Structural breaks, inflation and interest rates: Evidence from the G7 countries

Clemente, Jesús; Gadea, María Dolores; Montañés, Antonio; Reyes, Marcelo Article Structural breaks, inflation and interest rates: Evidence from the G7 countries Econometrics Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Clemente, Jesús; Gadea, María Dolores; Montañés, Antonio; Reyes, Marcelo (2017) : Structural breaks, inflation and interest rates: Evidence from the G7 countries, Econometrics, ISSN 2225-1146, MDPI, Basel, Vol. 5, Iss. 1, pp. 1-17, https://doi.org/10.3390/econometrics5010011 This Version is available at: https://hdl.handle.net/10419/171910 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ econometrics Article Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries Jesús Clemente 1, María Dolores Gadea 2, Antonio Montañés 1,* and Marcelo Reyes 1,† 1Department of Economic Analysis, University of Zaragoza, Gran Vía 2, 50006 Zaragoza, Spain; [email protected] 2Department of Applied Economics, University of Zaragoza, Gran Vía 2, 50006 Zaragoza, Spain; [email protected] *Correspondence: [email protected]; Tel.: +34-976-76-2221 † Our beloved Marcelo Reyes passed away on 27 July 2015. We will always miss you. Academic Editor: Pierre Perron Received: 24 August 2016; Accepted: 25 January 2017; Published: 17 February 2017 Abstract: This study reconsiders the common unit root/co-integration approach to test for the Fisher effect for the economies of the G7 countries. We first show that nominal interest and inflation rates are better represented as I(0) variables. Later, we use the Bai–Perron procedure to show the existence of structural changes in the Fisher equation. After considering these breaks, we find very limited evidence of a total Fisher effect as the transmission coefficient of the expected inflation rates to nominal interest rates is very different than one. Keywords: unit roots; structural breaks; interest rates; inflation; Fisher effect JEL Classification: C22; E43 1. Introduction One of the most important results from classical economic theory is that the movements of nominal variables have no impact on real economic variables. This result, which can be verified by testing the long-run neutrality proposition, implies that a permanent movement in the inflation rate has no effect on the equilibrium real interest rate. The traditional way to represent this phenomenon is to decompose nominal interest rates into two separate components that reflect expected inflation and the “real” interest rate. Following Fisher’s (1930) study [ 1 ], which is very influential, this relationship can be stated through the well-known Fisher equation: Rt=πe t+rt(1) where R represents the nominal interest rate, πe is the expected rate of inflation and r is the (ex-ante) real interest rate. In simple economic models, this last variable is determined by deep structural parameters, such as investor preferences or the marginal efficiency of capital, and is often assumed to be constant over long horizons. According to (1), moneylenders need a nominal interest rate that compensates them for the purchasing power lost over the duration of the loan, which is proxied by the expected inflation. Thus, if there is no money illusion, then a change in the expected inflation rate should be fully transmitted to the nominal interest rate to maintain a constant real interest rate. Equation (1) provides useful information, both for theoretical research and for those making economic policy decisions. For example, if the Fisher effect holds, then the expected inflation is a good predictor of the nominal interest rate. Further, there is evidence of the superneutrality of money hypothesis. Consequently, it comes as no surprise that a significant body of literature analyzes the Econometrics 2017,5, 11; doi:10.3390/econometrics5010011 www.mdpi.com/journal/econometrics Econometrics 2017,5, 11 2 of 17 relationship between nominal interest rates and inflation or, more exactly, whether the so-called Fisher effect holds. The most common approach starts by estimating the following equation: Rt=α+βπt+1+et(2) which implicitly assumes the presence of perfect rational expectations (πt+1=πe t) and that αreflects the (ex-ante) real interest rate. It is clear that, whenever the value of the parameter β , often referred to as the Fisher coefficient, is equal to one, this equation is equal to (1), and therefore, we should conclude that the Fisher effect holds. At first sight, the analysis of this effect appears to be quite straightforward, in the sense that it only requires an estimation of (2) and a subsequent test of the null hypothesis H o : β= 1. However, the literature confirms that there are several points that should be considered to accurately estimate this parameter and to test this hypothesis. Our study proposes a different statistical methodology to test the relationship between inflation and the nominal interest rate, adding to the controversy over which technique is the most suitable for testing the Fisher effect. 1 Here, we consider the appropriate treatment of the time series properties of the variables, as well as the possible presence of changes in the values of the parameters α and β . In this study, we consider the importance of these two points. With respect to the first, there seems to be an almost unanimous opinion in the literature about the existence of unit roots in both the nominal interest rate and the inflation rate. Therefore,”standard” econometric models are no longer valid; rather, the co-integration approach should be employed. There are several examples of the use of this unit root/co-integration approach, beginning with the seminal studies of Rose (1988) [ 4 ] and Mishkin (1992) [ 5 ], whose methodology was subsequently applied in the more recent studies of Crowder and Wohar (1999) [ 6 ], Koustas and Serletis (1999) [ 7 ], Rapach (2002) [ 8 ], Laatsch and Klein (2003) [ 9 ] and Rapach and Weber (2005) [ 10 ], amongst many others. Some recent studies opted to use the panel data unit root/co-integration approach, as is the case of Westerlund (2008) [11] and Ozcan and Ari (2015) [12]. Nevertheless, some authors, such as Cox et al. (1985) [ 13 ], Malliaropoulos (2000) [ 14 ], Lanne (2001) [15], Olekalns (2001) [16], Gil-Alaña (2002) [17] and Atkins and Coe (2002) [18], questioned the presence of a unit root in the evolution of both the nominal interest rate and the inflation rate. Similarly, some other authors suggest the possibility that these variables may follow a long-memory process. We can cite the papers of Baum et al. (1999) [ 19 ], Phillips and Perron (1998) [ 20 ], Tsay (2000) [ 21 ], Sun and Phillips (2004) [ 22 ], Gil-Alaña (2004) [ 23 ] and Gil-Alaña and Moreno (2012) [ 24 ], in the case of the nominal interest rate, and Hassler and Wolters (1995) [ 25 ] and Bos et al. (1999) [ 26 ] with respect to the inflation rate. In light of this, the use of the unit root/co-integration approach is now open to debate. In addition to the doubts raised by the authors above, we tentatively offer a new source of criticism in this study based on the potential non-constancy of the parameters included in the Fisher equation in the spirit of Lucas’s critique (Lucas (1976) [ 27 ]). Our argument is based on the fact that most of the studies analyzing the Fisher effect use sample sizes covering the period from the 1970s to the present day. However, none of these appear to account for the different monetary policies in effect during this very lengthy period of time, making the constant parameter hypothesis doubtful. Instead, we argue that it is more appropriate to consider the hypothesis that some structural breaks affect the Fisher relationship. They may arise, if we consider that the presence of which can be understood if we consider, for example, that the real interest rate is the consequence of the interaction between savings and investment, and it may change when savings owners modify their behavior. In this regard, and as Chadha and Dimsdale (1999) [ 28 ] point out, demographic change, technological progress, fiscal incentives, changes in the taxation of profits, the size of the public 1 Recently, Caporale and Pittis (2004) [ 2 ], and Panopoulou (2005) [ 3 ] emphasized that this is a key issue in the empirical evidence supporting the Fisher relationship. Econometrics 2017,5, 11 3 of 17 debt, investors’ perception of risk and the degree of regulation or deregulation of capital markets could alter the constant and inflation parameters. Another source of possible variation in the parameters of (2) comes from the fact that the influence of inflation on the nominal interest rate can also vary. More robust inflation targeting and a more active monetary policy, as indicated by Söderlind (2001) [ 29 ] and Olekalns (2001) [ 16 ], or constraints on capital markets could be important determinants of the final value of these parameters. Against this background, this study aims to analyze the Fisher effect for the G7 group of countries by explicitly accounting for the both variables and, more importantly, that the presence of structural breaks can affect the parameters of the Fisher equation. In order to illustrate this starting hypothesis, we begin by testing the time series properties of nominal interest and inflation rates. If we can find evidence that leads us to better characterize these variables as being I(0), then we should not use the co-integration approach because applying, similar arguments as Malliaropoulos (2000) [ 14 ] does, this may lead to spurious evidence of the Fisher effect. Furthermore, and in order to reflect the possible non-constancy of the Fisher equation, we allow for the presence of some breaks in the relationship between the nominal interest rate and the inflation rate. In a stationary scenario, we can apply Bai and Perron’s (1998, 2003) [ 30 , 31 ] proposed procedure to test for the stability of the Fisher effect equation. This method also has the advantage of providing consistent estimations of both the number of breaks and the periods when these occur. Finally, we can use the results obtained by applying these techniques to estimate the Fisher relationship when we incorporate the structural breaks and the dynamic effects. The rest of the paper is organized as follows. In Section 2, we describe the tests we employ to test for the time series properties of the variables. When these are applied to the nominal interest and inflation rates of the economies of the G7 countries, we find that they allow us to reject the unit root null hypothesis, a result that suggests that it is more advisable to analyze the Fisher effect in a stationary framework, rather than in a non-stationary one. In light of this result, in Section 3, we first propose the use of the Bai–Perron procedure to determine the presence of structural breaks in the Fisher equation. We then apply this procedure to analyze the Fisher effect for the economies of the G7 countries. Section 4closes the paper with a review of the most important conclusions. 2. Fisher Effect with Non-Integrated Variables Following Nelson and Plosser’s (1982) seminal study [ 32 ], most empirical analyses based on the use of variables measured as time series begin by studying the time properties of the variables. If these are better characterized as being integrated, then researchers use co-integration techniques. If, by contrast, they are stationary, then we can use standard econometric techniques. The study of the Fisher effect is a scenario in which we can clearly appreciate the application of this strategy and, since Mishkin’s (1992) [ 5 ] classic study, most of the literature devoted to this issue has followed such an approach. However, some studies appear to have raised some questions about the appropriateness of the unit root model when seeking to accurately describe the evolution of both inflation rates and nominal interest rates. Malliaropoulos (2000) [ 14 ] and Baum et al. (1999) [ 19 ] showed that USA nominal interest and inflation rates can be better represented using broken trend stationary models. This finding is very important in the sense that, at least for the USA data, it casts doubts on the adequacy of the co-integration approach to test for the Fisher effect. A common method under this approach is to test whether the real interest rate is integrated. If we can conclude that the real interest rate is not integrated, this will be interpreted as evidence of the Fisher effect. However, this method is only valid when the nominal interest rate and the expected inflation rate are integrated. To better appreciate this, let us consider an expected inflation ( π) and a nominal interest rate ( R ) represented as I(0) variables. Any combination of these variables, say R−β π , will also be an I(0) variable. However, this does not imply that the Fisher effect holds, because it only does so when the parameter β is one. Thus, in the presence of I(0) variables, admitting that the real interest rate is not integrated, does not necessarily imply that the Fisher effect holds. Econometrics 2017,5, 11 4 of 17 This finding requires a careful analysis of the time properties of the nominal interest rates and inflation rates, which is precisely the aim of the next subsection. 2.1. Analysis of the Time Properties of the Nominal Interest Rates and Inflation Rates We have already made the point that an analysis of the time properties of the nominal interest rates and inflation rates should be carried out carefully, and should certainly not be regarded as just a prior step in using co-integration techniques. There is a great range of statistics devoted to this issue. For example, most of the studies related to this area base their analysis on augmented Dickey–Fuller (ADF) tests (Dickey and Fuller (1979) [ 33 ]; Said and Dickey (1984) [ 34 ]), the methods presented in Phillips and Perron (1988) [ 20 ] or subsequent modifications of these types of statistics proposed by Ng and Perron (2001) [ 35 ], which compare the performance of a wide range of unit root statistics. For example, these authors consider the ADF GLS , which is based on the very popular ADF test. Following Elliot et al. (1996) [36], this can be obtained by estimating the following model: yt=δt+ρyt−1+ ` ∑ i=1 φi∆yt−i+εt(3) where δt reflects the deterministic elements, 2 and subsequently calculating the pseudo t-ratio to test whether the parameter ρ is one. The differences between this and the simple ADF test lie in the fact that ADF GLS is based on the use of GLS (Generalized Least Squares) estimation methods instead of OLS (Ordinary Least Squares) estimators and on determining the value of the lag truncation parameter ( ` ) by using an information criterion, called MIC (Modified Information Criteria), also proposed in Ng and Perron (2001) [ 35 ]. This type of statistics is not useful to reject the presence of a unit root in nominal interest rates and inflation. This is why some authors have recently employed different statistics to analyze the time series properties of the variables to take advantage of the cross-sectional information of a database. Thus, it seems suitable to use a panel data approach to test for the presence of a unit root in the variables in the Fisher equation. In order to select the most appropriate type of panel data unit root test, we should first know the characteristics of the database, because of the possible presence of a cross-sectional correlation between the variables. It is common to begin by testing for the null hypothesis of cross-sectional independence using Pesaran’s (2004) CD (Cross Dependence) statistic [37], which has the following definition: CD =v u u t 2T N N ∑ j=1 ˆ ρ2 j∼N(0, 1)(4) where T is the sample size, N the cross-sectional dimension and ˆ ρ is the pair-wise Pearson’s correlation coefficients ˆ ρj , j= 1, ..., n , n=N(N− 1 )/ 2 of the residuals obtained from augmented Dickey–Fuller type regression equations. If we cannot reject this null hypothesis, then we should use the CIPS statistics because they correct the distortion caused by the cross-sectional correlation. Following Pesaran (2007) [ 38 ], the CIPS (cross-sectionally augmented panel unit root test) statistic is defined as follows: CIPS =N−1N ∑ i=1 ¯ ti(5) 2In our present case, we only include an intercept in the model specification. Econometrics 2017,5, 11 5 of 17 with ¯ tibeing the OLS t-ratio to test the Ho:αi=0 in the following cross-sectional ADF regressions: ∆yit =δit +αiyit−1+γi¯ yt−1+ p ∑ j=1 φij ∆yi,t−j+ p ∑ j=0 ϕij ∆¯ yt−1+εit (6) where ¯ yt−1 denotes the cross-sectional mean of yit . Tables II(a)–(c) in Pesaran (2007) [ 38 ] provide the critical values for the CIPS tests, in addition to a proposed truncated version of this statistic, commonly referred to as CIPS*, which will be used in the following section. 2.2. Empirical Evidence from the G7 Countries As we mentioned earlier, the methodology to employ to analyze the Fisher effect depends on the time properties of the variables that are necessary to study it, namely the nominal interest rates and inflation rates. Thus, we should be careful when determining the integration order of these variables. To that end, we apply the statistics presented in the previous section to the nominal interest rates and inflation rates of the G7 countries. We take two different measures of the nominal interest rates. First, we select a short-run variable, measured through the three-month treasury bill rate (or equivalent) for each sample country. Second, we take the 10-year government bond (or equivalent) for each sample country as a measure of the long-run behavior of nominal interest rates. We obtain the annualized inflation rates from the Consumer Price Index (CPI). We obtain all data from the OECD Main Economic Indicators. Finally, the quarterly data, where possible, cover the sample period 1970:Q1–2015:Q4. 3 Figures 1–3illustrate these variables, whilst Tables 1and 2report the results of applying the previously-mentioned statistics to our database. Table 1reflects the results of the CD statistic to test the null hypothesis of no cross-sectional dependence. We can easily reject this null hypothesis, and consequently, we should employ panel data unit root tests that account for its presence. The CIPS* statistic, whose results are presented in Table 2, takes into account the cross-sectional dependence. As we can see, there is only very robust evidence against the unit root null hypothesis. However, some countries may exhibit the presence of the unit root in any of the analyzed variables. 4 In order to explore this possibility, we have considered several subgroups of countries. We have taken all of the possible combinations of five and six countries, and the values of the CIPS* statistic always allows the rejection of the null hypothesis, the average p-value being lower than 0.01 Thus, this lack of evidence against the null hypothesis matches the results of Constantini and Lupi (2007) [ 40 ] and Lee and Chang (2007, 2008) [ 41 , 42 ], who reject the presence of a unit root in the inflation rate for different sample sizes of OECD countries using the LM (Lagrange Multiplier) tests proposed in Lee and Strazicich (2003, 2013) [ 43 , 44 ], which consider the presence of broken trends in the evolution of these variables. These statistics can also provide evidence against the unit root null hypothesis for the nominal interest rates, as is reflected in Gadea et al. (2009) [ 45 ]. Thus, the global consideration of all of this evidence leads us to an analysis of the Fisher effect using I(0) variables instead of the much more common approach of using I(1) variables. 3 The Italian short-term interest rates for 1970:Q1–1970:Q4 were estimated using the evolution of Italy’s long-term interest rates. 4See Pesaran (2012) [39] in this regard. Econometrics 2017,5, 11 6 of 17 -15 0 15 30 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 CANADA -15 0 15 30 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 FRANCE -15 0 15 30 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 GERMANY -15 0 15 30 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 ITALY -15.00 0.00 15.00 30.00 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 JAPAN -15 0 15 30 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 UK -15 0 15 30 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 USA (a) Figure 1. Cont. Econometrics 2017,5, 11 7 of 17 (b) Figure 1. Cont. Econometrics 2017,5, 11 8 of 17 0 5 10 15 20 25 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 CANADA 0 5 10 15 20 25 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 FRANCE 0 5 10 15 20 25 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 GERMANY 0 5 10 15 20 25 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 ITALY 0 5 10 15 20 25 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 JAPAN 0 5 10 15 20 25 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 UK 0 5 10 15 20 25 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 USA (c) Figure 1. ( a ) Expected Inflation rates; ( b ) Long-run nominal interest rates; ( c ) Short-run nominal interest rates. Econometrics 2017,5, 11 15 of 17 We also considered the presence of some breaks in the Fisher equation in order to capture the different monetary regimes that co-exist across the sample. Using a procedure recently proposed in Bai and Perron (1998, 2003) [ 30 , 31 ] confirms our hypothesis, offering robust evidence of the existence of different regimes in the relationship between nominal interest rates and inflation rates. This procedure also offers an excellent scenario for testing for the Fisher effect, considering the presence of breaks in the relationship that affects both parameters. The results based on this method show that there is a clear connection between nominal interest rates and expected inflation rates. However, there is no evidence of a total Fisher effect for the G7 countries. Inflation is not always transmitted to nominal interest rates. In fact, we should note that the Fisher coefficient estimates have very high variations. The changes in the monetary policy produced an adjustment in the transmission of the effect of inflation to nominal interest rates. We also observed the existence of four different regimes in the relationship between nominal interest rates and expected inflation rates in the estimated periods, in which the regimes changed during the late 1970s, mid-1980s, mid-1990s and the late 2000s. It is remarkable to notice that there is no break associated with the first oil crisis (around 1973), despite the fact that previous studies analyzing real interest rates offered evidence of a break at that time. We should nevertheless note that these studies consider that the β coefficient of the Fisher equation is equal to one, a value that is consistently rejected for most of the cases analyzed in the present study. Finally, we observed that the transmission of the expected inflation to nominal interest rates was greater in Italy than in the other countries and was very low in Japan, the UK and Canada. France, the USA and Germany also showed periods with a significant transmission of the inflation rates to nominal interest rates, even exceeding the value of one. To sum up, our findings show that regime changes govern the Fisher equation. The estimations show a link between nominal interest rates and expected inflation, but a weak Fisher effect, which does not support the monetary neutrality hypothesis. The values obtained for the Fisher coefficients lead us to conclude that there is “under-adjustment” of nominal rates to inflationary expectations and, consequently, of their transmission to real rates. Furthermore, as stated above, the weakness of the Fisher effect increases with the credibility of monetary policy. Acknowledgments: The authors benefited from the helpful comments made by the Editor and four anonymous referees; this version owes much to them. Financial support from the Ministerio de Ciencia y Tecnología under Grants ECO2014-58991-C3-1-R, ECO2014-58991-C3-2-R and ECO2015-65967-R is gratefully acknowledged. They also acknowledge support from the CASSETEM consolidated research group. The usual disclaimer applies. Author Contributions: The authors contributed equally to this work. Conflicts of Interest: The authors declare no conflict of interest. References 1. Fisher, I. The Theory of Interest; MacMillan: New York, NY, USA, 1930. 2. Caporale, G.M.; Pittis, N. Estimator Choice and Fisher’s Paradox: A Monte Carlo Study. Econom. Rev. 2004 , 23, 25–52. 3. Panopoulou, E. A Resolution of the Fisher Effect Puzzle: A Comparison of Estimators. IIIS Discussion Paper, 67, 2005. Available online: https://ssrn.com/abstract=680401 (accessed on 15 July 2016). 4. Rose, A.K. Is the Real Interest Rate Stable? J. Financ. 1988,43, 1095–1112. 5. Mishkin, F. Is the Fisher effect for real: A Reexamination of the Relationship between Inflation and Interest Rates. J. Monetary Econ. 1992,30, 195–215. 6. Crowder, W.J.; Wohar, M.E. Are Tax Effects Important in the Long-Run Fisher Relationship? Evidence from the Municipal Bond Market. J. Financ. 1992,54, 307–317. 7. Koustas, Z.; Serletis, A. On the Fisher Effect. J. Monetary Econ. 1999,44, 105–130. 8. Rapach, D.E. The Log-run Relationship between Inflation and Real Stock Price. J. Macroecon. 2004 ,24, 331–351. Econometrics 2017,5, 11 16 of 17 9. Laatsch, F.; Klein, D.P. Nominal Interest Rate and Expected Inflation: Results from a Study of US Treasury Inflation-Protected Securities. Q. Rev. Econ. Financ. 2003,43, 3405–3417. 10. Rapach, D.E.; Weber, C. Are Real Interest Rates Really Nonstationary? New Evidence from Tests with Good Size and Power. J. Macroecon. 2005,26, 409–430. 11. Westerlund, J. Panel cointegration tests of the Fisher effect. J. Appl. Econom. 2008,23, 193–233. 12. Ozcan, B.; Ari, A. Does the Fisher hypothesis hold for the G7? Evidence from the panel cointegration test. Econ. Res.-Ekon. Istraz. 2015,28, 271–283. 13. Cox, J.C.; Ingersoll, J.E.; Ross, S.A. A theory of the term structure of interest rates. Econometrica 1985 ,53, 385–407. 14. Malliaropulos, D. A Note on Nonstationarity, Structural Breaks and the Fisher Effect. J. Bank. Financ. 2000 , 24, 695–707. 15. Lanne, M. Near Unit Root and the Relationship between Inflation and Interest Rate: A Reexamination of the Fisher Effect. Empir. Econ. 2001,26, 357–366. 16. Olekalns, N. An Empirical Investigation of the Structural Breaks in the Ex Ante Fisher Effect. Research Paper Number 786; Department of Economics, University of Melbourne, Melbourne, Australia, 2001. 17. Gil-Alaña, L.A. A Mean Shift Break in the US Interest Rate. Econ. Lett. 2002,77, 357–363. 18. Atkins, F.J.; Coe, P.J. An ARDL Bounds Test of the Long-term Fisher Effect in the United States and Canada. J. Macroecon. 2002,24, 255–266. 19. Baum, C.F.; Barkoulas, J.T.; Caglayan, M. Persistence in International Inflation Rates. South Econ. J. 1999 ,65, 900–913. 20. Phillips, P.; Perron, P. Testing for a Unit Root in Time Series Regression. Biometrika 1988,75, 335–346. 21. Tsay, W.J. The long memory story of the real interest rate. Econ. Lett. 2000,67, 325–330. 22. Sun, X.; Phillips, P.C.B. Understanding the Fisher Equation. J. Appl. Econom. 2004,19, 869–896. 23. GilAlaña, L.A. Estimation of the order of integration in the UK and the US interest rates using fractionally integrated semiparametric techniques. Eur. Res. Stud. 2004,7, 29–40. 24. Gil-Alaña, L.A.; Moreno, A. Fractional integration and structural breaks in U.S. macro dynamics. Empir. Econ. 2012,43, 427–446. 25. Hassler, U.; Wolters, J. Long Memory in Inflation Rates: International Evidence. J. Bus. Econ. Stat. 1995 ,13, 37–45. 26. Bos, C.S.; Franses, P.H.; Ooms, M. Long Memory and Level Shifts: Reanalysing Inflation Rates. Empir. Econ. 1999,24, 427–449. 27. Lucas, R.E., Jr. Econometric Policy Evaluation: A Critique. Carnegie-Rochester Conf. Ser. Public Policy 1976 ,2, 19–46. 28. Chadha, J.S.; Dimsdale, N.H. A Long Review of Real Rates. Oxf. Rev. Econ. Policy 1999,15, 17–45. 29. Söderlind, P. Monetary Policy and the Fisher Effect. J. Policy Model. 2001,23, 491–495. 30. Bai, J.; Perron, P. Estimating and Testing Linear Models with Multiple Structural Changes. Econometrica 1998 , 66, 47–78. 31. Bai, J.; Perron, P. Computation and analysis of multiple structural-change models. J. Appl. Econom. 2003 ,18, 1–22. 32. Nelson, C.R.; Plosser, C.I. Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications. J. Monetary Econ. 1982,10, 139–162. 33. Dickey, D.; Fuller, W. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. J. Am. Stat. Assoc. 1979,74, 427–431. 34. Said, S.E.; Dickey, D. Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order. Biometrika 1984,71, 599–607. 35. Ng, S.; Perron, P. Lag Length Selection and the Construction of Unit Root Tests With Good Size and Power. Econometrica 2001,69, 1519–1554. 36. Elliot, G.; Rothenbert, T.J.; Stock, J.H. Efficient tests for an autoregressive unit root. Econometrica 1996 ,64, 813–836. 37. Pesaran, M.H. General Diagnostic Tests for Cross Section Dependence in Panels. IZA Discussion Paper 1240, 2004. Available online: http://www.econ.cam.ac.uk/research/repec/cam/pdf/cwpe0435.pdf (accessed on 1 August 2016). Econometrics 2017,5, 11 17 of 17 38. Pesaran, M.H. A simple panel unit root test in the presence of cross-section dependence. J. Appl. Econom. 2007,22, 265–312. 39. Pesaran, M.H. Testing Weak Cross-Sectional Dependence in Large Panels. IZA Discussion Paper 6432, 2012. Available online: http://ftp.iza.org/dp6432.pdf (accessed on 1 August 2016). 40. Costantini, M.; Lupi, C. An analysis of inflation and interest rates. New panel unit root results in the presence of structural breaks. Econ. Lett. 2007,95, 408–414. 41. Lee, C.C.; Chang, C.P. Mean reversion of inflation rates in 19 OECD countries: Evidence from panel Lm unit root tests with structural breaks. Econ. Bull. 2007,3, 1–15. 42. Lee, C.C.; Chang, C. P. Trend stationary of inflation rates: Evidence from LM unit root testing with a long span of historical data. Appl. Econ. 2008,40, 2523–2536. 43. Lee, J.; Strazicich, M. Minimum LM Unit Root Tests with Two Structural Breaks. Rev. Econ. Stat. 2003 ,40, 1082–1089. 44. Lee, J.; Strazicich, M. Minimum LM Unit Root Test. Econ. Bull. 2013,33, 2483–2492. 45. Gadea, M.D.; Montañés, A; Reyes, M. The European Union Currencies and the US Dollar: From post-Bretton-Woods to the Euro. J. Int. Money Financ. 2004,23, 1109–1136. 46. Atkins, F.J.; Chan, M. Trend breaks and the Fisher Hypothesis in Canada and the United States. Appl. Econ. 2004,36, 1907–1913. 47. Garcia, R.; Perron, P. An Analysis of the Real Interest Rate under Regime Shifts. Rev. Econ. Stat. 1996 ,78, 111–125. 48. Bierens, H.J. Nonparametric Nonlinear Co-Trending Analysis, with an Application to Inflation and Interest in the U.S. J. Bus. Econ. Stat. 2000,18, 323–337. 49. Lanne, M. Nonlinear dynamics of interest and inflation. J. Appl. Econom. 2006,21, 1157–1168. 50. Panopoulou, E.; Pantelidis, T. The Fisher effect in the presence of time-varying coefficients. Comp. Stat. Data Anal. 2016,100, 495–511. 51. Bai, J. Estimation of a Change Point in Multiple Regression Models. Rev. Econ. Stat. 1997,79, 551–563. 52. Andrews, D.W.K. Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica 1991,59, 817–858. 53. Fama, E.F. Term structure forecast of interest rates, inflation and real returns. J. Monetary Econ. 1990 ,25, 59–76. 54. Fahmy, Y.A.F.; Kandil, M. The Fisher effect: New evidence and implications. Int. Rev. Econ. Financ. 2003 ,12, 451–465. 55. Evans, M.; Lewis, K. Do expected shifts in inflation affect estimates of the long-run Fisher relation? J. Financ. 1995,50, 225–253. 56. Rapach, D.E.; Wohar, M.E. Regime Changes in International Real Interest Rates: Are They a Monetary Phenomenon? J. Money Credit Bank. 2005,37, 887–906. 57. Tobin, J. The interest-elasticity of transactions demand for cash. Rev. Econ. Stat. 1956,38, 241–247. 58. Mundell, R. Inflation and Real Interest. J. Polit. Econ. 1963,71, 280–183. 59. Rapach, D.E. International Evidence on the Long-run Impact of Inflation. J. Money Credit Bank. 2003 ,33, 23–48. 60. Clarida, R.; Galí, J.; Gertler M. Monetary policy rules and macroeconomic stability evidence and some theory. Q. J. Econ. 2000,115, 147–180. c  2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).