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.     

On the joint Fourier–ESTAR testing of PPP

The purchasing power parity (PPP) is the hypothesis that the real exchange rate series are stationary. This study briefly reviews and applies six competing unit root test procedures to test PPP. Reflecting the existing literature, the results are mixed. The Kiliç test is the most favourable while the Kapetanios, Shin, and Snell (KSS) test is the least favourable to PPP and the standard ADF test lies in between. The same conclusion applies to the Fourier extensions of those three tests. The results support a recently suggested F-test for the significance of Fourier terms in unit root test equations.     

Does extracting inflation from stock returns solve the purchasing power parity puzzle?

In a recent study by Chowdhry et al. (American Economic Review 95: 255–276, 2005), they suggest that the empirical failure of relative purchasing power parity (PPP) may be because the official inflation data are too sticky. Thus, after extracting the unobservable pure price inflation from equity markets, they find strong evidence supporting relative PPP in the short run. As a replication study, this paper first replicates their original findings successfully. We further investigate whether long-run relative PPP holds using the pure price inflation data constructed by Chowdhry et al. (2005). After constructing pure real exchange rate series using their pure price inflation data, we implement both unit root and cointegration tests on the pure real exchange rates. According to the test results, the evidence suggests that relative PPP does not hold in the long run. Thus, it may be too early to suggest a resolution of the PPP puzzle.     

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.     

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.     

STRUCTURAL BREAKS AND UNIT ROOTS IN AUSTRALIAN MACROECONOMIC TIME SERIES

Abstract.  We examine the unit root properties of 16 Australian macroeconomic time series using monthly data spanning the period 1960–2004. In addition to the standard Augmented Dickey Fuller (ADF) test, we implement one- and two-break endogenous structural break ADF-type unit root tests as well as one- and two-break Lagrange multiplier (LM) unit root tests. While the ADF test provides relatively little evidence against the unit root null hypothesis, once we allow for structural breaks we are able to reject the unit root null for just under half of the variables at the 10% level or better.     

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.     

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.     

A nonlinear approach to testing the unit root null hypothesis: an application to international health expenditures

In this article, we examine the unit root null hypothesis for per capita total Health Expenditures (HEs), per capita private HEs and per capita public HEs for 29 Organization for Economic Co-operation and Development (OECD) countries. The novelty of our work is that we use a new nonlinear unit root test that allows for one structural break in the data series. We find that for around 45% of the countries, we are able to reject the unit root hypothesis for each of the three HE series. Moreover, using Monte Carlo simulations, we show that our proposed unit root model has better size and power properties than the widely used Augmented Dickey–Fuller (ADF) and Lagrange Multiplier (LM) type tests.     

Testing the validity of PPP theory for African countries

This study examines the purchasing power parity theory for 14 African countries by applying a recent composite time series method that incorporates the Fourier approximation. The structural breaks are modelled as a gradual smooth process by means of a Fourier component. The Fourier unit root test failed to find any evidence showing that real exchange rates for these 14 countries have mean-reverting tendencies. However, both cointegration and Fourier cointegration tests detect a stable long-term relation between the nominal exchange rate and relative price levels for 8 out of 14 countries; moreover, for five countries Fourier component in cointegration analysis is found to suit quite well.     

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 AGRICULTURAL TERMS OF TRADE IN BANGLADESH: AN ECONOMETRIC ANALYSIS OF TRENDS AND MOVEMENTS, 1952–2006

This paper investigates the trends and movements of agricultural prices, industrial prices and the agricultural terms of trade in Bangladesh with annual data for the period 1952–2006. The ADF and KPSS tests results suggest that both agricultural and industrial prices have a unit root while the agricultural terms of trade is trend-stationary. These results remain unchanged if allowance is made in the unit root test for the possibility of a structural break during 1971–1975 (when Bangladesh gained independence from Pakistan and experienced economic shocks) by applying the two-step procedure of Perron (1989 ). A simple Nerlovian agricultural price determination model is specified within the framework of aggregate demand and aggregate supply. The Johansen cointegration test results for the periods 1953–2006 and 1973–2006 suggest that there exists a cointegral relationship between agricultural prices, industrial prices, per-capita real income and the real exchange rate between the Bangladeshi taka and the US dollar under the restriction that per-capita real income and the real exchange rate are 'long-run forcing variables' in the sense of Pesaran and Shin (1995 ), and Pesaran, Shin and Smith (1996 ). The paper estimates a four-variable vector error-correction (VEC) model and conducts an impulse response analysis for the post-independence period, 1973–2006.     

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.     

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.     

Stochastic unit root processes: Maximum likelihood estimation,and new Lagrange multiplier and likelihood ratio tests

We show in this study that the maximum likelihood estimators of stochastic unit root (STUR) processes are consistent and asymptotically normally distributed. We also present two new tests for STUR. We first propose a Lagrange multiplier test and show that it has a standard χ² distribution asymptotically. We also propose a likelihood ratio test and show that it has an asymptotic distribution of 50–50 mixture of χ² and a point mass at 0. As an empirical example, we test the existence of STUR in the Canadian real exchange rate and explore the implication of STUR on the validity of purchasing power parity.     

On PPP,unit roots and panels

In this paper we use a combination of time series unit root and cointegration analysis and the Bai and Ng (Econometrica 72:1127–1187, 2004) factor model approach to assess the purchasing power parity hypothesis for four real exchange rate panels. Our main findings are twofold: First, we find robust evidence for nonstationary common components in the real exchange rate panels and hence no evidence for PPP. Second, the presence of nonstationary common components is consistent with rejections of the unit root null hypothesis when applying a battery of first and second generation panel unit root tests, which are known to be adversely affected in the presence of common nonstationary components.     

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.     

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。     

Structural break,nonlinearity and asymmetry: a re-examination of PPP proposition

In this study, we examine the validity of the PPP proposition for 28 European countries. For this purpose, we propose a new unit root test procedure that allows for both gradual structural breaks and asymmetric nonlinear adjustment towards the equilibrium level. Small-sample properties of the new tests are examined through Monte-Carlo simulations. The simulation results suggest that the new tests have satisfactory size and power properties. We then apply these new tests along with other unit root tests to examine stationarity properties of real exchange rate series of the sample countries. Our tests reject the null of unit root in more cases when compared to alternative tests. Overall, we find that the PPP proposition holds in majority of the European countries examined in this article.     

Is per capita real GDP stationary in five southeastern European countries? Fourier unit root test

This study uses the newly developed Fourier unit root test advanced by Enders and Lee (2004, 2009) to investigate the time-series properties of real GDP (Gross Domestic Product) for five Southeastern European countries for the period from 1969 to 2009. The empirical results from several conventional unit root tests indicate that the per capita real GDP for all of the countries studied are non-stationary; however, when Enders and Lee (2004, 2009) Fourier unit root tests are conducted, one rejects the unit root hypothesis of real GDP per capita in all countries under study. These results have important policy implications for these five Southeastern European countries under study.