A THRESHOLD COINTEGRATION TEST OF THE FISHER HYPOTHESIS : CASE STUDY OF 5 EUROPEAN NATIONS

A perennial favorite among monetary and financial economists is the superneutrality hypothesis, conceptualizing the relationship between nominal interest rates (rt) and inflation (πt). The empirical evidence is far from unanimous. This failure is contributed to the fact that previous studies have ignored the stochastic features of these variables, i.e., their inherent nonlinearities, which have resulted in only a partial adjustment (temporal co-movement) between the variables. To model the true dynamics of “rt” and “πt”, now, we have an appropriate and powerful metric in the form of the “threshold cointegration” methodology. We propose to apply it to revisit this as of yet unsettled question, for a set of five European countries namely, Belgium, France, Germany, Italy and Sweden. We find evidence in favor of the presence of linear cointegration for all countries, but threshold cointegration for Belgium and Germany, and mixed evidence for France. Error correction results are given for Belgium and Germany and these indicate a partial Fisher effect with the cointegrating vector being greater than one. This is possibly due to tax effects. INTRODUCTION A perennial favorite research topic among monetary and financial economists is the age old “Fisher equation,” which conceptualizes the degree (and extent) to which nominal interest rates incorporate changes in expected inflation, thus keeping the real interest rate unaffected. The validity or otherwise of this hypothesis has fundamental ramifications for both theory and policy. As an example, this hypothesis upholds the super-neutrality of money and justifies using nominal interest rates as a good predictor of future inflation. Two things seem to stand out in the literature. One is the conflicting results regarding its existence / non-existence in an absolute sense. Here for example we have Mishkin (1992) which examines the hypothesis for postwar USA, and finds evidence in support (and against) it over different periods of time. Secondly, when nominal interest and inflation do co-move, it’s a case of partial co-movement and not a one-to-one correspondence in the long run. One reason forwarded for this “on again-off again” relationship between the two variables is their inherent nonlinearity, resulting only in partial adjustment when and only when their difference reaches some threshold. This has been examined lately by Evans and Lewis (1995), Garcia and Perron (1996) and Bierens (2000) to name a few. Southwestern Economic Review 42 Here we apply the recently available Hansen-Seo (2002) test of bivariate threshold cointegration, which through Monte Carlo simulation has been proven to be a very powerful test. Its strongest feature is its ability to model the true dynamics of the interest rate and inflation series, where proactive policy results in “mean reversion” only when the difference between the variables reach some threshold. It is applied it to the case of five major European economies namely Belgium, France, Germany, Italy and Sweden, with monthly data on the CPI (for the inflation rate) and the 3 month treasury certificate rates (for the short term interest rate) ranging from 1960 to 2004. They were chosen because they are all highly industrialized open market economies and major players in the European Economic Community. In the next section we carry out a brief review of the literature on this topic, followed by a brief description of the data set. The following section gives a brief description of the Hansen-Seo (2002) test and results followed by our concluding remarks. LITERATURE REVIEW The concept originated in Fisher (1896) and was extended in 1930. According to Professor Fisher nominal interest responds to the changing inflation rate by smaller amounts and with a time lag. The justification is the presence of ‘money illusion,’ which implies the inability of people to distinguish between nominal and real variables, at least in the short run. A practical manifestation of the presence of money illusion would be that lending institutions would not fully transmit their expected change in the inflation rate to the nominal interest rate, even if they do correctly estimate the expected inflation( rt). The concern with testing the Fisher hypothesis is that it is a long run phenomenon and more and more evidence is coming to the fore that economic / financial variables undergo structural changes over time say due to policy changes and / or business cycle fluctuations. Granville and Mallick (2004) find evidence in favor of the Fisher effect in the U.K. after examining data for 1900 – 2000. Carneiro, Divino, and Rocha (2002) find evidence in favor of the Fisher effect in Argentina and Brazil, but not Mexico, through an examination of monthly data for the period 1980 – 1997. Sun and Phillips (2004) find little support for the Fisher hypothesis in the United States. But the early empirical studies using linear cointegration, have not included the presence of regime shifts. The rationale provided for the failure of the Fisher hypothesis runs the gamut of logic from money illusion to the negative effect of inflation on money demand to the negative correlation between inflation and real interest rates. Madsen (2005) states that the rejection of the Fisher equation is often due to the omission of supply variables from the Fisher equation as this will lead to an upward bias for the coefficient of expected inflation and make it easier to reject the Fisher hypothesis. This study proposes a technical / econometric reason for the failure of the hypothesis, in terms of the stochastic properties of the variables under consideration. It is also propounded as the reason for the partial acceptance of the Fisher hypothesis, i.e., why it held over some periods and not over others. To model the true dynamics of interest rate and inflation over time, we use the “threshold cointegration” model which is a recent contribution in economics. It was first used in the biological and physical sciences, to model systems whose behavior changes once they reach some “saturation” point. In the field of international finance, Davutyan and Pippenger (1990) and Balke and Fomby (1997) A Threshold Cointegration Test of the Fisher Hypothesis: Case Study of 5 European Nations 43 amongst others, have used it to examine the character of the purchasing power parity hypothesis. They contend that due to the presence of transaction costs (which are lump sum costs) agents do not adjust continuously, but rather discretely once the price differential is greater than the transaction cost. Now this is a step function in the sense of zero market activity before the bound or threshold has been reached, and complete action once it has been crossed. In the cointegration sense, the error correction mechanism is inactive inside the boundary, but kicks in once the threshold has been crossed. Thus the equilibrium error is modeled as a threshold autoregression in the sense of mean reversion only from outside the band, i.e. the variables are nonstationary (have unit roots) inside the band. In the context of the Fisher correlation hypothesis, both nominal interest rate and inflation are nonstationary (and do not trend together under normal circumstances), but once the limits of social / political comfort are reached, proactive policy (for example contractionary / expansionary monetary policy) will kick in and the variables will become “mean reverting,” and hence start behaving like stationary entities. Their actual behavior depends on the width of the “tolerance band,” say for example the differential between the higher (H) and lower (L) bounds as (TH–TL). Mean reversion or tendency towards forming a cointegrating vector will be evident only at the limits and / or outside the band. Conventional estimates of this long run relationship has always assumed a “constant difference” and thus resulted in biased estimates. Million (2004) uses threshold cointegration to examine the Fisher hypothesis in the United States, and finds that “the policy maker.changes his behavior depending on the level of inflation: whenever the inflation rate decreases below a level of tolerable inflation the policy maker is more reluctant to conduct an active policy.However, in a context of increasing inflation.the monetary authorities change nominal interest rates so that inflation rates will go back to acceptable levels. ” Adusei and Kunst (2002) find evidence in favor of threshold cointegration between long rates and inflation but not for short rates and inflation. Given the mixed evidence in favor of the Fisher hypothesis, a re-examination is warranted. Furthermore, since there is no theoretical reason for imposing linearity on the hypothesis, a testing procedure that encompasses both linearity and nonlinearity would yield the most robust results. The Hansen-Seo approach allows us to do this, and therefore we feel our results on the Fisher hypothesis will be robust and will contribute to the literature in this field. DATA DESCRIPTION The data is from the OECD data set, available from the Estima Corporation. All of the data is monthly. The inflation proxy is the CPI (all items, nonseasonalized) and the short term interest proxy is the treasury certificate (3 month rate). The time period is Belgium [1960(1) – 1998(12)], France [1970(1) – 1998(12)], Germany [1960(1) – 1998(12)], Italy [1978(1) – 1998(12)] and Sweden [1982(1) – 2004(04)]. HANSEN – SEO THRESHOLD COINTEGRATION MODEL Threshold cointegration introduced by Balke and Fomby (henceforth, BF1997) combines nonlinearity and cointegration by allowing for nonlinear adjustments over the long run. It begins by testing for the presence of a bound or threshold where the null hypothesis is of linearity. Hansen –Seo (2002) extend the Southwestern Economic Review 44 BF and the Lo and Zivot (2001) test to examine for the presence of an unknown cointegrating vector where they test the term structure