Political Economy of Sovereign Debt: Cycles of Debt Crisis and Inequality Overhang

Transcription

1 Poltcal Economy of Soveregn Debt: Cycles of Debt Crss and Inequalty Overhang Alessandro Dovs Penn State Mkhal Golosov Prnceton Al Shourdeh Wharton Aprl 5, 2015 Prelmnary and Incomplete Abstract We study optmal fscal and redstrbutve polcy n an open economy wthout commtment. We show that hgh level of nequalty n the past creates strong ncentves for default on external debt; what we refer to as nequalty overhang. Our man result s that optmal repayment polces for economes wth hgh levels of debt nvolve large reductons n external debt postons, resemblng extreme austerty measures. Such repayment polces lead to cyclcal dynamcs n external debt and fscal polces such as transfers and pensons (even n a determnstc envronment). Fnally, we show that large external debt reductons concde wth ncreases n fracton of government debt held by the domestc ctzens. We thank Andy Abel, Mark Aguar, Manuel Amador, V. V. Char, Joao Gomes, Emmanuel Farh and Patrck Kehoe for valuable comments. 1

2 1 Introducton Recent events n the Euro zone have hghlghted the poltcal determnants of countres external debt polces. Followng the crss n 2009, many european countres have mplemented hghly unpopular fscal consoldaton programs, the so-called austerty measures, n order to reduce ther external debt burden. More recently, ths lack of popularty has resulted n resurgence of poltcal partes that advocate ant-austerty measures suggestng a possble cyclcal pattern n debt and more broadly fscal polces. More systematcally, as shown by Voth (2012) and Pontcell and Voth (2012), large austerty measures typcally lead to socal unrest and n many cases reversal of these polces. The man purpose of ths paper s to provde a poltcal economy model of determnaton of fscal polcy where polces are determned under lack of commtment and n presence of redstrbutve motves. We show that such cycles whch feature austerty arse naturally as a result of the nteracton between lack of commtment and redstrbutve motves. The cyclcal movements n external debt and tax polcy are of the followng form: when external publc debt s low, the government runs large redstrbutve programs, large defcts and accumulaton of publc foregn debt. Eventually the maxmal amount of external debt that can be ssued s reached and the government must undergo a large fscal consoldaton assocated wth a drastc adjustment of external publc debt poston, large nequalty and ncrease n the share of government debt held by domestc resdents. The burden of adjustment s on current generatons. The dynamcs s cyclcal because the large fscal consoldaton allows future governments to pursue lax fscal polces (ths s actually what makes the arrangement credble today). We llustrate ths mechansm n an overlappng generatons economy where n each perod a contnuum of households wth heterogeneous labor productvtes are born. Households work, consume and save for retrement when they are old. Government uses dstortonary taxes on earnngs and assets as well as external and domestc debt to rase revenues to spend on transfers to the young and to the old and to fnance some exogenously gven government consumpton. We consder two scenaros for the determnaton of polces. Frst, we consder the case n whch polces are chosen by a planner that lacks commtment and has motves to redstrbute resources wthn and across generatons. Second, we consder the case n whch polces are the outcome of an explct probablstc votng game along the lnes of Lndbeck and Webull (1987) (See also Song et al. (2012), Farh et al. (2012), and Scheuer and Woltzky (2014) for smlar applcatons to dynamc settngs.) As t s standard n probablstc votng models, the equlbrum polces are the result of a game between 2

3 fcttous planner n each perod that chooses polces to maxmze a weghted average of the welfare of the generatons alve n the current perod. Relatve to the frst setup, there are some elements of strategc nteractons among the fcttous planners. Our man result about cyclcalty of fscal polces apply to both of the setups. In our setup, governments have two motves for the governments to renege on prevous promses, e.g., repayments of government debt, penson payments and wealth taxes. Frst, the government has a foregn motve to default n that t s tempted to repudate ts external debt to reduce the payments t makes to foregn lenders. Second, the government has a domestc motve to renege on past promses due to the presence of wealth nequalty (formed n the past) and redstrbutve motves. The government has an ncentve to exproprate wealth and redstrbute the resultng resources across the populaton, thereby reducng nequalty. The force that balances these motves and prevents default - defned broadly as renegng on promses made by prevous governments - s the dsruptons n prvate credt markets assocated wth t. The nterplay between the two ncentves to default s the crtcal mechansm that drves our novel results. Ths can be seen from the effect of an ncrease n wealth nequalty on ncentves to default on external debt. In partcular, when wealth nequalty s hgh, the domestc motve to renege on promses s hgh and so the amount of foregn debt that can be credbly supported s low. Hence, when current ncome nequalty s hgh (and so future wealth nequalty s hgh) the current government can credbly ssue a lower amount of debt than when nequalty s low. We call ths mechansm nequalty overhang. The cyclcal nature of polces follows from the nequalty overhang. To understand the forces operatng, consder a stuaton n whch nherted foregn debt s suffcently hgh so that the current government cannot roll t over n a credble way. The current government s then forced to reduce the debt t passes to future governments. We call ths epsodes fscal consoldatons. Because of lack of commtment, the government s unable to equally share the burden of foregn debt repayments across generatons, t must necessarly cut back from transfers and tolerate hgh level of ncome and consumpton nequalty wthn a generaton. Hgh level of nequalty concdes wth stronger ncentves for default n the future and as a result, future government should be compensated wth low level of external debt n order not to default. Ths mples that the reducton of foregn debt must be substantal to make the arrangement credble because when nequalty s hgh, low foregn debt can be ssued. Ths large reducton n debt leaves the future governments wth few resources commtted to repayng foregn lenders. Ths allows the government to mplement large redstrbutve program, to ssue a lot of foregn debt forcng future governments nto fscal consoldatons. 3

4 Addtonally, we show that fscal consoldatons are accompaned by an ncrease n the share of government debt held domestcally. Ths s manly due to the fact that makng consoldatons credble requres a future compensatons. Hence t s optmal for the current government to promse hgh consumpton to the current young households when they reach the old age. Ths can be acheved through a combnaton of hgh penson promses and by ssung large amount of domestc debt. To ncentvze young households to save, the government must subsdze the nterest rate they receve relatve to the nterest rate prevalng on nternatonal credt markets. The cyclcal pattern of fscal polces and nequalty overhang s consstent wth several observatons from latn amercan countres. In partcular, some studes have ponted to the a negatve relatonshp between nequalty (typcally ncome nequalty measured by the Gn ndex) and a country s lkelhood of default See Berg and Sachs (1988) and more recently Azenman and Jnjarak (2012). Furthermore, that fscal polces are cyclcal have long been observed n varous latn amercan economes. Of specal nterest s the studes done by Dornbusch and Edwards (Dornbusch and Edwards (1991), Dornbusch and Edwards (1989)) and Sachs (1989). These authors observe that fscal polces n Latn Amerca seem to be cyclcal and drven by populsm. As we wll dscuss, some features of these polces are consstent wth the dynamcs n our mode. Fnally, the mplcaton of our model that durng fscal consoldaton epsodes government debt s clentele become more concentrated among domestc households s consstent wth the recent experence of the European countres as well some of the latn amercan economes experencng debt crss. Related Lterature. To be completed. The rest of the paper s organzed as follows. Secton 2 descrbes the model. Secton 3 characterzes the equlbrum where polces are chosen by a planner wthout commtment. Secton 4 characterzes the poltcal economy envronment. Secton 5 dscusses generalzatons of the model. Secton 6 provdes emprcal support for our results. 2 Model Setup In ths secton, we descrbe the basc framework n whch we analyze the determnants of polces. We consder an overlappng generatons economy populated by a contnuum of heterogeneous households together wth the government. 4

5 Households. Tme, t, s dscrete and t = 0, 1,. At the begnnng of each perod, a generaton of households are born and lve for two perods. Each generaton born at t s conssted of a contnuum of households who draw a productvty type θ t when they are born. They work, consume and save when young and consume when old. We assume that θ { θ 1 < < θ N} and that Pr ( θ t = θ ) = µ where the average value of θ s normalzed to 1,.e., N =1 µ θ = 1. We refer to households wth productvty type θ, as households of type. The labor productvty of an agent of type s gven by Zθ, where Z s a common factor affectng productvty of all households. Households value consumpton and labor supply accordng to the followng preferences: ( ) U c t,0, 1 y ( ) t θ + βu c t,1 where c t,0, c t,1 are consumpton when young and old, respectvely whle y t s the effectve hours worked by the agent when young Zy t s ncome. In most of the paper we focus on a case where the utlty functon s gven by ( ) log c t,0 + ψ log 1 y t θ + β log c t,1 (2) In secton 5.1, we dscuss ths choce of utlty functon and ts role n the results as well as extenson our results to other preferences. A young ndvdual of type, has a t n wealth at the end of the perod. Fnally, there s an ntal old generaton at t = 0 whose wealth dstrbuton are gven by { a } 1 =1,,N whle ther consumpton s gven by c 1,1. Technology. Labor s the only nput for producton and total output n the economy s gven by Z µ y t. Government. Government provdes transfers to agents when young, T t, pensons to households when old P t and pays for government purchases G. It fnances these expenses wth revenues rased from taxng labor ncome, taxng assets saved for retrement as well as borrowng from the rest of the world. 1 Gven the structure of government fnances, the government budget constrant s gven by (1 + r t ) B t + (1 + r ) δ t B t + T t + P t + G = τ l,t Z (1) µ y t + τ a,t µ a t 1 + B t+1 + B t+1 (3) 1 For now, we assume that the government s the only entty n the economy whch s able to borrow and lend from the rest of the world. Later**** we show that t s possble to decentralze the same allocatons by allowng households to access nternatonal credt markets whle government can mposes captal control va taxaton of nternatonal asset ncome. 5

6 where B t, and B t are, respectvely, face value of government s domestc and foregn debt, T t s transfers to the young, p t s publc pensons for the old, τ l,t s the tax rate on earnngs, τ a,t s the tax rate on assets (prvate pensons), r s the nterest rate on government s nternatonal debt whle ˆr t s the nterest rate on government s domestc debt. In addton, δ t [0, 1], s the fracton of the foregn debt that s repad n each perod. Note that snce the government can mpose asset taxes on domestc holdngs of ts debt, t s wthout loss of generalty to assume that all domestc s repad. Gven the above government polces, we can wrte households budget constrant as c t,0 + a t Zy t(1 τ l,t ) + T t (4) c t,1 (1 + ˆr t+1 ) a t(1 τ a,t+1 ) + P t+1 (5) In addton, the ntal old smply consume ther after-tax asset ncome and pensons, or c 1,1 = a 1 (1 τ a,0) + P 0. Note that we have assumed that government are the only domestc entty that can borrow and lend n nternatonal credt markets. Whle ths s an extreme assumpton, when the government has the ablty to mpose captal controls (taxes on foregn transactons) t s wthout loss of generalty. Ths s because when government can mpose captal controls, taxes on foregn transactons can be mposed n such a way that domestc households have no ncentve to trade wth the rest of the world and only hold domestc debt. Markets. goods markets clear. That s, Feasblty of allocatons requres that domestc credt market, as well as µ c t,0 + µ a t = B t+1 (6) µ c t 1,1 = Z µ y t + B t+1 (1 + r ) δ t B t Compettve Equlbrum wth Taxes. As t s standard n the Ramsey approach, the above market structure as well as households optmzaton puts a constrant on the set of allocatons that can be acheved by the government. Before descrbng determnaton of polces, our noton of compettve equlbrum makes precse the type of restrcton the above market structure puts on government s choce. Defnton 1 Gven a sequence of government polces {B t, B t, τ l,t, τ a,t, T t, P t } t=0 as well as nternatonal nterest rate, r, a compettve equlbrum wth taxes s gven by c t,0, c t,1, y t, a { } t together wth prces {ˆr t } t=0 where () c t,0, c t,1, y t, a t maxmzes (1) subject to (4) and (5), () domestc bond nterest rate, ˆr t, adjust so that domestc credt markets clear,.e., (6) holds. 6 t=0

7 2.1 Characterzng the set of Compettve Equlbra Our approach for characterzng optmal polcy n ths paper s the prmal approach as n ***StokeyLucas. That s, we characterze the set of allocatons that can be supported by compettve equlbra wth taxes and subsequently drve propertes of polces from allocatons. To do so, we frst characterze the set of (nteror) allocatons that can be mplemented as a compettve equlbrum. Namely, we resort to a result developed by ***Wernng and leave the dervaton to the appendx. Lemma 2 Suppose that households preferences are gven by (8.1). Gven ntal asset dstrbuton for the ntal old, { a } 0 =1,...,N, and an ntal foregn government debt, B 0, an allocaton { { } } c t,0, c 1t 1, y t, a t can be supported as a compettve equlbrum wth taxes f {1,,N} t=0 and only f t satsfes the followng: 1. there exst a vector of market weghts that { Φ t = ( ϕ ) } t {1,,N} where t=0 µ ϕ t = 1 such c t,0 = ϕ tc t,0, c t,1 = ϕ tc t,1, θ y t = ϕ t (1 Y t) (7) where C t,0, Y t, and C t,1 are the aggregate consumpton of the young, aggregate effectve hours worked, and aggregate consumpton of the old households that are born at t, respectvely. 2. The market weghts satsfy 3. Aggregate allocatons satsfy the feasblty condton: ϕ ψ θ 1 t = 1 +. (8) 1 + ψ + β 1 Y t C t,0 + C t 1,1 = ZY t + B t+1 (1 + r ) δ t B t (9) Proof can be found n the Appendx ***. The above lemma, characterzes the set of allocatons that can be supported n a compettve equlbrum wth taxes. The frst condton n Lemma 2 s a drect result of lnearty of the tax functon. Lnearty of the tax functon that the margnal rate of substtuton between consumpton when young and old and earnngs should be equated across households. 2 Log preferences then mply that (7) must hold. The second property n Lemma 2 2 The market weghts ϕ t are the Negsh weghts assocated wth the compettve equlbrum wth taxes. 7

8 s the so-called mplementablty constrant and s derved from the consoldated budget constrant assocated wth (4) and (5). As the above lemma establshes, unlke the standard Ramsey approach n representatve agent models (for examples as n Lucas and Stokey (1983) or Char and Kehoe (1999)), the compettve equlbrum mposes no constrant on aggregate allocatons besdes feasblty. In other words, any aggregate allocaton that satsfes feasblty for whch market weghts exsts to satsfy the above can be supported as a compettve equlbrum wth taxes. It does, however, mpose restrctons on dstrbuton of consumpton and earnngs as descrbed by the above lemma. 3 A Plannng Problem In ths secton, we establsh the man results of our paper as the outcome of a plannng problem wthout commtment. In partcular, we show three man results. Frst, hgher nequalty lowers the capacty of the country to borrow nternatonally. Second, allocatons exhbt cyclcal dynamcs,.e., convergence of allocatons to ther steady state value s cyclcal. Fnally, downward adjustment n external debt are concdent wth an ncrease n domestc holdngs of government debt. Our approach n ths secton s to study a plannng problem wthout commtment where the objectve of the planner s a weghted average of households utlty wthn and across generatons. In partcular, at each pont n tme, the planner s objectves are gven by ˆβ s t s=t α µ u s + ˆβ 1 α µ u t 1,1. (10) where u t s the utlty of a young household of type born at t whle u t 1,1 (c = βu t 1,1 s that of an old household of type at t. The coeffcent α s the welfare weght assgned to a household of type wthn a generaton whle ˆβ t s the welfare weght assgned to generaton t. We normalze α s so that µ α = 1. Thus the planner sets polces descrbed n secton 2 n order to maxmze (10). In secton 4, we study a probablstc votng model and dscuss how t can lead to smlar welfare functons. We make two assumptons wth respect to ths objectve that are crucal to our analyss: Assumpton 3 ˆβ (1 + r ) 1. The frst assumpton states that the prce of borrowng funds from nternatonal credt 8 )

9 markets s at most equal to the ntergeneratonal rate of tme preferences for the domestc planner. Assumpton 4 (Redstrbutve Motves) α s weakly decreasng n. The second assumpton states that the government uses hgher welfare weghts on ndvduals wth lower labor productvty. One mplcaton of ths assumpton s that optmal labor ncome taxes are always postve. One socal welfare functon that satsfes ths assumpton s utltaran objectve for whch α = 1. Another example s the so-called Rawlsan or max-mn welfare functon where α 1 = 1 and α = 0 for values of > 1. Optmal polcy wth commtment. Before dscussng the key propertes of optmal polcy wthout commtment, t s helpful to menton what happens when the planner can commt. Wth commtment, ndependent of the ntal level of external debt, B 0, the government s able to use nternatonal markets to equate consumpton and lesure across generatons. As a result, consumpton of the young, consumpton of the old, output and labor ncome taxes are constant. Note that labor ncome taxes are chosen to acheve certan level of redstrbuton wthn generatons whle the allocaton of consumpton across generatons are chosen to acheve redstrbuton across generatons. In other words, commtment enables the government to dstrbute the burden of the ntal debt on all future generatons whle acheve ts desred cross-generaton consumpton and tax smoothng. Incentves to retract from promsed polces. There are two man reasons that the optmal polces descrbed above are not tme consstent. Frst, as t s typcal n open economy models, f the government s a net debtor, t has strong ncentves to default on ts promsed repayment polces. Second, at each perod there s a non-degenerate dstrbuton of wealth among the old households and snce the government s nequaltyaverse t has strong ncentve to exproprate all the wealth va a 100% tax on wealth and redstrbute t equally among the old. As t becomes clear, the nteracton between these two ncentves for renegng on promsed polces drves most of our results. Optmal polcy wthout commtment. We now descrbe the constrants mposed by the planner s lack of ablty to future polces. We start our analyss by a rather nformal approach to modellng lack of commtment by the government. We assume that lack of commtment, smply mples that at each pont n tme, the value of the planner s objectve cannot fall below a certan level W. The value of W s assocated wth an allocaton where the young do not save, the old only consume the pensons receved from the government, and the economy s n fnancal autarky wth respect to the rest of the world. Gven these constrants, the government optmally chooses the labor ncome taxes and lumpsum transfers to the old and young. Formally, an allocaton s sad to be sustanable f t 9

10 satsfes where β ˆβ W = 1 max 1 ˆβ c 0,c 1,y,τ l,t α µ u t 1,1 + ˆβ s t s=t s.t. ( α µ u c 0, y ; θ ) + βˆβ µ c 0 + c 1 + G = µ Zy θ (1 τ l ) u c,0 + u y = 0 c 0 = (1 τ l) Zy + T α µ u s W. (11) α µ u (c 1 ) (12) We refer to (20) as the sustanablty constrant. Whle our analyss here s rather nformal, In Appendx, we formalze our modelng of commtment by developng a formal game between the planner, households and foregn lenders and show that an allocaton can be the equlbrum n such a game f and only f t satsfes the characterzaton n Lemma 2 and satsfes (20). The basc dea s that upon any renegng on polces by the planner (for example, default on external debt), domestc households as well foregn lenders react by excludng the government from nternatonal and domestc credt markets. Therefore, n ths game, t s wthout loss of generalty to assume that default does not occur n equlbrum. Because of ths, n what follows, we set δ t = 1. Usng the above restrctons, we can thus defne the best sustanable equlbrum s an allocaton that satsfes the condtons n Lemma 2 and (20) and t maxmzes 10 at tme 0. Formally, the best sustanable equlbrum s the soluton to the the followng optmzaton problem: max ˆβ t t=0 [ α µ log c t,0 (1 + ψ log y t/θ ) ] + β log c t,1 + βˆβ α µ log c 1,1 (P) 10

11 subject to c t,0 = ϕ tc t,0, c t,1 = ϕ tc t,1, y t = 1 ϕ t (1 Y t), t 0 ϕ t = ϕ ψ θ 1 (Y) = 1 +, t ψ + β 1 Y t B 0 = 1 (1 + r t=0 ) t [ZY t C t,0 C t 1,1 ] ˆβ s t [ α µ log c s,0 (1 + ψ log y s/θ ) ] + β log c s,1 + βˆβ α µ log c t 1,1 W s=t c 1,1 = a 1 + P 0 C 1,1 = µ a 1 + P 0 { } I a 1, =1 B 0 : gven Note that n the above optmzaton problem, we have mposed that frst perod asset holdngs are not taxed. Note that n our envronment, snce there s no captal, taxes on asset holdngs can be set to 0 wthout loss of generalty domestc debt ssuance by the government can affect domestc nterest rate and thus government can affect the ntertemporal margn by ssung domestc debt. Ths s not true n perod 0 as the planner can wthout cost mpose a hundred percent tax on ntal assets and wpe out the undesred ntal nequalty. Instead, we assume away ths ntal motve for taxaton of assets n order to keep the problem statonary. Ths modfcaton s purely for statonarty and does not change our man results. 3 A Recursve Formulaton. Problem (P) has a mult-dmensonal state varable gven by the dstrbuton of debt n the economy - domestc and foregn. To make ths problem tractable, we solve t n two stages. Frst, we solve the problem for all generatons except the ntal old. Second, we solve the problem for the ntal old for a gven dstrbuton of debt n the economy. Solvng the problem n two stages has the beneft that the plannng problem n the frst stage can be reduced to a recursve problem where there s sngle state varable; the promsed utlty to the ntal young gong forward. Formally, we defne the promsed utlty for the planner by 3 Ths s n contrast wth Char and Kehoe (1990) and the subsequent lterature. In ther paper, frst perod s always dfferent than the subsequent perods n that the government can exproprate all ntal captal. 11

12 V t = ˆβ s t s=t α µ [ log c s,0 + ψ log (1 y s/θ ) + β log c s,1 Ths s the value to the planner from generatons that are born n perod t onwards. Gven ths value, we can wrte the recursve formulaton of the problem of effcently allocatng resources to generaton that are born from perod 0 onward. Ths problem n ts dual form s represented by the followng Bellman equaton: subject to ˆB (V) = max C 0,C 1,Y ZY C r C r ˆB ( V ) (P1) ] U p (C 0, C 1, Y) + ˆβV = V β ˆβ Up 1 (C 1, Y) + V W where U p (C 0, C 1, Y) s the value to the planner from a generaton whose aggregate consumpton when young and old are gven by C 0 and C 1 whle the output produced s Y. Note that gven these aggregates, dstrbuton of consumpton and lesure and consequently socal welfare s determned by the constrant (8). The functon U p 1 (C 1, Y) s smlarly defned for the old. Use log preferences, we can wrte U p (C 0, C 1, Y) = log C 0 + β log C 1 + ψ log (1 Y) + (1 + ψ + β) H (Y) U p 1 (C 1, Y) = log C 1 + H (Y) where the functon H (Y) captures the nequalty averson motves that are present n the planner s socal welfare functon H (Y) = α µ log ϕ (Y) Gven the value functon ˆB (V), the frst stage problem s gven by W ({ } ) a 1, B β ( ) 0 = max α P 0,V 0 ˆβ µ log a 1 + P 0 + V 0 (P2) 12

13 subject to P 0 µ a 1 + ˆB (V 0 ) = (1 + r ) B 0 (13) β ( ) α ˆβ µ log a 1 + P 0 + V 0 W (14) Note that gven the statonarty of the plannng problem n (P), the problem of the planner at date t who nherted external debt B t and asset holdng dstrbutons gven by { a t} I =1 s dentcal to the problem n stage 2. Thus the forces dentfed n the above problem are also present over tme. The followng proposton connects the soluton to (P) to that of (P1) and (P2). Proposton 5 If an allocaton solves the plannng problem n (P) and the assocated promsed utlty to the government at tme 0 s gven by V 0, then the allocatons must be generated from the polcy functons n (P1) whle V 0 and ntal pensons P 0 are the soluton to (P2). Conversely, f an allocaton generated from the polcy functon n (P1) and (P2) satsfes then t must be the soluton to (P) lm sup ˆβ t V t = 0 t Proposton 5 whch s smlar to the standard prncple of optmalty (see Stokey et al. (1989) s proved n the Appendx. The followng lemma establshes the basc propertes of the value functon ˆB (V): Lemma 6 The value functon ˆB(V) s strctly decreasng, strctly concave and dfferentable. The proof uses standard dynamc programmng technques and s therefore left for the Appendx. 3.1 Inequalty Overhang We can use program (P2) to show our frst man result; hgher level of nequalty lowers external debt capacty. We refer to ths result as nequalty overhang. Consder the unconstraned verson of the program (P2) that maxmzes the objectve subject to the resource constrant (13). When the value of ths objectve, W u ({ a ) 1}, B 0, s greater than or equal to W, the soluton to ths unconstraned problem concdes wth that of (P2). However, when W u ({ a ) 1}, B 0 < W, the constrant set n (P2) s an empty 13

14 set the maxmzed value s lower than W and thus no feasble allocatons exst that delver the value W. In words, the planner cannot avod default on external debt and tolerate asset nequalty for values of ({ a 1}, B 0 ) such that W u ({ a 1}, B 0 ) < W. Ths mples that for any dstrbuton of ntal asset holdngs, { a 1}, we can defne external debt capacty B ({ a 1}) by the hghest value B that satsfes W ({ } a 1, B ) = W. The followng proposton contans our man result about external debt capacty changes wth nequalty: Proposton 7 The value functon W ({ a 1}, B ) s decreasng n B. Furthermore, an ncrease n { a 1} n the sense of second order stochastc domnance ncreases the value functon W ({ a } 1, B ) (. As a result, debt capacty B {a 1 } ) ncreases n response to an ncrease n the sense of second order stochastc domnance. The above result s very ntutve; when ntal asset nequalty ncreases, the value to the planner from the ntal old decreases. Ths ncreases the government s ncentve to default. As a result, foregn lenders are less wllng to lend and therefore, debt capacty s lower. Although, ths result holds wth respect to nequalty n asset holdng among the old, snce n our model asset dstrbuton among the old s closely ted to ncome nequalty n the perod before, the same effect holds wth respect to ncome nequalty. In other words, f due to changes n government polces, ncome nequalty ncreases, external debt capacty must decrease. Next, we descrbe how ths effect can cause cyclcal dynamcs n external debt. 3.2 Cyclcalty of Debt In ths secton, we study dynamcs of debt over tme. Our man result s that due to the nequalty overhang, convergence of external debt to ts steady state, s cyclcal. We show ths by showng that the polcy functon for contnuaton utlty n (P1) s decreasng whenever the sustanablty constrant bnds whle t s ncreasng when the sustanablty constrant s slack. The followng theorem states ths result: Theorem 8 V (V) and C 1 (V) are U-shaped: There exsts V such that for all V < V, V (V) and C 1 (V) are decreasng and for all V V, V (V) and C 1 (V) are ncreasng. Addtonally, for all V V, the sustanablty constrant s bndng whle for all V > V the sustanablty constrant s slack. 14

15 The proof s deferred to the appendx. Mechancally, for low values of V, the country needs to do lots of repayment whch leads to a hgh value of output. A hgh value of output mples a hgh level of wthn generaton nequalty. Due to nequalty overhang, hgh level of nequalty creates strong motves for default and as a result, the future old and future generatons should be promsed a hgh level of utlty,.e., low level of debt. Mathematcally, the non-monotoncty of the polcy functon s a consequence of the fact that current and future promsed utlty, V and V respectvely, are substtute. An ncrease n V, when accompaned by a decrease n V allows the planner to lower nequalty among the future old and as a result current young. Therefore, the change n consumpton requred to delver V s smaller. In other words, when the sustanablty constrant s bndng, the objectve functon n (P1) s sub-modular n V and V. Ths s n contrast to many economc applcatons as studed by Hopenhayn and Prescott (1992). The cyclcalty of the allocatons mpled by the polcy functons n (P1) also translate nto external debt. In partcular, n perod t, the value of external debt s gven by B t = ˆB (V t ) C 1 (V t 1 ) = ˆB ( V (V t 1 ) ) C 1 (V t 1 ) When the sustanablty constrant s bndng at t, an ncrease n V t 1 leads to a decrease n C 1 (V t 1 ) as well as V (V t 1 ). Snce ˆB ( ) s a decreasng functon, an ncrease n V t 1 must lead to an ncrease B t ; the movements n B t and V t are n opposte drectons. Thus B t follows the same cyclcal behavor as V t. 3.3 Repatraton of Government Debt In ths secton, we descrbe the behavor debt holdngs of domestc households and ts relaton wth respect to external debt. Note that n our model a verson of Rcardan equvalence holds. Ths can be seen va a perturbaton argument n a compettve equlbrum wth taxes. Consder a change n transfers to a partcular generaton that leaves the present value of the transfers unchanged together wth ts assocated adjustment n domestc debt that keeps government budget constrant hold. Snce the present value of transfers s unchanged, the consumpton and producton behavor of all the generatons remans unchanged. Ths mples that domestc debt and transfers are ndetermnate. Ths result s remnscent of a smlar result n Bhandar et al. (2013) an nfnte horzon model. Gven ths ndetermnacy, we focus on a decentralzaton where, n each generaton, the households wth lowest productvty do not want to access credt markets. In other 15

16 words, transfers to the young and the old are so that c 1 t,0 = Zy 1 t (1 τ l,t) + T t c 1 t,1 = P t+1 Knowng the above, we can wrte B t+1 = µ a t where a t s the asset holdngs by the young households of type that are born at t. Usng the budget constrant n (5) and the assumpton that asset taxes are not used n equlbrum, we can wrte B t+1 = µ a t = µ (c t,1 P t+1) = C t,1 c 1 t,1 = (1 ϕ1 t)c t,1 In the above formulaton, we have used the property that ndvduals wth lowest productvty are hand-to-mouth. The above mples that we can defne domestc debt as a functon of the state of the economy gven by the functon B(V t ) where V t s the government s payoff at t as B(V) = ψ 1 θ ψ + β 1 Y(V) C 1(V) (15) where C 1 ( ) and Y ( ) are the polcy functons n (P1) and we have used the defnton of ϕ 1 from (8). The above relatonshp ponts towards the evoluton of domestc debt over tme. Mechancally, when V decreases and sustanablty constrant s bndng, C 1 (V) and Y (V) both ncrease. Ths mples that B (V) s a decreasng functon of V. Therefore, for low values of V t, or epsodes that nvolve large reducton n value of external debt, aggregate consumpton of the old, C t,1 together wth share of consumpton gong to the more productve young households, 1 ϕ 1 t, must be hgh. Hence, total domestc debt must be hgh durng epsodes n whch foregn debt s repad. Intutvely, as establshed above for epsodes of large repayment of foregn debt, nequalty ncreases and so does after tax ncome of hghly productve households. Ths mples that the young productve households demand for savng ncreases. The government n return ncreases ts domestc debt ssuance, n response to hgh demand for savng from the young households. 16

17 We summarze ths dscusson n the followng Theorem: Theorem 9 Let B(V) be defned by (15). Then, B(V) s U-shaped n V. Furthermore, arg mn V B(V, s) = arg mn V V (V, s). 4 Poltcal Economy Model So far, we have consdered an envronment n whch polces are chosen by a planner that lacks commtment. In ths secton, we explctly consder a poltcal process through whch polces are determned. To do so we follow the probablstc votng model of Lndbeck and Webull (1987). We show that our man results extend to ths envronment. In partcular, there are cycles and fscal consoldatons concdes wth an ncrease n the share of domestc holdngs of government debt. 4.1 Poltcal Economy Game The poltcal economy game descrbed here s akn to that of Lndbeck and Webull (1987) (See also Farh et al. (2012) and Scheuer and Woltzky (2014) for applcatons to dynamc settngs). We assume that n each perod, poltcal competton occurs between two partes j = A and B. The tmng of the game s as follows: Stage 1. At ( the begnnng of the perod, each party ) j {A, B} proposes a polcy gven by σ t,j = δ t,j, τ a,t,j, P t,j, T t,j, τ l,t,j, B t+1,j, B t+1,j. Stage 2. Households vote for ther preferred polcy and the party wth majorty of the votes wns the electon. In case of a te, each party wns the electon wth probablty 1/2. Stage 3. Polces are mplemented. As n Lndbeck and Webull (1987), we assume that households decson to vote s affected by an addtve utlty shock that s ndependent of ther labor ncome or asset holdngs. In partcular, we assume that an old household of type s utlty from the electon of party j {A, B} s gven by u t 1,1,j + ε,o t,j where u t 1,1,j s the utlty of the old household under σ t,j whle ε,o t,j s a contnuous random varable. Smlarly, for a young household of type, the payoff from electon of party {A, B} s gven by u t,j + ε t,j where uj t, s the young household s utlty under polcy σ t,j and ε t,j s a contnuous random varable. We assume that ε t,j (ε,o t,j ) are random varables that are dentcally and 17

18 ndependently dstrbuted across young (old) households of type.note that the utlty of the young household depends on polces mplemented at t + 1 and thus, u t,j should be calculated usng expectaton of future polces. Ths create strategc nteracton between polcy decsons over tme. We assume that each party s objectve s to maxmze the probablty of wnnng an electon. For a gven polcy choce by each party ( σ A t, σb t ), the probablty of wnnng the electon by party A s gven by µ F o ( ) u t 1,1,A u t 1,1,B + µ F ( u t,a u t,b where F s the cumulatve dstrbuton for the random varable ε t,a ε t,b and F o s defned accordngly for the old. We assume that ε t,j (ε,o t,j ) s are [ dstrbuted ] such [ that ε t,a ε t,b ] and ε,o t,b ε,o t,a are dstrbuted unformly over the ntervals 1 1,, and 1 1,, 2α 2α 2ωα 2ωα respectvely. Addtonally, we assume that α s small enough so that u t,a u t,b s always nteror to the support of F a smlar property holds for u t,1,a u t,1,b. These assumptons mply that probablty of wnnng the electon for party A s gven by ω ( ) µ α u t 1,1,A u t 1,1,B + ) µ α ( u t,a u t,b We make the followng assumpton regardng the dstrbuton of shocks to preferences regardng the partes: Assumpton 10 The dstrbuton of ε t,j and ε,o t,j are such that α1 α N. Ths assumpton s the analog of Assumpton 4 n secton 3. It mples that polcy outcomes are redstrbutve towards households wth low ncome and low assets. To complete the descrpton of the poltcal economy game, we need to specfy the behavor of foregn credtors. As n the prevous secton, we assume that there s a compettve pool of foregn credtors who prce the arrow securtes dependng on the repayment polces of the soveregn. We assume that foregn credtors dscount rate s gven by (1 + r ) 1. We can thus defne the equlbrum of the poltcal economy game between foregn credtors, domestc households and the poltcans. Let h t represent the hstory of actons by all players up to perod t. Then, a subgame perfect equlbrum (SPE, henceforth) of the polcy game s descrbed by the followng: 1. A sequence of polces optmally chosen by each party at each perod t, σ t,j. Ths strategy s a functon that maps a hstory of the game, h t, to the set of polcy choces 18 )

19 n perod t. We refer to the the mplemented polcy sequence determned by the outcome of the electons descrbed above as ρ t. We refer to the sequence of polcy proposals, σ t,j, by σ. { } 2. Allocatons and prces x = c t 1,1, c t,0, y t, a t, r t, ˆr t consttute a compettve equlbrum from any perod t=0 onwards. A par (σ, x) s sad to be an SPE f t satsfes the above condtons. Note that, although we have assumed away aggregate shocks to the state of the economy, due to the poltcal uncertanty, agents nvolved n the polcy game need to calculate expectaton of future outcomes. Thus, the noton of compettve equlbrum should be adjusted for the sad expectatons. 4.2 Characterzaton of SPE Outocomes In ths secton, we start our analyss by characterzng the set of equlbra of the poltcal economy game. We focus on the symmetrc equlbra and derve necessary and suffcent condtons that allocatons resultng from the equlbra of the poltcal economy game must satsfy. The probablstc votng game between the two partes s symmetrc n that when the partes use the same strateges, they wn the electon wth probablty 1/2. In general, the party whch chooses polces that delver a hgher weghted average of the utltes gven by ω α µ u t 1,1 + α µ u t,0 (16) wll be the wnner of the electon. Ths mples that gven future strateges by future poltcans, any pure strategy Nash equlbrum of the electon game must nvolve symmetrc polcy proposal by the two partes. Furthermore, the outcome of the electon game n each perod must maxmze the objectve n (16). We can thus thnk of a fcttous planner n each perod that chooses polces as to maxmze (16). Thus, any equlbrum outcome of the polcy game s the outcome of a game between the fcttous planners n each perod who each maxmze (16). Note that ths does not rule out strategc nteracton among the fcttous planners due to the fact that each planner s based toward the lvng generaton. The followng lemma characterzes the set of allocatons that can be mplemented as a SPE of the poltcal economy game. 19

20 Lemma 11 Gven the nternatonal nterest rate r, ntal foregn debt, B 0, and an ntal dstrbuton of assets for the ntal old, { a } { } 1, allocatons c t 1,1, c t,0, y t, a t, prces {ˆr t, r t }, and t=0 government polces {B t, B t, τ l,t, τ a,t, T t, P t } t=0 are a SPE outcome f and only f: 1. The allocatons, prces and government polces are a compettve equlbrum wth taxes; 2. The allocatons satsfy the followng poltcal sustanablty constrant for all t 0 ω α µ u t 1,1 + α µ u t,0 V, where V s the value of the worst equlbrum and t s gven by the followng programmng problem: V = max c 0,c 1,y,τ l,t s.t. ω α µ u (c 1 ) + ( α µ u c 0, y ; θ ) (17) µ c 0 + c 1 + G = Z µ y θ (1 τ l ) u c,0 + u y = 0 c 0 = (1 τ l) Zy + T The proof for ths lemma can be found n the appendx. The dea s smlar to Char and Kehoe (1990) and Abreu (1988). We can thnk of the value of V as beng the analog of W n secton 3. It s mportant to note that by the worst SPE, we mean the subgame perfect equlbrum that provdes the lowest value to every fcttous planner n each perod. To derve the mplcatons for polces and allocatons assocated wth the poltcal economy game we need to specfy a selecton crteron to chose among the set of equlbrum outcomes n Lemma 11. We consder two alternatves. Frst, smlarly to what we dd n secton 3, we consder the best SPE outcome. (Where by best SPE outcome we mean the SPE outcome that maxmzes a welfare functon smlar to the one ntroduced n secton 3.) Second, we consder a selecton crteron n the sprt of the canoncal Eaton and Gersovtz (1981) model of soveregn default. We are gong to show that n both cases - wth some mnor qualfcatons - the man conclusons derved n secton 3 reman vald. 4.3 Best SPE Outcome We now turn to characterze the best SPE outcome wth log-log utlty. We rank outcomes accordng to the welfare functon that we ntroduced n the secton 3 that attaches a Pareto 20

21 weght of ˆβ t α to an agent of type born at t 0. Note that the objectve s tme-consstent due to geometrc dscountng. Under our preference specfcaton (8.1), the welfare functon (10) can be wrtten solely n terms of aggregate allocatons and ntal penson payments as β/ ˆβ ( ) µ log (1 τ a,0 )a 0 + P 0 + ˆβ t [log C 0t + Ω (Y t ) + β log C 1t+1 ], (18) t=0 where Ω (Y) = ψ log (1 Y) (1 + ψ + β)h (Y). The problem for the planner at t = 0 s then to choose an aggregate allocaton {C 0t, C 1t, Y t } t=0 and tme zero polces {P 0, τ a,0, δ 0 } that maxmze (18) subject to the present value verson of the consoldated budget constrant for the country t ( ) 1 t 1 + r [ZY t C 0t C 1t G] B 0 δ 0 (19) and the sequence of poltcal sustanablty constrants from t = 1 and onward, ω [log C 1t + H (Y t 1 )] + [log C 0t + Ω (Y t ) + β log C 1t+1 ] V, (20) and for t = 0, ω ( ) µ α log (1 τ a,0 )a 0 + P 0 + [log C 0t + Ω (Y t ) + β log C 1t+1 ] V. (21) The man result of ths secton s that the best SPE outcome has cycles smlar to the ones n secton 3. Lettng v t be the average utlty for a generaton, v t = log C 0t + Ω (Y t ) + β log C 1t+1 and denotng by v ss ts statonary value, we have that: Proposton 12 The best SPE outcome of the poltcal economy game has cycles. The equlbrum outcome path s such that when v t < v ss then v t+1 > v ss and vce versa. Perods n whch v t s below v ss are characterzed by ) large reducton n total government debt, ) hgh ncome nequalty, ) f β s suffcently low foregn debt s reduced. The opposte happens when v t s above v ss. The dynamcs of the best SPE outcome s then consstent wth the cycles we descrbed n secton 3. When total ndebtedness s low and utlty for current generaton s hgh, we 21

22 observe an ncrease n government debt, especally foregn debt, and ncome nequalty s low. Ths ncrease n ndebtedness translates nto low utlty for future generatons and hgh ncome nequalty. To satsfy the poltcal sustanablty constrant, (20), the current government must reduce the resources next perod that are commtted to foregn lenders, B, and future old, C 1, so that future government does not have an ncentve to default gven the large nequalty. [to be completed] 4.4 Markov Equlbrum We now consder a dfferent selecton n the sprt of the standard Eaton and Gersovtz (1981) model. We focus on equlbra that have the followng propertes: ) strateges are the same after two hstores wth no default f the nherted debt s equal n the two hstores, ) f the government defaults trggers reverson to worst equlbrum (we could have stochastc re-entry, nothng would change). We say that the government defaults on promses made by prevous governments f t does not repay nherted foregn debt or t taxes assets of the ntal old above a certan level exogenously specfed (ths wll not matter other than for perod zero). In the appendx we consder the case n whch there s a reverson to the worst equlbrum also when the current government reneges on the penson promses made by prevous government. Formally, we make our selecton operatonal by settng up the equlbrum recursvely, wth state varable (B, z) where B = ( B, { a }) and z {0, 1} records f prevous government defaulted n the past. We adopt the conventon that z = 1 f the government defaulted n the past. Gven our selecton, f z = 1 then value for the current government s V AUT for all B, V (B, 0) = V AUT. Takng as gven the decson of the future governments, denoted by a bar, the value functon for the government that nherted a state (B, 0) s gven by V (B, 0) = max {v (B), V AUT } (22) where the value v s the value assocated wth honorng debt oblgatons and t s gven by v (B) = max π=(p,c 0,Y,B ) ω ( ( ) µ log a + P + log C 0 + ˆΩ (Y) + β log µ a 0 + P ( B )) (23) 22

23 subject to ( ) µ a + P + C 0 + B + G ZY r B (24) v ( B ) V (25) a + P ( ( B ) = ϕ (Y) µ a + P ( B )) (26) where ˆΩ (Y) = Ω (Y) βh(y), P and v are the polcy rule and the value functon for the future government, and ϕ (Y) = 1 + s the consumpton share for agent. ψ θ ψ + β 1 Y The constrant (24) s smply the consoldated budget constrant for the country n sequental form. The constrant (25), guarantees that next perod government has no ncentve to default. The current government leaves a state to next perod government such that t fnds not optmal to default. Ths s not a restrcton on government actons. In fact, suppose to the contrary that the current government chooses B such that v (B ) < V AUT. Then t follows that the prce of foregn debt equals zero and so no resources can be rased from foregn lenders. Moreover, snce there s a default next perod, prvate agents optmalty mples that a = 0 for all. Hence, assumng that B > 0 we have that v < V, contradctng optmalty for the current government. Fnally, constrant (26) ensures that assets holdngs { a } are consstent wth optmalty of the households savng decsons. Wth log-preferences, ths amount to assume that next perod consumpton share of type agent s equal to current consumpton share ϕ (Y). An equlbrum s then a fxed pont of P ( B P, v ) = P (B) and v ( B P, v ) = v (B) for all B such that v (B) V AUT (27) wherep and v are the polcy rule and the value assocated wth the problem n (23). Frst order approach.the presence of (26) and the large dmensonalty of the state B makes the characterzaton of the Markov equlbrum as stated n (23) cumbersome. To provde a characterzaton, we are gong to formulate the problem for the current government usng a frst order approach. To ths end, notce that optmalty for the current 23

24 government gven an nherted { a } requres that 1 = ω C 0 µ 1 (a + P) = v (B) B. (28) Hence, the current government can control the consumpton receved by current young next perod by choosng B that satsfes (28). Explotng the nsght n (28), we consder the followng auxlary problem: w ( ˆB ) = max log C C 0,Y,C 0 + Ω (Y) + β log ( C ) 1 1,B (29) subject to ˆB + C 0 + G ZY + B 1 + r ω [ H (Y) + log ( C ( 1)] + w B + C 1) VAUT µ ω ϕ (Y) C = w ( B + C ) 1 1 The value w s the maxmal value for generaton born n the current perod gven that resources ˆB = B + C 1 have been commtted (by prevous government) to foregn lenders and old households subject to budget feasblty, the poltcal sustanablty constrant for the government next perod and a constrant that guarantees that next perod government fnds optmal to choose the promsed allocaton to next perod old. To see why ths s the case, notce that optmalty and envelope condton mply that 1 C 0 = w ( ˆB ) = µ ω ϕ (Y) C 1 = µ ω a 0 + P and so the allocatons generated by (29) satsfy (28). The problem at t = 0 s only slghtly dfferent because ntal condtons do not necessarly satsfy (28). We can wrte: ˆv (B) = max ω P ( ) ( ) µ log a + P + w µ a + P + B. (30) In the appendx we show that outcomes obtaned from the polcy rules assocated wth (29) and (30) are a MPE outcome. We can then consder (29) to characterze the equlbrum outcome. 24

25 It s partcularly smple to characterze the equlbrum outcome assumng that penson payments cannot be negatve. Assumpton 13 P 0 The next proposton characterzes the polcy functons n (29) under ths assumpton. Proposton 14 Under Assumpton 13, the poltcal sustanablty constrant n problem (29) s always bndng. Moreover, the polcy functons assocated wth the problem are such that: ) ˆB ( ˆB) s decreasng, ) Y( ˆB) s ncreasng, and ) f β s suffcently small B ( ˆB) s decreasng. Part ) of the states that total debt oblgatons for the next perod, ˆB, are decreasng n current oblgatons, ˆB. Ths mmedately mples that the equlbrum outcome path has cycles. When nherted oblgatons, ˆB t, are above ther statonary value, ˆB ss, next perod are gong to be below ˆB ss. The opposte happens when ˆB t < ˆB ss. Part ) and ) mples that when the current government s gong through a perod of fscal consoldaton by reducng total oblgatons passed to the future government then current government must tolerate hgh ncome nequalty, foregn debt decreases and the share of soveregn debt held by domestc resdent s ncreasng. The ntuton for ths result s the same as the one developed n secton 3. It s nterestng to notce that austerty-lke epsodes happens along the equlbrum outcome path when polces are chosen by governments that cares only about the welfare of current generatons. Even n ths case t s optmal for the government to reduce foregn debt and tolerate large nequalty. The current government prefers to run austerty-lke measures than defaultng on the oblgatons chosen by prevous government. Renegng on these promses wll result n a collapse n domestc credt market whch wll further lower the utlty of the current government. 5 Extensons and Dscusson 5.1 The Role of Assumptons In ths secton, we dscuss the role of varous assumpton underlyng our results. The Role of Imperfect Redstrbuton. A crucal assumpton n our analyss s the nablty of the government to perfectly redstrbute resources among households. To see ths, suppose that nstead of an affne tax schedule, the government had access to ndvdual dependent taxes and transfers. That s, suppose that transfers to the young and old households can depend on households productvtes. Ths would mply that 25

26 the government can acheve ts desred level of redstrbuton, namely that consumpton among households wth dfferent productvtes are allocated so that α u t,a ) = αj u j t,a ) for a = 0, 1. In other words, dstrbuton of consumpton s ndependent of output and hence constant over tme. As a result, the sustanablty constrant n (20) can be wrtten as β [ log C1 + H ] + V ˆβ W where H s the payoff to the government of havng the desred level of nequalty and snce dstrbuton of consumpton s constant over tme, s constant. Ths, n turn, mples that once the sustanablty constrant bnds, the value of consumpton for the old and contnuaton value, V s ndependent of the state of the economy. Ths result holds n most models wthout commtment; see for example Thomas and Worrall (1988) among many others. Ths mples that mperfect redstrbuton plays a crucal role n our man result. The Role of Preferences. One possblty s that our result s due to strong ncome effects mpled by log-log preferences. It s possble that the decreasng pattern of nequalty as a functon of promsed value, V, s because as V ncreases, ncome effect mples that output should declne whch n turn mples lower nequalty. Whle the problem wth general preferences cannot be characterzed analytcally, here, we consder GHH preferences of the form u(c, l) = log(c v(l)) where v(l) = ψl 1+1/ɛ /(1 + 1/ɛ), where ɛ > 0 s the Frsch elastcty of labor supply. Wth GHH preferences, the ncome effect s not present at the ndvdual level. As we wll show, however, the same result holds. In the Appendx, we show va numercal smulatons that smlar results hold for more general balanced-growth-preferences. Wth GHH preferences specfed above, a result smlar to the log-log case holds and government objectve s gven by 4 ( ( )) U p (C 0, C 1, Y) = log C 0 v + β log C 1 + (1 + β) Yˆθ where ˆθ s a weghted average productvty measure gven by N ˆθ = ( µ j θ j) 1+ɛ j=1 4 We establsh these formulas n the Appendx??. 1 1+ɛ N α µ log ϕ t =1 26