Part I Demand-Led Growth in the Classical Approach

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1 Par I Demand-Led Growh in he Classical Approach

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3 Public Deb and Aggregae Demand: Some Unconvenional Analyics Robero Ciccone. Inroducion This chaper explores some basic quesions abou he effecs on he economic sysem of financing public expendiure by issuing deb. I develops wihin a heoreical framework differing from ha which is currenly predominan boh in pure heory and in applicaions o specific problems such as hose addressed here. In paricular, he approach in his chaper ress on wo basic and closely relaed premises. The firs is he classical explanaion of income disribuion in erms of circumsances of a social and insiuional characer, and hence he rejecion of he view of disribuion as deermined by he forces of demand and supply held by he dominan heory in is various formulaions. The second is he applicaion of he Keynesian principle of effecive demand o he long-run or rend levels of oal oupu, which are regarded here as dependen on he size of he aggregae demand ulimaely deermined independenly of oupu in condiions of full employmen (or naural unemploymen ). Aggregae demand herefore ses an upper limi on he levels of aciviy obainable in he long run (and, needless o say, in he shor run oo), which would generally be insufficien o allow for he full employmen of available resources. The close relaionship beween he wo premises sems from he naural compaibiliy of he classical heory of disribuion wih a deerminaion of oupu levels ino which he available quaniy of labour and oher resources do no ener as direcly relevan circumsances. The analyical srucure of classical heory, characerised by he absence of relaions of a necessary characer beween he deerminaion of disribuion and he deerminaion of oupu levels, makes i possible o sudy changes in variables such as he aggregaes of oupu, 5

4 6 Public Deb and Aggregae Demand consumpion, invesmen, public expendiure and so on wih no need o consider he effecs ha hose changes may have on disribuion and he price sysem. The analysis will herefore be carried ou on he assumpion of a given disribuion of income and associaed price configuraion. Wihin he heoreical framework oulined above, he work seeks o single ou some basic relaions and proposiions concerning he effecs of public deficis and public deb ha migh, if valid, serve as a foundaion o address he issue under he condiions possibly se by specific conexs..2 Public deb as addiional privae wealh Le us sar by defining some relaions beween he relevan magniudes. In a closed economy he necessary equaliy beween aggregae expendiure and aggregae oupu, i.e., beween oal savings and oal invesmen, enails he ideniy S p = I + D where S p is privae savings, I privae invesmen and D public defici. In our heoreical framework, he level of income is deermined by he level of aggregae demand, i.e., by he sum of privae and public expendiure, which implies ha ha ideniy is saisfied, hrough changes in he level of income, by he adjusmen of he flow of privae savings o he sum of privae invesmen and public defici. An increase in public defici ΔD caused by a given increase in public expendiure is herefore counerbalanced by an equal increase in he flow of privae savings ΔS p. In oher words, hrough he influence of public expendiure on aggregae demand and hence on he level of income, an increase in public defici generaes addiional privae savings, savings ha would have no been formed in he absence of he increase in he defici. The flow of privae savings is in urn equivalen o he addiion o he sock of privae secor wealh in he period, gross of capial depreciaion: ΔW p = S p = I + D where ΔW P sands for he gross variaion in privae wealh. Our poin is ha public deficis add o privae invesmen by generaing savings, and herefore wealh, in he hands of he privae secor. As a resul, he

5 Robero Ciccone 7 size of privae wealh a any given ime would be larger, he larger he sum of he public deficis buil up in he pas. I should be eviden how his conclusion relaes o he view of oal oupu as governed by aggregae demand independenly of he availabiliy of resources. In neoclassical heory, where he level of income is deermined (apar from emporary deviaions) by he supply of resources wih consequen adjusmen of aggregae demand, he size of privae wealh is insead basically independen of he flows of public deficis. In ha heoreical framework, he condiion of full employmen, or naural unemploymen, enails a corresponding level of income wih he associaed amoun of savings. Privae savings and he formaion of privae wealh are herefore se independenly of he sum of public deficis and privae invesmen, wih a rade-off arising beween he laer wo uses of privae savings unless i is mainained, as in he Ricardian equivalence argumen, ha public deficis cause an increase in he share of savings ou of full-employmen income, hus displacing privae consumpion raher han privae invesmen. 2 We can say herefore ha wihin he heoreical framework adoped here, no consrain is imposed on he size of public deb by he size of privae wealh, since he laer increases o he same exen as he increase in public deb. Nor is any paricular significance o be aached o a variaion in he proporion of privae wealh consiued by governmen deb, as an increase in ha proporion, for example, would be no more han he arihmeical consequence of he fac ha he sock of public bonds held by privae agens has grown proporionally more han oher ypes of asses consiuing privae wealh, such as real capial, and should no be misaken for a negaive influence on capial accumulaion. While public expendiure and deficis may play a role in raising he level of aggregae demand and income, no negaive consequences need herefore arise for he economic sysem from he relaed accumulaion of public deb as such. I is, however, precisely he capaciy of public expendiure o produce relevan and lasing effecs on aggregae demand ha is quesioned in much of he curren lieraure, ofen by claiming ha, a leas in he long run, he values of fiscal mulipliers are quie low, if no indeed zero or negaive, due o he depressing effec of fiscal expansion on some componens of privae expendiure. 3 Examinaion of he argumens assering his allegedly negaive influence shows, however, ha hey are based eiher on relaions peculiar o neoclassical heory and unwarraned in he analyical framework adoped here or on quie arbirary premises or procedures.

6 8 Public Deb and Aggregae Demand The mos radiional case of displacemen of privae expendiure is obviously he crowding ou of privae invesmen due o he higher ineres rae caused by an increased public defici. To sar wih, he dependence of he level of invesmen on he ineres rae is a ypical neoclassical concep and one ha finds no analyical foundaion, a leas in he guise of a relaion of general characer (as implied by he funcional form i is usually given), in our heoreical conex. Moreover, he debaes on capial heory have shown ha he idea of an inverse relaion beween he ineres rae and invesmen is quesionable even wihin he boundaries of neoclassical heory. In urn, he supposed rise in he ineres rae is iself par of he same concepual picure, since i would be generaed by he compeiion beween public defici and privae invesmen as alernaive uses for scarce privae savings, he amoun of he laer being esablished by he full-employmen level of income. This scarciy has insead no place in our framework, where privae savings adjus o he sum of public defici and privae invesmen hrough changes in he level of income, which implies, as poined ou above, analogous adjusmen beween he corresponding magniudes of sock. A differen and heoreically more neural reason is someimes pu forward o explain he rise in he ineres rae following an increase in public defici (or even in ax-financed public expendiure), namely ha he expansionary effec of public spending feeds he demand for ransacion money and hus pushes he ineres rae up if he supply of money remains unchanged. While he analyical premises for he resul are no sricly neoclassical in his case, and can indeed be found in a purely Keynesian seing, i is he very noion of he supply of money remaining unchanged in he presence of an increasing demand for money ha is wholly arbirary. The paricular sock of money in exisence is in no sense naural and raher reflecs he arges of he moneary auhoriy, among which he level of he ineres rae is cerainly paramoun. The assumpion ha he cenral bank would no adjus he money supply and hus le he ineres rae rise herefore amouns o he assumpion of an unjusified swich o a more resricive moneary policy. I follows ha a reasonable ceeris paribus condiion would raher be o ake he cenral bank s arges as given and hence assume an adjusmen of he supply of money designed o keep he ineres rae a he same level. Anoher argumen in suppor of he depressive influence of public defici on he expendiure of privae agens concerns he laer s consumpion. The grounds for mainaining ha privae consumpion would be reduced by an increase in public defici lie in he so-called ineremporal budge consrain imposed on he governmen, whereby he presen

7 Robero Ciccone 9 value of fuure deb of he public secor (as well as he fuure deb of any agen) mus be zero. If his consrain is o be me, each presen flow of public defici mus have as a counerpar an equal presen value of fuure budge surpluses and hence of ax increases, if we refer for simpliciy o unchanged fuure levels of expendiure. On he assumpion ha households are forward-looking, he expeced fuure change in he fiscal regime would induce hem o increase savings o he same exen as he presen value of he addiional fuure axes, coinciding wih he presen increase in public defici. I is hus claimed ha due o his behaviour on he par of households, he increase in public defici is offse by an equal fall in privae consumpion wih no ne effec on aggregae demand and he level of income. Closer examinaion reveals, however, ha he irrelevance of aggregae demand wih respec o he deerminaion of income is acually a presupposiion raher han a consequence of he behaviour of households oulined above. In order o have a raional foundaion, his behaviour mus be based on he Ricardian equivalence, 4 he subsance of which can be seen as consising of wo elemens: a) households perceive ha wealh in he form of public bonds is bound o be cancelled ou by he addiional fuure axes imposed by he governmen s ineremporal budge consrain; b) hey wish o leave a given amoun of wealh o heir heirs. As a resul of a), households are promped o increase heir savings (reducing consumpion) o he same exen as hey subscribe new public deb, so ha he laer is bequeahed in addiion o, and no in he place of, he (real) wealh hey wish o hand down o he nex generaion. As should already be eviden, he need for households o reduce consumpion in order o increase savings reveals ha he level of income is conceived as independen of aggregae demand from he very ouse. The role played by he reducion of privae consumpion is in fac o preven he public defici from crowding ou privae invesmen and herefore he real wealh o be bequeahed. If he level of income is insead seen as depending on aggregae demand, an increase in defici spending would generae addiional income and privae savings, and he invariance of privae invesmen would require no reducion in privae consumpion, which would, on he conrary, be free o increase ogeher wih he increase in income. Therefore, even wih regard o he argumen jus discussed, he ineffeciveness of fiscal policy proves o be embedded in is very premises. In conclusion, here appears o be no general reason wihin he heoreical framework adoped here o presume ha he influence of public defici on aggregae demand is offse by corresponding conracions of privae expendiure, eiher for invesmen or consumpion. On

8 20 Public Deb and Aggregae Demand he conrary, recogniion ha defici spending helps o keep aggregae demand, and herefore he level of income, higher han i would oherwise be makes i possible o aribue i wih a posiive influence no only on privae consumpion bu also on invesmen levels, especially in a long-run perspecive. Once demand is seen as he facor governing levels of aciviy also in he long run, i is reasonable o suppose ha a leas he dimensional share of invesmen, namely he par conneced wih he size of producive capaciy, is affeced by he prospecive levels of demand and herefore by he rajecories of fiscal policy (and economic policy in general) involved in deermining hem..3 Deb oupu raio and public expendiure reducions: he case of a single period If, as is usual, he raio of public deb o domesic produc is aken as a measure (albei no necessarily a meaningful measure) of deb, he influence of defici spending on boh erms of he raio renders is relaion wih ha measure more complex han is commonly acknowledged. Le us consider alernaive fiscal policies, characerised by differen levels of public expendiure, while assuming unchanged ax raes. Le he index A denoe magniudes ha would obain under he curren policy and indexes R and E magniudes ha would obain respecively under a resricive policy (wih lower flows of public expendiure) and an expansionary policy (wih higher flows). We assume a closed economy in which public expendiure and privae invesmen do no depend in any predeermined way on he level of oupu and privae consumpion is a consan proporion of he privae secor s curren disposable income. Moreover, he share of he laer consising of ineres on public bonds is enirely saved, a simplifying assumpion ha does no affec our resuls qualiaively because i in fac cus off one of he channels hrough which public deficis can feed aggregae demand and herefore acs agains our argumen. Apar from is heoreical premises, a furher difference of our argumen wih respec o convenional reamen of he subjec is ha he effecs of a change in fiscal policy will be sudied by comparing he alernaive values ha he raio of deb o domesic produc would ake under one policy or he oher in he same period or series of periods. This way of reasoning is a variance wih he more usual procedure whereby he deb raio resuling, or expeced o resul, over a period of ime from a policy change is compared wih he value of he raio calculaed a some dae prior o he policy change. As we shall see

9 Robero Ciccone 2 laer (Secion.7), he reason for adoping his approach is ha policy changes apply o some previously planned policy and he counerpars of he resuls obainable by he swich are herefore he effecs ha he older policy would coninue o produce if sill in force raher han he pas values of relevan variables. If we assume for he momen ha privae invesmen flows are no affeced by fiscal policy and can be herefore aken as given in he face of changes in he laer, he level of income a ime under he currenly planned fiscal policy would be Y A = m(i + GA ) where I and G sand respecively for privae invesmen and public expendiure, and m is he income muliplier. Given he assumpions saed above, m = c( z) where c is he (marginal and average) share of consumpion ou of privae disposable income and z he (marginal and average) ax rae. 5 The muliplier is herefore assumed o produce all is effecs on income wihin he same period in which any given level of auonomous expendiure, eiher privae or public, akes place. The admied arbirariness of his assumpion loses much of is relevance when he analysis exends o several periods, as i does here, and is global resuls do no herefore depend on how he direc and indirec effecs of individual flows of expendiure are acually spread ou over ime. Wih a resricive policy enailing lower public expendiure G R < GA, he level of income a ime would insead be Y R = m(i + GR ) wih a difference in he level of income equal o ΔY R = YA YR = m(ga GR ) = mδgr On he oher hand, he lower public expendiure reduces he defici a ime wih respec o ha which would resul wih policy A: ΔD R = DA DR = ( mz)δgr

10 22 Public Deb and Aggregae Demand As expressed by he erm ( mz), he cu in expendiure reduces he defici less han is amoun, as each uni of lower spending also reduces public revenues by is muliplied effec m on he level of income imes he ax rae z. 6 If we assume for simpliciy ha ineres on public deb sars o be paid one period afer issue, he sock of deb a wih policy R is lower han wih policy A by he same amoun as he reducion in he defici: ΔB R = BA BR = ( mz)δgr where B sands for he sock of deb. Using he previous relaions, we can now express he raio of public deb o domesic produc ha would obain a wih policy R: B R Y R A B ( mz) ΔG R = Y A mδg R The purpose of he adopion of he resricive policy is o lower he raio of deb o domesic produc below he level ha would be obained wih he acual policy, i.e., o obain B R Y R A B < Y A The laer condiion evidenly requires he reducion in he domesic produc o be proporionally smaller han he reducion in he deb, i.e., mδg R Y A R mz ΔG < ( ) B A which, afer subsiuing for m and simple algebraic manipulaion, reduces o B A <( c z A Y )( ) The quaniy ( c)( z) hus ses he upper limi of he raio of deb o domesic produc wihin which a reducion in public expendiure in a given period would be effecive in reducing he deb raio below he level ha would obain in he same period under he planned spending policy. For values of he raio above ha limi, a lower level of public

11 Robero Ciccone 23 expendiure would resul in a higher raio, whereas a higher level would resul in a lower raio. The idea behind his resul is quie simple: he larger he size of deb wih respec o domesic produc, he smaller he effec ha a given reducion of public expendiure would produce on he former in relaion o he laer. Beyond a cerain hreshold, he negaive effec of less public spending on domesic produc would be proporionally larger han on he sock of deb and he raio would consequenly prove higher han i would have been wih an unchanged public defici (and vice versa). In oher words, he magniude ( c)( z), which represens he marginal (and average) propensiy o save of he privae secor in relaion o domesic produc in our analysis, also provides he raio beween he difference in he sock of privae wealh and he difference in domesic produc, boh differences resuling from he implemenaion of policy R insead of policy A in period : ΔWp R ( c)( z)= ΔY R where ΔW p R represens he amoun by which privae wealh a ime would be less under policy R han i would under he curren policy A. 7 The lesser formaion of privae wealh would, however, be precisely he counerpar of he lower accumulaion of public deb engendered by policy R, i.e. ΔW p R = ΔB R, and he las equaliy enails ΔB ( c)( z)= R ΔY R The marginal rae of privae savings is herefore equal o he marginal difference in he raio of deb o domesic produc generaed by policy R as agains policy A. I is obvious ha he deb raio obainable wih policy R will prove lower han ha obainable wih policy A only if he laer is lower han he marginal difference generaed by policy R, i.e., only if B A Y A R B < Δ ΔY R which explains why he magniude ( c)( z) funcions as he upper limi of he A deb raio for he resricive policy o be effecive in reducing he deb raio. The quaniy ( c)( z) can hus be aken as he hreshold for he curren deb raio, above which he effecs of changes in he level of

12 24 Public Deb and Aggregae Demand public expendiure on he deb raio would be opposie o hose commonly expeced. I should be noed ha, making allowances for our simplifying assumpions, he values ha he hreshold can plausibly ake are quie small. For c = 0.70 and z = 0.30, for example, is magniude would be as small as 0.2, which is much lower han he raios of public deb o domesic produc generally observable in real economies..4 Expendiure reducions over a number of periods So far we have considered he quesion of he effecs of a change in he level of public spending ha akes place in a single period. As relaions in he longer run are obviously wha maer mos, we shall now go on o sudy he effecs of variaions in public expendiure exending over a series of periods. As regards he absolue amoun of deb, a series of lower flows of defici spending obviously reduces he sock of deb below he level i would oherwise have found. This effec, which increases wih he lengh of he series of reducions and he scale of heir amouns, is enhanced by he increasing reducion in ineres oulays caused by he cumulaive effec on he sock of deb. We shall now consider a policy R ha cus he levels of public expendiure from ime o ime wih respec o he previously planned policy A and express he sock of public deb a he final ime in relaion o he deb which would have obained a wih policy A. If we assume a zero ineres rae for he momen, he relaion beween he wo socks of deb a ime would be: B R B A = ( mz) ΔGs R where ΔG R s = GA s GR s is he reducion of public spending in period s which policy R enails in comparison wih policy A. If we now inroduce a posiive ineres rae i on public deb, each reducion of deb in comparison wih policy A generaes furher reducions as ime goes on hrough he lower flows of oulay on compound ineres enailed. 8 In greaer deail, one uni of lower deb a ime s generaes a lower deb a ime by an amoun of ( + i) s, and he relaion beween he deb socks herefore becomes B R B A mz Gs R s = ( ) Δ ( + i)

13 Robero Ciccone 25 In order o idenify he condiion ha mus be fulfilled in order for he resricive policy R o lower he raio of public deb o domesic produc a ime, le us now express he raio as B Y R R B ( mz) s G ( i) = = Δ + Y mδg A s R s A and impose he condiion ha i mus prove smaller han he deb raio wih policy A: R B ( mz ) Δ G ( + i) Y mδg A s R s A R B < Y A A This condiion requires he reducion in he domesic produc o be proporionally smaller han he reducion in he sock of deb: mδg Y R A mz s s ΔG i < ( ) = = ( + ) B A s R s from which, by rearranging and expressing he value of m, we obain: B Y A A ΔG R s = ΔG ( + i ) s R s <( c)( z) We hus find once again a condiion conaining he inversion hreshold of he deb raio in relaion o changes in he level of public expendiure. In comparison wih he resul obained by considering a single period, he magniude ha mus remain below he hreshold if policy R is o bring abou a lower deb raio is sill he value ha he deb raio would assume a wih policy A, his ime muliplied by a quaniy evidenly lower han. (I should be remembered ha he reducions ΔG R s are regarded as posiive values.) As migh be expeced, he condiion o be fulfilled is herefore less resricive han in he case of a single period as a resul of he cumulaive effecs of he series of reducions in public spending. The relaion we have jus obained gains in ransparency if he magniude ha expresses he effecs of he succession of reducions in expendiure is ransferred o he righ-hand side, hus reinsaing his side in he posiion of an inversion hreshold for he curren policy deb raio as in he single-period case: B Y A A <( c)( z) Δ G ( + i) ΔG s R s R [.]

14 26 Public Deb and Aggregae Demand The quaniy on he righ-hand side of [.] can be seen as he value of he inversion hreshold of he deb raio a ime correced by he cumulaive effecs of he lower flows of public spending. The correcion operaes in such a way as o make he hreshold variable in relaion o he series of reducions in expendiure wih respec o policy A, increasing is value, from he second period of he sequence, above he value ( c)( z) iniially assumed by he hreshold. In acual fac, he fracion on he righ-hand side generally increases wih he number of periods and herefore he series of expendiure reducions, even hough i migh show some decreasing sreches afer a sufficien number of periods and depending on he acual values of ΔG R s, bu in any case remaining above he iniial value ( c)( z). 9 Figure. shows he behaviour of he hreshold, which we shall indicae as T(), leaving aside any possibiliy of a drop and herefore assuming is monooniciy. Le us hen suppose ha over ime policy A would produce he deb raio B A Y A shown in Figure.2, saring from a value higher han he iniial level of T() and hen proceeding along a rising rend, which is assumed o be linear for simpliciy. We shall also assume ha he spending reducions enailed by policy R are such as o make he hreshold T() increase more rapidly han he deb raio resuling from policy A, so ha he hreshold cus he rend of he deb raio afer a cerain number of periods and he laer finds is way below he hreshold. The inersecion poin in herefore marks a divide beween he wo regions in which he values of he R deb raio would sand: he norhwes region H, where he R deb raio would exceed he A raio, and he souheas region L, where he R raio would be lower han he A raio. T( ) ( c)( z) Figure. The hreshold

15 Robero Ciccone 27 H B A /Y A L ( c)( z) T( ) τ Figure.2 Threshold and presen-policy deb raio H B A /Y A L B R /Y R ( c)( z) T( ) τ Figure.3 Effecs of a resricive policy (invesmen given) The specific rend of he R deb raio would of course depend boh on he values of he spending flows enailed by policy R, which are hose defined by he assumed reducions from he levels planned by policy A, and on he assumed rend of he A deb raio. In order o simplify he graphic exposiion, le us represen also he rend of he R deb raio in linear form and assume ha i is downward sloping, as shown by he hick line in Figure.3. Neiher he decreasing course of he curve nor is monoonic behaviour is herefore a necessary characerisic of he rend of he R raio, no leas because of he influence of public spending on aggregae demand and oupu. The conclusions here are, however, no sricly dependen on he shape of he R raio curve, and he assumpion ha he slope of he laer is negaive is no more special han any oher. 0

16 28 Public Deb and Aggregae Demand We can hus see ha as long as he deb raio associaed wih policy A sands above he hreshold, he deb raio produced by policy R would in urn say above he A raio, and up o ha poin he effecs of he resricive policy could herefore be said o be perverse, as hey are opposie o hose expeced. On he oher hand, he above exercise shows ha afer a number of periods he deb raio produced by policy R would fall below wha would be generaed by policy A. This resul migh be aken o mean ha he resricive policy is ulimaely effecive in bringing abou a deb raio lower han oherwise, he delay and indeed he opposie oucome ha he process goes hrough before reaching he arge being conceivably no so relevan if he main concern is he long-run behaviour of magniudes. Furhermore, he reducions in he levels of public spending seem o be capable, oher hings remaining equal, of making he T() curve quie seep, and herefore rapidly increasing. Appealing o he emporary naure of he perverse effecs of a resricive policy in order o diminish heir imporance, a reacion ofen observed when such consequences ake place in acual economies, implicily ress, however, on a belief in an inheren endency of aggregae oupu o move owards is poenial level and hence denies he auonomous role of demand in deermining oupu. In he above analysis, he obsacle ha prevens he lower levels of public spending from reducing he deb raio, even o he poin of raising i, is in fac he negaive effec hey have on levels of oupu. This depressing influence is permanen and he comparaive diminuion ha he raio evenually undergoes is obained despie such influence, raher han because of is disappearance. As a maer of fac, he reducion of he deb raio wih respec o wha i would be under policy A is obained hrough a comparaive reducion in boh he sock of deb and domesic produc, wih he former decreasing proporionally more han he laer afer a number of periods due o he cumulaive acion of spending cus and lower ineres oulays. The perverse effecs on he deb raio are herefore he manifesaion of a change in he rend levels of oupu caused by he resricive change in fiscal policy and should be kep disinc from any sor of shor-run consequences due o emporary circumsances or agens reacions o ha policy. This is reinforced by he consideraion ha, as will be argued shorly, i is precisely he persisence of he depressive effecs of he resricive policy ha is liable in he long run o cause furher changes enhancing hose effecs and consequenly exending he number of periods for which he policy could generae a comparaively higher deb raio.

17 Robero Ciccone 29.5 Furher on public expendiure reducions: negaive feedbacks on privae invesmen The effecs of given reducions in public spending have been examined so far on he assumpion ha he ax rae, he propensiy o consume of he privae secor and he ineres rae on public bonds all remain consan. I has also been assumed ha he oher componen of auonomous expen diure, namely privae invesmen, does no aler he series of is magniudes in relaion o he adopion of a differen fiscal policy and ha herefore he effecs on oupu levels of sequences of differen levels of public spending are limied o hose produced by he laer differences alone (he acion of he income muliplier being of course aken ino accoun). The las of hese assumpions appears o be he mos resricive. As already poined ou, here is no need in he heoreical framework adoped here for he ineres rae o depend eiher on he size of he public deb, however i may be measured, or on measures of fiscal policy or more generally on changes in he levels of aciviy, and i is herefore legiimae o ake i as given in he even of changes in hose circumsances. The same holds all he more for he ax rae, which is compleely under governmen conrol. As regards he privae propensiy o consume, while here could be reasons in suppor of is dependence on long-run levels of income, aking his dependence explicily ino accoun would only make he value of he muliplier variable wihou alering he principle of which he muliplier is he quaniaive expression, namely ha he level of aggregae oupu is governed by demand. The general characer of he analysis underaken here does no require us o go beyond he principle as such, and reaing he propensiy o consume as given consiues a simplifying device ha imposes no subsanial resricions on he resuls obained. Differen consideraions insead apply o he assumpion ha he levels of oupu generaed by a given fiscal policy do no affec he invesmen plans of he privae secor. Given our key principle ha oupu is limied, in he long run no less han in cycle flucuaions, by he level of demand, i follows as a naural corollary ha demand also influences he level of privae invesmen. A leas as regards he share of gross invesmen ha could be described as dimensional, i.e., relaed o he desired scale of producive capaciy, sric dependence is quie obvious on he levels of oupu ha firms expec o be profiably aained or mainained in he periods ahead and hence on fuure levels of demand. I is quie reasonable, on he oher hand, o presume ha he rends

18 30 Public Deb and Aggregae Demand of expeced demand are influenced by he levels of demand ha have prevailed in he pas periods, so ha lower levels of public spending will negaively affec privae invesmen hrough heir depressing impac on aggregae demand. Moreover, privae invesmen may be influenced even by he planned levels of public spending if, as is conceivable, firms ake governmen planning ino accoun in forming heir views abou fuure marke condiions and herefore oupu rends. The conclusion ha privae invesmen is negaively affeced by lower levels of public expendiure has imporan consequences for our analysis. Le ΔI R s indicae he reducion (aken as algebraically posiive) in gross privae invesmen ha would be obained in period s under he resricive fiscal policy R compared wih wha i would be in he same period under policy A. Due o he influence of he lower levels of invesmen on levels of income and herefore on public revenues, he absolue amoun of public deb ha would resul a ime from he applicaion of policy R since ime is now larger. As above, his can be expressed in relaion o wha i would have been under policy A: R A s R s B = B ( mz) ΔG ( + i) + mz ΔI ( + i) s R s where he las erm on he righ-hand side represens he effec on he final sock of deb of he lower revenues (wih consequen higher oulay on ineres) caused by he lower flows of privae invesmen expendiure. Correspondingly, he level of income a ime falls by comparison wih wha i would be under policy A because of he lower levels of public spending and privae invesmen in he period: Y R = YA m(δgr + ΔIR ) For he deb raio a ime under policy R o be lower han i would be under policy A, he decrease in he level of income mus be less han proporional o he decrease in he sock of deb, ha is Y A Y Y R A B < A B B A R and, herefore, using he above relaions: m G I mz G i mz I R R s s R s s ( ) ( ) = s ( ) = Δ + Δ s s R ( < = Δ + + = Δ + i Y B A A ) s

19 Robero Ciccone 3 Expressing he value of he muliplier m, he laer inequaliy may be wrien in he form: B Y A A <( c)( z) Gs R i s s ( + ) = Δ I z ( + ) ΔG + ΔI ΔG + ΔI R R Δ R s s i R R [.2] The expression on he righ-hand side of relaion [.2] is he value now assumed by he inversion hreshold T() of he deb raio. Comparison wih inequaliy [.], where no changes in he levels of privae invesmen are considered, reveals wo differences. In addiion o he reducion in public spending in period, he denominaor of he firs fracion conains he reducion in privae invesmen in he same period, which obviously reduces he value of he fracion (besides reinforcing he possibiliy of some decreasing sreches in is behaviour). The magniude of he hreshold is furher reduced by he negaive erm in z, which could, if is values were sufficienly large, even give he hreshold a decreasing course, in his case no necessarily resriced o limied sreches alone. 2 The size of his negaive effec on he value of he hreshold evidenly depends on he size of he decreases in he flows of privae invesmen ha policy R generaes by comparison wih policy A. Even hough his kind of influence does no lend iself o shaping in a general form, i is reasonable o expec ha boh he amouns and he duraion of reducions in public spending would, hrough heir impac on aggregae demand, direcly affec he amouns by which privae invesmen flows would be lower under policy R han policy A. In conclusion, by augmening he negaive influence of he resricive policy on oupu levels, reducions in privae invesmen engender wo effecs. The firs is a drop in he values of he hreshold curve, which swiches o he righ and may become decreasing from a cerain poin on. 3 The second is an increase in he values of he deb raio ensuing from he resricive policy in any given period due o he simple fac ha lower income levels generae lower public revenues. This effec would be seen graphically in an upward movemen of he line represening he rend of he R deb raio. In Figure.4, T 0 () indicaes he hreshold curve ensuing wih unchanged invesmen levels and T he hreshold associaed wih a series of invesmen reducions (by comparison wih wha would happen under policy A) saring from period, while he wo downwardsloping lines inersecing hem represen he rends of he R deb raio ha would obain respecively under he firs and he second hypohesis abou invesmen behaviour. As we can see, wih no change in

20 32 Public Deb and Aggregae Demand R 0 R B A /Y A T 0 ( ) T ( ) B R /Y R ( c)( z) τ 0 τ Figure.4 Effecs of a resricive policy (invesmen reacing once) invesmen flows, he R policy would poenially bring he deb raio below he level enailed by policy A in period 0 (line R 0 ). As a resul of he curailmen of privae invesmen flows a, however, he hreshold curve becomes T () from hen on wih he corresponding upward movemen in he rend of he R deb raio (line R ). The momen a which he laer would fall below he policy A raio hus changes from period 0 o period and he course of he R deb raio would be represened by he bold broken line. There is, however, nohing o rule ou he possibiliy of he coninuaion of lower levels of demand and oupu, and heir addiional reducion enailed by he lower invesmen levels, subsequenly generaing even larger reducions in privae invesmen flows. In Figure.5, he decreases in invesmen, again by comparison wih he invesmen flows under policy A, are supposed o have increased sill furher since no only period 2 bu also period 3 wih consequen successive swiches of boh he hreshold curve and he rend of he R deb raio. The laer would hus remain above he rend of he A deb raio for a number of periods, falling below i only if and when he reducion of privae invesmen flows (by comparison wih wha would occur under policy A) sops for a sufficien lengh of ime. Moreover, his resul would evenually be obained wih levels of domesic oupu and privae invesmen ha could be lower by any degree han hose resuling from policy A. Even more drasically, policy R could prove oally incapable of bringing he rend of he deb raio below ha of policy A if he reducion in privae invesmen flows were o become sufficienly large evenually o cause a decreasing course of he T() curve. This case is represened in Figure.6, where he decrease in privae invesmen induced by policy

21 Robero Ciccone 33 R 0 R R 2 R 3 B A /Y A T 0 ( ) T ( ) T 2 ( ) T 3 ( ) B R /Y R ( c)( z) 2 3 τ 3 Figure.5 Effecs of a resricive policy (invesmen reacing over ime) R 0 R R 2 R 3 B R /Y R B A /Y A T 2 ( ) T ( ) T 0 ( ) T 3 ( ) (-c)(-z) 2 3 Figure.6 Effecs of a resricive policy (hreshold evenually downward sloping) R in period 3, compared wih he invesmen levels ha would obain under policy A, is supposed o be such as o generae a downwardsloping hreshold curve. In his case, he laer would no inersec he rend of he A deb raio and consequenly, despie he coninuaion of a resricive policy, he rend of he R deb raio would coninue o sand above ha of he A raio. 4.6 The case of increases in public expendiure We have hus seen ha he aainmen of a comparaively lower deb raio is no guaraneed by he exension of he number of periods for which a policy of reduced public spending is implemened. In he absence of compensaory changes in oher elemens of auonomous

22 34 Public Deb and Aggregae Demand demand, which here would be no reason o expec, precisely he prolongaion of such a policy, wih is negaive influence on long-run demand rends, would possibly if no indeed ineviably lead o a drop in flows of privae invesmen. In he case represened in Figure.5, his shifs he goal of reducing he deb raio furher ino he fuure wih no guaranee ha he process will no fall ino a ailspin, hus moving he posiion of he hreshold curve T() furher and furher o he righ. The already uncerain reducion of he deb raio becomes impossible in he case represened in Figure.6, where sufficienly srong reducions in flows of privae invesmen cause he slope of he T() curve o become negaive and he resricive policy gives rise o a permanen increase in he deb raio. Furhermore, his uncerainy of resuls, even as regards heir sign, is accompanied by a cerain and permanen relinquishmen of higher levels of income and employmen by he communiy, somehing ha could be described in he erms of he dominan heoreical framework as an insance of Pareo inferioriy. These conclusions promp examinaion of he siuaion ha would insead arise wih higher levels of public spending. Le E be an expansionary policy enailing increases in expendiure wih respec o he curren policy A. If we ake ino accoun he increases in privae invesmen ha would be induced by he higher levels of demand, he sock of public deb a ime under policy E, as agains he deb ha would resul from policy A, is: E A s E s B = B + ( mz) ΔG ( + i) mz ΔI ( + i) s E s where ΔG E s and ΔIE s respecively represen he increases in public expendiure and privae invesmen in he generic period s by comparison wih wha would obain under policy A. The level of income in period would correspondingly be higher by he amoun ΔY E = m(δge + ΔIE ) The condiion required for policy E o produce a lower deb raio a han policy A is once again ha he proporional increase in he level of income exceeds he proporional increase in he absolue sock of deb: m G I mz G i mz I E E s s E s s ( ) ( ) = s ( ) = Δ + Δ s s E ( > = Δ + = Δ + i Y B A A ) s

23 Robero Ciccone 35 which, rearranging he erms and expressing he value of he muliplier m, provides he value ha he deb raio wih policy A mus be above in order for he said resul o be obained: B Y A A G i I i s c z E s Δ ( + ) s E >( )( ) z ( ) Δ + ΔG + ΔI ΔG + ΔI E The righ-hand side of he above inequaliy represens he inversion hreshold of he B A raio, in his case a lower boundary, in order for Y A he expansionary policy o generae a lower deb raio a. As can be seen, he expression of he hreshold is sricly analogous o wha was found in considering a resricive policy, and i herefore behaves in he same way. On he assumpion ha privae invesmen would respond posiively o he higher aggregae demand riggered by he expansionary policy, in Figure.7 T 0 () represens he hreshold curve assuming no change in invesmen flows as agains wha would obain wih policy A, and he curves T (), T 2 (), and T 3 () insead exemplify he successive forms of he hreshold curve resuling from increasingly large comparaive increases in he flows of privae invesmen. In he same figure, he line E 0 represens he course ha he E deb raio would ake if invesmen flows were he same as under policy A, and he lines E, E 2, E 3 sand for he pahs of he raio generaed by he increasing levels of invesmen enailed by he corresponding T.() curve. As he figure shows, each furher increase in invesmen flows moves boh he hreshold curve and he E deb-raio line o he righ, hus shifing he ime E E E s B E /Y E ( c)( z) E 0 E T 0 ( ) T ( ) E 2 T 2 ( ) E 3 T 3 ( ) B A /Y A 2 3 τ 3 Figure.7 Effecs of an expansionary policy (invesmen reacing over ime)

24 36 Public Deb and Aggregae Demand a which he wo curves joinly inersec he rend line of he A deb raio and he E deb raio overakes he laer progressively from 0 o, hen 2 and finally 3. As a resul of he expansionary policy, he rend followed by he E deb raio would herefore lie below he one generaed by he curren policy for a number of periods which would be larger, he larger and more persisen he effecs produced direcly and indirecly on aggregae demand. In symmery wih he findings of our examinaion of a resricive policy, one resul of our analysis is ha he rend of he expansionary policy deb raio would lie permanenly below ha of he curren policy if he resuling increases in privae invesmen flows reached levels high enough o generae a downward-sloping T() curve. This is he case represened in Figure.8, where he rise in privae invesmen from period 3 is supposed o be such as o make he T 3 () curve negaively sloped and preven i from inersecing wih he B A Y A he B E Y E line would never overake he B A Y A line. In urn, line, and he expansionary fiscal policy would succeed in keeping he rend of he deb raio below ha of he curren policy indefiniely..7 Final remarks and conclusions As saed a he ouse, unlike he more usual procedure of comparing he resuls of a policy change wih magniudes calculaed a some earlier ( c)( z) E 0 E E 2 T 2 ( ) T 0 ( ) T ( ) E 3 T 3 ( ) B A /Y A B E /Y E 2 3 Figure.8 Effecs of an expansionary policy (hreshold evenually downward sloping)

25 Robero Ciccone 37 ime, our invesigaion compares a given rend of he deb raio generaed by he currenly planned fiscal policy wih he rend ha would be generaed by eiher a comparaively resricive or a comparaively expansionary policy. The jusificaion pu forward for his procedure is he fac ha a change in fiscal policy, and paricularly in public spending, is generally formulaed in erms of variaions o be made on curren policy. I is herefore more appropriae o evaluae he effecs produced by he policy change over a given period hrough comparison wih wha would have been he resul of curren policy during he same period raher han wih values prior o he change. This holds all he more if, as is evidenly he case for he deb raio and for objecives of fiscal policy in general, he level of overall oupu consiues a relevan variable and is seen as demand deermined by and hence dependen on he economic policies in force. Neverheless, he analysis can be easily supplemened if desired hrough he inroducion of a specific value of he deb raio ha fiscal policy can be expeced according o some views of greaer or lesser concepual validiy o ake as a benchmark for he acual deb raio. On he obvious assumpion ha his arge raio is lower han he one obainable wih he curren policy, i could be represened by a horizonal line drawn below he B A Y A line used in our graphs. The addiion of such a line in Figures.5 and.6, which show how difficul if no indeed impossible i is for a resricive fiscal policy o bring he rend of he deb raio below he level resuling from he curren policy, would hen enable us o deduce analogous and acually sronger conclusions abou he abiliy of his kind of policy o bring he deb raio ino line wih an even lower arge value. Adopion of he same procedure in Figures.7 and.8 would sugges ha his adjusmen would be more efficienly pursued by means of an expansionary policy. Summing up, he chaper has endeavoured o show analyically ha once a posiive influence of public expendiure on oal oupu is acknowledged, an inverse relaion may hold, also in he long run, beween levels of defici spending and values of he raio of public deb o domesic produc. The resuls sugges ha if a lower deb raio consiues a arge of economic policy, as is currenly he case in several counries, hen regardless of he validiy or oherwise of ha objecive, resricive fiscal policies may prove ineffecive and even self-defeaing by generaing higher raher han lower values of he deb raio. On he conrary, expansionary policies may produce comparaively lower values of he raio, and defici spending would herefore be superior

26 38 Public Deb and Aggregae Demand o fiscal rerenchmen wih regard no only o levels of aciviy and employmen bu also o wha is ofen referred o as an index of solidiy of he financial posiion of governmens. 5 The conclusions drawn here apply o policies implemened over series of periods and hold in his sense for he long run, no jus he shor. This is due o he fac ha, conrary o wha we find in much of he mainsream lieraure, he heoreical framework adoped here enails no need o counerbalance changes in fiscal policy wih opposie changes in privae expendiure, no maer how lagged. The key idea of his chaper, namely ha oupu is deermined by demand, naurally implies insead ha gross invesmen, he primary auonomous componen of privae spending, direcly depends in urn on he rend in levels of demand. Flows of privae invesmen would hus respond o and hence assis changes in aggregae demand raher han counerbalancing hem. By furher enhancing he influence ha fiscal policy can have in he long run on oupu levels, his behaviour of privae invesmen reinforces he resul ha conrary o he orhodox view, lower values of he deb raio can be obained more easily, and less painfully, hrough expansionary fiscal policies. Noes. An applicaion of he Keynesian principle of effecive demand o he role of public spending and, more generally, o fiscal policy was pu forward in a fairly large body of lieraure mainly daing from he 940s and 950s, which found perhaps is mos radical expression in Lerner s funcional finance (Lerner, 943). A major elemen disinguishing hose conribuions from his chaper is he fac ha while he former ofen fail o specify he naure of he limi ha aggregae demand imposes on oal oupu, i.e., wheher i is purely cyclical in characer or exends o he rend of aciviy levels (cf. Ciccone, 2002, pp. 2 3, fn. 6), aggregae demand is explicily regarded here as deermining overall oupu in boh he shor and he long run. 2. For he premises implici in he assumpion ha agens behave in his way, see Secion.2 below. 3. A vas lieraure has developed focusing specifically on quaniaive esimaion of he change in he level of oal oupu aribuable o a change eiher in public expendiure or in ax raes or levels, a raio generally labelled he muliplier of fiscal policy or simply fiscal muliplier (for a recen survey of his lieraure, see Ramey, 20; see also Barba, 200 for a criical discussion of he heoreical foundaions of he claim ha fiscal conracions can also be expansionary, which is sill relevan o much of he work a issue). Many of hese sudies appear o be inspired by he assumpion, implicily or

27 Robero Ciccone 39 explicily derived from orhodox heory, ha a change in fiscal policy can have no significan or in any case lasing influence on he level of demand, as i is bound o cause opposie changes in some componens of he laer (privae invesmen, privae consumpion or expors), so ha he size of is effec on oupu is expeced o be relaively small or even opposie in sign (bu see Fazzari e al., 202 for an argumen developed in a differen direcion). This is so by consrucion in he simulaions carried ou hrough he use of models, he resuls of which obviously depend on he characerisics of he models adoped, which ofen reflec he se of relaions peculiar o neoclassical heory. The size and sign of fiscal mulipliers are alernaively invesigaed by means of pure empirical work relying on no heoreical srucure and based exclusively on hisorical daa. This is no wihou cos. Due o he dependence of fiscal magniudes on several variables, including domesic oupu, a major problem encounered by his kind of research is he idenificaion of changes in fiscal quaniies (e.g. he primary balance) ha can be aribued o deliberae policy acions and herefore reaed as exogenous raher han resuling from he prevailing economic condiions (see he objecions raised in his regard in IMF, 200). The mass of work on fiscal mulipliers has in fac produced esimaes ha differ widely according o he assumpions and procedures adoped, e.g. ranging from 3.8 o +3.8 for public expendiure (cf. Van Brusselen, 2009, p. 8; esimaes for ax-cu mulipliers are repored o range beween 4.8 and +3.0). The issue herefore sill remains a maer for heory raher han somehing ha can be decisively seled on empirical grounds. In he approach adoped here, which regards demand as deermining he level of oupu, he influence of public spending on oupu can accordingly be expressed by he full acion of he income muliplier wih no need for counerbalancing variaions in oher consiuens of demand. 4. As is well known, i was Barro (974) who originally pu forward he idea ha households would reduce consumpion by he same amoun as he issuing of public deb, so ha deb- and ax-financing of public expendiure would supposedly be equivalen in heir effecs on agens behaviour. This aricle made no reference o Ricardo and he connecion wih an analogous poin made by Ricardo was laer noed by Buchanan (976), since when he concep has ofen been referred o as Ricardian. While claiming ha he way in which public spending is financed should be a maer of indifference o he individual on logical grounds, Ricardo mainained, however, ha his equivalence is no effecively perceived, as fuure axes are in fac assigned less imporance han presen axes. Unlike Barro, Ricardo hus mainains ha deb financing would reduce savings by comparison wih he siuaion in he case of ax financing (cf. Ricardo, 95, pp. 86 7). 5. The rae z is here aken as represenaive of any kind of deducion from produced income accruing o he public secor as a whole as well as axes and fees paid on purchases of goods and services. The consancy of z also rules ou herefore any changes in public charges (e.g. for healh services), which could furhermore come ino conflic wih he assumed invariance of income disribuion.