Money and Monetary Policy in a Kaldor-Pasinetti-Sraffa-Keynes Framework

Transcription

1 Money and Moneary Policy in a Kaldor-Pasinei-Sraffa-Keynes Framework Peer Dochery School of Finance and Economics Universiy of Technology, Sydney Absrac This paper invesigaes he role of money and he ransmission of moneary policy in a model characerised by ineres-insensiive expendiures and unemploymen equilibria. I firs oulines he srucure of wha is called a Kaldor-Pasinei-Sraffa-Keynes (KPSK) model where oupu is deermined by he principle of effecive demand and expendiures are deermined by income disribuion, prices are deermined along Sraffian lines. I secondly explores he role of money in his kind of model, assuming firs an exogenous money supply and hen an endogenous one, and compares he difference beween hese wo ses of moneary arrangemens for he model s key macroeconomic variables: oupu, employmen and prices. I provides evidence in suppor of he proposiion ha endogenous money is a necessary condiion for he aainmen of an unemploymen equilibrium in his kind of model. I hirdly examines he operaion of a Taylor rule in he conduc of moneary policy wihin a KPSK model, comparing is impac wih ha in a neoclassical macro model where such rules generae full employmen. The paper concludes wih some observaions abou he relaionship beween he conceps of money supply endogeneiy, he ineres-insensiiviy of expendiures and money non-neuraliy in models of he KPSK variey. JEL Classificaion Numbers: E, E2, E42, & E52. Keywords: Endogenous money, money non-neuraliy, long period unemploymen. Thanks o he Deparmen of Economics a he Universiy of Oawa for research suppor and o Tony Aspromourgos, Peer Flaschel, Marc Lavoie, Gordon Menzies, Louis-Philippe Rochon, Mario Seccareccia, John Smihin and Graham Whie for commens and suggesions wihou implicaing hem in he final produc. Peer Dochery, School of Finance and Economics, Universiy of Technology, Sydney, P.O. Box 23 Broadway, NSW, 2007, Ausralia; Ph ; Fax ; peer.dochery@us.edu.au.

2 . Inroducion The role of money and moneary condiions in explaining he exisence of long period unemploymen has received increasing aenion in recen years. The original objecive of Keynes The General Theory was, of course, o explain why unemploymen could characerise an economy s equilibrium raher han simply represening an inermediae sae on an adjusmen pah owards equilibrium. A he cenre of Keynes heory of oupu and employmen was he principle of effecive demand. Bu unforunaely he core sysem buil around his principle graviaes o full employmen wih he passage of sufficien ime. According o he Keynes effec, wage deflaion in he face of unemploymen reduces he demand for money, reduced demand for money causes reducions in ineres raes, and hese reducions simulae ineres-sensiive invesmen spending unil unemploymen is eliminaed. Corell (994, 58) idenifies hree possible mechanisms capable of circumvening his effec: nominal wage rigidiy; invesmen or expendiure ineres-insensiiviy; and a srucurally fixed ineres rae. The Cambridge criique provides heoreical jusificaion for he second of hese mechanisms (see Garegnani 978, 348) while Fazzari, Hubbard & Peersen (988, 43) provide empirical suppor in ha hey find lile evidence for he role of cos of capial effecs on invesmen spending. Corell s paper very usefully explores he hird mechanism which has come o be associaed wih endogenous money of he accommodaionis form. Dochery (2006) re-examines he role of endogenous money in prevening he graviaion of sysems wih ineres-sensiive expendiures o full employmen and concurs wih Corell (994) ha endogenous money is sufficien o disrup such graviaion. He also argues ha he combinaion of endogenous money and money illusion on he par of workers is sufficien o generae Keynesian unemploymen equilibrium. Such models are no, however, very saisfacory for explaining long period unemploymen since he assumpion of money illusion is problemaic and since such models ignore he imporance of he Cambridge criique. Recogniion of he Cambridge criique, however, by designing expendiures o be ineres-insensiive raises quesions abou he role of endogenous money. Since ineres-insensiiviy is sufficien o generae unemploymen equilibria, is endogenous money also required in alernaive macro models? This paper cass furher ligh on his quesion and is implicaions for moneary policy. I examines he moneary characerisics of a simple Kaldor-Pasinei-Sraffa-Keynes (KPSK) model buil around he principle of effecive demand and incorporaing ineres-insensiive expendiures wih endogenous money. Secion 2 oulines he srucure of he model and is equilibrium and sabiliy feaures. Secion 3 examines he role of endogenous money wihin he model. Secion 4

3 2 hen considers a series of moneary policy approaches wihin he model ha cas furher ligh on is operaion. The argumen and main findings are summarised in he final secion. 2. The Kaldor-Pasinei-Sraffa-Keynes (KPSK) Model Three feaures are cenral o he model oulined in his secion. I has a is core he principle of effecive demand, reflecing he major conribuion of Keynes The General Theory. Secondly, unlike The General Theory, i reflecs he cenral insigh of he Cambridge criique so ha invesmen does no have he rae of ineres as an argumen. Thirdly, i conains endogenous money, reflecing Corell s (994) observaion discussed above and he conribuions of Kaldor (970, 986) and Moore (988) in paricular. In order o ouline he essenial feaures of he model, a highly simplified form is assumed. The economy is saic wih zero real growh over ime. There is only one producive secor. Workers income arises solely from heir supply of labour and capialis income arises solely from profis. Each of hese assumpions causes significan insighs of he heories from which hey are drawn o be ignored. Bu his process will faciliae combining hese heories in a way ha makes i easier o undersand and inerpre how he enire sysem is funcioning. The model is oulined in equaions () o (5) below. Equaions () o (6) encapsulae he heory of demand drawn from Keynes (936), Kaldor (956) and Pasinei (974). Equaion () represens he principle of effecive demand by which oupu is deermined as he sum of lagged oal consumpion spending (C,), lagged invesmen spending (I ) and auonomous governmen spending (G). Toal consumpion spending is given in equaion (2) as he sum of consumpion by workers and capialiss respecively. The former, in he firs se of square brackes on he righ hand side of (2), is made up of auonomous worker consumpion ( C ) and a proporion ( s w ) of aggregae real wages (W ) ne of axes (where h is he single marginal and average ax rae). The laer, in he second se of square brackes, is similarly comprised of auonomous capialis consumpion ( C) and a proporion ( s c ) of aggregae real profis (P ) ne of axes. Aggregae c real wages are deermined in equaion (3) as he produc of he real wage rae per uni of labour (w ) and he volume of employmen, iself he produc of he uni labour requiremen, or labouroupu raio, ( l ) and he level of oupu (Y ). Aggregae profis are deermined residually in equaion (4) from an aggregae budge consrain according o which aggregae real wages and profis sum o aggregae oupu (Y ). Invesmen spending is deermined in equaion (5) and represens one possibiliy for reflecing he Cambridge criique. In a dynamic conex his expression would allow changes in oupu o w

4 3 affec invesmen spending via a classic acceleraion mechanism bu in he presen, saic conex invesmen simply replaces capial as i wears ou, mainaining he economy s abiliy o produce he equilibrium level of oupu. Thus equaion (5) deermines invesmen as he produc of he rae of economic depreciaion of he capial sock ( ), he uni capial requiremen, or capial-oupu raio, (k), and he curren level of oupu. Boh and k are assumed o be echnologically given. Equaion (6) deermines he rae of unemploymen (UE ) as he number of unemployed, being he exogenously given labour supply (L*) less he demand for labour, as a proporion of he exogenous labour supply. The demand for labour is he produc of he uni labour requiremen and he volume of real producion. Y = C + I + G () C = C + ( s ) ( ) W ] + [ C + ( s ) ( ) P ] (2) [ w w c c W = w l Y (3) Y = W + P (4) I = v k (5) Y UE * * = ( L l Y ) / L (6) w r = [ k ( r l r n r + )] =, π (8) = i + σ n, (9) i = i * (0) i π () * = i + π = MWG λ (2) MWG e = + βπ β 2UE α (3) (7) e e e π = π + ( π π ) (4) j w w λ = (5) w Equaions (7) o () encapsulae he Sraffian heory of disribuion. The real wage rae is given by equaion (7). This is a version of he sandard Sraffa pricing equaion derived from he

5 4 expression for he rae of profi (r ) (shown in he Appendix) and deermines he real wage in erms of he echnical condiions of producion and he real rae of profi. The real rae of profi is deermined by equaions (8) o (). Equaion (8) defines he real rae of profi as he nominal rae of profi less he inflaion rae ( π ). Equaion (9) deermines he nominal rae of profi ( r, ) using he nominal rae of ineres (i ), as a bench mark o which an exogenous risk premium ( σ ) is added. Equaion (0) reflecs he model s implici assumpion of endogenous money. The cenral bank supplies whaever volume of money is required by he sysem o deliver is arge nominal ineres rae (i*). This arge rae is deermined in equaion () where he cenral bank arges a consan real rae of ineres of ( i ). The nominal rae in he curren period is hus he arge real rae plus he observed inflaion rae from he previous period. The model s inflaion dynamics are given in equaions (2) o (5) in erms of a conflicing claims framework. The usual form for such a framework is o specify wo equaions (cf. Lavoie 2002, 79) such as hose in (6) and (7). Equaion (6) deermines he money wage (MW ) pursued by workers in erms of he difference beween heir desired real wage (w*) and he e lagged real wage (w - ), and he expeced price level ( p ). Ω and Ω2 are posiive adjusmen parameers. Equaion (7) specifies a price equaion used by firms o pursue a arge rae of reurn or mark-up over inpu coss represened by he expeced money wage ( MW ). Thus prices are increased whenever he arge real rae of profi (r*) exceeds he lagged rae of profi (r - ). Ω3 and Ω4 are also posiive adjusmen parameers. e n MW Ω ( w * w ) + Ω 2 = p (6) p Ω3 ( r * r ) + Ω4 e e = MW (7) Ineracion beween hese wo equaions deermines price and inflaion dynamics. As Rowhorn s (977, 29) original exposiion indicaes, precise dynamics depend on he coefficien values which reflec he relaive marke power or bargaining srenghs of workers and capialiss. These will vary from place o place and ime o ime and are very differen in he 2000s compared o heir values in he 970s for mos wesern economies. Equaions (6) and (7) could also be specified in erms of he raes of change of money wages and prices raher han heir levels. The form aken by wage-price dynamics in he KPSK model is slighly differen o his sandard represenaion of conflicing claims. The rae of profi in he KPSK model is deermined by moneary policy and he exogenous risk premium in equaions (8) o (0). We assume ha

6 5 firms always realise he rae of profi in equaion (8) by he appropriae seing of oupu prices. These prices are deermined in line wih he real wage corresponding o he arge rae of profi given he money wage. In growh erms, he rae of price inflaion ( π ) will be equal o he rae of money wage growh (MWG ) less he rae of change in real wages ( λ ). This is shown in equaion (2) and is a dynamic version of equaion (7) above. The money wage dynamics of equaion (6) may also be expressed in growh erms as follows: MWG = Ω π (8) 5 ( λ * λ ) + Ω 6 e Bu an alernaive formulaion of his approach would be for workers o specify a real wage or rae of real wage growh as he basis for money wage claims. Money wage growh would hen be equal o arge real wage growh plus expeced inflaion. Equaion (9) follows his specificaion where β capures he exen o which workers have he power o achieve heir arge. While he value of his parameer would vary as agued above, i could be expeced o be less han one. MWG [ * e = β λ + π ] (9) * Rowhorn (977, ) furher explores he deerminans of his counerpar of λ and argues ha he level of aggregae demand is significan in his respec. Equaion (20) ses ou he possible impac of aggregae demand on arge real wage growh in erms of Okun s Law and unemploymen: λ (20) * = ε θ 2UE According o (20), workers have a basic real wage growh arge of ε bu as aggregae demand in he economy falls, oupu falls and unemploymen rises. Workers realise ha heir bargaining power may be weaker on accoun of compeiion beween unemployed workers and hey moderae aspiraions for real wage growh by θ 2 for each percenage poin of he workforce ha is unemployed. Equaion (20) may be subsiued ino (9) o obain a single expression for he rae of money wage growh as follows: MWG e = + βπ βθ 2UE εβ (2) Equaion (3) in he model is idenical o equaion (2) excep for a recalibraion of parameers wihα = εβ and β 2 = βθ 2 for he sake of simpliciy. Equaion (4) deermines he expeced

7 6 rae of inflaion by a simple adapive expecaions mechanism and equaion (5) simply defines he rae of real wage growh. Equaions () - (5) encapsulae he essenial elemens of Keynes principle of effecive demand and he Kaldor-Pasinei heory of income disribuion. This approach o disribuion sresses he impac of aggregae disribuive shares on consumpion and hence oupu. I is, however, reconcilable wih Sraffa s (960) approach o value and disribuion which deermines disribuive prices raher han aggregae shares (cf. Garegnani 984). Equaion (3) explicily links he wo approaches by showing he aggregae share of wages in erms of he Sraffian real wage rae and echnical producion coefficiens given he level of oupu deermined by he principle of effecive demand. The Sraffian equaion also allows us o incorporae Sraffa s suggesion ha he free disribuive variable be he wage rae wih he rae of profi being deermined by he rae of ineres (Sraffa 960, 33). Bu here he Kaldor-Pasinei dimension of he heory of disribuion provides he ransmission mechanism by which his closure of he disribuive sory also affecs oupu. Essenially moneary policy deermines he ineres rae via equaions (0) and () and he rae of profi by equaion (8). This deermines he real wage by equaion (7) and he aggregae real wage by equaion (3) which hen has an impac on consumpion via equaions (2) and (4). Unemploymen is deermined by a version of Okun s Law expressed in equaion (6). The Sraffian componen of he model essenially deermines income disribuion via moneary policy while he Kaldor-Pasinei componen of he model examines he impac ha his disribuion, scaled o he aggregae level, has on effecive demand and oupu. The inflaionary process is affeced by disribuion and oupu bu will no feedback on hese variables in long run equilibrium. The KPSK sysem represened in equaions () o (5) may be reduced o a smaller se of equaions as described in he Appendix. The reduced form of he model is given in equaions (22) o (24) below: UE Y 2 θ Y ky = A (22) + + l θ UE kue = ( k) A (23) L * θ e ( jβ ) π ( j π + jβ β UE = α j (24) + ) where θ = ( h) ( s ) + ( h) ( s s ) [ k ( i + σ + )] c c w and A = C + C G. w C +

8 7 Equaion (22) is, however, separable and can be explored independenly. This second order linear difference equaion in oupu possesses he ineremporal equilibrium given in expression (25) (once again see he Appendix for he derivaion of his expression): Y ** = A θ k (25) This ineremporal equilibrium has a familiar Keynesian form alhough he muliplier is more complex han in he usual Keynesian case. The expression for θ in (22), indicaes ha he muliplier process in he KPSK model depends on he proporion of income spen wih each augmenaion of income bu his proporion depends on he relaive propensiies o consume of workers and capialiss, expressions s ) and s ), and he disribuion of income. The ( w ( c disribuion of income is in urn deermined by moneary policy and he echnical condiions of producion. The k erm indicaes ha invesmen impinges on he muliplier process since he proporion of capial ha depreciaes each period depends on he volume of producion. However, equilibrium oupu is equal o a muliple of auonomous expendiure where he muliple depends on disribuion and moneary condiions in he model. The model is hus characerised by money non-neuraliy. Sabiliy of his equilibrium depends on wheher he absolue value of he roos of he characerisic equaion corresponding o (22) are less han uniy. The expression for hese roos involves a complex combinaion of he model s parameer values including he capial-oupu raio and he rae of depreciaion. This expression is shown in he Appendix and is evaluaed for specified reasonable parameer values and a range of capial-oupu raios and depreciaion raes. The shaded area in Table indicaes combinaions of he capial-labour raio and he depreciaion rae for which he absolue value of boh roos is less han one. Since a capial-oupu raio of around one and a depreciaion rae of 5% would be reasonable for an economy like ha of Ausralia, he bordered area indicaes wha migh be regarded as a range of reasonable combinaions for hese wo variables. Since his bordered area is well wihin he shaded region, we conclude ha he KPSK model is sable for reasonably specified values of is parameers. Deerminaion of equilibrium oupu from equaion (22) hen feeds ino equaion (23) o deermine equilibrium unemploymen, which feeds ino equaion (24) o deermine equilibrium inflaion. These equilibrium values are shown in expressions (26) and (27):

9 8 UE ** l = A L * θ k (26) π e ** lβ 2 = [ α β 2 + β L * A ] θ k (27) The condiions for sabiliy of hese resuls are also shown in he Appendix and unambiguously hold for he parameer values specified in Table. The KPSK model of oupu, disribuion and inflaion hus provides a coheren alernaive o he neoclassical paradigm. k/d Sable Sable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable 4.50 Sable Sable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable 4.00 Sable Sable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable 3.50 Sable Sable Sable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable 3.00 Sable Sable Sable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable 2.50 Sable Sable Sable Unsable Unsable Unsable Unsable Unsable Unsable Unsable Unsable 2.00 Sable Sable Sable Sable Unsable Unsable Unsable Unsable Unsable Unsable Unsable.50 Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable Unsable.40 Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable Unsable.30 Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable Unsable.20 Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable Unsable.5 Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable Unsable.0 Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable Unsable.05 Sable Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable.00 Sable Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable 0.95 Sable Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable 0.90 Sable Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable Unsable 0.85 Sable Sable Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable 0.80 Sable Sable Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable 0.75 Sable Sable Sable Sable Sable Sable Sable Sable Unsable Unsable Unsable 0.50 Sable Sable Sable Sable Sable Sable Sable Sable Sable Unsable Unsable 0.25 Sable Sable Sable Sable Sable Sable Sable Sable Sable Sable Sable Table : Sabiliy Characerisics of he Model for Combinaions of he Capial-Oupu Raio and Depreciaion Rae wih: s c = 0.39; s w = 0.06; ibar = 0.02; σ = The Role of Endogenous Money in he KPSK Model The KPSK model oulined in Secion 2 incorporaes boh endogenous money and ineres insensiive invesmen expendiure. Given he argumen ha each of hese srucural feaures is capable of delivering an equilibrium characerised by unemploymen, i will be insrucive o explore money s role in he model. Our saring poin in his exploraion is a recogniion ha money is non-neural wihin he model. The operaion of endogenous money, of course, enails fixing he real ineres rae. This deermines income disribuion and, wih he echnical condiions of producion and invesmen behaviour, he muliplier. An ineres rae se oo high implies a smaller muliplier and lower equilibrium oupu. In his way, moneary condiions have real effecs.

10 9 I is imporan o noe ha his resul does no depend on money illusion. Dochery (2006) explores he naure of unemploymen equilibrium in a model which is also characerised by he principle of effecive demand and endogenous money, bu which has ineres-sensiive expendiures. Deerminacy of he unemploymen resul in his model requires money illusion on he par of workers which serves as he model s nominal anchor. Wihou money illusion, he price level is indeerminae in ha kind of model. The reason for his is ha he equaliy of acual and expeced inflaion in he Phillips curve equaion requires a specific value for unemploymen. This is, of course, he NAIRU and i implies a verical long run Phillips curve. If unemploymen is differen from his level, prices mus rise or fall coninuously. For example, if unemploymen is above he NAIRU, workers will reduce heir wage demands and his will reduce he rae of price inflaion. As acual inflaion falls, expeced inflaion falls and his furher reduces acual inflaion. In a neoclassical model his process is usually runcaed by he presence of an exogenous money supply. If deflaion reduces he demand for money, an exogenous and fixed money supply implies falling ineres raes. Invesmen will hen be simulaed and oupu will rise hus reducing unemploymen and moving i closer o he NAIRU. The movemen o full employmen also ends he movemen of prices when he money supply is exogenous and fixed, rendering he price level deerminae. When he money supply is endogenous his mechanism canno operae. Bu he price level can be made deerminae if he expeced rae of inflaion is removed from he Phillips curve equaion. In his case no paricular level of unemploymen is associaed wih equaliy of acual and expeced inflaion and here is no NAIRU. Worker concern wih he nominal value of wages may be influenced by he level of unemploymen and his boh locks down he sysem s nominal dimensions and allows effecive demand o deermine unemploymen (see Dochery 2006). However, in he presen model here is no money illusion since workers arge and pursue a real wage objecive. Wha allows us o combine endogenous money and a lack of money illusion is he conflicing claims srucure of he wage-inflaion dynamics. This delivers he same heoreical resul as money illusion bu wihou he unsaisfacory naure of ha assumpion. Workers pursue claims for real wages bu he marke power of firms limis he success of hese campaigns so ha no paricular level of unemploymen is implied by he realisaion of expecaions. The long run Phillips curve is hus no verical bu downward sloping even in he absence of money illusion. Expressions for he shor run and long run Phillips curves are shown in equaions (28) and (29) respecively: π (28) e = [ αβ λ ] + βπ ββ 2 UE

11 0 π [( αβ λ ) β β UE ] (29) = 2 β The shor run Phillips curve in (28) has he usual srucure excep ha he coefficien on expeced inflaion akes a value differen from uniy. Thus changes in expeced inflaion can move he Phillips curve up and down in he usual way. Bu in he long run when expecaions are realised, he curve akes he form shown in equaion (29). If β is equal o uniy, he denominaor in he firs erm on he RHS will equal zero and he rae of inflaion will be undefined. This is he usual neoclassical case and in his case he KPSK model would have no nominal anchor. The brackeed erm in (29) would be equal o zero and unemploymen would have o be equal o he NAIRU for inflaion expecaions o be realised. However, when β akes a value less han one, indicaing a limi o he abiliy of workers o realise heir real wage objecives, he long run Phillips curve has a negaive slope. Thus unemploymen deermined by he principle of effecive demand feeds ino he deerminaion of long run inflaion via he exen o which workers pursue real wage growh inconsisen wih ha deermined by moneary policy. π LRPC π SRPC 2 π 2 A SRPC 0 UE UE Figure : Equilibrium and Sabiliy Feaures of he Model wih Endogenous Money and an Absence of Worker Money Illusion

12 This is shown in Figure. The slope of he long run Phillips curve in equaion (29) is given by β β 2 /(-β ) which mus be greaer han he slope of he shor run curve given by β β 2 when β <. If we assume ha he long run curve is given by LRPC, ha he shor run curve is iniially given by SRPC and ha unemploymen is a an equilibrium value of UE, curren inflaion mus be π which is above is long run equilibrium value of π 2. This can only be because expeced inflaion is currenly above acual inflaion. This will cause a revision of expeced inflaion downwards by equaion (4) above, which will shif he shor run Phillips curve in Figure downwards unil i reaches SRPC 2. Given his shor run curve, acual and expeced inflaion will be idenical (a poin A) wih unemploymen of UE. However a differen level of unemploymen, deermined by a differen level of effecive demand, would generae a differen long run equilibrium value for inflaion along he long run Phillips curve. Money is hus non-neural in he KPSK model. The fixed ineres rae associaed wih an endogenously deermined money supply generaes a disribuion of income which in urn generaes unemploymen a a posiion of long run equilibrium. I is worh poining ou ha while invesmen spending is ineres-insensiive in he sense ha cos of capial effecs play no role in he formulaion of firms plans for capial expendiure, changes in ineres raes do have clear implicaions for spending. This is cenral o he naure of he model s non-neuraliy. The nominal dimensions of he model are rendered deerminae by he naure of conflicing claims over income disribuion and in paricular by workers lack of complee conrol over nominal wage oucomes despie he absence of money illusion. A second and relaed dimension of money s role in he model may be seen by examining he sysem s reacion o an exogenous increase in invesmen spending. Le us assume a permanen increase in he rae of depreciaion from 5% o 6%. In order o consider he impac of his shock o invesmen we assume a se of values for he sysem s parameers and exogenous variables. These values are oulined in Table 2. We hen use hese assumpions o calculae equilibrium values for he sysem s endogenous variables. These are shown in Table 3. We hen shock he sysem wih a % increase in he rae of depreciaion hus increasing real invesmen and rack he response of key variables. This invesmen shock simulaion was srucured so ha he sysem operaed a he original equilibrium from periods o 20 before increased invesmen his he sysem in period 2. The response of key variables is presened in Figures 2 and 3. Panel A in Figure 2 shows he impac ha he shock o he rae of depreciaion has on he level of invesmen spending which rises by abou 0% from is iniial level. Panel B shows he consequenial effec of his increase on he level of oupu which expands by abou 3.33%. This increase in producion in urn reduces

13 2 he rae of unemploymen as indicaed in Panel C. The increased rae of depreciaion also reduces he real wage via equaion (7). Since more capial is used in he producion process each period, less oupu is available o pay real wages and he real wage rae falls. This ranslaes ino reduced aggregae real wages via equaion (3) and hus ino a reduced wage share. The change in depreciaion hus has wo opposing influences on equilibrium income. According o he firs, Variable Value Variable Value s w C w.5 s c C c 0. σ G k L* 6.00 l i 0.02 β β j α Table 2 : Parameer and Exogenous Variable Assumpions Variable Value Variable Value Y w 4.89 C π I 4.25 π e W MWG P r 0.20 UE 0.05 i Table 3 : Iniial Equilibrium Values for Endogenous Variables

14 3 invesmen rises, simulaing aggregae demand and oupu. According o he second, income is redisribued from workers (wih high propensiies o consume) o capialiss (wih lower propensiies o consume), dampening aggregae demand and oupu. However, he expression for θ in equaion (22) above indicaes ha he firs of hese effecs will always dominae he second, causing he ulimae reducion in unemploymen shown in Figure 2. Panel A Invesmen Saving Index Panel B Oupu Index

15 Panel C Unemploymen per cen Figure 2 : The Response of Invesmen, Saving, Oupu, and Unemploymen o a Permanen % Increase in he Rae of Depreciaion Panel A Nominal Profi Rae Real Profi Rae Rae Panel B Expeced Inflaion Money Wage Growh Acual Inflaion per cen

16 5 Panel C Nominal Ineres Rae Real Ineres Rae Rae Figure 3 : The Response of he Rae of Profi, Inflaion and Ineres Raes o a Permanen % Increase in he Rae of Depreciaion The higher level of invesmen spending which ulimaely increases equilibrium income should have poenial moneary effecs. A he mos basic level, greaer income should cause increased real demand for money which should place pressure on real ineres raes. In he KPSK model, his would aler income disribuion back in favour of capialiss, reducing he impac of he invesmen expansion. Bu he model precludes his kind of effec by equaions (0) and (). The fixed real ineres rae implicily assumes ha any increase in real demand for money is accommodaed by he cenral bank. Corell (986) argues ha here may also be poenial financing problems associaed wih he invesmen expansion ha could force real ineres raes o increase. Panel A of Figure 2, he doed line shows he response of he sum of privae and public saving o he invesmen shock. A any poin in ime afer he shock bu before he economy reaches he new equilibrium, invesmen runs ahead of saving and his defici requires financing. In addiion, if savers do no wish o hold he securiies issued by he firms aemping o finance he addiional invesmen, furher upward pressure on ineres raes may resul. Dochery (2005, ) argues, however, ha in eiher of hese cases here will be porfolio reallocaions in response o such higher ineres raes which will evenually resul in a greaer volume on he marke of wha ever securiy he cenral bank uses o conduc moneary policy. This higher volume will reduce he price of his securiy and raise is ineres rae unless he cenral bank purchases he unwaned volume, providing liquidiy sufficien o finance he savings-invesmen gap unil equilibrium is reached or porfolio preferences are saisfied. All of his is implied by equaions (0) and () and consiues he second role of money in he model. The expansion does, however, have effecs on nominal variables. The reduced level of unemploymen increases he bargaining power of labour which pushes for higher real wages via

17 6 equaion (20). This feeds ino a push for higher nominal wages and inflaion via equaions (3) and (2) respecively, and becomes self-reinforcing via he effec on expecaions in equaion (4). The higher raes of money wage growh and he resuling higher equilibrium level of inflaion are shown in Figure 3. Higher inflaion leads o higher nominal ineres raes due o he moneary policy of sabilising he real ineres rae. This is also shown in Figure 3. A hird perspecive on he role of money in he model is obained by considering he impac ha a swich o a fixed exogenous money supply would have on he model s key variables. Once again we assume ha he model operaes a he equilibrium specified in Table 3 for he firs 20 periods. In period 2 he cenral bank swiches from supplying money endogenously and aemps insead o enforce a sric money growh rule of 5.7% per period. Nominal ineres raes are hus no longer given by equaions (0) and () bu by equaion (30) below: Y Y 2 + β 3 + m (30) Y 2 = i π i According o his equaion ineres raes adjus upwards from he previous period as he sum of real GDP growh and he rae of price inflaion exceeds he exogenous rae of moneary growh (assumed here o be 5.7% per period).the inclusion of equaion (30) ransforms he reduced sysem in equaions (A6) and (A7) in he Appendix ino a highly complex, nonlinear sysem in unemploymen and expeced inflaion. Simulaions for his sysem indicae ha i is highly unsable and very quickly generaes large values for all variables. Variable ime pahs for hese simulaions have, herefore, no been repored excep for he iniial periods following period 2 for ineres raes, unemploymen and inflaion. These are shown in Figure 4. Unemploymen even slighly above he original equilibrium causes reducions in workers arge real wage. This iniially reduces money wages and inflaion. This can be seen from Panel A in Figure 4. Lower inflaion causes wo furher effecs: a fall in inflaion expecaions and a fall in nominal ineres raes. The effec on real ineres raes depends on which of hese effecs dominaes. Panel A in Figure 4 indicaes ha real ineres raes iniially fall. Unemploymen hus falls and generaes a reverse se of effecs. Bu he changes in real ineres raes cause flucuaions in oupu which feedback on boh he ineres rae and unemploymen so ha soon large variaions in nominal ineres raes, real ineres raes, inflaion, unemploymen and oupu inerac o feed each oher and cause explosive oscillaions in he sysem. This occurs for a wide range of parameer values. The KPSK sysem is hus highly unsable when endogenous money is replaced wih exogenous money. Panel A in Figure 4 is curiously reminiscen of he increased volailiy of ineres raes

18 7 during he Fed s monearis experimen (cf. Mishkin 2006, 38) and he significan increase in boh he level and volailiy of unemploymen in Panel B of Figure 4 is no dissimilar o he paern of unemploymen in he years ha followed his experimen. When he money supply is endogenous, he real rae of ineres is sabilised and does no quickly reac o variaions in inflaion or aciviy which such reacions feed in he exogenous money case. Endogenous money is hus an essenial par of he KPSK sysem which is characerised by ineres-insensiive invesmen expendiure and which generaes unemploymen equilibria despie an absence of money illusion. Endogenous money and he framework surrounding i performs he hreefold funcion of providing ineres rae sabiliy, a mechanism by which moneary condiions have real effecs and he financial means by which expendiures have heir independence from saving in disequilibrium. Panel A Nominal Ineres Rae Real Ineres Rae Rae Panel B Expeced nflaion Money Wage Growh Acual Inflaion per cen

19 Panel C Unemploymen per cen Figure 4 : Response of he Ineres Raes, Inflaion and Unemploymen o a Swich from Endogenous o Exogenous Money The following secion explores he implicaions of how money funcions in he KPSK model for he operaion of moneary policy. In paricular wo relaed quesions are considered: why would cenral banks mainain moneary condiions which generae unemploymen? And: wha impac would some form of Taylor rule have on an economic sysem of he KPSK variey since cenral banks use such rules raher han rules which permanenly fix real ineres raes? 4. Moneary Policy in he KPSK Model Cenral banks do no, of course, run naïve rules which permanenly fix he real rae of ineres. Insead, hey use moneary policy couner-cyclically in response o economic condiions as hey sand in relaion o specified arge values. This secion explores he operaion of couner-cyclical moneary policy wihin he KPSK model using a form of Taylor rule. I also examines a second poenial use of moneary policy wihin he KPSK model which is o change income disribuion. We consider hese issues in urn. Many cenral banks follow an inflaion argeing regime and se he nominal ineres rae according o some varian of Taylor s (993) now famous rule. According o his rule, he nominal ineres rae should be se equal o a base real rae of ineres ( i ) plus lagged inflaion plus an upwards adjusmen for he exen o which acual lagged inflaion exceeds arge inflaion plus an addiional upwards adjusmen for he degree o which lagged oupu exceeds poenial oupu. The cenral bank in our model will follow a similar rule o his bu wih he oupu gap replaced by he deviaion of he lagged unemploymen rae from some arge unemploymen rae (UE*) since unemploymen is he variable of cenral ineres in his paper raher han oupu. Equaion (3) expresses his form of he Taylor rule and he approach will be o allow he

20 9 economy o operae a he original equilibrium considered above for weny periods wih he cenral bank fixing he real rae of ineres and hen o have i swich o a Taylor rule in period 2 wih a arge inflaion and unemploymen boh se a heir equilibrium levels (5.7% for inflaion and 5.0% for unemploymen). Thus a period 2 we replace equaion () in he original model above wih equaion (3). We will also consider a number of policy changes underaken in period 0. Boh he inflaion and unemploymen arges will be increased and decreased by beween % and 2% from heir iniial arge values in four separae cases o be considered. i = * * i + π + β 3 ( π π ) β 4 ( UE UE ) (3) Resuls for he iniial swich o a Taylor Rule in period 2 and hen a reducion in he inflaion arge from 5.7% o 4.0% in period 0 are shown in Figure 5. As one migh expec, here is lile Rae Panel A Nominal Ineres Rae Panel B Expeced Inflaion Money Wages Growh Acual Inflaion Rae

21 20 per cen Panel C Unemploymen Figure 5 : Swich o Taylor Rule in Period 2 wih Reduced Inflaion Targe in Period 0. Panel A Nominal Ineres Rae Rae Rae Panel B Expeced Inflaion Money Wages Growh Acual Inflaion

22 Panel C Unemploymen per cen Figure 6 : Swich o Taylor Rule in Period 2 wih Reduced Unemploymen Targe in Period 0. change o he behaviour of any of he model s variables a period 2 when he cenral bank swiches o he Taylor rule. The equilibrium values of ineres raes (boh nominal and real) inflaion, money wage growh, and he rae of unemploymen all remain unchanged beween periods 2 and 00. Since arges are me for boh inflaion and unemploymen under he equilibrium of he baseline model, ineres raes simply mainain heir original values. Bu he behaviour of he sysem when arge inflaion is reduced is more ineresing. Panel A shows ha since inflaion is now above arge, he nominal ineres rae is raised. This also causes an iniial increase in he real ineres rae, an increase in he real rae of profi and a reducion in he real wage wih he impac being o reduce consumpion spending and oupu and o increase unemploymen. The increased unemploymen rae implies ha unemploymen is now above arge and his acs o dampen ineres raes. The model is, however, very sable and converges o equilibrium relaively quickly. Bu noice ha he equilibrium raes of inflaion and unemploymen, shown in Panels B and C, are no equal o heir arge values. Boh raes are above arge. The reason for his is sraigh forward. Since inflaion above arge mandaes an ineres rae decrease, while unemploymen above arge mandaes an ineres rae increase, here comes a poin (depending on he relaive values of he bea coefficiens) where hese mandaes offse each oher leaving he nominal ineres rae unchanged. In he case where he inflaion arge is raised from is iniial equilibrium value in he baseline case, jus he opposie siuaion occurs wih boh variables below arge. This case is no shown due o space consideraions. A hird case, idenical o he firs, bu where he unemploymen arge is reduced in period 0 from 5.0% o 4.0% is shown in Figure 6. Panel A indicaes ha he change in arge generaes an

23 22 iniial reducion in he ineres rae. The lower nominal rae reduces boh he real raes of ineres and profi and increases he real wage. This redisribues income oward workers and increases aggregae consumpion and oupu. Unemploymen hus falls. Bu worker bargaining power is increased by his reducion in unemploymen and boh he rae of growh of money wages and he rae of inflaion rise. In equilibrium, he same resul obains as for he reducion in he inflaion arge wih boh inflaion and unemploymen seling a values above arge because of he offseing effecs ha hese posiions have on he policy rae. In he case where he unemploymen arge is raised from is iniial equilibrium value in he baseline case, he opposie resul o his hird case obains wih boh variables below arge. This case is also no shown. The firs funcion of moneary policy, herefore, according o which i follows some form of Taylor rule also generaes sable equilibrium oucomes in he KPSK model bu provides a possible explanaion for persisen unemploymen. If he economy begins from a posiion where eiher inflaion or unemploymen are above heir arge values, offseing ineres rae requiremens mandaed by he Taylor rule may leave ineres raes a wha is essenially heir equilibrium values for he sysem. The corresponding equilibrium values for inflaion and unemploymen would hus be differen o heir arge values, unemploymen being higher han desired. The second funcion of moneary policy o be considered in his secion is is use o change income disribuion. This could be modeled in a number of ways bu in he approach aken here he cenral bank permanenly increases he fixed, arge, real rae of ineres used o deermine he curren nominal ineres rae from 2% o 3%. The economy hus operaes a he original equilibrium for 20 periods bu in period 2 he cenral bank increases is arge real rae of ineres. The reacion of he sysem o such an innovaion depends crucially on he values of parameers β, he abiliy of workers o ranslae heir inflaion expecaions ino money wage growh, and β 2, he exen o which unemploymen dampens he formulaion of arge real and, herefore, nominal wages. Two cases are, herefore, considered. In he firs, β and β 2 are se a relaively low levels (0.65 and 0.5 respecively) ha reflec a relaively poor bargaining posiion of labour bu a he same ime a small effec of he impac of unemploymen on he formulaion of arge real wages. The impac of he policy change under hese circumsances is illusraed in Figures 7 and 8. Panel A in Figure 7 shows ha he policy of raising he real rae is successful alhough he real rae iniially overshoos is arge before seling down o a new higher equilibrium level. In Panel B of Figure 7, his has he expeced effec of increasing he real rae of profi by half a percenage poin and reducing he real wage, shown in Panel C. The consequen

24 23 change in income disribuion a he aggregae level reduces consumpion spending and hus oupu, and increases unemploymen. This is shown in Panel A of Figure 8. Since unemploymen is higher, he bargaining power of labour is reduced, money wage growh falls and inflaion subsequenly declines. This is shown in Panel B of Figure 8. Lower inflaion implies lower nominal ineres raes as shown in Panel C and hence he lower nominal rae of profi in Panel B of Figure 7 despie he higher real rae of profi. In he second case β and β 2 are se a much higher levels (0.9 and 0.8 respecively). These values reflec a more inensive conflic over income disribuion where any change in inflaion expecaions, for example, feeds ino higher demand for money wages more successfully, raising acual inflaion and affecing he real rae of profi. This has real effecs hrough is impac on income disribuion and he consequen effec on unemploymen feeds back on he formulaion of money wages in such a way as o creae significan cyclical variaion. The impac of he policy change under hese circumsances is illusraed in Figures 9 and 0. The increased real rae of Panel A Real Ineres Rae Rae

25 24 Panel B Nominal Profi Rae Real Profi Rae Rae Panel C Real Wage Index Figure 7 : Response of Real Rae of Ineres, Raes of Profi, and he Real Wage o a % increase in he Targe Real Ineres Rae. Low Values for β and β 2. Panel A Nominal Ineres Rae Rae

26 25 Panel B Expeced Inflaion Money Wage Growh Acual Inflaion per cen Panel C Unemploymen per cen Figure 8 : Response of he Nominal Ineres Rae, Inflaion and Unemploymen, o a % increase in he Targe Real Ineres Rae. Low Values for β and β 2. Panel A Nominal Ineres Rae Rae

27 26 Panel B Expeced Inflaion Money Wage Growh Acual Inflaion per cen Panel C Unemploymen per cen Figure 9 : Response of he Nominal Ineres Rae, inflaion andunemploymen o a % increase in he Targe Real Ineres Rae. High Values for β and β 2. Panel A Nominal Ineres Rae Rae

28 27 Panel B Expeced Inflaion Money Wage Growh Acual Inflaion per cen Panel C Unemploymen per cen Figure 0 : Response of he Nominal Ineres Rae, Inflaion and Unemploymen o a % increase in he Targe Real Ineres Rae. High Values for β and β 2 and Taylor Rule. ineres increases he real profi rae, redisribues income from workers o enrepreneurs and reduces oupu. Unemploymen rises and money wage growh and inflaion fall. This fall happens slowly and as i does, nominal ineres raes also fall. Bu he model is consrained by a zero nominal ineres bound. Evenually nominal ineres raes hi his bound and when his happens a crisis is precipiaed. Furher reducions in he inflaion rae, now increase he real rae of ineres, exacerbaing he policy change. Deflaion feeds iself via he adapive expecaions mechanism (as indicaed in Panel C of Figure 9) causing an amplificaion of he real ineres rae effec so ha a massive redisribuion of income reduces oupu and increases unemploymen dramaically. These effecs are shown in Panels A and B of Figure 9. The sign of key variables such as he real wage evenually change as he sysem explodes, which causes a reversal in he deflaionary paern and he sysem re-converges oward equilibrium. Bu he paern may recur muliple

29 28 imes before sabilising (unless he equilibrium nominal ineres rae is negaive in which case he paern will simply recur indefiniely). These resuls are consisen wih he findings of Rowhorn (977, 227) who finds dynamic insabiliy when disribuional conflic is inense depending on he iniial posiion of he sysem. A Taylor rule, however, prevens he emergence of he periodic financial crises represened in Figure 9 even wih high values for β and β 2. The operaion of he rule adds an addiional sabilising influence on ineres raes when inflaion or unemploymen begin o respond o he srong dynamic forces of he sysem. Figure 0 depics he sysem a is original equilibrium for periods o 20 and hen he swich in period 2 o a Taylor rule as before. In period 4, however, he base real rae, i, is increased from 2% o 3% wih he high values for β and β 2. In Panel A of Figure 0 he nominal rae is increased in line wih an increase in he base real rae. This increased he real rae of profi, reduces he real wage and redisribues income in a way ha reduces consumpion and increases unemploymen. This is shown in Panel B. This in urn causes he deflaion ha evenually led he nominal ineres bound being hi. However, he model sabilises in his case. Conclusion This paper has explored he behaviour of a model characerised by he Keynesian principle of effecive demand adjused o accommodae he influence of income disribuion in he Kaldor- Pasinei radiion, a Sraffian heory of value and disribuion, ineres-insensiive expendiures and endogenous money. I has shown ha such a model is sable under reasonable assumpions abou key parameer values and generaes equilibria characerised by persisen unemploymen. The model hus displays long run money non-neuraliy. The paper has also shown ha endogenous money is a necessary condiion for sabiliy in a Kaldor-Pasinei-Sraffa-Keynes (KPSK) sysem and ha he model canno funcion wih an exogenous money supply. I has also explored he impac of a Taylor rule wihin he KPSK framework. In conras o he neoclassical model where a Taylor rule operaes o deliver he appropriae money supply for a given inflaion arge, a Taylor rule in he KPSK model helps o explain why cenral banks migh se ineres raes a levels oo high for full employmen.