An Improved Panel Unit Root Test Using GLS-Detrending

We propose to combine recent developments in univariate and mul- tivariate unit root testing in order to construct a more powerful panel unit root test. We extend the GLS-detrending procedure of Elliott, Rothenberg and Stock (1996) to a panel Augmented Dickey-Fuller test. The .nite sample power properties of the new test demonstrate a very large gain when compared to existing tests, especially for small panels. We then investigate the topic of Purchasing Power Parity for the post Bretton-Woods period via this new test. The results show strong rejections of the unit root hypothesis.DF-GLS, panel unit root

An Improved Panel Unit Root Test Using GLS-Detrending

We propose to combine recent developments in univariate and multivariate unit root testing in order to construct a more powerful panel unit root test. We extend the GLS-detrending procedure of Elliott, Rothenberg and Stock (1996) to a panel Augmented Dickey-Fuller test. The finite sample power properties of the new test demonstrate a very large gain when compared to existing tests, especially for small panels. We then investigate the topic of Purchasing Power Parity for the post Bretton- Woods period via this new test. The results show strong rejections of the unit root hypothesis.DF-GLS test, Panel unit root

Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi�cation of countries according to the "growth shift", "level shift" and "linear trend" hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.growth shift, level shift, structural change, trend breaks, unit root

Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi?cation of countries according to the ?growth shift?, ?level shift? and ?linear trend? hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.growth shift, level shift, structural change, trend breaks, unit root

Convergence to Purchasing Power Parity at the Commencement of the Euro

We investigate convergence towards Purchasing Power Parity (PPP) within the Euro Zone and between the Euro Zone and its main partners using panel data methods that incorporate serial and contemporaneous correlation. We find strong rejections of the unit root hypothesis, and therefore evidence of PPP, in the Euro Zone for different numeraire currencies, as well as in the Euro Zone plus the United States, with the US dollar as the numeraire currency, starting between 1996 and 1999. The process of convergence towards PPP, however, begins earlier, generally in 1992 or 1993 following the adoption of the Maastricht Treaty.PPP EURO PANEL UNIT ROOT

Median-Unbiased Estimation in DF-GLS Regressions and the PPP Puzzle

Using median-unbiased estimation, recent research has questioned the validity of Rogoff’s “remarkable consensus” of 3-5 year half-lives of deviations from PPP. These half-life estimates, however, are based on estimates from regressions where the resulting unit root test has low power. We extend median-unbiased estimation to the DF-GLS regression of Elliott, Rothenberg, and Stock (1996). We find that median-unbiased estimation based on this regression has the potential to tighten confidence intervals for half-lives. Using long horizon real exchange rate data, we find that the typical lower bound of the confidence intervals for median-unbiased half-lives is just under 3 years. Thus, while previous confidence intervals for half-lives are consistent with virtually anything, our tighter confidence intervals now rule out economic models with nominal rigidities as candidates for explaining the observed behavior of real exchange rates. Therefore, while we obtain more information using efficient unit root tests on longer term data, this information moves us away from solving the PPP puzzle.PPP, median unbiased, detrended half life

Short Note on the Unemployment Rate of the “French overseas regionsâ€

This article analyzes the hysteresis hypothesis in the unemployment rates of the four “French overseas regions†(Guadeloupe, Martinique, Guyana, Reunion) [FORs] over the period 1993-2008. We use standard univariate and panel unit root tests, among them Choi (2006) and Lopez (2009) that account for cross-sectional dependence and have improved performance when the number of countries and the time dimension of the data are limited. Our results cannot reject the null hypothesis of a unit root and so find evidence supporting hysteresis in the unemployment rates for the FORs.Hysteresis, Unemployment, Panel unit root test, cross-section dependence, convergence

A Fast Algorithm for Multi-Machine Scheduling Problems with Jobs of Equal Processing Times

Consider the problem of scheduling a set of tasks of length p without preemption on $m$ identical machines with given release and deadline times. We present a new algorithm for computing the schedule with minimal completion times and makespan. The algorithm has time complexity O(min(1,p/m)n^2) which improves substantially over the best known algorithm with complexity O(mn^2)