Does the Fisher Hypothesis Hold in Sweden? An Analysis of Long-Term Interest Rates under the Regime of Inflation Targeting

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1 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July Does he Fisher Hypohesis Hold in Sweden? An Analysis of Long-Term Ineres Raes under he Regime of Inflaion Targeing Takayasu Io School of Commerce, Meiji Universiy, Tokyo, Japan ABSTRACT This paper examines he validiy of he Fisher hypohesis in Sweden by analyzing inflaion expecaions and long-erm ineres raes from January 1993 o February 2015 under a regime of inflaion argeing. The Fisher hypohesis holds for he mauriies of 2, 3, 4, 5, and 7 bu no 10 years. The resuls show ha changes in inflaion expecaions move in he same direcion and degree as nominal long-erm ineres raes for he mauriies of 2, 3, 4, 5, and 7 years. This can primarily be aribued o he credibiliy of he inflaion-argeing framework in Sweden for he las 20 years and he success i has achieved in locking inflaion expecaions ino he arge range wihin hese mauriies. In he mauriy of 10 years, his credibiliy has never been as cerain. Keywords: Fisher Hypohesis, Inflaion Targeing, Long Term Ineres Raes 1. INTRODUCTION According o Fisher (1931), he expeced rae of inflaion will be refleced in he nominal ineres raes, wih real ineres raes holding consan. This is known as he Fisher hypohesis. In order for i o hold, he nominal ineres rae mus move one-o-one wih he expeced rae of inflaion. This paper examines he validiy of he Fisher hypohesis in Sweden by analyzing inflaion expecaions and long-erm ineres raes from January 1993 o February 2015 under a regime of inflaion argeing. This paper can be disinguished from previous work in ha i analyzes long-erm ineres raes in he mauriies of 2, 3, 4, 5, 7, and 10 years from he inroducion of inflaion argeing policy. Long-erm swap raes are used because hey are closely conneced wih benchmark ineres raes for long-erm lending. There are several reasons o invesigae he validiy of he Fisher hypohesis by analyzing long-erm ineres raes in connecion wih moneary policy. Sweden adoped an inflaion argeing policy in January 1993 when he Riksbank announced ha i would arge a rae of inflaion wihin 2%±1% afer Moneary policy can influence boh inflaion and ineres raes, which in urn influence general economic aciviy. If he Fisher hypohesis holds, his implies ha changes in inflaionary expecaions do move in he same direcion and degree as he nominal long-erm ineres raes. This means ha real long-erm ineres raes are sable. This gives corporaions an incenive o make

2 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July commimens and plan heir invesmen because real long-erm ineres raes are a very imporan facor in invesmen decision making. This can primarily be aribued o he credibiliy of he inflaion-argeing framework and he success i has achieved in locking inflaion expecaions ino he arge range. There are no consisen conclusions as o he analysis of he Fisher hypohesis. Resuls differ depending on he counries, periods, and ineres raes under consideraion. Hawrey (1997) and Michell e al. (2007) analyze he hypohesis in connecion wih he moneary policy of inflaion argeing. Hawrey (1997) finds ha while he Fisher effec is no esablished prior o he 1980s financial deregulaion in Ausralia, here is subsequen evidence (following deregulaion) ha he relaionship was resored. Michell e al. (2007) conclude ha he long-run Fisher hypohesis canno be confirmed in is srices form in Souh Africa, bu changes in inflaion expecaions do move in he same direcion as he nominal long-erm ineres rae. This suggess ha moneary policy has an influence on he real long-erm ineres rae, which has posiive implicaions for general economic aciviy, hus confirming he credibiliy of he inflaion argeing framework. Oher han hese wo sudies, he following works analyze he Fisher hypohesis; Akins (1989), Akins and Chan (2004), Badillo e al. (2011), Berumen (1999), Berumen and Jelassi (2002), Berumen e al. (2007), Bonham (1991), Carneiro e al. (2002), Granville and Mallick (2004), Hawrey (1997), Herwarz and Reimersans (2011), Inder and Silvapulle (1993), Io (2009), MacDonald and Murphy (1989), Mishkin(1992), Moosa and Kwiecien (2002), Payne and Ewing (1997), Tsong and Lee (2011), Tsong and Lee (2013), Yu (1997), Wallace and Warner (1993), Woodward (1992), and Wong and Wu (2003). Cooray (2003) provides a survey for he Fisher hypohesis. Akins (1989) conducs he Engle and Granger coinegraion es using he Consumer Price Index (CPI) and 90-day ineres raes in he US and Ausralia from 1953 hrough He finds ha he Fisher hypohesis holds for boh. He also conducs he Granger causaliy es o find he impac of CPI on nominal ineres raes. Akins and Chan (2004) find suppor for he hypohesis ha boh he nominal ineres rae and inflaion in Canada are saionary around a deerminisic rend wih wo breaks. Their resuls indicae ha here are hree regimes in he relaionship beween ineres raes and inflaion. Badillo e al. (2011) infer ha here is a full Fisher effec, as found by Weserlund (2008), for a panel of Organizaion for Economic Cooperaion and Developmen (OECD) counries. However, if we explicily inroduce he common facors in he Fisher equaion, he CupBC and CupFM esimaors of he slope parameer on inflaion are significanly lower han uniy, which implies he exisence of a parial Fisher effec. Berumen (1999) assesses he effec of expeced inflaion and inflaion risk on ineres raes wihin he Fisher hypohesis framework. Using UK quarerly daa from 1958 hrough 1994, he concludes ha boh he expeced inflaion and he condiional variabiliy of inflaion posiively affeced he UK hree-monh Treasury bill rae. Berumen e al. (2007) es he validiy of he Fisher hypohesis for he G7 counries as well as 45 developing economies. The Fisher relaion holds in all he G7 counries, bu in

3 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July only 23 of he developing counries. There is a posiive and saisically significan relaionship beween ineres raes and inflaion uncerainy for 6 of he G7 and 18 of he developing counries, while he relaionship is negaive for 7 of he developing counries. Berumen and Jelassi (2002) find evidence for he Fisher hypohesis in 16 of 26 counries. I is also likely ha he Fisher hypohesis holds more for he developed han he developing counries in heir sample. The Fisher hypohesis canno be rejeced for 9 ou of 12 developed and for 7 ou of 14 developing counries. Bonham (1991) uilizes he Engle and Granger coinegraion es using hree-monh Treasury bills and CPI in he US from 1955 hrough He concludes ha he Fisher hypohesis holds for he US. Carneiro e al. (2002) analyze monhly daa for he period 1980 hrough 1997 for hree counries wih a recen hisory of chronic high inflaion; Argenina, Brazil, and Mexico. A coinegraion analysis provides evidence of a sable long-run equilibrium relaionship beween nominal ineres raes and he inflaion rae for Argenina and Brazil. Granville and Mallick (2004) use annual daa over a long ime horizon from 1900 hrough 2000 for he UK. They conclude ha he coinegraing relaionship beween he wo variables suggess a significan long-run equilibrium wih a posiive coefficien of more han one during he saed period. Io (2009) concludes ha he Fisher hypohesis holds in he ineres raes of 2, 3, 4, 5, 7, and 10 years only in he period from Ocober 1987 hrough June 1991 when he moneary policy of he Bank of Japan was ighening. Inder and Silvapulle (1993) use he Engle and Granger coinegraion es o compare bankers accepance raes and CPI in Ausralia and conclude ha he Fisher hypohesis does no hold. MacDonald and Murphy (1989) conduc he Engle and Granger coinegraion es using hree-monh Treasury bills and CPI in he US, Canada, UK, and Belgium from 1955 hrough They find ha he Fisher hypohesis is effecive in all hese counries. They divide heir sample ino wo. The firs subsample is from 1955 hrough 1973 (second quarer), which is a fixed exchange regime. The second is from 1973 (hird quarer) hrough They conclude ha he Fisher hypohesis holds in he US and Canada in he firs subsample, bu he validiy of he hypohesis canno be found in any of he four counries in he second. Mishkin (1992) resolves he issue of why a srong Fisher effec occurs only during cerain periods and no ohers. There is no empirical evidence for a shor-run Fisher effec in which a change in expeced inflaion is associaed wih a change in ineres raes, bu some evidence does suppor he exisence of a long-run Fisher effec in which inflaion and ineres raes have a common sochasic rend when hey exhibi rends. These resuls indicae ha a srong Fisher effec will appear only in samples where here are rends in he inflaion and ineres raes. Michell-Innes e al. (2007) conclude ha he shor-run Fisher hypohesis does no hold during he relevan period under he inflaion argeing moneary policy framework in Souh Africa. Moosa and Kwiecien (2002) examine he viabiliy of using shor-erm ineres raes o forecas inflaion as implied by he Fisher hypohesis. They demonsrae, using quarerly

4 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July daa for OECD counries and allowing for seasonaliy in he inflaion rae, ha i is possible o obain a model wih a high degree of forecasing accuracy and efficiency. Payne and Ewing (1997) examine he Fisher hypohesis for nine less-developed counries. They conclude ha i holds only in Malaysia, Pakisan, and Sri Lanka. Tsong and Lee (2011) show firsly ha due o he higher power obained by he inclusion of covariaes, he es can overwhelmingly rejec he uni roo null for he 16 indusrialized counries. The empirical resuls of Tsong and Lee (2013) for six OECD counries sugges ha alhough he nominal ineres rae and inflaion move ogeher in he long run, he coinegraing coefficiens beween he wo variables display an asymmeric paern depending on he sign and size of he shocks. Yu (1997) examines he nominal ineres rae using he IS-LM model incorporaing he Fisher hypohesis. Eigh differen ineres raes are considered for differen sample periods ending in He concludes ha he Fisher hypohesis holds only for he federal fund and AAA bond raes. Wallace and Warner (1993) es he Fisher hypohesis using 3-monh Treasury bills, 10-year Treasury bonds, and CPI. They conduc he Johansen coinegraion es and conclude ha he Fisher hypohesis does no hold from 1953 hrough Woodward (1992) ess he Fisher hypohesis using inflaion-indexed securiies o obain direc daa of inflaion expecaions and real ineres raes. He concludes ha he coefficiens on he expeced rae of inflaion are approximaely equal o one. Wong and Wu (2003) find more suppor for he Fisher hypohesis when he model is esimaed by an insrumenal variables esimaion mehod using long-horizon daa han by ordinary leas squares (OLS) using shor-horizon daa. 2. DATA 2.1. Expeced Rae of Inflaion As described by Io (2009), some form of disribued lag on pas inflaion is used as a proxy for inflaionary expecaions when analyzing he Fisher hypohesis. This approach is found in Gibson (1970). Using he heory of raional expecaions pioneered by Muh (1961), and he heory of efficien markes advanced by Fama (1970), an alernaive approach o model expecaions can be developed. This approach is adoped by Fama (1975), Lahiri and Lee (1979), and Levi and Makin (1979). Wih he incorporaion of hese heories ino he Fisher hypohesis, mehods examining he ime series properies of he variables can be developed. These mehods are used by Io (2009), MacDonald and Murphy (1989), and Wallace and Warner (1993). Woodward (1992) uses inflaion-indexed securiies o obain direc daa of inflaion expecaions and real ineres raes. Sweden issues inflaion-indexed Governmen Bonds, bu he liquidiy of he marke and he accumulaion of hisorical daa are no enough. This paper uses he mehod of Wallace and Warner (1993) o consruc a proxy for inflaion expecaion. They poin ou ha if inflaion raes in he pas have been uni roo processes, innovaion will influence he change of raes in he fuure. When E(π+j),

5 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July defined as he expeced raes of inflaion (hey are j periods forward based on informaion a he period, are random walked,π+1=π +ε+1 (ε+1 is an innovaion of inflaion raes) is esablished. Here equaion (3) is esablished as for he expeced rae of inflaion a he ime of j. E (π+j) =π (3) Accordingly,π defined as he realized raes of inflaion a he ime, denoes he expeced raes of inflaion in fuure. Thus, he realized raes of inflaion are used as a proxy for inflaion expecaion afer confirming ha hey are uni roo processes. This paper uses he annual changes (inflaion rae) of he CPI released by Saisics Sweden. 3.2 Nominal Ineres Rae As for nominal ineres raes, Swedish ineres rae swaps of 2, 3, 4, 5, 7, and 10 years are used from January 1993 o February 2015 on a end of monh basis. The raes are averages of he bid and offer rae. These daa are provided by Daasream. The marke for ineres rae swaps has grown exponenially since he 1990s. According o a survey by Bank for Inernaional Selemens (BIS), he noional ousanding volume of ransacions of ineres rae swaps amouned o 461,281 billion US dollars a he end of December 2013 as described in BIS (2014).Figures 1 shows he daa of CPI (annual changes) and he 5- and 10-year ineres raes. 3. METHODOLOGY 3.1 Uni Roo Tes I is necessary o check if he daa used in his paper conain uni roos because empirical analysis from he mid-1980s hrough he mid-1990s shows ha daa such as ineres raes, foreign exchange, and socks are nonsaionary, Therefore, he Phillips/Perron (PP) es and he Kwiaowski/Phillips/Schmid/Shin (KPSS) es are used. The PP es defines he null hypohesis as uni roos exis and he alernaive hypohesis as uni roos do no exis. Fuller (1976) provides he able for he PP es. The KPSS es defines he null hypohesis as uni roos do no exis and he alernaive hypohesis as uni roos exis. Firsly, he original daa are checked o see if hey conain a uni roo. Nex, he daa wih firs difference are analyzed o see if hey have a uni roo o confirm ha he daa are a I (1) process. The same mehod is used in Io (2009).

6 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July % Figure 1 CPI and Long Term Ineres Raes CPI Y2 Y Jan-93 Feb-94 Mar-95 Apr-96 May-97 Jun-98 Jul-99 Aug-00 Sep-01 Oc-02 Nov-03 Dec-04 Jan-06 Feb-07 Mar-08 Apr-09 May-10 Jun-11 Jul-12 Aug-13 Sep-14 Noes: Sample period is from January 1993 o February CPI is inflaion rae. Y2 and Y10 are swap raes of 2 years and 10 years. Daa source is Daasream Coinegraion Tes A coinegraion framework is presened o analyze he relaionship beween he nominal ineres rae and he expeced rae of inflaion. Nonsaionary ime series vary widely wih heir own shor-run dynamics, bu heir linear combinaion can someimes be saionary such ha hey show comovemen wih long-run dynamics. This is called coinegraion by Engle and Granger (1987). In he es of he Fisher hypohesis using coinegraion, equaion (1) is esimaed by OLS o find if he residual conains a uni roo. i = α + β E (π ) + + u (1) j i = nominal ineres raes E (π+j) = expeced rae of inflaion When series i and E (π+j) are boh nonsaionary I (1), hey are said o be in a relaionship of coinegraion if heir linear combinaion is a saionary I(0). The coinegraion relaionship beween i and E (π+j) implies ha nominal ineres raes and he expeced rae of inflaion move ogeher in a long-run equilibrium. In addiion o esing wheher nominal ineres raes and expeced inflaion raes have a coinegraion relaionship, he coinegraion vecor (1,-1), β in equaion (1), is checked using he mehod of dynamic OLS (Sock and Wason, 1993). Equaion (2) is used o es if β = 1 can be rejeced. ΔE-j(π+j-i) are he lead and lag variables of he expeced inflaion raes. If β = 1 canno be rejeced, he nominal ineres raes change o a degree equivalen o he expeced inflaion raes. The coinegraion vecor es is only conduced on a pair of

7 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July samples when hey have a coinegraion relaionship. The same mehod is used in Io (2009). p + j ) + bi E i ( + j i + i= p i = α + β E ( π π ) u (2) The Fisher hypohesis holds when he expeced inflaion raes and nominal ineres raes are in boh a coinegraion and one-o-one relaionship. The mehods for esing he Fisher hypohesis can be summarized as follows: (1) Tes daa if hey are I (1) by uni roo ess. (2) Conduc he coinegraion es on pairs of daa confirmed o be I (1). (3) Conduc he coinegraion vecor es on pairs of daa confirmed o be in coinegraion. 4. RESULTS 4.1 Uni Roo Tes The resuls of he PP es and he KPSS es on he original daa do no eliminae he possibiliy ha he original daa have uni roos because all resuls of he PP es (wih and wihou rend) and he KPSS es (lag 4) show nonsaionariy. The resuls are shown in Tables 1 and 2. Before reaching a conclusion, daa wih he firs difference need o be checked o see if hey have uni roos. If hey are confirmed as no having uni roos, he original daa are considered o be I (1). Table 1 PP Uni Roo Tes Resuls (Original Series) Variable Wihou Trend Wih Trend CPI() Y Y Y Y Y Y Noes: * indicaes significance a he 5% level. 5% criical values are 2.89 (wihou rend) and 3.45 (wih rend).

8 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July Table 2 KPSS Uni Roo Tes Resuls (Original Series) Lag = 4 Lag = 12 Variable Trend Saionary Level Saionary Trend Saionary Level Saionary CPI() 0.167* 0.478* Y * 3.451* 0.157* 1.705* Y * 4.204* 0.155* 1.744* Y * 4.280* 0.160* 1.770* Y * 4.337* 0.165* 1.788* Y * 4.406* 0.181* 1.811* Y * 4.58* 0.199* 1.826* Noes: * indicaes significance a he 5% level. 5% criical values are ( rend saionary) and ( level saionary). According o he resuls of he PP and KPSS ess on he daa wih firs difference, he daa are considered no o have uni roos. The resuls are shown in Tables 3 and 4. I can be concluded ha all he daa used for he analysis are I (1). Thus, i is appropriae o use nonsaionary ime series models. Table 3 PP Uni Roo Tes Resuls (Firs Differenced Series) Variable Wihou Trend Wih Trend CPI() * * Y * * Y * * Y * * Y * * Y * * Y * * Noes: * indicaes significance a he 5% level. 5% criical values are 2.89 (wihou rend) and 3.45 (wih rend).

9 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July Table 4 KPSS Uni Roo Tes Resuls (Firs Differenced Series) Lag = 4 Lag = 12 Variable Trend Saionary Level Saionary Trend Saionary Level Saionary CPI() Y Y Y Y Y Y Noes: * indicaes significance a he 5% level. 5% criical values are ( rend saionary) and ( level saionary). 4.2 Coinegraion Tes Ineres raes in all mauriies excep for 10 years are in a relaionship of coinegraion wih he expeced rae of inflaion. However, he 10-year ineres rae is no. The resuls of he coinegraion es show ha ineres raes in he mauriies of 2, 3, 4, 5, and 7 years move ogeher wih he expeced rae of inflaion in a long-run equilibrium. The resuls are shown in Table 5. Table 5 Coinegraion Tes Resuls Variable Tes Saisics CPI -Y * CPI -Y * CPI -Y * CPI -Y * CPI -Y * CPI -Y Noes: * indicaes significance a he 5% level. 5% criical value is from MacKinnon (1991). The ess of he coinegraion vecor are conduced on all pairs of daa excep for he 10-year ineres rae. As for he coinegraion vecor es, β = 1 canno be rejeced for all mauriies. The resuls show ha all he mauriies excep for he 10-year ineres rae are in a one-o-one relaionship. The resuls are shown in Table 6. From he ess of coinegraion and he coinegraion vecor, i can be concluded ha he Fisher hypohesis holds for he mauriies of 2, 3, 4, 5, and 7, bu no 10 years.

10 Review of Inegraive Business and Economics Research, Vol. 5, no. 3, pp , July Table 6 Coinegraion Vecor Tes Resuls Variable β Modified SE Modified Value Y * Y * Y * Y * Y * Noes: * means ha β = 1 canno be rejeced since modified value is smaller han 5% criical value (1.96). 5. CONCLUDING REMARKS The purpose of his paper is o examine he validiy of he Fisher hypohesis in Sweden by analyzing long-erm ineres raes from January 1993 o February 2015 under he regime of an inflaion argeing policy. The Fisher hypohesis holds in he mauriies of 2, 3, 4, 5, and 7, bu no 10 years. The resuls of his paper parially suppor hose of Hawrey (1997) and Michell e al. (2007) who analyze he validiy of he Fisher hypohesis under a regime of inflaion argeing. The resuls imply ha changes in inflaion expecaions do move in he same direcion and degree as he nominal long-erm ineres raes in he mauriies of 2, 3, 4, 5, and 7 years. In hese cases, real long-erm ineres raes are sable. This can be primarily aribued o he credibiliy of he inflaion-argeing framework over a period of almos 20 years and he success i has achieved in locking inflaion expecaions ino he arge range wihin hese imeframes. However, in he mauriy of 10 years, his credibiliy has never been as cerain as in he shorer periods. Thus, i can be concluded ha he Riksbank has been almos successful in sabilizing inflaionary expecaions and real ineres raes. This sudy can be exended ino muliple-counry analyses of counries operaing inflaion argeing. ACKNOWLEDGEMENT This paper is a resul of individual research projec provided by he Insiue of Social Sciences, Meiji Universiy. The auhor highly appreciaes gran-in-aid from he Insiue. He is also graeful for commens made by anonymous reviewers and paricipans a SIBR-Thammasa 2016 Bangkok Conference on Inerdisciplinary Business and Economics Research. REFERENCES

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