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.     

Nonlinear trends in real exchange rates: A panel unit root test approach

We analyze the possibility of nonlinear trend stationarity as the alternative to unit roots in 23 OECD real exchange rates, 1974–1998, by adding nonlinear time terms to the CIPS panel unit root test of Pesaran (2007). We follow a thorough bootstrapping approach and propose a technique to adjust statistical significance for the use of multiple tests over several time trend orders. The unit root null that all real exchange rates have unit roots is rejected at better than the 0.05 level. Bootstrapped results from a procedure of Chortareas and Kapetanios (2009) suggest that the hypothesis that all are stationary is reasonable. We argue that nonlinear trend stationarity is the most likely alternative hypothesis for at least some of the real exchange rates because: (1) the strongest CIPS rejection occurs when quadratic trends are specified; (2) nonlinear time terms are statistically significant at the 0.10 level; (3) the actual CIPS statistics are more consistent with CIPS sampling distributions from bootstrapped nonlinear trend stationary processes than from linear trend or mean stationary processes.     

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.     

Why panel tests of purchasing power parity should allow for heterogeneous mean reversion

Recent studies of purchasing power parity (PPP) use panel tests that fail to take into account heterogeneity in the speed of mean reversion across real exchange rates. In contrast to several other severe restrictions of panel models and tests of PPP, the assumption of homogeneous mean reversion is still widely used and its consequences are virtually unexplored. This paper analyzes the properties of homogeneous and heterogeneous panel unit root testing methodologies. Using Monte Carlo simulation, we uncover important adverse properties of the panel approach that relies on homogeneous estimation and testing. More specifically, power functions are low and assume irregular shapes. Furthermore, homogeneous estimates of the mean reversion parameters exhibit potentially large biases. These properties can lead to misleading inferences on the validity of PPP. Our findings highlight the importance of allowing for heterogeneous estimation when testing for a unit root in panels of real exchange rates.     

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.     

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.     

Purchasing power parity in ASEAN-5 countries: revisit with cross-sectional dependence and structural breaks

This paper re-examines the purchasing power parity (PPP) hypothesis for a panel of ASEAN-5 countries. The panel unit root and cointegration tests, which incorporate cross-sectional dependence and multiple structural breaks, are innovatively used for testing the PPP hypothesis. We could not find evidence that supports the existence of a long-run equilibrium between the relative price ratio and the nominal exchange rate for the whole period. Nevertheless, there is evidence of a cointegrating relationship for the post-crisis period. Our finding implies that a flexible exchange rate regime is suitable for the individual ASEAN countries.     

Equality of Real Returns on Canadian and US Treasury Bills: A Fractional Cointegration Analysis

This paper empirically analyzes the long memory relationship between the real returns on Canadian and US Treasury bills. A fractional cointegration approach, instead of conventional integer integration (unit root) and cointegration approaches, is used in analyzing the relationship. The advantage of fractionally integrated models is that they allow a smooth transition from a stationary process to a unit-root process. Furthermore, such models embody unit-root models as a special case. The models are therefore more general and appropriate for empirical analysis. By using fractionally integrated models, one also resolves the problems of an inconsistency in test results associated with using unit root and cointegration approaches. Briefly, it is found that the real returns on Canadian and US Treasury bills are fractionally integrated and the order of integration is significantly less than unity. Furthermore, the difference between the real returns follows a stationary process. This indicates that the Canadian and the US capital markets as well as product markets are well integrated. Furthermore, the domestic monetary authorities will not be able to influence the domestic real interest rate independent of the other market in the long-run.     

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.     

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.     

Asymmetric adjustments in the spread of lending and deposit rates: Evidence from extended threshold unit root tests

In this paper, we test for asymmetric adjustments in the spread of the U.S. prime lending rate and 3-month certificate of deposit rate. In doing so, we extend the pioneering threshold unit root tests of Enders and Granger (1998) to more flexible models where the deterministic terms and short-run dynamics, in addition to the persistent parameters, can differ in two regimes. While some previous works have tested for asymmetric adjustments in the spread of lending and deposit rates using threshold unit root tests, the deterministic terms and short-run dynamics were assumed to be symmetric, which can lead to bias and less accurate conclusions if these conditions do not hold. Overall, we find that the spread in lending and deposit rates is stationary but adjustment to the equilibrium is asymmetric. In particular, we find more rapid adjustment when the spread is narrowing below a threshold level than when widening above this level. Several theoretical implications are suggested.     

Searching for evidence of long-run PPP from a post-Bretton Woods panel: separating the wheat from the chaff

This paper reexamines the issue of long-run PPP using multiple panel tests in the framework of confirmatory analysis. Application of six panel tests under competing null hypotheses to the real exchange rates of 21 industrial countries yields seemingly contradictory evidence on the parity during the post-Bretton Woods period. Regardless of numeraire currency, four I(1) panel tests unanimously reject the null hypothesis in favor of long-run PPP, whereas two I(0) panel tests lend little support to the parity at conventional significance levels. Confirmatory analysis suggests that this puzzling result can be explained either by nonlinear dynamics of the real exchange rates or by a mixture of I(0) and I(1) series in the panel. Monte Carlo experiments indicate that potential mix of I(0) and I(1) series is more relevant to the empirical finding. The use of a sequential classification method sorts out six real exchange rates which exhibit most persistent deviations from long-run equilibrium. Systematic behavior of these series can be characterized better by country specific factors than by observable macroeconomic variables.     

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.     

结构突变对实证估计方法选择的影响：以人民币汇率为例

本文在详细归纳结构突变的单位根检验方法基础上,以2002—2007年间人民币汇率为例探讨了结构突变对于模型估计方法选择的影响。采用结构突变的单位根检验方法得到的检验结果否定了不考虑结构突变的传统ADF检验结果,揭示出人民币兑日元汇率时间序列为结构突变的平稳序列。本文结论表明,是否考虑结构突变将会导致对估计方法作出截然不同的选择,不考虑结构突变可能会带来“伪协整”问题。     

Purchasing power parity, unit roots, and dynamic structure

Recent studies of purchasing power parity (PPP) account for the possible presence of unit roots in nominal exchange rates and relative price indices by applying standard unit-root tests to real exchange rates, which are ratios of nominal exchange rates and relative price indices. These studies occasionally find evidence of PPP, but as a whole, the evidence is not definitive. Standard unit-root tests impose a restrictive dynamic structure between nominal exchange rates and relative price indices. I specify and estimate a generalized dynamic structure. I reject the dynamic restrictions implicit in standard unit-root tests of PPP, and find stronger evidence of PPP than do most other recent studies.     

人民币实际汇率波动对中国贸易影响的实证分析

本文利用1994-2008年的季度时间序列数据,在VAR模型的基础上,运用单位根检验、协整分析、格兰杰因果检验和方差分解等技术分析人民币实际汇率对中国进出口贸易的影响。分析结果表明,人民币实际汇率变动是影响中国进出口贸易的重要因素,马歇尔-勒纳条件在中国是成立的。从短期来看,人民币实际汇率变动是影响出口贸易的主要因素;然而从长期来看,国外需求的变动是影响出口贸易变动的主要因素。     

Temporal aggregation and purchasing power parity persistence

This paper uses a unique new monthly US-UK real exchange rate series for the January 1794-December 2009 period to reexamine the academic debate over purchasing power parity (PPP). The consensus view described by Rogoff (1996) is that PPP holds in the long-run, but short-run deviations are very persistent, with half-lives ranging from 3 to 5 years. Most of the literature using long time series relies on the annual data developed by Lee (1976) and Lothian and Taylor (1996), which were both constructed from underlying higher-frequency data sources. Estimates of purchasing power parity persistence using these series may therefore be subject to temporal aggregation bias. We find evidence of aggregation bias which indicates the half-life of PPP deviations has been overestimated in much of the previous literature. We also find that estimates of the half-lives are further reduced once we account for the Harrod (1933)-Balassa (1964)-Samuelson (1964) effect. The result of aggregation bias appears to be robust even when considering the case that real exchange rates exhibit nonlinear dynamics.     

购买力平价理论的实证检验法综述

本文介绍了自 2 0世纪 70年代以来开放经济理论的基石———购买力平价及实际汇率的相关实证检验方法。以发达国家双边汇率作为样本数据进行检验 ,发现在样本期间足够长、样本数量足够多的情况下 ,PPP假设成立。此外 ,由于实际汇率对PPP的均值复归呈现出显著的非线性特征 ,今后的研究方向应当是建立非线性汇率动态模型。     

A test of purchasing power parity for emerging economies

The concept of purchasing power parity (PPP) is examined here for its applicability to the soft currencies of a large group of emerging/developing economies. PPP is tested through the use of the technique of cointegration. Based on data covering the period of 1975–1997, cointegration tests of price indices and exchange rates are conducted for 27 countries (against the U. S.). The results provide relatively strong evidence (for 14 countries) in favor of the long-term applicability of PPP as a cointegration concept. Further tests on real exchange rates indicate that the symmetry and proportionality conditions implied by PPP are rejected in all but one case. The latter tests also show that departures from long-term exchange values can last for several years and that a priori restrictions imposed on the cointegrating vector can lead to a false rejection of the PPP concept.     

Deviations from Purchasing Power Parity

This study uses univariate and multivariate unit root tests to analyze the random walk behavior of real exchange rates for the period 1979–1989. The univariate test fails to reject the random walk model, but the multivariate test indicates that part of the real exchange rates is predictable, a result supporting purchasing power parity. Further analysis of the random walk component in real exchange rates shows that it is quite persistent: for all currencies it takes about five to eight years for this shock to diminish to half its size.