Identifying Changes in Mean,Seasonality, Persistence and Volatility for G7 and Euro Area Inflation*

We propose an iterative decomposition that tests and accounts for multiple structural breaks in the mean, seasonality, dynamics and conditional volatility, while also accounting for outliers. Considering each component separately within each iteration leads to greater flexibility compared with joint procedures. Monte Carlo analysis shows the procedure performs well. Applied to monthly CPI inflation in G7 countries and the Euro area, we uncover mean and seasonality breaks for all countries and, allowing for these, changes in persistence are generally also indicated. Further, volatility reductions are widespread in the early to mid 1980s, with some countries exhibiting increases from 1999 onwards.     

New Methods for Forecasting Inflation,Applied to the US*

Models for the 12‐month‐ahead US rate of inflation, measured by the chain‐weighted consumer expenditure deflator, are estimated for 1974–98 and subsequent pseudo out‐of‐sample forecasting performance is examined. Alternative forecasting approaches for different information sets are compared with benchmark univariate autoregressive models, and substantial out‐performance is demonstrated including against Stock and Watson's unobserved components‐stochastic volatility model. Three key ingredients to the out‐performance are: including equilibrium correction component terms in relative prices; introducing nonlinearities to proxy state‐dependence in the inflation process and replacing the information criterion, commonly used in VARs to select lag length, with a ‘parsimonious longer lags’ parameterization. Forecast pooling or averaging also improves forecast performance.     

Maximum Eigenvalue Test for Seasonal Cointegrating Ranks*

The maximum eigenvalue (ME) test for seasonal cointegrating ranks is presented using the approach of Cubadda [Oxford Bulletin of Economics and Statistics (2001), Vol. 63, pp. 497–511], which is computationally more efficient than that of Johansen and Schaumburg [Journal of Econometrics (1999), Vol. 88, pp. 301–339]. The asymptotic distributions of the ME test statistics are obtained for several cases that depend on the nature of deterministic terms. Monte Carlo experiments are conducted to evaluate the relative performances of the proposed ME test and the trace test, and we illustrate these tests using a monthly time series.     

Testing for Fractional Integration Versus Short Memory with Structural Breaks*

Although it is commonly accepted that most macroeconomic variables are non‐stationary, it is often difficult to identify the source of the non‐stationarity. Integrated processes and short‐memory models with trending components, possibly affected by structural breaks, imply similar features in the data and, accordingly, are hard to distinguish. The goal of this article is to extend the classical testing framework of I(1) versus I(0) + trends and/or breaks by considering a more general class of models under the null hypothesis: fractionally integrated (FI) processes. The asymptotic properties of the proposed tests are derived and it is shown that they are very well‐behaved in finite samples. An illustration using US inflation data is also provided.     

Weak Identification of Forward‐looking Models in Monetary Economics*

Recently, single‐equation estimation by the generalized method of moments (GMM) has become popular in the monetary economics literature, for estimating forward‐looking models with rational expectations. We discuss a method for analysing the empirical identification of such models that exploits their dynamic structure and the assumption of rational expectations. This allows us to judge the reliability of the resulting GMM estimation and inference and reveals the potential sources of weak identification. With reference to the New Keynesian Phillips curve of Galí and Gertler [Journal of Monetary Economics (1999) Vol. 44, 195] and the forward‐looking Taylor rules of Clarida, Galí and Gertler [Quarterly Journal of Economics (2000) Vol. 115, 147], we demonstrate that the usual ‘weak instruments’ problem can arise naturally, when the predictable variation in inflation is small relative to unpredictable future shocks (news). Hence, we conclude that those models are less reliably estimated over periods when inflation has been under effective policy control.     

Contemporaneous threshold autoregressive models: Estimation,testing and forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta [1998. Modelling economic relationships with smooth transition regressions. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York, pp. 507–552.], in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finite-sample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen [1992. The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP. Journal of Applied Econometrics 7, S61–S82.] procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed.     

Measuring Inflation Expectations Using Interval‐Coded Data*

To quantify qualitative survey data, the Carlson–Parkin method assumes normality, a time‐invariant symmetric indifference interval, and long‐run unbiased expectations. These assumptions are unnecessary for interval‐coded data. In April 2004, the Monthly Consumer Confidence Survey in Japan started to ask households about their price expectations a year ahead in seven categories with partially known boundaries. Thus one can identify up to six parameters including an indifference interval each month. This paper compares normal, skew normal (SN), skew exponential power (SEP), and skew t (St) distributions, and finds that an St distribution fits the data well. The results help us to better understand the dynamics of heterogeneous expectations.     

Further Evidence on the Statistical Properties of Real GNP*

The well‐known lack of power of unit‐root tests has often been attributed to the short length of macroeconomic variables and also to data‐generating processes (DGPs) departing from the I(1)–I(0) models. This paper shows that by using long spans of annual real gross national product (GNP) and GNP per capita (133 years), high power can be achieved, leading to the rejection of both the unit‐root and the trend‐stationary hypothesis. More flexible representations are then considered, namely, processes containing structural breaks (SB) and fractional orders of integration (FI). Economic justification for the presence of these features in GNP is provided. It is shown that both FI and SB formulations are in general preferred to the autoregressive integrated moving average (ARIMA) [I(1) or I(0)] formulations. As a novelty in this literature, new techniques are applied to discriminate between FI and SB. It turns out that the FI specification is preferred, implying that GNP and GNP per capita are non‐stationary, highly persistent but mean‐reverting series. Finally, it is shown that the results are robust when breaks in the deterministic component are allowed for in the FI model. Some macroeconomic implications of these findings are also discussed.     

Econometric Evaluation of the New Keynesian Phillips Curve*

We give an appraisal of the New Keynesian Phillips curve (NPCM) as an empirical model of European inflation. The favourable evidence for NPCMs on euro‐area data reported in earlier studies is shown to depend on specific choices made about estimation methodology. The NPCM can be re‐interpreted as a highly restricted equilibrium correction model. We also report the outcome of tests based on variable addition and encompassing of existing models. The results show that economists should not accept the NPCM too readily.     

Further Evidence on PPP Adjustment Speeds: the Case of Effective Real Exchange Rates and the EMS*

Two different approaches intend to resolve the ‘puzzling’ slow convergence to purchasing power parity (PPP) reported in the literature [see Rogoff (1996) , Journal of Economic Literature, Vol. 34.] On the one hand, there are models that consider a non‐linear adjustment of real exchange rate to PPP induced by transaction costs. Such costs imply the presence of a certain transaction band where adjustment is too costly to be undertaken. On the other hand, there are models that relax the ‘classical’ PPP assumption of constant equilibrium real exchange rates. A prominent theory put together by Balassa (1964, Journal of Political Economy, Vol. 72) and Samuelson (1964 Review of Economics and Statistics, Vol. 46) , the BS effect, suggests that a non‐constant real exchange rate equilibrium is induced by different productivity growth rates between countries. This paper reconciles those two approaches by considering an exponential smooth transition‐in‐deviation non‐linear adjustment mechanism towards non‐constant equilibrium real exchange rates within the EMS (European Monetary System) and effective rates. The equilibrium is proxied, in a theoretically appealing manner, using deterministic trends and the relative price of non‐tradables to proxy for BS effects. The empirical results provide further support for the hypothesis that real exchange rates are well described by symmetric, nonlinear processes. Furthermore, the half‐life of shocks in such models is found to be dramatically shorter than that obtained in linear models.     

A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks*

We develop a unit‐root test based on a simple variant of Gallant's (1981) flexible Fourier form. The test relies on the fact that a series with several smooth structural breaks can often be approximated using the low frequency components of a Fourier expansion. Hence, it is possible to test for a unit root without having to model the precise form of the break. Our unit‐root test employing Fourier approximation has good size and power for the types of breaks often used in economic analysis. The appropriate use of the test is illustrated using several interest rate spreads.     

Convergence of Prices and Rates of Inflation*

We consider how unit‐root and stationarity tests can be used to study the convergence of prices and rates of inflation. We show how the joint use of these tests in levels and first differences allows the researcher to distinguish between series that are converging and series that have already converged, and we set out a strategy to establish whether convergence occurs in relative prices or just in rates of inflation. Special attention is paid to the issue of whether a mean should be extracted in carrying out tests in first differences and whether there is an advantage to adopting a (Dickey–Fuller) unit‐root test based on deviations from the last observation. The asymptotic distribution of this last test statistic is given and Monte Carlo simulation experiments show that the test yields considerable power gains for highly persistent autoregressive processes with ‘relatively large’ initial conditions. The tests are applied to the monthly series of the consumer price index in the Italian regional capitals over the period 1970–2003.     

Observed Inflation Forecasts and the New Keynesian Phillips Curve*

This paper investigates the empirical success of the New Keynesian Phillips Curve (NKPC) in explaining US inflation when observed measures of inflation expectations are used in conjunction with the output gap. The paper contributes to the literature by addressing the important problem of serial correlation in the stylized NKPC and developing an extended model to account for this serial correlation. Contrary to recent results indicating no role for the output gap, we find it to be a statistically significant driving variable for inflation, with this finding robust to whether the inflation expectations series used relates to individual consumers, professional forecasters or the US Fed.     

Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment*

We introduce a general class of periodic unobserved component (UC) time series models with stochastic trend and seasonal components and with a novel periodic stochastic cycle component. The general state space formulation of the periodic model allows for exact maximum likelihood estimation, signal extraction and forecasting. The consequences for model‐based seasonal adjustment are discussed. The new periodic model is applied to postwar monthly US unemployment series from which we identify a significant periodic stochastic cycle. A detailed periodic analysis is presented including a comparison between the performances of periodic and non‐periodic UC models.     

The Impact of Short‐ and Long‐run Exchange Rate Uncertainty on Investment: A Panel Study of Industrial Countries*

We examine the relationship between aggregate investment and exchange rate uncertainty in the G7, using panel estimation and decomposition of volatility derived from the components generalized autoregressive conditionally heteroscedastic (GARCH) model. Our dynamic panel approach takes account of potential cross‐sectional heterogeneity, which can lead to bias in estimation. We find that for a poolable subsample of European countries, it is the transitory and not the permanent component of volatility which adversely affects investment. To the extent that short‐run uncertainty in the CGARCH model characterizes higher frequency shocks generated by volatile short‐term capital flows, these are most deleterious for investment.     

Local Asymptotic Power of Breitung's Test*

In this article, we derive the local asymptotic power function of the unit root test proposed by Breitung [Journal of Econometrics (2002) Vol. 108, pp. 343–363]. Breitung's test is a non‐parametric test and is free of nuisance parameters. We compare the local power curve of the Breitungs’ test with that of the Dickey–Fuller test. This comparison is in fact a quantification of the loss of power that one has to accept when applying a non‐parametric test.     

The Relative Importance of Symmetric and Asymmetric Shocks: The Case of United Kingdom and Euro Area*

We show how a simple model with sign restrictions can be used to identify symmetric and asymmetric supply, demand and monetary policy shocks in an estimated two‐country structural VAR for the UK and Euro area. The results can be used to deal with several issues that are relevant in the optimal currency area literature. We find an important role for symmetric shocks in explaining the variability of the business cycle in both economies. However, the relative importance of asymmetric shocks, being around 20% in the long run, cannot be ignored. Moreover, when we estimate the model for the UK and US, the degree of business cycle synchronization seems to be higher. Finally, we confirm existing evidence of the exchange rate being an independent source of shocks in the economy.     

Exchange Rates and Fundamentals: Evidence from Long‐Horizon Regression Tests*

This article considers the long‐run relationship between nominal exchange rates and fundamentals from a different perspective. We apply a long‐horizon regression approach proposed by Fisher and Seater (1993) and find evidence supporting the explanatory power of exchange rate models. In particular, the Taylor‐rule model outperforms other conventional models. We then use the inverse power function (IPF) proposed by Andrews (1989) to investigate the power of the Fisher–Seater test. The IPF analysis provides additional evidence supporting exchange rate models.     

Testing the Null of Cointegration with Structural Breaks*

We propose a Lagrange Multiplier‐type statistic to test the null hypothesis of cointegration allowing for the possibility of a structural break, in both the deterministic and the cointegration vectors. Our proposal focuses on the presence of endogenous regressors. The test complements the usual non‐cointegration tests so as to obtain stronger evidence of cointegration. We consider the cases of known and unknown dates of the break. In the latter case, we show that minimizing the Sum of Squared Residuals results in a super‐consistent estimator of the break fraction. Finally, the behaviour of the tests is studied through Monte Carlo experiments.     

HEGY Tests in the Presence of Moving Averages*

We analyze the asymptotic distributions associated with the seasonal unit root tests of Hylleberg et al. (1990) for quarterly data when the innovations follow a moving average process. Although both the t‐ and F‐type tests suffer from scale and shift effects compared with the presumed null distributions when a fixed order of autoregressive augmentation is applied, these effects disappear when the order of augmentation is sufficiently large. However, as found by Burridge and Taylor (2001) for the autoregressive case, individual t‐ratio tests at the semi‐annual frequency are not pivotal even with high orders of augmentation, although the corresponding joint F‐type statistic is pivotal. Monte Carlo simulations verify the importance of the order of augmentation for finite samples generated by seasonally integrated moving average processes.