29 August Abstract. This note surveys some empirically implementable indices of the sustainability of a country s scal- nancial-monetary program

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1 Measuring Fiscal Susainabiliy Willem H. Buier Professor of Inernaional Macroeconomics Universiy of Cambridge and Consulan, European I and II Deparmens, Inernaional Moneary Fund 29 Augus 995 Conens ITRODUCTIO SOME BASIC ACCOUTIG FISCAL SUSTAIABILITY IDICATOR #: THE PUBLIC DEBT-GDP RATIO PRIMARY GAPS FISCAL SUSTAIABILITY IDICATOR #2: THE OE-PERIOD PRIMARY GAP LOG-RU SOLVECY FISCAL SUSTAIABILITY IDICATOR #3: THE PERMA- ET PRIMARY GAP FISCAL SUSTAIABILITY CRITERIO # 4: THE DISCOUTED PUBLIC DEBT FISCAL SUSTAIABILITY CRITERIO # 5: THE LOG- RU IFLATIO RATE IMPLIED BY THE FISCAL-FIACIAL PLAS Absrac. This noe surveys some empirically implemenable indices of he susainabiliy of a counry s scal- nancial-moneary program. ITRODUCTIO. The radiional nancial performance crieria (governmen budge de ci limis, ceilings on domesic credi (expansion) by he banking sysem, ceilings on credi exended o he non- nancial public secor, oors on inernaional reserves) ha are o be observed by counries under IMF programs are inherenly myopic. Recen aemps o adjus, correc and exend hese measures can all be inerpreed as moves o ake a longer-erm view of scal, nancial and moneary policy condiionaliy. This change c Willem H. Buier

2 Measuring Fiscal Susainabiliy c Willem H. Buier 2 of approach is moivaed by a recogniion of wo facs. Firs, even if he privae secor were myopic, longer-run scal- nancial and moneary dynamics will ineviably work heir way ino fuure shor-run economic performance. Today s long-run becomes omorrows shor run. Second, and probably even more imporanly, privae agens, far from being myopic, are forward-looking in wage and price behavior and in he posiions hey assume and he prices hey are willing o pay in domesic and inernaional nancial marke. This means ha even shor-run performance depends on curren and pas anicipaions of medium-and long-erm behaviour of policy insrumens and variables exogenous o he economy in quesion. The long-run cass is shadow forward ino he presen hrough anicipaing acions of raional, calculaing privae agens. If a longer-run perspecive is o be aken (even if we are only or mainly ineresed in shor-erm performance), he righ place, indeed he only place, o sar is he comprehensive balance shee or presen value budge consrain of he consolidaed public secor. This will permi us o hink sysemaically abou hree ses of issues cenral o he Fund s concerns. Firs, he issue of governmen solvency or sovereign defaul. Second, he issue of nancial crowding ou of privae saving and invesmen by govermen borrowing and hird, he moneary (and hence he in aion) implicaions of alernaive scal- nancial-monery programs. 2. SOME BASIC ACCOUTIG. We sar in equaion from he basic single-period budge ideniy (sources and uses of funds) of he combined public secor or CPS, ha is, consolidaed (or combined) non- nancial public secor (FPS) and public secor nancial insiuions (PFI). The laer include he cenral bank and all oher public secor nancial agencies such as developmen banks, impor-expor banks and publicly owned commercial banks. C T E F + A PRIV +i B d +i E (B R ) () B d B d + E (B B )+H H E (R R ) C is he nominal value of governmen consumpion spending in period : T is he nominal value of axes ne of ransfers and subsidies in period : I includes, wih a negaive sign, social securiy healh and reirmen bene s and public secor pension bene s. E is he nominal spo exchange rae (he domesic currency price of foreign exchange in period : is he foreign currency value of foreign aid. F is he nominal value of he gross cash ow from he public secor capial sock in period :

3 Measuring Fiscal Susainabiliy c Willem H. Buier 3 A is he nominal value of gross domesic capial formaion in he public secor in period : PRIV is he nominal value of privaizaion proceeds in period : i is he nominal ineres rae on domesic currency denominaed public deb in period : B d is he nominal face value of he ne sock of domesic currency-denominaed ineres-bearing liabiliies of he consolidaed FPS and PFI, including arrears, ousanding a he beginning of period : This includes he ne non-moneary nancial liabiliies of he cenral bank vis-a-vis he privae secor and he foreign secor. i is he nominal ineres rae on foreign currency denominaed public deb in period : B is he foreign currency face value of he ne sock of foreign currencydenominaed ineres-bearing liabiliies of he consolidaed FPS and PFI, excluding o cial foreign exchange reserves, bu including arrears, ousanding a he beginning of period : This includes he ne non-moneary nancial liabiliies of he cenral bank ha are denominaed in foreign exchange. R is he foreign currency value of he sock of o cial inernaional reserves (denominaed in foreign currency) a he beginning of period : H is he nominal sock of non-ineres bearing base money or high-powered money ousanding a he beginning of period : We also de ne he following: H CU + RR (2) P (K K ) A DEP P PRIV (3) P k DEP P ± K (4) F P ½ K (5) CU is he nominal sock of domesic currency in he hands of he public a he end of period : RR is he nominal value of bank reserves held wih he cenral bank a he end of period : P is he domesic GDP de aor in period : K is he public secor capial sock a he end of period valued a curren reproducion cos, ha is, measured in physical unis, which are assumed o be real GDP unis. The nominal reproducion cos of public secor capial is herefore

4 Measuring Fiscal Susainabiliy c Willem H. Buier 4 assumed o be he GDP de aor, alhough a capial producion cos index disinc from he GDP de aor could be added wihou complicaions. DEP is he nominal value of public secor capial consumpion or depreciaion in period : P k is he domesic currency value of he price obained for a uni of public secor capial privaized in period : ± is he proporional rae of physical depreciaion of he public secor capial sock in period : ½ is he gross real cash (or nancial) rae of reurn on public secor capial in period : The curren or consumpion accoun primary surplus (ha is, he non-ineres, non-invesmen, non-privaizaion) surplus of he consolidaed public secor and cenral bank, S c,isde nedinequaion6 S c T +E C (6) The convenionally de ned primary (non-ineres) surplus of he consolidaed public secor and cenral bank, S, is de ned in equaion 7. Unlike S c i includes capial formaion and privaizaion. S S c + F + PRIV A (7)! P S c k + F [P (K K )+DEP ]+ P PRIV Public secor gross dissaving by he consolidaed public secor and cenral bank or he consumpion accoun de ci of he consolidaed public secor and cenral bank, D c,isde nedinequaion8. D c S c (F DEP )+i B d +i E (B R ) (8) The convenionally de ned nancial de ci or borrowing requiremen of he CPS, D,isde nedinequaion9 P k D D+A c DEP PRIV (9)! P D c k + P (K K ) P PRIV P k S +i B d +i E (B R ) From equaions and 3 o 5 we obain equaion 0

5 Measuring Fiscal Susainabiliy c Willem H. Buier 5 C T E +[ P P k P k ]PRIV +i B +i E (B R ) (F DEP ) P (K K )+B d B +E d [B R (B R )] + H H (0) We also de ne he following. ¾ (H H )=(P Y ) () ¾ is seigniorage as a fracion of GDP, ha is he change in he nominal sock of base money divided by nominal GDP. B B d + E (B R ) (2) B is he nominal face value (measured in domesic currency) of he oal ne sock of non-moneary nancial deb of he CPS a he end of period : ¹B B P K (3) ¹B is he nominal face value of he oal ne sock of non-moneary angible liabiliies of he governmen a he end of period. I subracs he public secor capial sock valued a curren reproducion cos from he ne sock of non-moneary nancial liabiliies. In wha follows, lower-case characers sand for he corresponding upper-case characer as a fracion of GDP. Leing Y denoe real GDP in period, we herefore have: c C =(P Y ); he public secor consumpion-gdp raio in period : T =(P Y ); axes ne of ransfers as a fracion of GDP in period : n E =(P Y ); foreign aid as a fracion of GDP in period : dep DEP =(P Y ); public secor capial depreciaion as a fracion of GDP. f F =(P Y ); public secor capial income as a fracion of GDP. priv PRIV =(P Y ); privaizaion receips as a fracion of GDP in period : b d B d =(P Y ); he raio of he ne sock of ineres-bearing deb denominaed in domesic currency a he end of period o period GDP: b E B =(P Y ); he raio of he ne sock of ineres-bearing deb denominaed in foreign currency a he end of period o period GDP: ½ E R =(P Y ); he raio of he sock of foreign exchange reserves a he end of period o o period GDP: s c S=(P c Y ); he curren or consumpion accoun primary surplus as a fracion of GDP. s S =(P Y ); he primary surplus as a fracion of GDP.

6 Measuring Fiscal Susainabiliy c Willem H. Buier 6 d c D=(P c Y ); CPS gross dissaving or he CPS curren accoun de ci, as a fracion of GDP. d D =(P Y ); he CPS nancial de ci or borrowing requiremen as a fracion of GDP. b B =(P Y ); he nominal value of he oal ne sock of non-moneary nancial liabiliies of he CPS a he end of period as a fracion of period GDP: ¹ b ¹B =(P Y ); he nominal value of he oal ne sock of non-moneary liabiliies of he CPS a he end of period ; :asafracionofperiodgdp: We also de ne he following: ¼ (P =P ) ; he rae of in aion in period : g (Y =Y ) ; he rae of growh of real GDP in period : ² (E =E ) ; he rae of depreciaion of he nominal exchange rae in period : r [( + i )=( + ¼ )] ; heperioddomesic real ineres rae. We now can rewrie he ideniy in equaion 0 as equaion 4 or 5 below. b ( + ¼ )( + g ) b ² + ( + ¼ )( + g ) (b ½ )+d ¾ (4)! +r ( + ² )( + i! ) ( + i ) b b + (b ½ +g ( + ¼ )( + g ) ) s ¾ (5) The erm ³ (+² )(+i ) (+i ) (+¼ )(+g ) (b ½ ) correcs for possible deviaions from uncovered inernaional ineres pariy. This is necessary because in he erm ³ +r b +g, all deb has he domesic real ineres rae impued o i. Ideniies 4 and 5 follow he unhelpful bu common pracice of lumping ogeher curren ransacions and capial ransacions in he primary de ci, s,andinhe nancial de ci, d. I would be concepually cleaner o use he alernaive represenaions of equaions 4 and 5 given in equaions 6 and 7 below. oe ha in equaion 6, (minus) ne public secor capial income (f dep ) is grouped ogeher wih ineres paymens [i B p + i E (B R )]=(P Y ), while privaizaion and (he negaive of) ne public secor capial formaion are reaed as nancing iems on a par wih explici borrowing. ¹ b ( + ¼ )( + g ) ¹ b + d c (6) P P k! ¼ + P k priv ( + ¼ )( + g ) k ² + ( + ¼ )( + g ) (b ½ ) ¾

7 Measuring Fiscal Susainabiliy c Willem H. Buier 7 Where d c s c i + ( + ¼ )( + g ) b i! ( + ² ) + ( + ¼ )( + g ) (b ½ ½ ± ) +g and k s c c n ¹ b! +r ¹ b s c (7) +g P P k!! r (½ + P k priv + ± ) ( + ² )( + i! ) ( + i ) k + (b ½ +g ( + ¼ )( + g ) ) ¾ oe from equaion 7 ha hree concepually di eren valuaions of public secor capial are relevan for he evoluion of he public secor s sock of non-moneary deb. The rs is he curren reproducion cos of a uni of public secor capial, assumed o be equal o P. This eners he de niion of ne non-moneary liabiliies as a fracion of GDP, ¹ b [B d + E (B R ) P K ]=(P Y ). The second is he price obained by he governmen for a uni of privaized public secor capial, P k. Equaions6 and 7 emphasize he obvious poin ha privaizaion only reduces he rae of increase in he governmen s ne non-moneary liabiliies if he privaizaion price exceeds he curren reproducion cos of governmen capial. The hird is he coninuaion value of a uni of public secor capial in he public secor, V. If he public secor capial sock is expeced o remain in he public secor forever, he coninuaion value in he public secor of a uni of public secor capial is given by equaion 8 (if he discoun raes i +j are reaed as non-sochasic). 2 V = lim E X! ky +i +j! P +j (½ +j ± +j ) (8) Presumably, wih a raional privae secor, P k canno exceed he presen discouned value of he quasi-rens he capial is expeced o earn afer privaizaion. 2 If he objecive of he governmen s privaizaion policy were o maximize is ne worh, V would, under risk-neuraliy, be deermined from he following recursion relaion: ( )V = P (½ ± ) +i + Max E [ V+, P + k +i ] If he public secor capial sock is expeced o remain in he public secor forever, equaion ( ) implies equaion ( ) (if he discoun raes i +j are reaed as non-sochasic). ( )

8 Measuring Fiscal Susainabiliy c Willem H. Buier 8 Thus he value o he governmen of a uni of public secor capial ha is expeced always o remain in he public secor is he presen discouned value of is expeced fuure quasi-rens in he public secor. The coninuaion value of he public secor capial sock in he public secor does no show up direcly (as V ) in he budge consrains, bu he sream of quasi-rens whose presen discouned value i is, does appear. 3. FISCAL SUSTAIABILITY IDICATOR #: THE PUBLIC DEBT-GDP RATIO. While in he never-never land of pure heory, unbounded deb-gdp raios are no inconsisen wih governmen solvency and susainable policy, de faco deb-gdp raios will of course have o remain bounded. Especially a he beginning of a sabilizaion program, a governmen rying o esablish or regain credibiliy, may use is a (sequence of) declining public deb-gdp raio(s) as a signal of is abiliy o mainain long-run solvency. Equaions 4 or 5 describe wha will happen o he deb-gdp raio during he nex period. Equaion 4 requires as daa inpus he growh rae of nominal GDP ((+¼ )(+ g ) ), he iniial oal public deb-gdp raio (b ), he proporional rae of depreciaion of he nominal exchange rae (² ), he iniial ne foreign deb-gdp raio (b ½ ), he nancial surplus of he public secor (d ) and seigniorage as a proporion of GDP (¾ ). Equaion 5 requires as daa inpus he growh rae of real GDP (g ), he domesic real ineres rae (r ), he iniial oal public deb-gdp raio (b ), he proporional rae of depreciaion of he nominal exchange rae (² ), he iniial ne foreign deb- GDP raio (b ½ ), he growh rae of nominal GDP (( + ¼ )( + g ) ), he foreign nominal ineres rae (i ), he domesic nominal ineres rae (i ), he primary surplus of he public secor (s ) and seigniorage as a proporion of GDP (¾ ): Pifalls: he nancial de ci-gdp raio and he primary de ci-gdp raios can be disored (made o look smaller in he shor-run a he expense of being made larger in he long run) by he following ricks: () Speeding up privaizaion receips, if he privaized asses would have yielded posiive fuure ne cash ow o he governmen had hey remained in he public secor (ha is, if hey had a posiive coninuaion value in he public secor). V = l m i! E P Q ³ k +i +j P +j (½ +j ± +j )+ l i Q j=0 ³ m! E laive bubbles are ruled ou, l i m! E +i +j V ++j =0and equaion ( ) expresses he value o he governmen of a uni of public secor capial ha is expeced alway o remain in he public secor as he presen discouned value of is expeced fuure quasi-rens in he public secor. Q ³ j=0 +i +j V ++j If specu- col col

9 Measuring Fiscal Susainabiliy c Willem H. Buier 9 (2) Cuing back governmen capial formaion, if he presen discouned value of he fuure ne cash ow o he governmen from hese invesmen projecs would have exceeded he cos of he projecs. To avoid hese problems, i may be preferable o look a he behavior (in he pas and anicipaed for he nex few years) of he public secor non-moneary nancial deb ne of he public secor capial sock valued a curren reproducion cos, ¹ b, given in equaions 6(5) and 7 raher han a he non-moneary nancial deb b, given in equaions 4 and PRIMARY GAPS. For noaional simpliciy, we now de ne he augmened primary surplus-gdp raio, ~s, as follows: ~s s [i ( + ² )+² i ] (b ½ ( + ¼ )( + g ) )+¾ (9) The augmened primary surplus herefore adds o he convenional primary surplus boh seigniorage (he resources appropriaed by he governmen by prining non-ineres-bearing base money) and he excess of he cos of borrowing by issuing domesic currency denominaed deb over he cos of borrowing by issuing foreign currency denominaed deb imes he ne sock of foreign deb. Given he iniial value of he oal non-moneary governmen deb-gdp raio a he beginning of period, b, he arge value of he deb-gdp raio periods laer, b +, he projeced fuure one-period real ineres raes during he nex periods, r +j, j =0; :::;, and he projeced growh raes of real GDP during he nex periods, g +j, j =0;:::;, he consan augmened primary surplus o GDP raio, ~s R,hawillachieveheargeisgivenby: 2 ~s X R(b b + )= 4 ky +g+j! 3 2 Y 5 4b j=0 +g+j! b (20) We shall refer o ~s R as he required -period (augmened) primary surplus-gdp raio. Wih consan real -period ineres raes r and consan -period growh raes of real GDP g, he required -period primary surplus-gdp raio simpli es o: ~s R (b b + )= ³ r g ( + g ) ³ +g +r 2 +g 4b +r! 3 b + 5 (2)

10 Measuring Fiscal Susainabiliy c Willem H. Buier 0 If he arge deb-gdp raio is he same as he iniial deb-gdp raio, equaion he required -period primary surplus-gdp raio simpli es o 2 ~s X R (0) = 4 ky +g+j! Y +g+j 4 j=0! 3 5b (22) Wih a consan -period real ineres rae r and a consan -period growh rae of real GDP g, he required -period primary surplus-gdp raio for his case becomes ³ r ~s g R(0) = +g When =;equaion 23 simpli es o b (23) ~s R(0) = (r g ) b (24) +g We also de ne he acual -Period (augmened) primary surplus-gdp raio, ~s A, o be ha consan augmened primary surplus-gdp raio whose presen discouned value over he nex periods is he same as he presen discouned value of he acually planned or expeced primary surplus-gdp raio over he nex periods, ha is, 2 ~s X A () = 4 ky +g+j! Y +g+j 4 j=0! 3 5b (25) When he real ineres rae and he real growh rae are consan, equaion 25 simpli es o 26 ³ r ~s g! X +g k A = ( + g ) ³ +g +r k= +r ~s +k (26) The -period primary gap (see Blanchard e. al. [990]) in period ; GAP, is de ned as he excess of he rquired -period (augmened) primary surplus-gdp raio, ~s R, over he acual -period (augmened) primary surplus -GDP raio, ~s A : GAP ~s R (b b + ) ~s A (27)

11 Measuring Fiscal Susainabiliy c Willem H. Buier Given an iniial deb-gdp raio and a arge deb-gdp raio for periods hence, he -period primary gap can be calculaed using forecass for real ineres raes, real growh raes and acual planned or expeced augmened primary surplus-gdp raios. oe ha primary gaps de ned wih reference o he public secor non-moneary nancial deb ne of he value of he public secor capial sock, ¹ b,canbede ned exacly analogously. The relevan primary surplus would be ~s c ;he augmened curren or consumpion accoun primary surplus (as a fracion of GDP), de ned by ~s c s c [i ( + ² )+² i ] (b ½ ( + ¼ )( + g ) )+¾ (28) Two paricularly simple special cases of he -period primary gap provide he second and hird scal indicaors. 5. FISCAL SUSTAIABILITY IDICATOR #2: THE OE-PERIOD PRIMARY GAP. When =and he iniial deb-gdp raio is he same as he arge deb-gdp raio a he end of he period, he primary gap calculaion simpli es o:! GAP ~s R(0) ~s r g A = b ~s (29) +g oe ha he calculaion of 29 does no require any forecass oher han hose going ino he calculaion of he curren real ineres rae and curren growh rae of real GDP. GAP, he one-period primary gap in period is he excess of he augmened primary surplus-gdp raio ha sabilizes his period 0 sdeb-gdpraio over he acual curren augmened primary surplus-gdp raio. Apar from he problems arising from he reamen of public secor capial formaion and privaizaion, he one-period primary gap may give a disored picure of he amoun of adjusmen ha would reasonably be required for wo furher reasons. The rs is ha he acual curren primary surplus may be a eced by ransiory (e.g. cyclical ) increases or reducions in public secor revenues and non-ineres expendiures. A cyclical correcion may herefore be in order. The second is ha he curren real ineres rae and growh rae of real GDP may be unrepresenaive of heir respecive long-run expeced average values. This sugges need for he longer-run perspecive adoped in he nex secion. 6. LOG-RU SOLVECY. When he long-run ineres rae is above he long-run growh rae of GDP, ha is if Q ³ lim +g+j! j=0 =0, he following governmen solvency consrain is assumed o hold for an economy wihou a nie erminal dae

12 Measuring Fiscal Susainabiliy c Willem H. Buier 2 Y lim! j=0 +g+j! b + =0 (30) When equaion 30 holds, he presen value budge consrain given in 3 applies o he governmen. This saes ha he curren face value of he deb canno exceed he presen discouned value of fuure primary surpluses and seigniorage. 3 X b = lim! ky +g+j! ~s +j (3) We can de ne he required permanen (augmened) primary surplus-gdp raio, ~s R as follows: 2 ~s X R = lim! 4 ky +g+j! 3 5 b (32) When he real ineres rae and he growh rae of real GDP are consan, equaion 32 becomes r ~s R = g! +g b (33) The required permanen (augmened) primary surplus-gdp raio is he consan (augmened) primary surplus GDP raio ha, if mainained inde niely, would ensure governmen solvency. I is also he consan primary surplus-gdp raio ha will ensure ha, ulimaely, he deb-gdp raio does no exceed any nie upper limi (including is curren value b ). 7. FISCAL SUSTAIABILITY IDICATOR #3: THE PERMAET PRIMARY GAP. The permanen primary gap, GAP, was proposed in Buier [983, 985 and 990a]. I measures he magniude of he permanen correcion required o be made o he acual curren and fuure planned augmened primary surplus-gdp raios in order o ensure governmen solvency. This measure was also proposed in Blanchard [990] and in Blanchard e. al. [990]. I is given by he excess of he required permanen primary surplus-gdp raio over acual permanen primary surplus-gdp raio: 3 oe ha, when he long-run ineres rae exceeds he long-run growh rae, governmen solvency is consisen even wih unbounded (and forever rising) deb-gdp raios as long as, ulimaely, he public deb grows a a rae less han he ineres rae.

13 Measuring Fiscal Susainabiliy c Willem H. Buier 3 GAP = ~s R ~s A (34) 2! X ky 3 2! 3 +g+j X ky +g+j = lim! 4 5 4b ~s +j 5 When he real ineres rae and he growh rae of real GDP are consan, becomes GAP = r g +g! [b X +g k= +r! k ~s +k] (35) The calculaion of he permanen primary gap requires forecass of he long-run real ineres rae and he long-run real growh rae and of he fuure primary surpluses ha would maerialize under curren spending and revenue-raising plans. The lazy man s (or myopic) alernaive, measured by MGAP, subsiues he curren augmened primary surplus-gdp raio, ~s, for he acual permanen augmened primary surplus-gdp raio, ha is r MGAP = g! +g b ~s (36) This is he same as he one-period gap, excep for he subsiuion of he long real ineres rae for he curren real ineres rae and he subsiuion of he long-run growh rae of real GDP for he curren growh rae of real GDP. 8. FISCAL SUSTAIABILITY CRITERIO # 4: THE DISCOUTED PUBLIC DEBT. The governmen solvency consrain Q lim! j=0 ³ +g+j Q b + lim! j=0 ³ B + +i +j =0, suggess ha he behavior of he discouned public deb PDV(b ) (he presen discouned value of he public deb discouned o a xed iniial dae, 0,say),can serve as a useful indicaor of poenial rouble. oe ha he discouned deb rises if and only if he augmened primary surplus is negaive. If he discouned deb has been rising signi canly and looks like coninuing o do so in he foreseeable fuure, good reasons mus be given why his upward rend will evenually be reversed. The measure is given by PDV(b ) o Y j=0 +i o +j! B (37)

14 Measuring Fiscal Susainabiliy c Willem H. Buier 4 9. FISCAL SUSTAIABILITY CRITERIO # 5: THE LOG-RU IFLATIO RATE IMPLIED BY THE FISCAL-FIACIAL PLAS. This is a sandard nancial programming exercise. For a reference, see e:g. Buier [993], Anand and van Wijnbergen [989] and Buier [990b].

15 Measuring Fiscal Susainabiliy c Willem H. Buier 5 REFERECES. Anand, Riu and Sweder van Wijnbergen [989], "In aion and he Financing of Governmen Expendiure: an Inroducory Analysis wih an Applicaion o Turkey", The World Bank Economic Review, 3, o., pp Blanchard, Olivier [990], "Suggesions for a new se of scal indicaors", OECD, Deparmen of Economics and Saisics Working Papers, o. 79, April., Jean-Claude Chouraqui, Rober P. Hageman and icola Soror, "The susainabiliy of scal policy: new answers o an old quesion", OECD Economic Sudies o. 5, Auumn 990. Buier, Willem H. [983], "The heory of opimum de cis and deb", in Federal Research Bank of Boson, Conference Series o. 27, The Economics of Large Governmen De cis, Ocober 983, pp. 4-69, reprined in W.H. Buier, Macroeconomic Theory and Sabilizaion Policy, Mancheser Universiy Press, [985], "A guide o public secor deb and de cis", Economic Policy, Ocober, pp [990a], "The arihmeic of solvency", In W.H. Buier, Principles of Budgeary and Financial Policy, MIT Press, pp [990b], "Some houghs on he role of sabilizaion and srucural adjusmen in developing counries", in W.H. Buier, Principles of Budgeary and Financial Policy, MIT Press, pp [993], "Consisency checks on he design of scal, nancial and moneary policy", Mimeo, LAC, IBRD, Ocober