ARE THE CURRENT ACCOUNT IMBALANCES BETWEEN EMU COUNTRIES SUSTAINABLE? EVIDENCE FROM PARAMETRIC AND NON‐PARAMETRIC TESTS

Using parametric and non‐parametric estimation techniques, we analyze the sustainability of the recently growing current account imbalances in the euro area and test whether the European Monetary Union has aggravated these imbalances. Two alternative criteria for the assessment of external debt sustainability are considered: one based on the transversality condition of intertemporal optimization, and the other based on the stationarity properties of the stochastic process of the debt–GDP ratio. Econometric sustainability tests are performed using the pooled mean‐group estimator and panel unit root tests, respectively. Variants of both test procedures with varying coefficients using penalized splines estimation are applied. We find empirical evidence suggesting that the introduction of the euro is associated with a regime shift from sustainability to unsustainability of external debt accumulation for the euro area. Copyright © 2012 John Wiley & Sons, Ltd.     

Detection of Structural Change in the Long‐run Persistence in a Univariate Time Series*

In this paper, we investigate a test for structural change in the long‐run persistence in a univariate time series. Our model has a unit root with no structural change under the null hypothesis, while under the alternative it changes from a unit‐root process to a stationary one or vice versa. We propose a Lagrange multiplier‐type test, a test with the quasi‐differencing method, and ‘demeaned versions’ of these tests. We find that the demeaned versions of these tests have better finite‐sample properties, although they are not necessarily superior in asymptotics to the other tests.     

Cross‐sectional Dependency and Size Distortion in a Small‐sample Homogeneous Panel Data Unit Root Test*

In this paper, we investigate the effects of cross‐sectional disturbance correlation in a homogeneous panel data unit root test. As reported by other authors, the unit root test has incorrect size in the presence of cross‐sectional correlation. We suggest that a previously known estimator can be used to reduce the size distortions. We supply response surface estimates for critical values and study the size characteristics of the proposed test. We find that the suggested estimator performs well in small‐sample homogeneous panel data unit root tests. The reduction in size distortion comes at a small cost of lower power against a stationary alternative.     

Evidence on purchasing power parity from univariate models: the case of smooth transition trend‐stationarity

Recent research has found that trend‐break unit root tests derived from univariate linear models do not support the hypothesis of long‐run purchasing power parity (PPP) for US dollar real exchange rates. In this paper univariate smooth transition models are utilized to develop unit root tests that allow under the alternative hypothesis for stationarity around a gradually changing deterministic trend function. These tests reveal statistically significant evidence against the null hypothesis of a unit root for the real exchange rates of a number of countries against the US dollar. However, restrictions consistent with long‐run PPP are rejected for some of the countries for which a rejection of the unit root hypothesis is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

London calling: Nonlinear mean reversion across national stock markets

This paper revisits empirical evidence of mean reversion of relative stock prices in international stock markets. We implement a strand of univariate and panel unit root tests for linear and nonlinear models of 18 national stock indices from 1969 to 2016. Our major findings are as follows. First, we find strong evidence of nonlinear mean reversion of the relative stock price with the UK index as the reference, calling attention to the stock index in the UK, but not with the US index. Our results imply an important role of the local common factor in the European stock markets. Second, panel tests yield no evidence of linear and nonlinear stationarity when the cross-section dependence is considered, which provides conflicting results from those of the univariate tests. Last, we show how to understand these results via dynamic factor analysis. When the stationary common factor dominates nonstationary idiosyncratic components in small samples, panel tests that filter out the stationary common factor may yield evidence against the stationarity null hypothesis in finite samples. We corroborate this conjecture via extensive Monte Carlo simulations.     

Unemployment hysteresis in Australia: evidence using nonlinear and stationarity tests with breaks

This study is an attempt to test the hysteresis versus the natural rate hypothesis in unemployment rate using time series data of the Australia covering the period 1978: 2–2010:12. For the analysis, we employed nonlinear as well as different linear tests (with incorporation of endogenously determined structural breaks) of unit root. We found that the Australian unemployment rate is nonlinear process, has a partial unit root and trend reverting. Therefore, we provide support for the structuralist hypothesis. This finding provides the importance of accounting for exogenous shocks in the series and gives support to the shifting natural-rate hypothesis of the Australian unemployment rate.     

Nonlinear IV unit root tests in panels with cross-sectional dependency

We propose a unit root test for panels with cross-sectional dependency. We allow general dependency structure among the innovations that generate data for each of the cross-sectional units. Each unit may have different sample size, and therefore unbalanced panels are also permitted in our framework. Yet, the test is asymptotically normal, and does not require any tabulation of the critical values. Our test is based on nonlinear IV estimation of the usual augmented Dickey–Fuller type regression for each cross-sectional unit, using as instruments nonlinear transformations of the lagged levels. The actual test statistic is simply defined as a standardized sum of individual IV t-ratios. We show in the paper that such a standardized sum of individual IV t-ratios has limit normal distribution as long as the panels have large individual time series observations and are asymptotically balanced in a very weak sense. We may have the number of cross-sectional units arbitrarily small or large. In particular, the usual sequential asymptotics, upon which most of the available asymptotic theories for panel unit root models heavily rely, are not required. Finite sample performance of our test is examined via a set of simulations, and compared with those of other commonly used panel unit root tests. Our test generally performs better than the existing tests in terms of both finite sample sizes and powers. We apply our nonlinear IV method to test for the purchasing power parity hypothesis in panels.     

The Flexible Fourier Form and Local Generalised Least Squares De‐trended Unit Root Tests*

In two recent papers Enders and Lee (2009) and Becker, Enders and Lee (2006) provide Lagrange multiplier and ordinary least squares de‐trended unit root tests, and stationarity tests, respectively, which incorporate a Fourier approximation element in the deterministic component. Such an approach can prove useful in providing robustness against a variety of breaks in the deterministic trend function of unknown form and number. In this article, we generalize the unit root testing procedure based on local generalized least squares (GLS) de‐trending proposed by Elliott, Rothenberg and Stock (1996) to allow for a Fourier approximation to the unknown deterministic component in the same way. We show that the resulting unit root tests possess good finite sample size and power properties and the test statistics have stable non‐standard distributions, despite the curious result that their limiting null distributions exhibit asymptotic rank deficiency.     

Are unemployment rates in OECD countries stationary? Evidence from univariate and panel unit root tests

This paper revisits the dynamics of unemployment rate for 29 OECD countries over the period of 1980–2013. Numerous empirical studies of the dynamics of unemployment rate are carried out within a linear framework. However, unemployment rate can show nonlinear behaviour as a result of business cycles or some idiosyncratic factors specific to labour market (Cancelo, 2007). Thus, as a testing strategy, we first perform Harvey, Leybourne, and Xiao (2008) linearity unit root test and then apply the newly ESTAR nonlinear unit root test suggested by Kruse (2011). This test has higher power than conventional unit root tests when time series exhibits nonlinear behaviour. Our empirical findings provide significant evidence in favour of unemployment rate stationarity for 25 countries. For robustness purpose, we have also used panel unit root tests without and with structural breaks. The empirical results show that unemployment hysteresis hypothesis is strongly rejected, when taking into account the cross-sectional and structural break assumptions. Thus, unemployment rate is expected to return back to their natural levels without executing any costly macroeconomic labour market policies by the OECD’s governments.     

Convergence of Prices and Rates of Inflation*

We consider how unit‐root and stationarity tests can be used to study the convergence of prices and rates of inflation. We show how the joint use of these tests in levels and first differences allows the researcher to distinguish between series that are converging and series that have already converged, and we set out a strategy to establish whether convergence occurs in relative prices or just in rates of inflation. Special attention is paid to the issue of whether a mean should be extracted in carrying out tests in first differences and whether there is an advantage to adopting a (Dickey–Fuller) unit‐root test based on deviations from the last observation. The asymptotic distribution of this last test statistic is given and Monte Carlo simulation experiments show that the test yields considerable power gains for highly persistent autoregressive processes with ‘relatively large’ initial conditions. The tests are applied to the monthly series of the consumer price index in the Italian regional capitals over the period 1970–2003.     

The relationship between power and level for generic unit root tests in finite samples

We show that the maximum power of a generic unit root test against any stationary alternative is equal to the true level of the test. We then use Monte Carlo methods to investigate the implications for several such tests. We show patterns of rejection probabilities over a variety of unit root and stationary processes. We discuss the implications of these results for some of the uses of unit root tests in applied work.     

Dickey–Fuller Type of Tests against Nonlinear Dynamic Models*

In this paper, we introduce several test statistics testing the null hypothesis of a random walk (with or without drift) against models that accommodate a smooth nonlinear shift in the level, the dynamic structure and the trend. We derive analytical limiting distributions for all the tests. The power performance of the tests is compared with that of the unit‐root tests by Phillips and Perron [Biometrika (1988), Vol. 75, pp. 335–346], and Leybourne, Newbold and Vougas [Journal of Time Series Analysis (1998), Vol. 19, pp. 83–97]. In the presence of a gradual change in the deterministics and in the dynamics, our tests are superior in terms of power.     

Panel Unit‐root Tests for Cross‐sectionally Correlated Panels: A Monte Carlo Comparison*

This paper deals with the finite‐sample performance of a set of unit‐root tests for cross‐correlated panels. Most of the available macroeconomic time series cover short time periods. The lack of information, in terms of time observations, implies that univariate tests are not powerful enough to reject the null of a unit‐root while panel tests, by exploiting the large number of cross‐sectional units, have been shown to be a promising way of increasing the power of unit‐root tests. We investigate the finite sample properties of recently proposed panel unit‐root tests for cross‐sectionally correlated panels. Specifically, the size and power of Choi's [Econometric Theory and Practice: Frontiers of Analysis and Applied Research: Essays in Honor of Peter C. B. Phillips, Cambridge University Press, Cambridge (2001)], Bai and Ng's [Econometrica (2004), Vol. 72, p. 1127], Moon and Perron's [Journal of Econometrics (2004), Vol. 122, p. 81], and Phillips and Sul's [Econometrics Journal (2003), Vol. 6, p. 217] tests are analysed by a Monte Carlo simulation study. In synthesis, Moon and Perron's tests show good size and power for different values of T and N, and model specifications. Focusing on Bai and Ng's procedure, the simulation study highlights that the pooled Dickey–Fuller generalized least squares test provides higher power than the pooled augmented Dickey–Fuller test for the analysis of non‐stationary properties of the idiosyncratic components. Choi's tests are strongly oversized when the common factor influences the cross‐sectional units heterogeneously.     

Residual based tests for cointegration in dependent panels

In the paper, we propose residual based tests for cointegration in general panels with cross-sectional dependency, endogeneity and various heterogeneities. The residuals are obtained from the usual least squares estimation of the postulated cointegrating relationships from each individual unit, and the nonlinear IV panel unit root testing procedure is applied to the panels of the fitted residuals using as instruments the nonlinear transformations of the adaptively   fitted lagged residuals. The t$t$-ratio, based on the nonlinear IV estimator, is then constructed to test for unit root in the fitted residuals for each cross-section. We show that such nonlinear IV t$t$-ratios are asymptotically normal and cross-sectionally independent under the null hypothesis of no cointegration. The average or the minimum of the IVt$t$-ratios can, therefore, be used to test for the null of a fully non-cointegrated panel against the alternative of a mixed panel, i.e., a panel with only some cointegrated units. We also consider the maximum of the IV t$t$-ratios to test for a mixed panel against a fully cointegrated panel. The critical values of the minimum, maximum as well as the average tests are easily obtained from the standard normal distribution function. Our simulation results indicate that the residual based tests for cointegration perform quite well in finite samples.     

Power of Tests for Unit Roots in the Presence of a Linear Trend*

Dickey and Fuller [Econometrica (1981) Vol. 49, pp. 1057–1072] suggested unit‐root tests for an autoregressive model with a linear trend conditional on an initial observation. TPower of tests for unit roots in the presence of a linear trendightly different model with a random initial value in which nuisance parameters can easily be eliminated by an invariant reduction of the model. We show that invariance arguments can also be used when comparing power within a conditional model. In the context of the conditional model, the Dickey–Fuller test is shown to be more stringent than a number of unit‐root tests motivated by models with random initial value. The power of the Dickey–Fuller test can be improved by making assumptions to the initial value. The practitioner therefore has to trade‐off robustness and power, as assumptions about initial values are hard to test, but can give more power.     

The Role of Sustainability‐Related Strategies on the Biofuel Industry: Trends,Prospects and Challenges

The aim of this study is to elucidate the sustainability‐related strategies on the biofuel industry. Our empirical analysis is based on a time series data set covering diesel demand in Greece over the period 1978–2014 and on the basis of these estimates we make forecasts for biodiesel consumption in the coming years (2015–2030) under three alternative scenarios. Our approach utilizes unit root testing to investigate possible co‐integrated relationships among the sample variables. The empirical findings indicate that diesel demand is income and price inelastic in both the long and the short run, while biodiesel demand seems to have an upward trend over the simulated period. We argue that the importance of biofuel in the Greek energy balance will change the form of the existing business strategies towards issues such as sustainability, green entrepreneurship and corporate social responsibility to achieve the environmental goals set by the EU Energy Roadmap 2050. Copyright © 2018 John Wiley & Sons, Ltd and ERP Environment     

Minimum wage is efficient wage in Turkish labor market: TAR–cointegration analysis

This study has two main purposes. First one is the necessity of taking minimum wages into account, if there is a purpose to analyze the relationship between wages and productivity in an economy which has high unemployment rates and informal employment. Second one is about the analyzing method of this relationship. We choose TAR cointegration analysis for this relation. First step of this analysis is testing for stationarity of the variables. However the low power of traditional unit root tests is examined and proved in many studies but not taken into account in TAR cointegration studies in literature. This study shows that traditional unit root tests are unfavorable for the variables which have TAR structures. Because of this shortcoming of traditional unit root tests, these results must be supported with TAR unit root tests.     

Bootstrap unit root tests in panels with cross-sectional dependency

We apply bootstrap methodology to unit root tests for dependent panels with N cross-sectional units and T time series observations. More specifically, we let each panel be driven by a general linear process which may be different across cross-sectional units, and approximate it by a finite order autoregressive integrated process of order increasing with T. As we allow the dependency among the innovations generating the individual series, we construct our unit root tests from the estimation of the system of the entire N cross-sectional units. The limit distributions of the tests are derived by passing T to infinity, with N fixed. We then apply bootstrap method to the approximated autoregressions to obtain critical values for the panel unit root tests, and establish the asymptotic validity of such bootstrap panel unit root tests under general conditions. The proposed bootstrap tests are indeed quite general covering a wide class of panel models. They in particular allow for very general dynamic structures which may vary across individual units, and more importantly for the presence of arbitrary cross-sectional dependency. The finite sample performance of the bootstrap tests is examined via simulations, and compared to that of commonly used panel unit root tests. We find that our bootstrap tests perform relatively well, especially when N is small.     

Nonlinear dynamics of interest rate and inflation

According to several empirical studies US inflation and nominal interest rates as well as the real interest rate can be described as unit root processes. These results imply that nominal interest rates and expected inflation do not move one‐for‐one in the long run, which is incongruent with theoretical models. In this paper we introduce a new nonlinear bivariate mixture autoregressive model that seems to fit quarterly US data (1953 : II–2004 : IV) reasonably well. It is found that the three‐month Treasury bill rate and inflation share a common nonlinear component that explains a large part of their persistence. The real interest rate is devoid of this component, indicating one‐for‐one movement of the nominal interest rate and inflation in the long run and, hence, stationarity of the real interest rate. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice‐versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.