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.     

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.     

Real exchange rate behaviour: evidence from black markets

The behaviour of real exchange rates (relative to the US dollar) is examined using monthly data obtained from the black markets for foreign exchange of eight Asian developing countries. The data span is 31 years. The black market real exchange rates do not show excess volatility during the recent float which is in sharp contrast to the results reported elsewhere. Unit root tests in heterogeneous panels and variance ratio tests confirm their stationarity. Thus, we find support for PPP but not for the ‘survivorship’ bias (Froot and Rogoff, 1995 ). There is little evidence of segmented trends. Issues raised by Rogoff ( 1996 )—of whether PPP would hold across countries with differing growth experience—and Lothian and Taylor ( 1996 )—of whether the degree of relative price volatility may bias results in favour of mean reverting real exchange rates—are addressed. Copyright © 2000 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.     

Is PPP sensitive to time-varying trade weights in constructing real effective exchange rates?

While the use of real effective exchange rates in stationarity tests of purchasing power parity (PPP) avoids the problems created using bilateral rates, these rates are often constructed using trade shares that are fixed at a single base year. This method fails to take into account the fact that trade shares can change drastically in parts of the world that are undergoing dramatic transformations. In this study, we apply linear as well as nonlinear stationarity tests to 52 currencies’ real effective rates, which were constructed using time-varying weights. Incorporating a time trend, we are also able to assess whether breakdowns in PPP are due to productivity differentials. We find that while nonlinear tests provide more evidence of “productivity bias” than do linear tests, they do not provide much more evidence of PPP. A comparison to a previous study that used fixed-weight data shows that there is somewhat more evidence of productivity bias using the new dataset, especially in Eastern Europe and Asia. We can conclude that PPP and a key cause of its breakdown are somewhat sensitive to the use of time-varying weights in these stationarity tests.     

PPP may hold better than you think: Smooth breaks and non-linear mean reversion in real effective exchange rates

This paper revisits some key topics in the literature on purchasing power parity (PPP). The study applies a set of newly developed unit root tests, which account for both nonlinearity and multiple smooth temporary breaks in series, to the real effective exchange rates (REERs) of 23 developed countries. The results suggest that PPP generally holds for various currency-based real rates. There is evidence in favor of linear stationarity in REERs for highly integrated economies. The REERs of most other countries tend to have nonlinear adjustment toward large long-swing type mean changes around constant equilibrium values.     

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.     

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.     

Testing long‐run PPP with infinite‐variance returns

This paper investigates the long‐run purchasing power parity hypothesis when exchange rate returns and inflation rates are assumed to be heavy‐tailed stochastic processes. More specifically, residual‐based and likelihood‐ratio‐based cointegration tests of PPP that explicitly allow for infinite‐variance innovations are applied to monthly data (1973:1–1999:12) for Belgium, Canada, Denmark, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, and the United Kingdom. Our test results are marginally less supportive of PPP when the innovations are assumed to be infinite‐variance, α‐stable processes. Copyright © 2003 John Wiley & Sons, Ltd.     

Regime switching as a test for exchange rate bubbles

This paper develops a new test for speculative bubbles, which is applied to data for the Japanese yen, the German mark and the Canadian dollar exchange rates from 1977 to 1991. The test assumes that bubbles display a particular kind of regime-switching behaviour, which is shown to imply coefficient restrictions on a simple switching-regression model of exchange rate innovations. Test results are sensitive to the specification of exchange rate fundamentals and other factors. Evidence most consistent with the bubble hypothesis is found using an overshooting model of the Canadian dollar and a PPP model of the Japanese yen.     

Testing Stationarity in Small‐ and Medium‐Sized Samples when Disturbances are Serially Correlated*

In this article, we study the size distortions of the KPSS test for stationarity when serial correlation is present and samples are small‐ and medium‐sized. It is argued that two distinct sources of the size distortions can be identified. The first source is the finite‐sample distribution of the long‐run variance estimator used in the KPSS test, while the second source of the size distortions is the serial correlation not captured by the long‐run variance estimator because of a too narrow choice of truncation lag parameter. When the relative importance of the two sources is studied, it is found that the size of the KPSS test can be reasonably well controlled if the finite‐sample distribution of the KPSS test statistic, conditional on the time‐series dimension and the truncation lag parameter, is used. Hence, finite‐sample critical values, which can be applied to reduce the size distortions of the KPSS test, are supplied. When the power of the test is studied, it is found that the price paid for the increased size control is a lower raw power against a non‐stationary alternative hypothesis.     

Tests for Stationarity in Series with Endogenously Determined Structural Change*

We consider tests of the null hypothesis of stationarity against a unit root alternative, when the series is subject to structural change at an unknown point in time. Three extant tests are reviewed which allow for an endogenously determined instantaneous structural break, and a related fourth procedure is introduced. We further propose tests which permit the structural change to be gradual rather than instantaneous, allowing the null hypothesis to be stationarity about a smooth transition in linear trend. The size and power properties of the tests are investigated, and the tests are applied to four economic time series.     

Real exchange rate,stationarity, and economic fundamentals

Using monthly data for the US/UK real exchange rate over the period 1921–2002, we find evidence that the mean reverting tendency of the real exchange rate is stochastic, and regime-dependent. There is one regime over which PPP holds as a long-run equilibrium relation, i.e. a stationary PPP regime, and another regime over which PPP does not hold, i.e. a non-stationary PPP regime. The transition from the non-stationary to the stationary regime is found to be affected by the real interest rate differential, and by the volatility of the nominal exchange rate. The real output differential does not appear to affect the transition probability.     

Size and power of tests of stationarity in highly autocorrelated time series

Tests of stationarity are routinely applied to highly autocorrelated time series. Following Kwiatkowski et al. (J. Econom. 54 (1992) 159), standard stationarity tests employ a rescaling by an estimator of the long-run variance of the (potentially) stationary series. This paper analytically investigates the size and power properties of such tests when the series are strongly autocorrelated in a local-to-unity asymptotic framework. It is shown that the behavior of the tests strongly depends on the long-run variance estimator employed, but is in general highly undesirable. Either the tests fail to control size even for strongly mean reverting series, or they are inconsistent against an integrated process and discriminate only poorly between stationary and integrated processes compared to optimal statistics.     

Trend‐stationary GNP: evidence from a new exact pointwise most powerful invariant unit root test

There has been a substantial debate whether GNP has a unit root. However, statistical tests have had little success in distinguishing between unit‐root and trend‐reverting specifications because of poor statistical properties. This paper develops a new exact small‐sample, pointwise most powerful unit root test that is invariant to the unknown mean and scale of the time series tested, that generates exact small‐sample critical values, powers and p‐values, that has power which approximates the maximum possible power, and that is highly robust to conditional heteroscedasticity. This test decisively rejects the unit root null hypothesis when applied to annual US real GNP and US real per capita GNP series. This paper also develops a modified version of the test to address whether a time series contains a permanent, unit root process in addition to a temporary, stationary process. It shows that if these GNP series contain a unit root process in addition to the stationary process, then it is most likely very small. Copyright © 2001 John Wiley & Sons, Ltd.     

Investigating the PPP hypothesis using constructed U.S. dollar equilibrium exchange rate misalignments over the post-bretton woods period

This paper investigates the PPP-hypothesis over the post-Bretton Woods period using a representation of the equilibrium exchange rate (EER) that is an alternative to the real exchange rate. The results provide evidence in support of the relative-PPP hypothesis over the current period of floating exchange rates (1974–2005); while stronger evidence is found for the post-Plaza Accord period (1986–2005). EERs based on export price indexes (EPI) and constructed traded goods price indexes (TPI) best demonstrate the mean reverting behavior of the spot exchange rate as opposed to those EERs based on CPI, PPI, or the GDP-deflator. This mean reverting behavior is slightly improved if one takes international interest rate differentials into account; however EERs extended by productivity differentials do not indicate any improvements over the base model. Over the post-Plaza Accord period average half-lives of less than 1 year are reported using TPI-based EERs, adjusted by interest rate differentials. For large misalignments, we find probabilities that the spot exchange rate will converge towards the constructed CPI-based equilibrium exchange rate of up to 80%. Lastly, over the post-Plaza Accord period, the TPI-based EERs are able to statistically significantly outperform the pure random walk at short-term forecast horizons of less than 1 year for some spot exchange rates.     

Conditional heteroscedasticity of exchange rates: further results based on the fractionally integrated approach

A recent article (Tse, 1998 ) published in this journal analysed the conditional heteroscedasticity of the yen–dollar exchange rate based on the fractionally integrated asymmetric power ARCH model. In this paper, we present replication results using Tse's ( 1998 ) yen–dollar series. We also examine the robustness of Tse's ( 1998 ) findings across different currencies, sample periods and non‐nested GARCH‐type models. Unlike Tse ( 1998 ), we find some evidence of asymmetric conditional volatility for daily returns of currencies measured against the dollar or the yen. Copyright © 2004 John Wiley & Sons, Ltd.     

THE DYNAMICS OF REAL EXCHANGE RATES: A RECONSIDERATION

In this paper we offer a bootstrap‐based version of the Cox specification test for non‐nested hypothesis to discriminate between ESTAR and MSAR models. Both models are commonly used for modeling real exchange rates dynamics. We show that the test has good size and power properties in finite samples. In an application, we analyze several major real exchange rates to shed light on the question of which model describes these processes best. This allows us to draw conclusions about the driving forces of real exchange rates. Copyright © 2013 John Wiley & Sons, Ltd.     

The Flexible Fourier Form and Local Generalised Least Squares De‐trended Unit Root Tests*

In two recent papers Enders and Lee (2009) and Becker, Enders and Lee (2006) provide Lagrange multiplier and ordinary least squares de‐trended unit root tests, and stationarity tests, respectively, which incorporate a Fourier approximation element in the deterministic component. Such an approach can prove useful in providing robustness against a variety of breaks in the deterministic trend function of unknown form and number. In this article, we generalize the unit root testing procedure based on local generalized least squares (GLS) de‐trending proposed by Elliott, Rothenberg and Stock (1996) to allow for a Fourier approximation to the unknown deterministic component in the same way. We show that the resulting unit root tests possess good finite sample size and power properties and the test statistics have stable non‐standard distributions, despite the curious result that their limiting null distributions exhibit asymptotic rank deficiency.     

Multiple Testing for No Cointegration under Nonstationary Volatility

With cointegration tests often being oversized under time‐varying error variance, it is possible, if not likely, to confuse error variance non‐stationarity with cointegration. This paper takes an instrumental variable (IV) approach to establish individual‐unit test statistics for no cointegration that are robust to variance non‐stationarity. The sign of a fitted departure from long‐run equilibrium is used as an instrument when estimating an error‐correction model. The resulting IV‐based test is shown to follow a chi‐square limiting null distribution irrespective of the variance pattern of the data‐generating process. In spite of this, the test proposed here has, unlike previous work relying on instrumental variables, competitive local power against sequences of local alternatives in 1/T‐neighbourhoods of the null. The standard limiting null distribution motivates, using the single‐unit tests in a multiple testing approach for cointegration in multi‐country data sets by combining P‐values from individual units. Simulations suggest good performance of the single‐unit and multiple testing procedures under various plausible designs of cross‐sectional correlation and cross‐unit cointegration in the data. An application to the equilibrium relationship between short‐ and long‐term interest rates illustrates the dramatic differences between results of robust and non‐robust tests.