Correct cointegration tests of the long-run relationship between nominal interest and inflation

The Fisher (1930) hypothesis suggests that a long-run equilibrium relationship exists between the non-stationary series: nominal interest and expected inflation. Testing such a cointegrating relationship is complicated by the presence of the unobserved ex antereal rate of interest in residuals from the cointegrating regression. Assumptions concerning the stochastic properties of the expected real rate of interest are examined, and two proxies for the ex antereal rate are employed in multivariate cointegration tests of the Fisher hypothesis.     

An examination of the Fisher Hypothesis: the case of Turkey

This study examines the famous Fisher Hypothesis (FH) for Turkey. FH asserts that nominal interest rates adjust on a one-to-one basis to expected changes in inflation rates. Using the Johansen cointegration method for the Turkish monthly interest rate and inflation rate data, we find that it is possible to determine the long-run relationship—but not the one-to-one basis—between nominal interest rates and inflation. Our findings suggest that full FH does not hold but there is a very powerfull Fisher effect in the case of Turkey from 1990 to 2003.     

The Fisher effect: new evidence and implications

Using monthly data in the 1980s and early 1990s, our results do not support the short-run Fisher effect since short-term interest rates are associated with negligible changes in expected inflation. However, inflation and nominal interest rates exhibit common stochastic trends in the long run. Consequently, the correlation between nominal interest rates and inflation rates increases with maturity until they move in a one-to-one relation at long horizon. This is evident by the correlation coefficients of the Johansen test for cointegration that increase with the maturity of US government securities from 2 to 5 years.     

A note on the specification of the fisher equation under inflation uncertainty

The effect of uncertainty on the relationship between the nominal interest rate and the expected rate of inflation, the Fisher equation, is examined both theoretically and empirically. It is found that the coefficient of the expected rate of inflation is significantly below unity. Variable rates of inflation tend to effect the nominal rate of interest positively, but real yields are apparently effected only by expected inflation, but not its variance.     

Evaluating the Fisher effect in long-term cross-country averages

This article uses long-term cross-country data to examine the Fisher hypothesis that nominal interest rates respond point-for-point to changes in the expected inflation rate. The analysis employs bounded-influence estimation to limit the effects of hyperinflation countries such as Brazil and Peru. Contrary to the results in Duck (1993), the present evidence does not support a full Fisher effect. By extending the empirical model to account for cross-country differences in sovereign risk, we find evidence consistent with the idea that interest rates fail to fully adjust to inflation due to variation in the implicit liquidity premium on financial assets.     

The Fisher effect,survey data and time-varying volatility

In this paper we study the Fisher hypothesis using Livingston survey data on inflation expectations. We propose a simple model for the ex-ante real interest rate where the standard deviation of survey forecasts is used to correct for heteroskedasticity. The findings of this paper contradict earlier studies. We find supportive evidence for the Fisher hypothesis that the nominal interest rate and expected inflation move one-for-one both in the short and the long run. Our results also suggest that the change of US monetary policy does not have significant effect on the dynamics of the ex-ante real interest rate such as previous work assumes.     

The inflationary bias of real uncertainty and the harmonic Fisher equation

Summary. We argue that real uncertainty itself causes long-run nominal inflation. Consider an infinite horizon cash-in-advance economy with a representative agent and real uncertainty, modeled by independent, identically distributed endowments. Suppose the central bank fixes the nominal rate of interest. We show that the equilibrium long-run rate of inflation is strictly higher, on almost every path of endowment realizations, than it would be if the endowments were constant.Indeed, we present an explicit formula for the long-run rate of inflation, based on the famous Fisher equation. The Fisher equation says the short-run rate of inflation should equal the nominal rate of interest less the real rate of interest. The long-run Fisher equation for our stochastic economy is similar, but with the rate of inflation replaced by the harmonic mean of the growth rate of money.Received: 25 February 2005, Revised: 26 May 2005, JEL Classification Numbers: C7, C73, D81, E41, E58.An earlier version of this paper “Inflationary Bias in a Simple Stochastic Economy,” as a 2001 Cowles Foundation Discussion Paper No. 1333.     

The Fisher hypothesis: a multi-country analysis

This paper tests whether the Fisher hypothesis holds for a sample of 26 countries by assessing the long run relationship between nominal interest rates and inflation rates taking into consideration the short run dynamics of interest rates. The empirical evidence supports the hypothesis that there is a one-to-one relationship between the interest rate and inflation for more than half of the countries under study.     

Does monetary policy affect the long-run expectations of non-stationary real interest rates?

In this article, we analyse whether the monetary policy affects the long-run expectation of the non-stationary real interest rate. The analysis is conducted through Beveridge–Nelson trend decomposition within a cointegrated vector autoregressive model based on the New Keynesian framework. We suggest an augmented test of the conventional co-integration test on the non-stationarity of the real interest rate, which checks whether the co-integration coefficient of inflation is one and the output gap affects the co-integration equilibrium of the nominal interest rate. We further suggest decomposing the long-run expectation of the non-stationary real interest rate into three trends: the interest rate shock (including the monetary shock), inflation shock and output gap shock. According to empirical analyses using monthly US data after the Korean War, the long-run expectation of the non-stationary real interest rate contains an interest rate shock trend and the impulse of the federal fund target rate induces a significant response of the interest rate shock trend. However, the interest rate shock trend has a very small portion of the long-run expectation of the non-stationary real interest rate, which may explain why the monetary policy was not particularly effective in the economic recovery after the global financial crisis.     

The effects of inflation uncertainty on interest rates: a nonlinear approach

In this article, we investigate the effects of inflation variability on short-term interest rates within a nonlinear smooth transition regression framework. The test results suggest that only the conditional mean of the inflation is a nonlinear process whereas the conditional variance is time variant but linear. Using the square root of conditional variance as a proxy for inflation risk, we estimate Fisher equation augmented with inflation risk. Although the estimated Fisher equations suggest that inflation risk reduces short-term interest rates, we find that the effects of inflation risk on interest rates are regime-dependent. Particularly, we find that the negative effects of inflation variability on nominal rates are greater in low-inflationary regimes when compared to high-inflationary regimes. On the other hand, it is found that both inflation and inflation uncertainty raise the expected inflation effect.     

市场结构反转下之费雪效应研究

本文主要目的系考量结构改变风险下,对台湾地区费雪效果之再检验。模型的使用选择ZivotandAd-rews(1992)对ADF单根检定之修正模型(简称Z&A修正模型)。该模型的优点,在于允许结构断裂点(break-point)由资料特性内生(endogenizing)决定,而非研究者主观判断。过去文献指出,检验费雪效果之结果,与选用之时间序列资料之定态与否有高度相关,因此本研究使用修正后之Z&A修正模型,更严密的检视资料分析过程之前置检验阶段,将有助于后续分析获得较精确之推论结果。Z&A修正模型发现名目利率、通货膨涨率之水平项即为定态序列,在修正冲击(shock)对序列的长期影响后,两总体变数在长期间是相当稳定的。而其进一步向量自我回归分析结果,显示台湾地区之费雪效果在此一期间并无法被支持。     

Monetary deregulation and inverting the inverted fisher effect

We find evidence that deregulation allowing interest payments on checkable deposits decreased (increased) the sensitivity of the real (nominal) rate of interest to expected inflation. Our results provide further confirmation of the Inverted Fisher Effect.     

Inflation and real short-term interest rates - A Kalman filter analysis of the term structure

This paper applies the Kalman filter technique to look at the relationship among real interest rates, inflation, and the term structure of interest rate under the expectations hypothesis. Using quarterly data from 1960:1 to 1991:1 for inflation, three month nominal short term interest rates and long term yields with maturities from one to five years, this paper finds that the expectations hypothesis of the term structure holds up well for the data under the assumptions of a time-varying premium and a random-walk real interest rate. In other words, a reconciliation of the expectations hypothesis with the data is attained by assuming time-varying term premium and non-stationary real interest rate.     

On some neglected implications of the Fisher effect

Following the lead of Fama [American Economic Review 65 (1975) 269–282] and of other influential articles, such as Mishkin [Journal of Monetary Economics 30 (1992) 195–215], it has become standard to interpret the Fisher effect as the ability of short-term interest rate to predict future inflation. However, in this article we demonstrate that by restricting to zero the instantaneous response of expected inflation to an interest rate shock, one can identify a disturbance that economic agents, according to the Fisherian framework, should evaluate as transitory. An important implication of this result is that short-term nominal interest rates cannot be interpreted as predictors, at least not long-run predictors, of inflation. We illustrate this result with an empirical application to US postwar data.     

Money Demand in an EU Accession Country: A VECM Study of Croatia

The paper estimates the money demand in Croatia using monthly data from 1994 to 2002. A failure of the Fisher equation is found, and adjustment to the standard money‐demand function is made to include the inflation rate as well as the nominal interest rate. In a two‐equation cointegrated system, a stable money demand shows rapid convergence back to equilibrium after shocks. This function performs better than an alternative using the exchange rate instead of the inflation rate as in the ‘pass‐through’ literature on exchange rates. The results provide a basis for inflation rate forecasting and suggest the ability to use inflation targeting goals in transition countries during the EU accession process. Finding a stable money demand also limits the scope for central bank ‘inflation bias’.     

Unit roots and persistence in the nominal interest rate: a confirmatory analysis applied to the OECD

Abstract.  This paper investigates the stochastic properties of long-term and short-term nominal interest rates for the OECD over the post-war era. For that purpose, we employ univariate unit root tests as well as panel unit root and stationarity tests that explicitly allow for cross-sectional dependence. Overall, we find overwhelming evidence that the nominal interest rate contains a unit root, which may be driven by a stochastic common factor. The computation of half-lives through impulse-response functions also points to a high degree of persistence. This has important implications for the cointegration analysis of the Fisher equation, the uncovered interest parity, and the term structure.     

Monetary Policy, Nominal Interest Rates, and Long–Horizon Inflation Uncertainty

Empirical evidence presented in this paper shows that the predictability of inflation at long horizons varies considerably across countries. Both simple theory and empirical evidence suggest that the crucial factor is the extent to which systematic monetary policy succeeds in preventing a unit root in inflation. The mechanism by which it does this appears however to be complicated by strong empirical evidence that nominal as well as real interest rates have real effects, which implies that monetary policy need not be so vigorous in reactions to inflation. This helps to explain why inflation rates in the US and (especially) Germany have been relatively predictable, despite monetary policy rules which appear to have been barely stabilising. The paper also presents tentative evidence that the power of nominal interest rate effects is inversely related to long–horizon inflation uncertainty, and hence ultimately uncertainty about monetary policy.     

Optimal Monetary Policy

Optimal monetary policy maximizes the welfare of a representative agent, given frictions in the economic environment. Constructing a model with two sets of frictions—costly price adjustment by imperfectly competitive firms and costly exchange of wealth for goods—we find optimal monetary policy is governed by two familiar principles. First, the average level of the nominal interest rate should be sufficiently low, as suggested by Milton Friedman, that there should be deflation on average. Yet, the Keynesian frictions imply that the optimal nominal interest rate is positive. Second, as various shocks occur to the real and monetary sectors, the price level should be largely stabilized, as suggested by Irving Fisher, albeit around a deflationary trend path. Since expected inflation is roughly constant through time, the nominal interest rate must therefore vary with the Fisherian determinants of the real interest rate. Although the monetary authority has substantial leverage over real activity in our model economy, it chooses real allocations that closely resemble those which would occur if prices were flexible. In our benchmark model, there is some tendency for the monetary authority to smooth nominal and real interest rates.     

Inflationary expectations and monetary policy: evidence from Bangladesh

This article first estimates inflationary expectations using a Blanchard–Quah VAR model by decomposing the nominal interest rate into expected inflation and the ex ante real interest rate. Then I utilize this expected inflation along with other macroeconomic variables as inputs to the monetary policy function in a recursive VAR model to identify exogenous policy shocks. To calculate inflationary expectations, I assume that ex ante real interest rate shocks do not have a long-run effect on the nominal interest rate. This article finds that the public expects lower inflation for the future during periods of high inflation. Estimated results from the recursive VAR suggest that a contractionary policy shock increases the real interest rate, appreciates domestic currency, and lowers inflationary expectations and industrial output. However, I find a lagged policy response from Bangladesh Bank to higher inflationary expectations.     

Neo‐Fisherism and inflation control

According to conventional central banking wisdom, an inflation‐targeting central bank should increase (decrease) its nominal interest rate target when inflation is above (below) its target. According to neo‐Fisherites, conventional central bankers have the sign wrong. Essentially all mainstream macroeconomic models tell us that increases in nominal interest rates increase inflation—in the short run and in the long run. This paper reviews neo‐Fisherian theory and evidence and addresses issues relating to inflation control in low real interest rate environments.