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.     

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.     

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.     

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.     

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.     

Purchasing power parity and the behavior of prices and nominal exchange rates across exchange-rate regimes

The evidence presented in this paper shows that purchasing power parity as a long-run proposition is indeed a very useful approximation. We see this quite clearly in the panel data for three historical periods examined here – the classical gold standard era from 1870 to 1914, the interwar period from 1921 to 1939, and the period after World War II from 1959 to 1998. Price-level behavior across countries differs in the way that PPP suggests when monetary arrangements differ and is highly similar when monetary arrangements are themselves similar. Inflation rates adjusted for exchange rate changes in general are highly correlated and bear a one-to-one relation to one another within and across the three periods and the varied monetary regimes that prevailed.     

The impact of exchange rate deviations from relative PPP equilibrium on the U.S. demand for foreign equities

Applying fixed-effects panel data, this study investigates the impact of U.S. dollar exchange rate movements during different exchange rate states (overvaluation and undervaluation) on the monthly real gross and real net purchases of foreign equities by U.S. residents over the post-Plaza Accord period. The foreign equities come from 22 developed and 25 developing countries. Previous research has posited two alternative hypotheses regarding the relationship between exchange rates and foreign investment. These are the wealth effect and the profit-oriented effect. The evidence herein suggests that these two hypotheses coexist. We find robust evidence for a negative relationship between the exchange rate movements of an undervalued U.S. dollar and the demand for foreign equities. For developed countries, the wealth effect dominates the profit-oriented effect when the U.S. dollar is overvalued, while, for developing countries, the profit-oriented effect dominates the wealth effect. The results emphasize the importance of considering exchange rate states derived from a relative PPP equilibrium when analyzing U.S. allocations to foreign equities. The findings with respect to the macroeconomic control variables are mainly in agreement with the predictions of international financial theory. Some of the results, however, disappear or become inconclusive for the period after the bankruptcy of Lehman Brothers. This may be explained by the increased uncertainty in international financial markets following this unprecedented event. The findings are robust with respect to different constructed equilibrium exchange rates.     

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 under different exchange rate regimes: Do they revert and,if so,how?

We propose an empirical model for deviations from long-run purchasing power parity (PPP) that simultaneously accounts for three key features: (i) adjustment toward PPP may occur via nominal exchange rates and relative prices at different speeds; (ii) different exchange rate regimes may generate regime shifts in the structural dynamics of PPP deviations; (iii) nonlinear reversion toward PPP in response to shocks. This empirical framework encompasses and synthesizes much previous empirical research. Using over a century of data for the G5 countries, we provide evidence that long-run PPP holds, the relative importance of nominal exchange rates and prices in restoring PPP varies over time and across different exchange rate regimes, and reversion to PPP occurs nonlinearly, at a speed that is fairly consistent with the nominal rigidities suggested by conventional open economy models.     

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.     

Testing PPP Hypotheses between Japan and the Six G7 Countries

The paper examines the purchasing power parity(PPP) theory of the foreign exchange rate of the yenagainst the currencies of the six G7 countries. We usethe error-corrected five-dimensional vectorautoregressive (VAR) model with structural changes inthe trend function. The data cover the period of thepost-Breton–Woods floating exchange rate system. Theresults reveal that the PPP relation alone determinesthe exchange rates for the USA, France, Germany, andItaly, while a linear combination of PPP and uncoveredinterest rate parity (UIP) relations determines that for Canada. Ina model without trend breaks, the PPP relations holdonly for Germany, which indicates that a correctspecification of the sampling distribution of data isimportant. The one-step prediction based on the errorcorrection model (ECM) outperforms the random walkmodel. The ECM is useful to predict the out-of-samplebehaviors of the exchange rates.     

Purchasing power parity: Modeling and testing mean reversion

A model of mean reversion of exchange rates to purchasing power parity is developed and tested where exchange rates are assumed to follow a mean reverting elastic random walk toward a stochastic PPP rate. The model recognizes the possibility that mean reversion towards PPP may be nonlinear which allows greater flexibility in the adjustment process. Regression equations consistent with the theoretical model are derived. The model is tested using long- and short-term data for six countries. While the results are generally consistent with the findings of previous studies, evidence is presented which demonstrates that the mean reversion process is not linear for some countries.     

Cointegrated Periodically Collapsing Bubbles in the Exchange Rate of “BRICS”

We test the occurrence of periodically recurring rational bubbles in the exchange rate of each of the “BRICS” countries currency relative to the US dollar. The forward exchange rate is used as a proxy for the expected exchange rate, different Purchasing Parity Power (PPP)-based rules for the fundamental exchange rate are considered, and its initial value is endogenously determined. For the chosen model, the regime switching equation satisfactorily fits the data, confirming the presence of rational bubbles for all countries. The dynamics of the exchange rate series for each country is interpreted with the help of the estimated bubbles. The bubbles are compared across countries, found to be cointegrated, and this is interpreted as evidence of the international transmission of exchange rate shocks between these countries.     

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.     

Are Real Interest Rates Equal Across Countries? An Empirical Investigation of International Parity Conditions

This paper conducts empirical tests of the equality of real interest rates across countries. The empirical evidence strongly rejects the hypothesis of real rate equality and the joint hypotheses of uncovered interest parity and ex ante relative PPP, or the unbiasedness of forward rate forecasts and ex ante relative PPP. The evidence suggests that it is worth studying open economy macroeconomic models which allow: 1) domestic real rates to differ from world rates, 2) time varying risk premiums in the forward market, or 3) deviations from ex ante relative PPP.     

Long-run purchasing power parity,prices and exchange rates in transition: The case of six Central and East European countries

This paper presents empirical results on the hypothesis of long-run purchasing power parity (PPP) with respect to the exchange-rate regimes in six Central and East European countries. The analysis employs cointegration theory to examine the movements of prices and exchange rates in transition to a market economy. Our results are based on system estimation procedures developed by Stock and Watson (1993) and Johansen (1991). We find moderate evidence to support long-run equilibria, however, the cointegrating vector values do not yield to easy interpretation and violate the symmetry and proportionality conditions suggested by PPP. We provide an explanation for such behavior and find that it is consistent with the existing literature on transition and foreign exchange markets.     

Purchasing Power Parity in the Long Run

This paper re-examines the evidence on Purchasing Power Parity (PPP) in the long run. Previous studies have generally been unable to reject the hypothesis that the real exchange rate follows a random walk. If true, this implies that PPP does not hold. In contrast, this paper casts serious doubt on this random walk hypothesis. The results follow from more powerful estimation techniques, applied in a multilateral framework. Deviations from PPP, while substantial in the short run, appear to take about three years to be reduced in half.     

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.     

关于购买力平价与汇率关系的实证研究

文章综述了购买力平价理论及实证检验结果，对25个国家和地区1975年以来的名义汇率与购买力平价的偏离程度进行了比较分析，并认为从静态来看，发展中国家名义汇率对购买力平价的偏离度远远大于发达国家，从动态来看，发展中国家在追赶过程中其名义汇率变动向购买力平价趋同。