Documento de Trabajo THE SYMMETRY UNDERLYING REAL INTEREST RATE BEHAVIOUR AND THE LINK TO INVESTMENT FLOWS: AN EX ANTE FORMAL TREATRMENT

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1 Documeno de Trabajo THE SYMMETRY UNDERLYING REAL INTEREST RATE BEHAVIOUR AND THE LINK TO INVESTMENT FLOWS: AN EX ANTE FORMAL TREATRMENT Alejandro PELÁEZ RUIZ-FORNELLS FACULTAD DE CIENCIAS ECONOMICAS Y EMPRESARIALES UNIVERSIDAD COMPLUTENSE DE MADRID VICEDECANATO Campus de Somosaguas, MADRID. ESPAÑA.

2 Esa publicación de Documenos de Trabajo preende ser cauce de expresión y comunicación de los resulados de los proyecos de invesigación que se llevan a cabo en la Faculad de Ciencias Económicas y Empresariales de la Universidad Compluense de Madrid. Los Documenos de Trabajo se disribuyen grauiamene a las Universidades e Insiuciones de Invesigación que lo solician. No obsane, esán disponibles en exo compleo en el archivo insiucional compluense e-prins con objeo de faciliar la difusión en Inerne de las invesigaciones producidas en ese cenro. hp://eprins.ucm.es/d.hml FACULTAD DE CIENCIAS ECONOMICAS Y EMPRESARIALES UNIVERSIDAD COMPLUTENSE DE MADRID VICEDECANATO Campus de Somosaguas MADRID. ESPAÑA

3 THE SYMMETRY UNDERLYING REAL INTEREST RATE BEHAVIOUR AND THE LINK TO INVESTMENT FLOWS: AN EX ANTE FORMAL TREATRMENT Alejandro PELÁEZ RUIZ-FORNELS

4 1 THE SYMMETRY UNDERLYING REAL INTEREST RATE BEHAVIOUR AND THE LINK TO INVESTMENT FLOWS: AN EX ANTE FORMAL TREATMENT.

5 2 Alejandro Francisco Peláez Ruiz-Fornells Deparameno de Economía Aplicada III (Políica Económica) Universidad Compluense de Madrid (Spain) Key words: Symmery ineres rae, capial sock, capial composiion, financial markes, business cycle, invesmen flows.

6 3 ABSTRACT From a purely speculaive approach and under he usual assumpions, a wellknown symmerical srucure appears, connecing neoclassical and Keynesian views of he markes. This framework admis graphical and formal explanaion. In previous work, we addressed his opic reaching some conclusions. Now ha he credi bus spreads worldwide, we focus on formal analysis leading o more advanced resuls linked o our previous perspecive ha seems o hold. Using an ex ane formal reamen, we conclude ha when applied o explain real ineres rae behaviour, his symmerical look shows a counercyclical paern of response for his variable in neoclassical approach, while being procyclical from Keynesian view. This implies eiher a magnifying or a sabilizing role for he real rae in each case and could affec he financial o real invesmen flows raio and, as a resul, aggregae capial sock composiion. The rend his raio could follow, hough difficul o explain, is of grea ineres o help explain he behaviour of financial markes. This appears as a key feaure o approach he focal poins of he financial markes reform.

7 4 THE SYMMETRY UNDERLYING REAL INTEREST RATE BEHAVIOUR AND THE LINK TO INVESTMENT FLOWS: AN EX ANTE FORMAL TREATMENT I. INTRODUCTION Prior o consider he behaviour of he real ineres rae from neoclassical or Keynesian views and under paricular circumsances, we need o assume ha financial markes end o behave in a more or less compeiive way, and ha Cenral Bank's reference rae follows he pah of a hypoheical 'noional rae' which would prevail if he perfec compeiion marke-clearing condiions were me. Under hese circumsances, when he economy undergoes an expansive rend, caused by a rise in aggregae demand, he real rae shows a differen paern of behaviour depending on he approach applied; neoclassical or Keynesian. As a resul, he raio of financial o real invesmen flows, and he composiion of he capial sock in he economy, could become affeced. In previous work, we addressed his problem using mainly graphical ools and reaching some general conclusions in erms of a symmerical srucure connecing neoclassical and Keynesian approaches, which comes o ligh. Now we focus on a formal approach leading o a similar oucome ha seems o hold. These ideas could show a narrow link o recen developmens in inernaional financial markes. Our previous se of conclusions using graphical analysis 1. In he figure below we depic he supply and demand schedules in neoclassical marke for loanable funds and in Keynesian marke for money. Marke for goods and services and Phillips curve are also shown

8 5 for each perspecive. NEOCLASSICAL MODEL KEYNESIAN MODEL i S i M/P M/P I I' L L 0 S, I 0 L, M Marke for Loanable Funds Money Marke P AS P AS AD AD AD AD 0 Y 0 Y Marke for Goods and Services Marke for Goods and Services Ph Ph 0 Phillips Curve U 0 Phillips Curve U An exogenous expansive shock will produce a shif o he righ in demand schedules, as well as a change in he corresponding equilibrium posiions on he Phillips curve. Taking ino accoun he differen slopes

9 6 and elasiciies of aggregae supply and Phillips curves prevailing in each model, we can compare he reacion of boh nominal ineres rae and inflaion rae, o reach some conclusions on he probable behaviour of he real ineres rae, afer he occurrence of an expansive exogenous shock he economy is supposedly undergoing. We can do his by virue of Fisher s equaion: i r e or r i e Assuming ha agens make heir conjecures following a process of expecaions, we will approximae he expeced rae by he ex pos effecive inflaion rae, which allows us o arrive o he real ineres rae by rewriing Fisher equaion as: r i Where: r real ineres rae for period i money ineres rae for period 2. When he economy undergoes an expansive shock -like he one depiced in he figure below-, he neoclassical Say s Law supply side approach, predics such a comparaive evoluion of boh nominal ineres rae and inflaion rae, ha would probably cause he real ineres rae o decrease. On he conrary, he Keynesian approach predics a probable increase in he real rae of ineres. 3. On he oher hand, when a bus akes place, he neoclassical approach

10 7 predics a probable increase, in he real rae of ineres, and he Keynesian demand side view, a probable decreasing rend for he real ineres rae. 4. As a resul, and in spie of he fac ha in economic lieraure real rae migh be considered an acyclical variable, in a graphical ex ane analysis, is paern of behaviour appears o be counercyclical in neoclassical Say s Law approach, while being procyclical from Keynesian view. 5. The differen response of he real ineres rae o exogenous demand side shocks, owes is explanaion o he relaive elasiciy values of supply and demand funcions considered in he analysis, and o he slope and elasiciy of he Phillips curve in each case. The laer reflecs he condiions in he markes for producion facors, he degree of moneary illusion amongs workers, he paricular assumpions on expecaions, or he level of unemploymen and is associaed variance (Fernández Díaz, 1977). Bu he differen elasiciy values of he funcions considered in he analysis correspond o he graphical ranslaion of he iniial assumpions and hypoheses of each model, owing hem in no lile par heir explanaion. Thus, he symmery affecing he real rae paern of behaviour and connecing boh models is relaed o he paricular se of assumpions of each, a leas o a cerain exen. 6. I remains o see wheher or no is one of hem oday, and in he foreseeable fuure, more capable han he oher o porray in is assumpions a more precise grasp of he economic realiy.

11 8 II. A SIMPLIFIED EX ANTE FORMAL ANALYSIS Following a purely speculaive perspecive and iniiaive, we inend o show ha our previous conclusions hold, when using a formal approach. In order o do so, we shall formalize boh models, which will enable us o reach more obvious resuls, and express hem in a more accurae form. We focus firs in he relaionship beween inflaion rae and nominal ineres rae. According o economic lieraure, boh seem o follow a similar pah hroughou he ime being procyclical and wih some lags. An increase in he former, usually akes place when he laer as well as he oupu level are also increasing, and vice versa. Neverheless, he daa doesn seem o confirm he exisence of a Fisher Effec. In oher words, he inflaion rae surge doesn mee an idenical nominal ineres rae upurn. As a resul, he real rae of ineres doesn remain seady, bu follows a cerain pah depending on which of he former incremens prevails. Thus, we shall compare boh for each model. We will use formal analysis o observe changes in nominal ineres raes and in effecive inflaion raes in response o an increase in aggregae demand, associaed o an expansive rend he economy migh be undergoing. In his way, comparing hem we will observe he final effec on he real ineres rae. However, in order o perform his ask, each approach requires a paricular se of analyic insrumens and a paricular se of assumpions on elasiciy values. From Keynesian demand side approach, changes occurring in real ineres raes are sudied by means of IS-LM analysis ha underlies he Neoclassical-Keynesian Synhesis Model. Agains his background, he elasiciies express a posiive pricesensiiviy of he aggregae supply, a relaively high response of savings and invesmen

12 levels o changes in naional income, and a relaively poor response of boh o he nominal ineres rae. 9 In he money marke, he speculaive componen of money demand surpasses he ransacional componen, he supply of real money balances being exogenous and hus, inelasic o he nominal ineres rae. The Phillips curve shows posiive absolue values of inflaion-elasiciy, and a negaive slope in a conex of moneary illusion and adapive expecaions. Alhough modern conribuions by new Keynesians have been buil on srong micro foundaions incorporaing he raional expecaions hypohesis, i is no our inenion o inroduce here bu he elemenary versions. This will keep our aenion focused on he underlying from demand o supply logical framework idenifying Keynesian hough, and differing from he from supply o demand Say s law neoclassical approach. On he conrary, from neoclassical Say's law approach, IS-LM analysis canno be used because of is incompaibiliy wih he posulae of he neuraliy of money and he loanable funds heory of ineres. From his approach, according o neoclassical elasiciies, income has lile influence on savings supply and on invesmen demand, boh being more clearly influenced by he money ineres rae. i S i E I 0 S, I

13 10 Loanable funds marke. (Where i E = equilibrium nominal ineres rae) Agains his background he price elasiciy of aggregae supply is null. The Phillips curve, being perfecly inelasic o inflaion, shows a verical shape over he naural unemploymen rae (NUR), in a conex of absence of moneary illusion. Similarly, when considering he neoclassical view i won be our inenion, o inroduce bu an elemenary version of he model. This will keep our aenion focused on he underlying from supply o demand Say s law logical framework, underlying neoclassical hough. 1. Keynesian demand side approach. A simplified formal reamen When examining his view, we need o admi some paricular assumpions: 1. The economy reaches is equilibrium far from full-employmen oupu level in a conex of moneary illusion. 2. As a resul, aggregae supply schedule has a posiive slope showing posiive price-elasiciy value, while Phillips curve is downward sloping. Boh reflec he marke condiions associaed o equilibrium wih involunary unemploymen, in a conex of moneary illusion. The slope of boh curves is relaively reduced in absolue value. 3. The agens are supposed o form heir conjecures on he evoluion of price level following a process of adapive expecaions. As a resul, we can approximae he expeced inflaion rae by he ex pos effecive inflaion rae. Thus, e

14 11 where sands for curren or expeced inflaion rae. 4. I exiss an underlying from demand o supply logical framework, opposie o Say s law. No all savings are ransformed ino invesmen, because agens can hold idle money balances. 5. The money ineres rae is no more deermined in he marke for loanable funds bu in he money marke, wih an exogenous real money balances supply under he conrol of he Moneary Auhoriy. Taking ino consideraion he previous assumpions, he expressions reflecing macroeconomic equilibrium are; 1.1. Aggregae demand The equilibrium in he marke for goods and services, IS schedule, occurs when: Y ( A bi) where Y: Aggregae level of oupu. 1 (1 c(1 ) m) Aggregae auonomous expendiure muliplier in open economy. A = Aggregae auonomous expendiure in open economy b = ineres-elasiciy of invesmen demand The equilibrium in he Money marke, LM Schedule, akes place when:

15 12 M p ky hi 1 M or: Y ( hi) k p where k = Income-elasiciy of he demand for real balances M p Supply of real balances h = Ineres-elasiciy of he demand for real balances The equilibrium in boh markes may be expressed by means of he aggregae demand funcion. Y M A (1) p where 1 = Fiscal policy muliplier including moneary secor and 1 k ( b ) h Hicksian crowding-ou b h Moneary policy muliplier 1 k ( b ) h

16 Aggregae supply From his Keynesian approach, he supply curve is upward sloping and shows posiive values for price-elasiciy. From his demand-side view, he equilibrium level of oupu is firs deermined wihin he demand side of he economy by means of he IS- LM analysis. Then solving he producion funcion, we can obain he employmen level needed o reach he equilibrium level of oupu. The former, in general no coinciden wih full employmen level, will be remuneraed a marginal labour produciviy. If an increase in producion akes place, he addiional employmen needed o suppor he expansion, is more han proporional o he increase in oupu. This shows ha he former can only occur under increasing uni labour coss condiions. And assuming ha he mark-up pricing equaion over he uni labour cos, is, P (1 ) w (2) a Where w Nominal wage Mark up level ( 0 if he firm has some kind of marke power) Y a Average labour produciviy L If remains seady; he rise in uni labour coss would be passed-hrough o final prices, which implies an upward-sloping aggregae supply curve, Y F p (3) Where dy dp 0

17 14 P AS 0 Y Unil now we have: Y Y M A (Aggregae demand) 1 p F p (Aggregae Supply) (3) Now we have o bear in mind ha our goal is no oher han o deermine he effec of a change in aggregae demand -associaed o an eiher expansive or resricive rend of he economy-, on he nominal ineres rae and on he inflaion rae. And aferwards, by calculaing he difference beween he boh, we will observe he effec on he real ineres rae. In order o do so, le s begin by considering an increase in aggregae auonomous expendiure (A), linked o an expansive rend he economy is supposedly undergoing. According o he aggregae demand schedule, (1) he income and producion level would increase by dy da And according o he expression of he aggregae supply (3), ha can be rewrien as follows: p f (Y )

18 15 The following change in prices would occur,. dp f ( Y) dy or, dp f ( Y ) da (4) Where dy da 1.3. Change in inflaion rae The change in he price level acceleraes inflaion rae. This change in inflaion rae has o be compared o he one affecing nominal ineres rae, in order o observe he evoluion of real ineres rae which consiues our main concern. Bu he change in inflaion rae has o be observed hrough Phillips curve ha in Keynesian view shows a regular downward sloping profile because he effecive e inflaion rae differs from is expeced level (i.e., ) According o expecaions-augmened Phillips Curve: e NUR U U (5) where U Curren Unemploymen level U Naural Unemploymen Level NUR 1 Adjusmen parameer, ha depends on he proximiy of he economy s producive poenial o he full employmen level. When 1 he economy is relaively far from full employmen as is seems in line wih Keynesian demand side approach opposie o Say s law. The downward sloping Phillips curve would in his case show a relaively fla profile.

19 16 I is possible o pu (5) as an expecaions-augmened aggregae supply curve Y Y ( e ) where Y NUR relaed income level. The laer is he surprise aggregae supply schedule, represening he oupu firms are willing o produce a differen inflaion raes. This curve considers ogeher he producion funcion and he employmen decisions in he labour marke, and can be rewrien as where e Y Y (6) This relaionship will allow us o obain he firs derivaive of he inflaion rae wih respec o he oupu level. d dy where 1 0 In oher erms, d (7) da where dy da

20 17 The expression (7) is a measure of he change in inflaion, caused by an upsurge in oupu level in response o an increase in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing. When alernaively surpasses, equals or falls behind he uni, he changes in inflaion rae will be respecively more han proporional, proporional or less han proporional o he changes in aggregae auonomous privae expendiure (he changes in aggregae demand). From an ex ane approach i is only possible o affirm ha in he Keynesian demand side view, opposie o Say s law, would be greaer han zero. Noneheless, he Keynesian approach opposie o Say s law, implies ha he economy is relaively far from full employmen and from he economy full producive poenial level, which suggess 1 in line wih a relaively fla downward sloping profile for he Phillips curve. Moreover, would normally be greaer han one ( 1), because auonomous expendiure muliplier) is always greaer han one. As we could expec, inflaion rae seems procyclical Change in nominal ineres rae Now we focus on he increase in nominal ineres rae aking place in he money marke, because of he excess demand caused by he elevaion of he ransacional componen of money demand in response o he expansion in oupu level in response o an upsurge in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing. In he equilibrium equaion for he money marke,

21 18 M ky hi p we solve for he nominal ineres rae: k 1 M i Y h h p In his expression, oupu hrough he money demand-, and prices -hrough he money supply-, are he wo variables affecing he nominal ineres rae. Therefore, we shall derive he expression wih respec o producion and prices. k 1 M di dy d h h p Subsiuing: k 1 M di da d h h p Where da dy or, k M di da dp 2 h p h where M M d dp 2 p p or, k M di da f 2 Y da h p h

22 19 Where, according o (4) dp f ( Y ) da Simplifying, k M di f Y da h p h (8) 2 As we may see, his relaionship shows he effec in nominal ineres rae, of changes aking place in money demand and money supply, in response o he expansion in he producion and price level caused by an increase in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing. Nominal ineres raes seem procyclical as well Change in real ineres rae Knowing ha: r i I s enough o compare (7) o (8) o reach some conclusions on he evoluion of he real ineres rae afer an expansive rend he economy is supposedly undergoing. k h M p h When (7) > (8), or, in oher words f Y 2 hen, an increase in aggregae auonomous expendiure linked o he expansive rend he economy is supposedly undergoing, causes he inflaion rae o increase more han he nominal ineres rae does. As a resul he real ineres rae ends o decrease, despie a Fisher Effec may appear in he long run.

23 20 k h M p h When (7) < (8) or, in oher words f Y 2 hen, an increase in aggregae auonomous expendiure, conneced o he expansive rend he economy is supposedly undergoing, causes he inflaion rae o increase less han he nominal ineres rae does. As a resul he real ineres rae ends o increase, despie a Fisher Effec may appear in he long run. k h M p h When (7) = (8), or, in oher words f Y 2 hen, an increase in aggregae auonomous expendiure, conneced o he expansive rend he economy is supposedly undergoing, causes he inflaion rae o increase in he same amoun han he nominal ineres rae does. As a resul, he real ineres rae ends o say unchanged, and he Fisher Effec holds even in he shor run. In he Keynesian demand-side view, opposie o Say s law, in order o compare (7) o (8), we need o esimae he relaionships elasiciies and parameers. Nowihsanding he fac ha Keynesianism gives a cenral role o he speculaive demand for money, depending on ineres raes, here is empirical evidence supporing a bigger role for wealh and oupu in money demand funcion ha depends on income level and disribuion. Furhermore, here are economies of scale in he possession of money. Goldfeld, Koyck and Almon daa for he USA show some 0.19 value for shorrun income elasiciy of money demand (0.68 for he long-run) (Goldfeld, 1973). I has always o be lesser han one, because echnological and insiuional changes encourage agens o reduce heir money demand which becomes compensaed by an increase in money velociy, associaed o financial innovaion processes. The demand for money is negaively correlaed o ineres raes, Goldfeld s daa

24 showing some -0,045 value for shor-run ineres elasiciy of money demand (-0,16 for he long run). 21 According o hese daa, in he relaionship (8), k h k, would be beween 4, 2 h k (in he shor run) and 6, 25 (in he long run) h Neverheless, money demand has los sabiliy because of he coninuous changes in money velociy. Wha s more, financial innovaion and uncerainy seem o play a significan role in he heerogeneous behaviour of agens (Cuhberson, K., 1997). In he Spanish financial sysem for example he hoarding of grea amouns of cash, mainly in 500 euros bills led o a recen fall in money velociy. This phenomenon is relaed o he nonofficial origin of money or coming from cerain secors of aciviy. The housing bubble caused by real esae speculaion, may be an explanaion. According o a Keynesian view, and as saed before 0 1, which reflecs a sof downward sloping Phillips curve, in narrow relaionship wih facor markes far from he full producive capaciy uilisaion, and hus, far from full employmen oupu level. According o he previous values, we may conclude ha (7) < (8). Or: k h f M p h Y 2 If and only if M 2 p h, which may be considered as normal. The previous resuls allows us o conclude ha an increase in aggregae auonomous expendiure linked o he expansive rend he economy is supposedly

25 undergoing, causes he inflaion rae o increase less han he nominal ineres rae does. As a resul he real ineres rae ends o increase. 22 This seems o provide a formal reamen for our previous se of conclusions, - reached by geomerical analysis-, abou real rae dynamics from Keynesian opposie o Say s Law, demand side view. In oher words, ha he real ineres rae seems o behave in a procyclical way. This surely has an impac on invesmen decisions, inroducing a shif in financial o real capial raio in he aggregae srucure of capial sock. The rend his raio will undergo isn easy o forecas, bu is of grea ineres o help explain he behaviour of financial markes. We may conclude ha real ineres rae probably plays he role of a procyclical variable from Keynesian demand side approach, wha ends o affec in a cerain way invesmen decisions and, as a resul, aggregae capial sock composiion. 2. Neoclassical say's law supply side approach. A simplified formal analysis When assuming his view, we admi some paricular assumpions: 1. No involunary unemploymen exiss wihin he labour marke. The economy reaches is equilibrium over full-employmen oupu level in a conex where no moneary illusion exiss. 2. The economic individual agens are supposed o form heir conjecures on he evoluion of he price level following a process of raional expecaions, wihou predicing error. Thus: e

26 This allows us o arrive o he real ineres rae using curren insead of expeced inflaion rae. In his way, we can wrie Fisher equaion as: 23 r i where: r real ineres rae for period i money ineres rae for period 3. I exiss an underlying from supply o demand logical framework, linked o Say s law which saes ha supply creaes is own demand. In oher words; aggregae oupu is produced o saisfy he aggregae demand which has in fac been deermined by aggregae supply. All savings are ransformed ino invesmen in he period, because he economic agens can mainain idle money cash balances. 4. As a resul, aggregae supply schedule is verical over full employmen oupu level, showing no price-elasiciy, while Phillips curve is verical over he naural unemploymen rae (NUR). Boh reflec he marke condiions associaed o equilibrium wihou involunary unemploymen, in a conex wihou moneary illusion. 5. The money ineres rae is no longer deermined in he money marke bu in he marke for loanable funds, and is no more under he complee conrol of he Moneary Auhoriy, hough remaining exogenous o a cerain exen. From his neoclassical view, he IS-LM analysis is no of use, because no longerm ineracion beween real and moneary secors is acceped. Cambridge approach o he quaniy heory, explains money demand as a funcion of he ransacions componen being proporionae o he general income level.

27 24 Thus: d M kpy Or: d M V py where M d = Demand for money. k = 1/V: Porion of he money income ha agens wish o mainain in cash. The inverse o money velociy. In neoclassical view, i is assumed o remain seady in he shor run as i depends on insiuional and echnological facors. V = Velociy of money. Y = Real general income level. The equilibrium in he marke for money can be expressed as: s M kpy s M V py where M s = Money Supply Assume ha despie a financial innovaion processes is aking place, V remains seady. And, solving for Y Y MV (9) p On he oher hand, he following equaion expresses he equilibrium in he marke for loanable funds: S( Y, i) I( Y, i) ( G T) ( X M )

28 25 or, sy ai IY bi ( G T ) ( X M ) where S( Y, i) sy ai s Marginal propensiy o save. a Ineres-elasiciy of loanable funds supply. i Money ineres rae. I( Y, i) IY bi ; I Income-elasiciy of invesmen demand. I gahers or includes, non observable argumens among which we find animal spiris wih srong influence on firms expecaions. b Ineres-elasiciy of invesmen demand. s and I, he more Keynesian elasiciies, are of scarce influence here, because he funcion is supposed o be more neoclassical. We need o bear in mind he fac ha i is he nominal ineres rae he one ha is deermined here in he marke for loanable funds. I is a loanable marke heory of ineres. See, for example, Fisher (1977 (1930), p.43), or Sargen (1987, chap.1). Neverheless, in he neoclassical view, he aggregae equilibrium in he marke for goods and services can be expressed as he equilibrium in he marke for loanable funds, by means of he following equaion: Y C I ( G T ) ( X M ) Where C ( 1 s) Y (1 a) i G G; T T; X X ; M M my Operaing, 1 Y A b 1 a i 1 (1 s)(1 ) I m Or, Y A b 1 a i (10)

29 Where 1 = muliplier of auonomous expendiure wihou 1 (1 s)(1 ) I m moneary secor. This fac owes is explanaion o he dichoomy beween real and moneary secors ha characerizes he neoclassical model, based upon Say s Law. A ( G T ) ( X M ) Auonomous expendiure 26 Finally, equaing (9) and (10) we arrive o he equilibrium in boh markes MV A b 1 a i p (11) or: ky M p equivalen o he prior equaion Y MV (9) p This expression shows an inverse relaionship beween price and producion levels ha can be graphed as he downward sloping aggregae demand curve of he neoclassical model. The values verifying i are equilibrium values for money and goods and services markes. P AD 0 Y

30 27 Le us begin again by considering an increase in aggregae auonomous expendiure (A), linked o an expansive rend he economy is supposedly undergoing. As a consequence, he income and oupu level would increase in: dy da 12 as no link can be found beween real and moneary secors, hrough he speculaive demand for money. In he same measure would have o increase he righ side of (11), as money in he neoclassical view is considered only a means of paymen Change in price level From his neoclassical approach, he supply curve shows a perfecly rigid verical profile -zero price-elasiciy-. From his supply-side view, he equilibrium level of oupu is deermined by labour marke equilibrium and producion echnology. The economy is a full-employmen level of oupu, because no involunary unemploymen exiss. Wihou moneary illusion a price surge will lead o an equivalen rise in money wages o preserve workers purchasing power. This will discourage employers o increase heir labour demand because real wages remain unchanged. Therefore, he oupu level remains unchanged while price rise hold. We would have a perfecly rigid verical profile supply curve, over he NURassociaed income level.

31 28 Y Y (13) P AS 0 Y Y Unil now we have Y MV (Aggregae demand) (9) p Y Y (Aggregae supply) (13) Under hese circumsances, o observe he change in prices caused by a cerain change in he income level due o an increase in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing, we need only use he demand schedule previously considered Y MV (9) p Solving for he price level MV p Y The derivaive of p wih respec o Y is

32 29 dp dy MV 2 Y or MV dp dy 2 Y (14) or MV dp da 2 Y (14) where dy da Which gives he response of he price level o a cerain change in income due o an increase in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing. Bu we have o bear in mind ha our goal is o deermine he effec of such a change in a componen of aggregae demand, -associaed o an eiher expansive or resricive rend of he economy-, on he nominal ineres rae and in he inflaion rae. And aferwards, by calculaing he difference beween he boh, we would observe he effec on he real ineres rae Change in inflaion rae The change in he price level acceleraes inflaion rae. This change in inflaion rae has o be compared o he change in nominal ineres rae, in order o observe he evoluion of real ineres rae which consiues our main concern. Bu he change in inflaion rae has o be observed hrough Phillips curve (5),

33 30 which in neoclassical view will show a perfecly rigid verical profile because he effecive inflaion rae equals is expeced level (i.e., e = ), and producion says a NUR-associaed oupu level. And again, according o he expecaions-augmened Phillips curve Being now e NUR U U (5) 1 0 adjusmen parameer which depends on he neighbouring of he economy o full producive capaciy, The neighbouring of he producive poenial o full employmen level. When 0, he economy is relaively close o full employmen as i seems in line wih Say s law neoclassical supply side approach. The Phillips curve would show a verical profile because unemploymen says a NUR level. We can pu (5) as U U e NUR Where 1 1 Or as an expecaions-augmened aggregae supply schedule, which can be rewrien as e Y Y (6) Where

34 Again, (6) will allow us o obain he firs derivaive of he inflaion rae wih respec o he oupu level. d dy Where 1 0 In oher erms, d (15) da where dy da The expression (15) is a measure of he change in inflaion, caused by an increase in oupu level in response o an upsurge in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing. When, alernaively surpasses, equals or falls behind he uni, he changes in inflaion rae will be respecively more han proporional, proporional or less han proporional o he changes in aggregae auonomous privae expendiure (he changes in aggregae demand). From an ex ane approach i is only possible o affirm ha in he neoclassical Say s law, supply side view would be posiive and greaer han one. Noneheless, he neoclassical approach implies ha he economy has reached full employmen and full producive poenial level, which suggess 1 in line wih a perfecly rigid verical profile Phillips curve.

35 32 Moreover would be even much bigger, because (auonomous expendiure muliplier wihou moneary secor and under neoclassical elasiciies condiions), is always greaer han one. In line wih he former saemens, and wih he raionaliy of economic agens, we would have as previously saed a verical profile Phillips curve, over he NUR level, and a perfecly rigid verical profile supply curve, wih he equilibrium saying a NURassociaed income level, wih: 0, and Under hese circumsances, in a conex of raionaliy and wihou moneary illusion, an expansive aggregae demand shock would produce an increase in expeced inflaion, which will cause he effecive rae o soar. A new equilibrium poin will be reached boh on he Phillips curve and on he aggregae supply schedule. The new equilibria will be me for higher price and inflaion rae levels. In boh cases, over NUR or NUR-associaed income level respecively. As i could be expeced, inflaion rae seems o be procyclical Change in nominal ineres rae Now we focus on he increase in nominal ineres rae. This is caused by he elevaion of he demand schedule for loanable funds in response o an increase in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing. funds: The previous relaionship expressing he equilibrium in he marke for loanable S I G T ( X M )

36 33 rewrien as: sy ai IY bi ( G T ) ( X M my ) allows us o solve for i: I s i my G T X M a b A change in oupu level in response o a variaion in aggregae auonomous expendiure (A) ransmis is effec o he money ineres rae. Thus, we compue he derivaive of i wih respec o Y, which gives: I s di m dy a b and subsiuing we have: I s di m da a b (16) where: dy da As we may see, his relaionship shows he effec in he financial markes equilibrium money ineres rae, of changes aking place in demand schedule for loanable funds, in response o he expansion in he oupu level caused by an increase in aggregae auonomous expendiure (A), linked o he expansive rend he economy is supposedly undergoing. As expeced, i seems ha nominal ineres rae is a procyclical variable Change in real ineres rae Knowing ha:

37 34 r i I s enough o compare (15) o (16) in absolue value o reach some conclusions on he evoluion of he real ineres rae afer an expansive rend he economy is supposedly undergoing. When (15) > (16), or, in oher words I s m, hen, an increase in a b aggregae auonomous expendiure linked o he expansive rend he economy is supposedly undergoing, causes he inflaion rae o increase more han he nominal ineres rae does. As a resul he real ineres rae ends o decrease, despie a Fisher Effec may appear in he long run. When (15) < (16), or, in oher words I s m, hen, an increase in a b aggregae auonomous expendiure, conneced o he expansive rend he economy is supposedly undergoing, causes he inflaion rae o increase less han he nominal ineres rae does. As a resul he real ineres rae ends o increase, despie a Fisher Effec may appear in he long run. When (15) = (16), or, in oher words I s m a b hen, an increase in aggregae auonomous expendiure, conneced o he expansive rend he economy is supposedly undergoing, causes he inflaion rae o increase in he same amoun han he nominal ineres rae does. As a resul, he real ineres rae ends o say unchanged, and he Fisher Effec holds even in he shor run. In he neoclassical Say s law supply-side view, in order o compare (15) o (16), we need o esimae he elasiciies. The lef side of he equaion akes a value similar o infinie: And o consider he righ side, we need again o esimae a, b, I,

38 35 and s. Recen research (Mulligan & Sala-i-Marin, 2000), shows a serious overesimaion of he predicive power of he Baumol-Tobin approach o money demand, o esimae ineres rae elasiciies a low nominal raes (under 5 or even 6%). Precisely hose have been he prevailing raes over he las years boh in Europe and he US. Furhermore, from he neoclassical Say s law supply side perspecive, a and b would always be greaer han Keynesian elasiciies I and s, because savings and invesmen are, in his view, more sensiive o relaive prices ineres raes-, han o quaniies wealh, income and oupu level-. As a resul, s would probably be greaer han I, because he laer includes a number of non-observable conjecures and argumens relaed o enrepreneurial expecaions and heir sensiiviy o oupu growh. In he same way, and according o Say s law which saes ha all savings are ransformed ino invesmen, we could imagine ha a change in ineres raes, would have a similar or equivalen effec on boh invesmen and savings. This implies ha a b. Or else, slighly lesser han b for i seems reasonable o hink ha a rise in raes, would have he effec of resraining invesmen more han i would encourage savings: I i S i Thus, he righ side would ake a relaively reduced absolue value and always lesser han he lef side. As a resul, an increase in aggregae auonomous expendiure linked o he expansive rend he economy is supposedly undergoing, causes he inflaion rae o increase more han he nominal ineres rae does. As a resul he real ineres rae will end o decrease, despie a Fisher Effec may appear in

39 36 he long run. Thus, we have: I s m a b We may conclude ha real ineres rae probably plays he role of a counercyclical variable from Say s Law neoclassical supply side approach, wha ends o affec in a cerain way invesmen decisions and, as a resul, aggregae capial sock composiion in erms of financial o real capial raio. The rend his raio could follow, besides difficul o explain is of grea ineres o help explain he behaviour of financial markes. III. SUMMARY OF CONCLUSIONS According o he previous simplified formal ex ane analysis, we conclude ha: 1. Inflaion rae is procyclical. Nominal ineres raes are procyclical. Boh are usually considered lagging variables. 2. In our analysis we didn sudy wheher he real rae is a leading a coinciden or a lagging variable, bu in spie of he fac ha real rae migh be considered in economic lieraure an acyclical variable, in a formal ex ane analysis, is paern of behaviour appears o be counercyclical in neoclassical Say s Law approach, while being procyclical from Keynesian view. 3. This implies a flucuaions enhancemen role for he real ineres rae in neoclassical Say s Law approach and a kind of auomaic sabilizing role for he real rae in Keynesian heory.

40 37 4. The laer could affec he raio of financial o real invesmen flows, and as a resul he composiion of he capial sock in he economy. The oucome migh have somehing o do wih recen developmens in financial markes. I remains o see wheher he empirical evidence on correlaions beween real GDP rae of growh and real ineres rae, suppors beer neoclassical or Keynesian resuls. In he exen ha hese resuls reflec he paricular assumpions of each model, he realism of he assumpions and specially he prevalence of his realism over ime, migh be crucial. Neverheless, he case for regulaing inernaional financial markes is becoming widely acceped. In he ligh of recen developmens ha shaered world markes, our previous consideraions could be of some ineres.

41 38 IV. REFERENCES Barro, Rober. J., and Xavier Sala-i-Marin World Real Ineres Raes NBER Working Paper (3317). Cuhberson, Keih Microfoundaions and he Demand for Money. The Economic Journal, 107 (443): Cuhberson, Keih, and Mark P. Taylor The Demand for Money: A Dynamic Raional Expecaions Model. The Economic Journal, 97 (Supplemen: Conference Papers): Edey, Malcolm, Michael Kennedy, and Adrian Orr Real Long-Term ineres raes: The evidence from pooled-ime series OECD Economic Sudies, 25: Fernández Díaz, Andrés Inflazione recessiva e sviluppo regionale, Rassegna Economica, 3 (maggio-giungo): Fernández Díaz, Andrés Políica Económica Coyunural. Madrid: Ediciones ICE. Fisher, Irving The Theory of Ineres: as deermined by impaience o spend income and opporuniy o inves i. Philadelphia, Pennsylvania: Porcupine Press. (Orig. pub. New York: Macmillan, 1930) Goldfeld, Sephen The Demand for Money Revisied. Brookings Papers on Economic Aciviy, 3: Goldfeld, Sephen The Case of he Missing Money. Brookings Papers on Economic Aciviy, 3: Mulligan, Casey B., and Xavier Sala-i-Marin Exensive Margins and he Demand for Money a Low Ineres Raes. Journal of Poliical Economy, 108(5): Peláez Ruiz-Fornells, Alejandro Una noa sobre la posible dinámica del ipo de inerés real desde los enfoques Neoclásico y Keynesiano. Información Comercial Española, ICE: Revisa de Economía, 747 (Noviembre): Sargen, Thomas J Macroeconomic Theory. Orlando, Florida: Academic Press Inc.