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.     

Evidence on purchasing power parity from univariate models: the case of smooth transition trend‐stationarity

Recent research has found that trend‐break unit root tests derived from univariate linear models do not support the hypothesis of long‐run purchasing power parity (PPP) for US dollar real exchange rates. In this paper univariate smooth transition models are utilized to develop unit root tests that allow under the alternative hypothesis for stationarity around a gradually changing deterministic trend function. These tests reveal statistically significant evidence against the null hypothesis of a unit root for the real exchange rates of a number of countries against the US dollar. However, restrictions consistent with long‐run PPP are rejected for some of the countries for which a rejection of the unit root hypothesis is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

Nonlinear adjustment,purchasing power parity and the role of nominal exchange rates and prices

Although the literature on purchasing power parity (PPP) is rich in controversy, the relative contribution of prices and nominal exchange rates to real exchange rate movements which restore PPP disequilibria has rarely been put under any close scrutiny. This paper as a first step applies a cointegrated VAR framework to test for stationary real exchange rates and linear adjustments in prices and nominal exchange rates. As a second step, ESTR error correction models are fitted to test whether nonlinear error correctional behaviour characterizes the data. The results clearly indicate that the nominal exchange rate is responsible for the nonlinear mean reverting behaviour in real exchange rates and also mainly drives overall adjustment. Applying dynamic stochastic simulations based on the estimated models, this study also confirms recent results that the half-life times of real exchange rate shocks are significantly smaller than the consensus benchmark of 3–5 years.     

The Yen Real Exchange Rate may be Stationary after all: Evidence from Non‐linear Unit‐root Tests*

The empirical literature that tests for purchasing power parity (PPP) by focusing on the stationarity of real exchange rates has so far provided, at best, mixed results. The behaviour of the yen real exchange rate has most stubbornly challenged the PPP hypothesis and deepened this puzzle. This paper contributes to this discussion by providing new evidence on the stationarity of bilateral yen real exchange rates. We employ a non‐linear version of the augmented Dickey–Fuller test, based on an exponentially smooth‐transition autoregressive model (ESTAR) that enhances the power of the tests against mean‐reverting non‐linear alternative hypotheses. Our results suggest that the bilateral yen real exchange rates against the other G7 and Asian currencies were mean reverting during the post‐Bretton Woods era. Thus, the real yen behaviour may not be so different after all but simply perceived to be so because of the use of a restrictive alternative hypothesis in previous tests.     

What is behind the real appreciation of the accession countries’ currencies?: An investigation of the PPI-based real exchange rate

In the paper, we calculate real equilibrium exchange rates (EER) for EU accession countries and compare these with the actual exchange rate movements since the mid-1990s. The real equilibrium exchange rates are derived from models of macroeconomic balance and tested for econometrically. It is found that productivity increases can be regarded as one source of the observed PPI-based real appreciation of the accession countries’ currencies. These productivity gains experienced in the process of economic catch-up imply an increased capacity to produce high-quality export goods and are a key driving force of exports. To a large extent real appreciation can, therefore, be viewed as an equilibrium phenomenon.     

Testing the random walk hypothesis for real exchange rates

This paper tests the random walk hypothesis for the log-differenced monthly US real exchange rates versus some major currencies. The tests we use are variance ratio test, Durlauf's (1991) spectral domain tests and Andrews and Ploberger's ( 1996) optimal tests. The variance ratio test is calculated by using Andrews' (1991) optimal data-dependent methods. Finite sample properties of these tests are also reported. Because the results of applying these tests to the real exchange rates are occasionally inconsistent, tests to synthesize these test results are proposed and applied to the real exchange rates. These tests have often been used in meta-analysis, but have not previously been used to synthesize different test results. Simulation results for these tests are also reported. For the real exchange rate data from the post-Bretton Woods period, these tests reject the null only for the Swiss franc. But when longer-horizon data are used, there is more evidence of serial correlations in the log-differenced real exchange rates. Copyright © 1999 John Wiley & Sons, Ltd.     

Equilibrium Exchange Rates in Transition Economies: Taking Stock of the Issues*

Abstract. In this paper, we present an overview of a number of issues relating to the equilibrium exchange rates of transition economies of the former soviet bloc. In particular, we present a critical overview of the various methods available for calculating equilibrium exchange rates and discuss how useful they are likely to be for the transition economies. Amongst our findings is the result that the trend appreciation usually observed for the exchange rates of these economies is affected by factors other than the usual Balassa–Samuelson effect, such as the behaviour of the real exchange rate of the open sector and regulated prices. We then consider three main sources of uncertainty relating to the implementation of an equilibrium exchange rate model, namely: differences in the theoretical underpinnings, differences in the econometric estimation techniques, and differences relating to the time‐series and cross‐sectional dimensions of the data. The ensuing three‐dimensional space of real misalignments is probably a useful tool in determining the direction of a possible misalignment rather than its precise size.     

Oil prices and exchange rates in oil-exporting countries: evidence from TAR and M-TAR models

The paper studies the long-run relation and short-run dynamics between real oil prices and real exchange rates in a sample of 13 oil-exporting countries. The purpose of the study is to examine the possibility of Dutch disease in these countries. Tests of cointegration using threshold and momentum-threshold autoregressive (TAR and M-TAR) models suggest the possibility of the disease in 3-out-of 13 countries??Bolivia, Mexico and Norway. For these countries, we also find that (a) oil prices have a long-run effect on the exchange rates; and (b) exchange rates adjust faster to positive deviations from the equilibrium; and (c) there is no evidence of short-run causality between real exchange rates and real oil prices in either direction. Over all, these findings suggest a weak link between oil prices and real exchange rates and thus limited evidence in favor of the Dutch disease.     

Structural breaks and GARCH models of exchange rate volatility

We investigate the empirical relevance of structural breaks for GARCH models of exchange rate volatility using both in‐sample and out‐of‐sample tests. We find significant evidence of structural breaks in the unconditional variance of seven of eight US dollar exchange rate return series over the 1980–2005 period—implying unstable GARCH processes for these exchange rates—and GARCH(1,1) parameter estimates often vary substantially across the subsamples defined by the structural breaks. We also find that it almost always pays to allow for structural breaks when forecasting exchange rate return volatility in real time. Combining forecasts from different models that accommodate structural breaks in volatility in various ways appears to offer a reliable method for improving volatility forecast accuracy given the uncertainty surrounding the timing and size of the structural breaks. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

On the Empirical Failure of Purchasing Power Parity Tests

Empirical research on the validity of the purchasing power parity (PPP) condition is generally based on real exchange rates built using the consumer price index (CPI), but fails to provide clear support to PPP. In this paper we show theoretically that, even if the law of one price (LOP) holds for traded goods, CPI‐based real exchange rates are not mean reverting, and are neither stationary nor integrated. Therefore, both unit root and stationarity tests should reject their null. Our theoretical results are validated both by simulations and an empirical application. Copyright © 2014 John Wiley & Sons, Ltd.     

Efficient tests of long‐run causation in trivariate VAR processes with a rolling window study of the money–income relationship

This paper develops a simple sequential multiple‐horizon non‐causation test strategy for trivariate VAR models (with one auxiliary variable). We apply the test strategy to a rolling window study of money supply and real income, with the price of oil, the unemployment rate and the spread between the Treasury bill and commercial paper rates as auxiliary processes. Ours is the first study to control simultaneously for common stochastic trends, sensitivity of test statistics to the chosen sample period, null hypothesis over‐rejection, sequential test size bounds, and the possibility of causal delays. Evidence suggests highly significant direct or indirect causality from M1 to real income, in particular through the unemployment rate and M2 once we control for cointegration. Copyright © 2007 John Wiley & Sons, Ltd.     

Purchasing Power Parity and the Taylor Rule

It is well known that there is a large degree of uncertainty around Rogoff's consensus half‐life of the real exchange rate. To obtain a more efficient estimator, we develop a system method that combines the Taylor rule and a standard exchange rate model to estimate half‐lives. Further, we propose a median unbiased estimator for the system method based on the generalized method of moments with non‐parametric grid bootstrap confidence intervals. Applying the method to real exchange rates of 18 developed countries against the US dollar, we find that most half‐life estimates from the single equation method fall in the range of 3–5 years, with wide confidence intervals that extend to positive infinity. In contrast, the system method yields median‐unbiased estimates that are typically shorter than 1 year, with much sharper 95% confidence intervals. Our Monte Carlo simulation results are consistent with an interpretation of these results that the true half‐lives are short but long half‐life estimates from single‐equation methods are caused by the high degree of uncertainty of these methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates

It has been documented that random walk outperforms most economic structural and time series models in out-of-sample forecasts of the conditional mean dynamics of exchange rates. In this paper, we study whether random walk has similar dominance in out-of-sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance. We first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out-of-sample setting and provide simulation evidence on its finite sample performance. Then we conduct a comprehensive empirical analysis on the out-of-sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates—Euro/Dollar and Yen/Dollar. It is found that some sophisticated time series models that capture time-varying higher order conditional moments, such as Markov regime-switching models, have better density forecasts for exchange rates than random walk or modified random walk with GARCH and Student-t innovations. This finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out-of-sample applications involving the probability density.     

Nonlinear dynamics of interest rate and inflation

According to several empirical studies US inflation and nominal interest rates as well as the real interest rate can be described as unit root processes. These results imply that nominal interest rates and expected inflation do not move one‐for‐one in the long run, which is incongruent with theoretical models. In this paper we introduce a new nonlinear bivariate mixture autoregressive model that seems to fit quarterly US data (1953 : II–2004 : IV) reasonably well. It is found that the three‐month Treasury bill rate and inflation share a common nonlinear component that explains a large part of their persistence. The real interest rate is devoid of this component, indicating one‐for‐one movement of the nominal interest rate and inflation in the long run and, hence, stationarity of the real interest rate. Copyright © 2006 John Wiley & Sons, Ltd.     

Nonlinear effects of exchange rate volatility on the volume of bilateral exports

In this paper, we investigate empirically the impact of exchange rate volatility on real international trade flows utilizing a 13‐country data set of monthly bilateral real exports for 1980–1998. We compute one‐month‐ahead exchange rate volatility from the intra‐monthly variations in the exchange rate to better quantify this latent variable. We find that the effect of exchange rate volatility on trade flows is nonlinear, depending on its interaction with the importing country's volatility of economic activity, and that it varies considerably over the set of country pairs considered. Copyright © 2003 John Wiley & Sons, Ltd.     

A forecast comparison of volatility models: does anything beat a GARCH(1,1)?

We compare 330 ARCH‐type models in terms of their ability to describe the conditional variance. The models are compared out‐of‐sample using DM–$ exchange rate data and IBM return data, where the latter is based on a new data set of realized variance. We find no evidence that a GARCH(1,1) is outperformed by more sophisticated models in our analysis of exchange rates, whereas the GARCH(1,1) is clearly inferior to models that can accommodate a leverage effect in our analysis of IBM returns. The models are compared with the test for superior predictive ability (SPA) and the reality check for data snooping (RC). Our empirical results show that the RC lacks power to an extent that makes it unable to distinguish ‘good’ and ‘bad’ models in our analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

HOW PUZZLING IS THE PPP PUZZLE? AN ALTERNATIVE HALF‐LIFE MEASURE OF CONVERGENCE TO PPP

Evidence of lengthy half‐lives for real exchange rates in the presence of a high degree of exchange rate volatility has been considered as one of the most puzzling empirical regularities in international macroeconomics. This paper suggests that the measure of half‐life used in the literature might be problematic and proposes alternative measures with desirable properties. Their focus on the cumulative effects of the shocks distinguishes them from the measures used in the literature. An empirical analysis of bilateral US dollar real exchange rates employing the alternative half‐life measure produces results consistent with theory and indicates that the PPP puzzle is less pronounced than initially thought. Copyright © 2012 John Wiley & Sons, Ltd.     

Normal mixture GARCH(1,1): applications to exchange rate modelling

Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling exchange rates, generalized two‐component normal mixture GARCH(1,1) models perform better than those with three or more components, and better than symmetric and skewed Student's t‐GARCH models. In addition to the extensive empirical results based on simulation and on historical data on three US dollar foreign exchange rates (British pound, euro and Japanese yen), we derive: expressions for the conditional and unconditional moments of all models; parameter conditions to ensure that the second and fourth conditional and unconditional moments are positive and finite; and analytic derivatives for the maximum likelihood estimation of the model parameters and standard errors of the estimates. Copyright © 2006 John Wiley & Sons, Ltd.     

FACTOR MODELS AND TIME‐VARYING PARAMETER FRAMEWORK FOR FORECASTING EXCHANGE RATES AND INFLATION: A SURVEY

A survey of models used for forecasting exchange rates and inflation reveals that the factor‐based and time‐varying parameter or state space models generate superior forecasts relative to all other models. This survey also finds that models based on Taylor rule and portfolio balance theory have moderate predictive power for forecasting exchange rates. The evidence on the use of Bayesian Model Averaging approach in forecasting exchange rates reveals limited predictive power, but strong support for forecasting inflation. Overall, the evidence overwhelmingly points to the context of the forecasts, relevance of the historical data, data transformation, choice of the benchmark, selected time horizons, sample period and forecast evaluation methods as the crucial elements in selecting forecasting models for exchange rate and inflation.