Does the Central Bank Set the Natural Rate of Unemployment?

Transcription

1 Does he Cenral Bank Se he Naural Rae of Unemploymen? Theoreical Consideraions on Wage Policies for he Transmission Mechanism of Moneary Policy by Sefan Collignon Inroducion Will he firs acion of he European Cenral Bank consis in rising or lowering ineres raes? In his paper I will no even ry o guess. Insead I will se ou a heoreical argumen under wha condiions an independen cenral bank which is commied o mainain price sabiliy will be able o cu or be obliged o rise ineres raes. Moneary orhodoxy seems o agree oday ha "Governmen normally inflaes in order o achieve real objecives" (Cukierman, 1992, p. 17). The sraegic ineracions beween nominal wage seers and a moneary auhoriy ha cares abou boh employmen and price sabiliy creae excessive inflaion wihou having any effec on he level of employmen (Barro and Gordon, 1983). By delegaing auhoriy o an independen cenral bank which cares "primarily" abou price sabiliy, he inflaion bias can be reduced wihou having an effec on average employmen. Such arrangemen is herefore welfare improving (Rogoff, 1985). This heoreical approach has been ranslaed ino he Saue of he European Sysem of Cenral Banks (ESCB) which sipulaes in ar. 2 and in ar. 105 (1) of he Treay on he European Union (TEU) ha "he primary objecive of he ESCB shall be o mainain price sabiliy". Such prioriisaion has occasionally been inerpreed as precluding he ECB from addressing any oher policy objecives (e.g. Crawford, 1996, p. 236). However, he same aricle of he ESCB saue insiss ha "wihou prejudice of he objecive of price sabiliy, i 1 shall suppor he general economic policies in he communiy wih a view of conribuing o he achievemen of he objecives of he Communiy as laid down in aricle 2 of his Treay." This laer aricle saes ha by esablishing an economic and moneary union, he European Communiy shall have as is ask "...susainable and non-inflaionary growh..., a high level of employmen and of social proecion, he raising sandard of living and qualiy of life..." Thus, he Treay of Maasrich clearly ses real economy objecives for EMU, subjec, of course, o he mainenance of price sabiliy. An efficien moneary policy by he ECB would have o maximise economic growh and employmen under he consrain of sable prices. Violaing he consrain will be a disqualifying faul; bu he bank's efficiency will be measured by real facors like economic growh and he unemploymen rae. This is no exacly he same as he usual model 1 he ESCB 1

2 where a cenral bank is concerned wih boh price sabiliy and high unemploymen and aims o minimise he cos of excess unemploymen and excess inflaion. In fac, if price sabiliy is viewed as a binding consrain, here can be no rade-off beween inflaion and oupu, nor beween heir flucuaions. This view of a cenral bank's asks sands in he conex of a familiar issue of economic heory: how are price inflaion and real economic aciviy conneced? A relaed quesion concerns he moneary ransmission mechanism: how much will a ighening or relaxing of ineres raes by he cenral bank affec inflaion and oupu? Empirical sudies usually produce large ideosyncraic variaions beween counries (Dornbusch e al. (1998) and hey are ofen inerpreed as obsacles o an efficien funcioning of European Moneary Union. However, wha is missing from he debae is a heory capable of explaining he srucures wihin he "black box" of he moneary ransmission mechanism. This paper aemps o conribue o such a heory. In he early days of Phillips-curve-economics a rade-off beween price sabiliy and unemploymen was widely assumed. Recenly, evidence of an inverse connecion beween inflaion and growh has emerged (Gylfason and Herberson, 1996) alhough i is far from clear ha his applies also o very low raes of inflaion. However, since Milon Friedman's (1968) presidenial address, he professional consensus has agreed ha a leas in he long run moneary policy is neural. The average level of employmen - or he naural rae - is deermined by condiions in he labour marke and oher "srucural" facors, while in he shor-run here is a rade-off in oupu-inflaion variabiliy. The sandard "acceleraionis" docrine claims ha if he supply-demand balance in he economy deviaes from he "naural" equilibrium, inflaion will accelerae or fall depending on he economy's ighness or slack. Moneary policy can only choose beween differen ampliudes of inflaion flucuaion versus flucuaions in real GDP (Taylor, 1979). The growh of moneary aggregaes will have no impac on economic aciviy and employmen, bu only resul in an increase of inflaion. From his orhodox poin of view, he efficiency margins of he ECB's policy acions would be raher small. For if he objecive o keep prices sable is inerpreed o cover boh, he level and he variance of he inflaion rae, European oupu variabiliy would have o be high and he level of average unemploymen would be deermined by he sacrifice raio required o bring inflaion down. This poses a dilemma for he ECB. High labour marke "flexibiliy" is ofen cied as a necessary condiion for a permanen reducion of average unemploymen in Europe 2, and he suggesed reforms focus on measures ha reduce social benefis and real wages. However, such policies sand in conflic wih he Treay on European Union's (TEU) aricle 2 which requess "a high level of employmen and of social proecion". Under hese circumsances, he European Cenral Bank may no be perceived as "efficien" and he European public may no develop he kind of consensus which backed he Bundesbank's commimen o price sabiliy and which may have been he foundaion of is success (Issing, 1997). Ye, moneary developmens in he 1990s have sared o raise some doub abou he orhodox model (Galbraih, 1997). In he Unied Saes unemploymen seems o have fallen below he naural rae for some considerable period of ime wihou inflaion having shown any significan 2 See for example IMF,

3 rise. This fac can be inerpreed as a fall in he naural rae and has led o he consrucion of imevarying NAIRU models (Gordon, 1996). Alhough moderae shifs in he non-acceleraing rae of unemploymen may sill appear reasonable in he US case, he large flucuaions in Europe seem oally arbirary (Collignon, 1998; Solow in: Solow and Taylor, 1998). Furhermore, for moneary policy ime-varying NAIRU models pose wo difficulies: Firs, if here is a rae of unemploymen, below which inflaion acceleraes, and if he exac posiion of his naural rae is uncerain and moving, wha would be he appropriae policy response by he cenral bank o a ransiory increase in inflaion? Could i no lead o an overly resricive moneary policy which by iself would keep he average rae of unemploymen higher han necessary? Secondly, if he average rae of unemploymen is affeced by moneary policy, hen he naural rae canno be posied as compleely exogenous and he neuraliy hypohesis would no even apply in he long run. These quesions are imporan for he conduc of moneary policy, given ha mos moneary policy rules such as seing arges for money supply or following Taylor ineres rae rules are based on he acceleraionis model. They would break down if he naural rae is iself endogenous o moneary policy. These difficulies are compounded in Europe by he uncerainies of he ransiion o European Moneary Union. Because of changes in he degree of openness, financial srucure and wage bargaining insiuions, he effecs of a unified European moneary policy may be differen from he simple weighed average of 11 naional policies. (Dornbusch e al, 1998). I will no dwell on hese ransiion problems in his paper. Insead, I wish o focus on he long erm effecs of moneary policy for economic growh and employmen and he mechanism hrough which moneary policy is ransmied o he real economy over he long run. As Modigliani (1963) poined ou, changes in ineres raes affec he economy hrough financial markes and wage selemens. In Collignon (1998b), I have aken a look a srucural differences in European financial markes. In his paper I will focus on he wage seing channel of he moneary mechanism. The res of he paper is organised as follows: Secion 2 esablishes ha he long-run equilibrium rae of unemploymen is endogenous o moneary policy. Secion 3 shows how he price level is deermined by he nominal ineres rae. Secion 4 describes he moneary policy objecive funcion based on a wage feedback mechanism. Secion 5 concludes. 2. Deermining he endogenous naural rae of unemploymen The idea of an equilibrium rae of unemploymen a which inflaion is sable has been derived from wo srands of hough (Dixon, 1995). The older radiion of a "naural rae" originaed in Chicago and focused on labour marke equilibrium. The newer concep of a non-acceleraing inflaion rae of unemploymen (NAIRU) has been developed by Layard, Nickell and Jackman a he LSE, puing he concep of non-acceleraing inflaion ino he framework of labour markes wih imperfec compeiion and focusing on wage bargaining. Alhough he laer version has permied progress in empirical research, he heoreical implicaions of he wo conceps are similar. They boh work wih an "acceleraionis" model where imbalances of supply and demand in he economy as a whole, measured by he deviaion of acual from poenial oupu or acual minus 3

4 average unemploymen, cause inflaion o speed up or down. The equilibrium or neural rae reflecs a long run saionary sae enirely deermined by "real" facors like echnology, populaion growh, preferences, labour marke insiuions ec. Moneary facors can cause emporary deviaions from he long run equilibrium, bu ulimaely money is neural in he sysem. This can be easily shown in he conex of he Painkin-Friedman-Phelps model of he naural rae 3. The naural rae reflecs he equilibrium in he labour marke where he real wage equals labour demand and supply. Conrary o Keynes who emphasized he role of nominal variables in he deerminaion of equilibrium employmen, Friedman's underlying idea is "classical" in he sense ha real wages are assumed o adjus o equae he quaniies of labour supplied and demanded 4. Bu if he unemploymen level is exclusively deermined by labour markes, hen goods prices and moneary policy, i. e. he oher markes in he Walrasian general equilibrium, canno influence oupu sysemaically. Hence, he aggregae supply curve is verical and money is neural. However, his resul depends enirely on he way he labour marke is modelled. To undersand his, le us look a labour supply and demand curves. The labour marke equilibrium The demand for labour is derived from companies seeking o maximise profis. Firms operae wih a sandard producion funcion depending on labour (L) and capial (K) a a given echnology (τ ) such as: (1) y = τf( K, L) wih F 0, F > 0, F < 0, F < 0, F > 0 L > K LL KK LK For furher reference we also define labour produciviy, i.e. he oupu per employee as: (1a) λ = τf ( k) f ( k) > 0, ( k) < 0 f. Wih λ = y L and he capial inensiy K L f k is he marginal produc of capial per uni of labour. τ reflecs Hicks-neural echnology, where he capial inensiy remains consan. Firms maximise shor erm profis by equalling he marginal produc of labour a a given capial sock o real wages. W (2) F L ( L) = P So ha, W (2a) L D = Φ, K P k =. ( ) 3 I have developed argumens similar o his paper in he conex of he Layard-Nickell-Jackman (1991) model in Collignon, The idea of inerpreing he real wage as he "price for labour" is, however, misleading. The real wage W/P is in fac he raio of wo nominal prices - ha for labour and ha for goods. Real wage flexibiliy wih respec o employmen would imply a sysemic difference beween he supply elasiciy of labour and goods. This is no obvious. See also Flassbeck and Spiecker,

5 where W is he nominal wage and P he price level and K he given capial sock. Equaions (2) and (2a) define he quaniy of labour demanded and he resuling demand curve is negaively sloped in he real wage-employmen space. Nex we look a labour supply. I is assumed o be an increasing funcion of he real wage and of a vecor of shif parameers X: W (3) L s = ϕ, X wih ϕ'>0 P The lieraure has produced a long lis of facors which migh shif he labour supply curve exogenously. Typically i includes populaion growh, he reservaion wage, he replacemen raio, facors affecing he job mach funcion, efficiency wages, rade union power, ec. Mos of hese iems come under he name of labour marke flexibiliy and are insiuionally deermined. The equilibrium rae of employmen is where supply and demand mee as in figure 1. A ha rae oupu is exclusively deermined by echnical facors and he aggregae supply curve is verical in a price-oupu space. Bu because of search coss, efficiency wages, and oher microeconomic disorions, he equilibrium employmen and oupu level is supposed o be lower han full employmen so ha a given "naural" rae of unemploymen is associaed wih a specific level of poenial oupu 5. W/P Figure 1 L Do L Fo FE 0 Unemploymen can resul from disorions or shor erm mispercepions of he real wage which would lead o emporary disequilibria from he naural rae or poenial oupu. Bu any deviaion of oupu or employmen would bring abou wage and price adjusmens which push he real wage back ino line wih he marginal produc of labour. Hence he naural rae is consan. This adjusmen is described by he expecaions-augmened Phillips curve, whereby workers are U* 5 Sricly speaking his naural unemploymen is "involunary" insofar as he labour supply curve reflecs he par of he labour force ha is willing o work. "Volunary" unemploymen could hen be shown o he lef of he Y-axis in figure 1. 5

6 ineresed in real wages and herefore ake inflaion expecaions and unemploymen (as a measure for labour marke ighness) in consideraion when bargaining for wage increases: & f u < 0 (4) w α π e + f ( u ) = 1 1 were w& and π e sand for he rae of wage increases and he expeced rae of inflaion; u is unemploymen. The coefficien α 1 is a parameer for wage indexaion which Friedman posulaed o be equal o one. 6 However, he acual real wage is idenically equal o he rae of labour produciviy (λ ) imes he wage share (σ ) in income. Hence: (4a) where w& π = λ& + σ& w w σ& is he rae of change of he wage share. Insering (4a) ino (4) yields: & (4b) σ ( ) ( ) e w = f u 1 π π λ & The naural rae hypohesis assumes ha expeced and acual inflaion coincide and ha he labour share (or is mirror he profi share) is consan. Thus, average unemploymen is no relaed o he seady sae inflaion rae and no long erm rade-off exiss. Provided he labour share remains consan and produciviy is exogenous, unemploymen could only be reduced by "surprise inflaion" which leads o acceleraing inflaion when expecaions cach up. Under raional expecaions, when he sysemaic predicion error is zero, unemploymen could only flucuae around he naural rae wih he unanicipaed price error (Sargen, 1973). Under hese circumsances, here is a rade-off beween inflaion and unemploymen only in he shor run. If moneary policy would aim o reduce unemploymen by raising inflaion, i will be neuralised by compensaing wage increases. Consequenly, in he long run he real wage would reurn o he equilibrium level and unemploymen reurns o he naural level. The cenral bank's only objecive can and mus be o keep prices sable. Two resricions are crucial in order o obain he naural rae hypohesis. Firs, he wage share mus be consan. If i where no, naural unemploymen would be inversely correlaed wih he wage share. However, from he ideniy (4a) i is obvious ha he wage share only remains consan when uni labour coss ( w & λ & ) change in exacly he same proporion as inflaion. Bu if uni labour coss are se by firms and workers and inflaion is se by moneary policy, hen he labour share and unemploymen are no deermined independenly of moneary policy, even if raional expecaions prevail. Of course, i is rue ha he labour share canno rise or fall indefiniely. Bu if deviaions from he seady sae can be shown o be persisen, "naural" unemploymen may well be ime-varying and endogenous o moneary policy. Wha we would need is a heory of policy-endogenous variaions of he mark-up (or profi share or real wages). 6 In he 1970's here was a large debae wheher α = 1 1 can be empirically verified. I urned ou ha his is always he case wih raional expecaions. We will reurn o his below. 6

7 Secondly, he model is based on he behaviour of shor erm profi maximising firms which implies a consan capial sock. Under his condiion, he level of he naural rae depends crucially on he shif parameers X. If hey shif he labour supply curve o he lef, srucural or "naural" unemploymen would rise. However, a vas amoun of evidence (see for example OECD, 1994; Blanchard and Jimeno, 1995; Ball, 1997, Solow in Solow and Taylor, 1998) shows ha alhough insiuional shifs may explain some variaions in he naural rae in he USA, i is impossible o explain he rapid and large increases in European unemploymen by exogenous, srucural changes in labour marke insiuions. 7 Thus, i is emping o search for endogenous facors a leas in European unemploymen rends. These facors need o explain shifs in he equilibrium rae of unemploymen. One approach incorporaes wealh effecs ino he labour supply curve. If wealh includes real balances, we are back ino a Keynesian world where money makes a difference, because real balances depend on prices. According o new Keynesians, he real effecs of moneary policy will hen be due o slow and parial adjusmen of prices. Bu ulimaely full adjusmen will be reached and we obain again (long erm) money neuraliy. An alernaive roue has been aken by real business cycle ( RBC ) heories which assume ha all prices adjus insananeously and fully. This implies ha he economy always finds iself on he labour supply curve and any flucuaion in employmen is volunary. Observed correlaions beween nominal and real variables reflec he response of moneary variables o real oupu and no he oher way round. These models have he advanage ha hey inroduce capial accumulaion and ineres raes explicily ino he labour supply funcion. Work effor, i.e. he shor erm supply funcion, depends on ineremporal subsiuion in labour supply: if oday's wages increase relaive o fuure income, households increase oday's labour relaive o fuure supply. Similarly, a rise in ineres raes increases he araciveness of working oday and saving relaive o working omorrow. Here, he ineres rae is considered as he ineremporal rae of subsiuion and no as a moneary policy insrumen. However, because his (real) rae of ineres is dependen on hrif and produciviy, higher savings will reduce he ineres rae. Thus, despie households' willingness o subsiue heir labour supply ineremporally, movemens in echnology and/or capial have offseing effecs on labour supply. Consequenly, he labour supply curve can be assumed o be consan (Romer, 1996; p.161). However, he labour demand curve is no necessarily consan because capial accumulaion or echnology shocks shif he marginal produc of labour and herefore also he supply curve (McCallum, 1989, p.193). Hence, equilibrium employmen is no fixed, and he naural rae of unemploymen varies wih produciviy shocks. In his case he acceleraionis model of moneary policy breaks down because any rae of unemploymen is "naural", while moneary policy is ineffecive in achieving any real effecs. An imporan criicism of RBC-models is ha echnology shocks are posulaed bu no explained, and ha observed evidence only conforms parially o heory, if a all (Mankiw, 1989). Furhermore, he ineremporal subsiuion of labour supply is a shor erm phenomenon, while 7 I has also been noiced ha progress has been made wih labour marke reforms in Europe, bu no significan impac on srucural unemploymen has been observed. Maybe his is so because acion has no been sufficien, as he OECD (1998) and IMF claim. Bu i could also follow from an inadequae explanaion model. 7

8 lile is said abou long erm facors (Barro and Grilli, 1994). In fac, he so-called neuraliy of money is ofen obained because he shor erm producion funcion is exrapolaed ino he long erm. This is clear when we refer back o he producion funcion (1). By definiion he capial sock is consan in he shor erm and variable in he long erm. Hence, over ime he marginal produc of labour and he real wage are a funcion of invesmen. Thus, explaining he "naural" rae requires an assessmen of capial accumulaion on labour supply and demand. In he following we will assume, in line wih orhodoxy, ha labour and profi shares remain unchanged in equilibrium. Changes in real wages herefore reflec changes in labour produciviy. We also neglec exogenous shif parameers such as he reservaion wage ec. The long erm evoluion of he naural rae depends now on he mode of capial accumulaion. We can disinguish wo polar cases where he naural rae of unemploymen remains unchanged. The firs pole is a Hicks-neural seady sae growh equilibrium, he second reflecs growing capial inensiy. However, in all inermediary cases, employmen is consrained by invesmen and he naural rae is undeermined. 1. If he capial sock grows a he same rae as he labour force, capial inensiy says consan. Labour produciviy and he real wage also remain unchanged (see equaion (1a) and (2)), unless wage bargaining disurbs he income disribuion (4a) 8 Thus all hree, he labour demand and he supply curve and he full employmen level move o he righ, because boh he capial sock and he labour force grow a he same rae (see figure 2). Hence, he naural rae remains sable, despie rapid growh in he labour force and capial sock. This is he sylised fac of he USlabour marke. W/P Figure 2 L Do L D1 FE 1 L Fo L F1 FE0 U 0 * = U 1 * 8 We absrac from Hicks-neural progress, i.e. τ = 0. 8

9 2. Alernaively, assume all invesmen is used o increase he capial inensiy of producion, while he labour force remains unchanged. Thus labour produciviy and he real wage rise. The labour demand curve is shifed upward by he increase in he capial sock. Wheher equilibrium unemploymen is also affeced depends on he labour supply curve. If labour produciviy is expeced o change permanenly, as i would if he capial inensiy increases, and he labour share remains consan, hen he real wage would also increase for any amoun of labour supply. In oher words, as hey ge wealhier households prefer leisure o working and he L S -curve shifs up. Thus again, he equilibrium rae of unemploymen is unchanged (see Figure 3). Figure 3 W/P L F1 L Do L D1 W/P 1 W/P 0 L Fo FE 0 U o *=U 1 * 3. Nex assume he inermediary case, where he labour force increases, bu also capial inensiy. In his case employmen is consrained by invesmen. In order o keep he naural rae consan, invesmen would have o be sufficien o accommodae boh, a growing labour force and a growing capial-labour raio. Thus, employmen growh depends on he invesmen funcion. We will formalise his idea below. Figure 4 shows he marginal case, where all invesmen is used o rise capial inensiy and produciviy, while he labour force grows from FE o o FE 1. The naural rae of unemploymen increases by he same amoun. 9 Given ha his case reflecs a growh disequilibrium or non-seady-sae, he quesion arises why he capial inensiy increases. A simple answer is ha he economy operaes below he producion-possibiliy fronier, so ha cach-up growh o a higher capial sock per worker is 9 This saemen does no imply ha he rise in produciviy is "bad" or responsible for unemploymen, bu simply ha he rae of invesmen is insufficien for absorbing he growing labour force. In fac he produciviy increase is "good", because Pareo-improving. 9

10 Pareo-opimising. 10 I is someimes argued 11 ha capial inensiy and produciviy rise because of disored incenives. Capial is subsiued when wage coss are "oo high" relaive o capial coss. However, we have explicily eliminaed his argumen by assuming ha he capial and labour shares remain consan. Furhermore, i is hard o find any empirical evidence for he labour subsiuion model. If anyhing, he labour share has fallen in Europe since he early 1980, when unemploymen sared o rise. Also, in Collignon (1998a) I have no been able o verify he claim ha wage pressure increases capial inensiy. Therefore cach-up growh seems a beer explanaion for Europe's and Japan's rising capial inensiy. Figure 5 shows he imporan European convergence o US-levels of capial inensiy beween 1960 and The capiallabour raio grew much more rapidly in Europe han in he Unied Saes, alhough he difference in capial per employee (convered ino ecu a purchasing power pariy) was sill significan in excep in Germany and France. On he oher hand, as able 1 shows, he labour force grew more rapidly in he US han in Europe, bu so did employmen. In Europe capial accumulaion was insufficien o absorb he growing labour force ino producion, so ha unemploymen rose. In Japan, on he oher hand, boh capial inensiy and employmen grew because invesmen was high. W/P Figure 4 L F1 L Do L D1 W/P 1 FE1 W/P 0 L Fo U 0 * U 1 * FE 0 I follows from his analysis ha he mode of capial accumulaion has far reaching implicaions no only for unemploymen, bu also for moneary policy. If he capial inensiy remains fairly 10 A leas i would be Pareo-opimising if a deerioraion of he unemployed's living sandard could be compensaed by ransferring some of he produciviy gains from he employed. This is exacly wha he European Social Model or Japan's life employmen end o achieve. 11 See for example IMF (1998). For a criical analysis, see Flassbeck and Spiecker,

11 consan, as in he USA, he naural rae will vary only marginally. The cenral bank would no commi a major error by following an acceleraionis model as we know from he Fed. However, if cach-up growh dominaes and he capial inensiy rises, as in Europe, hen equilibrium employmen is fixed, even if he labour force grows. Hence he naural rae of unemploymen rises. Bu because new invesmen normally shifs he labour demand curve firs and he supply curve only subsequenly, acual unemploymen will emporarily fall below he naural rae. An acceleraionis cenral bank would now ighen moneary policy. As (real) ineres raes rise, invesmen falls shor of he expansionary effecs which would be required o accommodae he growing labour force. An acceleraionis response funcion of moneary policy would preven an expansion of oupu and employmen while he faul could be blamed on rising real wages and capial-labour subsiuions. Bu if real wages would progress less han produciviy, as hey did over mos of he pos-breon Woods period (see Figure 6), hey would lower he labour share which violaes he assumpion of disribuional consancy. If, however, he rae of capial accumulaion is higher han he increase in capial inensiy, a growing labour force could be absorbed ino employmen. In order o show he impac of capial accumulaion on unemploymen, we need a model ha incorporaes ineres raes. If we assume, conrary o RBC-heory ha ineres raes are se by he cenral bank raher han by ime preference, invesmen may exceed or fall shor of planned savings, implying emporary disequilibria from he naural rae of ineres. However, he "naural" rae of unemploymen would become endogenous o macro-economic policy. Furhermore, if ineres raes also affec prices, hen he aggregae supply curve is no longer verical in he priceoupu space and money canno be neural. Thus, inegraing ineres raes and capial accumulaion ino he model makes heory less simple han he radiional naural rae hypohesis 12. Inroducing capial accumulaion In order o show he impac of capial accumulaion we sar wih a simple neoclassical growh model la Solow. The economy is on a balanced growh pah when acual invesmen equals he (ne) increase of he capial sock required o keep he labour force and echnological progress growing a heir naural raes. Oupu and capial grow a he same rae, and his rae is equal o he growh of he labour force plus echnological progress. The capial-labour raio is consan. Hence in he seady-sae: I dτ (5) &y = = n + P K τ 0 12 Sargen (1973) has shown ha wih adapive expecaions he Fisher equaion whereby an exogenous jump of inflaion leads o an equivalen jump in bond yields, will only hold under he very monearis assumpion ha poenial oupu is independen of curren and pas real raes of ineres. Wih raional expecaions i is he deviaion of oupu from is normal level ha is independen of he sysemaic pars of moneary policy, bu also he real ineres rae. Benjamin Friedman (in Solow and Taylor (1998), p. 56), raises he quesion wheher he naural rae model has become so relevan for policy making precisely because i has been so simple:" we have pleny of heories, ypically focusing on various kinds of eiher human or physical capial formaion, according o which moneary policy plausibly has very long-lasing real effecs. They are jus no simple heories". 11

12 where &y is he GDP growh rae and n he rae of growh of he labour force. I is he value of invesmen (capial equipmen purchases) and P 0 K is he capial sock valued a replacemen coss. In order o keep hings simple, we will henceforh assume ha dτ τ = 0. We now inroduce an invesmen funcion ino he model. The invesmen decision a firm level - and in aggregae - can be modelled by Tobin's q. This relaion is defined as he raio of he marke value of he enerprise o capial replacemen cos (Tobin and Brainard 1977), or simply he raio of he inernal rae of reurn of an invesmen projec o he risk-free money marke ineres rae (Bofinger e al., 1996, p. 556). This definiion implies absracing from ime-varying erm premia and defaul risk, so ha capial markes deermine long erm bond raes as he average expeced level of he money marke rae over he relevan horizon. The q-raio is (6) q = 1 + i K 1 + i = 1 + i K E (π ) (1 + i π ) R r where i K is he inernal rae of reurn, R he expeced real reurn on invesmen and r = i π he real shor-erm ineres rae. π is he curren rae of inflaion and E(π ) is he expeced average rae over he life of he capial equipmen 13. Enrepreneurs compare he rae of reurn from producive invesmen o alernaive invesmen opporuniies in risk-free domesic moneary asses. Unless real capial yields a leas as much as moneary asses, here is no incenive o increase capaciies. q reflecs he excess reurn or economic profi ha producive invesmen would earn over and above he placing of funds in risk-free securiies. Hence he equilibrium value is q =1. 14 In models wih neo-classical producion funcions, R is equivalen o he marginal produc of capial (F K ), a echnical variable dependen on he size of he capial sock. Invesmen will hen be deermined by he growh of he capial sock o he poin where he marginal produc of capial (F K R) is equal o r and q = 1. Since invesmen will adjus o profiable opporuniies, q represens profis as enrepreneurial quasi-rens which end o disappear over ime if ineres raes remain unchanged. Once i has adjused, he prevailing ineres is he "naural rae of ineres" (i*) in he Wicksell-sense and q( i) = q (i*)=1 15. The speed of his arbirage depends on he cos 13 Noe ha q also depends on inflaion acceleraion. During periods of disinflaion, when fuure inflaion is expeced o fall, q will be lower han in a sable inflaion environmen. This implies ha for a given curren real rae, he marginal efficiency of capial has o be higher under disinflaionary condiions. 14 In realiy, invesmen may already sop a an earlier rae, say q, if a minimum profi rae is required for invesmen, bu we will absrac from hese complicaions here. Because R and r are no easily measured, empirical sudies prefer he formulaion whereby q is he raio of he marke value of an invesmen projec o he replacemen cos. Under cerain assumpions he wo formulaions are idenical, bu wha maers for invesmen is he q raio on he margin, i.e. he incremen of marke valuaion for he cos of he associaed invesmen. Average q values for exising capial sock may be quie differen from he supposed equilibrium value 1. Bu a he margin, q should be close o uniy (Tobin and Golub, 1998). 15 Wicksell (1998) showed he adjusmen process o go from he moneary ineres rae o real capial via credi demand. If, however, he cenral bank ses he money marke ineres rae and keeps he discoun window open, 12

13 of adjusmen: if hese coss were zero, q would insananeously jump o q. Therefore, as long as adjusmen coss are posiive, shor-erm moneary policy measures can have real effecs by lifing or lowering q, hereby inducing an adjusmen process in he capial sock. As a resul, ransiory disequilibria following policy measures could become long lasing 16. In our simplified model, q is a funcion of he ineres rae i which we suppose o be conrolled by he cenral bank. In realiy, movemens of q should reflec a weighed average of differen raes for differen mauriies and risks, as deermined in financial markes. However, his realism is no necessary for he argumen I wish o make. Because prices move wih some ineria 17, we may also consider r also as exogenously given and can herefore assimilae i and r o moneary policy. 18 In more complex models, q is also relaed o he real exchange rae and fiscal policy 19 (Collignon, 1997). Because we have aken i as exogenously given by moneary policy, our model implies ha he marginal produc of capial (F K R) will adjus o r - and no he oher way round (Riese, 1986). In a Keynesian environmen, R mus iself be a funcion of r, because an increase in real ineres raes would have negaive consequences for effecive demand, which in urn would affec he fuure cash-flow of he firm as well as he inernal rae of reurn. 20 We can now show, how moneary policy measures by he cenral bank will affec Tobin's q. Assuming we sar in equilibrium, aking he oal differenial of (6) yields (6a) 1 dq = r dr R 2 r dr In he shor-run, he inflaion rae is fixed so ha dr = di. In equilibrium q =1 and herefore R=r. Insering hese values ino (6a) and dividing by di yields: dq 1 = = 1 < 0 di r (6b) qi [ Ri ] R i measures he degree by which expecaions on he reurn on capial are affeced by variaions in ineres raes. Normally, his value should be negaive. In a sricly neoclassical world, where R hen he process mus be inversed and real capial adjuss o he moneary rae. We will deal wih he price consequences of he Wicksellian process in he nex secion. 16 They could even become very long lasing if capial accumulaion incorporaes echnological progress, so ha he marginal producs of capial and labour increase (see equaion (1)) 17 This is no a necessary condiion for our argumen. Over he long run when he inflaion rae changes, i is more useful for comparaive purposes o use he real shor erm rae r, bu for didacic reasons I prefer o focus on i. 18 This is a very simplified model of he ransmission mechanism. A more appropriae descripion of moneary policy wih ineres rae argeing is given by Goodfriend (1998). I am aware ha in realiy, risk and uncerainy as well as he srucure of he banking sysem and financial markes rouble he link beween moneary policy insrumens and capial coss significanly. For a sudy of how shor erm affec long erm ineres raes in Europe, see Gebauer, Müller e al., If Ricardian equivalence holds, fiscal policy will no affec q. 20 In he General Theory, Keynes (1936, chap. 18) made grea effors o prove ha R was independen from r. If all agens had absolue perfec foresigh, including abou he iming of ineres rae increases, hen his would indeed be he case. 13

14 reflecs he marginal produc of capial R = 0 and q = 1 i. This implies ha moneary policy is r only effecive if real ineres raes are posiive. When he expeced rae of reurn is negaively influenced by moneary policy ( R < 0) 21, q i would be smaller han he facor 1. Thus, in r general, q i is negaive and is absolue value raher large. Finally, we can deermine he rae of capial accumulaion as a funcion of Tobin's q : I P K (7) = a0 + ϕ [ q( i) q( i*) ] 0 where q is he "normal" value of Tobin's q (possibly 1) ha defines he Wicksellian naural rae i*, wih ϕ ( + ) = +, ϕ ( 0 ) = 0, ϕ( ) = - and a 0 he auonomous or naural rae of capial accumulaion. Growh equilibrium occurs when he savings ou of ne income suppor ne invesmen, so ha: a q i q s Py O + = = P K (8) ϕ [ ( ( ) )] 0 s f '( k ) k wih s as savings rae and Py as ne income. 22 If q = q, our sysem is in equilibrium and ex ane savings equal invesmen. The capial-oupu raio adjuss o savings and he naural growh rae of invesmen: (8a) K y = s a o As we saw in (5), o keep he unemploymen rae consan, he capial sock will have o grow a he rae of he labour force (n ) plus he increase in he capial/labour raio (dk/k) plus he rae of Hicks-neural echnological progress ( d τ τ ). Bu he acual rae of employmen growh (n) is consrained by he rae of accumulaion: (9) I P K 0 dk d = n + + τ k τ Comparing (9) o (5) shows ha for a given rae of capial accumulaion an increase in he capial inensiy would push he employmen rae below he equilibrium level. This allows a neoclassical explanaion of rising unemploymen, where he capial labour raio increases when labour is 21 This migh be he case when he cenral bank follows an aggressive ineres rae policy o comba inflaion as in Goodfriend (1998) 22 We also assume ha he GDP-deflaor is he same as he capial cos deflaor, i.e

15 subsiued by capial. Bu his subsiuion also rises produciviy. In fac, if we absrac from Hicks-neural echnological progress ( d τ τ = 0 ), an increase in he capial inensiy k is he only way o increase produciviy. This can be derived from (1a) which is a monoonically increasing 1 k = f λ exiss wih he derivaive funcion. Therefore, is inverse ( ) (10) dk τ = dλ f '( k ) Hence, he rise in capial inensiy depends on he increase in produciviy: (11) dk τ = dλ f '( k) If produciviy remains consan ( d λ = 0 ), he capial-labour raio does no change and we have balanced growh where he rae of growh of he capial sock will be idenical wih employmen growh. However, he neoclassical hypohesis only applies o he special case when q = q, because only hen would he rae of accumulaion be given auonomously, say by "animal spiris". Wih Tobin's invesmen funcion, a cu in ineres raes would increase profis and simulae invesmen, hereby lifing he rae of capial accumulaion. The capial-labour subsiuion argumen hen loses is force because he ineres rae cu shifs he consrain ouwards. Bu his has also imporan consequences for he deerminaion of he naural rae. A he poin q = q he acual rae of unemploymen becomes he new "naural rae", because he deviaion of he acual from he naural rae is only emporary. By subsiuing (11) ino (9) and (7), we obain he long erm dynamic labour demand funcion: τ dλ (12) n = a0 + ϕ ( q q) f '( k) k If we assume ha long erm labour supply is growing a he same rae as he labour force n, we ge he seady sae equilibrium where labour demand and supply are in balance ( n = n ), invesmen equals saving q( i) = q( i*) and he capial-labour raio remains consan (wih dλ = 0). Hence n = a Labour marke flow-disequilibria are caused by discrepancies in savings and invesmen or by changes in he capial-labour raio: τ (12a) n n = ϕ ( q q ) f '( k) dλ k Nex, we look a he evoluion of socks. We know ha he labour force grows a he naural rae: 23 This reflecs a "Golden Age" (Robinson, 1965 p.99) or Harrod-equilibrium wih (8a) as naural rae of ineres as i*. K s = and Wicksell's Py n 15

16 (13a) N = N ( + n ) 0 1 and he employmen level a (13b) L = L ( + n ) 0 1 Thus he employmen rae is (13c) L N L0 ( 1+ n n) N 0 and he rae of unemploymen (13d) U L0 = 1 ( 1+ n n) N 0 where L 0 and N 0 are iniial values. Obviously, if employmen grows a a rae faser han he labour force, he employmen rae increases and unemploymen falls. Bu from equaion (12) we know ha a deviaion of employmen growh from is naural rae is only possible if produciviy changes due o a change in he capial inensiy (i.e.. dλ > 0) or because planned invesmen deviaes from saving ( q q ). This allows an ineresing insigh. Le i 0 be he iniial rae of ineres a which q( i0 ) = q( i*), so ha, he economy is in equilibrium wih n = n and i o =i* and he iniial rae of unemploymen as a naural rae. Nex, assume auhoriies raise ineres raes. Thus, expeced profis fall, q( i ) < q( i0 ) for i > i 0 and because of (12) employmen grows less han he labour force ( n < a0 = n). Hence, unemploymen increases above he naural rae. However, his deviaion of he acual from he naural rae is only emporary. Because q-profis are now negaive, he capial sock will adjus o he new condiions of profiabiliy. Disinvesmen will ake place unil he expeced marginal reurn on capial equals he higher ineres rae. A his poin, he acual rae of unemploymen becomes he new "naural" rae, because i is he level of unemploymen which corresponds - as in Friedman (1968) - wih Wicksell's naural rae of ineres. Thus, he new naural rae i *=i is higher han he previous equilibrium rae i* = i 0, and he level of equilibrium unemploymen is also higher. In his model parial adjusmen is due o he speed by which he capial sock changes. A variaion of he ineres rae will only cause a emporary deviaion of he rae of employmen growh from is naural level. However, his emporary deviaion will cause a permanen shif in he employmen level: while he unemploymen rae rises above is naural level as long as q < q, i will sabilise a 16

17 a higher naural rae when q = q. The inverse logic applies o a cu in ineres raes 24. Consequenly, he naural rae of unemploymen is a funcion of he ineres rae. This resul is obained by incorporaing Tobin's invesmen funcion ino a neo-classical Solow growh model. I allows us o explain why he naural rae of unemploymen is closely relaed o he acual rae, as many hyseresis models claim. By implicaion here are muliple equilibria for he naural rae of unemploymen. We could, however, obain he same resul in a neoclassical model where invesmen is always equal o savings if we made he savings raio dependen on ineres raes insead of using he invesmen rae as a funcion of q. As is well known, a change in he saving rae has a level effec and no a growh effec. Thus, he equilibrium unemploymen rae would shif wih savings/invesmen shocks and hen remain sable. So far we have esablished he fac ha he equilibrium or naural rae of unemploymen is a funcion of moneary policy. 25 By lowering ineres raes, he cenral bank can achieve a permanen increase in he level of employmen and poenial oupu and he inverse when i rises ineres raes. However, his may have consequences for inflaion ha we now need o discuss. 1. Deermining he price level From a monearis poin of view, oupu is fixed by he naural rae of employmen and he described Wicksellian process would simply lead o an expansion of money supply and rising prices (Issing, 1990; p.92-94). However, in our model he addiional money supply serves o increase invesmen above planned savings and he higher capial sock produces higher oupu. Hence, here are no only price bu also oupu effecs. The quesion is, how o separae he wo. The acceleraionis model claims ha if acual GDP rises above (below) poenial GDP, wage and price inflaion will accelerae (decelerae), so ha moneary policy mus inervene o sabilize prices. This can be done by a policy rule for moneary aggregaes which reflecs he growh of poenial oupu. Ye, given ha cenral banks effecively use shor erm ineres raes as heir policy insrumen, ineres rae rules have recenly gained more prominence. Bes known are Taylor-rules where cenral banks adjus shor erm ineres raes in response o deviaions of inflaion from a arge and o he deviaions of real GDP from poenial oupu (Taylor in: Solow and Taylor, 1998, p. 50): (14) i = π + g( y y )+ h( π π *)+ r * were π * is he arge inflaion rae and r* is he implici real ineres rae in he cenral bank's reacion funcion which coincides wih Wicksell's naural (real) rae of ineres in our previous 24 Wicksell claimed ha he deviaion of he acual from he naural rae se a "cumulaive" process in moion. However, wih diminishing reurns o capial, he oupu ends o be saionary wih shifing seady saes dependen on ineres raes. As for price movemens, we will see in he nex secion ha a cumulaive process requires a pricewage spiral. 25 As Solow (Solow and Taylor, 1998, p. 11) pu i: "The long-run aggregae supply curve may be verical, bu is locaion is endogenous o macroeconomic policy." 17

18 secion. g and h are posiive. This rule effecively means ha he cenral bank rises shor erm real ineres raes above he implici rae when i perceives inflaion or oupu o exceed heir average raes. Thus, as long as inflaion is on arge, i is impossible ha he economy grows faser han he average ( y ) which eners he cenral bank's reacion funcion. I has been observed ha he Taylor-rules come close o mimicking he acual behaviour of cenral banks (Solow and Taylor, 1998, p. 94; Clarida and Gerler, IMF, 1998). This is no surprising, for hey work as a selffulfilling prophesy 26. There are wo problems wih moneary policy feedback rules which incorporae explici growh arges: firs, hey limi poenial growh o he arge. Secondly, hey blur he disincion beween profi and wage inflaion. While he former represens a emporary shif in he price level, only he laer leads o he cumulaive process which is correcly called inflaion. Wih he oupu gap as an indicaor for fuure inflaion, a cenral bank wishing o keep prices sable is always jusified o rise ineres raes and kill economic growh. However, if we could disinguish beween emporary increases in he price level and susained inflaion, i would be possible o limi resricive moneary policies only o he laer. The analyical ool by which his disincion can be made is he price mark-up. In early Keynesian models, prices were linked o wages by a fixed mark-up. This fied he Phillips curve rade-off beween inflaion and unemploymen. By focusing on he real wage, Friedman (1968) implicily made he mark-up (he inverse of he real wage) a funcion of unemploymen. Alhough flucuaing in he shor run, i was supposed o be sable in he seady sae where he naural rae prevailed. However, even Friedman's naural rae of unemploymen would be variable if he seady sae mark-up would shif in he long run. Keynes' own heory of he mark-up, as developed in he Treaise of Money (1930), was much more elaborae alhough in he General Theory he hid i behind he concep of user cos. 27 The link beween he price level and profiabiliy was shown by Keynes' (1930) fundamenal equaion. He spli he price level ino wo erms: he firs covers sandard cos of producion, he second reflecs aggregae excess profis or "enrepreneurial income" (Keynes, 1936, p. 53) which "is posiive, zero or negaive, according as he cos of new invesmen exceeds, equals or falls shor of he volume of curren savings" (Keynes, 1930, p.122). These Q-profis are caugh by Tobin's q Thus if we furher spli coss of producion ino wage coss (uni labour cos W/λ) and he (renal) cos of ne capial (i o b), hen Keynes' fundamenal equaion can be reformulaed as: (15) P = W + iobq λ 26 A leas his is rue for he Unied Saes where he capial-labour raio has sayed nearly consan over he las hree or four decades. In Europe, he case is somewha differen, as he rising average unemploymen shows. 27 Riese (1986, 1994) has reformulaed he heory o a fully-blown heory of inflaion. See also Collignon, The concep is also found in Myrdal (1933). Tobin was apparenly no aware of his link beween q and Q. See Tobin and Golub, 1998, p. 150; Schmid, 1995; Collignon

19 The aggregae mark-up over uni labour cos is now no longer a fixed or arbirary empirical value. I depends on he financial srucure of he economy and on he macroeconomic environmen as deermined by moneary policy. Le us assume for simpliciy ha all capial goods are financed by bonds (B) for which he nominal ineres rae i 0 is o be paid. b is herefore he raio of ousanding bonds (B) which are equal o (hisoric) value of capial (P 0 K) per uni of oupu (y). As usual, q can also be inerpreed as he shadow price of capial. Formulaion (15) deermines he price level as a funcion of ineres raes wihou he simplifying assumpions abou money demand ha dominaes he IS-LM model. If q( i0) = q( i*) = 1, he marke value of he invesmen projec is equal o is replacemen coss and is ne presen value is zero. This reflecs herefore he "normal" capaciy uilisaion of he firm, a which he mark-up is jus sufficien o cover he cos of capial 29 or he deb service i 0 b. Thus, when q( i0) = q( i*) = 1, we have he equilibrium price level (P*) deermined by uni labour coss (W/λ) and he normal (renal) cos of capial per oupu. (15a) W P* = + λ i b o Prices are se as a mark-up on wages (uni labour coss) in order o cover capial cos and if possible o make a profi. Is size depends on he firms' financial srucure a he microlevel, bu also on ineres raes which are se by moneary policy. 30 In order o simulae new invesmen, expeced profis mus be higher han capial coss and ineres raes need o be cu. Excess demand would hen push he acual price level above he equilibrium P*. Q-profis would las unil he capial sock has adjused o he new equilibrium ( q = q = 1 ). A ha poin excess demand has disappeared and he price level has reurned o P*. Hence, equaion (15) implies ha prices and profi margins rise in he early phase of an economic boom because q >1, bu fall subsequenly when compeiion and addiional supply push q back. 31 Therefore, a demand induced acceleraion of inflaion is always ransiory - unless i leads o furher inflaionary movemens. Moneary policy affecs simulaneously prices (via q and i 0 ) and oupu quaniies (via invesmen and demand) - bu only unil q has reurned o he level of q. In line wih equaion (12) and (13), he oupu-effec permanenly shifs income and employmen levels, bu no growh raes. The price effec has a emporary componen relaed o he adjusmen from one income level o anoher and a persisen elemen relaed o he cos srucure of he firm For simpliciy we assume average equal marginal coss. 30 In a neo-classical model, he cos of capial would mach he marginal produc of capial. Q-profis can hen be inerpreed as a kind of macroeconomic producer surplus which can be posiive or negaive. In models wih imperfec compeiion, he price mark-up is added o oal marginal cos, so ha he mark-up would vary wih q(i). In our definiion, he mark-up covers he cos of capial plus q-profis. The reason is ha in a Keynesian framework quaniies adjus o prices, so ha he price of capial (= credi) is he independen variable and he sock of capial (including is marginal produc) adjuss. 31 For evidence on ime-varying mark-ups see Forsman e al., 1997, and Marins e al., As we will see below, his could also explain Sims' famous price puzzle. Eichenbaum in a commen o Sims' (1992) price-puzzle saed: "I know of no business cycle heory which is consisen wih he noion ha moneary conracions lead o prolonged periods of inflaion". Keynes' (1930) heory would no imply exacly his; bu he 19