-effects specification identifies the association between changes in the nonfinancial share and changes in log ACW. Because the annuitized components of ACW (e.g., Social Security) are relatively flat by construction, changes infinancialwealthwillbothraiseACWanddecreasetheshareofnonfinancialwealth,leadingto anegativecoefficientonthenonfinancialshare. When the expectations block is added in column (3), the age coefficient estimates are dampened, particularly in the case of ages 71–75, where the estimate falls by about 40%. The positive and significant estimates on the bequest probabilities and the life-expectancy ratio suggest that theselife-cycleexpectationsplayanimportantroleinshapingsavingbehaviorinretirement. The probabilityofenteringanursinghome,however, doesnotappearforbeeconomicallyorstatisticallysignificant. Finally,addingthevariablesforhouseholdcompositionincolumn(4)actuallystrengthensthe upward-sloping age pattern, bringing it almost in line with the age pattern in column (1). Here, the effects are driven by the indicator variable for married, which has a negative and significant coefficient estimate. The most common marital transition in retirement occurs with the death of a spouse. Because the household needs to support one fewer person, this transition will tend to increase the amount of ACW for a given level of comprehensive wealth, which explains why we seeanegativeassociationbetweenchangesinmaritalstatusandchangesinlogACW. Overall,thelayeredOLSfixedeffectsregressionssuggestthelife-cyclevariablesexplainsome, but not most, of the age pattern in ACW during retirement. Even in the specification with all of the life-cycle covariates, the age pattern of ACW increases with age and remains statistically significant. We do not interpret this as evidence that these factors are not the key drivers behind theslowdrawdownofretirementresources,butratherthattheylikelyinteractinstructuralways notcapturedbyourlinearregressionspecification. 4 Inequality in Annualized Comprehensive Wealth 4.1 Changesininequalitywithageandovertime Inequality in annualized comprehensive wealth is not constant, but can vary cross-sectionally with age and also change over time. The age variability is driven in part by age-related variance in medical expenses, bequest motivations, and survival expectations. The time dimension, by 30

Table5: OLSFixed-EffectRegressionsofACWonHouseholdCharacteristics (1) (2) (3) (4) (1) (2) (3) (4) Age61–65 -0.008 -0.010 -0.019∗∗∗ -0.015∗∗ (0.007) (0.007) (0.007) (0.007) Age66–70 0.009 0.008 -0.007 -0.001 (0.010) (0.010) (0.010) (0.010) Age71–75 0.046∗∗∗ 0.046∗∗∗ 0.027∗∗ 0.036∗∗∗ (0.014) (0.014) (0.013) (0.014) Age76–80 0.095∗∗∗ 0.100∗∗∗ 0.078∗∗∗ 0.088∗∗∗ (0.018) (0.017) (0.017) (0.017) Age81–90 0.161∗∗∗ 0.162∗∗∗ 0.147∗∗∗ 0.157∗∗∗ (0.022) (0.022) (0.021) (0.021) HHreturn 0.489∗∗∗ 0.509∗∗∗ 0.512∗∗∗ (0.061) (0.060) (0.060) Log(OOP) 0.009∗∗∗ 0.008∗∗∗ 0.008∗∗∗ (0.001) (0.001) (0.001) Financialshare 0.310∗∗∗ 0.253∗∗∗ 0.248∗∗∗ (0.032) (0.032) (0.032) Nonfinancialshare -0.456∗∗∗ -0.515∗∗∗ -0.523∗∗∗ (0.028) (0.027) (0.028) P(Beq>10k) 0.001∗∗∗ 0.001∗∗∗ (0.000) (0.000) P(Beq>100k) 0.001∗∗∗ 0.001∗∗∗ (0.000) (0.000) P(Beq>500k) 0.002∗∗∗ 0.002∗∗∗ (0.000) (0.000) Lifeexp.ratio 0.003∗∗∗ 0.003∗∗∗ (0.001) (0.001) Nursinghomeprob 0.000 0.000 (0.000) (0.000) No.livinginHH -0.001 (0.002) Married -0.028∗∗∗ (0.008) N 159405 159405 159405 159405 HHFE Yes Yes Yes Yes YearFE Yes Yes Yes Yes Financialblock No Yes Yes Yes Expectationsblock No No Yes Yes HHsize/marriageblock No No No Yes Notes: The table reports coefficient estimates from OLS fixed-effect regressions of ACWonhouseholdcharacteristics.Allregressionsincludesurveyyearfixedeffects, andstandarderrorsareclusteredatthehouseholdlevel. Datacomefromthe1998– 2022wavesoftheHRS. 31

contrast,capturesbroaderyear-to-yeartrendsinportfoliocompositionandtheeffectofeconomywideshocks(suchasinflationandassetreturns)onhouseholdwealth. We examine patterns of inequality in annualized comprehensive wealth using four common statistics: theGinicoefficient,the90–10ratio,thetop10percentshare,andtheTheilindex.35 Figure 16 shows how these four measures of inequality evolve with age and across cohorts. Most of the measures show generally increasing inequality with age, especially for the older cohorts. Themeasuresalsosuggestgenerallyhigherinequalityatages51–60formorerecentcohorts, thoughthispatternisnotconsistentlyobservedafterage60. The increase in inequality with age could reflect factors highlighted by the life-cycle model. First, there is survivorship bias at older ages: wealthier individuals tend to live longer, so that households observed at advanced ages are increasingly drawn from higher-wealth groups. Second, heterogeneity in bequest motives leads some households to preserve financial and nonfinancial wealth later in life, while others draw down resources more quickly. Finally, the rising inequality may reflect the increasing variance of medical expense and long-term care shocks at olderages(FrenchandJones,2004). Figure17tracestheevolutionofinequalityinACWacrossyears. Allfourmeasuresvaryacross years, but some common patterns emerge. At the onset of the financial crisis in 2008, inequality was higher than it was in 2000, due in part to rising house prices, which disproportionately increased in higher-wealth areas. Similarly, all four measures show that inequality fell during the peak period of the financial crisis from 2010–2012, as financial and housing asset prices declined sharply,shavingmorewealthofftheupperendofthedistributionthanthelower. Inequalitythen increased markedly through 2018 as financial asset prices recovered.36 The movements in 2020 and 2022 likely reflect the disruptive effects of the COVID-19 pandemic on asset valuations and housingconditions. 4.2 Impactofhouseholdcharacteristicsoninequality The results in Figure 16 suggest that inequality increases with age and may be higher in recent cohorts, which likely reflects differences in household characteristics across age and time. An important question is whether inequality rises with age independently, or whether the observed 35The Theil index is an entropy-based measure of inequality that equals zero under perfect equality and rises as resourcesbecomemoreconcentrated.ItisdefinedasT= 1 ∑n xi ln (cid:0)xi (cid:1) ,where,inthiscase,x isahousehold’sACW n i=1 x¯ x¯ i andx¯istheaverageACWacrosshouseholds. 36A large literature documents the evolution of inequality around the Financial Crisis. See, for example, Bricker etal.(2012),Pfefferetal.(2013),Christelisetal.(2015),andShchepelevaetal.(2022). 32

Gini Coefficient Theil Index 0.65 0.7 0.60 0.6 0.55 0.50 0.5 0.45 0.4 0.40 0.3 51−55 56−60 61−65 66−70 71−75 76−80 81−85 86−90 >90 51−55 56−60 61−65 66−70 71−75 76−80 81−85 86−90 >90 Age Age Share Held by the Top 10% 90−10 Ratio 60 0.45 50 0.40 40 0.35 30 0.30 20 51−55 56−60 61−65 66−70 71−75 76−80 81−85 86−90 >90 51−55 56−60 61−65 66−70 71−75 76−80 81−85 86−90 >90 Age Age Silent & Older Early Boomers Late Boomers Cohort: (b. 1945 and before) (b. 1946−1954) (b. 1955−1964) Figure16: Inequalitymeasuresbyageandcohort Notes: Thefiguredepictsfourmeasuresofinequalityinannualizedcomprehensivewealthacrosssurvey years. Clockwisefromtopleft: Ginicoefficient, Theilindex, top10percentshare, and90–10ratio. Data comefromthe1998–2022wavesoftheHRS. Gini Coefficient Theil Index 0.54 0.65 0.60 0.52 0.55 0.50 0.50 1998 2002 2006 2010 2014 2018 2022 1998 2002 2006 2010 2014 2018 2022 Year Year Share Held by the Top 10−Percent 90−10 Ratio 0.41 40 0.40 0.39 35 0.38 30 0.37 1998 2002 2006 2010 2014 2018 2022 1998 2002 2006 2010 2014 2018 2022 Year Year Figure17: InequalitymeasuresoverHRSsurveyyears Notes: Thefiguredepictsfourmeasuresofinequalityinannualizedcomprehensivewealthacrosssurvey years. Clockwisefromtopleft: Ginicoefficient, Theilindex, top10percentshare, and90–10ratio. Data comefromthe1998–2022wavesoftheHRS. 33

pattern primarily reflects changes in other household characteristics. To assess the importance of these characteristics on measured inequality, we estimate recentered influence function (RIF) regressions(seeFirpoetal.(2009)),whichallowustoevaluatetherelationshipbetweencovariates anddistributionalmeasuressuchastheGinicoefficient,the90–10ratio,thetop10-percentwealth share,andtheTheilindex. Arecenteredinfluencefunctiondescribeshowacovariateaffectsadistributionalstatistic,such as the Gini coefficient. Let the inequality statistic of interest be a functional ν(F) that maps the population distribution F of ACW (here denoted Y) into a real number (for example, the Gini coefficient or the Theil index). For each observation y of Y, the influence function measures how ν(F)wouldchangeifweaddedinfinitesimalmassatthepointy: ν (cid:0) (1−ϵ)F+ϵ ∆ (cid:1) −ν(F) y IF(y;ν,F) = lim , ϵ→0 ϵ where ∆ placesallitsmassony. Therecenteredinfluencefunctionaddsbackthestatisticitself: y RIF(y;ν,F) = ν(F)+IF(y;ν,F), ensuringthat E[RIF(y;ν,F)] = ν(F). Firpoetal.(2009)showthattheimpactofcovariatesonthe distributionmeasurecanbeestimatedbyregressingtheRIFontheexplanatoryvariables. Table 6 presents the RIF regression estimates for the Gini coefficient, the 90-10 ratio, the Theil index,andthetop-10%share. Thecoefficientestimatesprovideameasureofhoweachinequality measure would change if we shifted a small amount of the population mass toward households withthatcharacteristic,holdingconstantthedistributionoftheothercovariates. Across all measures, the coefficients on the age dummies show little systematic relationship between age and inequality until after age 80. Even controlling for other characteristics, there is substantial inequality in ACW among the oldest households. Interestingly, the results suggest thatincreasingtheproportionofBabyBoomersandmorerecentgenerationsrelativetothoseborn before1948wouldreduceinequality. Education also matters for inequality. A higher share of high-school–educated households is associated with significantly lower inequality across all measures, including the Gini coefficient, the90–10ratio,theTheilindex,andthetop10percentshare. Incontrast,ahighershareofcollegeeducatedhouseholdsisassociatedwithhigherinequalityacrosseachofthesemeasures. Together, theseresultsindicate thateducationalcompositionplaysanimportant roleinshapinginequality 34

inretirementresources. Raceandethnicityarealsostronglycorrelatedwithinequality. AhighershareofBlackorHispanic households is associated with significantly higher inequality in ACW. These results reflect considerable dispersion in ACW within these groups, even after controlling for other household characteristics. The bequest expectations – both intending to leave and intending to receive – show a surprising pattern. Increasing the share of households with higher reported probabilities of leaving bequests would actually lower inequality, presumably because many of the households in the middle of the ACW distribution plan to leave some sort of bequest. Households expecting to receive bequests are also associated with lower inequality for all four measures. One interpretation isthatthesehouseholdsmayhavelessincentivetoaccumulatesubstantialresourcesontheirown. Household-specific rates of return are strongly and positively associated with inequality (at leastfortheGiniandthe90-10ratio),suggestingthatreturnsmayplayanimportantroleinsharingthedistributionofACWinretirement. Portfoliocompositionandriskexposurevarysystematicallyacrosshouseholds, particularlybyeducation, wealth, andrace/ethnicity(seethecompositional figures in the appendix). Households with more exposure to higher-return assets, such asequities,experiencedalargerrun-upinwealthafterthefinancialcrisis,whichlikelyincreased the dispersion of comprehensive wealth. Independent of actual saving behavior, differences in householdreturnsarelikelytomagnifyinequalitythroughoutthedistribution. Looking at the other coefficients, out-of-pocket medical costs are associated with declining inequality, at least for two of our measures, perhaps indicating that higher-resource households are more likely to engage in ”optional” higher-expense medical spending, while lower-resource households rely more on Medicaid. Finally, increasing the share of married households would tendtoreduceinequality,whileincreasingtheshareoflargerhouseholdswouldincreaseitslightly. Takentogether,theresultssuggestthathouseholdreturns,demographics,andcohort-specificenvironmentscombinetoinfluencemeasuredinequalityinannualizedcomprehensivewealth. Taken together, the RIF regressions indicate that much of the observed inequality in annualized comprehensive wealth reflects differences in household characteristics. Education, cohort, race and ethnicity, bequest motives, medical expenses, and marital status are all associated with our measuresof inequality. Household returnsappear to beparticularly importantin explaining the distribution of annual retirement resources. Given the transition from DB pensions to retirement accounts, this could have implications for the future evolution of inequality in retirement 35

resources. Table6: RIFRegressionsofInequalityMeasures. Gini 90–10ratio Theil Top10%share Age66–70 0.000 0.239 -0.023 -0.003 (0.007) (0.288) (0.026) (0.008) Age71–75 -0.002 -0.134 -0.039 -0.008 (0.008) (0.310) (0.031) (0.010) Age76–80 0.010 0.439 -0.020 0.006 (0.009) (0.320) (0.036) (0.011) Age81–90 0.055∗∗∗ 1.989∗∗∗ 0.171∗∗ 0.056∗∗∗ (0.013) (0.339) (0.071) (0.016) HighSchool -0.070∗∗∗ -5.433∗∗∗ -0.121∗∗∗ -0.042∗∗∗ (0.004) (0.246) (0.014) (0.004) College 0.034∗∗∗ 2.887∗∗∗ 0.099∗∗∗ 0.024∗∗ (0.008) (0.308) (0.038) (0.010) Boomers(1948–1965) -0.036∗∗∗ -0.009 -0.131∗∗∗ -0.051∗∗∗ (0.010) (0.349) (0.041) (0.012) Post-Boomers(1966+) -0.055∗∗ -1.915 -0.179∗∗∗ -0.067∗∗ (0.023) (1.467) (0.064) (0.027) Black 0.019∗∗∗ 1.916∗∗∗ 0.038∗∗∗ 0.010∗∗∗ (0.003) (0.283) (0.010) (0.003) Hispanic 0.059∗∗∗ 6.578∗∗∗ 0.136∗∗∗ 0.042∗∗∗ (0.006) (0.404) (0.018) (0.007) P(Beq>10k) -0.126∗∗∗ -8.750∗∗∗ -0.234∗∗∗ -0.089∗∗∗ (0.006) (0.285) (0.027) (0.007) P(Inherit) -0.067∗∗∗ 0.503 -0.224∗∗∗ -0.086∗∗∗ (0.011) (0.554) (0.040) (0.013) Lifeexp.ratio 0.003 0.177∗∗∗ -0.000 0.002 (0.002) (0.044) (0.010) (0.003) HHreturn 0.333∗∗∗ 41.068∗∗∗ 0.432 0.109 (0.126) (2.681) (0.624) (0.158) Log(OOP) -0.003∗∗∗ -0.923∗∗∗ -0.003 0.001 (0.001) (0.041) (0.004) (0.001) Married -0.082∗∗∗ -3.508∗∗∗ -0.224∗∗∗ -0.072∗∗∗ (0.006) (0.209) (0.031) (0.008) HHsize 0.006∗∗∗ -0.007 0.020∗ 0.007∗∗∗ (0.002) (0.091) (0.011) (0.003) Constant 0.632∗∗∗ 20.613∗∗∗ 0.824∗∗∗ 0.477∗∗∗ (0.012) (0.603) (0.055) (0.015) Observations 111,031 111,031 111,031 111,031 Notes: Thedependentvariableistherecenteredinfluencefunction(RIF)ofeachinequalitymeasure. Regressionsincludeafullsetofyeardummies,aswellasdummiesfor5-yearagebuckets. Columnsreport resultsfortheGinicoefficient,the90–10ratio,theTheilindex(GE(1)),andthetop10percentshare. Standarderrorsareshowninparentheses. Statisticalsignificancedenotedby* p < 0.10,** p < 0.05,and*** p<0.01. 5 Conclusion We applied a comprehensive measure of annual household resources to the 1998–2022 waves of the HRS in order to investigate the extent of inequality in retirement preparation. The annual measure provides a way to compare retirement resources across families with different composi- 36

tion and longevity expectations. Although previous work has investigated the typical trajectory ofannualresources,thispaperfocusesontheinequalityinannualresources,withanemphasison the roles of education, race, cohort, household portfolio composition, and household-level asset returns. We report three main findings. First, the average and median ACW increases with age for allcohorts,reflectingthefactthathouseholdsacrossgenerationsdecumulatewealthmoreslowly than the basic life cycle model would predict. There is, however, considerable heterogeneity in thetrajectoriesofACW.Muchoftheupward-slopingtrajectoryforthesampleasawholeappears tobedrivenbytheexperiencesofhouseholdswithacollegedegreeand,toalesserextent,White households. Animplicationofthisfindingisthatgapsinretirementpreparationacrosseducation anddemographicgroupsarelikelytowidenwithageduringretirement. Second, we find that inequality in annual resources increases with age. This is true for the Gini coefficient, the Theil index, the top 10% share, and the 90-10 ratio. Third, we show that household-specific returns on equity, fixed income, and housing play a crucial role in shaping these patterns. In particular, differences in returns are strongly associated with higher values of the Gini coefficient and the 90–10 ratio, highlighting the importance of asset-market fluctuations inamplifyinginequalityduringretirement. Whileourresultsareprimarilydescriptive,theyunderscoretheimportanceofthefactorsthat havedominatedthemorerecentliteratureonlife-cycleconsumptionandsaving: theimportance ofprecautionarysavingagainstmedicalshocks,theroleofbequests,frictionsinthehousingmarket, differential longevity, and the connection between household portfolio choice and aggregate movementsinassetpricesovertime. 37

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7 Appendix White . Black 0.00 0.25 0.50 0.75 1.00 Non−Hispanic Hispanic 0.00 0.25 0.50 0.75 1.00 College High School . <High School 0.00 0.25 0.50 0.75 1.00 Top 10% Bottom 10% . Middle 40% 0.00 0.25 0.50 0.75 1.00 Fraction of ACW Wealth Category: annuitized housing financial other wage Figure 18: Average annualized comprehensive wealth (ACW) composition by wealth bracket, education,andrace/ethnicity. Notes: The bars in the top panel show the average composition of ACW for respondents aged 61-70 by wealthcategoryforthebottom10percentholdersofwealth,themiddle40percent,andthetop10percent. Thebarsinthesecondpanelshowthecompositionbyeducationgroup,andthebarsinthebottompanel showthecompositionbyraceandethnicity(White,Black,Non-Hispanic,andHispanic). Datacomefrom the1998-2022wavesoftheHRS. 42