Naonal Publc Deb and Fscal Insurance n a Moneary Unon wh Ramsey Taxes Kenneh Klezer Deparmen of Economcs Unversy of Calforna Sana Cruz, CA 95064 July 2013 Absrac Opmal fscal polcy s suded n an nerdependen non-moneary global economy whou lump-sum axaon and wh nernaonally negraed fnancal markes. Publc deb s ssued by naonal governmens responsble for servcng her own deb and fnancng publc expendures by axng domesc labor ncome. The global economy can represen a moneary unon ha s a prospecve fscal unon. The exenson of Ramsey axaon o nerdependen economes llusraes how he poenal gans from fscal unfcaon n a moneary unon depend on resrcons on governmens ables o ssue conngen publc deb. One of he consequences of moneary unfcaon s he loss of unancpaed nflaon as a ool of fscal polcy. Ths s capured n he model by reducng governmen access o conngen markes. The paper begns wh he benchmark case n whch governmens can ssue sae conngen deb and hen consders he resrcon o shor maury non-conngen deb conracs followed by endogenous deb markes under asymmerc nformaon. One resul s ha opmal ax raes depend on curren accoun balances when publc deb markes are no complee. Under endogenously ncomplee conracs for publc deb, naonal governmen deb ends o rse over me oward a deb lm. The nroducon of a fscal nsurance scheme wh mperfec nformaon s analyzed usng hs case o show how such schemes affec deb dynamcs and welfare when governmens can only ssue convenonal deb. The consraned opmal fscal nsurance s characerzed.
1 1. Inroducon The Eurozone s curren dffcules wh publc ndebedness and deb susanably have creaed sgnfcan worres abou mananng he euro. The crss has gven rse o reconsderaon of he resrcons on publc deb and he role of fscal federalsm for he unon. The dynamcs of publc deb wh a common currency are he subjec of hs paper. The role of publc deb s analyzed n a nonmoneary model wh dsoronary axaon. The absence of lump-sum axes creaes a meanngful role for governmen deb n an economy subjec o uncerany. Alhough only real aspecs of fscal polcy are suded, he absence of money n he model does no mean ha comparsons of publc fnance wh ndependen naonal currences and wh a common currency canno be formed. These comparsons are only vald when all nomnal prces are perfecly flexble and nflaon jus affecs he value of nomnal publc deb. The source of uncerany s modeled as shocks o governmen expendures. The analyss sudes opmal axaon of labor ncome under resrcons on how governmens can share rsk wh credors. The economy s an nerdependen global economy wh free rade and fnancally negraed prvae secors. Comparson of he allocave effecs of consrans on he ably of governmens o ssue conngen deb porrays possble consequences of currency unfcaon for fscal polces and publc deb dynamcs. I also allows he consderaon of he role for fscal nsurance n a currency unon. The prmary focus of he analyss s on he mporance and consequences of he requremen ha naonal governmens bear responsbly for meeng he cos of domesc publc spendng and publc deb servcng by rasng domesc ax revenues. A subsanal leraure sudes he role of fscal polces and publc deb n moneary unon. Drecly relaed papers nclude Beesma and Jensen 2005 who sudy fscal nerdependence and sablzaon when publc goods ener household uly and axes are lump sum and Ferrero 2009 who analyzes opmal fscal and moneary rules for sablzaon n a moneary unon whou lump-sum axes. One focus has been he mporance of dosyncrac counry-specfc shocks on resource allocaon when governmens lose he capacy o use moneary polcy for sablzaon purposes. The role of fscal federalsm or fscal nsurance schemes has been consdered n hs conex. 1 Because hs paper sudes he economy wh separae naonal fscal polces n compeve equlbrum, ax dsorons gve rse o gans from fscal nsurance n he presence of uncerany. The prospecs ha one counry s governmen mgh force nflaonary ncreases for he enre unon o manan naonal solvency or o seek balous hrough hreas o prvae solvency s anoher mporan opc movaed by he euro. 2 The possbly of balous s no ncluded n he analyss of opmal fscal polces wh commmen here. The analyss of how deb behaves wh separae naonal budges usng convenonal publc deb nsrumens n a rsky economy s an npu o hnkng abou deb
2 managemen o avod sraegc fscal polces ha seek o ake advanage of me nconssen no-balou clauses or legslaed lms on deb o oupu raos. The man purpose of hs paper s o see how he leraure on dynamc Ramsey axaon can be used o dscuss he evoluon of deb and gans from fscal negraon. To hs purpose, polcy coordnaon s no a opc. Insead, he paper sudes he characerzaon of opmal fscal polces n nerdependen open economes whou fscal unfcaon and wh consrans ha hghlgh he consequences of adopng a common currency. For smplcy, labor s he only facor of producon n he model economy. I produces radable goods usng a lnear echnology, and lesure represens a nonradable good. The only ax s a proporonal ax on labor ncome mposed a he naonal level. Capal s lef ou because s ncluson would only complcae expressons whou addng anyhng o he dervaon of opmal capal ncome axaon n closed economes. The sarng pon for analyzng he role of publc deb wh opmal axaon for a moneary unon whou fscal unon s he case n whch governmens can ssue sae-conngen deb. Ths s a sraghforward exenson of he approach aken by Lucas and Sokey 1983. Bengno and De Paol 2010 derve opmal lnear axes wh sae-conngen deb for a small open economy. In hs mulple counry global economy verson, households and frms can rade freely across borders on complee markes n an unceran envronmen. Governmens can also rade n sae conngen secures. Equvalenly, hey can fnance prmary defcs and surpluses by ssung sae conngen one-perod deb. The suaon analyzed requres ha each governmen manan responsbly for fnancng he cos of s publc expendures hrough domesc axaon. A naonal governmen bears sole fnancal responsbly for servcng s publc deb. Thus, household wealh wll dffer across counres because publc expendure needs vary across counres. In he opmal ax equlbrum, he margnal excess burden of axaon s no equaed across counres. The poenal gans from fscal unfcaon are presen value effcency gans. A common fscal auhory would mpose a equal rae ax on labor n each counry n he model economy and would need o redsrbue fnancal wealh lump sum n an nal perod o realze Pareo gans. The benefs of fscal unfcaon do no arse from rsk sharng. In equlbrum, he dosyncrac rsk of random naonal expendures s shared across counres hrough household and governmen access o complee markes. Insead, he only gans for from fscal unfcaon n hs verson come from convergence of ax raes ha are already fully smoohed wh respec o dosyncrac naonal shocks o reduce he aggregae excess burden of axaon n presen value. The ably of each governmen o ssue conngen deb s hen resrced, bu households sll rade nernaonally on complee markes. Thus, curren accoun ransacons are carred ou n sae conngen
3 clams. The economy dffers from he closed represenave household economy wh unceran governmen expendures and he lmaon ha he governmen only ssues rsk-free real bonds suded by Ayagar, e al 2001 by allowng households n each counry rade wh one anoher and hold deb ssued by oher governmens. Taxes and he excess burden of dsoronary axaon are no smoohed across saes of naure when governmens can only ssue non-conngen publc deb. Smoohng akes place over me roughly as under Barro s 1979 ax smoohng hypohess. The dynamcs for naonal publc deb replcae he resuls of Ayagar, e al. When publc secor deb or cred s lmed only by solvency consrans for he governmen and households, hen he resrcon of publc deb o non-conngen deb mpars an downward drf o naonal publc deb whch converges o suffcen publc cred o elmnae he excess burden of axaon n he lm. Ayagar, e al show ha mposng gher lms on publc deb or cred removes he convergence resul, and publc deb need no converge a all. In he nerdependen global economy, households canno share he rsk of ax dsorons on lesure consumpon whch s no radable, alhough rsk sharng n raded goods s complee. The consran ha governmens can only ssue non-conngen deb reduces sharng of hs n radable goods as well. An exercse for consderng he effecs of moneary unfcaon mgh be he comparson of allocaons and welfare wh and whou sae conngen publc deb. Ths comparson s n he spr of Bohn s 1988, 1990 demonsraon ha unancpaed nflaon wh perfecly flexble prces and sngle perod deb can mplemen he sae conngen opmum. Wh separae currences, ndependen moneary polces and floang exchange raes, he sae conngen deb economy models he use of unancpaed nflaon for he sole purpose of renderng non-conngen nomnal publc deb no conngen real publc deb. In hs sory, he cos of adopng moneary unon whou changng anyhng on he fscal sde oher han denomnang publc deb n uns of he common currency s a reducon n he smoohng of he margnal excess ax burden over expendure flucuaons. The cos of requrng member counres o fnance her own publc expendures wh domesc ax revenues hen ncreases wh a currency unon. The nerpreaon of nflaon axaon as mplemenng sae conngen publc deb wh non-conngen nomnal deb ssues leads o volale nflaon as demonsraed by Char, Chrsano and Kehoe 1991. Wh rgd nomnal prces, nflaonary surprses are cosly. Su 2004 and Schm-Grohe and Urbe 2004 show ha prce sckness sgnfcanly reduces he opmal volaly of nflaon and amplude of flucuaons n real deb paymens. 3 A nermedae approach o he fully sae conngen deb model and he non-conngen deb model whou money and nomnal rgdes endogenzes marke ncompleeness by addng nformaon asymmeres. The modelng sraegy assumes each governmen has prvae nformaon abou why chooses he level of publc expendures does each perod. Bond holders do no
4 observe he margnal benefs for he governmen of publc expendures. In he consraned opmum, each governmen ssues sae conngen bu he requremen of ncenve compably consrans he amoun hey can ssue across saes of naure resrcng rsk sharng beween he governmen and s credors. The sharng of rsk n he margnal excess ax burden s ncomplee wh prvae governmen nformaon. Ths can sgnfcanly reduce he degree of varaon n deb paymens n he opmum whch ranslaes o less volale nflaon n he flexble prce moneary economy nerpreaon. Slee 2004 and Slee and Yelekn 2006 analyze he prvae governmen nformaon economy wh a represenave household n he closed economy under parcular household and governmen preferences. Ther approach s adaped o he nerdependen global economy model. In parcular, households connue o rade on complee asse markes nernaonally sharng radable goods consumpon rsk. Alhough naonal governmens have more nformaon abou he expendure shocks ha affec households n equlbrum, ncenve compably consrans he ably of governmens o rade on complee markes. Prvae nformaon of he governmen reduces s ably o share he rsk of ax ncreases and decreases. Ths generaes he asymmery ha households can use markes o an exen governmens canno. An mporan consequence of prvae nformaon s ha publc deb and he excess burden of axaon grow sochascally over me. 4 The assumpon ha a governmen has prvae nformaon ha deermnes publc expendures can be movaed by consderng a counry wh a large number of heerogenous households. Indvduals observe her margnal benef from publc goods bu no he benefs of ohers, or he governmen can have dsrbuonal objecves n he provson of publc goods ha vary. Oher nerpreaons can made n erms of polcal economy or fscal nsuons. Bond holders may be less nformed abou governmen spendng preferences for a counry wh less ransparen budge makng for example, wh more off-balance shee budgeng, more nfluence of prvae lobbes, or facng a more conenous polcal envronmen. Bond holders can face less cerany ha hey know how a governmen wll behave f a counry has hgh urnover of eleced leaders. Fscal nsurance schemes can address dosyncrac counry rsk across naonal governmens of nerdependen economes. A muual fscal nsurance scheme wh a zero balance a every dae can mprove welfare n he presence of dosyncrac naonal fscal shocks when governmens only ssue non-conngen publc deb. Whle dosyncrac expendure shocks can be pooled, aggregae rsk arsng from fscal polces can only be addressed usng sae conngen deb nsrumens. Any aggregae rsk would requre deeper fscal negraon n he sense ha a cenral fscal auhory would need o ssue deb or he use of unancpaed nflaon for purely fscal purposes. A welfare-mprovng fscal nsurance scheme mus
condon nergovernmenal ransfers on boh curren publc expendures and ousandng publc deb. The condonaly on ousandng publc deb arses from ncenve compably n he presence of prvae nformaon under commmen of he counres o poolng arrangemen. The analyss of opmal axaon and publc deb requres deb lms o be mposed on he governmen. Wh resrcons on conngen publc deb, lms are mposed and hese are reached wh posve probably n fne me. The las subsanve secon of he paper dscusses deb lms when governmens can defaul as soveregn debors. Deb lms need o be self-enforcng, and boh debors and credors can gan from allowng deb repaymen o vary wh governmen expendures when hese boundares are reached. In hs secon, he mplcaons of endogenous deb lms for fscal nsurance schemes s dscussed. The paper proceeds by descrbng he economy n Secon 2 and exendng he sae conngen publc deb model n Secon 3. The fourh secon dscusses he consequences of resrcng publc deb o be ssued n non-conngen bonds. Secon 5 consders he model wh prvae governmen nformaon. Secons 6 and 7 dscuss fscal nsurance schemes and endogenous deb lms, respecvely. The las secon concludes. 2. Fscal Polcy Envronmen The model economy s composed of N counres ha engage n free rade and do no mpose axes sraegcally o nfluence he erms of rade. Ths envronmen envsons an economc unon wh a common currency and separae naonal fscal polces. I s a non-moneary model, and he N counres compose a closed economy. Each counry s represened by a sngle household and a fscal auhory. There are wo goods, a radable good produced usng labor and nrnscally valued lesure. These can be nerpreed as aggregae radable and nonradable goods. Each governmen mus fnance a flow of publc expendure on raded goods usng lnear axes on labor ncome. Labor s he only facor of producon because he emphass here s on he role of naonal publc debs wh cooperave axaon. Inroducng capal would only layer sandard resuls on capal ncome axaon ono he model. The economy has an nfne horzon and s sochasc. The random varables are governmen expendures. In each counry =1,...,N, he preferences of he represenave household are represened by he uly funcon, β u c, 1, n U0 = E 0 =0 and oupu s produced usng he lnear echnology wh un producvy, y =. u c, l s assumed o n 5
6 srcly concave and wce connuously dfferenable for c>0 and 0 <l 1. The margnal ules sasfy lm c 0 u c c, l and lm l 0 u l c, l. The expecaon s aken wh respec o dae 0 nformaon. The household faces a budge deny gven by +1 a +1 +1 = a +1 p + 1 τ n c where s he sae of naure a dae wh fne suppor Θ.Each s a N dmensonal vecor. s he hsory of saes, 0,...,. Fnancal asses are gven by a a he begnnng perod n hsory and are denomnaed n uns of consumpon. The labor ncome ax, gven by he ax rae τ,slnearand can be sae conngen. p +1 s he relave prce of a un of he consumpon good delvered n sae +1 condonal on he hsory n erms of he good avalable n. Facor markes are compeve so ha he pos-ax reurn o labor equals 1 τ. The household also faces a convenonal solvency consran o close s budge over he nfne plannng horzon and has nal fnancal asses of a. 0 Ths framework allows for general sochasc processes for he N levels of governmen expendures, g. The exensons of he benchmark model wll resrc hese o be Markovan and use ndependen and dencal dsrbuons for exposon. For smplcy of exposon, I assume ha he suppor, Θ,s ndependen of me. The frs sep s o defne a compeve equlbrum for he economy. The allocaon s gven by he N-dmensonal consumpon and lesure choces of he N households a each dae n each. The Arrow-Debreu prces of he consumpon good n erms of he numerare good, consumpon a dae 0 n he predeermned sae 0, are denoed by q. The relave prces of lesure n erms of he numerare are q 1 τ. Thus, p +1 +1 q +1 = q. In a compeve equlbrum, he resource consran, N n c g 0, 1 =1 s sasfed for every for each dae. Fnancal marke equlbrum requres he sum of ne foregn asses N a b =0 across all counres be zero. Ths equlbrum condon s for every for each dae, whereb =1 s he ousandng sock of publc deb for governmen due a
me n. The household budge consran s gven by a 0 q c 1 τ n 2 =0 The fscal polces mus also be specfed. A fscal polcy s a conngen sequence of governmen expendures, axes and governmen deb for each of he N counres for each dae and hsory. The fscal polcy for governmen s defned by he sequence { g,τ,b } over all for each 0. A feasble fscal polcy for governmen mus sasfy a budge consran gven by b 0 =0 q τ n g, 3 { for equlbrum prces q }. Ths s derved by solvng he budge deny, +1 p +1 b +1 +1 = b τ n + g, forward and mposng he solvency consran gven by, lm q b. 1, and governmen expendures are The labor ncome rae s resrced o be no greaer han one, τ non-negave. In he benchmark case, each governmen can ssue sae-conngen deb n eher posve or negave amouns. In a compeve equlbrum, he publc secor budge consran gven by 3 holds for each governmen s fscal polcy a he equlbrum prces. In equlbrum, he allocaon s resource feasble sasfes condon 1, households maxmze her uly over her respecve budge consrans gven prces and labor ncome ax raes and frms maxmze profs a each dae and sae. The second sep s o deermne opmal fscal polcy. A socal planner solves he opmal ax problem gven resrcons on reallocang naonal budgeary responsbly. The man assumpon for hs paper s ha each governmen mus fnance he enrey of s publc expendures and nal publc deb oblgaons hrough axes mposed on domesc labor ncome as ndcaed by 3. A fscal polcy for he planner s defned o be a N-uple of polces { g,τ,b } for each =1,...,N. The planner s objecve s he sum of he ules of he represenave households for he N counres gven by N W c, ñ=e 0 λ β u c, 1 n =1 =0 where c and ñ represen he N-uples of he sae-conngen sequences of naonal consumpon and labor supples, { c } and { n }. The parameers, λ, are mulplers ha are endogenously deermned 7
n he opmum. Ther values depend upon he dsrbuon of household wealh a me 0 and are relaed o equlbrum margnal ules. Wh lump-sum axes, he λ are nversely proporonal o equlbrum margnal ules a me 0. In he opmal ax problem, he dsrbuon of ules across counres also depends on he socal cos of ax dsorons and he varaon n he presen value of governmen oblgaons across counres. The Ramsey problem for he planner s o choose a compeve equlbrum ha maxmzes s objecve wh respec o a fscal polcy gven nal fnancal asses, a 0 and b 0 for each =1,...,N. The planner assgns a fscal polcy { g,τ,b } o each naonal governmen =1,...,N akng accoun of he endogeney of equlbrum household consumpons, labor supples, savng plans and prces and of he requremen ha each governmen s budge consran 3 s sasfed a equlbrum prces. 3. Independen Fscal Polces wh Sae-Conngen Deb The benchmark case s an exenson of he Lucas and Sokey 1983 economy wh sae-conngen publc deb o an economy wh mulple governmens wh separae neremporal publc secor budge consrans. In hs model here are heerogeneous households of number N each consumng a dfferen nonradable good lesure and payng axes o a fscal auhory ha mus fnance naonal publc expendures. The purpose of hs secon s fnd ou how he separae fscal responsbles of governmens affec equlbrum and welfare wh sae-conngen deb. In subsequen secons, he ably of he governmens o ssue sae-conngen publc deb wll be consraned bu households wll sll be able o rade wh each oher on complee markes. I adap he prmal approach o solvng he opmal Ramsey ax problem whch uses he frs-order condons for he household opmum o elmnae he ax rae, τ, and relave prces, q, from he neremporal budge consran o form an mplemenably consran. In hs economy, however, he planner faces a separae budge consran for each naonal governmen. The household frs-order condon for he lesure-consumpon choce can be subsued whn each naonal budge consran, bu he relave prces of sae conngen consumpon, q, depend on he demands for radable goods by all consumers. The margnal raes of subsuon n sae conngen commodes are equal across borders under free rade. The mposon of hese frs-order condons wll appear as an addonal consran n he planner s problem. The mplemenably consrans are formed from he naonal budge consrans as E 0 q 1 u l =0 u c n g = b 0 for each =1,..., N. 4 8
The addonal mplemenaon consran s β u c u c 0 = q for each =1,...,N. 5 For hs case, n whch governmens access complee asse markes for deb ssues, subsung he sochasc dscoun facor for each counry s household usng 5 no ha counry s publc secor budge consran 4 does no maer for fndng he Ramsey soluon. Dong so allows he planner o mpose dfferenal axes on raded commodes, ha s, arffs, across counres. For governmens ha have access o complee markes for deb, dfferenal naonal commody axes are redundan o naonal labor ncome axes n he Ramsey opmum. The consrans are expressed separaely n he benchmark case o be used as publc fnance consrans are added. In addon o he budge consrans for each governmen, he planner needs o sasfy he lfeme budge consrans for all N households and he global resource consran 1 for each dae. The lfeme budge consran for household can be rewren as E 0 u q c l n = a 0. 6 u =0 c These consrans deermne he allocaon of goods consumpon across households gven he nal dsrbuon of ne foregn asses, f0 = a 0 b 0. For each possble choce of fscal polces, prvae consumpons, labor supples and oupus are deermned by households and frms n compeve equlbrum akng axes and deb ssuance as gven. To fnd an opmum for he planner, I need o nclude he budge consrans for each governmen and each household plus he frs-order condons goods marke equlbrum and he resource consrans. However, he necessary condons for he Ramsey fscal polces can be derved by maxmzng he planner s objecve over he consran se whou he household budge consran f he frs-order condons for compeve equlbrum n goods and labor markes are ncluded. When households rade on complee markes, he lfeme budge consrans are needed o deermne he allocaon of goods consumpon a dae 0, ha s, he endogenous welfare weghs, {λ }. To keep hngs hrfy, much of he analyss drops he household budge consran and akes he λ as gven. I hen use he complee markes for prvae rade o nerpre λ n erms of u c 0. The complee markes case requres fndng a soluon o N max E 0 λ β u c {c,n,q, 1 n } =1 =0 subjec o condons 4, 5 and 1 gven he allocaon of nal publc deb ousandng, { b0}.the necessary condons for an opmum nclude he frs-order condons wh respec o consumpon of 9
goods and of lesure n hsory, and λ u l + u c λ u c + u c u c 0 ϕ u l u c 0 u c ϕ u cl u c u l u u c n lc u cc n +1 ϕ + ζ u ll u c n u cc u c = η +1 + ζ u cl u c 10 7 = η, 8 where ϕ s he mulpler for he governmen budge consran 4, ζ s he mulpler for he frs-order condon consran 5 and β η s he mulpler for he resource consran 1. The frs-order condon for he planner wh respec o he relave prces, q,s N ζ = N ϕ s, 9 =1 =1 where s = 1 u l n u g s he prmary surplus for governmen a me. c The rgh-hand sde of he condons 7 and 8 s he same for all N counres. Consder frs how he rao of he lef-hand sde of equaon 7 for dae for 1, mulpled by β o he smlar expresson for dae 1 for 1. Ths s he rao of he socal margnal ules of consumpon and equals he rao, βη 1,, of socal margnal coss of consumpon n hese daes and saes. Wh complee markes, hs η 1 1 s he compeve equlbrum prce, q 1, u. To see hs, noe ha q 1 1 c 1, = u j c 1, for each u 1 c u j c 1 par of households,, j. Usng he derved rao of he margnal socal ules for households and j, he quany u χ ϕ l u c u lc u cc n + ζ u cc u c 1 u c 0 mus be consan over me. Usng he households frs-order condons for commody marke equlbrum 5 and he frs-order condon n consumpon for he fscal opmum 7 leads o he equaly, χ j + λ j u j c 0= χ k + λ k u k c 0, for each par of counres, j, k {1,..., N}. The rao of he margnal ules of commody consumpon across counres depends on each counry s sochasc process for governmen expendures and s nal ousandng publc deb hrough he χ erm as u j c u k c = λ k χ k λ j + χ j. Ths condon yelds he dsrbuon of consumpon across counres gven he dsrbuon of nal household fnancal wealh under he opmal fscal polcy.
Consder he case ha he ules are addvely separable beween consumpon of commodes and of lesure so ha he cross paral dervave erms vansh and χ = ϕ 1 τ n + ζ u cc u c 1 u c 0. The mulpler, ζ, measures he sharng of rsk across households n he opmum. Noce ha he sum of he erms, ϕ 1 τ n + ζ, and he frs-order condon 7 ogeher mply N ϕ 1 τ n + N ϕ s = N ϕ n g =1 =1 =1 s a consan f consumpon s compleely smoohed across daes and saes for all households n compeve equlbrum. Ths measures he welfare cos of he resrcon o lnear axes on he surplus he planner seeks o allocae across households for commody consumpon. The varaon expressed by he curvaure of he uly funcon n χ adjuss hs socal cos for ncomplee smoohng of aggregae oupu ne of governmen expendures. If he ules are addvely separable n commody and lesure consumpon, hen he compeve equlbrum allocaon for he consumpon of goods canno be mproved upon gven he dsrbuon of nal household wealh. In hs case, he dosyncrac effecs of naonal expendure shocks on oupu wll be fully shared across counres hrough complee markes n conngen commodes. The effecs of dsoronary axes on lesure consumpons do no affec he margnal condons for he allocaon of commodes. The excess burden of axaon on oupu s shared by all households along wh he sysemc componens of expendure shocks. Separable uly ensures ha effcen smoohng of consumpon n commodes s acheved n a compeve equlbrum wh complee markes n secures for commodes only. These welfare saemens are no rue n general f ules are no separable. Lesure s a non-raded good. I s well undersood n he absence of ax dsorons ha nernaonal rade n conngen secures for radable commodes only s nsuffcen o mplemen effcen rsk sharng n radable goods f ules are no separable. Wh he resrcon of ax nsrumens o lnear labor ncome axes, he same resul follows for hs economy. Ths devaon ough o also be refleced n he mulplers ζ n he Ramsey equlbrum so ha her nerpreaon s no sraghforward. Combnng he wo frs-order condons for goods and lesure consumpon leads a relaonshp ha mplcly defnes he labor ncome ax rae, λ u c 0+ϕ u l u c u cc ϕ u l = ϕ u ll u n + ζ u u lc cc cl u c u. cl u c n 11 10
Wh separable ules, he las erm vanshes and he frs-order condon 7 shows ha he weghed sum of prmary governmen surpluses equals zero wh he weghs beng he mulplers on he governmen budge consrans. The socal cos of payng for surpluses n some counres hrough dsoronary labor ncome axes s offse by he socal cos of defc fnancng of publc expendures n oher counres. The mulplers, ϕ, measure he excess burden of axaon n erms of socal margnal uly he planner s objecve. If he sharng of commody consumpon rsk s complee he separable ules case, hen he socal cos of rasng revenue usng dsoronary axes s mnmzed n he Ramsey equlbrum wh free rade. The governmen budge consrans and nal ne foregn asses deermne he dsrbuon of uly across counres and he relave values of he ϕ. The ndvdual naonal ax raes can be backed ou of he necessary condons usng he household consumpon-lesure choces gven he value of hese mulplers. A sandard example helps o smplfy and llusrae equlbrum. Le he uly funcon be separable and dsplay consan elascy of subsuon: u c, l= c1 σ 1 σ + α l 1 γ 1 γ, for σ, γ>0. For hese ules, equaon?? can be used o derve a smple expresson for he ax rae for counry j, τ j = ϕ φ j n j 1 + χ u c 0 λ j u c 0+ϕ j φ n j 12 11 where φ n j =1+γ nj s one plus he Frsch elascy of labor supply. The ax rae only vares 1 n j over daes and saes wh he elascy of labor supply. If he Frsch elascy s consan, hen so s he ax rae for he counry. Opmal rsk sharng wh separable ules yelds a consan ϕ whch measures he excess burden of axaon due o he resrcon o lnear labor ncome axes. Ths formula s smlar o soluon for he ax rae for a sngle counry verson of he economy gven by τ = ϕφ n j 1 + ϕσ 1+ϕφ n, where σϕ replaces χ u c 0. The essenal dfference s he closed economy problem consrans he naonal rade balance, n g c, o equal zero. Prvae rsk sharng n he nerdependen global economy, smoohs consumpon across saes hrough he rade balance usng conngen conracs. Neglecng o add he consran ha he sochasc dscoun facor mus equal he compeve equlbrum relave prce of fuure consumpon n erms of nal consumpon wll lead o an equvalen formula o equaon 11 under he assumpon of separable ules. Dong so, however, allows he planner o use commody axes whch wll n he nonseparable uly case. If lump-axes were avalable o each governmen, he mulplers ϕ
13 and ζ would all equal zero and he mulplers, λ, would equal he nverse of he nal margnal ules for boh commodes and lesure. To llusrae he role of nernaonal rsk sharng, consder he example n whch governmen expendures for each counry follow a common nvaran Markov chan and always sum o a consan. Wh no aggregae uncerany, he ax raes are all consan wh complee markes when ules are separable and dsplay consan elascy of subsuon n commodes. The consan ax raes, labor supples and consumpons for each counry are deermned by s nal publc expendures, g 0. If, nsead, here s aggregae uncerany he sum of he g s Markov, he ax rae for each counry, τ, s an nvaran funcon of he curren sae. Alhough all axes depend on he nal sae ha s, dsrbuon of he nal realzaon of publc expendures, nnovaons n ax raes depend only on he curren sae hrough he elascy of labor supply. Thus, he approach replcaes he resuls of Lucas and Sokey 1983 for a global economy. Dfferences n ax raes and he excess burdens of dsoronary axaon across he counres arse because ndvdual budge consrans are mposed on naonal governmens. The assumpon of conngen publc deb s convenen for seeng he role of naonal fscal responsbly. The overall welfare cos s measured by unequal shadow prces for nal publc deb, ϕ. Consder how a sngle fscal auhory ha mus sasfy a sngle aggregae publc secor budge consran for a fscal unon chooses opmal labor ncome axes for each counry. Under dencal household preferences and a ularan objecve, should mpose he same ax on all households. Non-radable commodes lesure should be unformly axed n he Ramsey equlbrum n a ularan fscal unon. Because counres are symmerc n he model economy, each counry n he opmum wll pay axes n he amoun T0 n presen value o fnance an equal N share of oal governmen oblgaons, [ T0 = 1 b N 0 + σ c j ] E β g c 0 =1 =0 j, where he presen value s compued usng he equlbrum prces for he fscal unon. Ths mples a redsrbuon of governmen deb a dae zero from counry j o he res of he fscal unon equal o c j b j 0 = bj 0 + E β g j c =0 j T j 0 0. For a Pareo mprovemen, he redsrbuon of publc deb mus be offse by a reallocaon of foregn asses across households. A counry wh hgh publc deb or fuure expendures needs o receve a ne wealh ransfer whch could be made by he paymen of an equal amoun of ne foregn asses o he res of he unon. For counry j, makng a ne paymen, f j 0 = bj 0, would keep household fnancal wealh, aj 0, σ
14 unchanged, mananng he nal dsrbuon of wealh across counres. These ransfers are capal leves on fnancal asses. If hese me 0 leves are feasble, hen he uly for each counry s hgher n he unon as effcency n he allocaon of labor s mproved and each counry receves he gven exogenous sream of publc expendure, { g}. The formaon of a fscal unon ha manans he saus quo dsrbuon of naonal welfare under ndvdual governmen budge responsbly leads o a poenal Pareo mprovemen f he shadow prces ϕ are no all equal n he pre-unon equlbrum. Fscal unfcaon decreases he oal excess burden of axaon from ϕ b 0 o ϕ b 0 where ϕ s he shadow prce for unon-wde publc deb n he opmum for a consoldaed fscal auhory. The ably of governmens o ssue conngen deb llusraes he rsk sharng benefs of creang a sngle ax auhory when only lnear facor ncome axes can be used o rase publc revenues. Whle assumng conngen deb s convenen, does no generae he observed hsory dependence of publc deb and axes emphaszed by Barro 1979. Resrcng fscal auhores o ssue sngle-perod maury deb whou sae-conngen paymens n a sochasc economy addresses hs ssue. Bohn 1988 and 1990 proposes ha one way governmens acheve sae conngences n publc deb s o ssue nomnal non-conngen deb. Unancpaed varaons n nflaon mpar sae conngen real reurns o non-conngen nomnal publc deb. 5 In he nerdependen global economy, flexble nomnal exchange raes allow dfferenal nflaon ha could possbly creae he changes n he real value of naonal publc debs requred o mplemen he sae conngen opmum f publc deb s ssued n naonal currency uns. Ths possbly s los n he adopon of a moneary unon. Dscussons of he fscal consequences of moneary unfcaon are ypcally based on Mundell s heory of opmum currency areas whch hghlghs he role of moneary and fscal polces for oupu sablzaon n he presence of nomnal rgdes. Wh resrced sae conngency n he ssuance of publc deb, anoher consequence s he loss of he capacy o use unancpaed nflaon as a fscal ool wh ndependen sochasc publc spendng. Ths movaes my comparson of he moneary unon economy wh and whou conngen publc deb n he nonmoneary model. Crudely, an economy wh perfecly flexble nomnal prces n domesc currences and non-conngen publc debs corresponds o he sae conngen publc deb verson of he model n hs secon. In he same economy, resrcng governmens o ssue only non-conngen publc deb porrays he opmal ax problem for a moneary unon n he nex secons. The argumen for usng hs approach s ha he ax dsoron and lms on conracng by governmens creaes a need for fscal polcy o address shocks orgnang n governmen demand. Therefore, models a role for a common fscal polcy beyond fscal coordnaon based on dosyncrac shocks o naonal economes.
15 A noe he leraure s n order here. Several papers consder he consequences of publc deb ssued n non-conngen bonds. Angeleos 2002 and Buera and Ncoln 2004 show how he erm srucure of non-conngen deb of dfferen maures can be used o mplemen he complee markes equlbrum under some resrcons. However, Buera and Ncoln demonsrae ha he governmen may only replcae he sae conngences usng he erm srucure of deb by akng and reversng very large shor and long posons. Char, Chrsano and Kehoe 1991 sudy opmal moneary and fscal polcy wh nomnal non-conngen deb. Unancpaed nflaon acs as a lump-sum levy on household holdngs of publc deb. They show ha opmal nflaon can be volale and s serally uncorrelaed n a moneary economy wh flexble nomnal prces. Char, Chrsano and Kehoe provde he raonale for comparng opmal axaon wh floang exchange raes and wh a sngle currency usng he model wh and whou sae-conngen publc deb. There are some caveas. The opmal moneary polcy yelds he Fredman rule and flucuaons n nflaon can be subsanal. If nomnal prces and wages are scky, hen unancpaed nflaon reduces welfare and here s a rade off beween reducng he excess burden of axaon and ncreasng flucuaons n margnal coss. Ths rade off wh non-conngen nomnal publc deb has been analyzed n he closed economy by Su 2004, Schm-Grohe and Urbe 2004, Bengno and Woodford 2005 and Lusg, Slee and Yelekn 2008. Bengno and De Paol 2010 analyze opmal axaon wh scky prces n a small open economy. The general resul s ha he opmal response of nomnal non-conngen deb s que mued n he presence of scky nomnal prces for sngle-perod deb maures. In numercal smulaons, he sochasc process for real paymens wh sngle-perod non-conngen nomnal deb dsplays small varance and provdes lle rsk sharng. The consraned opmum seems o approxmae he consraned opmum for real-ndexed non-conngen deb. Lusg, Slee and Yelekn show ha wh longer maury deb, nflaon responds o a rse n governmen expendure wh a lag so ha nomnal prces are rese n ancpaon of he prce level rse and real reurns on long maury nomnal deb fall. 4. Fscal Polces wh non-conngen Deb Agans hs background, I consder he opmal behavor of non-conngen publc deb n he nerdependen global economy. The purpose s o undersand how he requremen ha each governmen bears responsbly for fnancng s curren and fuure expendures and payng off s deb works n a moneary unon wh dosyncrac naonal uncerany. The opmal fscal polcy problem needs o be modfed when he ndvdual naonal governmens canno use sae conngen secures o manage publc deb. In conras wh he analyss of opmal fscal polcy wh real non-conngen deb n closed
economes, households can rade prvae sae conngen secures. Ayagar, e al 2001 analyze opmal axaon wh rsk-free governmen bonds n a represenave household closed economy. There are no pares oher han he represenave household and he governmen o share rsks so governmen deb s he only secury ha can serve a rsk sharng purpose. In he global economy model, households are heerogeneous across counres so ha sharng rsk beween households and sharng rsk beween governmens and households are no redundan moves for rade. The move for households o rade secures wh each oher s o share he rsk of ax ncreases o pay for dosyncrac flucuaons n naonal governmen spendng. Wh lump-sum axaon, resrcng parcpaon n complee markes n radable goods o households would no affec resource allocaon. When only dsoronary ax nsrumens are avalable o he governmens, he consran ha governmens can only ssue rsk-free bonds bu households can connue o rade sae-conngen secures reduces welfare and nroduces deb dynamcs. Inroducng hs consran on publc fnance exends he model of Ayagar, e al o he mul-counry envronmen wh open capal accouns. The opmal ax problem needs o accoun for he dfference beween radable prvae asses, f, and governmen deb, b. Because hey can rade on complee markes, he opmzaon problem for each household s unchanged from he prevous secon. The frs-order condons are he same, bu he sandard mplemenably condon wren from he household lfeme budge consrans 6 canno be used because he wo asses mus be dsngushed when he governmen can only mpose dsoronary axes. Household porfolos conan boh prvae, nernaonally raded, conngen clams and non-conngen bonds ssued by he naonal governmens. If axes were lump-sum, hen he non-conngency of governmen deb would make no dfference. Eher he household budge consran or he governmen budge consran could have been used o formulae he mplemenably condon n he prevous secon. Wh non-conngen publc deb, a sequence of mplemenably condons s needed for each governmen. As before, he frs-order condon derved from household opmzaon under free commody rade wll appear wh a separae mulpler n he opmzaon problem o avod he use of arffs. The consrans for governmen are gven by he sngle-perod budge deny, p 1 b +1 + τ n g b 1, where b 1 equals ousandng sngle-perod publc deb a he begnnng of perod. The dependence on he hsory of shocks hrough dae 1, 1, raher han on, ndcaes he non-conngency of deb ssued n perod 1 for repaymen n perod. The marke dscoun facor for b s +1 p whch s no conngen on dae + 1 shocks. In compeve equlbrum, hs prce equals he expecaon of he 16
sochasc dscoun facor, E βu c,+1 c,. Solvng he sngle-perod governmen budge deny forward /u mposes a budge consran for each dae gven hsory 1 gven by b 1 E q s τ n g. s s s s s s s= q A deb lm needs o be mposed o ensure exsence of an equlbrum. For he closed economy, Ayagar, e al mpose ad hoc upper and lower lms on publc ndebedness. They demonsrae ha n he absence of a lower bound on publc deb, publc cred can grow unl he governmen has suffcen asses o fully fnance fuure publc expendures. In examples, hs occurs when he publc expendures converge o a non-rval saonary dsrbuon. Usng he nsgh from Ayagar, e al, deb lms are mposed as a no lendng upper bound and an ad hoc lower lm on publc deb, 0 b +1 b, 12 for all 0. The seres of mplemenably condons for each governmen are gven by E s= q s q 1 ul,s s u c,s s n s s g s s = b for each and all. The frs-order condon for commody consumpon s β s u c,s s = q s for each = 1,...,N. q u c, The planner s opmzaon problem s o maxmze he objecve E 0 N λ β u 1 for each = 1,...,N and for all 0 c, 1 n =1 =0 wh respec o he conngen consumpons and labor supples, { c }, for each counry subjec o,n condons 13, 5, 1 and 12gven he allocaon of nal fnancal wealh across households, { a0}, of nal publc deb { b0}. The exsence of a soluon and suffcency of he necessary condons for an opmum are dscussed n Ayagar, e al. The exenson o he mulple counry economy nvolves a lnear summaon across counres ha does no change properes such as concavy, compacness or dfferenably so ha her suffcen condons carry over. The mulplers assocaed wh he consrans are μ for 13, ζ for 5, η for 1 and ν and for he upper and lower deb lms, respecvely. As n 1 ν 2 Ayagar, e al, new mulpler, ψ = ψ 1 + μ ν 1 + ν 2 and ψ 0 = μ 0 s nroduced o rearrange he summaon of he governmen mplemenably condons n he Lagrangan. 17 13
N The Lagrangan for he Ramsey problem becomes L = E 0 =1 where λ =0 β u c, 1 + n ψ q z μ q b 1 + ν q 1 b + ζ β u c, u c,0 q + β η x, 18 s he rade balance for counry and x = c n z = τ g 1 = u n g l, n u c, g s he prmary surplus for governmen. The frs-order condons wh respec o radable goods consumpon and labor supply are and λ u l, + ψ λ u c, + ψ u c, u c,0 u c, u c,0 u l, u c, u l, u c, u cl, u c, u cc, u u c, ll, u c, u lc, u c, n n 1+ + ζ u l, u c, u cc, u c, u c, u c,0 + ζ u cl, u c, = η 14 u c, u c,0 = η, 15 respecvely. The mposon of he compeve equlbrum frs-order condon for household consumpon of commodes requres ha χ 1 u c,0 ψ u l, u n ζ c, u cc, mus be consan for each over all hsores. The wo frs-order condons for he planner 14 and 15 combne as λ u l, u c, +ψ u c, u c,0 u l, u c, u cl, u c, N u l, u cc, u ll, u c, u c, u c, u c, n u l, 1+ u c, The frs-order condon wh respec o he nernaonal prces, q,s =1 ψ z μ b 1 + ν 1 b ζ =0. +ζ u c, u c,0 u cl, u c, u cc, u c, As before, hs condon ncorporaes he sharng of rsk across households usng he complee marke srucure hey face. The shadow cos of naonal debs, defcs and when bndng, deb lms, are shared by households across counres. The cross-paral dervave erms n equaon 17 ndcae he effec of he non-nsurably of nonradable goods consumpon across counres on rsk sharng n commodes. In he sae conngen deb case, he mulplers μ +1 = ν 1 = ν 2 =0for all 0, and he mulpler μ 0 s dencal o he shadow prce ϕ wh complee markes for governmen deb. Dfferenaon of he Lagrangan wh respec o b leads o E q +1 μ +1 =0 16 =0. 17
19 and ψ = E q +1 ψ +1 E q +1 1, for posve deb below he deb lm ν = ν = 0. Ayagar, e al explan how her analogous 1 2 verson for he closed economy s a rsk-adjused marngale ha does no necessarly converge. Whou a bound on publc secor lendng, each governmen wll accumulae asses unl ψ converges o zero and he excess burden of axaon vanshes along wh he ax rae. In nsances n whch he excess burden of axaon converges, ψ s a nonnegave marngale, ψ = E ψ +1. The mulpler μ 0 wll be posve unless nal publc deb, b, s suffcenly large and negave o fnance all fuure expendures. 0 can be ψ a marngale f he equlbrum process for he common sochasc dscoun facor converges. For example, when flucuaons n governmen expendures vansh n fne me. If governmen expendures follow an nvaran non-rval Markov chan, hs s no assured and convergence wh a no lendng lm canno occur. Ayagar, e al also fnd ha ad hoc deb lms are reached wh posve probably n fne me for serally uncorrelaed governmen expendures. Snce he necessary condons wh respec o ousandng publc deb for he many governmen model wh prvae rsk sharng are he same, hs resul carres over mmedaely. Wh perssen randomness, non-conngen publc deb does no converge f publc cred accumulaon s bounded. The example wh separable ules dsplayng consan elasces of subsuon llusraes how he addon of he curren accoun affecs he frs-order condon for he opmal ax rae. Subsung he soluons no equaon?? f he deb lms do no bnd leads o he expresson for he labor ncome ax rae for counry, τ = ψ φ n 1 χ u o λ u o + ψ φ n. 18 Conrasng hs expresson wh he sae-conngen deb case shows ha he mulpler, ψ, replaces he mulpler ϕ. The ax rae vares wh he realzed sae,,ame. μ measures he shadow cos of he resrcon ha he governmen can only ssue non-conngen deb and can be eher posve or negave. A posve realzaon a dae means ha ψ 1. Thus, he socal cos of dsoronary axaon for >ψ counry ncreases wh a posve μ. The mulpler s posve for expendure realzaons such ha he governmen would opmally ssue less sae-conngen deb and s negave for realzaons such ha sae-conngen deb would be hgher han opmal non-conngen deb. Wh ndependenly dencally dsrbued g, hgh expendure saes wh ousandng publc deb lead o an ncreasng excess burden of axaon measured by ψ, and conversely for low expendure saes. If he governmen could ssue sae conngen deb, he planner would rade deb n hgh μ saes for deb n low μ saes, smoohng he excess burden of axaon across saes a each dae. Dong so, he planner would equalze he shadow
20 prce of publc deb across each for each dae and over all mes. The mulplers ψ all collapse o μ 0 = ϕ. 5. Opmal Taxaon and Increasng Publc Deb The economes wh sae-conngen deb and wh non-conngen real deb are conrasng exreme cases. An nermedae approach allows for sae-conngen deb bu resrcs he varaon of deb paymens across saes endogenously. Ths verson of he economy leads o very dfferen dynamcs for governmen deb han hose generaed by he exogenous non-conngen deb model. The dea s o lm he degree of publc deb conngen paymens by endogenzng marke ncompleeness. The model economy can be modfed o endogenous rsk sharng by assumng asymmerc nformaon abou governmen expendures. The assumpon ha he governmen observes s expendure shock bu households do no s a smple way o nroduce he noon ha he governmen has more nformaon abou s acves han do he holders of publc deb. Ths can be nerpreed as he governmen havng more nformaon abou how publc spendng choces are made. For example, he governmen may know he margnal socal benef of publc expendures n a polcal equlbrum bu ax payers and credors do no observe dsurbances o he polcal value of publc expendures known o he governmen. In erms of he model, he governmen observes he realzaon of he random varable,, prvaely each perod. Ths varable gves he margnal benef of publc expendure for he governmen. In he spr of applyng models of borrowng wh prvae nformaon o a moneary unon, I assume ha he prvae secor can make ransacons ha he governmen canno due o governmen moral hazard. The governmen has a dsadvanage sharng rsk relave o households who face complee markes. Whle he governmen has more nformaon abou s expendures, whch are he source of sochasc shocks n hs economy, wh endogenous marke ncompleeness has less capacy o share he unceran coss of expendure shocks han do prvae agens. However, he governmen mus choose a ax polcy o mnmze he socal cos of ax dsorons. Households can smooh her rsk of pos-ax ncome bu hey canno reduce he excess burden of axaon. In he mulple counry economy, households all have he same nformaon abou he realzed sae of naure. In an ncenve compable equlbrum under planner commmen, all governmens ruhfully repor her prvae nformaon. Households and frms hen observe he sae and can condon conracs among hemselves on hs nformaon. There s no moral hazard n prvae ransacons, so ha here s no reason ha households canno share consumpon rsk conngen on hsores. I assume ha prvae agens can rade on complee sae conngen markes even hough naonal governmens canno.
21 Ths approach sars by addng naonal publc goods expendure o he household uly funcon wh sochasc margnal uly of publc goods. By choosng a uly funcon ha s addvely separable n publc goods, household opmzaon wh respec o commody and lesure consumpon wll no be affeced drecly by he governmen s choces of publc spendng. Fscal polces only affec households hrough axes and he global resource consran. Ths modfcaon would be superfluous whou prvae nformaon as does no affec n any way he analyss wh and whou conngen publc deb n ha case. Ths model follows he approach o Ramsey axaon wh prvae nformaon developed by Slee 2004 for he closed economy. Much of he analycs from Slee 2004 and Slee and Yelekn 2006 apply o he global economy model wh ndependen publc secor budge consrans. Agan, he planner s opmzaon problem uses lnear sums of he separae objecves and consrans for ndvdual counres so ha her proofs of exsence and suffcen condons for opmaly of a soluon o necessary condons apply mplcly. Each household uly funcon s gven by W c,n,g; = u c, 1 g 1 η + n 1 η where he { g} for all N counres s aken as gven by every household n he compeve equlbrum. The planner for he unon wll maxmze he sum of hese welfare funcons over he N counres under he assumpon ha has prvae nformaon abou he ase shocks, for each governmen. Tha problem seeks he consraned opmal fscal polcy ha characerzes a cooperave equlbrum raher han a noncooperave equlbrum for a game played among naonal governmens. The dsrbuon of can depend on 1 or be resrced for smplcy. For example, can be ndependenly and dencally dsrbued over me for counry alhough each governmen faces s own dsrbuon. Thomas and Worrall 1990 model rsk sharng wh prvae nformaon abou he endowmen of a rsk-averse household radng wh a rsk neural nsurer. Rsk sharng mus be ncenve compable n equlbrum. Incenve compably consrans he degree of rsk sharng ha can be acheved so ha he household faces resdual rsk n equlbrum. In essence, he fnancal wealh of he rsk averse household declnes sochascally and household deb converges o he naural deb lm as margnal uly dverges o nfny. The Thomas and Worrall economy s exended o general equlbrum wh a connuum of dencally rsk-averse households by Akeson and Lucas 1992 o show how he dsrbuon of wealh evolves n he prvae nformaon economy. When appled o he opmal ax problem by Slee 2004, publc deb converges oward he naural deb lm. The deb ssued by he governmen can be conngen bu he governmen s polces mus be ncenve compable and he governmen reveals he acual value of
observes o s credors n equlbrum. In applyng hs leraure o he nerdependen global economy, he assumpon ha households are able o rade n complee conngen markes n prvae secures s mporan. I allows adopon of he analycs o fnd equlbrum wh planner commmen when he counres are fne n number. I also assumng addvely separable uly wh consan elascy of subsuon from he ouse snce allows lnear aggregaon across households n he dfferen counres. Begn wh he ncenve compably consrans for each governmen wh respec o s repor of s realzed margnal benef,. Each governmen draws s ndependenly from a common dencal dsrbuon a each dae o smplfy exposon. Qualave conclusons wll no dffer n subsance f he are assumed o be ndependen Markov random varables. Aggregae uncerany s allowed snce counres are no nfnesmal.. The welfare objecve for governmen s gven by }, { } = E 1 { V c,n,g β W c,n,g ;, 19 =0 where s a repor o he planner of he acual observed by governmen. The ncenve compably consran for governmen s V { } { } c,n,g, {c } { V,n,g, } { } for all possble reporng sraeges. The mplemenably condon s gven by 1 ul, E 1 q n g = b u =0 0 21 c, where he argumens depend on he hsory recall, hs s he vecor of he naonal hsores over all N governmens. The resource consran s sll gven by equaon 1. A no lendng consran for he planner s mposed o rule ou soluons ha converge o he accumulaon of publc cred suffcen o elmnae he labor ncome ax for each member counry. For he closed economy wh a represenave household, Slee 2004 demonsraes convergence o a zero ax seady sae f he governmen s allowed o accumulae cred. Slee and Yelekn 2006 mpose a no lendng consran on he governmen o elmnae hese equlbra whch occur f nal publc deb s low enough. The same no lendng consran and an mplc upper bound on deb are mposed for he global model as n he prevous case wh exogenous ncomplee publc deb markes. The no lendng consran for governmen s 1 u l, n g + E q 1 s u l,s n s g s 0. 22 u c, s=+1 q u c,s 22 20