مداخلات بانک مرکزی و فرضیه فیشر: یک آستانه بررسی هم انباشتگی

The long-run relationship between nominal interest rates and inflation is examined, allowing for structural breaks and asymmetric mean reversion. From a Threshold AutoRegressive (TAR) test applied to the residuals of the cointegration relationship (while allowing for both a break in the mean of the long-run equation and a smooth regime-transition), there is strong evidence for non-linear mean reversion properties for the real interest rates of the US Treasury Bill market. This suggests asymmetric changes to inflation shocks in the Central Bank's reaction function. The existence of different regimes is consistent with some interpretations of the monetary policies run by the Fed, such as credibility and opportunism.

Despite intensive empirical studies and an extensive literature, it seems that no consensus has emerged about the statistical properties of the real rate of interest and more generally about the validation of the Fisher effect, which is a relationship that postulates a nominal interest rate in any period equal to the sum of the real interest rate and the expected rate of inflation. It is important to understand this lack of consensus for two main reasons. First of all, the real interest rate is a crucial determinant of investment, savings and all intertemporal decisions. This means that a potential non-stationarity of the real interest rate would have important consequences concerning the effects of monetary policies and also for economic and financial models. Secondly, it seems that many studies using theoretical models (such as the Capital Asset Pricing Model (CAPM)) or econometric methodologies (such as the Generalized Moments Methods (GMM)) routinely assume that the real interest rate is stationary. This should be very confusing, as empirical works indicate that this is not so or at best holds only over short periods. The statistical characterisation of the real interest rate has therefore been investigated by many macroeconomists, unfortunately with contradictory findings. As the literature clearly indicates, the nominal interest rate is non-stationary (Fama and Gibbons, 1982 and Mankiw and Miron, 1986); it has, however, proven difficult to provide definitive evidence concerning the ex ante real interest rate, since it is inherently unobservable. For instance, Rose (1988) tested for cointegration using the techniques suggested by Engle and Granger (1987). At the annual frequency, none of the tests indicated cointegration at even the 10% significance level. By conducting a re-examination of the Fisher effect in the postwar United States, Mishkin (1992) noted the Fisher effect's lack of robustness to the period considered and found that the evidence did not support a short-run relationship in which a change in expected inflation is associated with an immediate change in interest rates. More recently, Garcia and Perron (1996) re-analysed the data using Markov Switching (MS) methods and found support for a stable real rate of interest, subject to infrequent changes in the constant. These authors concluded that the ex ante real rate of interest was effectively stable, but subject to two mean shifts over the period 1961–1985. To summarize, the empirical evidence gives a mixed picture of the statistical properties of the real rate of interest, and it is probably fair to say that the generating mechanism for the real rate is not well understood. However, as has been mentioned by Coakley and Fuertes (2002), the growing interest in inflation targeting and the opportunistic behaviour of the Central Banks are two of the reasons for exploring asymmetries in the key variables studied here. According to the proponents of the opportunistic approach (Orphanides and Wilcox, 1996), when inflation is moderate but still above the long-run objective, the Fed should not take deliberate anti-inflation action, but rather should wait for external circumstances (such as favourable supply shocks and unforeseen recessions) to deliver the desired reduction in inflation. The main goal of this article is thus to resolve the Fisher effect ‘puzzle’ for the period 1951–1999 with the application of recent econometric methods to the quarterly US Treasury Bill real interest rates. The main innovation of our methodology is therefore to undertake an investigation of potential asymmetries (as a smooth transition extension of the Self-Exciting Threshold AutoRegressive (SETAR) model) with cointegration tests robust to structural changes. We will perform linearity tests and unit root tests in a two-step cointegration framework. As a first step, we conduct cointegration tests by allowing a break in the mean shift for the constant in the long-run equation, following the approach of Gregory and Hansen (1996). As a second step, following Balke and Fomby (1997), we undertake Threshold AutoRegressive (TAR) tests for the residuals of the long run relationship, allowing a smooth transition from one regime to another. Empirical findings show here strong evidence for a threshold cointegration relationship for quarterly nominal interest rates and inflation. The article is structured in the following way. The next section will describe the Fisher effect as a switching regime cointegration relationship, whose linearity will be tested in the context of a LSTAR model. Section 3 will display the main econometric results obtained from the US data. The last section concludes the article.

Throughout this article, we have examined the long-run relationship between inflation and nominal interest rates, with an application to the US data, and have showed strong evidence for a threshold behaviour in the real interest rate. The introduction of structural breaks in the cointegration relationship helped us to remove some structural instability from the long-run equilibrium prior to the analysis of asymmetries in the short-run dynamics. Strong evidence for a smooth transition was detected between the regimes of high and low real interest rates. These asymmetries are interpreted as differential adjustments to small and large equilibrium errors relative to the threshold. This results in a gradually changing strength of adjustment for larger deviations from the equilibrium. Usually, this kind of non-linear behaviour results from non-synchronous interventions, heterogeneous agents and some intervention costs, as in the T-Bill market. However, this also gives us some information about the credibility of the Central Bank when real interest rates were at their highest level for a long period, as a difference between the pre and post-Volcker era. Moreover, following Orphanides and Wilcox (1996), this could also be interpreted as a feedback effect of an opportunistic behaviour of the Central Bank for the T-Bill market. In some cases, the Fed did not take deliberate anti-inflation measures, but waited for external circumstances (such as favourable supply shocks and unforeseen recessions) to deliver the appropriate monetary policy. To summarise, the results suggest that the policy maker (still pursuing an objective of price stability) changes his behaviour 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 (by changing nominal rates for instance), but merely engage in a policy of watchful waiting (which is consistent with a stance of inflation targeting). However, in a context of increasing inflation (which will correspond to our low regime where real interest rates are low and/or decreasing, ceteris paribus), the monetary authorities change nominal interest rates so that inflation rates will go back to acceptable values. This evidence should also resolve the puzzle of why the Fisher effect appears to be strong in some periods but not in others. Just as this analysis predicts, a long-run Fisher effect appears to be strong in the periods when interest rates and inflation exhibit stochastic trends: these two series will have a common trend and thus there will be a strong correlation between inflation and interest rates. However, as soon as these variables do not exhibit stochastic trends simultaneously (as in the high regime), a strong correlation between interest rates and inflation will not appear. It is exactly in these periods that Mishkin (1992) was unable to detect any evidence for a Fisher effect. Indeed, according to Mishkin, the findings of a long-run effect are more consistent with the views expressed in Fisher (1930) than with the standard definition of the so-called Fisher effect in the last 20 years. The evidence in this article thus supports a return to Irving Fisher's original characterisation of the inflation–interest rate relationship, as soon as we take non-linear features into account. Interesting results could also be obtained via the introduction of the output gap in the regression equation, which is left for subsequent research. Furthermore, more information could be obtained from a more precise study of the links between the instruments of the Fed and the yields to maturity of the 3-month Treasury Bills.