Inflation Dynamics in Finland 1990Q1-2012Q1

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1 Powered by TCPDF ( Inflaion Dynamics in Finland 990Q-202Q Economics Maser's hesis Pauliina Turunen 202 Deparmen of Economics Aalo Universiy School of Business

2 AALTO UNIVERSITY / SCHOOL OF BUSINESS ABSTRACT Economics, Maser s hesis Pauliina Turunen INFLATION DYNAMICS IN FINLAND 990Q 202Q The objecive of his hesis is o sudy wheher inflaion dynamics in Finland can be described using he New Keynesian Phillips curve (NKPC) over he period 990Q 202Q. The NKPC explains curren inflaion wih forward-looking inflaion expecaions and curren real marginal cos. The assumpion of raional expecaions is relaxed in his hesis and boh Consensus Economics and Saisics Finland s survey daa are used as proxies for inflaion expecaions. Since hese expecaions are expecaions for consumer prices, inflaion is measured wih annual change in he Consumer Price Index. Oupu gap is used as a proxy for real marginal cos. The NKPC is esimaed wih boh Ordinary Leas Squares (OLS) and Generalised Mehod of Momens (GMM). The variables are also analysed using he frequency domain mehod, which gives informaion on he dynamics of boh correlaions and lead-lag relaionships of variables a differen frequencies. Esimaions in his hesis show ha once he raional expecaions hypohesis is relaxed and survey-based inflaion expecaions are used, inflaion in Finland can be explained wih he New Keynesian Phillips curve over he period 990Q 202Q. The analysis of variables in his hesis shows ha he dynamics of variables used in he NKPC esimaions varied a differen frequencies. Key words: New Keynesian Phillips curve, inflaion, inflaion expecaions, real marginal cos, frequency domain i

3 TABLE OF CONTENTS Inroducion.... Background....2 Objecive of he Thesis Resuls of he Thesis Srucure of he Thesis Micro Foundaions of he New Keynesian Phillips Curve Profi Maximisaion and Flexible Prices Profi Maximisaion and Rigid Prices Price Rigidiy in he Aggregae Economy and he New Keynesian Phillips Curve Laes Research on he New Keynesian Phillips Curve Real Marginal Cos Inflaion Expecaions Inflaion Persisence The Daa Inflaion Inflaion Expecaions Real Marginal Cos The Dynamics of Inflaion, Inflaion Expecaions and Real Marginal Cos Inflaion and Inflaion Expecaions Inflaion and Real Marginal Cos Esimaion Resuls Ordinary Leas Squares Esimaions Generalised Mehod of Momens Esimaions Concluding Remarks from he Esimaions Conclusions References ii

4 LIST OF FIGURES AND TABLES Figure. Inflaion measured wih annual change in Consumer Price Index in Finland 990Q 202Q Figure 2. Inflaion forecass for he following year. Inflaion forecass of Consensus Economics (CE) 990Q 202Q and Saisics Finland s Consumer Survey (CS) 996Q 202Q Figure 3. Inflaion forecass and inflaion compared 990Q 202Q Figure 4. Inflaion forecass for he following year and inflaion compared 990Q 202Q Figure 5. Seasonally adjused GDP in millions of euros a reference year 2000 prices in Finland 990Q 202Q Figure 6. Oupu gap esimaed using he Hodrick Presco filer for period 990Q 202Q Figure 7. Oupu gap and inflaion in Finland 990Q 202Q Figure 8. Scaer plo showing relaionship beween oupu gap and inflaion in Finland 990Q 202Q Figure 9. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and Consensus Economics inflaion forecas for he following year in Finland 990Q 202Q Figure 0. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and Saisics Finland s Consumer Survey inflaion forecas for he following year in Finland 996Q 202Q Figure. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and Consensus Economics inflaion forecas for he following year in Finland 996Q 202Q Figure 2. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and oupu gap in Finland 990Q 202Q. Oupu gap is he difference beween log real GDP and is flexible price equilibrium, esimaed using he Hodrick Presco filer Figure 3. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and oupu gap in Finland 996Q 202Q. Oupu gap is he difference beween log real GDP and is flexible price equilibrium, esimaed using he Hodrick Presco filer Table. The New Keynesian Phillips curve esimaion resuls using OLS Table 2. Correlaions beween oupu gap and boh Consensus Economics and Saisics Finland s Consumer Survey inflaion forecas Figure 4. NKPC residuals. The model of NKPC wih Consensus Economics inflaion forecas for period 990Q 202Q wih a non-fixed (on lef) and fixed (on righ) discoun facor Figure 5. NKPC residuals. The model of NKPC wih Saisics Finland s Consumer Survey inflaion forecas for period 996Q 202Q wih a non-fixed (on lef) and fixed (on righ) discoun facor Table 3. The New Keynesian Phillips curve esimaion resuls using GMM and Consensus Economics inflaion forecas as inflaion expecaions, Finnish daa beween 990Q and 202Q Table 4. The New Keynesian Phillips curve esimaion resuls using GMM and Saisics Finland s Consumer Survey inflaion forecas as inflaion expecaions, Finnish daa beween 996Q and 202Q Table 5. The New Keynesian Phillips curve esimaion resuls using GMM and Consensus Economics inflaion forecas as inflaion expecaions, Finnish daa beween 996Q and 202Q iii

5 INTRODUCTION. Background Inflaion has been of ineres o economiss for many decades. Worldwide inflaion was quie sable for hree decades unil he laes financial crisis ha commenced in year Afer his, inflaion and deflaion fears have followed each oher. Inflaion has been recognised as an imporan vehicle o drive he economy back o is long-run growh pah. Research on inflaion dynamics has largely been based on he Phillips curve. The foundaions of his research are he papers of Phelps (967) and Friedman (968) emphasising expecaions in inflaion process and developing he expecaions-augmened Phillips curve. A he momen he mos widely recognised model among he cenral banks o explain inflaion dynamics is he New Keynesian Phillips curve. I was developed in a synhesis of New Keynesian macroeconomics and Real Business Cycle (RBC) heory in he 990s. The New Keynesian Phillips curve (NKPC) explains curren inflaion by forward-looking inflaion expecaions and curren real marginal cos. The NKPC combines rigidiies, imperfec compeiion and forward-looking expecaions. The New Keynesian Phillips curve emphasises rigidiies in price and wage seing o explain persisence of inflaion. The firs models of nominal rigidiies were he models of Fischer (977) and Phelps and Taylor (977). The rigidiies in he NKPC are usually based on models of Taylor (980) and Calvo (983). In Taylor s model only a fracion of wages are rese in each period and wages are assumed o be fixed for a cerain number of periods. In Calvo s model only a random fracion ( ω) of firms are able o rese heir prices each period and all oher firms keep heir prices unchanged. Imperfec compeiion is an imporan assumpion behind nominal price and wage rigidiy, since i allows firms o se heir prices and labour o se is wage demands. The mos applied model is he model of monopolisic compeiion by Dixi and Sigliz (977). Forward-looking expecaions are usually assumed o be raional in he sudies of NKPC. Raional expecaions have been a popular assumpion in macroeconomics afer Lucas (976) inroduced hem o he Phillips curve.

6 Even hough here seems o be a sound heory behind modelling inflaion dynamics, i has no done well describing he empirical daa. I is ineresing o expand his vas lieraure using Finnish daa. There are some sudies ha concenrae on Finnish inflaion from he perspecive of he NKPC, bu heir conclusions are conradicory. According o Juselius (2006a, 2006b) Finnish inflaion is primarily deermined by excess demand in he produc marke and no by he sandard NKPC. However, Paloviia and Mayes (2006) found ha when using he OECD inflaion forecas as empirical proxy for inflaion expecaions and he privae consumpion deflaor as a measure of inflaion, Finnish inflaion dynamics can be described using he NKPC..2 Objecive of he Thesis The objecive of his hesis is o sudy wheher inflaion dynamics in Finland can be described using he New Keynesian Phillips curve over he period 990Q 202Q. Afer deriving he heory behind he New Keynesian Phillips curve and presening he laes research, his hesis concenraes on analysing he variables in he NKPC esimaions and esimaing he New Keynesian Phillips curve. In his hesis, he heory of he New Keynesian Phillips curve ha is presened combines he heories presened by Walsh (2003) and Paloviia (2008). The compeiion is assumed o be monopolisic and prices are adjused randomly according o Calvo s (983) model. The assumpion of raional expecaions is relaxed and inflaion expecaions are measured by survey-based inflaion expecaions. In he empirical par of his hesis boh Consensus Economics and Saisics Finland s survey daa are used as proxies for inflaion expecaions. Inflaion is measured wih annual change in he Consumer Price Index. Oupu gap, calculaed as he difference beween log real GDP and is flexible price equilibrium, is used as a proxy for real marginal cos. The NKPC is esimaed wih wo widely used mehods among NKPC lieraure: Ordinary Leas Squares (OLS) and Generalised Mehod of Momens (GMM). The variables are also analysed using he frequency domain mehod o gain undersanding of inflaion in Finland. This mehod gives informaion on correlaions and lead-lag relaionships beween variables a differen frequencies. 2

7 .3 Resuls of he Thesis Esimaions in his hesis show ha once he raional expecaions hypohesis is relaxed and survey-based inflaion expecaions are used, inflaion in Finland can be explained wih he New Keynesian Phillips curve over he period 990Q 202Q. In all esimaions he coefficien for oupu gap is correcly signed and significan. The analysis of variables in his hesis shows, however, ha he dynamics of variables used in he NKPC esimaions varied a differen frequencies. I also shows ha inflaion expecaions are lagging variables for inflaion in he shor-run..4 Srucure of he Thesis The res of his hesis is srucured as follows. Chaper 2 derives he heory behind he New Keynesian Phillips curve. Chaper 3 summarises he laes research on he New Keynesian Phillips curve. Chaper 4 presens he daa. Chaper 5 analyses he dynamics of Finnish inflaion, inflaion expecaions and real marginal cos proxy. Chaper 6 shows he esimaion resuls and chaper 7 concludes he hesis. 2 MICRO FOUNDATIONS OF THE NEW KEYNESIAN PHILLIPS CURVE This chaper derives he New Keynesian Phillips curve from is micro foundaions. The main objecive of he NKPC is o explain inflaion, which can be described as a coninuous rise in he general price level. Therefore he heory of inflaion requires he heory of price formaion. The heory of NKPC assumes monopolisic compeiion, nominal rigidiies and forwardlooking expecaions. Monopolisic compeiion means ha individual firms produce differeniaed producs and have a power o se nominal prices, while heir pricing decisions have no effec on overall price level. Firms se nominal prices o maximise heir profis. However, nominal price rigidiy means ha i akes ime o rese he price when economy is hi by a shock. Because of nominal price rigidiies, firms use forward-looking expecaions in seing nominal prices. Since monopolisic compeiion has been assumed, he prices are se 3

8 some margin over marginal coss. Aggregaion of firms price decisions leads o aggregae inflaion and he NKPC. The heory of profi maximisaion and flexible prices presened in subchaper 2. follows he heory presened by Walsh (2003). Theories of profi maximisaion and rigid prices in subchaper 2.2 and price rigidiy in he aggregae economy and he New Keynesian Phillips curve in subchaper 2.3 follow he heory presened by Paloviia (2008). 2. Profi Maximisaion and Flexible Prices The heory presened in his hesis consiss of firms ha hire labour and produce and sell differeniaed producs in monopolisically compeiive markes, while households supply labour and purchase goods for consumpion. Boh firms and households behave opimally. Firms maximise heir profis, while households maximise he expeced presen value of uiliy. Firm j can se price p j for is differeniaed produc according o profi maximisaion, since markes are monopolisically compeiive. There is a coninuum of firms j [ 0, ] and he firm j produces he quaniy c j of he differeniaed produc. The assumpion is ha each firm produces only one variey of he differeniaed produc. Each firm j chooses a price p j ha maximises is profi subjec o wo consrains. The firs consrain is he producion funcion ha summarises he available echnology, and he second is he demand curve ha each firm faces. This chaper derives he profi maximisaion problem in an economy where prices are flexible. The producion funcion is assumed o be c = Z N, (2.0) j j 4

9 where c j is he quaniy of he differeniaed produc produced by firm j a ime, labour inpu in firm j a ime, Ε ( Z ) = N j is Z is an aggregae produciviy disurbance a ime and. For simpliciy, labour is he only facor of producion and he consan reurns o scale has been assumed. The quaniy c j of he differeniaed produc produced by firm j a ime is assumed o be same as he demand d j for he differeniaed produc produced by firm j a ime. The demand curve d j can be wrien as d j θ p j = C P, (2.02) where p j is a price for he differeniaed produc produced by firm j a ime, P is an aggregae price level a ime, θ is he price elasiciy of demand for differeniaed produc produced by firm j and C is an aggregae level of consumpion. In he firm s profi maximisaion problem, he consrain of producion funcion can be expressed in he form of marginal cos funcion. Therefore, before analysing he firm s profi maximisaion problem, real marginal cos funcion λ is derived from he cos minimisaion problem. The firm s cos minimisaion problem as shown in equaion (2.03) is o choose labour inpu N j o minimise coss subjec o marginal produciviy of labour Z muliplied by labour inpu N j being greaer han or equal o he quaniy c j of he differeniaed produc produced. Equaion (2.03) akes ino accoun a real wage W, where W is a wage P a ime and P is an aggregae price level a ime. Here firm j can only have a decision power on labour inpu N j and he quaniy c j of he differeniaed produc produced. 5

10 W min N j N (2.03) j P subjec o Z N c. j j The Lagrangian funcion (2.04) is used o derive real marginal cos funcion λ. W P N j ( Z N c ) λ (2.04) j j The firs order condiion for labour inpu N j is W λ Z = 0. (2.05) P Solving equaion (2.05) for firm s real marginal cos λ yields W P λ =. (2.06) Z The firm s profi maximisaion problem is presened in equaion (2.07), where firm j chooses price p j o maximise profis a ime. p j c j p j P max λ (2.07) I is assumed ha all firms have he same producion echnology and face demand curves wih consan and equal demand elasiciy. Since all firms face he same profi maximisaion problem, he problem can be wrien as follows p max c p λ. (2.08) P 6

11 Since he New Keynesian Phillips curve explains inflaion in he shor run and shor run coss are mainly wage coss, he deviaion of real marginal cos from is seady-sae value has a linear relaionship wih oupu gap, if addiionally perfec compeiion in he labour marke is assumed and all oupu is consumed as Galí (2008) has shown. There is a monoonic relaionship in producion funcion beween oupu and labour inpu. Since shor-run coss are mainly wage coss, he firm s real marginal cos λ is real wage divided by marginal produciviy of labour as derived above and shown in equaion (2.06). A he same ime, households provide labour inpu and perfec compeiion in he labour marke is assumed; i.e., he real wage has o be equal o he marginal rae of subsiuion beween leisure and consumpion. If all oupu is consumed and he goods marke is in equilibrium, households opimal labour supply gives a relaionship beween real wage and oupu. Therefore here is also a relaionship beween firms real marginal cos and aggregae oupu. Approximaion gives a relaionship beween oupu gap and he deviaion of real marginal cos from is seady-sae value. Since oupu gap can be used as a proxy for real marginal cos, he profi maximisaion problem in equaion (2.08) can be expressed as follows p max p P y y ζ ( ) c, (2.09) where y y is oupu gap a ime i.e. a difference beween oupu y and is flexible price equilibrium marginal cos. y a ime. Variable ζ shows a linear relaionship beween oupu gap and real This chaper derived profi maximisaion problem in an economy where prices are flexible. The NKPC heory assumes prices o be rigid and herefore he profi maximisaion problem is also subjec o price rigidiy. The following chaper 2.2 derives he profi maximisaion problem in an economy where price rigidiy is deermined by Calvo (983). 7

12 2.2 Profi Maximisaion and Rigid Prices The profi maximisaion problem of firms in he absence of price rigidiy ha was derived in he previous chaper 2. and presened in equaion (2.09) can be used as an inpu in firms profi maximisaion problem where prices are assumed o be rigid. Prices are assumed o be rigid following he approach developed by Calvo (983). Each period a fracion firms adjus heir price while a fracion ω makes no adjusmen. ω of all Firms adjusing heir price are randomly seleced and hey maximise he expeced discouned value of curren and fuure profis shown in equaion (2.0). The choice of price p a ime affecs he profis a some fuure dae T if he firm has no had an opporuniy o adjus he price beween imes and T. The probabiliy of no price adjusmen beween imes and T T is ω. The aggregae price level in an economy where prices are assumed o be rigid can be approximaed around he seady-sae equilibrium. Therefore, log-linearisaion is used o approximae equaions presened in his and he following subchaper. Log-linearisaion is a widely used mehod ha gives a good approximaion in a moderae inflaion environmen. The opimal price p is expressed in he following equaion (2.0) T = [ log p log P ζ ( y y )] = 0 T ( ωβ ) Ε, (2.0) where β is a discoun facor ha is 0 < β <. T T T Solving equaion (2.0) for opimal price T = ( ωβ ) T Ε log p = log p = ( ) ωβ T = T = ( ωβ ) ( ωβ ) T T Ε Ε p yields [ log P + ζ ( y y )] T [ log P + ζ ( y y )] T T T T T T ( + ) [ log P + ζ ( y y )] + ( ωβ ) ( ωβ ) Ε [ log P + ζ ( y y )] log p = ( ) ωβ T = + [ log P + ζ ( y y )] + ωβε log p log p = ( ) + ωβ. (2.) T T T 8

13 Deducing he erm log p log P on boh sides of he previous equaion (2.) gives [ log P + ζ ( y y )] + ωβε log p log P log P = ( ωβ ) + log p log P = ( ωβ ) ζ ( y y ) ωβ log P + ωβε log p+ [ Ε log p log P ] log p log P = ( ) ζ ( y y ) + ωβ + ωβ. (2.2) Adding and deducing he erm log P + on righ hand side of equaion (2.2) yields [ Ε log p log P + log P log P ] log p log P = ( ) ζ ( y y ) + ωβ ωβ. (2.3) p Since log( ) P is opimal relaive price P p ˆ and log( ) P p+ is inflaion raeπ, log( ) P + is opimal relaive price as follows p ˆ + and log( P + ) is inflaion rae π +. Equaion (2.3) can be wrien P [ p π ] pˆ = ( ) ( ) + Ε ˆ + ζ y y ωβ + + ωβ. (2.4) Firms se opimal relaive price according o equaion (2.4) in an economy where prices are rigid. Price rigidiy in he aggregae economy and he New Keynesian Phillips curve are derived in he following chaper Price Rigidiy in he Aggregae Economy and he New Keynesian Phillips Curve In Calvo s model he aggregae price level P a ime is a weighed sum of opimal price se a ime and he aggregae price level P prevailed in he previous period. The weighs are a fracion of firms ω adjusing he price and ω reaining he previous price respecively. The aggregae price level P is shown in equaion (2.5). Each period a fracion ω of all firms adjus heir price while a fracion ω make no adjusmen. p log P = ω log P + ( ω) log p (2.5) 9

14 Deducing a erm ω log P on boh sides of equaion (2.5) gives equaion (2.6) ha can be rearranged o ge finally opimal relaive price p ˆ expressed as a funcion of inflaion rae π. log P ω log P = ω log P log P (2.6) + ( ω)log p ω Rearranging he erms in equaion (2.6) yields equaion (2.7). ω (log P log P ) = ( ω)(log p log P ) (2.7) Equaion (2.7) can also be expressed as follows P p ω log( ) = ( ω)log( ). (2.8) P P P p Since log( ) is inflaion rae π and log( ) is opimal relaive price P P can be wrien as follows ( ) pˆ p ˆ, equaion (2.8) ωπ = ω. (2.9) Solving equaion (2.9) for opimal relaive price expressed as a funcion of inflaion rae π as follows p ˆ, opimal relaive price p ˆ can be pˆ ω = π. (2.20) ω Since opimal relaive price p ˆ can be expressed as a funcion of inflaion rae π as was shown in equaion (2.20) also opimal relaive price ˆ + p can be expressed as a funcion of inflaion rae π + as follows ω ω pˆ + = π +. (2.2) 0

15 And herefore equaion (2.4) in previous chaper 2.2 can be wrien as follows ω π = ( ωβ ) ζ ( y ω y ω ) + ωβε π ω + π + + ( ω)( ωβ ) ω π = ζ ( y y ) + ( ω) βε π + π + ω ω ( ω)( ωβ ) π = ζ ( y ω y ) + ωβε π + + ( ω) βε + ( ω)( ωβ ) π ( = ζ y y ) + βεπ +. (2.22) ω π + The New Keynesian Phillips curve ha is derived in his chaper is usually expressed in he following form { π } κŷ π = βε + +, (2.23) ( ω)( ωβ ) where κ = ζ > 0 and yˆ = ( y y ). ω In his hesis he raional expecaions hypohesis is relaxed and he following modified New Keynesian Phillips curve is obained π = βπ + +, (2.24) κŷ ( ω)( ωβ ) where κ = ζ > 0 and yˆ = ( y y ). ω Inflaion expecaions π + in equaion (2.24) are no necessarily raional. The empirical par of his hesis uses survey-based inflaion expecaions.

16 3 LATEST RESEARCH ON THE NEW KEYNESIAN PHILLIPS CURVE The New Keynesian Phillips curve ofen faces criicism over is esimaion. Since he heory of he NKPC is well-grounded, here have been many aemps o improve is empirical fi. These include discussions on he appropriae proxy for he real marginal cos. The formaion of inflaion expecaions has also been examined, and he role of pure forward-looking raional expecaions in inflaion dynamics has been quesioned. Even lagging variables have been added ino empirical esimaions, in order o es forward-looking behaviour and o inroduce sronger inflaion persisence. In he following subchapers he real marginal cos, inflaion expecaions and inflaion persisence are looked a more closely. 3. Real Marginal Cos The real marginal cos is he change in real oal cos ha arises when he quaniy produced increases by one uni. Since he real marginal cos is impossible o measure, he proxy for i has o be esimaed. Boh he oupu gap and he real uni labour cos have been widely used proxies. Oupu gap is he difference beween he acual oupu and he oupu ha would prevail if prices in he economy were flexible. I is common o use derending mehods such as he Hodrick Presco filer o esimae he oupu gap. However, he empirical fi of he NKPC heory has no been good when derending mehods have been used o esimae he oupu gap. Galí and Gerler (999) inroduced he labour income share, equivalen o he real uni labour cos, o gain beer fi beween he heory and empirical daa. Rudd and Whelan (2005) showed evidence agains he labour income share version of he NKPC, since he discouned sum of curren and expeced fuure labour income share explained only a lile of he variaion in inflaion. In a recenly published paper, Mazumder (200) shows ha real uni labour cos in he U.S. has been counercyclical, also casing doub on real uni labour cos as a proxy for a real marginal cos. 2

17 3.2 Inflaion Expecaions Raional expecaions have been widely used in he esimaions of NKPC. Laely inflaion expecaions have also been modelled wih learning processes (see e.g. Molnár and Sanoro 200). Learning has been used o eiher supplemen or replace raional expecaions. Evans and Honkapohja (200) summarised he learning processes in heir widely recognised book. Some sudies have relaxed he assumpion of raional expecaions by inroducing surveybased inflaion expecaions. Robers (997) and Paloviia (2006) have sudied inflaion in he U.S. and euro area respecively, using survey-based inflaion expecaions as a proxy for inflaion expecaions. Robers came o he conclusion ha inflaion expecaions are less han perfecly raional. Paloviia found ha he European inflaion process can be modelled using NKPC if survey-based inflaion expecaions are applied even when derended oupu or labour income share are used as proxies for marginal coss. In a more recen sudy, Ball and Mazumder (20) found ha inflaion expecaions in he U.S. have significanly sayed a a fixed level, regardless of any movemens in acual inflaion showing evidence agains raional expecaions. There are also papers sudying he imporance of forward-looking expecaions in he NKPC. Including boh he forward- and backward-looking componens ino he equaion gives he possibiliy o assess he imporance of hese erms in inflaion dynamics. Galí and Gerler (999) came o he conclusion ha even hough here is some backward-looking behaviour in he model, he forward-looking behaviour plays an imporan role. Alhough Paloviia (2006) found ha he European inflaion process can be modelled using he NKPC, she also found ha European inflaion can be modelled more accuraely wih a hybrid Phillips curve, which has an addiional lagged inflaion erm. The imporance of forward- and backward-looking erms differs beween counries and ime periods. In a low inflaion counry or period, he forward-looking expecaions usually dominae, while in a high inflaion counry or period he backward-looking expecaions are he ones ha dominae (see e.g. Paloviia 2006). On he oher hand, Paloviia and Mayes (2005) found ha he use of real-ime daa in esimaions increases he imporance of he forward-looking erm. Including real-ime daa ino he esimaions is an ineresing aspec since he NKPC is based on opimisaion, where real-ime daa on variables are used as an inpu. Cogley and Sbordone (2008) found ha inflaion can be explained by he forward-looking NKPC if rend inflaion is allowed o flucuae. This 3

18 means ha he flexible price inflaion rae is allowed o flucuae. In heir sudies inflaion is explained by forward-looking expecaions, and he backward-looking erm had no weigh. 3.3 Inflaion Persisence In he NKPC nominal price rigidiy has been given a major role in explaining he persisence of inflaion. I can be implemened in he macroeconomic model wih sae-dependen or imedependen pricing. In sae-dependen pricing models he frequency of price change is a resul of he profi maximisaion problem ha is dependen on some defined economic variables. In he ime-dependen pricing models he price change is a resul of he passage of ime. The vas number of macroeconomic research uses he ime-dependen pricing approach, since i is easier o apply han sae-dependen pricing. The mos frequenly used ime-dependen pricing models are he models of Calvo (983) and Taylor (980). However, he persisence of inflaion canno be explained only by frequency of price reopimisaion, since he NKPC esimaions (see e.g. Eichenbaum and Fisher 2007) show significanly lower frequency for price re-opimisaion han he survey resuls sugges. The same kinds of resuls are obained using scanner daa o sudy price seing. Eichenbaum e al. (20) sudied nominal rigidiies using weekly scanner daa conaining informaion on prices, quaniies and coss from more han,000 sores of a major U.S. reailer. They found ha nominal rigidiies ake he form of ineria in he mos ofen quoed prices and coss wihin a given quarer, called reference prices and coss. Weekly prices and coss changed frequenly and flucuaed around reference values. The duraion of reference price is almos one year, while he median price duraion is only hree weeks. Whereas he duraion of reference cos is wo quarers and median cos duraion is wo weeks. While coss change more frequenly han prices, prices are more volaile han coss. Anoher ineresing finding in heir sudy was ha mark-ups were held wihin relaively narrow bounds and herefore showed evidence for he sae-dependen pricing approach. Since persisence of inflaion canno be explained only by frequency of price re-opimisaion or he nominal rigidiies in price adjusmen, real price rigidiies have been inroduced o he models. Real price rigidiy is explained by supply and demand side facors (see e.g. Bergin and Feensra 2000). Supply side facors include firm specific facors of producion such as 4

19 firm specific capial (Alig e al. 20) and labour (Woodford 2005). Chrisiano e al. (2005) found ha inflaion persisence can be acquired by saggered wage conracs and variable capial uilisaion. They sudied inflaion persisence wih a dynamic general equilibrium model and found ha observed persisence afer an expansion (conracion) in moneary policy can be explained by moderae amouns of nominal rigidiies if a sharp increase (decrease) in marginal cos is prevened. Demand side facors include a concave demand curve. Dossche e al. (200) sudied a scanner daa se from a large euro area supermarke chain and found ha iems and produc caegories had a wide variaion of esimaed price elasiciies and curvaures of demand curves. Their resuls suppor he use of a concave demand curve, alhough he fracion of iems showing convex demand was subsanial. They also found ha he degree of curvaure is much lower han is generally imposed and herefore he concave demand curve alone fails o generae sufficien real price rigidiy. 4 THE DATA The NKPC ha was derived in chaper 2 ook he following form π = βπ + +, (4.0) κŷ ( ω)( ωβ ) where κ = ζ > 0 and yˆ = ( y y ). ω Since his hesis uses quarerly daa, he NKPC can be presened as follows π = βπ + +, (4.02) 4 κŷ ( ω)( ωβ ) where κ = ζ > 0 and yˆ = ( y y ). ω In equaion (4.02) inflaion π a ime is explained by he expeced inflaion π +4 a ime for he period + 4 and by oupu gap ŷ i.e. a difference beween oupu y and is flexible price equilibrium y a ime. A discoun facor β is usually near bu less han. Paloviia (2006) uses 0.97 as a fixed discoun facor. 5

20 Inflaion is measured wih annual change in he Consumer Price Index (CPI). Boh Consensus Economics and Saisics Finland s survey daa are used o proxy inflaion expecaions. Oupu gap is he difference beween log real GDP and is flexible price equilibrium a ime. Time series of CPI, Saisics Finland s survey daa for inflaion expecaions and real GDP are published by Saisics Finland. Consensus Economics survey daa for inflaion expecaions is obained from Consensus Forecass publicaions ha are published by Consensus Economics Inc. The daa availabiliy projeced some resricions o NKPC esimaions. Real GDP is published quarerly 990Q onwards and Saisics Finland s survey daa for inflaion expecaions is published monhly 995M0 onwards. Time series for boh he annual change in CPI and Consensus Economics survey daa for inflaion expecaions are published monhly and were available for he whole period 990Q 202Q. Because of resricions in daa availabiliy, he NKPC is esimaed for wo ime periods, 990Q 202Q and 996Q 202Q. The flexible price equilibrium of log real GDP a ime is approximaed by using he Hodrick Presco filer, where he smoohing parameer is 600. Hodrick Presco filer is a widely used mehod o define flexible price equilibrium. Hodrick and Presco (997) divided he naural logarihm of he variable c from he flexible price equilibrium as follows y ino he flexible price equilibrium y and deviaion y = y + c for =,..., Τ (4.03) The flexible price equilibrium y is a soluion o he following minimisaion problem Min { y } Τ 2 Τ ( ) [ ( ) ( )] 2 y y + y+ y y y HP = λ. (4.04) = = 2 Equaion (4.04) minimises he variance of he variable around he flexible price equilibrium subjec o he second difference of he flexible price equilibrium. The parameer λ (lambda) is a posiive number which penalises he variabiliy in growh rae of he flexible price equilibrium. Therefore, he lambda conrols he smoohness of he rend growh pah. If λ = 0, he variable is on he rend growh pah and he rend growh pah is allowed o 6

21 flucuae a lo. If λ =, he rend growh pah approaches he linear rend. There is a rade off beween how well he rend componen fis he daa and he smoohness of he rend. The lambda depends on he frequency of he observaions. The shorer he periods beween observaions are, he larger he lambda is. This hesis uses a sandard recommendaion for quarerly daa, where he lambda is Inflaion Inflaion is an annual change in prices. I is usually measured wih he annual change in he Consumer Price Index (CPI), in which he weighs of differen producs and services are aken from naional accouns ha rely on a household budge survey. This hesis uses annual change in he CPI as a measure of inflaion, since boh Consensus Economics and Saisics Finland s survey daa are expecaions for an average annual change in consumer prices. Figure shows an annual change in he CPI in Finland for he period 990Q 202Q. Saisics Finland publishes annual change in CPI monhly. In his hesis quarerly series are calculaed using monhly average figures. The New Keynesian Phillips curve esimaions ofen use an annual change in GDP deflaor as a measure of inflaion (see e.g. Cogley and Spordone 2008). The GDP deflaor is an implici price deflaor and is calculaed dividing GDP a curren prices by GDP a reference year prices. The GDP deflaor akes ino accoun final consumpion expendiure, gross fixed capial formaion and ne of expors and impors of goods and services. The major difference beween Consumer Price Index and GDP deflaor is ha Consumer Price Index akes ino accoun he ne impors of goods and services while GDP deflaor akes ino accoun he ne expors of goods and services. The annual change in CPI does no fi he NKPC heory as well as an annual change in GDP deflaor, since he CPI also includes he prices of impored iems. The GDP deflaor includes only iems ha are produced in Finland. However, he annual change in CPI is a close approximaion o he moneary policy variable of euro area ha is a year-on-year increase in consumer prices over he medium erm. 7

22 Figure. Inflaion measured wih annual change in Consumer Price Index in Finland 990Q 202Q. Figure shows ha inflaion has been quie volaile in period 990Q 202Q. However, in 993 he Bank of Finland announced an explici inflaion arge. The aim of he inflaion arge was o sabilise he rae of inflaion permanenly a a level of 2 per cen by he year 995. In 999 Finland joined he euro area, where he primary objecive of moneary policy is o mainain price sabiliy, aiming a year-on-year increase in consumer prices of below, bu close o, 2 per cen over he medium erm. 4.2 Inflaion Expecaions The assumpion of raional expecaions is relaxed in his hesis and inflaion expecaions are measured wih boh Consensus Economics and Saisics Finland s survey daa. Boh of hese inflaion forecass are published monhly. Consensus Economics surveys financial and economic forecasers for heir esimaes of a range of variables including consumer price inflaion. These forecass are published in Consensus Forecass publicaion. Consensus Economics inflaion forecas is an average change in consumer prices on previous calendar year. This inflaion forecas is made monhly for he curren and following years and herefore here is need o consruc a series of inflaion forecas over he following 2 monhs. The series is consruced following Gerlach (2007). Inflaion forecas over he following 2 monhs is a weighed average of forecass for curren and following years, where he weighs depend on he monh in which he forecas is made. Inflaion forecas over he following 2 monhs is calculaed as follows 8

23 E m 2 m m { π } = E { curren year} + E { following } m + 2 m m year 2 2, (4.05) where m is he respecive number of monh in which inflaion forecas is made, January being number, February number 2, March number 3 ec. Saisics Finland has gahered Consumer Survey inflaion forecas monhly since Ocober 995. In he survey expeced inflaion is measured by asking consumers he percenage change of consumer prices in he following 2 monhs. Since boh Consensus Economics and Saisics Finland s Consumer Survey inflaion forecass are now monhly series ha forecas consumer price inflaion over he following 2 monhs, he quarerly series can be calculaed using monhly average figures. Figure 2 shows boh Consensus Economics (CE) and Saisics Finland s Consumer Survey (CS) inflaion forecass made a ime for he following year CE inflaion forecas CS inflaion forecas Figure 2. Inflaion forecass for he following year. Inflaion forecass of Consensus Economics (CE) 990Q 202Q and Saisics Finland s Consumer Survey (CS) 996Q 202Q. According o he raional expecaions hypohesis, inflaion expecaions a ime n for period canno differ sysemaically from acual inflaion a ime, if he model describing he economy is correc. Therefore, i is ineresing o compare inflaion forecass made a ime 4 for period and inflaion a ime. Figure 3 shows ha boh inflaion forecass seem o 9

24 be backward-looking and are less volaile han acual inflaion. Hirvonen (2008) sudied Saisics Finland s Consumer Survey daa and concluded ha inflaion expecaions seem o be deermined by experienced curren inflaion. Consensus Economics inflaion forecas seems o follow almos he same kind of paern as Consumer Survey inflaion forecas does. In oher sudies of Saisics Finland s Consumer Survey daa, Kangassalo and Takala (2005) found ha consumers emphasise prices of frequenly bough commodiies when forming inflaion expecaions. On he oher hand, Lehinen (2007) found ha inflaion in frequenly bough commodiies in Finland was greaer han in oher commodiies beween years 2000 and The sudies of Kangassalo and Takala (2005) and Lehinen (2007) may explain some par of he higher level of Consumer Survey inflaion forecas compared o boh Consensus Economics inflaion forecas and acual inflaion. Figure 4 shows daa as i is enered ino he New Keynesian Phillips curve esimaions. I compares inflaion forecas made a ime for period +4 and inflaion a ime CE inflaion forecas CS inflaion forecas Inflaion Figure 3. Inflaion forecass and inflaion compared 990Q 202Q. 20

25 CE inflaion forecas CS inflaion forecas Inflaion Figure 4. Inflaion forecass for he following year and inflaion compared 990Q 202Q. 4.3 Real Marginal Cos Real marginal cos is a change in real oal cos ha arises when he quaniy produced increases by one uni. As was shown in chaper 2. he deviaion of real marginal cos from is seady-sae value has a linear relaionship wih oupu gap, if all oupu is consumed and perfec compeiion in he labour marke is assumed. Therefore oupu gap is used as a proxy for real marginal cos. Oupu gap is calculaed as he difference beween log real GDP and is flexible price equilibrium a ime. Figure 5 shows developmen of real GDP in Finland beween 990Q and 202Q. GDP is seasonally adjused and expressed a reference year 2000 prices. 2

26 44,000 40,000 36,000 32,000 28,000 24,000 20, Figure 5. Seasonally adjused GDP in millions of euros a reference year 2000 prices in Finland 990Q 202Q. Figure 6 shows oupu gap for period 990Q 202Q. Oupu gap is a difference beween log real GDP and is flexible price equilibrium a ime. I is calculaed using he Hodrick Presco filer wih a smoohing parameer of Figure 6. Oupu gap esimaed using he Hodrick Presco filer for period 990Q 202Q. Since oupu gap is used as a driving variable for inflaion, i is ineresing o see how oupu gap series is ineracing wih inflaion. Figure 7 shows ha inflaion is a lagging variable o oupu gap. 22

27 Oupu gap Inflaion Figure 7. Oupu gap and inflaion in Finland 990Q 202Q. In addiion o he above figures in his chaper, i is also necessary o analyse inflaion and oupu gap in a scaer plo. Figure 8 shows ha here is some evidence ha oupu gap correlaes wih inflaion. This correlaion is an assumpion behind NKPC heory Inflaion Oupu gap Figure 8. Scaer plo showing relaionship beween oupu gap and inflaion in Finland 990Q 202Q. 23

28 5 THE DYNAMICS OF INFLATION, INFLATION EXPECTATIONS AND REAL MARGINAL COST Before esimaing he NKPC, he variables are analysed using he frequency domain mehod o gain undersanding of inflaion in Finland. The frequency domain mehod akes ino accoun he dynamic naure of ime series, since he variables can be analysed a differen frequencies. I gives informaion on he dynamics of boh correlaions and lead-lag relaionships of variables a differen frequencies. The correlaions and lead-lag relaionships in he frequency domain are measured wih coherence and phase of he cross specrum respecively. In a widely recognised book by Hamilon (994) he coherence of he cross specrum h YX (ω) or populaion coherence beween X and Y measures he join effec he cycles of frequency ω have on X and Y. I combines he real c YX (ω) and imaginary q YX (ω) componens of populaion cross specrum s YX (ω) from X o Y as follows h YX 2 [ c ( ω) ] + [ q ( ω) ] 2 YX YX ( ω) =, (5.0) s ( ω) s ( ω) YY XX where 0 h ( ω) for all ω as long as he X and Y are covariance-saionary wih YX absoluely summable auocovariance marices. s YY (ω) and s XX (ω) represen he populaion specrum of Y and X respecively. The coherence can be inerpreed as a measure of correlaion beween he ime series Y and X a differen frequencies. If he coherence is close o one (zero), he series Y and X are highly (slighly) relaed a he frequency ω. The phase of he cross specrum θ (ω) is he following θ( ω) = an q c YX YX ( ω). (5.02) ( ω) The slope of he phase funcion or diagram gives he delay in ime periods. If he slope is zero here is no lead-lag relaionship. In his hesis he posiive (negaive) slope means ha inflaion is a lagging (leading) variable a he frequency ω. 24

29 Each frequency ω corresponds o he ime aken for variables o go hrough heir complee sequence of values. In his hesis, frequency 0.5 corresponds o he period of wo years, frequency.0 corresponds o he period of one year, frequency.5 corresponds o he period of 8 monhs and frequency 2.0 corresponds o he period of 6 monhs. The following subchaper 5. concenraes on he correlaions and lead-lag relaionships beween inflaion and inflaion expecaions, while subchaper 5.2 concenraes on he correlaions and lead-lag relaionships beween inflaion and oupu gap. 5. Inflaion and Inflaion Expecaions In his chaper inflaion is analysed wih boh Consensus Economics and Saisics Finland s Consumer Survey inflaion forecas using frequency domain mehod. This analysis uses inflaion a ime and inflaion forecass a ime for + 4. Inflaion and Consensus Economics (CE) inflaion forecas is sudied for period 990Q 202Q in figure 9 and for period 996Q 202Q in figure. Figure 0 sudies inflaion and Saisics Finland s Consumer Survey (CS) inflaion forecas in period 996Q 202Q. Boh coherence and phase of he cross specrum are seen in hese figures. The coherence of he cross specrum measures correlaion beween inflaion and inflaion forecass a differen frequencies. The phase of he cross specrum shows which ime series is leading and he exen of he lag. Figures 9 and show ha here is correlaion beween inflaion and he Consensus Economics inflaion forecas a boh high and low frequencies. However, he correlaion is highes a low frequencies. This means ha he highes correlaion is a frequencies where i akes more han one year for he variables o go hrough heir complee sequence of values. This correlaion is 0.9 for period 996Q 202Q and approximaely 0.7 for period 990Q 202Q. Figure 0 shows ha here is correlaion beween inflaion and Consumer Survey inflaion forecas only a frequencies where i akes more han one year for he variables o go hrough heir complee sequence of values. Figures 9, 0 and show ha inflaion forecass are leading inflaion a medium frequencies, while a he highes frequencies inflaion is a leading variable. A negaive (posiive) slope means ha inflaion is a leading (lagging) variable. If he slope is zero, here is no lead-lag 25

30 relaionship. The major difference beween he dynamics of differen forecass and inflaion is ha he Consumer Survey inflaion forecas is lagging inflaion a frequencies ha correspond o a period of eigh monhs, whereas he Consensus Economics inflaion forecas is lagging inflaion a frequencies ha correspond o a period of six monhs. The degree of he slope signals he exen of he lag. A he highes frequencies he lag is large, meaning ha i akes ime for inflaion o affec inflaion expecaions. The resuls ha here are no lead-lag relaionships a low frequencies are in accordance wih he resuls ha a low frequencies here is correlaion beween inflaion and inflaion forecass. Since he NKPC explains inflaion in he shor run, he high frequencies are he frequencies ha are mos imporan o concenrae on. The resuls above are ineresing, because a he highes frequencies inflaion forecass for he following year are led by inflaion while he lag is large, meaning ha i akes ime for inflaion o affec inflaion expecaions for he following year. This confirms he inferences made in chaper 4.2 ha inflaion forecass are backward-looking. Figure 9. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and Consensus Economics inflaion forecas for he following year in Finland 990Q 202Q. 26

31 Figure 0. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and Saisics Finland s Consumer Survey inflaion forecas for he following year in Finland 996Q 202Q. Figure. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and Consensus Economics inflaion forecas for he following year in Finland 996Q 202Q. 5.2 Inflaion and Real Marginal Cos In his chaper inflaion is analysed wih oupu gap using he frequency domain mehod. This analysis uses inflaion a ime and oupu gap a ime. Inflaion and oupu gap is sudied for period 990Q 202Q in figure 2 and for period 996Q 202Q in figure 3. Boh coherence and phase of he cross specrum are seen in hese figures. The coherence of he cross specrum measures correlaion beween inflaion and oupu gap a differen frequencies, while he phase of he cross specrum shows which ime series is leading and he exen of he lag. 27

32 Figures 2 and 3 show ha here is correlaion beween inflaion and oupu gap a boh high and low frequencies. However, he correlaion is highes a low frequencies. This means ha he highes correlaion is a frequencies where i akes around wo years ime for he variables o go hrough heir complee sequence of values. This correlaion is approximaely 0.8 for period 996Q 202Q, while i is jus above 0.6 for period 990Q 202Q. Figures 2 and 3 show ha oupu gap is leading inflaion a medium and high frequencies, while a he highes frequencies inflaion is a leading variable. A negaive (posiive) slope means ha inflaion is a leading (lagging) variable. If he slope is zero, here is no lead-lag relaionship. The degree of he slope shows he exen of he lag. A medium and he highes frequencies he lag is quie small, meaning ha i only akes a lile ime for oupu gap o affec inflaion and for inflaion o affec oupu gap respecively. The resuls ha here are no lead-lag relaionships a low frequencies are in accordance wih he resuls ha a low frequencies here is correlaion beween inflaion and oupu gap. Since he NKPC explains inflaion in he shor run, he high frequencies are he frequencies ha are mos imporan o concenrae on. The resuls above are ineresing, because a high frequencies inflaion is boh lagging and leading oupu gap. In NKPC oupu gap is used as a driving variable for inflaion. Figure 2. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and oupu gap in Finland 990Q 202Q. Oupu gap is he difference beween log real GDP and is flexible price equilibrium, esimaed using he Hodrick Presco filer. 28

33 Figure 3. The coherence (lef) and phase (righ) of he cross specrum beween inflaion and oupu gap in Finland 996Q 202Q. Oupu gap is he difference beween log real GDP and is flexible price equilibrium, esimaed using he Hodrick Presco filer. 6 ESTIMATION RESULTS The NKPC is esimaed wih boh Ordinary Leas Squares (OLS) and Generalised Mehod of Momens (GMM). Esimaions are run wih boh Consensus Economics (CE) and Saisics Finland s Consumer Survey (CS) inflaion forecass wih a non-fixed and fixed discoun facor. The fixed discoun facor is Esimaions wih Consensus Economics inflaion forecas are done for boh periods 990Q 202Q and 996Q 202Q, while esimaions wih Consumer Survey inflaion forecas are done only for period 996Q 202Q. In he firs subchaper 6. NKPC is esimaed wih OLS and in he second subchaper 6.2 wih GMM. 6. Ordinary Leas Squares Esimaions The Ordinary Leas Squares (OLS) esimaion resuls for he NKPC are presened in able. According o he heory of NKPC he coefficien for real marginal cos is posiive. The coefficien κ for oupu gap is correcly signed and significan in all esimaions and ges values beween The Consumer Survey inflaion forecas gives he lowes coefficiens for oupu gap, while Consensus Economics inflaion forecas gives he highes. These esimaion resuls are robus, since hey are largely no affeced by he choice of period or measures for inflaion expecaions. 29

34 In OLS esimaions a non-fixed discoun facor β ges values ha are significan and beween As can be noiced, he values for discoun facor are affeced by boh he choice of period and measures for inflaion expecaions. The lowes non-fixed discoun facor is received when Consumer Survey inflaion forecas is used as a measure of inflaion expecaions, whereas he highes is received wih he Consensus Economics inflaion forecas for he period 996Q 202Q. The highes non-fixed discoun facor is approximaely he same as he fixed discoun facor used in his hesis and in sudies of Paloviia (2006). If he coefficien 2 R is used as a crierion for he esimaion s goodness of fi he bes esimaions are received wih non-fixed discoun facor β. The highes coefficien is received when he Consensus Economics inflaion forecas is used for he period 990Q 202Q. Table. The New Keynesian Phillips curve esimaion resuls using OLS. π + = βπ + 4 κŷ Model β κ 2 DW JB R NKPC wih CE inflaion forecas, (0.029) 990Q 202Q NKPC wih CE inflaion forecas and fixed discoun facor β, 990Q 202Q NKPC wih CS inflaion forecas, (0.036) 996Q 202Q NKPC wih CS inflaion forecas and fixed discoun facor β, 996Q 202Q NKPC wih CE inflaion forecas, (0.046) 996Q 202Q NKPC wih CE inflaion forecas and fixed discoun facor β, 996Q 202Q Noe: Numbers in parenhesis are sandard errors Significance a 5% level Significance a % level Significance a 0.% level 0.28 (0.032) (0.035) (0.037) (0.043) (0.037) (0.036)