SUBSTITUTION TEST BETWEEN INFLATION AND UNEMPLOYMENT IN IRAN: AN APPLICATION OF KALMAN FILTER

Transcription

1 Assisan Professor Amir Mansour TEHRANCHIAN, PhD Faculy of Economics and Adminisraive Science Deparmen of Economics, Universiy of Mazandaran, Babolsar, Iran Masoud BEHRAVESH, MSc Young Researchers and Elie Club Marand Branch, Islamic Azad Universiy, Marand, Iran (Corresponding Auhor) SUBSTITUTION TEST BETWEEN INFLATION AND UNEMPLOYMENT IN IRAN: AN APPLICATION OF KALMAN FILTER Absrac. The presen paper addresses subsiuion relaion beween inflaion and unemploymen in Iran, drawing on Kalman filer for To achieve his end, four scenarios were designed. The resuls of hese scenarios indicaed ha of he four only he hird scenario models he variable coefficien in a random walk way and in which he coefficiens are significan and compaible wih heoreical principles. Moreover, he resuls implied a reverse relaionship beween inflaion and unemploymen in Iran. Recommendaions emergen from his sudy include adoping policies which would provoke supply and also reducing inflaionary expecaions. Keywords: Inflaion Rae, Unemploymen Rae, Kalman Filer, Iran. JEL Classificaion: C13, E24, E31, J Inroducion Decreasing inflaion rae and unemploymen is among he mos imporan objecives followed by economic heoreicians and policy-makers. Nowihsanding heir social effecs, inflaion and unemploymen can lead o he loss of an amoun of economic resources and capaciies. Fisher (1926) firs demonsraed he indirec relaion beween inflaion and unemploymen-whose direcion was from inflaion o unemploymen-using he daa relaed o he US beween 1915 and Phillips (1958), followed sui in his paper published and addressed he "The Relaion beween Unemploymen and he Rae of Change of Money Wage Raes in he Unied Kingdom". He concluded ha here is an indirec relaionship beween he wo variables in long erm.

2 Amir Mansour Tehranchian, Masoud Behravesh, Change in Inflaion Change in Inflaion Unemploymen Unemploymen Figure 1. Linear Phillips Curve Figure 2. Convex Phillips Curve Figure 1 depics a linear Phillips curve. The rade-off parameer,, is consan. In Figure 2, increases wih he unemploymen gap, in a capaciy consrain inerpreaion (Noe ha a posiive unemploymen gap is defined here as unemploymen being below u*, he NAIRU). From an inflaion asymmery poin of view, however, i can also be said ha is bigger, or ha he curve becomes more verical, when inflaion increases (Aubyn, 2000). Showing he relaionship beween inflaion and economic growh in Phillips curve is done on he basis of Okun s (1962) law. Okun invesigaed he relaionship beween unemploymen rae and economic growh rae in ime spans in he US. Okun s law is an empirical relaionship which expresses ha for each 2.5 percen of growh beyond he normal exen in he real GDP (which keeps up for one year); unemploymen would decrease by 1 percen. According o his rule, here is a posiive relaionship beween inflaion rae and economic growh rae. In a sudy in Briain beween 1862 and 1957, Lipsey (1960) confirmed Phillips findings. He found a nonlinear relaionship beween he change in wages and change in unemploymen rae. According o Keynes, workers suffer from money illusion. Given his illusion, herefore, he wages do no increase as he prices rise: as he real wages decrease, hiring hrough agencies increase and so do employmen and producion. Consequenly, here is a negaive relaionship beween inflaion and unemploymen bu a posiive relaionship beween inflaion and producion (Da Silva, 2013). Friedman s (1968) and Phelps (1968) analyses of Phillips curve-which are based on comparaive expecaions-show ha, in shor erm, he expeced inflaion of labour is lower han real inflaion. Phillips curve, herefore, has a negaive slope and moves wih changes in expecaions. In long erm, however, he expecaion of labour is fully formed and he real inflaion becomes equal o expecaions. As a resul, wages rise in andem wih prices, overall supply becomes verical and so does Phillips curve. This means here is no, in long erm, a relaionship beween inflaion and unemploymen and beween producion and employmen. According o he classic heories, prices and wages are oally flexible, and informaion exiss in is fulles form and expecaions are formed in a raional way. In his approach,

3 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer marke equaliy akes place fas and he overall supply curve is verical. As a resul, Phillips curve is verical oo and here is no a relaionship beween inflaion, unemploymen and producion. In Iran, high unemploymen rae and inflaion have always brough abou concerns. On one hand, excluding some porion of he labour, unemploymen diminishes he amoun of producion; on he oher, i leads o a decrease in skill and efficiency of he labour by separaing people from work environmen. Inflaion decreases shopping power of groups wih sable income by widening class gap and income difference-which disurbs resource allocaion consequenly. Recognizing and explaining he relaionship beween inflaion and unemploymen in he counry s economy, herefore, occupy an imporan posiion in economic decisionaking. Given he imporance of his issue and ha inflaion and unemploymen are among he chronic phenomena in Iran, he objecive of he curren projec is o empirically invesigae he relaionship beween inflaion and unemploymen. To achieve his end, he paper has been divided ino five secions. A firs, he relaed lieraure is examined in heoreical and empirical erms. In secion 3, he research mehodology is inroduced. Secion 4 presens he findings of he research, and he final secion presens he conclusions. 2. The Relaed Lieraure 2.1 Theoreical Analyses Mos of he heoreical analyses are devoed o he relaionship beween inflaion and unemploymen as are discussed in Phillips curve. Schools of economics have analysed he relaionship, given he inellecual infrasrucure and heoreical principles. Fisher (1926) was he firs one o prove an indirec relaionship beween inflaion and unemploymen, using he saisical daa relaed o he US beween 1915 and His sudies demonsraed ha he relaionship was one-way-from inflaion o unemploymen. Phillips (1958) used he daa relaed o 1861 o 1957 in Briain and concluded ha here was an indirec relaionship beween he wo variables. In a sudy in Briain beween 1862 and 1957, Lipsey (1960) confirmed Phillips findings, using he radiional heory of marke behaviour. According o his heory, in case of excess demand, prices would rise and in excess supply, prices would go down. Moreover, he more markes ge disan from equilibrium, he more remarkable would be he change rae. Increase in he excess demand for labour would lead o a rise in wages. Also, wih increase in excess demand for labour, more unemployed individuals would underake some financial jobs; ha is o say, here is a negaive relaionship beween unemploymen and excess demand. The difference beween Lipsey s (1960) and Phillips (1958) sudies is ha he former addressed he relaionship beween he

4 Amir Mansour Tehranchian, Masoud Behravesh, variaions of he above-menioned variables raher han he relaionship beween unemploymen rae and wage rae. The resuls indicaed ha here was a non-linear relaionship beween variaions in money wage rae and variaions in unemploymen rae, which is in sep wih Phillips findings. Lipsey (1960) rejeced Phillips (1958) hypohesis regarding hreshold effec on unemploymen rae-hreshold effec being he amoun of criical wage for affording life, less han which would make life difficul for workers. To make up for he expenses beyond he wages, workers aemp o raise heir wages by bargaining hrough unions. Lipsey (1960) explained ha Phillips curve was obained hrough he horizonal addiion of Phillips curves in he markes of differen indusries and ha adoping a policy which causes change in he disribuion of unemploymen rae in individual markes would lead o he oal shif of he curve. As was menioned before, he early Phillips curve expressed he relaionship beween unemploymen and wage inflaions. Policy-makers, however, deermine he objecives of inflaion, more ofen han no, in erms of change raes in prices raher han in wages. Consequenly, in order for he analysis based on Phillips curve o be useful for policy-makers objecive, i is necessary o ransform i o a price change relaion. Samuelson and Solow (1960) were he firs o adop such an approach. Their presupposiion was ha agencies deermined he sales prices hrough a sable rule (average producion cos) in which he prices are se by uni labour cos plus profi margin. W N P ( 1) (1) Y Where P indicaes he price levels, W he nominal wage rae, N employmen level and Y real producion level. The following is obained: P W (2) Where: is he rae of labour produciviy growh. Consequenly, (2) shows he possibiliy of non-inflaion increase of nominal wages, given he increase in produciviy. Samuelson and Solow (1960) inroduced Phillips curve as an indicaor of a rade-off beween inflaion and unemploymen. They were he firs o show he relaionship beween inflaion and unemploymen like his: e 1 bu (1 ) e 1 Where )π( is inflaion rae, prediced inflaion rae, U demand pressure in labour marke and in ( 1 ) indicaes he produciviy rae of labour. (3)

5 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer These researchers demonsraed ha policy-makers adap o moneary policies o achieve various combinaions of unemploymen and inflaion. Each poin on he curve can be considered an achievable policy-making objecive and he choice of his poin on curve depends on he esimae of unemploymen expense and inflaion. Policy-makers can op for low unemploymen-high inflaion combinaion or high unemploymen-low inflaion one. Tha is o say, subsiuion beween inflaion and unemploymen is feasible. They found ou ha rade-off beween inflaion and unemploymen is no sable in long erm; moreover, here is room for improving his rade-off process. Policies like reraining, esablishing employmen banks, ec. may add o he efficiency of labour marke and lead o he displacemen of he curve in a way ha he rise in wage would cause a fall in unemploymen. In he 1960s, he concep of shor-erm Phillips curve was developed by Friedman (1968) and Phillips (1968) on he basis of expecaions. In fac, wo basic poins were he hear and soul of Friedman s moneary school: The firs poin was naural rae of unemploymen obained hrough combining expecaions in he shor-erm Phillips curve. From he perspecive of moneary school, here is no a permanen relaionship beween inflaion and unemploymen. They considered he shor-erm Phillips curve as emiing from he presupposiion ha labour marke was coninuously in a sae of balance. The second poin was ha here was an exraordinary emphasis on he role of money on economy. For Friedman, he effecs of changes caused by he volume of money in shor and long erm were oally differen. Tha is o say, changes in money supply could affec he real variables in economy and bring abou expansionary effecs in shor erm. On he conrary he rise in he volume of money, in long erm, could only have influence on inflaion wihou he abiliy o remarkably affec producion. One of he seps in developing Phillips s equaion was he adding of expecaions o he early Phillips equaion by Friedman and Phelps. Friedman and Phelps challenged he early Phillips s equaion simulaneously ye independen of each oher, believing ha i could no clearly explain he facs. They, herefore, increased is adapabiliy by adding expecaions o i. The objecive Phelps (1968) was following in he lae 1960s was o express he relaionship beween inflaion and unemploymen by pricing behaviour and wages. He placed he expecaions of agens a he op of his analysis, disinguished beween expeced and non-expeced inflaion and addressed macroeconomic inerpreaions of his disincion. His refashioning of he curve came o be known as Phillips generalized expecaion curve. As opposed o he previous sudies like Lipsey (1960), Phillips emphasized ha i was he difference beween expeced inflaion and real inflaion ha was relaed o unemploymen. His analysis differed

6 Amir Mansour Tehranchian, Masoud Behravesh, from he earlier views which regarded higher employmen as possible hrough inflaionary supply policies. Wha is imporan for Friedman is no inflaion rae bu he prediced inflaion (expeced inflaion rae). There is no a sable and permanen rade-off beween inflaion and unemploymen. There is a naural rae of unemploymen (U N) which is compaible wih he real expecaions and he main forces in economy. Unemploymen can only rank below inflaion if he former inensifies he laer. Or i can rank above i hrough creaing ani-inflaion. Friedman (1968) and Phelps (1968) argued separaely ha Phillips curve, as a rade-off process beween unemploymen and inflaion, is no a sable and longerm equaion o be capialized on by policy-makers. They argued ha boh workers in labour supply and agencies in labour demand would consider he real wages and ha employmen would be acivaed when a sudden inflaion occurs which escapes he noice of workers. Ye in long erm, during which he sudden inflaions fade away, expecaions are offse by he experience of he curren inflaion (comparaive expecaions) and unemploymen reurns o is balance raea rae compaible wih all inflaion raes fully prediced in he sable sae, indicaing ha he long-erm Phillips curve is verical in he naural rae of unemploymen. They believe ha Phillips curve moves in ime and shifs o he op and he righ due o he rise in he rae of expeced inflaion. Under inflaion, unemploymen would rise and under increasing unemploymen inflaion would rise seeply. Combining Phillips curve and expecaions wih he process of learning on he basis of error, he well-known acceleraion hypohesis was developed in he 1970s and caugh much of policy-makers aenion. The hypohesis, which is a corollary of naural rae of unemploymen, expresses ha since here is no a long-erm rade-off beween inflaion and unemploymen, all aemps a fixing unemploymen on a level lower han naural one would lead o a permanen risen inflaion. Tha is due o he fac ha price acceleraion is so ha he real inflaion is more han he expeced one, provided ha moneary expansion is suppored. Such a moneary expansion upholds he sudden inflaions and prevens unemploymen from reurning o is balanced level. In long erm, Phillips s curve is verical in a specific naural rae, i.e., in he naural rae of unemploymen. Acceleraion hypohesis or Phillips curve balanced on he basis of expecaions is widely acceped by economiss bu has no become popular ye. A grea many number of economiss, however, have acceped he difference beween he long and shor erm curves bu sill believe ha he long-erm variable has a negaive and seeper slope han he shor-erm one. Sargen and Wallace (1975) indicaed ha moneary policy did no have anyhing o do wih producion procedure and employmen. They uilized he raional expecaion heory abou he naural rae of unemploymen balanced by Friedman and Phelps; he resuls proved ha expeced inflaion could no have an effec on employmen bu ransiory and unexpeced inflaion could reduce

7 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer unemploymen o a level lower han he naural rae of unemploymen. They believed ha sysemaic moneary policy-making could only affec he expeced inflaion and could no affec unexpeced unemploymen and inflaion. The supporers of his school, herefore, do believe in he exisence of verical Phillips curve in shor and long erms: hey do no believe in he relaionship beween inflaion and unemploymen unless some deviaions in producion and employmen from heir naural levels occur due o expecaion errors. The New Classical School's aiude oward employmen and unemploymen was ha hese issues concerned he decisions of individuals: decision-akers make predicions abou wages on he basis of wage in he presen and deermine heir labour supply accordingly (Greenwald and Sigliz, 1987). Given ha hese predicions migh urn ou o be wrong, he creaion of flucuaion in employmen and unemploymen becomes is naural oucome. New Keynesians, no unlike Keynes himself, began from his poin ha unemploymen and economic flucuaions are he mos pivoal maers in economy. They placed an accen on he foundaions of microeconomics and believed in he raional expecaions assumpion bu no in he clariy of new classical marke. On he conrary, new Keynesians argue ha a leas in shor erm, wages and unemploymen do no ge balanced bu, on he conrary, he conracual arrangemen in he employmen marke keeps wages fixed for a cerain ime span. Consequenly, he wage balance sops in he course of conrac, which migh symie privae secor s balancing power in face of random ensions. If he sae is able o balance is policies in facing random ensions more quickly han privae secor (which can do his by renegoiaing workers conrac), here can be circumsances for implemening he policies of demand side. For he new Keynesians, unemploymen is mosly uninenional; he argumen of his group is sronger han new classics when i comes o explaining unemploymen. In a nushell, he assumpion regarding balance in labour marke espoused by New Classics has caused hem o move away from heir objec of analysis and o be finally unable o explain unemploymen. New Keynesians believe ha fixing he conracual wages is a key phenomenon in he real world-which should be considered in developing a model. Furhermore, hey believe in he exisence of relaionship beween inflaion and unemploymen in shor erm-a relaionship ha has emerged from fixing he conracual wages. Ye hese work conracs, if assumed raional, canno be rue for long erm. In shor erm, herefore, he falling Phillips curve would be seeper han Phillips curve wih Keynesian assumpions. Ye, he curve would no be verical in shor erm as opposed o New Classics; i is due o lack of clariy in marke. Neverheless, in long erm, i ends o be he verical Phillips curve like oher economic schools. New Keynesians (Blanchard and Jordi (2007); Clarida e al., (1999)) have argued in recifying radiional Keynesians heories ha in real world here are

8 Amir Mansour Tehranchian, Masoud Behravesh, some degrees of moneary illusion which makes i impossible for wage earners o have a complee balance in relaion o inflaionary expecaions. In oher words, expeced inflaion rae is aken ino accoun in he process of deermining wages albei parially because: 1. Agencies auomaically refuse o raise he wages. 2. Workers are no fully aware of siuaion in labour marke and of he sae of labour supply and demand. 3. Workers are no able o predic he fuure inflaion rae exacly. According o wha is said above, Phillips curve will be: e P P F( u),0 1 New Keynesians consider expeced inflaion rae o be dependen on prices in e he pas. In long erm, hen, i looks like Friedman's model P P. So: 1 P F( U ) (5) 1 According o he equaion above, here is a rade-off beween unemploymen and fully prediced inflaion. In oher words, long-erm Phillips curve has a negaive seep bu is seeped in comparison o shor-erm curve. 2.2 Some Empirical Evidence On one hand, he amoun of lieraure on Phillips curve is so much ha giving a comprehensive review here is no possible; on he oher hand, he resuls of hese sudies are so variegaed ha reaching a consensus seems o be ou of reach. There are a few influenial sudies which could be caegorized as pioneer in macroeconomics. This secion is a brief overview of a number of recen sudies conduced beween years 1985 and 2009, which are relevan o our discussion. Benderly and Zwick (1985) invesigaed he relaionship beween inflaion and unemploymen in he Unied Saes beween 1955 and Unlike Modigliani (1977), hey demonsraed in heir research ha variables of unemploymen rae and money growh rae are he effecive facors in explaining inflaion rae. Grubb (1986) esimaed he paern of naural rae of unemploymen for ime spans for 19 counries of OECD. The mos ousanding resul of his research is ha inflaion rae is no only affeced by inflaion rae bu also by he naural rae of unemploymen. Apel and Jansson (1997) invesigaed he relaionship beween inflaion and unemploymen and came up wih an equaion sysem for esimaing poenial producion and unemploymen rae compaible wih non-acceleraing inflaion rae of unemploymen (NAIRU). Debell and Vickery (1998) used he seasonal daa for ime span and invesigaed Phillips curve for Ausralia. This research esimaes he paerns of shor-erm Phillips curve in linear and non-linear form. The funcion obained from his research indicaes he reverse relaionship beween he variables above. Gomez (4)

9 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer and Julio (2000) esimaed Phillips curve for Colombia using Kalman filer and OLS. The resuls implied ha 1 percen fall in unemploymen rae would cause a rise in he prediced exen of inflaion. Guerrero and Milion (2004) sudied he relaionship beween inflaion and unemploymen, using raional expecaions. The sudy draws on Markov-Swichingpaern. Even hough he resuls of his research demonsraed he verical Phillips curve for a leas weny years, he curve had a negaive slope in he era of economic insabiliy ( ). Scheibe and Vines (2005) modelled inflaion in China, using oupu gap Phillips curve, also known as he difference beween poenial and acual oupus. They esimaed he rerospecive as well as prospecive curve. Rerospecive, radiional Phillips curve was a useful poin of deparure for modelling inflaion in China. The prospecive curve, however, proved o be more appropriae han he rerospecive one. The researchers arrived a he long-erm Phillips curve, using he daa relaed o The resuls indicaed ha oupu gap, foreign exchange price and expeced inflaion played an imporan role in explaining inflaion. Paul (2009) invesigaed Phillips curve for India. Drawing on OLS and given he indusrial secor, he underook he shor-erm rade-off beween inflaion and oupu gap. 3 Mehodology The saisical daa for his sudy include he ime series of Kalman (1960) filer was used o invesigae he subsiuion relaion beween inflaion and unemploymen. One of he mos imporan applicaions of Kalman filer is o updae he curren value of ξ on he basis of Y observaions. All in all, in his mehod, he updaed figures can be obained by having he values of F, Q, A, H or R. Anoher applicaion of Kalman filer is in hose equaions wih random variable coefficien in ime. Using OLS in a regression equaion esimaed on he basis of ime series observaions, one can only come up wih an esimae of model s parameers in ime. As is discussed in economic maers, variables are subjec o change and oscillaion in ime. Kalman (1960) presens a mehod by applying which in regression models a vecor of variable coefficiens in ime can be obained. In every ime period in his mehod, he daa relaed o he previous periods as well as he new informaion are used for esimaing he coefficien of he nex sage. The model wih variable coefficien esimaed by Kalman filer is a non-linear funcion of X. Tha is o say, even hough opimal answers could be reached (in case, of course, hey are disribued normally); i canno be a linear picure of ξ on Y wih abnormal inerfering componen. In he lieraure on economerics, Kalman filer is considered an algorihm which coninuously updaes he informaion perinen o equaions in a sysem. In addiion o he advanages his mehod has, i makes i possible o accuraely predic maers regarding limied samples. Furhermore, an accurae likelihood funcion can be planned for ARMA

10 Amir Mansour Tehranchian, Masoud Behravesh, and, finally, he esimaes of VAR models can be obained by variable coefficiens in ime. In his mehod, if ϒ is he coefficien vecor in ime, he dynamic models of V in erms of unobservable variables of ξ vecor (rx1) which is sae vecor can be shown hus: F V (6) 1 1 Y ÁX H W (7) Where F, Á and H are he marixes of (rxr), (nxk) and (nxr) respecively. X is he (kx1) vecor combined of exogenous and predeermined variables. 6 is called sae equaion and 7 is called observaion equaion. I is assumed ha V vecor whose dimension is (nx1) are vecors wihou serial correlaion. Q, E( V V ) (8) 0, OherPo in s Q, E( WW ) (9) 0, OherPo in s Here, Q and R are he marixes of (rxr) and (nxn), respecively. We have he following for τ and : E ( VW ) 0 (10) Since X is a vecor for exogenous variables which are predeermined, i does no include ξ +s or W +s for s=1, 2, values. X, for example, may include inhibied values of variable or variables dependen on and for all values of. I is assumed here ha are no correlaed. Tha follows: E( V 1) 0; 1,2,..., T (11) E( W 1) 0; 1,2,..., T (12) In mos cases, X1, X2,..., XT, ϒ1, ϒ2,..., ϒ are observable for an economic analys. Thus, one of he mos imporan objecives of economeric echniques is o deermine he values of unobservable variables in a sysem on he basis of observaions on hand. According o his, he numerical values of F, Q, Á, H and R are observable and esimable. Kalman filer has many applicaions in economy-specifically in economerics. The firs and mos imporan applicaion may be o calculae he leas squares of predicion in sae variable on he basis of observaions. ( ) E( ) (13) ( X (14) 1 1) andy (, 1,..., 1, X, X1,..., 1

11 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer (14) Indicaes 1 linear picure on and is he fixed componen of i. Kalman filer can seadily calculae he values of hese predicions and esimae he values of leas mean squared errors. Kalman s calculaion mehod is rerogressive, which begins wih values of 1 0. The prediced value of obained on his basis does no conain an observaion of Y on X. This is, in fac, he non-condiional mean of. And MSE is: E( ) (15) ( ) ( 1 E 1 1 E P E ) (16) In general, if all vecors of F uniary roo are locaed wihin he circle, he process on whose basis ξ is formed will have a sable covariance. Thus, he mean uncondiional ξ can be obained by mahemaic expecaion via his equaion: F V (17) 1 * 1 E( 1) F * E( ) (18) Since ξ possesses some feaures of sable covariance, we will have: ( I F)* E( ) 0 (19) r Since 1 canno be a componen of uniary roo, (I r-f) will be regular and he equaion will have he common soluion E (ξ =0). Uncondiional variance ξ can be obained by muliplying (17) by is ranspose and hen obaining mahemaical expecaions from he wo sides of he equaion. F * V * F V F * E( * )* F E( V * V ) E( * 1 1) E (20) If he marix of ξ covariance is shown wih, equaion 20 will be: This is solved hus: FF Q (21) 2 1 I ( F F). Vec( Q) Vec( ) (22) r In general, assuming ha roos are locaed wihin he uniary circle, Kalman repeiion mehod can begin wih hese primary values ( 1 0) =0 and ( P 1 0) =0, which include he following relaionship: 2 1 I ( F F). Vec( ) Vec( P1 0) r Q (23) Now if some of he uniary roos of F fall ouside, or on, he circle or if he primary values of sae variable have no been obained in he course of previous equaions, he primary values of ( 1 0) can be obained on he basis of 1 wih he

12 Amir Mansour Tehranchian, Masoud Behravesh, bes guess. ( P 1 0) Marix is a posiive one which includes he exen of confidence regarding he guess abou he primary value of 1. Larger values in ( P 1 0) marix, herefore, indicae a relaively high lack of confidence regarding he real value of The Paern Gomez and Julio (2000) exrapolaed Phillips curve for Colombia. Based on sudies conduced by Laxon e al.(1999), nonlinear Phillips curve was invesigaed. Using Kalman filer and OLS, he resuls were explained. The model used was as follows: * e U U U (24) ˆ ˆ ˆ S ˆ S ˆ S (25) e U * * U 1 U (26) e Where is he inflaion rae in erms of CPI, he inflaion rae * expeced, U NAIRU naural rae of unemploymen (see equaion 26), U unemploymen rae, S he index of supply shock (measured by he mehod M presened by King and Wason, 1994) and impored inflaion. Equaion 24 can be wrien as follows: * e U U U By simplifying he erms in parenheses, (28) will be obained: 1 * a Where Z and U. U Using (25), (26) and (28), we will have: M (27) e a Z (28) a a 1 a (29)

13 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer 1 2 S az S 1 (30) S 2 M 1 a U Where. The shif equaion is obviously non-saic, because i is changed wih ime. In he 2 sae equaion, Z coefficien changes wih ime as well. If variance becomes a =0, he value of U* will become sable. In ha even, he model can be esimaed by OLS mehod. az M S 1S 1 2S 2 (31) Where U*=a/ϒ. Researchers have come up wih supply shock index, bringing ino play he role of supply shock and using King and Wason s (1994) mehod: A A S 100 (log P log P 1) 100 (log P log P 1) (32) This can be simplified hus: A A log P log P 1 S 100 log (33) log P log P 1 A Where P is he inflaion rae in erms of CPA and P of he inflaion rae of food producs. According o he heoreical principles, i is likely ha in (31) he coefficien of impored inflaion and he supply side shock are posiive. Also, given he sign nex o Z, which is he reverse o unemploymen, i can be found ou if he curve for Iran is falling or rising. 3.2 Tesing Expecaions in Iran I goes wihou saying ha changing expecaions oward sensiive variables like inflaion migh change he primary resuls alogeher. Because of his, economiss have ried o define expecaions in form of cerain models so ha hey can make predicions. This sudy ess wo commonly used mehods in modelling expecaions, i.e., adapive expecaions and raional expecaions.

14 Amir Mansour Tehranchian, Masoud Behravesh, a. Adapive Expecaions This ype of expecaions is one of he mos imporan approaches o his issue. I is defined in erms of correcing errors in ime. According o his approach, people make a decision regarding he fuure of a variable, using is pas informaion. Adapive expecaions were firs developed by Cagan (1956). His model was aken from firs ype difference linear models. I was mos probably for esing and solving problems in he hen common economeric mehods. In his mehod, economic unis learn from heir pas experiences for shaping heir expecaions and draw closer o he realiy. The model can be wrien hus: P E( P ),0 1 E( P 1) 1E( P ) (34) The equaion above indicaes ha expecaions of inflaion for period +1 are formed in period. Hereα is a correcion coefficien which indicaes a proporion of expeced inflaion in he inflaion experienced in he previous period, which is added o he model a each sage. b. Raional Expecaions This ype was firs inroduced by Muh (1961). He used all he informaion available and drew on an opimal mehod in he framework of microeconomics. Ten years laer, i was applied by Lucas and Sargen (1979) o macroeconomics. Kara and Tuger (2005) show inflaion due o raional expecaions, drawing on Muh (1961): f E I ) (35) ( f Where he inflaion rae is in + f ime, I is he informaion available in ime and E is he mahemaical operaor of expecaions. From (35) he following can be concluded: Whereby we have: f E ( I ) 0 (36) f f f (37) f If regression analysis shows ha is a saisically significan funcion of I, raional expecaions hypohesis (null hypohesis) can be rejeced. In oher words, predicaion canno build an opimal siuaion which can be rue for all informaion available. Obaining all informaion can be an impracical and expensive process; ha is why he informaion available is always emphasized. Bran and Mial (1981) refer o his poin under parial raional expecaions. Wha adds o he complexiy of he issue is he definiion of informaion available or devising he expecaions variable on he basis of raional expecaions. To shed ligh on he issue a hand, esing raional expecaions hypohesis is poined ou. Raional expecaions hypohesis are esed in wo ways as is elaboraed on by Afield e al. (1991).

15 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer Firs mehod: In his mehod, an aemp is made a modelling his ype of expecaions by heoreical inerpreaions. E 1 v (38) In his equaion, is he real value of index price in curren period, E 1 expecaions perinen o ha have been shaped in -1 and v he predicion error ha does no correlae wih he informaion in -1. Whenever E 1 is observable, he following can be conjecured: 1E 1 0 (39) is random error wih mean 0 and variance 1. On his basis, if 1 1 and H 0: 0. 0, in which case we canno rejec hem, i can be concluded ha we have acceped he raional expecaions. Second mehod: If and is pas values are esimaed in a regression model, we will have: k k v 1 (40) Whenever i is assumed ha here are direc observaions abou E define E 1 on he basis of pas values of as follows: E kk v2 Subracing 41 from 40, we will have: 1, we can (41) E ) ( )... ( ) ( v v ) (42) 1 ( k k k 1 2 Now we can define he following hypohesis: H0 : i i, i 1,2,..., k (43) H 0 being rejeced means rejecing raional expecaions bu in boh condiions wha are needed for a reliable conclusion are direc observaions abou he expecaion variable E 1 on he basis of raional expecaions. Because of his, some of researchers have ried o define and subsiue he above-menioned expecaion variable. Expecaion variable refers o he aiude of people oward he model on whose basis we can predic he variable by using he pas informaion, curren informaion and he knowledge abou fuure plans. For insance, some make hese predicions on he basis of he ideas of expers, economiss and businessmen and some oher migh use he variable of ineres rae and he changes i undergoes o elaborae on he expecaion variable of price index. Since Iranian economy lacks he expecaion variable o esimae (42) and also because of he role governmen plays in money and capial marke, ineres rae is

16 Amir Mansour Tehranchian, Masoud Behravesh, no deermined in a free marke; deermining he ineres rae by he governmen, herefore, has caused a lack of balance in marke. In pracice, here is no expecaion variable as such. This research resors o a subsiuion variable o es raional expecaions approach. In order o achieve his, variables of price index in ransporaion, housing and fuel are used. I seems ha a remarkable lo of people are sensiive oward hese indices and consider hem as he inflaion of coming year. Since he governmen has some pars of ransporaion and fuel in is conrol, i is quie raional o hink ha consumers in large ciies for whom ransporaion coss are very imporan ake hese indices as he symbol of governmen s plans. As a resul, hese indices are used for defining E 1 whereby (42) is esed. Table 1 shows he variable of ransporaion expenses and able 2 he price index of housing and fuels as he expecaion variable. Table 1. The Variable of Transporaion Price Index Independen Variables Coefficien Sandard Deviaion T Coefficien Probabiliy Level B B B B Source: Calculaions by he Auhors Table 2. The Variable of Housing and Fuel Price Index Independen Variables Coefficien Sandard Deviaion T Coefficien Probabiliy Level B B B B Source: Calculaions by he Auhors Price index of ransporaions, housing and fuel were considered as he subsiue for he expecaion variable of various inhibiions in CPI (Consumer Price Index) by using daa regarding CPI. The mos appropriae CPI inhibiion on he basis of Akaike (1974, 1976); Schwarz (1978); Hannan and Quinn s (1979) as 2 2 well as R and R sandards is four. In he nex sage, given (42), he hypohesis claiming ha CPI inhibiion coefficiens are zero was esed. If in Wald es saisic F and Chi-Square are larger han he values of heir probabiliies, H 0 canno be suppored. The resuls of Wald es and he values of F saisics and Chi- Square are summarized in Table 3.

17 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer Table 3. Wald Tes Housing and Fuel Index Transporaions Index Probabiliy Value Saisic Probabiliy Level Value Saisic Level Saisic F Chi-Square Saisic F Chi-Square Source: Calculaions by he Auhors As can be seen here, given he values of saisic F and Chi-Square and he values of corresponding probabiliies, H 0 (raional expecaions) is rejeced and he oher hypohesis (adapive expecaions) is confirmed. 3.3 Esimaing he Paern Using Kalman Filer Given he sudy conduced by Gomez and Julio (2000), he following paern can be esimaed by Kalman filer: a Z M S 1S 1 2S 2 (44) In his equaion, Z coefficien is o change in ime. Here are four scenarios regarding esimaing Z : Scenario 1: In his scenario, Z coefficien is modelled in form of a sable mean in ime along wih inerference erms. Scenario 2: Z coefficien is modelled as an AR (1) process. Scenario 3: Z coefficien is modelled as a random walk. Scenario 4: Z coefficien is modelled as a random walk process wih a drif erm. 4 Resuls Each one of he equaions obained by he menioned scenarios is called a ransfer funcion. Given he supply shock, various saes for sae space equaion can be concepualized. Supply shock is calculaed by King and Wason (1994) index. A firs, he sae space equaion is esimaed by using oil price for he four scenarios. The resuls are shown in ables 4 o 7. Table 4. Esimaion of Z coefficien on he basis of scenario 1 Name of he Variable Coefficien Saisic Z Probabiliy Level π π S

18 Amir Mansour Tehranchian, Masoud Behravesh, S S M Sv σe Source: Calculaions by he Auhors Alhough all coefficiens in Table 4 are significan, he signs do no correspond o he heoreical foundaions. For example, oil shock and is firs and second suspensions have a negaive effec on inflaion. Also, he inflaion of las year has a negaive effec on inflaion. In oher words, he more he inflaion of las year, he lesser will be he inflaion in he curren year. In his esimaion, impor inflaion has an influence like he firs suspension. Of all he variables, inflaion wih he firs inhibiion has a posiive effec on inflaion and in sep wih he heoreical foundaions. Here wha is insignifican is he ransfer equaion. This sae, herefore, canno be he bes esimaion. Table 5. Esimaion of Z Coefficien on he Basis of Scenario 2 Name of he Variable Coefficien Saisic Z Probabiliy Level e π π S S S M Sv AR(1) Source: Calculaions by he Auhors Given he resuls of scenario 2, none of he coefficiens is saisically significan. Thus, no saemen can be made regarding his scenario. Table 6. Esimaion of Z coefficien on he basis of scenario 3 Name of he Variable Coefficien Saisic Z Probabiliy Level π π S S S M Sv σe Source: Calculaions by he Auhors

19 Subsiuion Tes beween Inflaion and Unemploymen in Iran: An Applicaion of Kalman Filer As i is shown in Table 6, all coefficiens are saisically significan. Inflaion in he firs and second inhibiion has a significan and posiive effec on he inflaion in he curren year. I can be concluded, herefore, ha people shape he expecaions on he basis of he inflaion of he las year (adapive expecaions). Moreover, he exen of he effec of inflaion in he las year on he inflaion in curren year is more han ha of wo years ago. In his esimaion, he coefficien of oil shock is 1.04 which indicaes ha oil shock has a significan and direc effec on inflaion. Of all he variables above, oil shock has he mos remarkable effec. The firs and second oil shock and impor inflaion have a reverse and meagre effec on inflaion, which hough significan is no in sep wih heoreical foundaions. In his scenario, Sv 1 has urned ou o be significan as well. Given is sign, which is posiive, i can be concluded ha he relaion beween inflaion and unemploymen is indirec. This sae, herefore, can be he bes esimaion. Table 7. Esimaion of Z coefficien on he basis of scenario 4 Name of he Variable Coefficien Saisic Z Probabiliy Level π π S S S M Sv Source: Calculaions by he Auhors In Table 7, none of he variables is saisically significan; whereby i can be concluded ha he daa regarding inflaion and unemploymen in scenarios 2 and 4 in which he coefficien of variable Z is modelled in he form of a AR (1) process and random walk process wih a drif erm do no mach. Only in scenarios 1 and 3 in which Z (α ) coefficien is in he form of a fixed mean in ime and random walk process, he coefficiens are significan. Invesigaing hese wo scenarios makes i clear ha only in scenario 3 where coefficiens are significan and in line wih heoreical foundaions, he ransfer equaion becomes significan.

20 Amir Mansour Tehranchian, Masoud Behravesh, 5 Conclusion In he course of he recen five decades, Iranian economy has gone hrough high inflaion and unemploymen raes. I is, herefore, obvious ha reducing and keeping in check hese wo facors simulaneously are among he mos imporan objecives of economic policy-makers and planners. The exisence of a subsiuion relaion beween inflaion and unemploymen implies he neuralizaion of macro policies and of a considerable porion of faciliies and resources o reduce he exen of hese wo facors. Given he poins menioned above and he resuls, i can be saed ha he relaionship beween inflaion and unemploymen in Iran can be proved. Furhermore, given he reverse relaionship beween inflaion and unemploymen, i can be concluded ha here is a subsiuion relaion beween inflaion and unemploymen in Iran. Having compared he resuls of a sae in which supply shock is oil price wih wo oher saes, i can be concluded ha oil price is very imporan in Iran and deserves more aenion. The resuls of a sae in which supply shock is liquidiy proved ha none of coefficiens in four scenarios is significan. Thus, being cerain regarding he parameers involved is no possible. Furhermore, when food price index was considered o be he supply shock, he only coefficiens which urned ou o be significan were hose in scenario 2 where α was modelled as an AR (1) process. SV 1, however, did no prove significan in his scenario. All in all, i can be concluded ha of shocks esed in his sudy, he only ransfer equaion urning ou significan was he scenario 3 wih oil shock. Moreover, only his scenario can sae ha here is a significan relaionship beween inflaion and unemploymen wih subsiuion in Iran. REFERENCES [1] Akaike, H. (1974), A New Look a he Saisical Model Idenificaion. I.E.E.E. Transacions on Auomaic Conrol, AC 19: ; [2] Akaike, H. (1976), Canonical Correlaion Analysis of Time Series and he Use of an Informaion Crierion. Mahemaics in Science and Engineering, 126: 27-96; [3] Apel, M and Jansson, P. (1999), Sysem Esimaion of Poenial Oupu and he NAIRU. Empirical Economics, 24 (3): ; [4] Afield, C., Demery, D. and Duck, N. (1991), Raional Expecaions in Macroeconomics: An Inroducion o Theory and Evidence. 2 h Ediion, Wiley- Blackwell Press; [5] Aubyn, M. S. (2000), Tesing for Asymmery in he Inflaion-Unemploymen Trade-off: Some Evidence for he USA. Working Papers, Deparmen of Economics a he School of Economics and Managemen (ISEG), Technical Universiy of Lisbon, No.2000/05;

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