The effect of recursive detrending on panel unit root tests

This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.

Pooled panel unit root tests and the effect of past initialization

This paper analyzes the role of initialization when testing for a unit root in panel data, an issue that has received surprisingly little attention in the literature. In fact, most studies assume that the initial value is either zero or bounded. As a response to this, the current paper considers a model in which the initialization is in the past, which is shown to have several distinctive features that makes it attractive, even in comparison to the common time series practice of making the initial value a draw from its unconditional distribution under the stationary alternative. The results have implications not only for theory, but also for applied work. In particular, and in contrast to the time series case, in panels the effect of the initialization need not be negative but can actually lead to improved test performance.

Panel cointegration tests of the Fisher effect

Most empirical evidence suggests that the Fisher effect, stating that inflation and nominal interest rates should cointegrate with a unit slope on inflation, does not hold, a finding at odds with many theoretical models. This paper argues that these results can be attributed in part to the low power of univariate tests, and that the use of panel data can generate more powerful tests. For this purpose, we propose two new panel cointegration tests that can be applied under very general conditions, and that are shown by simulation to be more powerful than other existing tests. These tests are applied to a panel of quarterly data covering 20 OECD countries between 1980 and 2004. The evidence suggest that the Fisher effect cannot be rejected once the panel evidence on cointegration has been taken into account. Copyright © 2008 John Wiley & Sons, Ltd.

A note on the pooling of individual panic unit root tests

One of the most cited studies in recent years within the field of nonstationary panel data analysis is that of Bai and Ng (2004), in which the authors propose PANIC, a new framework for analyzing the nonstationarity of panels with idiosyncratic and common components. The problem is that the asymptotic validity of PANIC as a platform for constructing pooled panel unit root tests based on averaging is not fully proven. This paper provides the required results, whose usefulness is verified through simulations. © 2009 Cambridge University Press.

New improved tests for cointegration with structural breaks

This article proposes Lagrange multiplier-based tests for the null hypothesis of no cointegration. The tests are general enough to allow for heteroskedastic and serially correlated errors, deterministic trends, and a structural break of unknown timing in both the intercept and slope. The limiting distributions of the test statistics are derived, and are found to be invariant not only with respect to the trend and structural break, but also with respect to the regressors. A small Monte Carlo study is also conducted to investigate the small-sample properties of the tests. The results reveal that the tests have small size distortions and good power relative to other tests. © 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Panel cointegration tests with deterministic trends and structural breaks

This paper proposes Lagrange multiplier (LM) based tests for the null hypothesis of no cointegration in panel data. The tests are general enough to allow for heteroskedastic and serially correlated errors, individual specific time trends, and a single structural break
in both the intercept and slope of each regression, which may be located different dates for different individuals. The limiting distributions of the test statistics are derived, and are found to be standard normal and free of nuisance parameters under the null. In
particular, the distributions are found to be invariant not only withrespect to trend and structural break, but also with respect to the presence of stochastic regressors. A small Monte Carlo study is also conducted to investigate the small-sample properties of the tests. The results reveal that the tests have small size distortions and good power even in very small samples.

New simple tests for panel cointegration

In this paper, two new simple residual-based panel data tests are proposed for the null of no cointegration. The tests are simple because they do not require any correction for the temporal dependencies of the data. Yet they are able to accommodate individual specific short-run dynamics, individual specific intercept and trend terms, and individual specific slope parameters. The limiting distributions of the tests are derived and are shown to be free of nuisance parameters. The Monte Carlo results in this paper suggest that the asymptotic results are borne out well even in very small samples. Copyright © Taylor & Francis, Inc.

Panel cointegration tests of the Fisher hypothesis

Recent empirical studies suggest that the Fisher hypothesis, stating that inflation and nominal interest rates should cointegrate with a unit parameter on inflation, does not hold, a finding at odds with many theoretical models. This paper argues that these results can be explained in part by the low power inherent in univariate cointegration tests and that the use of panel data should generate more powerful tests. In doing so, we propose two new panel cointegration tests, which are shown by simulation to be more powerful than other existing tests. Applying these tests to a panel of monthly data covering the period 1980:1 to 1999:12 on 14 OECD countries, we find evidence supportive of the Fisher hypothesis.

Pooled unit root tests in panels with a common factor

This paper proposes new pooled panel unit root tests that are appropriate when the data exhibit cross-sectional dependence that is generated by a single common factor. Using sequential limit arguments, we show that the tests have a limiting normal distribution that is free of nuisance parameters and that they are unbiased against heterogenous local alternatives. Our Monte Carlo results indicate that the tests perform well in comparison to other popular tests that also presumes a common factor structure for the cross-sectional dependence.

Multiple states of financially distressed companies: Tests using a competing-risks model

This study examines the determinants of multiple states of financial distress by applying a competing-risks model. It investigates the effect of financial ratios, market-based variables and company-specific variables, including company age, size and squared size on three different states of corporate financial distress: active companies; distressed external administration companies; and distressed takeover, merger or acquisition companies. A sample of 1,081 publicly listed Australian non-financial companies over the period 1989 to 2005 using a competing-risks model is used to determine the possible differences in the factors of entering various states of financial distress. It is found that specifically, distressed external administration companies have a higher leverage, lower past excess returns and a larger size; while distressed takeover, merger or acquisition companies have a lower leverage, a higher capital utilisation efficiency and a larger size compared to active companies. Comparing the results from both the single-risk model and the competing-risks model reveals the need to distinguish between financial distress states.

Error-correction-based cointegration tests for panel data

This article describes a new Stata command called xtwest, which implements the four error-correction-based panel cointegration tests developed by Westerlund (2007). The tests are general enough to allow for a large degree of heterogeneity, both in the long-run cointegrating relationship and in the short-run dynamics, and dependence within as well as across the cross-sectional units.

Mixed signals among tests for panel cointegration

In this paper, we study the effect that different serial correlation adjustment methods can have on panel cointegration testing. As an example, we consider the very popular tests developed by Pedroni [Pedroni, P. (1999). Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bulletin of Economics and Statistics 61, 653670., Pedroni, P. (2004). Panel cointegration: asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis. Econometric Theory 20, 597-625.]. Results based on both simulated and real data suggest that different adjustment methods can lead to significant variations in test outcome, and thus also in the conclusions. © 2007 Elsevier B.V. All rights reserved.

The local power of the CADF and CIPS panel unit root tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.

A way through the dark and thorny thickets? The adjudication of ‘serious injury’ under the narrative tests in the Transport Accident Act 1986 (Vic) and the Workplace Injury Rehabilitation and Compensation Act 2013 (Vic)

The so-called narrative test provides the means by which injured persons who satisfy the statutory and common law definition of serious injury may bring proceedings for common law damages under s 93 of the Transport Accident Act 1986 (Vic) and s 134AB of the Accident Compensation Act 1985 (Vic) (or, for injuries after 1 July 2014, under ss 324-347 of the Workplace Injury Rehabilitation and Compensation Act 2013 (Vic)). These are among the most litigated provisions in Australia. This article outlines the legislative and political background to these provisions, the provisions themselves, and an account of the statutory and common law requirements needed to satisfy the provisions.