Convergence in Per Capita Carbon Dioxide Emissions Among G7 Countries: A TAR Panel Unit Root Approach

The subject of this paper is the examination the convergence of per capita carbon dioxide emissions of the G7 countries during the 1960–2005 period in a nonlinear panel analysis framework. In this approach, first the linearity of the series was tested, and when the linearity was rejected, the threshold autoregressive (TAR) panel unit root test, which splits the data into two regimes, was employed to examine the stationarity properties of the series. Because the null of linearity was rejected in the first step, we tested the stationarity of the series using the TAR panel unit root test. In the TAR panel unit root test, we found that the United Kingdom was the transition country whose per capita carbon dioxide (CO₂) emissions determined the switch from one regime to the other. The results showed that convergence existed in the first regime and divergence, in the second. When we tested whether absolute or conditional convergence existed, we found that the per capita CO₂ emissions were conditionally converging in the first regime.     

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.     

FURTHER EVIDENCE ON REAL INTEREST RATE EQUALIZATION: PANEL INFORMATION,NON‐LINEARITIES AND STRUCTURAL CHANGES

Previous studies applying traditional unit root tests generally have difficulty providing widespread evidence supporting the real interest rate parity hypothesis (RIPH). This paper aims to analyse the empirical fulfilment of RIPH for 17 OECD countries by employing many recently developed unit root tests. Power of the tests is raised by taking different approaches, such as using cross‐sectional information, accounting for non‐linear adjustment towards the equilibrium and allowing for structural changes. The combined results of the tests using panel information show that broad evidence in favour of RIPH prevails for 13 of the 17 countries. By contrast, univariate tests fail to make widespread rejections of the unit‐root hypothesis. Our evidence reveals a high degree of market integration for developed countries, and the effect of monetary policies as a stabilization tool might be limited at least in the long run.     

汇率非线性因素在部分亚洲货币汇率中的特征——检验购买力平价论的新方法

当真实汇率运动实际上是非线性过程,而假设它为线性时,那么检验购买力评价理论的标准单位根检验通常是低效力的。文章运用带有单位根的门限自回归模型模拟了包括中国在内的6个亚洲主要新兴市场国家货币兑美元的真实汇率,发现它们都具有较强的非线性,说明了传统的线性方法不再具备模拟真实汇率的能力,且除人民币以外的其他5种货币的真实汇率都表现出了平稳非线性特征,在异动时期具有均值回归的趋势。周期性的金融危机是导致中国以外的其他5个国家货币的真实汇率出现异动的主要因素。人民币真实汇率的非线性行为则表现出了与其他国家不同的特点,导致它出现异动的主要因素为人民币对内和对外价格的相互背离,人民币真实汇率没有表现出向均值调整的趋势,甚至在异动时期呈现了向均值偏离的趋势。     

Investigation of the nonlinear behaviour in real exchange rates in developing regions

This article examines whether the purchasing power parity (PPP) theory holds or not for the economies in different developing regions located in Africa, Asia and Latin America. In order to investigate this issue, a nonlinear panel unit root test is used to determine if some or all of the real exchange rates in a panel follow a stationary exponential smooth transition autoregressive process. By applying the nonlinear panel unit root test, our results demonstrate an empirical support for the theory of PPP for the economies in developing regions.     

Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

We suggest a Monte Carlo simulation-based unit root test of the purchasing power parity theory for Latin American countries. Under the null hypothesis, we use a Markov regime-switching (MS) model with unit root in the conditional location and MS volatility dynamics. Under the alternative hypothesis, the proposed test incorporates Markov regime-switching autoregressive moving average (MS-ARMA) plus MS volatility dynamics. Under both the null and alternative hypotheses, one of the volatility models estimated is Beta-t-EGARCH, which is a recent dynamic conditional score volatility model. We use data on real effective exchange rate time series for 14 Latin American countries. For each country, we estimate by Monte Carlo simulation the critical values of the unit root test. We provide an economic discussion of the unit root test results and also study the robustness of MS-ARMA plus MS volatility with respect to smooth transition autoregressive models with Fourier function.     

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 for nonlinear panel unit roots under cross-sectional dependency — With an application to the PPP hypothesis

In this paper we propose a number of nonlinear panel unit root tests that are robust to cross-sectional dependency. These tests may be used to test the null hypothesis of non-stationarity against the alternative that some or all of the time series in the system of equations follow a stationary exponential smooth transition autoregressive (ESTAR) process. In contrast to previous research we relax the assumption that the cross-correlation structure is driven by a common-factor and consider an endogenous correlation structure. Based on the size and power results from the Monte Carlo simulations we recommend using the Wald version of our cross-sectional dependent robust nonlinear panel unit root (CDR-NPU) method.Finally, in an empirical application we demonstrate that our more powerful nonlinear method, in contrast to previous methods, can provide support for PPP even in smaller samples. In consistency with the univariate tests in Bahmani-Oskooee et al. (2008) our CDR-NPU tests support the theory that less industrialized economies exhibit stronger and more distinct nonlinear adjustment patterns towards PPP.     

Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process

The paper considers nonlinear logistic smooth transition autoregressive (LSTAR) process and aims to detect the unit root under the null hypothesis of a random walk process against the alternative of a stationary LSTAR process and to estimate the parameters of the process in Bayesian framework using MCMC. The simulation study is carried out for investigating the performance of the Bayes estimators for parameters and Bayesian unit root test and it has been observed that the estimates of parameters of the LSTAR process are close to the true parameter values. It has been observed that the Bayesian unit root test performs well and the power of the test is high even for the boundary cases having root close to unity, at least when the sample size is large. Since the LSTAR models are widely applied for real exchange rate modeling, the theoretical results are illustrated empirically for the real exchange rates of ten OCED countries.

     

A RE‐EXAMINATION OF REAL INTEREST PARITY IN CEECs USING ‘OLD’ AND ‘NEW’ SECOND‐GENERATION PANEL UNIT ROOT TESTS

This study applies ‘old’ and ‘new’ second‐generation panel unit root tests to check the validity of the long‐run real interest rate parity (RIP) hypothesis for ten Central and Eastern European Countries (CEECs) with respect to the Euro area and an average of the CEECs’ real interest rates. When the ‘new’ panel unit root tests are carried out relative to the Euro area rate as reference, we confirm the results of previous studies that support the RIP hypothesis, and the results of the ‘old’ tests used as a benchmark. Nevertheless, when the ‘new’ tests are performed using the average of the CEECs’ rate as reference, our results are mitigated, revealing that the hypothesis of CEECs’ interest rates convergence cannot be taken for granted. From a robustness analysis perspective, our findings indicate that the RIP hypothesis for CEECs should be considered with caution, because the RIP hypothesis is sensitive to the retained reference rate for computing the real interest rate differential, and also to the retained countries in the sample.     

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.     

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.     

Is real GDP stationary? Evidence from a panel unit root test with cross-sectional dependence and historical data

We use historical data that cover more than one century on real GDP for industrial countries and employ the Pesaran panel unit root test that allows for cross-sectional dependence to test for a unit root on real GDP. At first, we find strong evidence against the unit root null. Our results seem to be robust to the chosen group of countries and, in most cases, the sample period. However, the sequential panel selection method reveals that the rejection of the unit root null is due to the stationarity of real GDP in a few countries only. Real GDP is less stationary mostly in fixed exchange rate regimes like the Gold Standard and the Bretton Woods system.     

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).     

Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?

Nonlinear models, especially threshold autoregressive [TAR] and exponential smooth transition autoregressive [ESTAR] classes, are widely applied for modeling real exchange rates in order to examine the validity of purchasing power parity [PPP]. Even though the nonlinear models are theoretically well-motivated, some of the recent findings cast doubts on their relevance for real exchange rates. In particular, the nonlinear models do not necessarily yield improved out-of-sample forecasts over linear models and add little value in resolving the well-documented PPP puzzle. Utilizing a nonparametric entropy measure of dependence proposed by Granger et al. (2004), we show, in this study, that the real exchange rates from four major countries had exhibited quite strong nonlinear serial dependence, which linear autoregressive models fail to replicate. Furthermore, the nonlinear TAR and ESTAR models estimated for the real exchange rates also have some difficulty in generating significant serial dependence structure actually observed in the data. Overall, other nonlinear models than the currently entertained TAR and ESTAR should be considered to study the dynamics of the real exchange rates.     

Purchasing power parity in transition countries: Sequential panel selection method

This study applies the Sequential Panel Selection Method (SPSM), proposed by Chortareas and Kapetanios (2009) to test the validity of long-run purchasing power parity (PPP) for a sample of 14 transition countries, using real effective exchange rates, from 1994 to 2012 (for both monthly and quarterly data). SPSM classifies the whole panel into a group of stationary series and a group of non-stationary series. In doing so, we can clearly identify how many and which series in the panel are stationary processes. Empirical results from the SPSM using the Panel KSS unit root test (Ucar and Omay, 2009) with a Fourier function indicate that PPP holds true for most of these transition countries studied. Our results have important policy implications for these transition countries under study.     

Macroeconomic performance index: a new approach to calculation of economic wellbeing

Since the rise of the global financial crisis, there has been revival of interest in performance indexes that measure the overall stance of the economy and the wellbeing of households. Such indexes typically consist of inflation, growth, employment and long-term interest rates. We develop such an index by appending exchange rate and weighting each variable by the inverse of its variance in order to prevent the more volatile variable to dominate the index. We call this macroeconomic performance index (MPI) and argue that such an index better explains the overall economic stance especially in emerging economies. We generate the index using data from three emerging economies, namely Turkey, Brazil and Poland. Our analysis indicates that the index has a nonlinear structure and hence we analyse its behaviour using threshold autoregressive (TAR) model. It is observed that MPI captures the economic stance and main economic incidents quite successfully in each subject country. To further see the relevance of the MPI, we run TAR cointegration analysis with consumer confidence indexes (CCIs) for the subject countries with TAR cointegration test. The results indicate long-term relationship between the MPI and CCI in all three countries.     

Mean-reversion in international real interest rates

This paper examines the mean-reversion property of real interest rates. Many past studies have reported puzzling outcomes of the mean-aversion of real interest rates for a number of countries. In the article, we employ panel unit root tests and carry out half-life estimation based on the bias-corrected bootstrap. These findings of the paper provide strong evidence that, in both major Western and East Asian capital markets (including several emerging ones), real interest rates are mean-reverting. In addition, we find evidence that the degree of mean-reversion of the real interest rates is positively correlated with that of output growth, which is consistent with the implications of standard intertemporal behavior.     

A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries

Existing tests of the unit root hypothesis against the alternative hypothesis of exponential smooth transition autoregressive (ESTAR) nonlinearity implicitly assume symmetry under the alternative. This paper proposes a simple unit root test against the alternative of symmetric or asymmetric ESTAR nonlinearity. In the event that the unit root hypothesis is rejected, a simple test of symmetric versus asymmetric ESTAR nonlinearity is also proposed. The asymptotic distributions of the test statistics are straightforward to establish and finite-sample performance is studied with Monte Carlo simulations. An empirical application involving the real exchange rates of four Nordic countries against the U.S. dollar illustrates the usefulness of the new tests.     

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.