It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately-- forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance, such as: Are expectations rational? (e.g., Keane and Runkle, 1990; Bonham and Cohen, 1995) Are financial markets efficient? (e.g., Fama, 1970, 1991) Do macroeconomic shocks cause agents to revise their forecasts at all horizons, or just at short- and medium-term horizons? (e.g., Campbell and Mankiw, 1987; Cochrane, 1988) Are observed asset returns "too volatile"? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)

We examine whether the U.S. rate of price inflation has become harder to forecast and, to the extent that it has, what changes in the inflation process have made it so. The main finding is that the univariate inflation process is well described by an unobserved component trend-cycle model with stochastic volatility or, equivalently, an integrated moving average process with time-varying parameters. This model explains a variety of recent univariate inflation forecasting puzzles and begins to explain some multivariate inflation forecasting puzzles as well. Key words: Phillips curve, trend-cycle model, moving average, great moderation JEL codes: C53, E37 *We thank Jonas Fisher for bringing several of the issues discussed in this paper to our attention in a 1999 conversation, Luca Benati for (more recent) helpful suggestions, and Matthew Shapiro, Robert Gordon, and two anonymous referees for helpful comments on an earlier draft. Replications files for the results in this paper can be downloaded from

Interest rates on long-term bonds are widely viewed as important for many economic decisions, notably business plant and equipment investment expenditures and household purchases of homes and automobiles. Consequently, macroeconomists have extensively studied the term structure of interest rates. For monetary policy analysis this is a crucial topic, as it concerns the link between short-term interest rates, which are heavily affected by central bank decisions, and long-term rates. The dominant explanation of the relationship between short- and longterm interest rates is the expectations theory, which suggests that long rates are entirely governed by the expected future path of short-term interest rates. While this theory has strong implications that have been rejected in many studies, it nonetheless seems to contain important elements of truth. Therefore, many central bankers and other practitioners of monetary policy continue to apply it as an admittedly imperfect yet useful benchmark. In this article, we work to quantify both the dimensions along which the expectations theory succeeds in describing the link between expectations and the term structure and those along which it does not, thus providing a better sense of the utility of this benchmark. Following Sargent (1979) and Campbell and Shiller (1987), we focus on linear versions of the expectations theory and linear forecasting models of The authors would like to thank Michael Dotsey, Huberto Ennis, Pierre-Daniel Sarte, and Mark Watson for helpful comments. The views expressed in this article are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Richmond or

Forward interest rates have become popular indicators of ination expectations. The usefulness of this indicator depends on the relative volatilty and the correlation of ination expectations and expected real interest rates. This paper studies U.S. and U.K. data, using a range of dierent tools and data sets. The forward rate rule perfoms reasonably well, in spite of signicant movements in the expected real interest rate. The reason is that the \noise" that movements in the expected real interest rate add to the ination expectations is balanced by a tendency for expected real interest rates and ination expectations to move in opposite directions. Keywords: Ination expectations, real interest rates, forward rates. JEL Classication Numbers: E31, E43, E44, and G12. 1Introduction It has long been recognized that the yield curve contains information about ination expectations. 1 Recently, Svensson [32] discussed the possibility of using the forward rate as an estimator of ination ...

this paper we have presented some additional empirical evidence on the hypothesis formulated by Mishkin (1990) about the term structure as an optimal predictor of the inflation path, and the other hypothesis found in the literature concerning the unbiasedness of interest di#erentials as predictors of future inflation di#erentials. Both issues are of extreme relevance to policy-makers, in particular to the monetary authorities, as the validity of the first hypothesis would enable them to use the maturity structure as a guide for monetary policy, and only if the second was rejected would it be possible to a#ect the level of economic activity through the real interest rate.

The believed that short term interest rates response positively to changes in price level, commonly known as the Fisher effect, are being investigated extensively by financial researchers. Over the long run the hypothesis implies the presence of equilibrium relationship between interest rates and inflation. Early evidence favouring the Fisher effect are found not to be consistent in certain period of time and countries. We re-examine the presence of the effect in the G7 countries. Our focus of analysis is to test the robustness of results supporting the long run Fisher effect derived based on cointegration analysis that relies on standard ARIMA representations. We argue on the inadequacy of the conventional unit root tests (Augmented Dickey-Fuller and Phillips-Perron) which are not capable of identifying a long memory process. We employ the ARFIMA (Autoregressive Fractionally Integrated Moving Average) model which generalized standard ARIMA by allowing fractional differencing. It is shown that using the conventional unit root tests, cointegration between interest rates and inflation as implied by the Fisher effect is supported. However, the evidence is not robust to the specification of the ARIMA process. Based on the generalized ARFIMA estimation, cointegration hypothesis between short term rates and inflation cannot be supported. Interest rates in the G7 countries are not link to inflation rate in the long run. The puzzling evidence rejecting the Fisher effect remains as the proposed relationship between interest rates and inflation is not real in theses countries. 2 Is the Fisher Effect for Real?: Testing the Robustness of Long Run Fisher Effect in

We would like to thank the seminar participants at the Bank of England (Monetary Policy Group) for their useful comments on an earlier version of this paper. 1 Stock returns and Inflation: Some New Evidence Using aggregate and industry-wise monthly UK data over a period of 44 years we examine the long run relationship between stock return index (St) and retail price index (Pt) in a VAR framework. Univariate tests confirm Pt as I(2); nevertheless pairs of St and Pt are co-integrated and share common I(1) trend. There is no evidence of shared I(2) trend. We find evidence of shifts in the co-integrating ranks and parameters, and accounting for these shifts improved estimates ’ precision. The long run price elasticity of return index is consistently above unity, a finding that stands in sharp contrast to the existing ones. Overall our results suggest that tax-paying stock investors are fully insulated against inflation in the long run. 2 Stock Returns and Inflation: Some New Evidence I.

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This paper examines the implications of inflation persistence for the inverted Fisher hypothesis that nominal interest rates do not adjust to inflation because of a high degree of substitutability between money and bonds. It is emphasized that the substitutability between nominal assets and capital renders the hypothesis inconsistent with the data when inflation persistence is high. Using a switching regression model, the analysis allows the reflection of inflation in interest rates to vary according to the degree of inflation persistence or forecastability. The hypothesis is supported by U.S. data only when inflation forecastability is below a certain threshold. [JEL C51, E43] MV = PY

The views expressed are those of the authors and do not necessarily represent the views of the Reserve Bank of Australia. We would like to thank members of Economic Group at the Reserve Bank of Australia for helpful comments. Naturally, This paper analyses the Fisher effect in Australia. Initial testing indicates that both interest rates and inflation contain unit roots. Furthermore, there are indications that the variables have non-standard error processes. To overcome problems associated with this and derive the correct small sample distributions of test statistics we make use of Monte Carlo simulations. These tests indicate that while a long-run Fisher effect seems to exist there is no evidence of a short-run Fisher effect. This suggests that, while short-run changes in interest rates reflect changes in monetary policy, longer-run levels indicate inflationary expectations. Thus, the longer-run level of interest rates should not be used to characterise the stance of monetary policy.