Reexamining the PPP hypothesis: A nonlinear asymmetric heterogeneous panel unit root test

In this study, we re-examine the PPP hypothesis in the light of the new developments in the unit root testing literature. The recent theoretical findings have pointed out that the real exchange rate series exhibit asymmetric nonlinear behavior. A unit root test applied to analyze the PPP hypothesis therefore, should also take into account this asymmetry inherent in the real exchange rate. Different unit root tests that consider the presence of these data features have been developed in the time series literature. However, a true attempt to test the PPP hypothesis should take a panel data approach. To this end, we propose a nonlinear heterogeneous panel unit root test where the alternative hypothesis allows for symmetric or asymmetric exponential smooth transition autoregressive nonlinearity and provide its finite sample properties. We apply our test to the real exchange rates of the 15 European Union countries against the US dollar. While the results of the linear and symmetric nonlinear heterogeneous panel unit root tests are against the PPP hypothesis, the asymmetric nonlinear heterogeneous panel test that we propose gives support for the PPP hypothesis as expected. Therefore, the conclusions drawn from the linear panel unit root tests or the nonlinear panel unit root tests that do not take asymmetry into account might be misleading.     

Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies

An IV approach, using as instruments non-linear transformations of the lagged levels, is explored to test for unit roots in panels with general dependency and heterogeneity across cross-sectional units. We allow not only for the cross-sectional dependencies of innovations, but also for the presence of co-integration across cross-sectional levels. Unbalanced panels and panels with differing individual short-run dynamics and cross-sectionally related dynamics are also permitted. We also more carefully formulate the unit root hypotheses in panels. In particular, using order statistics, we make it possible to test for and against the presence of unit roots in some of the individual units for a given panel. The individual IV t -ratios, which are the bases of our tests, are asymptotically and normally distributed and cross-sectionally independent. Therefore, the critical values of the order statistics as well as the usual average statistic can be easily obtained from simple elementary probability computations. We show via a set of simulations that our tests work well, whereas other existing tests fail to perform properly. As an illustration, we apply our tests to the panels of real exchange rates, and find no evidence for the purchasing power parity hypothesis, which is in sharp contrast with the previous studies.     

Re-examining the real interest rate parity hypothesis (RIPH) using panel unit root tests with asymmetry and cross-section dependence

This paper investigates the validity of the real interest rate parity hypothesis (RIPH) using a panel unit root approach. For this purpose, first we estimate the possible nonlinear data-generating processes of the real interest rate differential series and using these estimates determine which panel unit root test is better for analyzing the RIPH. To this end, smooth transition autoregressive and threshold autoregressive (TAR) models are estimated for two different panels of countries: G7 and post-Soviet transition economies. The results show that the data displays both strong asymmetry and high transition speed. Therefore, secondly, we propose a new panel unit root test where the alternative is stationary with asymmetric TAR adjustment, and provide their empirical power properties. Finally, we demonstrate that our newly proposed test is able to provide conclusive evidence in favor of the RIPH in contrast to the other panel unit root tests considered.     

The real exchange rate and the black market exchange rate in developing countries

This article tests for the validity of the Purchasing power parity (PPP) theory using both the black market and the official exchange rates for panels with cross sectional dependency. The test is conducted using a newly developed, nonlinear IV panel unit root test that properly handles cross-sectional dependency for thirty-seven developing countries. We find that the null of joint unit root hypothesis is rejected for the whole panel, using the black market exchange rate, and for sub-panels of African and high inflation countries, using either exchange rate. The black market-based real exchange rates are, therefore, shown to provide stronger evidence for the purchasing power parity theory than do the official rates. This finding is consistent with the observation that black market exchange rates better represent market forces and thus are more relevant when testing for the validity of the PPP theory in developing countries.     

A reappraisal of the evidence on PPP: a systematic investigation into MA roots in panel unit root tests and their implications

Panel unit root tests of real exchange rates—as opposed to univariate tests—usually reject non-stationarity. These tests, however, could be biased if the real exchange rate contained MA roots. Indeed, two independent arguments claim that the real exchange rate, being a sum of a stationary and a non-stationary component, is possibly an ARIMA (1, 1, 1) process. Monte Carlo simulations show how systematic changes in the parameters of the components, of the test equation and of the correlation matrix affect the size of first and second-generation panel unit root tests. Two components of the real exchange rate—the real exchange rate of a single good and a weighted sum of relative prices—are constructed from the data for a panel of countries. Computation of the relevant parameters reveals that panel unit root tests of the real exchange rate are severely oversized, usually much more so than simple augmented Dickey-Fuller tests. Thus, the evidence for purchasing power parity from first and second-generation panel unit root tests may be merely due to extreme size biases.     

Is there a unit root in the inflation rate? New evidence from panel data models with multiple structural breaks

In this article, we examine whether or not the inflation rate for 17 OECD countries can be modelled as a stationary process. We find that (1) conventional univariate unit root tests without any structural breaks generally reveal that the inflation rate contains a unit root; (2) the KPSS univariate test with multiple structural breaks reveals that for 10 out of 17 countries inflation is stationary; and (3) the KPSS panel unit root test reveals strong evidence for stationarity of the inflation rate for panels consisting of countries which were declared nonstationary by univariate tests.     

Non-linear quantile unit root test and PPP: more evidence from Africa

It is now a common practice to establish stationarity of the real exchange rate as a sign of purchasing power parity (PPP) hypothesis. In this article, we consider the real effective exchange rates of 29 African countries. When we apply conventional linear unit root tests, we find support for the PPP in eight countries. However, when we shift to the newly introduced non-linear quantile unit root test, support for the PPP increases to 15 countries.     

The real exchange rate in Brazil Mean reversion or random walk in the long run?

This paper studies the behavior of the real exchange rate in Brazil over the longest possible period for which data are available: 1855–1990. Does the real exchange rate follow a random walk or does it revert to its mean, possibly nonstationary, level? The evidence is mixed. Formal tests can not reject the hypothesis of nonstationary behavior, although the judgement is borderline. However, time-series identification favors a stationary interpretation, and simple autoregressive processes for the real exchange rate yield extremely robust and satisfactory estimates.     

Real interest rates: nonlinearity and structural breaks

Real interest rate is a crucial variable that determines the consumption, investment and saving behavior of individuals and thereby acts as a key policy tool that the central banks use to control the economy. Although many important theoretical models require the real interest rates to be stationary, the empirical evidence accumulated so far has not been able to provide conclusive evidence on the mean reverting dynamics of this variable. To resolve this puzzle we re-investigate the stochastic nature of the real interest rates by developing unit root tests for nonlinear heterogeneous panels where the alternative hypothesis allows for a smooth transition between deterministic linear trends around which stationary asymmetric adjustment may occur. When the newly developed panel unit root tests are applied to the real interest rates of the 17 OECD countries, we were able to uncover overwhelming empirical support in favor of mean reversion in the short-run and long-run real interest rates. Therefore, these results show that the conclusions drawn from a miss-specified test that ignores the presence of either nonlinearity, structural breaks or cross sectional dependence can give quite misleading results about the stochastic behavior of the real interest rates.     

Testing a theoretical model of mortgage demand on UK data

This study explores whether the long-run purchasing power parity (PPP) hypothesis holds for selected real exchange rates from Turkish economy during the period 1982M1–2003M12. In addition to conventional unit root tests, five different unit root test procedures have been applied including efficient point-optimal tests, extended M tests and GLS-detrended variants of DF tests, to four monthly real exchange rate series defined in terms of both producer and consumer price indices. The countries analysed are the USA, the UK, Germany and Italy which are major trade partners of Turkey. Mixed evidence is found for the long-run PPP hypothesis when real exchange rate is defined in terms of German DM and Italian Lira. However, the empirical analysis reveals that the PPP hypothesis holds strongly in the long-run for the UK£ and US$ based real exchange rates series using either PPI or CPI. In corroboration with other studies in the literature, the bias correlated half-life estimates suggest relatively faster speeds of adjustment supporting the view that the deviations from the PPP rate dissipate rather quickly for relatively high inflation countries.     

Some cautions on the use of nonlinear panel unit root tests: Evidence from a modified series-specific non-linear panel unit-root test

The purpose of this paper is to examine the relevance of applying nonlinear panel unit root test to examine the non-linear mean reversion behaviors of real exchange rates. We find that nonlinear panel unit root test may achieve lower power performance as compared to its alternative of linear panel unit test when the data generating process does not contain significant non-linear components. This finding post cautions to researchers in modeling and testing real exchanges behavior. We also develop a modified series-specific nonlinear panel unit root test and find evidence in favor of purchasing power parity hypothesis for China's four ASEAN trading partners in the period of February 1997 to August 2009.     

Digging out the PPP hypothesis: an integrated empirical coverage

We use several popular tests to test the validity of the Purchasing Power Parity (PPP) hypothesis. In particular, we analyze four classes of tests??standard univariate unit root tests, co-integration, panel unit root tests, and unit root tests for nonlinear frameworks??for a dataset consisting of 20 bilateral exchange rates. Through this approach, we ascertain the effectiveness of each methodology in assessing the validity of PPP. Overall, our results suggest little evidence to support PPP. Among the conducted tests, the Panel Analysis of Nonstationarity in the Idiosyncratic and Common components (PANIC) provides the richest insights by disentangling the possible sources of non-stationarity of real exchange rates. The relevance of using price indices with different characteristics is also pinpointed.     

City CPI Convergence in Mexico

This paper tests the purchasing power parity hypothesis within a single developing country currency area: Mexico. This work stems from research in comparing price movements across countries and a growing literature on price dynamics within a single currency area. The author uses city Consumer Price Index data for 34 cities in Mexico over the period 1982–2000. He followed the standard procedure of testing for I(1) processes in relative city prices, or city real exchange rates, using univariate and panel unit root tests. The main results of the paper are: First, Mexican city relative prices are stationary—the data rejects the hypothesis that city real exchange rates contain a random walk, but only using panel unit root techniques. Finally, regional demand and supply homogeneity implies stronger evidence for price parity within regions, while there is considerable evidence of regional price convergence, regional homogeneity does not guarantee faster convergence.     

Hysteresis vs. natural rate of US unemployment

This paper investigates the stochastic nature of the unemployment rate allowing for cross-section dependence from a panel of US state-level data. We first employ the PANIC method to identify the common and idiosyncratic components. Powerful recursive mean adjustment (RMA) methods are used to test for unit roots. We find significant evidence of a nonstationary common component when the data from the most recent recession are included. Even when stationarity is empirically supported, the bias-corrected half-life of the common component appears very long, casting doubt on the usefulness of the natural rate hypothesis.     

Examining the evidence of purchasing power parity by recursive mean adjustment

This paper revisits the empirical evidence of purchasing power parity under the current float by recursive mean adjustment (RMA) proposed by So and Shin (1999). We first report superior power of the RMA-based unit root test in finite samples relative to the conventional augmented Dickey–Fuller (ADF) test via Monte Carlo experiments for 16 linear and nonlinear autoregressive data generating processes. We find that the more powerful RMA-based unit root test rejects the null hypothesis of a unit root for 16 out of 20 current float real exchange rates relative to the US dollar, while the ADF test rejects only 5 at the 10% significance level. We also find that the computationally simple RMA-based asymptotic confidence interval can provide useful information regarding the half-life of the real exchange rate.     

Breaking Trend Functions in Real Exchange Rates: Evidence from Seventeen OECD Countries

This paper tests for unit roots in dollar-based and DM-based real exchange rates using quarterly data (from 1957:i to 1995:iv) for seventeen OECD countries. The results show that the unit root hypothesis cannot be rejected even if allowance is made for the possibility of a one-time change in the mean of the series at an unknown point in time. This is evidence against the hypothesis of absolute long-run purchasing power parity over this period.     

Long‐Run PPP under the Presence of Near‐to‐Unit Roots: The Case of the British Pound–US Dollar Rate*

Empirical tests typically provide evidence that the British pound–US dollar exchange rate and the relative wholesale price index contain exact unit roots and exhibit cointegration. However, the cointegrating vector is significantly different from [1, ?1], thus raising doubts on the validity of the purchasing power parity (PPP) hypothesis. Following Elliott (1998 ), we show that if the exchange rate and relative price series contain near‐to‐unit roots in the context of a bivariate system, then any inference on the “cointegrating” vector and consequently on PPP, which is based on standard cointegration estimation methods, will be misleading. We then argue that the existing evidence against the PPP hypothesis in the British pound–US dollar market can be attributed to the finite sample bias of the standard cointegration estimators, arising from an endogenous and “nearly” nonstationary regressor. We also show that when robust procedures are employed the evidence favors the PPP hypothesis.     

Removal of farm subsidies in a regional economy: a computable general equilibrium analysis

There are a number of studies that examine the purchasing power parity (PPP) hypothesis. The empirical findings from the extant literature for the PPP hypothesis are mixed. This article applies univariate and panel Lagrange Multiplier (LM) unit root tests with one and two structural breaks to real exchange rates for 15 Asian countries. The univariate LM unit root tests find evidence of PPP for two-thirds of the sample. The results from the panel LM unit root test support long-run PPP for the Asian countries in the sample. The results from the LM panel unit root tests differ from those of existing panel unit root tests of PPP for Asian countries that have not allowed for the existence of structural breaks.     

The Behaviour of the Real Exchange Rate: Evidence from an Alternative Price Index

Although the long–run purchasing power parity (PPP) hypothesis is expected to hold across tradable goods, all price indices available to researchers for testing the validity of PPP contain some proportion of non–tradable goods prices, which may generate substantial persistence in the real exchange rate. We construct time series for quarterly price indices that minimize the presence of non–tradable goods for six major economies. Applying recently developed nonlinear econometric techniques to the resulting five US dollar real exchange rate series for the recent floating exchange rate regime, we provide evidence that the nonlinear mean reverting properties of these real exchange rate series are stronger than the mean reverting properties of real exchange rate time series constructed using the consumer price index (CPI). In turn, these results have a natural economic interpretation.
(J.E.L.: F31).     

Output dynamics of the G7 countries--stochastic trends and cyclical movements

Using a time series framework, the paper studies the interactions of the annual real per capita GDP data of the G7 countries. Evidence is found of six common nonstationary processes behind the international output dynamics. In addition, there is evidence for the existence of a common business cycle among these countries. The trend and cycle components of each output series are obtained with a procedure that accounts for the presence of both the common nonstationary and cyclical factors. It is found that the relative variability and the correlation of the trend and cycle components are not similar across the G7 countries.