Household Debt, the Labor Share, and Earnings Inequality
Abstract
We show that the secular decline in real interest rates in the United States, which began in the early 1980s and persisted for nearly four decades, reduced the laborâs share of output and the unemployment rate, and increased earnings inequality. We establish this link using a model of frictional labor markets, estimated from household-level data, in which unemployment risk is only partially insurable. Rising debt resulting from lower interest rates reduces the value of unemployment, leading to lower equilibrium wages relative to productivity and a lower unemployment rate. Wage dispersion also rises. The model is consistent with panel-data reduced-form evidence linking unemployment duration, assets, debt, and post-unemployment wages. In the model, a decline in the real interest rate of the magnitude observed in the data generates a decline in the laborâs share of 6 percentage points and in the unemployment rate of 0.3 percentage points. The variance of log earnings rises from 0.66 to 0.75.
Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Household debt, the Labor Share and Earnings Inequality Mark Robinson, Pedro Silos, Diego Vilan 2025-028 Please cite this paper as: Robinson, Mark, Pedro Silos, and Diego Vilan (2025). “Household debt, the Labor Share and Earnings Inequality,” Finance and Economics Discussion Series 2025-028. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.028. 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.
Household Debt, the Labor Share, and Earnings ‗ Inequality Mark Robinson† Pedro Silos ‡ Diego Vilán § Abstract WeshowthattheseculardeclineinrealinterestratesintheUnitedStates,whichbegan intheearly1980sandpersistedfornearlyfourdecades,reducedthelabor’sshareof outputandtheunemploymentrate,andincreasedearningsinequality. Weestablish thislinkusingamodeloffrictionallabormarkets,estimatedfromhousehold-leveldata, in which unemployment risk is only partially insurable. Rising debt resulting from lowerinterestratesreducesthevalueofunemployment,leadingtolowerequilibrium wages relative to productivity and a lower unemployment rate. Wage dispersion also rises. The model is consistent with panel-data reduced-form evidence linking unemploymentduration,assets,debt,andpost-unemploymentwages. Inthemodel, a decline in the real interest rate of the magnitude observed in the data generates a declineinthelabor’sshareof6percentagepointsandintheunemploymentrateof0.3 percentagepoints. Thevarianceoflogearningsrisesfrom0.66to0.75. Keywords: LaborShare,HouseholdIndebtedness,ReservationWage JELClassificationNumbers: J30,E24,E27 ‗WethankMatthiasPaustianandAndrewFiguraforhelpfulconversations,andMusaOrakforproviding thedataontheskill-premium. Theviewsexpressedinthispaperaresolelytheresponsibilityoftheauthors andshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystem oranyotherpersonassociatedwiththeFederalReserveSystem. †Email: markrobinson6@gmail.com ‡Correspondingauthor. DepartmentofEconomics,TempleUniversity,2ndFloor,GladfelterHall,1115 PolettWalk,Philadelphia,PA19122USA.Email: pedro.silos@temple.edu. §BoardofGovernorsoftheFederalReserveandGeorgetownUniversity. Email: diego.vilan@frb.gov.
1 Introduction Startingintheearly1980sandcontinuingthroughthe2010s,realinterestratesdroppedin the UnitedStates andmuch of thedeveloped world. Researchers havepointed to various reasonsforthisdecline,includingrisingsavingsratesfromEastAsia,lowerinvestment demand, and demographic changes. Regardless of the exact causes, this drop in real interest rates caused a rise in household debt, both in unsecured forms like credit cards andinsecuredformslikemortgages. Thispaperexploreshowthesecularriseindebthas impacted labor markets, showing that falling real interest rates contributed to a decline in labor’sshareofoutput,alowerunemploymentrate,andgreaterearningsinequality. The key premise is that higher debt (or fewer savings) makes being unemployed less sustainable. This occurs because unemployment risk is only partially insurable: unemploymentbenefitsrunoutafteracertainperiod,andsavingsorborrowingcanonly coverexpensesforsolong. Ashouseholdstookonmoredebtinresponsetofallingreal interestrates,theirfinancialsituationsweakened,leavingthemmorefinanciallyvulnerable, and forcing them to accept lower wages to exit unemployment. We formalize this idea using a standard job search model with a financial market, where households can save or borrow (up to a point) at a fixed real interest rate. Workers can become unemployed withsomeexogenousseparationprobability,buttheirjob-findingprobabilitydependson households’balancesheets. Unemploymentbenefitsactasaformofinsurancebutexpire afterasetperiod,requiringunemployedworkerstorelyontheirsavings—ortoborrow furtheriftheyarealreadyindebt—tocoverexpenses. Theriseindebtasaresultofthe declineinrealinterestrates,lowersthevalueofunemploymentrelativetoemployment. As aresult,theriseindebtcausesadeclineintheunemploymentrateandlowersthelabor’s sharebecauseworkersmustacceptlowerwagesrelativetotheirproductivity. Finally,the riseindebtalsoincreasesearnings(wage)inequality. Theintuitionisthatasthemarginal utilityofconsumptionrises(lowassets)thevalueofworkers’alternativetoemployment 1
dropsproportionatelymoreatlowwages. Inotherwords,thereservationwagepolicyis concave in assets. In the model, the labor market is segmented by skill to be consistent withtheevidencethatthelabormarketexperiencesaredifferentfordifferentgroupsof workers (see Gregoryet al. (2024)): some workers facehigher separation rates with short employmentspellsandotherworkersarevirtuallyshieldedfromlabormarketshocks. We map this heterogeneity to observed levels of education. Workers of different education levels face disparate labor market experiences affecting their wealth accumulation. For instance,asset-to-incomeratiosaresignificantlyhigherforhigher-skilledworkers. TomotivatethestructuralmodelweusetheSurveyofIncomeandProgramParticipation (SIPP)in2017through2019toestimatereduced-formrelationshipsbetweenlabormarket variablesandhouseholds’balancesheets. Takingadvantageofthehigh-frequencypanel dimension, we link unemployment duration and wages post-unemployment-spells to different types of debt and financial assets. This analysis uncovers a strong negative relationshipbetweenunemploymentdurationandcreditcarddebt,andaweakerbutstill significantrelationshipwithmortgagedebt. Whenregressingunemploymentondifferent types of assets, the coefficients have the anticipated (positive sign) but the relationship appearsmodest. Finally,wefindastrongpositiverelationshipbetweenunemployment durationandfirstwages(orearnings)post-unemployment. Wecomplementthisevidence withdatafromthe2019SurveyofConsumerFinances(SCF).Despitenotbeingapanel,the SCFallowsustoshowhowrobusttherelationshipbetweenassets/debtandearningsis,as theassets/debtinformationintheSCFisquitedetailed. Conditionalonseveralcontrols, thepositiverelationshipbetweenearningsandnetworthisrobust. Thesereduced-form results,especiallythosefromtheSIPP—ahigh-frequencypanelparticularlywellsuited to study unemployment — are a contribution in themselves. They complement recent evidencebyHerkenhoffetal.(2023)whorelateaccesstocredittounemploymentdynamics. Focusingonlyondisplacedworkers,andnotonallunemployedworkers,thatpaperfinds moreaccesstocreditduringunemploymentincreasesunemploymentduration. Whilethis 2
result appears to be at odds with our premise, it is actually consistent. Available credit acts as an asset that allows workers better consumption smoothing while unemployed. We showthatbeing indebtis correlatedwithlowerunemployment duration,andthis is particularlytrueforcreditcarddebt,andtosomeextentwithmortgagedebt. However,we aresilentabouthowthatdebtlevelaffectstheavailabilityofcreditwhileunemployed. Our empiricalresultsalsocomplementevidenceshowninBloemenandStancanelli(2001)who employing a Dutch survey on reservation wages and wealth, find that financial wealth increasesreservationwages.1 WecalibratethemodeltotheUSeconomyasdescribedbytheSIPPduringtheyears 2017 through 2019. These years were characterized by low real interest rates, a low labor’s share, high household indebtedness, and high earnings inequality. Taking the real interest rate observed in the data as exogenous (set at 0.18% monthly), we set the model’s parameters so that the model describes the US economy in 2018 accurately in regardstodebttoincomeratios,earningsinequality,andunemploymentinsurancepolicies. With the model’s structural parameters in hand we validate the model using reduced form relationships between unemployment duration, households’ balance sheets, and post-unemployment wages. As in the data, the model predicts a negative relationship between unemployment duration and debt, as well as a positive relationship between durationandpostemploymentwages. Ourcounterfactualexerciseistosettherealinterest ratetotheleveltotheyear1982(about0.5%monthly). Wecomparethiseconomywiththe oneintheyears2017-2019: relativetothelowinterestrateeconomytheunemploymentrate risesslightly(about0.3percentagepoints),wagesrelativetoproductivity(thelabor’sshare) rises about 6 percentage points. The higher interest rate economy features substantially less earnings inequality; the variance of log earnings drops from 0.75 to 0.66. In the model,theskillpremium—theaveragewagesofworkerswithacollegedegreerelativeto workerswithonlyahighschooldiploma—risesfrom1.39in1982to1.55in2018. These 1Theeffectofhomeownership,butnotonmortgagedebt,onpost-employmentwageshasbeenexamined empiricallybyYang(2019). 3
resultssuggestthatboththeriseintheskillpremiumandthefallinlabor’sshare,apart fromoriginsthataretechnologicalinnature,havebeencausedinpartbytheinterplayof frictionallabormarkets,theriseindebt,andthepartialinsuranceofunemploymentrisk. Thedownwardtrendinlabor’sshare—thefractionofeconomicoutputthataccruesto workers—representsanimportantstructuralshiftintheeconomywithpotentiallybroad economic implicationsforlabor productivity, incomegrowth, andhousehold inequality. As such, the decline of the labor share has attracted significant attention and has been written about extensively. Some possible reasons for the drop range from the effects of globalization and technological changes to debilitated worker unions. In this paper, we arguethattheriseinU.S.householddebtoverthatperiodhasalsobeenafactorcontributing tothedeclineinthelaborshare. Similarly,thereisavastliteraturethatexaminestherisein earningsinequalityanditsrelationshiptojobpolarizationorcapital-skillcomplementarity, for example. This paper proposes an alternative channel, in which earnings dispersion grew over time due to increasing household indebtedness. The dispersion in financial wealth, and in particular the increase in the number of households with rising levels of debt,generatesdispersioninreservationwages,andhenceinactualwages. Our work highlights the critical role that the decline in real interest rates has played in shaping several well-documented trends over the past four decades: the decrease in household saving rates and the corresponding rise in debt, the increase in earnings inequality, and the decline in labor’s share of income. These developments have been central to three major areas of research at the intersection of wealth and labor market dynamics—areastowhichourworkcontributes. Thefirstareaconcernstherelationshipbetweenwealthandlabormarketbehavior. A growingbodyofresearchexamineshowtheabilitytosave—andtheconstraintsimposedby limitedborrowingcapacity—affectsemploymentoutcomes,wagedynamics,andinequality. Thesemodelsoftenemphasizehowlabormarketrisksandfrictionsinteractwithwealth accumulation,showingthatfactorssuchason-the-jobsearch,unemploymentspells,and 4
restrictedaccesstocreditcanleadtosubstantialdisparitiesinindividualoutcomes. While webuildon manyofthe mechanismsdevelopedin thisliterature,our focusshiftstoward understanding broader macroeconomic trends—specifically, how changes in the real interestratealonecaninfluencelabormarketinequalityandthedistributionofincome. A second relevant area of research explores the causes behind the long-run decline in labor’s share of income. Much of this literature emphasizes shifts in the balance of power between firms and workers, driven by structural changes such as globalization, automation, the erosion of unions, and increasing market concentration. However, the precise mechanisms remain contested. We contribute to this literature by proposing a novelexplanation thatemphasizestheinterplaybetween labormarketsearch frictionsand householdwealth. Finally, our work contributes to a third strand of literature focused on the rise in earningsinequality. Oneprominentexplanationpointstotheshiftingdemandforskills, particularlytheincreasingcomplementaritybetweencapitalandhigh-skilledlaborrelative tootherworkers. Theweakeningofunions,thedeclineintherealvalueoftheminimum wage, and broader deregulation have all contributed to slower wage growth for many. Global economic integration has further amplified these effects by exposing some jobs to international competition, while disproportionately benefiting others that are either shieldedorinhighglobaldemand. Webringtogethertheseareasofresearchtoexplorethefollowingquestion: howmight astandardsearchmodelofthelabormarket,embeddedwithuninsurableriskandallowing for precautionary savings, account for changes in both labor’s income share and wage inequalityinresponsetoadeclineinrealinterestrates?2 Theremainderofthepaperisorganizedasfollows. First,wepresentempiricalevidence showing that between 1982 and 2019, the labor share decreased while household debt increased. Thethirdsectionintroducesamechanismthatoffersaplausibleexplanationfor 2WeincludeamorecomprehensiveliteraturereviewinAppendixA. 5
this decline and proposes a model capable of capturing the relevant dynamics. Section fouroutlinesthemodel’scalibration,followedbySectionfive,whichconductsanextensive setofvalidationtests. Sectionsixpresentstheresultsofourmaincounterfactualanalysis, comparing two economies within our framework: one with high interest rates and anotherwithrelativelylowerrates. Finally,Sectionsevenconcludeswithkeyfindingsand implications. 2 Data The study’s principal focus lies with the interaction of the dynamics of the labor share, earningsinequalityandhouseholddebt. Figure1plotsthelaborshareascalculatedbythe U.S.BureauofLaborStatisticssuggestingthisdownwardtrendwasrelativelymildand steadyuntiltheearly2000sandhasbecomesignificantlymorepronouncedsincethen. The steepestpartofthedecline-from63percentin2000toapproximately57percentin2018followedamoderatedownwarddriftinthe1980sandearly1990s,andaslightrecoveryin thelate1990s. Figure1: U.S.LaborShare1947-2023 6
Figure 2 presents various measures of U.S. household indebtedness in the postwar period. Drivenbyperiodsoflowinterestratesandfinancialinnovations—suchascredit cards and home equity loans—U.S. households have steadily increased their leverage sincetheendofWorldWarII3.WhileoverallhouseholddebtasashareofGDPhasrisen consistently,mortgageandnonmortgagedebthavefolloweddistincttrajectories. Mortgage debthasshownasteadyincreasesincethe1980s,withrapidaccelerationintheearly2000s, culminatinginasharppeakaroundthe2008financialcrisis. Thiswasfollowedbyamarked decline, reflecting deleveraging in the housing market, before stabilizing and experiencing minorfluctuationsinthe2010sandearly2020s. Incontrast,nonmortgagedebthasfollowed amoregradualupwardtrend,characterizedbyperiodsofsteady,moderategrowth. While it has not exhibited the extreme volatility of mortgage debt, it has grown consistently, peakingintheearly2020sbeforedecliningslightly. Overall,consideringthathousehold indebtedness increased while the labor share declined over the same period, this trend raisesimportantquestionsabouthowhouseholdnetworthinfluencesthedistributionof economicoutputbetweenworkersandothereconomicagents. Finally,Figure3presentsameasureoftheskillpremium,definedastherelativewage ofskilledversusunskilledworkersfrom1963to2019. WeusedatafromtheU.S.Census CurrentPopulationSurvey(CPS)andfollowthemethodologyoutlinedbyOhanianetal. (2023). The figure shows that after an initial decline in the late 1970s to early 1980s, the skillpremiumhasfollowedastrongandsustainedupwardtrajectory,particularlyfrom themid-1980sonward,withsomefluctuationsaroundtheearly2000s. Bytheendofthe period, the ratio reaches its highest level, indicating a persistent and widening wage gap betweenskilledandunskilled workersand anoverallincrease inearningsinequality over time. 3FurtherempiricaldetailsanddisaggregatedseriescanbefoundinAppendixE. 7
Figure2: HouseholdDebt(1980-2024) 2.1 FinancialWealthandWages: Measurement Ourhypothesisaboutthesemacroeconomicaggregatescentersonthreekeyhouseholdor individual-level variables: net worth (debt), unemployment duration, and earnings. To explain the decline in the labor share, we posit that lower asset levels (or higher debt)resulting fromreducedinterestrates influencereservationwages,leading to shorter periods of unemployment. We analyze individual and household-level data from two major surveys: the Survey of Consumer Finances (SCF) and the Survey of Income and ProgramParticipation(SIPP)toinvestigatethebehaviorofthesevariables. 8
Figure3: SkillPremium(Skilledvs. Unskilled) Each survey offers distinct advantages. The SCF provides high-quality asset data but lacks information on unemployment duration. We therefore use the SCF to explore the relationship between earnings (or wages) and measures of net worth, debt, or assetto-income ratios. The SIPP, while less detailed in its asset data, offers panel-based, high-frequency data that includes information on unemployment duration. This allows us to examine the connections between asset positions, earnings, and unemployment dynamics. Our analysis employs a reduced-form approach, acknowledging that no causalitycanbeinferredfromtheestimatedregressions. Weemploythe2019SurveyofConsumerFinancespublicreleasetostudytherelationship 9
between ahousehold’snetworthandwages. Weutilizea sampleof128,600represented householdswhowereemployedthatyearandmadeatleast$30,160inyearlywages;that numberistheamountahouseholdearningafull-timeminimumwagewouldreceive4. Table 1 highlights the 2019 SCF public release’s mean and median net worth across varioushouseholdcharacteristics. Cross-sectionaldifferencesinnetworthacrossgroups abound. Forinstance,familieswherethereferencepersonheldacollegedegreehadmore thantwicethemediannetworthcomparedtotheoverallsample. Additionally,disparities innetworthacrossdifferentgroupsgenerallyreflectsimilarpatternsseeninincome,with thoseinthehighestincomepercentilespossessinganetworthmorethantentimesgreater than the median. Finally, as individuals save for retirement throughout their working years,alife-cyclepatterninnetworthbecomesevidentinthedata. Table 2 compares the mean net worth across different family characteristics for the 2019 SCF public release with those families that the study focuses on: those that were employed and earned at least the minimum income. While the general patterns seen in the full sample appears to carry on, the net worth of the older age groups seems to be substantially higher. This could reflect a higher concentration of high earners that have postponedretirementinoursample,giventhatoursurveydesignrequiresthereference persontobeemployedatthetimeofthesurvey. 4Thisismeanttorepresentahouseholdoftwopeople,working2,080hoursayear,makingatleast$7.25 perhour. Toavoidrisk-sharingconsiderationsonecouldalsofocusexclusivelyonsingleworkersand/or unmarriedcouples. Althoughresultsarerobusttothissurveydesign,thenumberofobservationsdrops significantlyandwechosetoperformouranalysiswiththefulloriginalsample. SeeappendixAppendixB fortherelevantsamplecomparison. 10
Table1: 2019SCF:Households’MedianandMeanNetWorthbySelectedCharacteristics (ValuesinThousandsofDollars) Characteristic MedianNetWorth MeanNetWorth AllHouseholds 141 866 IncomePercentile ≤20 11 131 20-39.9 53 159 40-59.9 106 253 60-79.9 232 489 80-89.9 437 996 90-100 1,849 5,596 EducationofReferencePerson NoHighSchoolDiploma 24 160 HighSchoolDiploma 86 353 SomeCollege 104 434 CollegeDegree 358 1,758 Race/EthnicityofReferencePerson WhiteNon-Hispanic 210 1,103 AfricanAmericanNon-Hispanic 24 162 HispanicorLatino 42 223 Asian — — AgeofReferencePerson(Years) ≤35 16 89 35-44 106 508 45-54 196 967 55-64 246 1,364 65-74 309 1,410 ≥75 294 1,110 11
Table2: 2019SCFSample: Households’MeanNetWorthbySelectedCharacteristics (ValuesinThousandsofDollars) Characteristic Sample SCF AllHouseholds 891 866 EducationofReferencePerson NoHighSchoolDiploma 207 160 HighSchoolDiploma 353 353 SomeCollege 384 434 CollegeDegree 1,608 1,758 Race/EthnicityofReferencePerson WhiteNon-Hispanic 1,112 1,103 AfricanAmericanNon-Hispanic 193 162 HispanicorLatino 270 223 Asian — — AgeofReferencePerson(Years) ≤35 116 89 35-44 591 508 45-54 1,039 967 55-64 1,518 1,364 65-74 2,898 1,410 ≥75 3,917 1,110 To betterunderstandthe relationshipbetweenreservationwages andnet worth, wages wereregressedonnet worth and aseriesof co-variates: race,education level, sex, age, and number of children. Regression results are shown in Table 3. In the top row, wages are regressedonnetworth(andtheotherco-variates.). Thenumbershownisthecoefficient onnetworth,withthestandarderrorinparenthesis. Thedatasuggeststhatraisingthenet worthofanindividualby$1,000isassociatedwithraisingtheirannualwagesby$6. For 12
peoplewithnegativenetworth,havingalower(morenegative)networthisactuallyassociatedwithlowerwages. Inthebottomrow,logwagesareregressedonthelogofpositive networthanddebt(andotherco-variates). Again,thenumbershownisthecoefficienton (log)networth,withthestandarderrorinparenthesis. Ourfindingssuggestthata1%increaseinanindividual’snetworthisassociatedwitha0.17%increaseintheirannualwages. Table3: CoefficientonNetWorth(NW) Variable AllData Non-NegNW Neg. NW Levels 0.0062***(0.002) 0.0063***(0.0022) -0.029(0.022) Logs n.a. 0.173***(0.010) -0.032**(0.015) SampleSize(N) 3,208 2,918 288 Significance: ***at1%,**at5%,*at10% Note: Thetableshowsresultswhenwagesareregressedonnetworth,usingdatafrom the2019SurveyofConsumerFinances. Othercovariatesincluderace,educationlevel, sex,age,andthenumberofchildren. Networthisdefinedasassets(includingnonliquid assets)minusliabilities. TheAppendixCreportscoefficientsforalltheotherindependent variables. Wefurtherassesstherobustnessofthesefindingsbyemployinganalternativedefinition of net worth, focusing exclusively on liquid assets and debts. Operating under the assumption that access to liquid resources may be crucial for labor market outcomes, we exclude housing components from our original net worth measure and re-run the regressions. The results appear to reaffirm the baseline specification in terms of signs and significance. Specifically, under a liquid net worth specification, a 1 percent rise in households’networthcontinuestobeassociatedwithanapproximate0.17percentrisein annualwages. 13
Table4: CoefficientonLiquidNetWorth(NWL) Variable AllData Non-NegNW Neg. NW Levels 0.0063***(0.002) 0.0061***(0.002) -0.0015(0.017) Logs n.a. 0.171***(0.009) -0.020*(0.012) SampleSize(N) 3,208 2,884 382 Significance: ***at1%,**at5%,*at10% Note: Thetableshowsresultswhenwagesareregressedonliquidnetworth,usingdata fromthe2019SurveyofConsumerFinances. Othercovariatesincluderace,education level,sex,age,andthenumberofchildren. Liquidnetworthisdefinedasassetsminus liabilitiesandthetotalequityvalueinahousehold’sprimaryresidence. TheAppendix Creportscoefficientsforalltheotherindependentvariables. 2.2 NetWorthandUnemployment: EvidencefromSIPP TheSurveyofIncomeandProgramParticipation(SIPP)isalongitudinalsurveyconducted by the U.S. Census Bureau to collect data on the income, employment, and program participation of individuals and households in the United States. The SIPP has recently changed,providingacontinuouspanelinwhichhouseholdsareinterviewedforfouryears. Weuse the 2017-2019 data, providing information on sourcesof income, including wages, business income, and government assistance programs. Wealth data is collected once per year. Employment dataincludes information onjob transitions, offering apicture of the labormarketdynamicsduringthisperiod. Weemployinformationcollectedinthesurveys of2018,2019,and2020,sothemaximumweobserveindividualsisfor36months.5 Webeginbyrestrictingworkerstothoseolderthan20andyoungerthan60. Wealso calculate an average level of earnings over each workers’ entire history. If that average is zero or missing, we eliminate that worker from the sample. For each worker, we 5We do not use the 2021 survey because it collects information about 2020 outcomes. The recession associated with the COVID-19 pandemic was so extreme and extraordinary that we discarded the 2021 survey. 14
calculate the duration of each unemployment spell (most workers only experience one unemployment spell over the entire three-year period). The empirical analysis will be basedonasampleof4,150unemploymentspells. Foreachunemploymentspellwerecord theworker’sageatthattime,financialvariables,maritalstatus,etc. Table5summarizesthe variablesemployedintheanalysis,showingtheaverage,standarddeviation,minimum, and maximum. The average unemployment duration is almost four months long, and there arelong-term unemployed in thesample with amaximum observed durationof 30 months. Theaverageageofworkersisabout36and60%ofthemareolderthan30. About 40%arecollege-educatedand20%areblack. Abouthalfarenevermarried,andtheyare earning,onaverage,roughly$3,600dollarspermonth. Wereportsixvariablesdescribingworkers’balancesheets. Thesevariablesareallat the individual level and not at the household level. As is well known, the distribution ofwealthisdisperse butlesssointheSIPPsinceitoversampleslowincomehouseholds. The highest net worth is only $7.6 million and the lowest level is a negative wealth of -$750,000. The averagenet worth is closeto $70,000, andof thatamount, roughly $3,000 are in checking accounts and about $5,500 in savings accounts. The average amount of unsecureddebtis$13,500ofwhich$1,800iscreditcarddebt. Theaveragemortgagedebt iscloseto$25,000. We link unemployment duration with earnings (or wages) and financial variables throughlinearregressions. Wemeasurefinancialvariables(e.g.,debt)witheitheradummy variable for positive levels or the ratio of the financial variable to a worker’s average earnings. All regressions we show below have duration as the dependent variable. In additiontovariablesrepresentingdebt,assets,orlabormarketcompensation,regressions control for a year dummy, a dummy for race, marital status, and gender, a dummy for receivingunemploymentcompensation,andacollegedummy. Table6showsthecoefficientsofregressionswherethefinancialvariableissomelevel ofdebt. Wefocusonallunsecureddebt,creditcarddebt,andmortgagedebt. Wemeasure 15
Table5: SummaryStatistics Variable Mean SD Max Min Age 36.2 11.0 59.0 21.0 Fraction>30y.o. 0.6 0.5 1.0 0.0 Race 0.2 0.4 1.0 0.0 College 0.4 0.5 1.0 0.0 Marital 0.5 0.5 1.0 0.0 NetWorth 69,396 322,234 7,611,900 -746,350 Unsec. Debt 13,538 44,567 746,750 0.0 CreditCardDebt 1,814 5,537 59,900 0.0 MortgageDebt 24,618 76,915 1,210,000 0.0 CheckingAcc. 3,028 12,298 202,000 0.0 SavingsAcc. 5,516 23,387 327,000 0.0 Unemp. Duration 3.9 3.4 30.0 1.0 Earnings 3,664 3,963 70,150 1,001 each variable by either an indicator variable that takesthe value of one when the worker holds any positive level of debt or the ratio of the debt balance relative to the worker’s average earnings.6 The coefficients are negative for all six debt variables, implying that a higher level of debt relative to earnings (or a positive level of debt relative to no debt) is associated to a shorter unemployment duration. The mortgage-to-earnings ratio is not significant, although the unsecured debt dummy is very close to significant at the 10% level. Overall, it appears that credit card debt is strongly and negatively associated with unemployment duration. From the perspective of the theoretical model we describe below, the ability to borrow to finance consumption while unemployed is an important determinantofthedurationofunemployment. Table7presentsthecorrespondingcoefficientswhenwereplacethevariablefordebt withavariableforassets. Wefocusonthreemeasuresofwealth: networth(totalassets minustotaldebts), checkingaccount balances,and savings accountbalances. Similar to ourapproachwithdebt,wemeasureassetsorwealthusingeitheranindicatorvariablefor 6Thereasontoexaminethedebttoearningsratio,asopposedtothedebtlevel,istodampenthepotential effectthatunobservedcharacteristicshaveonduration. Theseunobservedcharacteristicscanaffectduration beyondtheeffectcapturedbythemeasureofformaleducationormaritalstatus. 16
Table6: Regression: UnemploymentDurationonDebt Variable Ind. Unse- Unse- Ind. Credit Credit Ind. Mort. Mort. > > > cured 0 curedRatio Card 0 CardRatio 0 Ratio Coefficient -0.25 -0.01** -0.43*** -0.09*** -0.39** -0.01 P-value (0.11) (0.03) (0.01) (0.01) (0.03) (0.33) R-squared 0.03 0.03 0.03 0.03 0.03 0.03 Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. All models regress unemploymentdurationonthesamesetofexplanatoryvariablesexceptforonevariable,whichrepresentsa typeofdebt. Weconsiderallunsecureddebt,creditcard,andmortgagedebt. Foreachtypeofdebt,we representitaseitheranindicatorvariableforpositivedebtlevel(e.g.,Ind. CC>0takesthevalue1ifthe individualhascreditcarddebt,andzerootherwise)orastheratiobetweendebtandtheindividual’saverage earningsoverherentiresample. TheAppendixDreportscoefficientsforalltheotherindependentvariables (seemaintextforthelistofvariables). positivebalancesortheratioofasset/wealthlevelstoearnings. Mostcoefficientsrelatedtoassetsorwealthareclosetozero,withsomebeingpositive and others negative. However, the estimates exhibit a high degree of uncertainty, as reflected in the large p-values. The only exception is the indicator for having a positive savings account balance, which is associated with a longer unemployment duration (a coefficientof0.57,significantatthe5%level). Overall,theseresultssuggestthatthelevel ofdebthasamuchstrongerrelationshipwithunemploymentdurationthanthelevelof assets. Table 8 shows the relationship between unemployment duration and subsequent earnings or wages post-unemployment spells. We use both wages and earnings as our model below does not distinguish between the two. For these regressions, we use the sameset ofcontrolsasfor theregressionslinking durationandfinancialassets/debt. The coefficient is significant for both earnings and earnings per hour, showing that longer durationisassociatedwithhigherearningspost-unemployment. In summary, the empirical results shown in thissection are suggestive of a close link betweenhouseholds’ financialassets/debts, their unemployment durationand thewages theyobtainpost-unemployment. Clearly,thesearesuggestiveassociationsandselection 17
Table7: Regression: UnemploymentDurationonAssets Variable Ind. Net NetWorth Ind. Checking Checking IndSaving Saving > > > Worth 0 Ratio 0 Ratio 0 Ratio Coefficient 0.12 -0.00 0.05 -0.03 0.57* -0.02 P-value (0.50) (0.19) (0.89) (0.31) (0.05) (0.37) R-squared 0.03 0.03 0.04 0.04 0.18 0.17 Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. All models regress unemploymentdurationonthesamesetofexplanatoryvariablesexceptforonevariable,whichrepresents networthorassets. Weconsiderallnetworth,checkingandsavingsaccounts. Foreachassetwerepresentit aseitherasanindicatorvariableforpositiveassetbalanceornetworth(e.g. Ind. CC>0takesthevalue1if theindividualhasapositivecheckingaccountbalance,andzerootherwise)orastheratiobetweennetworth orassetsandtheindividual’saverageearningsoverherentiresample. TheAppendixDreportscoefficients foralltheotherindependentvariables(seemaintextforthelistofvariables). Table8: Regression: UnemploymentDurationonEarnings Variable Earnings Earnings PerHour Coefficient 0.36** 2.83*** P-value (0.04) (0.00) R-squared 0.18 0.84 Note: ***,**,and*indicatesignificanceatthe1%,5%,and10%levels,respectively. Thetablereportstwo regressionsofunemploymentdurationonearnings(firstcolumn)andearningsperhour(secondcolumn)in additiontoallothervariablesalsousedinthedebtandassetregressions. Earningsorwagesaremeasuredas thefirstearnings(orwage)levelobservedafteranunemploymentspell. TheAppendixDreportscoefficients foralltheotherindependentvariables(seemaintextforthelistofvariables). andother issuespreventanycausalanalysisfroman increaseindebt tounemployment durationandearnings. Thegoalofthestructuralmodelpresentedbelowispreciselyto quantifyacausalchannelfromadropininterestratestohigherdebttolowerwagesand higherearningsinequality. 18
3 Model Ourquantitativeanalysisisbasedonamodelinwhichrisk-averseworkersreceivewage offers drawn from a distribution and decide whether to accept or reject them. These decisionsdependontheirfinancialposition,causingacceptancerates—andconsequently, job-findingrates—tovarywithassetholdings. Workerscansaveorborrowinarisk-free asset,andthelabormarketisassumedtobefrictionalratherthanperfectlycompetitive, whereworkerswouldotherwisebepaidtheirmarginalproduct. Thesefrictionsnaturally giverisetoheterogeneityinunemploymentdurationsandlabormarketoutcomes. We donotexplicitlymodel theoriginofthewage-offerdistributionthatworkersface. Inotherwords,wedonotspecifywhyfirmssetthewagestheydo. Instead,ourfocusison how acceptedoffers—and consequently, observed wages—respondto changes ininterest ratesthroughtheirimpactonassetholdings. Wepositthatthelevelofwageoffersislinked totheoutputofafirmemployingaworker. Consequently,ifaggregateproductivityinthe economy changes, we would expect the wage offer distribution to adjust accordingly. One possibleinterpretationofourexogenouswagedistributionisthatitarisesfromaBurdett andMortensen(1998)orPostel-VinayandRobin(2002)framework,inwhichfirmsbalance offeringlowerwageswithloweracceptanceprobabilitiesagainsthigherwageswithhigher acceptanceprobabilities. Thelaborshareisdefinedastheratioofaveragewagestoagivenproductivitylevel, 𝐴 .7 Toisolatetheeffectsofinterestratechangesonthedistributionofactualwages,wehold 𝐴 constant across the two periods we compare. Specifically, after calibrating the model for 2019, we exogenously reset the interest rate to its 1982 level while allowing all other modelvariablestoadjustendogenously. Thisapproachenablesustoidentifytheimpact ofhigherleverageonthemodel’sendogenousvariables. Sinceproductivityisexogenous andweabstractfromcapital,assumingthatproductivitydoesnotchangebetween1982 7Inthecalibrationbelow,weset𝐴sothataveragewagesrelativetoproductivitymatchthelaborshare observedin1982. 19
and2019iswithoutlossofgenerality8. Afewpotentiallyimportantdimensionsareabstractedfrom. First,weexcludecapital tofocusonthelabormarket;alowerlaborshareheresimplymeansalowerwagerelative tolaborproductivity. Inasettingwithcapital,highercapitaldemandwouldincreaselabor productivity. Second,wedonotmodelhowfirmentryrespondstochangesininterestrates. Incorporating entry would require modeling the firm’s decision on the optimal posted wage. Here,ouremphasisisonworkers’behaviorandthewayassetholdingsaffecttheir compensation. Third, the model does not account for on-the-job search; in other words, agents in the model do not seek alternative opportunities once they become employed. Themodel’ssetupandtimingarediscussednext. 3.1 Setupandtiming Time is discrete, and there is a unit mass of infinitely-lived agents indexed from zero to 𝑠 one. Thereisasingleconsumptiongoodwhosepriceisalways1. Duringtimeperiod , 𝑖 agent hasthefollowingutilityfunction: ∞ (cid:213) 𝑉 = E 𝛽𝑡𝑢(𝑐 ) 𝑖𝑇 𝑠 𝑖𝑡 𝑡=𝑠 where: 𝑐1−𝛾−1 𝛾 ≠ 1 𝑢(𝑐) = 1−𝛾 log (𝑐) 𝛾 = 1 𝛾 and isexogenous. In the model, agents are heterogeneous along several dimensions. Crucial to our 8We are interested in measuring wages relative to productivity (the labor share), and if we allow productivitytochangeexogenously,thefirmofferdistributionandthedistributionofacceptedwageswill changeaswell. However,thedistributionofacceptedwagesrelativetoproductivitywillnot. Thisexercise allowsustoisolatechangesintheendogenousvariablesthatarisesolelyfromchangesininterestrates. 20
analysisarethoseaspectsthatmightinfluencethelaborsupplydecision. Becauseagents’ unemployment experiences and savings rates vary significantly, we posit that there are ex-antefactors(notmodeledinourframework)thatleadthemtohavedifferentemploymentto-unemploymentseparationprobabilities,discountfactor,accesstodebt,andotherkey parametersdiscussedbelow. Tokeepthisex-anteheterogeneitymanageable,weclassify agentsintothreedistinctgroupsbasedoneducationlevels. Agents are initially differentiated by their employment status: they can either be employed or searching for a job. Employed agents are further differentiated by their 𝑤 𝑎 wage level 𝑖𝑡. Agents begin each period with a wealth 𝑖𝑡 and receive interest income 𝑎 𝑟 𝑟 > 𝑎 equal to 𝑖𝑡 , where 0 is the exogenous interest rate (if 𝑖𝑡 is negative, then the agent 𝑎 𝑟 insteadmakesaninterestpayment;thatis,wealthisdecreasedby 𝑖𝑡 ). Agentsalsoreceive 𝑒 an earnings payment 𝑖𝑡, which includes both wages and unemployment payments. If 𝑤 employed, the earnings payment is wage 𝑖𝑡; if unemployed the payment is exogenous 𝑏 (𝑛) 𝑗 𝑛 𝑗 ,where denotesanagent’sskilllevel,and denotesunemploymentduration. Thatis to say, in the model, unemployment insurance increases with the agent’s productivity, but benefitsareonlyprovidedforafixednumberofperiods. Allresourcesgatheredbyagents, whetherfromwagesorunemploymentpayments,canthenbeusedforconsumptionor wealthaccumulationpurposesandwillinfluencelaboroutcomesasdescribedinsection 3.2. Due to the risk of unemployment that agents face every period, they will seek to self-insureagainstthiseventuality. Theycandosobyaccumulatingassetsviasavings,or byborrowingagainsttheirfutureearnings. Anagent’swealthlevelcanbecomenegative 𝑎 < but can never fall below the exogenous limit, 0. During any particular period, an 𝑗 𝑐 𝑎 agent simultaneously chooses an amount to consume 𝑖𝑡 and next-period wealth 𝑖,𝑡+1 , 21
𝑗 suchthat,foranagentofskilllevel thebudgetconstraintis: 𝑐 + 𝑎 ≤ 𝑎 ( +𝑟)+ 𝑒 𝑖𝑡 𝑖,𝑡+1 𝑖𝑡 1 𝑖𝑡 𝑎 ≥ 𝑎 𝑖,𝑡+1 𝑗 𝑐 ≥ 𝑖𝑡 0 Once the consumption-savings decision is made, the agent’s employment status for the next period is determined. From an agent’s point of view, both the job-separation 𝛿 𝑓 (𝑤𝑜) probability 𝑗,andthewage-offerdistribution 𝑗 areexogenous. Atthispoint,there 𝛿 aretwopossibilitiesforemployedagents: withprobability 𝑗 theagentwillbeunemployed −𝛿 nextperiod,andwithprobability1 𝑗 theagentwillcontinuetobeemployedatthesame wage, 𝑤 𝑖𝑡 = 𝑤 𝑖,𝑡+1 . An employed agent never experiences a raise or salary cut, although agents who go from employment to unemployment and are subsequently rehired may experienceachangeintheirwage. 𝑤𝑜 Unemployedagents,ontheotherhand,receiveanewwageoffer, ,everyperiodthey 𝑖𝑡 areunemployed. Eachofferisdrawnfromanexogenouswagedistributionspecifictothe −𝜌 agent’s type. With probability 1 each period the agent is able to choose whether to accept or reject the offer. If the offer is accepted, the agent will be employed at a wage 𝑤 𝑖,𝑡+1 = 𝑤 𝑖 𝑜 𝑡 next period. If rejected, the agents keep searching and will continue to be 𝑡+ 𝜌 unemployedinperiod 1. Finally,withprobability theagenthastoexogenouslyaccept the job offered. This feature of the model is designed to capture, in a reduced form, the stigma that can be associated with long unemployment spells and why some workers might prefer to accept a less-than-ideal job offer. Furthermore, consistent with the data we assume that this reputation concern is more relevant for medium and high-skilled workers9. Table9belowsummarizesthemodel’stiming. 9Researchonthestigmaassociatedwithunemploymentdurationhighlightsitssignificantimpactonlabor marketoutcomes. Kroftetal.(2013)foundthatthelikelihoodofreceivingjobcallbacksdeclinessubstantially withlongerperiodsofunemployment,emphasizingthestigmaeffect. Similarly,ErikssonandRooth(2014) demonstrated that employers often perceive long-term unemployed individuals as less motivated, even 22
SummaryofTiming StateinPeriod𝑡 Unemployedwithwealth 𝑎 𝑖𝑡 andduration𝑛 Employedwithwealth 𝑎 𝑖𝑡 andwage𝑤 𝑖𝑡 Choose 𝑐 𝑖𝑡 and 𝑎 𝑖,𝑡+1 s.t. Choose 𝑐 𝑖𝑡 and 𝑎 𝑖,𝑡+1 s.t. 𝑐 𝑖𝑡 +𝑎 𝑖,𝑡+1 ≤ 𝑎 𝑖𝑡 ( 1 +𝑟)+𝑏(𝑛) 𝑐 𝑖𝑡 +𝑎 𝑖,𝑡+1 ≤ 𝑎 𝑖𝑡 ( 1 +𝑟)+𝑤 𝑖𝑡 and and FirstAction 𝑎 ≥ 𝑎 𝑎 ≥ 𝑎 𝑖,𝑡+1 𝑖,𝑡+1 and and 𝑐 𝑖𝑡 ≥ 0 𝑐 𝑖𝑡 ≥ 0 𝜌 𝛿 Transition Joboffer. Probability that Probability thatagentis Probabilities agentisforcedtoaccept. separatedfromjob Ifnotforced, SecondAction N.A. acceptorrejectjoboffer Wealthis 𝑎 𝑖,𝑡+1 . Wealthis 𝑎 𝑖,𝑡+1 . Ifofferaccepted, Ifseparatedfromjob, S 𝑡 t + at 1 einPeriod employedwithwage𝑤 𝑖,𝑡+1 = 𝑤 𝑖 𝑜 ,𝑡 . unemployed. Ifrejected, Otherwise, unemployed. employedatwage𝑤 𝑖,𝑡+1 = 𝑤 𝑖𝑡 Table9: Thistablesummarizesthetimingofactionstakenbyemployedandunemployedworkers. The right column shows actions for the employed and the resulting changes in the relevant variables. Theleftcolumnshowsthesamefortheunemployedworkers. 3.2 TheHouseholdProblem Anemployedagentwithwealth 𝑎 andwage 𝑤 solvesthefollowingrecursiveproblem10: whentheirqualificationsareidenticaltoothercandidates. BlanchardandDiamond(1994)linkedlong-term unemploymenttohysteresisinlabormarkets,showinghowitperpetuatesstigmaandcreatespersistent joblessness. Supportingthesefindings,Ghayad(2014)usedfieldexperimentstorevealthatunemployment durationisamorecriticalfactorforemployersthangapsinexperience,furtherillustratinghowprolonged unemploymentcandisadvantagejobseekers. 10Foreasierreadability,timeandskillsubscriptshavebeeneliminatedinthissection. Inturn,ifavariable carriesa𝑡+1subscript,thishasbeenreplacedbyanapostrophe(thus,𝑎 𝑖,𝑡+1 hasbeenreplacedwith𝑎′ ). 23
𝐸(𝑎,𝑤) = max {𝑢(𝑐)+𝛽(𝛿𝑈(𝑎′, 0 )+( 1 − 𝛿)𝐸(𝑎′,𝑤))} (3.1) 𝑐,𝑎′ 𝑎( +𝑟)+𝑤 ≥ 𝑐 + 𝑎′ s.t.: 1 𝑎′ ≥ 𝑎 𝑐 ≥ 0 Whendecidinghowmuchtoconsumeandhowmuchtosave,anunemployedagentwith 𝑎 𝑛 wealth ,andwhohasbeenunemployedfor periods,facesthefollowingoptimization: 𝑈(𝑎,𝑛) = max {𝑢(𝑐)+𝛽(( 1 −𝜌)E 𝑤𝑜 𝑉(𝑎′,𝑤𝑜,𝑛 + 1 )+𝜌E 𝑤𝑜 (𝑎′,𝑤𝑜))} (3.2) 𝑐,𝑎′ 𝑎( +𝑟)+𝑏 ≥ 𝑐 + 𝑎′ s.t.: 1 𝑎′ ≥ 𝑎 𝑐 ≥ 0 𝑤𝑜 Whendecidingwhethertoacceptorrejectajoboffer ,anunemployedagentwith 𝑎 wealth solvesthisproblem: 𝑉(𝑎,𝑤𝑜,𝑛) = max (𝐸(𝑎,𝑤𝑜),𝑈(𝑎,𝑛)) (3.3) 𝑎 𝑤 It follows that for each level of wealth , a wage offer will be accepted if and only 𝐸(𝑎,𝑤) ≥ 𝑈(𝑎) 𝐸 𝑤 𝑈 𝑤 if . Since isincreasingin and isnotdependenton ,itfollowsthat 𝑎 𝑤∗(𝑎) 𝐸(𝑎,𝑤) ≥ 𝑈(𝑎) 𝑤 ≥ 𝑤∗(𝑎) foreach thereissomevalue atwhich ifandonlyif . This valueisthereservationwageandcanbedefinedas: 𝑤∗(𝑎) = {𝑤 : 𝑉(𝑎,𝑤) = 𝐸(𝑎,𝑤) = 𝑈(𝑎,𝑛)} (3.4) 𝑎 𝑤(𝑎,𝑛) 𝑛 Asafunctionofassets thereservationwagefunction forgeneralduration is 24
concave,asshowninFigure4 Reservation Wage (w ) ∗ w (a,n) ∗ Assets (a) a 0 𝑎 Figure4: Thefigureshowsthereservationwageasafunctionofwealth foragenerallevel 𝑛 of duration . Forlargeenough unemployment benefits thereservation wage is positive evenattheborrowingconstraint. 3.3 Steady-StateEquilibrium The model’s stationary equilibrium is determined by individuals’ optimal decisions over job acceptance and asset accumulation when facing an exogenous interest rate and a distribution of wage offers. Each unemployed agent weighs the value of remaining unemployed (with its associated benefits and savings possibilities) against the value of acceptingaparticularwageoffer,whichdependsoncurrentassets. Onceemployedata givenwage,agentschooseconsumptionandsavingsinresponsetothewageincomeand anexogenouslygivenborrowinglimit,potentiallyaccumulatingassetsovertime. Giventhese policyrules,theeconomy’sdistributionofassets andwagesevolves each periodaccordingtoatransitionfunctionthataccountsforstochasticjoboffers,employment transitions (including job separation), and individual savings decisions. A stationary equilibrium emerges when the cross-sectional distribution of agents over employment 25
status,wages,andassetholdingsnolongerchange. Inpartialequilibrium,theinterestrate andthewageofferdistributionarefixed,sotheresultinginvariantdistributioncharacterizes howmanyagentsholddifferentlevelsofassetsandacceptdifferentwagesinthelongrun. 4 Calibration The modelis calibrated to match moments correspondingto the United States economy duringtheyears2017-2019.11 Themodelperiodissetequaltoonemonth,andweassume that the per-period utility function is of the constant relative risk aversion class. We set 𝛾 the coefficient of relative risk aversion, , at 2.5, in line with the literature. Since in the data,therearelargedifferencesinemploymentoutcomesbyeducationlevels(aswellas differencesinsavingsbehavior), wemaptheex-anteskill levelinthemodeltoeducational attainmentinthedata. Wegroupworkersintothreecategoriesdefinedbytheireducation. Thefirstgroup(low-skill)consistsofindividualswithahighschooldiplomaorless. The second group (medium skill) includes those who have earned a bachelor’s degree or who have some college (e.g. an associate’s degree). The highest-skilled group, (labeled high skill), comprises individuals with a master’s degree, doctorate, or other forms of postgraduateeducation. Theannualnominalinterestratein2018wasabout4.4%,andtheyear-over-yearinflation rate was roughly 2.2%, so we set the real interest rate to 2.2% annually, which implies a 0.18% monthly.12. The employment separation rate 𝛿 is taken directly from SIPP data, asthelikelihoodoftransitioningfromemploymenttounemployment. Theemployment separationratesatthemonthlyfrequencyforthelow-skill,medium-skill,andhigh-skilled workers are 1.22%, 0.85%, and 0.469%, respectively. Finally, we set the probabilities of a mandatoryacceptanceofanoffertosmallnumbers: 1%forthelow-skillgroup,and3%for 11Thereasontocalibratethemodeleconomytotherecentpast(asopposedtocalibratingittotheearly eighties)isduetothequalityofthemicrodata. TheSIPPin2017—2019isofhigherqualitythanthatofthe earlyeighties. 12Specificallyas(1+0.022)1/12−1=0.0018 26
themiddleandhigh-skillgroups. Theremainingparametersarecalibratedsothatthemodelreplicatescertainfeaturesof 𝑏 theUSeconomyin2018. Tocalibratetheunemploymentbenefits asafunctionofduration, welookatdifferentstate-levelpolicies. Thesesetamaximumdurationofunemployment benefits. Abenefitthatexpiresafteranunemploymentdurationof4monthsappearsto beagoodapproximationtoactualunemploymentbenefitspolicies. Wethereforesetthe followingpolicy: 𝑏 𝑗 (𝑛) = 𝑏 𝑗 𝑖𝑓 𝑛 ≤ 4 𝑏 𝑗 (𝑛) = (4.1) 𝑏 𝑗 (𝑛) = 0 𝑖𝑓 𝑛 > 4 𝑏 To calibrate the baseline benefits 𝑗 we target the average unemployment payment relative to average earnings by skill level. In other words, 24%, 19%, and 15% for low, middle, and highskill respectively. Note thatin thedata the unemployment benefit can be zero if there is no take-up or if the unemployment spell is long enough and benefits have been exhausted. Therefore, in the data, during periods in which workers receive unemploymentbenefitsthereplacementrateislargerthanthecalibratedshares. 𝑓(𝑤) Theexogenouswageofferdistribution isassumedtobelog-normal,withnormal- 𝜎 izedmeaninlevelsequalto1(forthelow-skillgroup)andstandarddeviation 𝑗. Themean 𝜇 𝑗 forthemediumandhigh-skillgroupsarecalibratedsothattheaveragewagesforthese two groups relative to the average wage of the first group match the analogous relative averages in the data. The standard deviation was set to match Gini index of workers’ earnings by skill level: 0.39 (low-skill), 0.435 (medium-skill), and 0.423 (high-skill). The averageearningsoflow-skilledworkersisnormalizedto1. IntheSIPPdata,theaverage earningsofthetwohigher-skillgroupsrelativetothelow-skilledgroupare1.49(forthe middle-skill)and2.37(forthehigh-skill). 𝑎 𝛽 Tocalibratethedebtlimit andthediscountfactor wetargetmomentsintheSIPP data thatrelate to financialassets and debt. Because thepurpose of assetsin the modelis tosmoothunemploymentrisk,weconstrainthetypesofassetsweconsiderwhenmapping 27
the data and the model moments. In particular, instead of a measure of net worth that includesallpossibleassets(real estate,art,etc)andall possibledebt(mortgage, student loans, etc) we calculate a measureof liquid net worth that includes purely financial assets: checking and savings accounts, stocks, bonds, CDs, and vehicles.13 We consider credit 𝑎 cardandvehicledebtasourmeasureofdebt. Theskill-specificdebtlimit iscalibratedto 𝑗 matchtheratioofthemeanliquidnetworthofthoseindebt(thatis,themeanliquidnet worthforthosewithnegativeliquidnetworth). Theratioinourthree-yearSIPPpanelis -1.78,-1.44,and-1.15%forlow,middle,andhigh-skilledworkersrespectively. Thediscount 𝛽 factor 𝑗 issettomatchmeanliquidnetworthdividedbymeanearnings. Theseratiosin thedataare2.43,4.33,and6.00forlow-,middle-andhigh-skillworkers. Table10reports theparametersalongwiththemomentsinthedatausedtoestimatetheparameters’values. Parameter Definition Target TargetValue EarningsGini 0.390 EarningsGini 𝜎 byskilllevel 0.435 SIPP2017–2019 (low,mid,high) 0.423 Debtlimit -1.78 MeanNegativeNet 𝑎 byskilllevel -1.44 WorthtoEarnings (low,mid,high) -1.15 Discountrate 2.43 MeanNetWorth 𝛽 byskilllevel 4.33 tomeanearnings (low,mid,high) 6.00 UnemploymentBenefit 23.7% MeanUnemploymentBenefit 𝑏 byskilllevel 19.0% toMeanEarnings (low,mid,high) 15.0% MeanofWageOfferDistribution 1.00 AverageEarnings 𝜇 byskilllevel 1.49 (lowskillnormalizedto1) (low,mid,high) 2.37 Table 10: Calibrated parameters, their definitions, and corresponding target moments forthethreeskilllevels(low,medium,high). Thecalibratedparametervalues(includingthosecalibratedexternally)areshownon 13Includingvehiclesdoesnotchangemomentsbyalargeamount. Despitenotbeingafinancialasset, vehiclesarefairlyliquidastheycanbesoldinlittletime. 28
Table11. Parameter LowSkill MidSkill HighSkill 𝛾 2.500 2.500 2.500 𝜌 0.010 0.030 0.030 𝛿 0.012 0.008 0.005 𝑎 -2.323 -3.769 -5.065 𝛽 0.951 0.968 0.975 𝜎 1.295 1.204 1.639 𝑏 0.230 0.285 0.376 𝜇 -0.694 -1.079 -2.505 Table11: Calibrationparametersandtheir values. To obtainmoments from themodel wesimulate a large number ofagents (onemillion for eachskill level), largeenough sothat their choicesrepresent drawsfromthe model’s stationary distribution. Table 12 compares the targeted data moments with the values generatedbythemodel. Themodelfitisoverallsatisfactoryespeciallyinthetwosetsof wealth/debt-relatedmoments. Themodelslightlyoverestimatesthenegativeliquidnet worth to earnings ratio for the low skilled (-1.63 vs 1.78) but the same moment for the mediumandhighskilledworkersareontarget. Themodelalsofitswelltheoverallliquid net worth to earnings only slightly underestimating this ratio for the low and high skilled workers. Themodelslightlyoverestimatesitforthemediumskill. TheGiniearningsin the data for the medium skill is larger than in the model (0.44 vs. 0.38) but the model’s earningsinequalityfortheothertwoskillgroupsisroughlyequaltothedata’s. 29
Moment Data Model NegativeNetWorthtoEarnings(L) -1.78 -1.63 NegativeNetWorthtoEarnings(M) -1.44 -1.44 NegativeNetWorthtoEarnings(H) -1.15 -1.16 LiquidNetWorthtoEarnings(L) 2.43 2.33 LiquidNetWorthtoEarnings(M) 4.33 4.44 LiquidNetWorthtoEarnings(H) 6.00 5.94 ReplacementRatio(L) 23.7% 23.8% ReplacementRatio(M) 19.0% 19.0% ReplacementRatio(H) 15.0% 15.2% GiniEarnings(L) 0.39 0.42 GiniEarnings(M) 0.44 0.38 GiniEarnings(H) 0.42 0.41 AverageEarnings(L) 1.00 1.00 AverageEarnings(M) 1.49 1.50 AverageEarnings(H) 2.37 2.46 Table 12: Moments generated by the model and their counterparts in SIPP 2017—2019 data. The 𝐿 𝑀 𝐻 labels , ,and refertotheskilllevelofworkers. 5 Model Validation Weaimtovalidatethemodelbyassessinghowwellitreplicatesmomentsinthedatathat werenottargetedinthecalibration. Inparticular,weare interestedinthemodel’sability toreplicaterelationshipsbetweenunemployment,assets,andwagesattheindividuallevel that are in line with the SIPP data. We begin by judging the model in terms of the asset distribution(howlargeiswealthinequality)aswellastheunemploymentratesbyskill. 30
Thetargetsinthecalibrationareaveragesofasset-to-incomeratiosandearningsinequality, butnowealthinequality. Table13showssomemomentsofthewealthdistributioninthe data(firstrow)andthemodel(secondrow). Themomentsarehowmuchoftotalwealthis heldbydifferentwealthpercentiles(thetop5%,top20%,thetop50%andthebottom10%). Themodelcaptureswealthinequalitybutfallsabitshortattheverytop—intheSIPPdata, thetop5%hold75%ofthewealth,whileinthemodel,theyhold53%. Nonetheless,the modelalignswellwiththedataforthetop20%,50%,andbottom10%. Sinceourfocusis ondebt, thefact thatthemodel anddataare thatclosefor wealthheldbythe bottom10% (6.4%vs5.04%)isencouraging. Table13: SummaryofNetWorthPercentiles Bottom10% Top50% Top20% Top5% Data -6.44% 106.58% 96.29% 75.38% Model -5.04% 112.98% 96.90% 53.33% Oneofourmodel’smainingredientsisunemploymentrisk,andwewantittoreflectthe riskfacedbyUSworkers. Theseparationratesareexogenousandtakenfromthedata,but job-findingratesareendogenous. Asignificant modeloverpredictionofunemployment ratesmayindicatethatjob-findingratesaretoolowsothatunemploymentisnotthatcostly. Fortunately, the unemployment rates in the model are close to those in the data. This is particularlytrueforthemosteducatedworkers. TheunemploymentratesinourSIPPpanel andinthemodelaregiveninTable14. Theonlyunemploymentratethatdeviatesslightly is that oflower-skilled workers. The model delivers an unemploymentrate of 5.66%while inthedatais 4.05%. Fortheothertwogroupsofworkers,the unemploymentrateinthe modelisvirtuallythesameastheempiricalanaloginSIPP.Tocalculatetheaggregateor overallunemploymentrate,weusethesharesofthethreegroupsofworkersinSIPP,to calculatetheaggregaterateinthemodel. Thesesharesare36.5%,51.1%,and12.3%forthe low,medium,andhighskillgroups,respectively. Theaggregateunemploymentrateinthe 31
modelis3.6%,whileinthedatais3.1%. Table14: SummaryofUnemploymentRates Aggregate LowSkill MediumSkill HighSKill Data 3.01% 4.05% 2.72% 1.44% Model 3.64% 5.66% 2.72% 1.51% Tables 15–17 present the results of regressions examining the relationship between assetsordebtandeitherunemploymentdurationorthefirstwageafteranunemployment spell. In Section 2, we established that a household’s level of wealth is a significant predictorofunemploymentduration. Consistentwiththisfinding,Table15showsthat, in the model, wealth is positively associated with longer unemployment duration. In themodel,anincreaseinwealthequivalenttotheaveragewageofalow-skilledworker (normalized to 1), represents a 16% rise in wealth. This change extends unemployment durationbyapproximatelytwodays. Thus, theimpactofassetsondurationisrelatively small. Furthermore,conditionalonthesamelevelofwealth,moreeducatedworkers tend toexperience shorterperiodsofunemployment. Unemploymentis alessdesirablestate forhigher-skillworkersastheirearnings,relativetounemploymentbenefits,tendtobe higher. That makes their unemployment spells shorter. This feature and the associated negativecoefficientsformediumandhighskillsarecommontoallreportedmodel-based regressionswithunemploymentdurationasthedependentvariable. Figure 5showsgraphicallytherelationship between duration andwealth/debt. The horizontal axis has ten wealth bins and the vertical axis has the median unemployment duration. The different lines represent the three different skill levels. The figure shows that the relationship is steeper, the lower the skill. This is especially clear for the lowest skillgroup,for whomdurationrisesrapidlywithwealth(themedian durationrisesby5 monthswhenwealthrisesfromthefirstbintothefourthbin). Whiledurationalsorises 32
Table15: Regression: UnemploymentDurationonWealth Variable Intercept Wealth MediumSkill HighSkill Coefficient 4.853*** 0.044*** -1.858*** -2.266*** Std. Error (0.034) (0.001) (0.052) (0.064) R-squared 0.09 Note: ***,**,and*indicatesignificanceatthe1%,5%,and10%levels, respectively. fortheother twoskill groups,the patternisflatter, exceptperhapsforthe change between thefirstandthethirdbin. Figure 5: Median Unemployment Duration by Skill Level. The figure plots the median unemploymentduration(aswellasthe40thand60thpercentilesofduration)asafunction ofwealth(representedby10bins). Eachlinecorrespondstoadifferentskilllevel. Table 16 shows that household debt is negatively related to duration, with a large coefficient(-0.575),whichimpliesthatworkerswhostartanunemploymentspellwitha higherlevelofdebt,experienceshorterunemploymentspells. Anincreaseindebtequalto theaveragewageoftheunskilledreducesunemploymentdurationbyabouttwoweeks. Theeffectofdebtisquantitativelyimportant. 33
Table16: Regression: UnemploymentDurationonDebt Variable Intercept Debt MediumSkill HighSkill Coefficient 5.478*** -0.575*** -1.620*** -1.592*** Std. Error (0.038) (0.019) (0.052) (0.062) R-squared 0.09 Note: ***, **, and*indicatesignificanceatthe1%, 5%, and10%levels, respectively. Finally,Table17illustratestherelationshipbetweenthelevelofwealthatthestartofan unemploymentspell andtheinitialwage earneduponre-employment. According toour hypothesis,householdswithhigherlevelsofassetsshouldbeabletocontinuesearching for better job opportunities, leading to higher starting wages. The model’s simulations appeartosupportthisidea,showingthatgreaterinitialwealthisindeedassociatedwith higherinitial wages uponreturningto work. Quantitatively,an increaseinwealthequal to the average level of unskilled wages raises wages by 0.6%. As can be inferred from the positive coefficients for the two skill levels, being a medium or high-skill worker is associatedwithahigherpost-unemploymentwagethanbeingalow-skillworker. Table17: Regression: FirstEmploymentWageonWealth Variable Intercept StartingWealth MediumSkill HighSkill Coefficient -0.354*** 0.006*** 0.459*** 0.872*** Std. Error (0.0048 (0.00) (0.012) (0.015) R-squared 0.81 Note: ***,**,and*indicatesignificanceatthe1%,5%,and10%levels,respectively. Overall,we have establishedthatthe modelreplicatesbothtargeted andnon-targeted moments. In what follows, we conduct the main exercise of the study, comparing the model’ssteadystateoutcomesundertwodifferentinterestratelevels. 34
6 Results In this section, we conduct the study’s primary counterfactual exercise to explore the following question: How did the rise in household debt, driven by a decline in real interestrates,impactlabormarketdynamics? Toaddressthis,wecomparetwotheoretical economies—onewithalowinterestrateandanotherwitharelativelyhigherrate. Usingthe 2017–2019calibrationasabaseline,theexerciseadjustsonlytheinterestratewhilekeeping allotherstructuralparametersunchanged. Whilesomeparameters(e.g.,separationrates) havelikelyevolvedovertime,thegoalofthisanalysisistoisolatethemodel’spredictions for labor market dynamics when the real interest rate is the sole variable that changes. Wethencompareasetofkeyendogenousoutcomesbetweenthehigh-interest-rateand low-interest-rateeconomies. Theannualnominalinterestratein1982wasabout12%andtheyear-over-yearinflation rate was roughly 6%, so we set the 1982 real interest rate to 6% annually, which implies a 0.50% monthly rate. Recall that the baseline interest rate is 0.18% monthly, so the fall in real interest rates between 1982 and 2018 was roughly 32 basis points at the monthly frequency. We generate a long time series for each agent type by drawing one million compensationproposals from the wagedistribution. These drawsin combination with the consumption, savings, and reservation wage policy functions, generate a million draws from the model’s stationary distribution over assets, employment status, and accepted wages. Fromthesesimulations,anymomentrelatedtothemodel’sendogenousvariables canbereadilycomputed. Table18presentstheendogenousoutcomesfortwoeconomies: onewiththebaseline calibrationandanotheridenticaleconomywheretheonlydifferenceisahigherrealinterest rate. We refer to the first as the 2018 economy and the second as the 1982 economy to reflecttheobserveddeclineininterestratesbetweentheseyears. Accordingtoourmodel, thisdeclineininterestrateshasseveraleffects. Wefocusonsixendogenousequilibrium 35
outcomes: thewealth-to-earningsratio,thepercentofindebtedagents,thelaborshare,the skillpremium,andtheunemploymentrate. Table18: High(1982)vsLow(2018)RealInterestRateEconomies 𝑙𝑜𝑔(𝑤) Wealth-to- Percentin Labor Var Skill Unemp. Earnings Debt Share Premium Rate 1982 4.28 46.5% 61% 0.66 1.39 3.93% 2018 4.24 49.7% 55% 0.75 1.55 3.64% Note: Theskillpremiumisdefinedastheratioofaverageearningsofthemiddle-skill groupofworkerstotheaverageearningsofthelow-skillgroupofworkers. First,lowerinterestratesleadtohigherindebtednessandlowersavings. Inthemodel, theproportionofthoseindebt(negativeliquidnetworth)declinesfrom49.7%to46.5%, so slightly over 3 percentage points. The decline in assets is reflected in a decrease in the wealth-to-earnings ratio, which falls from 4.28 to 4.24. Notably, the drop in assets is evenmorepronouncedbecauseearningsalsodecline,from1.58to1.42. Asaresult,the reductioninagents’liquidwealthissubstantial. Toquantifytheimpactoflowerinterestratesonthelabor’sshare,wefollowatwo-step approach. First,wedefinethelaborshareastheratioofaveragewages(earnings)toaverage productivity. We estimate the economy’s average productivity in 1982 by multiplying the average earnings (1.58) by the observed labor share for that year (61%), yielding an averageproductivityof2.59. Next,assumingthislevelofproductivityremainsconstant from1982to2018,anearningslevelof1.42in2018impliesalaborshareofapproximately 55%. In other words, relative to productivity, the labor’s share of earnings declined by six percentage points over this period. This result aligns with estimates from the BLS, whichindicateadeclineofapproximatelysevenpercentagepointsoverthesameperiod, decreasingfrom63.6%to56.4%. The decline in asset levels and the increase in debt contributed to greater earnings 36
inequality. Themodelattributes thisrisein inequalityto the concavityof thereservation wage function. At lower asset levels, the reservation wage declines rapidly, leading to greaterdispersioninearningsasmoreworkersaccumulatefewerassetsorfallintodebt. Accordingtothemodel,thevarianceoflogearningsincreasedfrom0.66in1982to0.75in 2018,reflectingthisgrowing inequality. Thisresultisconsistentwithotherstudies, such as Heathcote et al. (2023), which find that individual earnings inequality has increased by approximately 9 log points on average for both men and women during this period. Otherauthors, suchas Lippiand Perri(2023)and Heathcoteet al.(2020), identifysimilar householdearningsdynamicsthathavecontributedtorisinginequality. We also calculate the skill premium, which, in line with the literature, is defined as theratio of average earnings ofcollegegraduates (mediumskill) tothose ofhigh school graduates (low skill). Using this measure, the model estimates a skill premium of 1.39 in 1982. As interest rates rise, the skill premium increases to 1.55 in 2018. This result is consistentwithstudieslikeOhanianetal.(2023)andKruselletal.(2000),amongothers, whichalsofindthattheskillpremiumhasincreasedfollowingsimilarpatterns. In the model, the rise in the skill premium follows a similar pattern to the overall increase in earnings inequality. Since low-skill workers have fewer assets, a decline in interestratesreduces theiraverageearnings moresignificantlydueto theconcavityofthe reservation wage function. The decline in labor’s share, along with the rise in earnings inequalityandtheskillpremium,suggeststhatthesetrendsmaynotbedrivensolelyby technologicalfactors. Instead,the modelinterprets theseshifts aslabor market responses to changes in household balance sheets. As noted in the introduction, this perspective presents an unexplored explanation within the extensive literature on these long-term trends. Finally,theunemploymentratedeclines,thoughtheeffectisrelativelysmall. Themodel predicts a decrease of 0.3 percentage points, from 3.93% to 3.64%, driven by lower asset accumulation and shorter unemployment duration. Since the model does not account for 37
business cycles, we compare this unemployment rate to the noncyclical unemployment rateestimatedbytheU.S.CongressionalBudgetOffice,whichdecreasedbyapproximately 1.6percentagepointsoverthesameperiod. 7 Conclusions ThisstudyoffersanovelexplanationforthedeclineintheU.S.laborshareandtheincrease inearningsinequalitybetween1982and2019,attributingittothefastriseinhousehold debt. Bylinkingincreasedhouseholddebt,andearningsandunemploymentdynamics, includingareductioninthelaborshare,thisresearchchallengestraditionalexplanations thatcenterontechnologicalorinstitutionalchanges. This conjecture is supported by several compelling arguments. First, it aligns with existing studies, such as those cited by Chaumont and Shi (2022), which indicate that individuals with higher wealthtend toengage inmore extensivejob searches and secure higher-paying positions. Second, it is consistent with the idea that financially stable unemployedworkerscanaffordtospendmoretimejobsearching,therebyincreasingtheir chancesoffindingbetter-payingopportunities. Third,thisexplanationchallengestheview thatcapitaldeepening istheprimarydriverofthelabor share’sdecline by highlighting thatmostempiricalstudies,asnotedbyLawrence(2015)suggestthatcapitalandlaborare grosscomplementsratherthansubstitutes. Thispaper’smodelsuggeststhattheriseinhouseholddebtcontributedtothedecline in labor’s share and the increase in earnings inequality. As household savings rates fell, real interest rates also declined—a trend inconsistent with a closed-economy assumption fortheU.S.duringthisperiod. Consequently,themodeltakesthedeclineininterestrates asgivenandexaminesitsimpactonlabormarketsthroughrisingpersonaldebt. Withimperfectunemploymentinsurance,workersengageinprecautionarysavingsto buffer against a potential job loss. As financial positions weakened and unemployment 38
becamelesssustainable,workersacceptedlowerwagestoexitunemployment. Thisreduced averageearningsrelativetoproductivity,loweringlabor’sshare. Earningsinequalityalso increasedduetotheconcavityofthereservationwagefunction: whenliquidnetworthis negative,acceptedwagesdropsharplybecauseunemploymentbecomesmorecostly. Giventheparsimonyofourmodelandthestraightforwardnatureofourmaincounterfactualexercise,weprimarilyinterpretourquantitativeresultsasanupperboundonthe predictedeffectsofdeclininginterestratesonlabormarketoutcomes. Aricherframework might yield results of a different magnitude. However, the qualitative conclusion remains robust: extended periods of low interest rates likely played a significant role in shaping labor market dynamics and earnings inequality, contributing meaningfully to the changes observedinthedata. Overall, this study offers a fresh perspective on the forces shaping U.S. labor share trendsandearningsinequality,highlightingthesignificantroleofrisinghouseholddebt. It provides empirical support for this hypothesis using data from two U.S. household surveys: theSurveyofIncomeandProgramParticipationfrom2017to2019andthe2019 SurveyofConsumerFinances. Additionally,thestudypresentsaparsimonioustheoretical frameworkthat,whileomittingcertainfactorsthatcouldinfluencethequantitativeresults, nonethelessintroducesamechanismthatplausiblyexplainsthedeclineinthelaborshare andproposesamodelcapableofcapturingtherelevantempiricalmoments. Incorporating furthercomplexityintothismechanismisthefocusofongoingandfutureresearch. 39
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Appendix A Literature Review Our work contributes to several interconnected areas of research, including the rise in earnings inequality, the dynamics between wealth and labor market behavior, the relationshipbetweeninterestratesandhouseholdborrowing,andthelong-termdeclinein labor’sshareofincome. Severaltheorieshavebeenproposedtoexplainthelong-termdeclineinlabor’sshare of income. Technological advancements, such as improved computers and automation, reducethecostofcapitalinvestmentandincentivizefirmstosubstitutelaborwithmachines. Karabarbounis andNeiman (2013) argue thatthe falling relative price of investment goods isaprimarydriveroflaborsharedecline,estimatinganaggregateelasticityofsubstitution greater than one. However, Lawrence (2015) challenge this conclusion, suggesting that substitutionbetweencapitalandlaborismorelimited. Thetransmissionofautomation effectsiscomplex;newtechnologycanbothdisplaceworkersandenhanceproductivity. GloverandShort(2020)andKohetal.(2020)analyzecapitaldeepeningasapotentialdriver, while Acemoglu and Restrepo (2020) highlight that robots uniquely displace workers from taskspreviouslyperformedbyhumans. Increasedtradeandforeigncompetitionhavealsobeencitedasfactors. Elsbyetal.(2013) findthatindustriesmostexposedtoimportcompetitionexperiencedthelargestdeclinesin laborshare. Similarly,AbdihandDanninger(2017)notethatsectorswithhighoffshoring potential show a weak but positive correlation with labor share shifts. Castro-Vincenzi and Kleinman (2020) document that industries reliant on intermediate inputs saw the mostsignificant laborshare declines. Alongside globalization,rising firm market poweris anotherpotentialculprit. DeLoeckeretal.(2020)provideevidencethataveragemarkups in the U.S. increased sharply after 1980, indicating a shift in income distribution from labortocapital. However,JaumandreuandDoraszelski(2019)andRaval(2023)question whether these markups truly explain labor share trends. Finally, deunionization has 43
weakenedworkerbargainingpower,reducingwagesrelativetoproductivity. Stansbury and Summers (2020) and Farber et al. (2018) link this to the decline in the union wage premium,whileBentolilaandSaint-Paul(2003)arguethatweakerunionslowerthelabor sharewhencapital-laborsubstitutionisinelastic. Holmesetal.(2012)furthersuggeststhat deunionizationmayaccelerateautomation,reinforcinglabor’sdecliningshareofincome. One leading explanation for the rise in earnings inequality since 1980 is skill-biased technologicalchange(SBTC).Ascomputerizationandautomationadvanced,thedemand forhighlyeducatedandtechnicallyskilledworkersgrewmorerapidlythanthedemand forless-skilledlabor. Thisshiftinlabordemandledtoawideningwagegapbetweenthese twogroups ofworkers(Katz andMurphy, 1992). Subsequentrefinements toSBTC theory highlightjobpolarization,wheremiddle-skilljobs(oftenroutineandeasilyautomated) declined, while high-skill and low-skill occupations expanded (Autor et al., 2008). This polarization pushed earnings at the top and bottom ends further apart, contributing to overallincomeinequality(AcemogluandAutor,2011). A second explanation focuses on institutional factors. The decline of labor unions, particularlyintheUnitedStates,reducedthebargainingpowerofworkersandcontributed to stagnant wages inmany middle-and low-wage occupations (Western andRosenfeld, 2011). Additionally, policy changes such as lower minimum wage relative to median wages andderegulationinvariousindustries haveplayeda partinwideningtheearnings distribution (Card and DiNardo, 2002). Globalization and increased trade also exposed lower-andmiddle-skilledjobstointernationalcompetition,whichrestrainedwagegrowth inthosesectorswhileenablinghigher-skilledworkerstobenefitfromexpandingglobal markets(FeenstraandHanson,1999). Lastly,agrowingbodyofresearchhighlightshowfallinginterestrateshavecontributed torisinghouseholdindebtedness,withvariousmechanismsandheterogeneitiesemphasized. Emiris and Koulischer (2023) develop a model of credit-constrained households andshowthat lowerinterestratesprimarily increaseborrowingamongwealthierandless 44
constrainedindividuals. EmpiricalevidencefromBelgiancreditregistrydataconfirmsthis, indicating that older households with existing housing wealth were most responsive to ratedeclines,witha1percentagepointdropininterestratesassociatedwitha7%increase inhouseholddebt. MartinsandVillanueva(2006)exploitaquasi-naturalexperimentin Portugaltoshowthatreformsreducingmortgageinterestsubsidiesledtoasignificantdrop inborrowing,confirming thathouseholdborrowingiselasticto interest rates, particularly amonglow-andmiddle-incomeborrowers. FusterandWillen(2017)focusontheU.S.housing market and find that reductions in mortgage payment sizes—due to lower adjustable interest rates—substantially decreased mortgage default risk, indicating that interest rates influencenotonlyborrowingbutalsorepaymentbehavior. Rannenberg(2023)presentsa macroeconomicmodellinkingrisingincomeinequalitytoadeclineinthenaturalinterest rate, which in turn fuels increased borrowing among non-rich households. This occurs as lowerrates reduce borrowingcosts and stimulatehousing demand, particularlyin the presence of collateral-based credit constraints. Finally, DeFusco et al. (2020) study the effects of macroprudential regulation targeting high-leverage mortgages and find that even modest regulatory costs significantly reduced borrowing volumes, underscoring the sensitivityofhouseholddebttointerestratesandlendingconditions. 45
Appendix B Alternative SCF Samples Table19: 2019vs2022SCFs. MeanNetworthbyselectedfamilycharacteristics(thousandsofUSD) Characteristic 2019 2022 All 865.7 1,063.7 IncomePercentile ≤20 131.3 129.7 20-39.9 159.1 218.7 40-59.9 252.6 385.4 60-79.9 489.2 436.8 80-79.9 995.5 1,264.7 90-79.9 5,595.8 6,629.6 Educationofreferenceperson Nohighschooldiploma 171.1 175.6 Highschooldiploma 310.1 413.3 SomeCollege 340.1 541.1 Collegedegree 1,572.2 2,003.4 Raceorethnicityofreferenceperson Whitenon-Hispanic 1,034.5 1,367.2 AfricanAmericannon-Hispanic 166.7 211.5 HispanicorLatino 240.4 227.5 Asian n.a. 1,826.9 Ageofreferenceperson(years) ≤35 88.5 183.5 35-44 507.5 549.6 45-54 966..5 975.8 55-64 1,363.8 1,566.9 65-74 1,409.5 1,794.6 ≥75 1,110.1 1,624.1 46
Table20: 2019SCFv.s. sample. Meannetworthbyselectedfamilycharacteristics(thousandsof USD) Characteristic Sample SCF All 821.7 865.7 (28.0) (18.0) IncomePercentile ≤20 85.3 131.3 20-39.9 64.0 159.1 40-59.9 139.4 252.6 60-79.9 302.8 489.2 80-89.9 685.4 995.5 90-100 4,569.7 5,595.8 Educationofreferenceperson Nohighschooldiploma 171.1 159.5 Highschooldiploma 310.1 353.1 SomeCollege 340.1 433.6 Collegedegree 1,572.2 1,758.4 Raceorethnicityofreferenceperson Whitenon-Hispanic 1,034.5 1,102.8 AfricanAmericannon-Hispanic 166.7 162.0 HispanicorLatino 240.4 222.8 Asian n.a. n.a. Ageofreferenceperson(years) ≤35 101.8 88.5 35-44 542.3 507.5 45-54 917.2 966.5 55-64 1,418.6 1,363.8 65-74 2,452.2 1,409.5 ≥75 2,368.2 1,110.1 47
Table21: 2019SCF.MeanNetworthbyselectedfamilycharacteristics(thousandsofUSD) Characteristic Work+MinWage Unmarried All 812.7 345.4 (28.0) (18.9) IncomePercentile ≤20 85.3 n.a. 20-39.9 64.0 n.a. 40-59.9 139.4 n.a. 60-79.9 302.8 n.a. 80-79.9 685.4 n.a. 90-79.9 4,569.7 n.a. Educationofreferenceperson Nohighschooldiploma 171.1 66.3 Highschooldiploma 310.1 177.7 SomeCollege 340.1 196.4 Collegedegree 1,572.2 731.6 Raceorethnicityofreferenceperson Whitenon-Hispanic 1,034.5 467.7 AfricanAmericannon-Hispanic 166.7 95.3 HispanicorLatino 240.4 129.1 Asian n.a. n.a. Ageofreferenceperson(years) ≤35 101.8 40.0 35-44 542.3 173.2 45-54 917.2 387.1 55-64 1,418.6 382.6 65-74 2,452.2 546.8 ≥75 2,368.2 682.0 48
Appendix C Evidence from SCF regressions Tables 22 and 23 below present regression results examining the relationship between wageincomeandbothnetworthandliquidnetworth,alongsidevariouscontrolvariables acrossdifferentsubsamples. Wedefineliquidnetworthasahousehold’stotalnetworth excludinganyhomeequity. Thetablesincludefivemodels,eachrepresentingadistinct subset of the data: All Data (Levels), Non-Negative Net Worth (Levels), Non-Negative Net Worth (Logs), Negative Net Worth (Levels), and Negative Net Worth (Logs). The numberof observationsvariesacrossmodels, withthe "AllData"model containing3,208 observations,whilemodelsrestrictedtonegativenetworthhavesignificantlyfewer. Each column reportsregression coefficients for the correspondingmodel, with standarderrors inparentheses. Statisticalsignificanceis denotedbyasterisks: *p<0.10,**p<0.05, and ***p<0.01. Networthgenerallyexhibitsapositiverelationshipwithwageincome. Asexpected, educationalattainmentplaysasignificantroleinwagedetermination,withindividuals whohavecompletedhighschool,somecollege,oracollegedegreeearningsubstantially higherwages. Thiseffectisparticularlypronouncedforthosewithacollegedegree,which isassociatedwiththehighestwagepremiumacrossallmodels. Theresultsalsohighlight disparities across race and gender. Black/African American and Hispanic individuals generally earn significantly lower wages than the reference group, reflecting persistent wagegaps. Likewise,femaleworkersearnconsiderablyless thantheirmalecounterparts acrossallmodels,reinforcingwell-documentedgenderwagedisparities. Finally,whileage ispositivelyassociatedwithwageincomeinsomecases,theeffectsizeremainsrelatively small. 49
Table22: WageIncomeonNetWorthplusControls Variable AllData Non-NegNW Non-NegNW NegativeNW NegativeNW (Levels) (Levels) (Logs) (Levels) (Logs) (Intercept) 3,396 12,652 9.289*** 49,733*** 10.489*** (7,543) (8,211) (0.098) (9,145) (0.204) NetWorth 0.006*** 0.006*** 0.173*** -0.029 0.032** (0.002) (0.002) (0.010) (0.022) (0.015) HighSchoolorGED 25,358*** 24,280*** 0.168*** 8,101 0.131 (3,608) (3,935) (0.033) (6,916) (0.107) SomeCollege 39,274*** 37,842*** 0.221*** 21,797*** 0.270*** (3,826) (4,090) (0.038) (6,285) (0.095) CollegeDegree 109,388*** 116,718*** 0.508*** 29,472*** 0.362*** (5,466) (5,956) (0.041) (6,487) (0.097) Black/AfricanAmerican -18,863*** -16,961*** 0.021 -7,357** -0.090** (4,114) (4,737) (0.022) (3,404) (0.041) Hispanic -13,780*** -14,425*** -0.056* 5,332 0.068 (3,692) (4,118) (0.031) (5,411) (0.066) OtherRace 37,709** 39,865** 0.124*** -10,288* -0.096 (11,890) (12,462) (0.039) (5,263) (0.073) Female -62,111*** -64,948*** -0.369*** -16,771*** -0.207*** (3,712) (4,293) (0.022) (2,842) (0.040) Age 1,542*** 1,377*** -0.0027** 96.21 0.0015 (168) (180) (0.0007) (140) (0.0021) Observations 3,208 2,918 2,918 288 288 Note: Asterisksindicatesignificancelevels: *p<0.10;**p<0.05;***p<0.01. 50
Table23: WageIncomeonLiquidNetWorth(NWL)pluscontrols Variable AllData Non-NegNWL Non-NegNWL NegativeNWL NegativeNWL (Levels) (Levels) (Logs) (Levels) (Logs) (Intercept) 1,474 10,283 9.355*** 38,259*** 10.713*** (7,389) (8,292) (0.078) (9,575) (0.122) NWL 0.006*** 0.006*** 0.171*** -0.0015 -0.020* (0.002) (0.002) (0.009) (0.017) (0.012) HighSchoolorGED 25,572*** 24,932*** 0.168*** 16,121** 0.174** (3,658) (4,328) (0.037) (5,847) (0.069) SomeCollege 39,665*** 39,316*** 0.216*** 28,823*** 0.319*** (3,869) (4,666) (0.046) (5,494) (0.064) CollegeDegree 110,808*** 120,908*** 0.501*** 43,902*** 0.452*** (5,416) (6,346) (0.045) (6,708) (0.071) Black/AfricanAmerican -19,329*** -18,281*** 0.011 -9,001** -0.127** (4,118) (4,778) (0.023) (4,751) (0.050) Hispanic -13,868*** -12,782*** -0.022 -7,104 -0.087 (3,719) (4,384) (0.031) (5,826) (0.070) OtherRace 38,598** 41,832** 0.161*** -10,753* -0.128 (12,079) (13,081) (0.037) (5,455) (0.071) Female -62,780*** -65,143*** -0.335*** -28,775*** -0.297*** (3,700) (4,403) (0.022) (3,607) (0.037) Age 1,597*** 1,434*** -0.0017** 499.46** 0.004 (161) (175) (0.0007) (183) (0.002) Observations 3,208 2,884 2,884 382 382 Note: Asterisksindicatesignificancelevels: *p<0.10;**p<0.05;***p<0.01. 51
Appendix D Evidence from SIPP regressions This section reports all the coefficients of the regressions estimated in Section 2. These regressionsrelateunemploymentdurationasthedependentvariableandassets,debt,and earningsdataasindependentvariables. Allthemodelsareoftheform: 𝑈𝑛𝑒𝑚𝑝𝐷𝑢𝑟 = 𝛼 +𝛽 𝐹𝐼𝑁 + 𝛾𝑋 0 , and where 𝑋 is a set of controls.14 The variable 𝐹𝐼𝑁 refers to a financial variable (e.g. unsecureddebttoincome,checkingaccounttoincome,etc). Whilethemodelstructureis thesame,weestimateseveralrelationshipsbetweenunemploymentdurationanddifferent 𝐹𝐼𝑁 variables. Tables 24and 25reportthe coefficients. Eachcolumnsshowscoefficients 𝐹𝐼𝑁 𝑈𝑆𝐸𝐶𝐷/𝑊 > whenthe variableischanged: 0isanindicatorvariablerepresenting positive levels of unsecured debt to income. We define analogous indicators for credit 𝐶𝐶𝐷/𝑊 > 𝑀𝐷/𝑊 > 𝑁𝑊/𝑊 > card debt, 0; for mortgage debt, 0; and net worth, 0. 𝐹𝐼𝑁 We also set to the values of the ratios themselves, not an indicator of whether the ratio is positive. In Table 25 we show results for having a positive balance in a checking 𝐶𝐻𝐸𝐶𝐾/𝑊 > 𝐶𝐻𝐸𝐶𝐾/𝑊 account 0 (and the ratio itself) or having a positive balance 𝑆𝐴𝑉/𝑊 𝑆𝐴𝑉/𝑊 in a saving account (and the ratio itself). The last column of Table 25 substitutes the log of the first wage after an unemployment spell. For that specification, 𝑋 𝑂𝐶𝐶 𝑂𝐶𝐶 the vector of controls also includes occupational dummies ( , , etc). These 2 3 dummiesrepresentbroadoccupationalgroupsthataccountforasubstantialamountof wagedifferences. 14Thecontrolsare: anindicatorvariablefornotbeingmarried(NotMarried),forreceivingunemployment benefits(𝑈𝐼 >0),forhavingacollegedegree(College),forbeingblack(Race),forbeingfemale(Female)and yeardummies(2019and2020). Inaddition,wecontrolforageandforthesquarefoage. 52
Table24: ModelSpecifications1-8 Specification (1) (2) (3) (4) (5) (6) (7) (8) Intercept 1.630* 1.511 1.486 1.422 1.477 1.474 1.449 1.412 𝑈𝑆𝐸𝐶𝐷/𝑊 > 0 -0.248* – – – – – – – 𝑈𝑆𝐸𝐶𝐷/𝑊 – -0.014** – – – – – – 𝐶𝐶𝐷/𝑊 > 0 – – -0.426*** – – – – – 𝐶𝐶𝐷/𝑊 – – – -0.089** – – – – 𝑀𝐷/𝑊 > 0 – – – – -0.392** – – – 𝑀𝐷/𝑊 – – – – – -0.005 – – 𝑁𝑊/𝑊 > 0 – – – – – – 0.211 – 𝑁𝑊/𝑊 – – – – – – – -0.005 NotMarried 0.519*** 0.526*** 0.476*** 0.506*** 0.458*** 0.502*** 0.430** 0.436** 𝑈𝐼 > 0 -1.289*** -1.353*** -1.254*** -1.324*** -1.250*** -1.296*** -1.418*** -1.429*** Year=2019 0.087 0.100 0.074 0.093 0.110 0.100 – – Year=2020 0.014 0.021 0.012 0.028 0.034 0.029 0.016 0.016 Female 0.049 0.059 0.036 0.043 0.050 0.059 -0.080 -0.067 Race 0.443** 0.457** 0.440** 0.429** 0.392** 0.408** 0.488* 0.458* Age 0.114** 0.115** 0.122** 0.119** 0.117** 0.116** 0.115 0.118 Age2 -0.001* -0.001* -0.001** -0.001** -0.001* -0.001* -0.001 -0.001 College -0.440*** -0.401*** -0.418*** -0.434*** -0.432** -0.462*** -0.326 -0.287 Observations 2,342 2,342 2,349 2,349 2,332 2,332 1,639 1,639 ResidualDF 2,332 2,332 2,339 2,339 2,322 2,322 1,630 1,630 AIC 12,593 12,591 12,625 12,626 12,545 12,550 8,707 8,706 Note: Asterisksindicatethelevelofsignificanceoftheparameters: *p<0.10;**p<0.05;***p<0.01. 53
Table25: ModelSpecifications9-13 Specification (9) (10) (11) (12) (13) Intercept 0.589 0.619 1.680 1.947 -10.186 𝐶𝐻𝐸𝐶𝐾/𝑊 > 0 0.047 – – – – 𝐶𝐻𝐸𝐶𝐾/𝑊 – -0.033 – – – 𝑆𝐴𝑉/𝑊 > 0 – – 0.173 – – 𝑆𝐴𝑉/𝑊 – – – -0.021 – log(First Wage) – – – – 2.831*** 𝑂𝐶𝐶 – – – – 2.811 2 𝑂𝐶𝐶 – – – – -1.303 3 𝑂𝐶𝐶 – – – – 0.689 5 𝑂𝐶𝐶 – – – – -1.186 6 𝑂𝐶𝐶 – – – – 12.421*** 7 𝑂𝐶𝐶 – – – – 2.501 9 Female 0.075 0.070 -0.077 -0.083 -2.696* Race 0.124 0.103 -0.165 -0.188 4.628* Age 0.149** 0.150** 0.088 0.080 0.300 Age2 -0.0016* -0.0016* -0.0010 -0.0009 -0.004 College -0.543*** -0.525*** -0.457** -0.420* -4.639*** 𝑈𝐼 > 0 -1.233*** -1.249*** -0.769** -0.790** -1.693 Not Married 0.585*** 0.597*** 0.373 0.373 -1.784 Year = 2019 0.116 0.131 – -4.791*** – Year = 2020 0.262 0.264 0.234 0.236 -1.348 Observations 1,338 1,338 694 694 32 Residual DF 1,327 1,327 684 684 15 AIC 7,142.5 7,141.2 3,519.7 3,519.2 150.88 Note: Asterisksindicatethelevelofsignificanceoftheparameters: *p<0.10;**p<0.05;***p<0.01. 54
Appendix E Household Debt Evolution Figure6: Housingvs. Non-housingDebt 55
Figure7: Non-housingDebtBalance 56
Cite this document
Mark Robinson, Pedro Silos, & and Diego Vilán (2025). Household Debt, the Labor Share, and Earnings Inequality (FEDS 2025-028). Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series. https://whenthefedspeaks.com/doc/feds_2025-028
@techreport{wtfs_feds_2025_028,
author = {Mark Robinson and Pedro Silos and and Diego Vilán},
title = {Household Debt, the Labor Share, and Earnings Inequality},
type = {Finance and Economics Discussion Series},
number = {2025-028},
institution = {Board of Governors of the Federal Reserve System},
year = {2025},
url = {https://whenthefedspeaks.com/doc/feds_2025-028},
abstract = {We show that the secular decline in real interest rates in the United States, which began in the early 1980s and persisted for nearly four decades, reduced the laborâs share of output and the unemployment rate, and increased earnings inequality. We establish this link using a model of frictional labor markets, estimated from household-level data, in which unemployment risk is only partially insurable. Rising debt resulting from lower interest rates reduces the value of unemployment, leading to lower equilibrium wages relative to productivity and a lower unemployment rate. Wage dispersion also rises. The model is consistent with panel-data reduced-form evidence linking unemployment duration, assets, debt, and post-unemployment wages. In the model, a decline in the real interest rate of the magnitude observed in the data generates a decline in the laborâs share of 6 percentage points and in the unemployment rate of 0.3 percentage points. The variance of log earnings rises from 0.66 to 0.75.},
}