The purchasing power parity puzzle is worse than you think

The ‘‘purchasing power parity puzzle’’ is the difficulty of reconciling very high short-term volatility of real exchange rates with very slow rates of mean reversion. The strongest evidence of slow mean reversion comes from least squares estimates of first-order autoregressive models of the long-horizon dollar-sterling real exchange rate. Using median-unbiased estimation methods, we show that these methods underestimate the half-lives of PPP deviations, and thus overestimate the speed of mean reversion. When the specification is amended to allow for serial correlation, the speed of mean reversion falls even further. This makes resolution of the purchasing power parity puzzle more problematic.First version received: May 2003/Final version received: July 2004We thank Lutz Kilian, James Lothian, Mark Taylor, and two anonymous referees for helpful comments and suggestions.     

Detecting intra-national PPP model in China: A median-unbiased estimation approach

This paper studies the speed of price adjustments toward the intra-national PPP level within China based on half-life measurement. We calculate the point estimates of half-lives and the corresponding confidence intervals using median-unbiased estimation methods to correct for downward bias in least squares estimates. The point estimates of half-lives indicate that the speed of mean reversion toward convergence between region pairs is fast. A strong conclusion about the high speed of adjustments is, however, unwarranted in some regions where the confidence intervals for half-life estimates are much wider than others.     

Are real exchanges rate series really persistent?: evidence from three commonwealth of independent states countries

This article sets out to examine the degree of persistence in the real exchange rates of Kazakhstan, Kyrgyzstan and Russia, and tests the validity of Purchasing power parity (PPP) using monthly data covering 1995:01–2013:12 period. The sum of autoregressive (AR) coefficients is used in order to examine persistence of the real exchange rate series and grid-bootstrap method is employed for the confidence intervals. The tests performed suggest two results: (1) Covering the full sample and sub-sample periods, excluding Kyrgyzstan in 1995:01–1998:07 and Russia in 2008:09–2013:12 periods, disregarding the structural breaks in the data generating process, there is high persistency in real exchange rates; (2) there is evidence in support of PPP covering the full sample for every country except for Kyrgyzstan in 1995:01–1998:07 and Russia in 2008:09–2013:12 periods.     

Inflation targeting and real exchange rates: A bias correction approach

This paper examines whether inflation targeting (IT) influences purchasing power parity (PPP) by a bias correction approach under cross-sectional dependence. The recursive mean adjustment (RMA) method proposed by So and Shin (1999) and Shin and So (2001) is employed to correct a downward bias in half-life estimates of real exchange rates. More importantly, the empirical results show that IT lowers variability of real exchange rates and plays an important role in providing favorable evidence for long-run PPP.     

Out‐of‐Sample Exchange Rate Forecasting and Macroeconomic Fundamentals: The Case of Japan

This study explores the respective out‐of‐sample exchange rate forecasting abilities of five macroeconomic fundamental models in comparison to a naïve random walk model for Japan during the post‐Bretton Woods era. To assess the influence of major economic changes, we estimate both linear and nonlinear models for all the macroeconomic fundamentals. Overall, most structural exchange rate models outperform a naïve random walk model in terms of forecasting accuracy in the short horizon. When the fundamentals are only linearly modelled, the forecasting ability of the Taylor rule is generally superior to other fundamental models. When the fundamentals are nonlinearly specified, the predictability of some other models rises dramatically to match that of the Taylor rule models in short and/or long horizons. Of importance, we determine that the yen/dollar exchange rate forecasting performance effectively improves in several fundamental models when influential economic changes are incorporated.     

The effects of small sample bias in Threshold Autoregressive models

This paper investigates Threshold Autoregressive (TAR) models that contain a limited number of observations in some regimes. Simulations show that within the context of the real exchange rate literature, parameter estimates exhibit significant small sample bias even with long time series data. These distortions create substantial power losses in attempting to identify values of coefficients from data.     

Modelling exchange rate volatility with random level shifts

Recent literature has shown that the volatility of exchange rate returns displays long memory features. It has also been shown that if a short memory process is contaminated by level shifts, the estimate of the long memory parameter tends to be upward biased. In this article, we directly estimate a random level shift model to the logarithm of the absolute returns of five exchange rates series, in order to assess whether random level shifts (RLSs) can explain this long memory property. Our results show that there are few level shifts for the five series, but once they are taken into account the long memory property of the series disappears. We also provide out-of-sample forecasting comparisons, which show that, in most cases, the RLS model outperforms popular models in forecasting volatility. We further support our results using a variety of robustness checks.     

A Test of Long-run Purchasing Power Parity Allowing for Structural Breaks*

If exchange rates and prices are integrated processes, standard econometric tests of the purchasing power parity (PPP) hypothesis may be biased towards rejection. This paper avoids this problem by using the Engle and Granger (1987) theory of cointegrated processes. If the absolute version of purchasing power parity is true, and nominal exchange rates and prices are integrated processes, inter-commodity arbitrage should ensure that the real exchange rate is stationary. The stationarity hypothesis is tested using Australian real exchange rate data for the 1890–1984 period We find that the effective real exchange rate cannot be modelled as a stationary process and therefore reject the absolute version of PPP. We also employ a test for structural breaks due to, for instance, the oil price shock and find mixed results. Another interpretation of our results is that the real exchange rate was affected by a series of permanent, real shocks during the sample period     

Purchasing power parity over two centuries: trends and nonlinearity

In two recent contributions Lothian and Taylor, and Cuddington and Liang, produced empirical evidence that annual data for the dollar-sterling real exchange rate spanning two centuries exhibited a non-linear deterministic trend. This trend could be proxying Harrod-Balassa-Samuelson effects. Lothian and Taylor showed that a linear stationary autoregressive mode, which embodied a cubic trend, implied much faster mean reversion of the real exchange rate to shocks than a model that excluded the trend. This article shows that both non-linearity and a deterministic trend can be allowed for in a theoretically appealing manner and that the fitted models provide a parsimonious explanation of both the dollar-sterling and franc-sterling real exchange rates over the two centuries of data. Generalized impulse response function analysis of the models demonstrates that the speed of adjustment to shocks can be even faster when trends are considered.     

Understanding forecast failure of ESTAR models of real exchange rates

The forecast performance of the empirical ESTAR model of Taylor et al. (2001) is examined for 4 bilateral real exchange rate series over an out-of-sample evaluation period of nearly 12?years. Point as well as density forecasts are constructed, considering forecast horizons of 1 to 22 steps head. The study finds that no forecast gains over a simple AR(1) specification exist at any of the forecast horizons that are considered, regardless of whether point or density forecasts are utilised in the evaluation. Non-parametric methods are used in conjunction with simulation techniques to learn about the models and their forecasts. It is shown graphically that the nonlinearity in the conditional means (or point forecasts) of the ESTAR model decreases as the forecast horizon increases. The non-parametric methods show also that the multiple steps ahead forecast densities are normal looking with no signs of bi-modality, skewness or kurtosis.     

The real exchange rate,regime changes and volatility shifts

We make use of a data-set with both long span and high frequency to test for purchasing power parity (PPP) while allowing for a structural shift in the volatility of the Mexico–US bilateral real exchange rate (RER). The Kim, Leybourne and Newbold (2002) unit root test, robust to changes in the innovation variance, indicates mean stationarity of the monthly RER, and hence evidence of PPP, for the full sample, 1930–2012, and various subsamples. The persistence of deviations of the real rate from its PPP level as measured by half-lives ranges from 1.37 to 2.41 years.     

THE COMPLEX RESPONSE OF MONETARY POLICY TO THE EXCHANGE RATE

We estimate a flexible non‐linear monetary policy rule for the United Kingdom to examine the response of policymakers to the real exchange rate. We have three main findings. First, policymakers respond to real exchange rate misalignment rather than to the real exchange rate itself. Second, policymakers ignore small deviations of the exchange rate; they only respond to real exchange under‐valuations of more than 4% and over‐valuations of more than 5%. Third, the response of policymakers to inflation is smaller when the exchange rate is over‐valued and larger when it is under‐valued. None of these responses is allowed for in the widely used linear Taylor‐type rules, suggesting that monetary policy is better analysed using a more sophisticated model, such as the one suggested in this paper.     

The persistence in real exchange rate: Evidence from East Asian countries

In this article, we examine the degree of persistence in monthly real exchange rate of six East Asian countries in relation to their two major trading partners, the United States and Japan, to study the validity of PPP for the 1976:01–2009:03 period. To investigate the persistency in real exchange rate series, we use sum of the autoregressive (AR) coefficients and the confidence interval for it using grid-bootstrap procedure recently developed by Hansen (1999). We have two findings: first, we find evidence for high persistency in real exchange rate in terms of the Japanese yen for five countries and for four countries in terms of the US dollar the for the full and pre-crisis sample periods. Second, for the post-crisis period, the presence of low persistency in real exchange rate supports PPP for three countries in terms of the Japanese yen and five countries in terms of the US dollar. These findings indicate that real exchange rate series of five East Asian countries are mean-revert based on their exchange rate policies and East Asian countries can form a currency union.     

TAYLOR RULE REACTION COEFFICIENTS AND REAL EXCHANGE RATE PERSISTENCE

Recent literature has established a link between the persistence of real exchange rates and the degree of inertia in Taylor rule monetary policy reactions functions. This paper provides a different view on this link by investigating how the size of Taylor rule reaction coefficients impacts the adjustment dynamics of the real exchange rate. Within a stylized sticky‐price open‐economy macro model, it is demonstrated that a stronger interest rate reaction to inflation in the Taylor rule raises the convergence speed of the real exchange rate. Conversely, raising the coefficient on the output gap or attending to the exchange rate in an open‐economy version of the Taylor rule slows down real exchange rate adjustment. In all cases, more rapid convergence comes at the cost of stronger initial real exchange rate misalignments in the wake of monetary policy shocks.     

An empirical test of purchasing power parity in selected developing countries: a panel data approach

Abstract

This paper examines the empirical validity of Purchasing Power Parity (PPP) for certain large developing economies by using a panel unit root methodology. The test results show that a long run real exchange rate depreciation trend exists in certain developing countries. Without considering this depreciation trend, it is hard to verify the stationarity and to explain the existence of the extremely long half-lives of the real exchange rates. When a linear time trend is included in the tests, the results tend to support the stationarity of the underlying real exchange rate processes, and the half-lives are significantly shorter and their range can be explained by transitory disturbances.     

Unemployment persistence in OECD countries after the Great Recession

The 2008 economic downturn in the United States resulted in a wave of contractionary effects across many OECD countries. This paper investigates the pattern of the unemployment persistence in the United States and other 28 OECD countries before and after the Great Recession. To detect possible changes in the pattern of unemployment persistence, we employ a mean bias-corrected estimation of the persistence parameter with a rolling window of five years. In addition, we estimate the most likely date of change in the trend function of unemployment to test whether there was any significant change in the pattern of unemployment persistence after the Great Recession. We find significant evidence of a structural break and hysteresis in unemployment rates, with a persistence parameter close to unity, across the United States and other 28 OECD countries. Besides, bootstrap permutation tests show that all half-lives and impulse response functions have significantly changed after the Great Recession. Therefore, our findings call for structural reforms aimed at improving labor market performance, to prevent upward shifts in unemployment across OECD countries from becoming permanent.     

Are OECD consumption–income ratios stationary after all?

This paper investigates the stochastic properties of the consumption–income ratio for a sample of 23 OECD countries over the period 1960–2005. For that purpose, we employ a battery of recently developed panel unit root and stationarity tests. Our findings from panel unit root tests which do not control for structural breaks appear in line with those from previous studies since they are clearly supportive of the unit root hypothesis. In stark contrast stand the results obtained from the application of a panel stationarity test with multiple breaks, which support the existence of regime-wise stationarity in OECD consumption–income ratios once we control for cross-sectional dependence through bootstrap methods. These findings are reinforced by the median-unbiased estimates of half-lives obtained from impulse-response functions which are found to be finite for the 23 OECD countries.     

Does purchasing power parity hold sometimes? Regime switching in real exchange rates

Standard unit root tests are not very powerful in drawing conclusions regarding the validity of Purchasing Power Parity (PPP). Rather than asking whether PPP holds throughout the whole sample period, we examine, in this study, if PPP holds sometimes by employing Hamilton-type (1989) Markov regime switching models. When at least one of multiple regimes is stationary, PPP holds locally within the regime. There are indeed various reasons that we should expect that the persistence of real exchange rates changes over time. Employing five real exchange rates spanning more than 100 years, we find herein strong evidence that the strength of PPP varies during the sample periods and that there exist stationary regimes in which PPP holds. Throughout the article, we also make comparisons to previous Markov regime switching estimation results by Kanas (2006) on the same data series. The new Markov switching model selection criterion of Smith et al. (2006), which is devised especially for discriminating Markov regime switching models, unambiguously indicates a preference for the Hamilton-type Markov regime switching model employed in this study. We also find that the evidence for PPP is not much different across different nominal exchange rate arrangements.     

On real interest rate persistence: the role of breaks

The role of structural breaks in long spans of ex-post real interest rates for 10 industrialized countries is studied. First, the persistence of the real interest is assessed with newly proposed low-frequency tests of Müller and Watson (2008). Second, the test of Leybourne et al. (2007) for a change in persistence of a time series is applied to the real interest rate. The results show that real interest rates over the full sample period do not fit a covariance-stationary or unit-root model, nor a fractionally integrated, near-unit-root or local-level model. Instead, the persistence of real rates changes over time and there are periods when the real rate is covariance-stationary and other periods when it follows a unit-root process.     

The inadequacy of linear autoregressive model for real exchange rates: empirical evidence from Asian economies

Utilizing the formal linearity test of Luukkonen, Saikkonen and Teräsvirta (Biometrika, 75, 491-499, 1998) as diagnostic tool, the empirical finding suggests that the linear autoregressive (AR) model is inadequate in describing the real exchange rates behaviour of 11 Asian economies. It is noted that the conventional battery of diagnostic tests is capable of identifying the inadequacy of the linear model in only three of these series. Moreover, the linearity nature of this behaviour has been formally rejected in favour of the non-linear smooth transition autoregressive (STAR) model. The finding of non-linearity in the data generating process of these real exchange rates warrants that the use of linear framework in empirical modelling and statistical testing procedures in the field of exchange rates may lead to an inappropriate policy conclusions.