Fourier nonlinear quantile unit root test and PPP in Africa

We test the PPP hypothesis in 29 African countries using a newly developed nonlinear Quantile unit root test with a Fourier function which accounts for smooth breaks. Simulation indicates that the proposed new test has higher power than the conventional Quantile unit root test as proposed by Koneker and Xiao (2004). Our empirical results provide support for the PPP hypothesis in 21 out of 29 African countries, a unique discovery using their real effective exchange rates. It appears that incorporating Fourier function to nonlinear Quantile unit root test gets us closer and closer to solving the PPP puzzle in Africa.     

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.     

Purchasing power parity with flexible Fourier stationary test for Central and Eastern European countries

This study applies stationary test with a Fourier function proposed by Enders and Lee (2004, 2009) to test the validity of long-run Purchasing Power Parity (PPP) to assess the nonstationary properties of the Real Exchange Rate (RER) for seven Central and Eastern European Countries (CEECs). We find that our approximation has higher power to detect U-shaped breaks and smooth breaks than linear method if the true data generating process of exchange rate is in fact a stationary nonlinear process. We examine the validity of PPP from the nonlinear point of view and provide robust evidence clearly indicating that the PPP holds true for all CEECs. Our findings point out their exchange rate adjustment is mean reversion towards PPP equilibrium values in a nonlinear way.     

Finite-sample size distortion of the AESTAR unit root test: GARCH,corrected variance–covariance matrix estimators and adjusted critical values

The behaviour of the asymmetric exponential smooth transition autoregressive (AESTAR) unit root test, which allows for asymmetric and nonlinear reversion to equilibrium, is examined in the presence of generalized autoregressive conditional heteroscedasticity (GARCH). It is found that while the test is relatively robust in the presence of ‘low volatility’ GARCH processes, it exhibits substantial size distortion when large values of the volatility parameter are considered. Attempted resolution via the routine application of heteroscedasticity consistent (or ‘corrected’) covariance matrix estimators (HCCMEs) is shown to result in overwhelming size distortion due to their impact upon the finite-sample distribution of the underlying test statistic. However, application of a corrected HCCME, in combination with critical values derived specifically under its use, results in the control of test size. Analogous results for the Dickey–Fuller (1979) test are presented to permit comparison with a test considering linear, symmetric adjustment. It is found that the AESTAR test is subject to far greater distortion than its linear, symmetric alternative. In summary, the results indicate that caution must be exercised when applying the AESTAR test to macroeconomic and financial time series, particularly if routine application of corrected covariance matrix estimators occurs.     

Quantile unit root test and the PPP in Africa

In this study, we apply the Quantile unit root test and revisit the Purchasing Power Parity (PPP) in 20 African countries using real effective exchange rates over the period 1971Q1 to 2012Q4. While traditional unit root tests fail to reject unit root hypothesis in most of the countries, results from Quantile unit root test reject unit root null hypothesis in Ghana, Mauritius, Niger, South Africa, and Togo, providing support for the PPP at least in these five countries. We further estimate the half-life based on Quantile autoregressive (QAR) model to be about 4.57–7.96 quarters (1–2 year).     

Quantile nonlinear unit root test with covariates and an application to the PPP hypothesis

In this article, we employ the methods initiated by Hansen (1995) to develop new quantile nonlinear unit root tests with covariates. The limiting distributions of our proposed tests are derived, which are dependent on nuisance parameter reflecting the correlation between the equation error and the covariates. To deal with this inferential difficulty, two alternative procedures based on either consistent estimate of the nuisance parameter or bootstrap implementation of the test are proposed. Monte Carlo simulations show that the proposed tests perform very well in finite samples and large power gains can be achieved by including correlated covariates in the testing equation. The proposed tests are applied to the PPP hypothesis. The empirical results indicate that the real exchange rates are not constant unit root processes.     

Sticky prices and purchasing power parity deviations: Empirical implications

This note tests one implication of the hypothesis that purchasing power parity (PPP) deviations are partly caused by different pricing behavior in goods and asset markets. Cross-country regressions of the variance of PPP deviations on the variance of money supply innovations support the hypothesis.     

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.     

Testing the purchasing power parity in panel data

This paper empirically tests the purchasing power parity (PPP) using panel unit root tests. We employ a battery of panel unit root tests: LM-bar statistic [Testing for unit roots in heterogeneous panels, Working paper, University of Cambridge] is employed to account for serially correlated errors. The statistic proposed by Breitung [Adv. Econom. 15 (2000) 161.] and the KPSS-based statistic of Hadri [Econ. J. 3 (2000) 148.] are also used. In addition, we also employ a SUR estimator to account for possible cross-sectional effect. Data of 45 economies from 1980 to 1999 are used to test the PPP hypothesis. We find that these estimators tend to get supportive results when the data frequency becomes lower, which substantially characterizes the long-run property of the PPP hypothesis.     

Purchasing power parity vs. uncovered interest rate parity for NAFTA countries: The value of incorporating time-varying parameter model

In 1994, the United States, Canada, and Mexico signed the North American Free Trade Agreement (NAFTA) to strengthen economic cooperation. To examine the effects of the NAFTA, this study revisits Purchasing Power Parity (PPP) for NAFTA countries by applying a time-varying cointegration model. Under the time-varying assumption, it improves the explanatory power of reality via the model specification test. Given that, the validity of PPP for NAFTA countries varies over time. Especially, the PPP elasticity based on the consumer price index (CPI) is more volatile than the producer price index (PPI) -based. Thus, the stabilization policy of the consumption sector must be a high priority over the production sector. Moreover, the validity of the Uncovered Interest Rate Parity (UIRP) is examined by the time-varying cointegration model. The aim is to compare the results of the PPP and UIRP. This suggests that the PPP is more useful than the UIRP in evaluating the movement of the exchange rate in the long-run.     

Panel asymmetric nonlinear unit root test and PPP in Africa

This study revisits purchasing power parity (PPP) theory for 20 African countries using panel asymmetric nonlinear unit root test proposed by Emirmahmutoglu and Omay (2014), through the sequential panel selection method of Chortareas and Kapetanios (2009). While standard panel unit root tests fail to support the PPP, the empirical results from panel asymmetric nonlinear unit root test do support the PPP. However, additional tests reveal that support in all 20 African countries is mostly due to stationarity of the real effective exchange rates of Ghana and Rwanda where the adjustment process towards equilibrium is nonlinear and asymmetric.     

The FMLS-based CUSUM statistic for testing the null of smooth time-varying cointegration in the presence of a structural break

In this paper we extend the FMLS-based CUSUM cointegration test (Xiao and Phillips, 2002) for testing the smooth time-varying cointegration null hypothesis. For this purpose we use Chebyshev time polynomials to specify time-varying coefficients under the null. We derive the limiting distribution of the statistic, which is pivotal with the order of the Chebyshev time polynomials, and we provide the critical values to conduct the proposed test.     

Asymmetric Behaviour of Inflation around the Target in Inflation‐Targeting Countries

We explore the asymmetric behaviour of inflation around the target level for inflation‐targeting countries. The first rationale behind this asymmetry is the asymmetric policy response of the central bank around the target. Central banks could have a stronger bias towards overshooting rather than undershooting the inflation target. Consequently, the policy response would be stronger once the inflation jumps above the target, compared to a negative deviation. Second rationale is the asymmetric inflation persistence. We suggest that recently developed Asymmetric Exponential Smooth Transition Autoregressive (AESTAR) model provides a convenient framework to capture the asymmetric behaviour of inflation driven by these two effects. We further conduct an out‐of‐sample forecasting exercise and show that the predictive power of AESTAR model for inflation is high for some countries in our sample, especially at long‐horizons.     

Revisiting purchasing power parity in G6 countries: an application of smooth time-varying cointegration approach

This study revisits purchasing power parity (PPP) for the G6 countries (i.e., Canada, Italy, Japan, France, Germany, the UK) using smooth time-varying cointegrating approach, proposed by Park and Hahn (Econom Theory 15:664–703, 1999). Using monthly data over the 1971M1–2013M12 period, our empirical results indicate that PPP holds in two out of six countries (i.e., France and Germany).     

Purchasing power parity in Brazil: a test for fractional cointegration

The purpose of this paper is to test the validity of the purchasing power parity (PPP) doctrine in Brazil. Historical data for the period 1855–1996 are considered. The period 1855–1990 is also analysed in order to compare the results with those obtained by Zini and Cati (1993) using the conventional cointegration analysis. This article uses fractional cointegration analysis, a flexible methodology which allows for more subtle forms of mean reversion. The tests performed are those of Geweke and Porter-Hudak (1983), and of Hurvich and Ray (1995). The critical values for both tests are generated by simulation because they are non-standard. The empirical results do not support the absolute PPP hypothesis but the relative PPP holds in the long run.     

Purchasing power parity for fifteen Latin American countries: Stationary test with a Fourier function

This study applies a stationary test with a Fourier function, proposed by Becker et al. (2006), to test the validity of long-run purchasing power parity (PPP) in fifteen Latin American countries over the period of December 1994 to February 2010. The empirical results from the univariate unit root tests indicate that PPP does not hold for these fifteen countries under study. However, a stationary test with a Fourier function indicates that PPP is valid for four of these 15 Latin American countries and they are Brazil, Chile, Ecuador and Uruguay. These results have important policy implications for these fifteen Latin American countries under study.     

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.     

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.     

Testing the relative purchasing power parity hypothesis: the case of Korea

This study examines the relative purchasing power parity (PPP) hypothesis using the data from the Korean won–US dollar and the Korean won–Japanese yen foreign exchange markets. We extract proxies for inflation from stock market returns of Korea, the United States and Japan based on the method used by Chowdhry, Roll and Xia in 2005. We explicitly test the relative PPP hypothesis in light of the short-run price volatility using monthly, bimonthly and quarterly data from 1 January 1998 to 31 December 2012. Our findings suggest that the empirical test results from the entire sample period do not support the relative PPP hypothesis. However, the results from the sample period excluding the Asian Financial Crisis period show that the relative PPP hypothesis holds for the Korean won–US dollar market with a moderate magnitude of inflation impact, but not for the Korean won–Japanese yen market. Abrupt changes in exchange rates during the crisis period may have affected the relationship between inflation and exchange rates. This result also suggests that factors other than inflation might have affected the Korean won–Japanese yen exchange rate.     

The pricing of time-varying beta

We generalize an asset pricing model based on the Arbitrage Pricing Theory (APT) allowing beta to be time-varying. Making beta a random variable adds flexibility to the model because permits a non-linear relation between individual returns and the set of factors, and accounts for the effect of possible omitted variables. We integrate the conditional APT with a general linear stochastic process for beta. We analyze the behavior of the conditional expected return, the conditional variance and conditional covariance of individual asset returns as functions of the conditional moments of beta. On considering time-varying betas we introduce another source of uncertainty (risk) independent of the factors. We need to disentangle if this extra risk is systematic or non-systematic. To this end, we introduce a modified conditional APT model that rationalizes why the time variation of beta may represent extra systematic risk. For a sample of individual stocks, we test the hypothesis of time-varying beta and the feasibility of the modified conditional APT. We present a test for time-varying beta based on the conditional second moments of returns. We find that there is strong evidence against constancy of betas in favor of a random coefficient model, and that the time variation of beta is due to non-systematic behavior of the firms and investors should be able to diversify this risk away.