Is the evidence for PPP reliable? A sustainability examination of the stationarity of real exchange rates

Some recent time series studies testing the stationarity of real exchange rates (RERs) produce conflicting results. Using nonlinear unit root tests and recursive analysis, this paper tests whether the evidence on the stationarity of RERs is sensitive to different numeraire currencies, different sample periods covering regional and global crises, and the inclusion of countries with different levels of economic or regional integration. The results indicate that evidence for a stationary RER could be substantially sensitive to sample period changes, but not so for the currencies of the countries involved in forming the euro area. We also find that financial crises have a notable impact on testing the stationarity of RERs, depending on the numeraire currency used. We discuss the policy implications of the findings.     

A century of purchasing power parity confirmed: The role of nonlinearity

Taylor (2002) claims that Purchasing Power Parity (PPP) has held over the 20th century based on strong evidence of stationary for century-long real exchange rates for 20 countries. Lopez et al. (2005), however, found much weaker evidence of PPP with alternative lag selection methods. We reevaluate Taylor’s claim by implementing a recently developed nonlinear unit root test by Park and Shintani (2005). We find strong evidence of nonlinear mean-reversion in real exchange rates that confirms Taylor’s claim. We also find a possible misspecification problem in using the ESTAR model that may not be detected with Taylor-approximation based tests.     

Local persistence and the PPP hypothesis

This paper examines the statistical properties of the bilateral real exchange rates of the U.S. vs. France, Germany, and the U.K. during the Post-Bretton-Woods period, and draws implications on the Purchasing Power Parity (PPP) hypothesis. Contrary to traditional studies that consider only unit root and stationary processes to describe the real exchange rate behavior, this paper considers an in-between process, the locally persistent process. The empirical results demonstrate the following two findings: (1) Locally persistent processes describe the real exchange rate movements better than unit root and stationary processes, which implies that PPP reversion occurs and PPP holds in the long-run. (2) The confidence intervals for half-life deviations from PPP under local persistence tend to be narrower than those obtained by assuming the ADF and the local-to-unity models.     

Getting PPP right: Identifying mean-reverting real exchange rates in panels

Recent advances in testing for the validity of Purchasing Power Parity (PPP) focus on the time series properties of real exchange rates in panel frameworks. One weakness of such tests, however, is that they fail to inform the researcher as to which cross-section units are stationary. As a consequence, a reservation for PPP analyses based on such tests is that a small number of real exchange rates in a given panel may drive the results. In this paper we examine the PPP hypothesis focusing on the stationarity of the real exchange rates in up to 25 OECD countries. We introduce a methodology that when applied to a set of established panel unit-root tests, allows the identification of the real exchange rates that are stationary. Our results reveal evidence of mean-reversion that is significantly stronger as compared to that obtained by the existing literature, strengthening the case for PPP.     

Common Stochastic Trends in a System of Exchange Rates

Univariate tests reveal strong evidence for the presence of a unit root in the univariate time-series representation for seven daily spot and forward exchange rate series. Furthermore, all seven spot and forward rates appear to be cointegrated; that is, the forward premiums are stationary, and one common unit root, or stochastic trend, is detectable in the multivariate time-series models for the seven spot and forward rates, respectively. This is consistent with the hypothesis that the seven exchange rates possess one long-run relationship and that the disequilibrium error around that relationship partly accounts for subsequent movements in the exchange rates.     

An examination of real interest rates in the United States, Canada, France, and Germany during the recent floating exchange rate period

This study reexamines the international linkage of ex-ante real interest rates using the theory of cointegrated processes. The univariate unit root tests suggest the existence of a nonstationary real interest rate in the United States, Canada, and (the former) West Germany. An ex-ante real interest rate is obtained by subtracting estimates of inflation from the nominal interest rate. The expected inflation rates are obtained by modeling changes in monthly CPI values as autoregressive moving average (ARMA) processes. A multivariate test for unit roots indicates that there are two cointegrating vectors, or one common stochastic trend, for the system of three nonstationary real interest rates. In addition, the log-likelihood ratio test fails to reject the null hypothesis that, in the long run, real interest rates in the United States are equal to those in Canada and West Germany.     

Further on nonlinearity,persistence, and integration properties of real exchange rates

Integration, nonlinearity, and persistence dynamics of several quarterly US-Dollar-denominated real exchange rates are investigated by using new unit root tests, simulated p-values for linearity tests, estimation of smooth transition autoregressive (STAR) models, and simulation of autocorrelation functions. This paper uses a simulation-based approach to study covariance stationarity and persistence dynamics of the estimated models. Findings in the paper provide evidence of nonlinear mean reversion for several series albeit with some persistence. Results also reveal considerable variation in the degree of persistence and timing of switches across extreme regimes in ESTAR models between Euro and non-Euro area currencies.     

Further Evidence on the Real Interest Rate Parity Hypothesis in Central and East European Countries: Unit Roots and Nonlinearities

This paper analyzes the empirical fulfillment of the real interest rate parity (RIRP) theory for a pool of central and east European countries. To do so, we apply the recently developed Ng and Perron (2001) unit root tests, which are corrected versions of existing unit root tests, and the Kapetanios et al. (2003) unit root test, which generalizes the alternative hypothesis to the globally stationary smooth transition autoregression model. We find evidence in favor of the empirical fulfillment of RIRP, particularly when taking into account the possibility of nonlinearities in the real interest rate differential.     

A cyclical model of exchange rate volatility

In this paper, we investigate the long run dynamics of the intraday range of the GBP/USD, JPY/USD and CHF/USD exchange rates. We use a non-parametric filter to extract the low frequency component of the intraday range, and model the cyclical deviation of the range from the long run trend as a stationary autoregressive process. We use the cyclical volatility model to generate out-of-sample forecasts of exchange rate volatility for horizons of up to 1 year under the assumption that the long run trend is fully persistent. As a benchmark, we compare the forecasts of the cyclical volatility model with those of the range-based EGARCH and FIEGARCH models of Brandt and Jones (2006). Not only does the cyclical volatility model provide a very substantial computational advantage over the EGARCH and FIEGARCH models, but it also offers an improvement in out-of-sample forecast performance.     

UNIT ROOT TESTING: A CRITIQUE FROM CHAOS THEORY

A counter-example from chaos theory is used to challenge the augmented Dickey-Fuller (ADF) test and common prewhitening techniques. The ADF test is applied to data constructed from a fully deterministic nonlinear (chaotic) process. The null hypothesis, that a unit root is present, cannot be rejected; “stationarity” is achieved by prewhitening. The largest Lyapunov exponent and the correlation dimension are estimated for the original and conditioned series in efforts to detect the nonlinearity and ascertain information regarding its specification. This is repeated in the presence of additive white noise. In no case is the procedure successful, nor is misspecification avoided. Along the way, the tests for nonlinearity provide evidence in support of the results of Nelson and Plosser (1982), that the removal of deterministic trends from time series that appear to be unit root processes can lead to spurious results.     

The behaviour of the real exchange rate: Evidence from regression quantiles

We test for mean reversion in real exchange rates using a recently developed unit root test for non-normal processes based on quantile autoregression inference in semi-parametric and non-parametric settings. The quantile regression approach allows us to directly capture the impact of different magnitudes of shocks that hit the real exchange rate, conditional on its past history, and can detect asymmetric, dynamic adjustment of the real exchange rate towards its long run equilibrium. It, therefore provides a detailed mapping of the real exchange rate behaviour, while being a robust alternative to previous unit root tests. The latter is confirmed by a simulation analysis comparing the power of the alternative tests. As concerns the real exchange rate, our results suggest that large shocks tend to induce strong mean reverting tendencies in the exchange rate, with half lives less than one year in the extreme quantiles. Mean reversion is faster when large shocks originate at points of large real exchange rate deviations from the long run equilibrium. However, in the absence of shocks no mean reversion is observed. Finally, we report asymmetries in the dynamic adjustment of the RER.     

The European Union currencies and the US dollar: from post-Bretton-Woods to the Euro

In this paper we study the evolution of the US dollar real exchange rate vis-à-vis the European Union currencies in the floating post-Bretton-Woods era, both before and after the birth of the Euro. In the first period we find that most of the persistence shown by this rate is due to the movements of the US dollar during the mid-1980s. Once these effects are isolated, we can conclude that the US dollar real exchange rate exhibits stationarity with those currencies that are closely linked to the German Mark. However, when we include the observations covering the period during which the Euro was created, we cannot reject the unit root null hypothesis for any currency.     

Equilibrium exchange rate determination and multiple structural changes

The large appreciation and depreciation of the US Dollar in the 1980s stimulated an important debate on the usefulness of unit root tests in the presence of structural breaks. In this paper, we propose a simple model to describe the evolution of the real exchange rate. We then propose a more general smooth transition (STR) function than has hitherto been employed, which is able to capture structural changes along the (long-run) equilibrium path, and show that this is consistent with our economic model. Our framework allows for a gradual adjustment between regimes and allows for under- and/or over-valued exchange rate adjustments. Using monthly and quarterly data for up to twenty OECD countries, we apply our methodology to investigate the univariate time series properties of CPI-based real exchange rates with both the U.S. Dollar and German Mark as the numeraire currencies. The empirical results show that, for more than half of the quarterly series, the evidence in favor of the stationarity of the real exchange rate was clearer in the sub-sample period post-1980.     

Cointegration Analysis of Audit Pricing Model: A Panel Unit Root Test Approach

In this study, we provide evidence on the stationarity of real audit fees and the major explanatory variables frequently used in the audit pricing models from a pooled data set, using panel unit root tests developed by Im et al. (1997). The panel unit root test supports the hypothesis of non‐stationarity of audit fees and their major determinants. We demonstrate that variables in the audit pricing model that were previously found to have impact on audit fees may turn out to be useless when more powerful tests like panel tests are applied to these variables. Our evidence implies that failing to employ appropriate procedure to test cointegration and to specify the appropriate model for audit fees and their determinants would generate results that may have exaggerated the effects of some variables on audit fees.     

Accounting Regulation,Financial Development,and Economic Growth

It is argued that the sustainability of external debts depends on the stationarity of the current account balance. This study tests for the stationarity of current account deficits for a sample of sixteen Latin American countries, employing a new test, advocated by Breuer et al. (2002), that allows one to test for unit roots in heterogeneous panel data sets. This version of the augmented Dickey-Fuller (ADF) test involves estimating ADF regressions within a seemingly unrelated regression (SURADF) framework. The benefits of creating a panel to overcome low test power are well known, but this particular test also offers key advantages over existing alternative panel data unit root tests. Unlike previous tests, this one identifies which members from within the panel are responsible for rejecting the null hypothesis of joint nonstationarity. In addition, the SURADF test does not presume disturbances that are independently and identically distributed. Using annual data covering the period 1979-2001, this study finds strong evidence in favor of current account mean-reversion for at least twelve Latin American countries.     

Bivariate relative city price convergence in the United States: 1918-1997

As in international tests of purchasing power parity, panel unit root tests have been successful in rejecting a unit root process in U.S. city relative prices over the period 1918-1997. However, there is an empirical question of what the rejection of a ‘panel unit root’, particularly with respect to real exchange rates, means. This paper employs a variety of univariate unit root and cointegration tests which have recently come to the fore. These tests improve the power and reduce size distortion found in standard unit root and cointegration tests such as the Dickey-Fuller and Phillips-Perron tests. I find considerable evidence for rejecting a unit root process in the majority of U.S. city relative prices over the entire sample period and two subperiods. Less successful are stationarity tests conducted on regions of the U.S.     

A Time Series Analysis of U.K. Construction and Real Estate Indices

This study assess the nonlinear behavior of U.K. Construction and Real Estate indices. Standard unit root tests show that both time series are I(1) processes. However, the empirical results show that the returns series for both indices deviate from the null hypothesis of white noise. Moreover, we have found evidence of nonlinearity but strong evidence against chaos for the returns series. Further tests show that the source of nonlinearity is rather different. Hence, the Construction index returns series displays weak nonlinear forecastability, typical of nonlinear deterministic processes, whereas the Real Estate index could be characterized as a stationary process about a nonlinear deterministic trend.     

Non-linear dynamics in international resource markets: Evidence from regime switching approach

This paper examines the nonstationary and nonlinear features of the non-renewable resource markets: the crude oil (US West Texas Intermediate and UK Brent), bituminous coal and natural gas markets. In particular, we achieve this goal by using the Markov switching unit root regression. This approach is attractive because it allows price to switch between stationary and nonstationary regimes (partial nonstationarity). It also allows price to switch between two stationary regimes (varied stationarity) or to switch between two nonstationary regimes (varied nonstationarity). The results of a range of non-linear tests show that the independently and identically distributed (i.i.d.) hypothesis or the random walk hypothesis is untenable for the non-renewable resource prices. The results from the Markov regression indicate that, in the cases of US West Texas Intermediate, UK Brent as well as bituminous coal, prices are characterized by the local nonstationarity in both regimes, and therefore varied nonstationarity is sustained. The price of natural gas is characterized by partial nonstationarity, indicating that this market is inconsistent with the efficient market.     

Do Interest Rates Follow Unit-Root Processes? Evidence from Cross-Maturity Treasury Bill Yields

Abstract. It is widely reported in the literature that interest rates follow integrated processes. Many empirical studies have, in fact, taken this result as a maintained hypothesis. This article demonstrates that the failure to reject the hypothesis that interest rates contain a unit root may be due to the severe power problem of standard test procedures in small samples. We analyze a panel of cross-maturity Treasury-bill yield series by employing a panel-based test. This test exploits cross-maturity variations of the data to improve estimation efficiency and is more powerful than standard tests for unit roots. The critical values of the test statistics are computed by Monte Carlo simulations tailored to our samples. It is found that the null hypothesis that each yield series contains a unit root can be decisively rejected. Our findings cast some doubt on previous studies that rely on the nonstationarity assumption of interest rates.     

Testing the Purchasing Power Parity Hypothesis for the New Member and Candidate Countries of the European Union: Evidence from Lagrange Multiplier Unit Root Tests with Structural Breaks

This paper investigates the validity of purchasing power parity (PPP) for the eleven Central and East European transition countries and three market economy countries, Cyprus, Malta, and Turkey. Unlike previous studies on PPP, this study uses Lagrange multiplier (LM) unit root tests that incorporate structural breaks in the data series. The findings indicate that in cases of one and two structural breaks, for a U.S. dollar-based real exchange rate series, there is little evidence supporting the validity of PPP. For a deutsche mark-based real exchange rate series, for the cases of both one and two breaks, there is evidence of stationarity of real exchange rates for eight sample countries, which is consistent with PPP. The results also indicate that the estimated half-life of a shock to the real exchange rate ranges from 1.25 (15.05 months) to 2.72 (32.72 months) years across countries. The empirical findings may provide direction for policy makers to coordinate monetary policies for the process of European monetary integration.