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.     

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.     

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.     

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.     

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。     

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.     

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.     

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 exchange rate predictability

We study whether the nonlinear behavior of the real exchange rate can help us account for the lack of predictability of the nominal exchange rate. We construct a smooth nonlinear error-correction model that allows us to test the hypotheses of nonlinear predictability of the nominal exchange rate and nonlinear behavior on the real exchange rate in the context of a fully specified cointegrated system. Using a panel of 19 countries and three numeraires, we find evidence of nonlinear predictability of the nominal exchange rate and of nonlinear mean reversion of the real exchange rate. Out-of-sample Theil’s U -statistics show a higher forecast precision of the nonlinear model than the one obtained with a random walk specification. Although the robustness of the out-of-sample results over different forecast windows is somewhat limited, we are able to obtain significant predictability gains—from a parsimonious structural model with PPP fundamentals—even at short-run horizons.     

A sequential purchasing power parity test for panels of large cross-sections and implications for investors

In this paper we use monthly time series data for not less than 64 countries and a new sequential approach to test for purchasing power parity (PPP). The results are strong in that the evidence in favor of PPP is very weak. In fact, for the US-dollar-based exchange rates the evidence is basically non-existent. In order to eliminate the effect of the base currency, we also apply the sequential PPP test to all pairs of exchange rates, and find similarly weak evidence of PPP. However, for those rates where evidence is found, using a technical trading rule, we find evidence of significant profits. The predictability of the stationary pairs is therefore important for investors.     

Trade concentration, openness, and deviations from purchasing power parity

Economists have often explained deviations from PPP in terms of random relative price changes. While all countries are subject to such real shock, empirical studies indicate that PPP seems to hold closer for some countries than others. This paper emphasizes two major reasons why we should expect systematic differences across countries in deviations from PPP: (a) the concentration of trade and (b) openness. The more diversified trade, the less susceptible the country to random shocks affecting individual goods, so that shifts in the PPP ratio are lower. The more open the economy, the greater the weight of traded goods in the overall price indices, so that if exchange rates are determined by traded goods prices, yet empirical tests of PPP use national price indices, PPP should hold better in more open economies.     

The confusing time-series behaviour of real exchange rates: Are asymmetries important?

Evidence regarding the time-series properties of real exchange rates is mixed. There is evidence that such rates exhibit both non-stationary and stationary behaviour. The current dominant belief is that rates are non-linear stationary, however, this is not accepted without question. This paper re-examines the time-series properties of five US dollar real exchange rates and argues that the confusing time-series properties arise largely as each series examined exhibits periods of non-stationary and stationary behaviour such that the sample over which any empirical exercise is conducted is of importance. However, extending a typical non-linear model used within the literature to allow for asymmetries improves the models ability to fit the data. Therefore, our results suggest that modelling asymmetries between positive and negative real exchange rate deviations is of importance, whereas extant research has typically rules out asymmetry. Indeed a forecasting exercise conducted over a 1-year horizon is particularly supportive of this model. Such a finding is of importance not only for academics but also finance practitioners involved in trading and portfolio management and finance managers who act in the foreign exchange market for goods market trading. It remains for future research to theoretically motivate the asymmetries found here.     

Forecasting exchange rates out-of-sample with panel methods and real-time data

This paper evaluates out-of-sample exchange rate forecasting with Purchasing Power Parity (PPP) and Taylor rule fundamentals for 9 OECD countries vis-à-vis the U.S. dollar over the period from 1973:Q1 to 2009:Q1 at short and long horizons. In contrast with previous work, which reports “forecasts” using revised data, I construct a quarterly real-time dataset that incorporates only the information available to market participants when the forecasts were made. Using bootstrapped out-of-sample test statistics, the exchange rate model with Taylor rule fundamentals performs better at the one-quarter horizon and panel estimation is not able to improve its performance. The PPP model, however, forecasts better at the 16-quarter horizon and its performance increases in panel framework. The results are in accord with previous research on PPP and Taylor rule models.     

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.     

Real exchange rates and time-varying trade costs

This paper re-examines the empirical modeling of Purchasing Power Parity (PPP) deviations in the presence of commodity market frictions. First, we show that a specific type of smooth transition models can closely approximate the functional form of the theoretical adjustment mechanism derived by Dumas (1992) [Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World, Review of Financial Studies,5:2153-180] for the case of constant as well as changing trade costs. Second, we develop, for the first time, an empirical model of the real exchange rate which allows for changes in the degree of market integration. By employing a long span of data on the Dollar-Sterling real exchange rate and a micro-founded proxy for trade frictions, we provide novel evidence of a significant relationship between the persistence of the real exchange rate and the level of trade costs. This finding suggests that both the difficulty of detecting PPP and the extend of Rogoff’s puzzle vary over time with the degree of trade restrictiveness. Finally, we highlight policy repercussions of our results.     

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.     

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.     

The Taylor Rule and Forecast Intervals for Exchange Rates

In this paper, we examine the Meese–Rogoff puzzle from a different perspective: out‐of‐sample interval forecasting. While most studies in the literature focus on point forecasts, we apply semiparametric interval forecasting to a group of exchange rate models. Forecast intervals for 10 OECD exchange rates are generated and the performance of the empirical exchange rate models are compared with the random walk. Our contribution is twofold. First, we find that in general, exchange rate models generate tighter forecast intervals than the random walk, given that their intervals cover out‐of‐sample exchange rate realizations equally well. Our results suggest a connection between exchange rates and economic fundamentals: economic variables contain information useful in forecasting distributions of exchange rates. We also find that the benchmark Taylor rule model performs better than the monetary, PPP and forward premium models, and its advantages are more pronounced at longer horizons. Second, the bootstrap inference framework proposed in this paper for forecast interval evaluation can be applied in a broader context, such as inflation forecasting.     

Testing for long-run PPP in a system context: Evidence for the US,Germany and Japan

This paper extends the current literature on PPP by re-examining the validity of the PPP hypothesis for the three key currencies of the recent floating exchange rate period, in a multilateral framework. We argue that PPP testing is more adequate in a system context, which takes into account the dynamic interactions of exchange rates and prices of more than two economies, simultaneously. In the system analysis framework, some form of causality among the variables under consideration is also assessed empirically with the aid of weak exogeneity tests. The results illustrate the importance of the multilateral testing. Positive evidence for PPP is found: long-run PPP is supported for the US and Germany but also for the US and Japan, in contrast to evidence of earlier empirical studies. In addition, causality is found running from the US prices to the exchange rates and German and Japanese prices.