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.     

On the regime-switching and asymmetric dynamics of economic growth in the OECD countries

This study estimates the SETAR and STAR models and examines the regime-switching and asymmetric dynamics of economic growth for a comprehensive set of 10 OECD countries. The SETAR models of both Tsay and Hansen consistently reject the null hypothesis of linearity against the alternative hypothesis of threshold nonlinearity for all the sample countries. The STAR model reinforces the evidence and rejects the null hypothesis of linearity against STAR nonlinearity for all the sample countries, except Italy. The sequential F tests for the nested nulls suggest LSTAR nonlinearity for Austria, Japan, Korea, Mexico, Netherlands and New Zealand, and ESTAR nonlinearity for Finland, Germany and Norway. The forecast evaluations suggest that the SETAR models of Tsay and Hansen perform better, as compared to the AR, ARMA and STAR models. The forecasting performance of the STAR model is approximately similar to the forecasting performance of the linear AR and ARMA rivals. The persistence of lower regimes (with negative-growth or moderate-expansions) necessitates the need for the adoption of expansionary economic policies. While the longer durations of upper regimes (with positive-growth or fast-expansions) support the sustainability of the expansionary economic policies, the adequate precautions need to be taken for the inflationary implications of these policies.     

Unit root testing against an ST–MTAR alternative: finite-sample properties and an application to the UK housing market

A class of smooth transition momentum-threshold autoregressive (ST–MTAR) tests is proposed to allow testing of the unit root hypothesis against an alternative of asymmetric adjustment about a smooth nonlinear trend. Monte-Carlo simulation is employed to derive finite-sample critical values for the proposed test and illustrate its attractive power properties against a range of stationary alternatives. The empirical relevance of the ST–MTAR test is highlighted via an application to aggregate house price data for the UK. Interestingly, house prices are found to exhibit structural change characterized a fitted logistic smooth transition process, with the newly proposed ST–MTAR test providing the most significant results of the alternative smooth transition unit root tests available.     

Testing for unemployment hysteresis in nonlinear heterogeneous panels: International evidence

Nonlinear behavior of unemployment is well documented in the literature, and thus linear unit root tests may not be appropriate in this case. This paper tests for hysteresis of unemployment for 29 OECD countries through the use of a new nonlinear panel unit root test developed by Ucar and Omay (2009). The test examines the joint null hypothesis of linearity and a unit root against the alternative hypothesis of nonlinear stationarity. Large power gains are achieved by both combining cross-sectional information with nonlinearities in the data. In addition, after the unit root null being rejected, we use a sequential panel selection method suggested by Chortareas and Kapetanios (2009) to classify the whole panel into a group of stationary countries and a group of non-stationary countries. The empirical findings show that the nonlinear panel test gives strong evidence in favor of the natural rate hypothesis of unemployment for 23 of 29 OECD countries, in contrast to those obtained by Chang's (2002) linear panel test that 17 countries display evidence of stationary unemployment.     

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.     

What do we know about real exchange rate nonlinearities?

Nonlinear modeling of adjustments to purchasing power parity has recently gained much attention. However, a huge body of the empirical literature applies ESTAR models and neglects the existence of other competing nonlinear models. Among these, the Markov Switching AR model has a strong substantiation in international finance. Our contribution to the literature is fivefold: First, ESTAR and MSAR models from a unit root perspective are compared. To this end, a new unit root test against MSAR is proposed as the second contribution. Thirdly, the case of misspecified alternatives in a Monte Carlo setup with real world parameter constellations is studied. The ESTAR unit root test is not indicative, while the MSAR unit test is robust. Fourthly, the case of correctly specified alternatives is considered and low power of the ESTAR but not for the MSAR unit root test is observed. Fifthly, an empirical application to real exchange rates suggests that they may indeed be explained by Markov Switching dynamics rather than ESTAR.     

THE INF‐T TEST FOR A UNIT ROOT AGAINST ASYMMETRIC EXPONENTIAL SMOOTH TRANSITION AUTOREGRESSIVE MODELS

This paper proposes a new test for a unit root against an alternative of asymmetric exponential smooth transition autoregressive models, by extending the infimum test developed by Park and Shintani. Simulation results suggest that the test performs reasonably well in finite samples. The proposed test is also applied to real exchange rates to examine their asymmetric and nonlinear mean‐reverting properties.     

Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests

This paper re-examines the efficient market hypothesis (EMH) in the Turkish stock market by utilizing the recent developments in nonlinear unit root tests. To this end, we first employ the linearity test developed by Harvey et al. (2008) and then carry out the nonlinear ESTAR unit root test recently developed by Kruse (2011). The results show that Borsa Istanbul stock price index series have nonlinear behavior and follow the random walk (non-stationary) process, supporting the EMH in Turkish stock market which has weak-form efficiency.     

Persistent misalignments of the European exchange rates: some evidence from non-linear cointegration

The asymmetric and persistent adjustment of the European real exchange rates is investigated using the framework of non-linear cointegration. The episodes of slow mean-reversion dynamics over the period from 1979 to 1999 are explained. A test of unit root against STAR cointegration is proposed and some complete estimations and stochastic simulations of ESTAR models are presented. The presence of effective non-linear adjustment during the moving of the currencies to their long-run fundamental equilibrium exchange rate value is discussed.     

Panel LM unit root tests with level and trend shifts

This paper considers a Lagrange multiplier (LM) based panel unit root test that allows for heterogeneous structural breaks in both the intercepts and slopes of a series. We note that many popular time series variables are likely to exhibit changing means and/or trends over time. Given that the usual tests will depend on the nuisance parameters indicating the locations of the trend breaks, we adopt a transformation procedure that makes our new panel unit root tests invariant to the nuisance parameters. To illustrate the importance of the power gain provided by our test, we examine the convergence hypothesis using relative ratios of per capita health care expenditures in 20 OECD countries. Our results provide evidence that the convergence hypothesis is supported.     

A new test for analysing hysteresis in European unemployment

This article proposes a new unit root test to analyse unemployment hysteresis. The test is able to incorporate cross-sectional dependence, unattended nonlinearity and unknown structural breaks in the time-series data. This study used data on unemployment in five European countries. The findings indicated that conventional unit root tests failed to reject the null hypothesis of hysteresis for all countries. However, the newly proposed unit root test was able to reject the null hypothesis for the Spanish unemployment rate.     

Is real GDP per capita a stationary process? Smooth transitions,nonlinear trends and unit root testing

The aim of this article is to provide additional evidence about the order of integration of constant price GDP per capita in a selection of countries. It does so by taking into account the possibility of non-linear deterministic trends and of asymmetric adjustment towards equilibrium. We find evidence of a global stationary ESTAR process around a nonlinear deterministic trend in almost half of the selected countries. These results show that nonlinearities affect real GDP series. By neglecting them, one can draw misleading conclusions from unit root tests. Specifically, the article questions the so-called stylised fact of a near unit root which has so influenced macroeconomic thought over the past two decades.     

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.     

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.     

购买力平价非线性检验方法的进展回顾及其对人民币实际汇率的应用

单位根检验下实际汇率通常的非平稳性与购买力平价相矛盾,然而考虑到国际套利交易成本,实际汇率可能遵循某种非线性均值回复行为。本文对近年来国际上对实际汇率的非线性均值回复领域的研究进行了回顾和总结,并选取带有约束的ESTAR模型对人民币实际汇率的非线性行为进行了实证分析,对其均值回复速度进行了估计,并给出了购买力平价下的均衡汇率。结果支持了人民币与美元的购买力平价关系。     

Dynamic persistence in the unemployment rate of OECD countries

Previous studies use a variety of increasingly advanced unit root tests to determine whether Blanchard and Summers (1986) hysteresis theory of unemployment or the classical ‘natural’ rate theory of Friedman (1968) and Phelps (1967, 1968) is most relevant for a given country. However these tests all specify a unit root under the null hypothesis against a stationary alternative, such as in the paper by Lee and Chang (2008), making the two theories of unemployment mutually exclusive over the sample period. This paper moves away from this dichotomy by allowing for switches between hysteresis and the natural rate theory using the recently developed test of Leybourne, Kim and Taylor (2007). We find that in countries like the United Kingdom, the natural rate theory is detected in the post-World War Two period of stabilisation: the time leading up to the seminal works of Friedman and Phelps. Hysteresis is found over the First World War and Great Depression periods, and in the period from the 1970s; a time characterised by rising trade union power. We also compute numerical measures of persistence using grid-bootstrap estimates of the autoregressive parameter, following Hansen (1999).     

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.     

中国实际利率平价的KSS非线性单位根检验

中国一直在进行资本和金融项目的渐进改革,通常描述和刻画这一经济规律变化的是利率平价理论。由于近十几年限制我国利率平价的制度约束条件均得到缓解,所以,本文利用基于ESTAR结构的KSS非线性单位根检验分析法,并连同ADF和PP检验一起对我国实际利率平价进行了实证,检验结果表明,实际利率平价假说成立,并遵循非线性稳态过程,利率的非对称调整导致信贷市场和金融市场的信息不对称。这说明短期内实际利率的调整特征是平滑转移的,在长期内,双边国家均无法实施相对独立的货币政策。     

Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence

Standard unit-root tests of the hysteresis hypothesis specify a unit root under the null against the stationary alternative of the natural-rate hypothesis,     

Asymmetric behavior of inflation differentials in the euro area: Evidence from a threshold unit root test

This paper tests the existence of persistent inflation rate differentials in the euro area by employing linear as well nonlinear unit root tests. Besides linear unit root tests, a two-regime threshold unit root test examines the conjecture that inflation rate differentials follow a nonlinear two-regime process towards a threshold, switching from the persistent regime to the transitory one and vice versa. The results imply that threshold nonlinearity is confirmed in 10 out of the 16 cases. However, we have found unit root regime-switching behavior only in six out of the 16 cases under investigation. This finding implies that these inflation rate differentials were persistent when they were low (regime 1), but transitory when they were high (regime 2). This asymmetric behavior can possibly be explained by the different degree of pressure exercised on governments, which is accompanied with different inflation rate differentials. On the contrary, despite the evidence of nonlinearity, the majority of the inflation rate differentials are found to be monotonically persistent. Our results have strong implications for policy makers. In particular, the documented persistency in the inflation rate differentials might have long-run costs in terms of price and macroeconomic stability.