Should Public Retirement Plans be Fully Funded? By Henning Bohn * University of California Santa Barbara. January Abstract

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1 Should Public Reiremen Plans be Fully Funded? By Henning Bohn * Universiy of California Sana Barbara January 011 Absrac Mos sae and local reiremen plans srive for full funding, a leas by acuarial sandards. Funding measured a marke values flucuaes and ofen falls shor. In a model where mos axpayers hold deb and face inermediaion coss, reurns on pension asses are less han axpayers coss of borrowing. Hence zero pension funding is opimal. Also, unfunded pension promises are properly discouned a a rae sricly greaer han he governmen s borrowing rae. Funding can sill be in axpayers ineress if legal enforcemen problems make unfunded pensions risky for employees, bu excep in special cases, he opimal funding raio is less han 100 percen. * Deparmen of Economics, UCSB, Sana Barbara, CA Phone: (805) bohn@econ.ucsb.edu. Home page: hp:// The paper was presened a he NBER conference on Reiremen Benefis for Sae and Local Employees: Impac on Budges, Public Deb and he Delivery of Services, Augus 010. I would like o hank Ken Smeers, he discussan, and he audience for valuable commens. The usual disclaimer applies.

2 Neiher a borrower nor a lender be (Shakespeare) 1. Inroducion Mos sae and local reiremen plans srive for full funding as measured by acuarial sandards. Funds are commonly invesed in risky asses. Hence acual funding raios he raios of asses o accrued benefi obligaions flucuae and are ofen less han 100%. Press repors abou underfunding naurally cause axpayer anxiey. Recen experience follows his paern. Though average funding raios were over 80% before he recen financial crisis, many sae and local pension funds are now seriously underfunded (Munnell e al. 008, 010). Concerns abou funding are reinforced by conroversies abou acuarial sandards. Some economiss have argued ha officially repored funding raios are inflaed because pension obligaions are compued a excessively high discoun raes (Novy-Marx and Rauh 009). This paper firs reviews hese issues broadly and hen examines he implicaions of an observaion seemingly ignored in he lieraure: Mos U.S. voers and axpayers are borrowers. (See Table 1 for evidence, discussed below). If borrowers incur posiive inermediaion coss or a leas if marginal inermediaion coss are increasing and posiive a sufficienly high deb levels here is a wedge beween he marke reurn on financial asses and he cos of borrowing. Posiive inermediaion coss have srong implicaions for public pension funding: Zero funding is opimal for axpayers who hold deb. The basic argumen is ha indebed axpayers are beer off if, insead of paying axes o fund public pensions ha earn he marke reurn, hey leave pensions unfunded, defer he axes unil pension payous are due, and use he funds o reduce heir deb, which accumulaes a a higher ineres rae. Because abou 75% of U.S. families are debors, his simple argumen suggess ha zero funding is opimal for a large majoriy of axpayers a srikingly negaive answer o his paper s ile quesion. To anicipae, he analysis will indeed show ha here is a srong case 1

3 agains full funding, and good case for zero funding as benchmark. The main challenge is o conver he simple argumen a he individual (debor) level ino a resul abou policy in general equilibrium. The wo main complicaions are (1) o explain why debors ineress should deermine public policy even hough on aggregae, here is as much lending as borrowing, and many debors also hold asses; and () o reconcile unfunded pensions wih he balanced-budge principle, which resrics public deb and seems popular wih voers. My model explains he coexisence of borrowing and lending in par by life-cycle consumpion smoohing, and in par by naional ax incenives. To capure life-cycle borrowing, he model considers a local communiy of aduls who live for hree periods young, middle, and old age. The young and middle-aged work, he old are reired. Young individuals borrow and middle-aged individuals are ne savers. A ax incenive arises because marginal (naional) income ax raes are generally higher in working age han in reiremen. This means reiremen savings have an afer-ax reurn sricly greaer han he marke reurn. Hence he middle-aged simulaneously borrow and hold reiremen asses, provided he ax incenives exceed he borrowing coss. In equilibrium, all ineresed axpayers hold deb. Noe ha he same ax incenive gives middle-aged axpayers an argumen agains public pension funding even if hey are no debors. They are beer off if, insead of using afer-ax income o fund public pensions, hey save more on a pre-ax basis and pay local axes laer, ou of less-axed reiremen income. Their incenives are aligned wih debors. To reconcile unfunded pensions wih resricions on public deb, he model makes wo assumpions. Firs, local axes are propery axes. Fuure propery axes are hen capialized ino house values, which dampens voer incenives o defer axes beyond heir lifeimes. Second, public deb is bounded because inermediaion coss increase on he margin, a leas a high levels of deb. Repeaed voing hen yields a finie equilibrium public deb. I show ha because curren voers (debors) have discoun raes greaer han he marke reurn, equilibrium deb is higher han he deb level ha would maximize house values. Resricions

4 on public deb are hen generally Pareo improving, can be susained as sequenial equilibrium in a voing game, and can be inerpreed broadly as balanced-budge resricions. In his seing, wih or wihou deb resricions, voing over pensions always yields zero funding as a unique oucome he oucome preferred by all voers over any oher funding level. In summary, he simple insigh ha borrowers prefer zero pension funding is valid in general equilibrium. The main model focuses on he case agains funding. This is no o deny ha here are argumens in favor of funding, which may explain why mos public reiremen plans have some funding. One imporan issue is legal ambiguiy, which makes unfunded promises poenially unenforceable. (Uninsurable defaul would have similar implicaions.) The argumen, which I presen in an exension, is ha if employees are risk averse and canno insure agains enforcemen problems, he employer mus pay a wage premium. A dedicaed reiremen fund ha provides credible collaeral hen allows employers o reduce oal compensaion. This creaes a radeoff beween axpayers inermediaion coss (he basic argumen) and reduced labor coss. The exended model yields parial funding near 100% if employees are highly risk-averse and highly dependen on he pension for heir reiremen consumpion. The analysis has implicaions for pension accouning and pension regulaions. Firs, he appropriae discoun rae for unfunded DB pensions is axpayers marginal coss of funds. If mos axpayers are borrowers, he appropriae discoun rae is a risk-adjused borrowing rae, which is higher han he safe ineres rae. Second, because funding is cosly and full funding is usually subopimal, regulaions ha impose full funding undermine employer incenives o offer DB plans. Mos privae employers phased ou heir DB plans afer cosly funding and insurance requiremens were imposed in he 1970s. If curren poliical anxieies abou public reiremen plans lead o excessive funding requiremens, he effecs may prove similarly desrucive. 3

5 The paper is organized as follows. Secion reviews pension funding in general. Secion 3 ses up an overlapping generaions model wih local propery axes o sudy pension funding. Secion 4 examines he impac of legal ambiguiies and defaul risk. Secion 5 commens on accouning implicaions. Secion 6 concludes. Proofs are in an appendix.. The Problem of Pension Funding This secion examines pension funding broadly, boh o review he lieraure and o inroduce key issues for he model. The focus is on U.S. sae and local governmen pensions and does no consider federal programs. To sar, one mus disinguish beween Defined Benefi (DB) and Defined Conribuion (DC) plans. Whereas DC plans promise only conribuions, DB plans promise a formula-deermined reiremen income in exchange for a reduced salary. Thus DB promises are a form of deferred compensaion and creae liabiliies for he employer. Funding means seing aside financial asses dedicaed o making promised paymens. Abou 80% of sae and local reiremen plans are DB plans (Munnell e al 008). The DB design raises several quesions: Wha is full funding, and does i ensure ha all promised paymens are covered? How does deferred compensaion relae o he principle of balanced budges, and does his principle impose a norm ha DB pensions should be fully funded? And wha are he coss and benefis of funding? 1.1. The Ambiguous Meaning of Full Funding There are a leas hree differen ways o inerpre full funding. I will call hem he accouning view, he finance view, and he populis view. The accouning view considers a reiremen plan fully funded if an acuarial measure of fund asses equals an acuarial measure of accrued liabiliies. Accouning rules for U.S. sae and local governmens are se by he Governmen Accouning Sandards Board (GASB). The key rule for pension accouning, GASB 5, gives plan sponsors a choice beween several 1 The paper does no address he cos and benefis of DB versus DC plans per se, excep wih regard o funding. Bohn (010) commens on DB versus DC more broadly. See Friedberg (010) for a review for labor marke issues. 4

6 differen acuarial mehods for pension obligaions (see Peng 009). A common approach is o use expeced reurns on asses o deermine he discoun rae on liabiliies. Measures of funding are he unfunded acuarial accrued liabiliy (UAAL), he gap beween liabiliies and asses, and he funding raio, which is he raio of asses over liabiliies. If a plan sponsor makes conribuions under GASB rules, asses should equal liabiliies on average, bu due o capial gains and losses, he funding raio will almos always differ from 100%. GASB rules specify ha any posiive or negaive UAAL mus be amorized over ime by raising or lowering new conribuions. The finance view also considers a pension fully funded if pension asses mach he presen value of promised pensions (e.g., Novy-Marx and Rauh 009). In conras o he accouning view, sae-coningen claims pricing is used o value obligaions, and economic raher han legal reasoning is used ascerain he scope of obligaions (Bulow 198). Because pension promises have srong legal proecions (see Brown and Wilcox 009; Peng 009), he defaul risk is widely considered negligible. Hence finance principles call for discouning a safe ineres raes, which are lower ha he discoun raes used by accounans. The resuling presen values are higher. So plans ha are well-funded by GASB sandards are ofen underfunded by finance sandards (Novy-Marx and Rauh 009). The analysis below will show ha inermediaion coss provide a raionale consisen wih sandard finance for discoun raes greaer han he safe ineres rae. By populis view, I mean he view refleced in newspaper sories ha porray any occurrence of underfunding as disurbing or scandalous. This view reas a pension plan as no fully funded unless pension asses cover all fuure obligaions in all saes of naure, even under adverse condiions, so ha here is no risk of a shorfall ha migh require employer conribuions. I may be emping for poliicians and regulaors o caer o negaive publiciy by imposing increasingly sringen valuaion sandards. However, a pursui of zero risk is probably fuile, and hreaens o reinforce he apparen mispercepion ha enough funding 5

7 migh somehow release he sponsor from is liabiliies. The analysis below will show ha funding requiremens generally reduce welfare... Balanced-Budge Rules and Deferred Compensaion Almos all sae and local governmens operae under balanced-budge rules. A separae capial budge allows for bond financing, usually subjec o voer approval, wih bonds repaid ou of operaing funds. Pension funds are commonly separae eniies, funded by conribuions from he operaing budge and dedicaed o paying reirees. Underfunded public pensions complicae his fiscal framework. A funding shorfall due o unexpecedly low invesmen reurns reduces governmen ne worh. A shorfall because of missed conribuions means ha he operaing budge undersaes employee compensaion. Hence mus one ask if he balanced-budge principle demands full funding, or oherwise consrains funding. The quesion is imporan because according o opinion polls, balanced budges are exremely popular. The lieraure on balanced budges unforunaely does no provide clear answers. A heoreical lieraure on naional deb has idenified poliical disorions ha end o favor excessive deb (see, e.g., Persson and Tabellini, 000; Alesina and Peroi, 1995). For example, uncerainy abou reelecion may shoren poliicians planning horizons and invie he use of deb as ool o consrain successor governmens. A fiscal rule imposing balanced budges is a naural correcive mechanism for such disorions. There may also be simple principal-agen explanaions of why voers like balanced budges. Voers mus monior poliicians who ac as heir agens. Credible informaion abou local budges is ofen unavailable or cosly. The poenial damages from poliical favoriism, corrupion, or oher monioring failures are much greaer if poliicians can incur deb han if expendiures are bounded by curren revenues. 3 For example, according o a Nov.009 CNN poll, 67% of U.S. voers agree ha he governmen should balance he budge even when he counry is in a recession and is a war. 3 Such informaion problems do no imply fiscal illusion he noion ha voers underesimae he long-run cos of deficifinanced expendiures. The issue here is risk reducion. An appropriae analogy is he quesion how much signaure auhoriy o give o an accounan conrol over curren accouns or also he power o borrow. 6

8 These argumens abou balanced budges do no direcly address public pensions and heir funding. One may argue by analogy ha he disorions ha favor excessive deb also favor borrowing hrough underfunded pensions. Then funding requiremens complemen a balanced-budge rule. If corrupion is a concern, however, funding rules ha place vas pools of financial asses under he conrol of poliicians may be quie dangerous. Monioring he performance of invesmen managers is difficul, especially if hey have auhoriy o inves in risky asses, so incompeence or fraud can be disguised as bad luck. Recurren scandals involving pay o play schemes sugges ha monioring is a problem. The problem would be eliminaed if public pensions were lef unfunded. The analysis below reas he populariy of balanced budges as a sylized fac ha economic heory should explain or a leas respec. The quesion how pension funding should be reaed wihin a balanced-budge framework is addressed as par of he analysis. Noe ha here is a lieraure on sae and local pensions wihou balanced budges. D Arcy e al. (1999) argue ha wih disorionary axes, opimal pension funding should be governed by ax smoohing argumens. They conclude ha a range of funding levels can be opimal, depending on he growh raes of axes and expendiures. Lucas and Zeldes (009) noe ha pension funding and invesmen sraegy would be irrelevan if Ricardian neuraliy applied; hey also examine ramificaions of ax smoohing. Bader and Gold (007) examine ax arbirage opporuniies in public pensions. The analysis here differs from his lieraure by acceping he populariy of balanced budges..3. Pension Reurns and Taxpayers Cos of Funds The financial siuaion of axpayers has received remarkably lile aenion in he pension lieraure. Because sae and local axpayers are he ulimae sponsors of public reiremen plans, heir opporuniy coss of funds should maer for deermining opimal funding levels. For axpayers, he decision how o fund heir governmen s public reiremen plan is fundamenally a choice o pay axes when pensions promises are made or o defer axes unil he promised pensions are due. 7

9 The implici assumpion in he lieraure seems o be ha axpayers are savers who have essenially he same invesmen opporuniies as he governmen (e.g., Lucas and Zeldes 009). Hence pension funding has zero opporuniy cos. For borrowers, however, paying axes o fund public pensions is cosly, because loan raes include charges for inermediaion coss he coss of screening, monioring, and oher adminisraive expenses. Hence loan raes are generally higher han he reurns available on invesmens. Table 1 documens he prevalence of deb among U.S. families. According o he Survey of Consumer Finances 007 (SCF), more han 80% of families wih heads of household under 65 hold deb. Reirees are somewha less indebed. Credi card deb is held by majoriies in he age brackes, insallmen deb by majoriies in he under-54 age brackes, and morgages by majoriies in he age brackes. Thus mos U.S. families hold deb, including he vas majoriy of working-age families. Table 1 also shows how ineres raes on popular ypes of loans compare wih Treasury raes. Spreads beween T-bills and credi card raes are abou 14%, spreads on car loans (he mos common insallmen loan) are abou 5%, and spreads on prime morgages are abou 1.7%. The inerpreaion is difficul because hese spreads include compensaion for defaul risk in addiion o inermediaion coss. A furher complicaion is ha if borrowers raionally move from low-cos o higher-cos loans as heir deb increases, average ineres spreads undersae he marginal coss of borrowing. In heory, a risk-adjusmen of invesmen reurns should yield he safe ineres rae as risk-adjused reurn, and a risk-adjusmen of loan raes should yield he safe ineres rae plus inermediaion coss. A useful benchmark is he spread beween he Prime rae and he T-bill rae, which is abou 3%. Because prime loans are graned only o he bes borrowers, he Prime spread is reasonable proxy for inermediaion coss. This suggess ha inermediaion coss are a significan opporuniy cos for borrowers. 4 4 Special consideraions apply for home morgages, because he ineres is ax-deducible for iemizers and i may reflec federal subsidies o housing lenders. Less han half of all morgage holders iemize, and many of hem hold oher debs, oo. Hence for mos homeowners, he marginal cos of funds exceeds he safe ineres rae. 8

10 Because mos families are in deb, he preferences of borrowers deserve aenion in hinking abou opimal public policy. A possible counerargumen is ha many borrowers also hold financial asses, noably reiremen savings. In addiion, one may wonder if a focus on borrowing is incomplee because aggregae ne worh is posiive which means borrowing is less han saving and because some borrowing is encouraged by ax incenives. To address hese complicaions, he nex secion presens a model ha includes deb subjec o inermediaion coss, reiremen saving, and saving incenives. 3. A Model of Local Governmen This secion examines a model of local public pensions. The model considers a communiy wih overlapping generaions of ax-paying residens/voers. The local governmen hires public employees o produce public services ha are financed by propery axes. Public deb and public pensions are capialized ino home prices, as in Apple and Schipper (1981). 5 To keep he model racable, I reduce he life cycle o hree periods and absrac from uncerainy Assumpions and a Benchmark Allocaion The communiy is populaed by overlapping generaions of individuals (aduls) who live for hree periods young, middle, and old age. Time is indexed by and cohors by age i (i=1,,3). The communiy has an exogenous number of residens ( N i ) in each cohor. The young supply one uni of labor and earn a wage w. The middle-aged supply e 1 unis of labor and earn ew. The old do no work and may receive ransfers TR from he naional i governmen. All individuals have preferences over consumpion ( c ), local public services ( g ), and housing. The wage w and he ineres rae r are consan and are deermined ouside he communiy. 6 Also assume perfec foresigh abou fuure governmen policy and no defauls on deb, so all opimizaion problems are deerminisic. 5 Home ownership is a convenien device o make voers care abou he communiy s long run fuure wihou having o model inergeneraional alruism. 6 I absrac from uncerainy only o simplify he exposiion. An earlier working paper (Bohn 010), which includes a sochasic model wih arbirary sae-coningen reurns, uncerain wages, and defaulable deb, shows ha he resuls here are 9

11 Assume he communiy has N houses ha can be owned by residens or by commercial owners. Owner-occupied houses provide a consumpion value v(g ) per period for he young and middle-aged, which on public services; assume v () is increasing and concave. Uiliy of individuals born in generaion is 1 h 1 U v(g )) u(c )) u(c 1 h 1 1 u(c 3 v(g ), (1) i where (0,1) capures ime preference, h [0,1] indicaes home ownership, and u() is increasing and sricly concave. (Ownership greaer han one is reaed as commercial.) Homeowners pay propery axes T. Commercial owners earn he value v(g ) as renal income per house, bu unlike residens, hey incur a managemen cos H 0. 7 So renal income is v(g ) T H. Assume N N 1 N (here are more houses han residenial buyers), so house prices are deermined by commercial owners. They capialize renal income a rae r, which yields a house price H 1 1r n 0 n. () v(g n ) T n H 1 Public services are produced by local governmen employees. Le producion wih L young and L middle-aged public employees be g G(L 1 /N,L /N), (3) where G is increasing, concave, and has consan reurns o scale. As simple benchmark, suppose he governmen pays non-deferred marke wages, balances is budge, and maximizes house prices. Then labor coss are wl 1 ewl and propery axes are T (wl 1 ewl )/N per house. Cos minimizaion requires G (l,1 l)/g 1 (l,1 l) e, which defines an opimal share of young workers l L 1 /(L 1 L ) and a uni cos T /g w l e(1l ) G(l,1l ) g. The opimaliy condiion v'(g ) g defines opimal public services g * (v') 1 ( g ) and opimal employmen L 1* implied house price is ln g* G(l,1l ) and L * (1l )N g* G(l,1l ). The also valid under uncerainy. In he sochasic version, a pricing kernel replaces he discoun facor 1/(1+r) and one mus ake expecaions over saes of naure; he economic argumens and he resuls are compleely analogous. 7 The assumpion of managemen is needed o ensure ha all residens will buy a house. 10

12 H * 1 n 0 1r n [v(g * ) g g * (1r) H ] r [v(g * ) g g * H ]. (4) Assume H v(g * ) g g * o ensure a posiive house price. A key assumpion is ha borrowers mus incur inermediaion coss, for example, screening and monioring coss. Inermediaion coss may differ by ype and amoun of deb, and here may be ax benefis for home morgages. To express he menu of borrowing choices parsimoniously, assume borrowers rank alernaive sources of deb by ne borrowing coss, which means inermediaion coss minus ax benefis. Le i d (d) denoe he resuling schedule of marginal coss, le i d (d) 1 d d i d (x) xdx be he average cos of deb d, and le 0 1 r d i (d) (1 r)(1 d i (d)) be he promised repaymen in period +1. Assume borrowing coss depend a mos on age and on homeownership ( h i H ), and assume: Assumpion 1: Marginal inermediaion coss d i are sricly increasing and coninuous i wih d as d and i d (h i H) 0. For homeowners, his allows i d (0) 0, which means inermediaion would be negaive up o d i ( i d ) 1 (0) h i H. The essence of Assumpion 1 is herefore ha marginal coss exceed ax benefis as he loan-o-value raio approaches 100%, and ha oher deb is cosly. The inermediaion coss have o be sufficienly srong o ouweigh he federal ax subsidy. Define ( i d ) 1 (x) 0 for all x i d (0), so ( i d ) 1 and d i ( i d ) 1 (0) are always defined. I will refer o deb d i d i as cosly deb. Income axes are a key moivaion for saving in reiremen plans. To model axes, assume he naional governmen axes income a consan raes i ha are age-specific. The moivaion is ha U.S. income axes are progressive and he age-earnings profile peaks in middle age, which means marginal ax raes end o peak in middle age. Age-specific ax raes are a simple way o capure hese sylized facs (wihou modeling progressiviy). Assume specifically: Assumpion : Taxes peak in middle age: 3 0 and

13 This means ax raes are highes in middle age, sricly posiive in working-age, and sricly less in reiremen han during peak earnings years. Income axes apply o wage income minus pension conribuions, o reurns on regular (axable) invesmens, and o pension payous. Wih income axes, employers have an incenive o offer reiremen plans. 8 In his deerminisic seing, asses in DB and DC plans earn a marke reurn equal o r. The only difference is ha DB plans give employers a choice of funding, whereas DC plans are always funded. Assuming employers compee for workers, all ax savings accrue o workers, and employer conribuions reduce cash wages one-for-one. If privae employers cos of capial is r, hey have no reason o defer funding. Hence one may assume ha privae employers offer DC plans and le employees make (and choose) he conribuions. The afer-ax reurn on reiremen saving a age i can be wrien as R i,i1 i 1 1 (1 r) 1. 1 i This is because one uni of afer-ax income a age i requires 1/(1 i ) unis of pre-ax income ha can be saved insead; he saving earns ineres r; and he accumulaed asses are axed a rae i1. 9 Assumpion 1 implies R 3 r and R 1 r, so reiremen conribuions are encouraged in middle age and discouraged in young age. Individuals mus hen accoun separaely for axable savings, pension savings, and deb. Le x i 0 denoe DC reiremen conribuions (for i=1,) and le X 1 (1 r) x x (1 r) (5) 1 i denoe reiremen income (pre-ax). Le a 0 denoe axable asses a he end of a period, and le d i 0 denoe deb. The individual budge equaions are: c 1 h 1 (H T ) (w x 1 )(1 1 ) d 1 a 1, (6) which says he young finance consumpion, home purchases, and propery axes from aferax wages and ne borrowing; 8 Individual IRA accouns deliver similar ax benefis as reiremen plans and can be subsumed here under DC plans. I is beyond he scope of his paper o explain why Congress has enaced laws ha in effec subsidize pension savings. My focus is on he implicaions. 9 This simple argumen ignores resricions on early wihdrawal. This is no a limiaion here because in his model, he middle aged will make posiive conribuions. 1

14 c 1 h 1 T 1 (h 1 h 1 )H 1 (ew x 1 )(1 ) d 1 a 1 [1 r(1 )]a 1 (1 r)(1 (d 1 ))d (7) 1 so he middle aged finance consumpion, propery axes, and changes in home ownership from afer-ax wages and changes in ne borrowings; and 3 c (1 3 )X TR h 1 H (1 r)(1 (d 1 ))d 1 [1 r(1 3 )]a 1. (8) which means he old consume heir reiremen income and housing wealh minus ne deb. In general, he individual problem of maximizing uiliy by choice of asses (a 1,a 1 ), deb (d 1,d 1), reiremen conribuions ( x 1, x 1 ) and home ownership ( h 1,h 1 ) involves a muliude of Kuhn-Tucker consrains ha may or may no bind, reflecing a range of possibly opimal borrowing and saving sraegies. To avoid disracing case disincions, assume all residens buy homes, he young wan o consume more han hey earn, and a home price is no enough o finance reiremen. Tha is: Assumpion 3: Model parameers are such ha individuals opimally choose h 1 h 1 c 1 3 w, and c H TR. Inuiively, home ownership is opimal if H is sufficienly high. Borrowing in young age is opimal if is sufficienly low and saving for reiremen is opimal if house prices and ransfers are no oo high. 10 These assumpions suffice o characerize he marginal raes of subsiuion beween periods. Define MRS 1 u'( ˆ c 1 ) u'( c ˆ 1 ) and MRS 1 3 u'( c ˆ 1 ) 3 u'(c ) 1, where c ˆ i c i v(g ). Then one obains (see appendix for all proofs): Proposiion 1: Under Assumpions 1-3: (a) The young incur cosly deb, d 1* d, and hey do no save ( x 1* a 1* 0). (b) The middle cohor makes reiremen conribuions x * Parameers ha saisfy Assumpion 3 exis. For example, suppose w=1, ew=1.5, he ineres rae is % annually for a 0- year generaional period, and =1/(1+r). Assume H is 5 imes annual wages, propery axes are 1% annually, so H=0.5 and T=0.05 per 0 year period. Assume v(g)=0., which is consisen wih H=0.5 for H =6.8%. Assuming axes and borrowing cos are approximaely zero, one finds ha home ownership is opimal and c 1 c c Assumpion 3 is saisfied because w=1 and H+TR=0.7 are less han consumpion. 13

15 (c) Boh cohors have marginal raes of subsiuion greaer han he marke ineres rae: MRS 1 (1 d (d 1 ))(1 r) 1 r and MRS 3 1 (1 r)(1 R 3 ) 1 r (9) (d) The middle cohor borrows d * 1 ( d ) 1 (R 3 ) and has no axable saving ( a * 1 0). The key poin of Proposiion 1 is ha boh cohors have marginal raes of subsiuion sricly greaer han 1 r. This provides a seing for local governmen policy where young and middle-aged voers have srong incenives o defer propery axes. Assume voing over policy akes place every period afer he housing marke clears. The old are hen indifferen abou propery axes and can be assumed o absain. Hence in his model, all voers wih an ineres in public policy are borrowers. In he following, o avoid reieraing ha he old are indifferen, le voers refer o hose who are no indifferen, i.e., usually he young and middle aged. Several model properies are worh noing. Firs, one can show ha wihou Assumpion 3, MRS 3 (1 r)(1 R 3 ) always holds, so R 3 r alone would be sufficien for MRS 3 1 r. Second, d * 1 0 holds if and only if d (0) R 3. To avoid case disincions, assume d (0) R 3 in he following, so he middle-aged hold non-zero deb. (From Table 1, his is he empirically relevan case.) Then MRS 3 1 (1 (d * 1 ))(1 r), so he Euler equaions for young and middle cohors can be wrien generically as MRS (1 d (d))(1 r). Third, if he naional ax sysem were changed o eliminae borrowing incenives in middle age (e.g., if 1 3 0), middle-age voers would become indifferen abou ax paymens ha are invesed in he marke. However, young voers discoun raes would sill exceed he marke rae r, and heir incenives o defer axes would no encouner opposiion. Hence all ineress voers would sill be borrowers. Fourh, he model implies ha he young should no conribue o pensions. Many young families in he U.S. indeed conribue almos nohing, which is someimes considered puzzling. According o SCF, 58% of families under 35 have no reiremen accouns a all. Hence zero conribuions are a useful benchmark. Finally, noe ha despie all he borrowing, aggregae 14

16 ne wealh in his communiy can be posiive, namely if reiremen asses plus housing wealh exceed he debs. The model is silen abou financial flows wihin a period. Since every reiree has incenives o ake a reverse morgage, one may inerpre his model as an economy where everyone holds deb from early adulhood unil he day of deah. This suggess ha if one subdivided he life cycle ino more han hree periods, reirees would have voing ineress like he middle-aged in his model and be indifferen only in heir final period of life. For inerpreing empirical daa, risk and he disincion beween risk premiums and inermediaion coss are imporan. Noe herefore ha he analysis here generalizes sraighforwardly o a sochasic seing wih risky asse reurns and defaulable deb. If he exogenous ineres rae r is replaced by an exogenous pricing kernel for sae-coningen claims, marginal raes of subsiuion differ from he pricing kernel by he same facors 1 d (d 1* ) and 1 (d * 1 ) 1 R 3 as in he deerminisic model (see Bohn 010). Because he economic forces here borrowing coss and ax incenives are no sochasic, absracing from uncerainy is wihou loss of generaliy. As rough calibraion of ax incenives, suppose ax raes for he middle-aged decline from 30% o 3 15% over a period of abou 0 years. Then (1 )/(1 3 ) 0.85/.70 (1 0.98%) 0, so R 3 provides an exra reurn of abou 1% annually. Recall from he discussion of ineres raes (Sec..3, Table 1) ha inermediaion coss on consumer deb are abou 3% (using he Prime rae spread as proxy). This suggess ha reiremen savers hold only deb wih relaively low inermediaion coss (e.g. morgages). I also suggess ha he marginal rae of subsiuion of he young is greaer han and furher away from he marke reurn han he marginal rae of subsiuion of he middle-aged. Nex consider voing. 3.. Voing over Policy: Inuiion Every period, he local governmen mus make several operaional and financing decisions. The operaional choices are abou public services ( g ), number of young and middle-aged 15

17 employees (L 1,L ), and abou heir compensaion plan (DB or DC). The financing decisions are abou public deb and he funding of pension promises. A simple marginal argumen provides useful inuiion o guide he analysis. Voers care abou policy because heir uiliy depends on propery axes, public services, and he house value when hey are old. Consider he presen value of hese iems discouned using he voer s own marginal rae of subsiuion. For middle-aged voers, his means V (v( g ) T ) 1 3 H MRS 1, because period- middle-aged value period- axes and public services, and hey sell heir house in period +1. The young value axes and public services in periods and +1, and hey sell heir house in period +, so V1 (v( g ) T ) 1 1 (v(g MRS 1 ) T 1 ) 1 3 H MRS 1. Using () and (9), hese values can be wrien as V 1 (v(g T ) n ) v(g n ) T n H and V 1 1 (v(g ) T ) 1 d (d * ) 1 1r n 1 1 d (d 1* ) (10) v(g 1 )T 1 1 (1r) (1 d (d 1* ))(1 d (d * 1 )) n 1 1r n (11) v(g n ) T n H I is sraighforward o show ha for each cohor, marginal changes in axes and services have an impac on voer uiliy ha is proporional o he impac on V i. 11 Hence (10) and (11) reveal how voers rade off curren versus fuure axes. Several insighs follow. Firs, boh cohors have effecively infinie planning horizons. This because fuure policy is capialized ino home prices. Second, voers discoun fuure axes by more han he marke discoun facor 1/(1 r). The exra discouning reflecs voers inermediaion coss. Hence inermediaion coss provide incenives o defer axes. Third, discoun raes are higher during each voer s own lifeime han hereafer. Hence a 11 For example, consider uiliy (1) for he middle-aged in period (which is U 1 ), inser (7) and (8) and h 1 h 1. Taking he oal differenials of U 1 and of V wih respec o ( g,t,h 1 ) one finds du 1 u'( c 1 )(v'dg 1 dt 1 ) u'(c )dh 1 c 1 ) v'dg 1 dt 1 u'(c ) u'( u'( c 1 )dv so changes in V are proporional o changes in uiliy. dh u'( c 1 ) 1 16

18 governmen conrolled by successive cohors has ime-inconsisen preferences. Curren voers, realizing ha he price of heir house reflecs fuure axes discouned a r, would like fuure voers o discoun axes a his rae. This gives hem a moive o suppor fiscal rules ha consrain public deb Consrains on Local Policy For a full analysis of voer choices, one mus formalize he consrains. This secion derives he consrains on public pensions and on public deb. The governmen as employer mus offer workers a wage and pension package ha provides he same uiliy as a privae job. Le w 1 and w 1 denoe cash wages in DB a plan, and le x 1 w w 1 and x 1 ew 1 w 1 denoe he difference beween privae and governmen wages. In his deerminisic seing, DB pensions offer workers no special risksharing or oher advanages over DC plans. Hence public employees wih DB plan solve he same opimizaion problem as privae-secor employees, excep ha ( x 1,x 1) and X are deermined by he employer. Noe ha a fully-funded DB plan, which earns he marke reurn, mus saisfy he same budge equaion (5) as a DC plan. Because privae secor workers choose (x 1,x ) 1 opimally, a funded DB plan canno offer employees anyhing beer. Hence he opimal funded DB plan replicaes DC conribuions and benefis hey are equivalen. In his model, he only difference beween DB and DC is ha in a DB plan, funding is a choice. 1 The analysis of DB plans wih arbirary funding simplifies because x 1* 0. Hence one may assume wihou loss of generaliy ha young workers in DB plans receive w 1 w, he same wage as in privae employmen. 13 Governmen oulays for DB pension benefis ( B ) hen reflec promises made o middle age employees in he previous period, so B X L 1. 1 The model absracs from many imporan differences beween DB and DC (see Friedberg 010), bu his helps focus on he paper s main quesion, he choice of funding. 13 A formal proof ha opimal DB pensions pay w 1 w would be sraighforward bu lenghy, because one would have o define noaion for muli-period pension accruals. In pracice, legal resricions may force DB plan sponsors o include he young. While he paper is no se up o examine accrual mehods, he opimaliy of x 1* 0 suggess cauion in using accouning mehods (such as enry-age-normal) ha mechanically allocae projeced benefis over an enire career. 17

19 Le U (x,x 1 ) denoe he maximum worker uiliy under a DB plan ha pays w ew x and promises X 1. A DC plan provide U (x *,(1 r)x * ) U DC. Hence DB plans mus saisfy U (x,x 1 ) U DC. To separae voing from employmen ineress, assume hroughou ha voers do no work for he local governmen. Turning o public deb, i migh be emping o simplify he analysis by ignoring deb. Bu given he common inerpreaion of underfunding as form of deb, i would be unconvincing o rea pension funding as a choice wihou also considering deb. Hence he paper akes up he challenge o explain why raional voers may favor consrains on deb and unfunded pensions. This requires modeling municipal deb. To ensure a finie equilibrium, assume ha public deb is subjec o inermediaion coss ha increase on he margin. Le D (D) be he marginal cos (here excluding ax benefis) and le D (D) 1 D 0 D D (x) xdx be he average coss. The ax-deducion for municipal ineres is imporan enough o model separaely. If invesors in municipal deb have a marginal ax rae 0 and incur marginal coss D (D), he marginal uni of deb mus pay an ineres rae (1 r r)(1 D (D)) 1 o mach he reurn on axable invesmens. 14 (1rr )(1 D (D )) 1r Define he ne marginal inermediaion coss D(D) 1 (1 1r) r D (D) r 1r, so ha ( 1 r r )( 1 D (D)) (1 r)( 1 D ( D)) ; similarly define ne average cos by D (D) (1 r 1r) D (D) r 1r. Assume: Assumpion 4: The local governmen s inermediaion coss D he margin and coninuous, wih D (0) D, D ( D ) D (D) as D. are sricly increasing on D 0, and r 1r(1 ) for some The value D defines he deb where marginal inermediaion coss mach he ax benefi, so ne coss are zero: ( D ) (1 r D 1r) D ( D ) r 1r 0. Because D (D) D (D), average inermediaion coss are sricly less han he ax benefi for all D D ; by coninuiy, D (D) 0 holds for a range D-values greaer han D. In 14 The inerpreaion is ha municipal deb buyers are a special group of ouside invesors ha gains a ax advanage from holding municipal deb. Their ax rae may differ from local residens ax raes. 18

20 his range, he average ineres rae on municipal deb, (1 r r)(1 D (D)) 1, is less han r. Empirical daa showing municipal yields below Treasury yields are herefore consisen wih ne inermediaion coss ha are posiive on he margin. To accoun for pension funding, consider he reiremen fund as separae eniy from oher governmen operaions. Assume he governmen pays cash wages w 1 L 1 w L direcly o employees and conribues P o a pension fund. Given an iniial fund balance F 0, end-ofperiod fund asses are F F * 0 P B, and F 1 (1 r)f. In he regular budge, propery axes on N homes pay for cash wages and for pension conribuions. Given iniial deb 0 D, end-of-period deb is D D 0 w 1 L 1 w L P N T, 0 and D 1 (1 r r)(1 D (D))D. Combining regular and pension budges, D F D 0 F 0 B w 1 L 1 w L N T. (1) Assuming invesors impose he ransversaliy condiion lim n F )/(1 r) n (D n 0, one obains an ineremporal budge consrain (IBC) 1 1r n 1 N T n 1r n W n D 0 B F 0 1 1r n D (D n )D n. (13) n 0 where W w 1 L 1 w L 1 n 0 1 r B propery axes are capialized, home prices are H 1 N 1 1r n n 0 1 N n 0 1 1r n n n 0 n 1 capures compensaion for period- labor. 15 Because v(g n ) W n H 1 D 0 0 N B F (14) r 1r (1 1r) r D (D n ) D n using (), (13) and r 1r (1 r 1r) D (D n ) D (D n ). Equaion (14) shows how house prices depend on governmen policy: The firs erm is he presen value of governmen services minus labor coss; he second erm shows ha iniial deb D 0 and unfunded pension promises B F 0 reduce H ; he hird erm shows ha he ax benefis of municipal deb and he average inermediaion coss are also capialized. 15 Raional invesors will also impose a naural deb limi, which is ha axes canno make house prices negaive. I assume public services are sufficienly valuable ha house prices are posiive for all policies considered in his secion. 19

21 Noe ha he ax benefis of municipal deb ne of inermediaion coss would be maximized if D n D n. A D, r 1r (1 1r) r D ( D ) 0, so he ax-deducibiliy of municipal ineres adds value o he house. (By comparison, deb exploi he ax benefis; deb D n D 3.4. Voing over Local Governmen Policy D n D would fail o would have marginal coss greaer han ax benefis.) Two voing scenarios are of ineres in his seing repeaed voing wih discreion, and voing consrained by fiscal rules. Firs consider discreionary voing, which means ha voers se curren policy variables and ake fuure policy as given. One finds: Proposiion : Under Assumpions 1-4, wih discreionary voing: (a) Voer references over pension funding F and over public deb D are single-peaked. (b) For all voers, F 0 maximizes uiliy, regardless of iniial condiions. (c) For each voer (age i), he preferred deb D i equaes he marginal coss of public deb ne of ax benefis wih he marginal coss of he voer s own deb: D (D i ) (1 1r) r D (D i ) r 1r i d (d i* d ), (15) so D i ( D ) 1 i d (d i* d ). Proposiion confirms ha zero pension funding is opimal for all voers. Proposiion also shows ha axpayers wih personal debs have an incenives o voe for more public deb unil he marginal coss of public deb maches heir own borrowing coss. The equilibrium deb is D D 1 or D D, depending on he median voer s age. Noe ha boh exceed D. If he inermediaion coss D are small a firs, equilibrium deb may be exremely high. Moreover, voers and invesors mus anicipae ha D n D i D for all n, which reduces house prices relaive o D. Irrespecive of curren deb, if voers were able o conrol fuure deb, hey would like o se D n D for all n 1, i.e., hey would value a mechanism ha limi fuure deb. 0

22 Hence consider fiscal rules. To avoid edious case disincions, assume he middleaged are he majoriy ( N N 1 ), so he discreionary oucome is D D, and ha d (d * d ) d d periods (so 1 (d 1* ), so D D 1. Then wo quesions arise. Firs, if voers could enac a permanen deb limi D n D ˆ n ), would hey do so? Because any limi ˆ D for hemselves and for all fuure ˆ D D would hold wih equaliy, he opimal deb limi ( D ˆ * ) is found by maximizing voer uiliy wih respec o Dˆ. The firs order condiion can be wrien as Since 0 r(1r) 1r(1r) (1 r ) 1r D(D * ) r 1r D (D* ) r(1r) 1r(1r) d (d * d ). (16) 1, D ˆ * is sricly less han D, hough greaer han D. The oucome D D ˆ * yields higher uiliy for middle-aged voers han he discreionary equilibrium. 16 Second, how can deb limis be enforced? Game heory provides an answer: Proposiion 3: There is a range of deb limis [ D ˆ min, D ˆ max ], which includes D ˆ * so ha for any D ˆ [ D ˆ min, D ˆ max ], D n ˆ D n is a sequenial equilibrium in a repeaed voing game wih he following rigger sraegies: D D ˆ if D i D ˆ i, and D D oherwise. D ˆ ˆ D * Assuming an iniial middle-aged generaion can choose D ˆ [ D ˆ min, D ˆ max ], i chooses, and so he equilibrium deb is D D ˆ *. One can show ha young voers also suppor a range of deb limis, and ha his range includes D ˆ * provided 1 d (d 1* d ) and d (d * d ) are no oo far apar. Then D ˆ * is a Pareo improvemen over boh D 1 and D. Consiuional and procedural rules ha regulae voing on deb are empirically relevan. Mos U.S. saes and local governmen operae in a balanced-budge seing ha allows deb issues only for capial projecs. Noe ha if r(1r) 1r(1r) is small, he deb has ne marginal coss close o zero. Hence he predicion of he model is ha fiscal rules should allow public deb up o a level where he marginal coss roughly mach he ax benefis, bu no much more. One may suspec ha capial deb can be evaluaed easily by lenders and raings agencies and has low inermediaion coss, whereas unsecured or floaing deb ˆ D * 16 As proof, noe ha D ˆ D is a feasible deb limi bu no opimal. 1

23 would require exensive due diligence o avoid adverse selecion and monioring. Hence he model is broadly consisen wih U.S. fiscal rules. 17 Reurning o pension funding, he main conclusion is ha raional voers have reason o suppor balanced-budge-ype consrains on public deb. Imporanly, here is no parallel argumen ha would jusify consrains on pension funding. Zero pension funding is he unique preferred oucome for all voers in all periods. Hence i is proper for balanced-budge rules o be silen abou pension funding. A furher implicaion is ha if an ouside regulaor or naional governmen were o resric deb relaive o he discreionary oucome, voers should approve. Bu if a regulaor were o impose minimum funding requiremens on public pensions (say, F Fmin 0 ), such resricions would reduce uiliy for everyone. 18 The possibiliy ha pension reurns differ from he marke ineres rae is worh discussing. If pension reurns were less, e.g., because public pension funds are cosly o adminiser, voers aversion o funding would be srenghened. Conversely, if pensions funds earned reliably above-marke reurns, he effecive cos of funding would be reduced. Voers who have sufficienly grea expecaions abou acive fund managemen would favor funding. This may provide a behavioral explanaion why many public reiremen plans are funded. In summary, he main resul is ha zero pension funding is opimal for raional axpayers who face inermediaion coss on heir own deb. Such axpayers are also emped o incur high public deb, bu hey prefer o suppor fiscal rules ha limi deb. The model implies ha such rules should no apply o borrowing via unfunded pension promises hus invalidaing popular analogies beween deb and underfunded pensions. 17 To be precise, he game-heoreic inerpreaion of fiscal rules is ha voers abide by such rules (say, a balanced budge) because hey expec a violaion o rigger a sring of discreionary oucomes ha would yield low uiliy. Proposiion 3 formalizes his inuiion. Noe ha a swich o discreion for a finie number of periods would also susain a range of deb levels less han D, so Proposiion 3 could be generalized. 18 A curren issue is he regulaion of reiree healh benefis. They are radiionally unfunded as consisen wih opimal policy here bu GASB 43 has creaed srong accouning incenives o sar funding.

24 4. Legal Ambiguiy and Defaul Risk Legal ambiguiy and pension defauls deserve aenion here because hey provide raional moives for axpayers o fund pensions even when funding is cosly. The key issues are (1) uninsurable risk and () he role of pension asses as collaeral. Employees covered by a DB plan ypically rely on a single pension for a large share of reiremen consumpion. The risk of non-paymen is a concenraed risk ha is difficul o insure. To arac employees, he employer mus compensae for uninsurable risk by offering a wage premium. If pension asses can serve as collaeral, funding may reduce he wage premium, perhaps enough o ouweigh he inermediaion coss argumen. By legal ambiguiy I mean he possibiliy ha a plan sponsor can successfully dispue he scope or exisence of pension obligaions. If a plan sponsor finds a legal flaw or oherwise challenges a pension paymen, an insurer could raise he same objecions. Hence employees canno insure agains legal ambiguiy. Employees mus always worry how he cours migh rule, and his uncerainy is uninsurable. For example, consider a plan ha promises a fixed percenage of final salary, which is hen indexed o inflaion, as is common in DB plans. Final salary is an ambiguous erm when he srucure of compensaion is evolving. A singy definiion excluding all bonus-ype paymens would allow he employer o cu pensions by reducing base salaries and insead paying repeaed bonuses. Wih inflaion, freezing nominal salaries would work similarly. A generous definiion would invie aemps o manipulae he iming of paymens o show an abnormally high final salary a pracice known as pension spiking. Indexing clauses may also cause rouble, e.g., if simple formulas become so unreasonable over ime ha a cour may no enforce hem. To model legal ambiguiy or more broadly, enforcemen problems ha creae uninsured risk assume here are wo possible oucomes for he pension plans, indicaed by s 1 s 1 saes of naure (, ). In a sochasic seing, hey could be inerpreed as wo oucomes ha divide each oherwise idenical sae of naure. Wih probabiliy, he promised benefis 3

25 X 1 are dispued and he plan sponsor successfully refuses addiional conribuions. Then beneficiaries share he available funds, so acual paymens are X(s 1 ) min{x 1,F 0 1 /L }. Wih probabiliy 1, promised benefis are honored, so X(s 1 ) X 1. As a behavioral exension, le employees percepion of enforcemen problems be disinc from he employer s view and be denoed by e. For simpliciy, assume ha and e are exogenous; ha he local governmen is conrolled by middle-age voers; ha voers marginal uiliy is approximaely he same in s 1 s 1 saes (, ); and ha public employees have power uiliy wih relaive risk aversion. The governmen s objecive is hen (wrien loosely o avoid elaborae noaion) o maximize V in expeced value subjec o he governmen budge consrain and subjec o he employmen consrain ha (1 )U (x,x 1) U (x,min{x 1,F 0 1 /L }) U DC. (17) The inuiion is ha whenever F 0 1 /L X 1, sae s 1 riggers a discree loss of reiree consumpion as compared o c 31(s ), and hence an upward jump in marginal uiliy. To saisfy (17) wih his fricion, x mus be reduced by an amoun ha includes a risk premium. Tha is, he governmen mus pay wages and benefis wih higher expeced value han if hey could commi o paying benefis wih cerainy. Le u' u'(c 1 3 (s ))u'(c 3 1 (s )) be he percenage gap beween employees marginal uiliies u'(c 3 1 (s )) beween saes (, ). Wih power uiliy, s 1 s 1 u' can be expressed in erms of he funding raio f F 0 1 /( X 1L ) 0, and he pension dependence (1 3 )X 1 /c 3 1 (s ) 0, which is he raio pension income o oal reiremen consumpion: 1 0. u'( f,) 1 (1 f ) Noe ha u' is decreasing in f, so funding reduces risk, and ha boh u' and he derivaive (u')/f are increasing in for all f 1. The laer suggess ha funding maers mos for reirees who rely heavily on heir DB pensions. One finds: Proposiion 4: In a seing wih inermediaion coss and enforcemen problems, he opimal funding raio f depends on how d (d * ) compares o 1 1 e u'( f,) : 1 e 4