A note on the use of the LLC panel unit root test

One of the single most cited studies within the field of nonstationary panel data analysis is that of LLC (Levin et al. in J Econom 98:1 - 24, 2002), in which the authors propose a test for a common unit root in the panel. Using both theoretical arguments and simulation evidence, we show that this test can be misleading unless it is based on the same bandwidth selection rule used by LLC. © Springer-Verlag 2008.

New tools for understanding the local asymptotic power of panel unit root tests

Abstract Motivated by the previously documented discrepancy between actual and predicted power, the present paper provides new tools for analyzing the local asymptotic power of panel unit root tests. These tools are appropriate in general when considering panel data with a dominant autoregressive root of the form ^ρi=1+^ciN-^κT-^τ, where i=1,...,N indexes the cross-sectional units, T is the number of time periods and ^ci is a random local-to-unity parameter. A limit theory for the sample moments of such panel data is developed and is shown to involve infinite-order series expansions in the moments of ^ci, in which existing theories can be seen as mere first-order approximations. The new theory is applied to study the asymptotic local power functions of some known test statistics for a unit root. These functions can be expressed in terms of the expansions in the moments of ^ci, and include existing local power functions as special cases. Monte Carlo evidence is provided to suggest that the new results go a long way toward bridging the gap between actual and predicted power.

Rethinking the univariate approach to panel unit root testing: using covariates to resolve the incidental trend problem

In an influential article, Hansen showed that covariate augmentation can lead to substantial power gains when compared to univariate tests. In this article, we ask if this result extends also to the panel data context? The answer turns out to be yes, which is maybe not that surprising. What is surprising, however, is the extent of the power gain, which is shown to more than outweigh the well-known power loss in the presence of incidental trends. That is, the covariates have an order effect on the neighborhood around unity for which local asymptotic power is negligible.

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.

On the importance of the first observation in GLS detrending in unit root testing

First-differencing is generally taken to imply the loss of one observation, the first, or at least that the effect of ignoring this observation is asymptotically negligible. However, this is not always true, as in the case of generalized least squares (GLS) detrending. In order to illustrate this, the current article considers as an example the use of GLS detrended data when testing for a unit root. The results show that the treatment of the first observation is absolutely crucial for test performance, and that ignorance causes test break-down.

The asymptotic distribution of the CADF unit root test in the presence of heterogeneous AR(p) errors

The CADF test of Pesaran (J Appl Econ 22:265–312, 2007) are among the most popular univariate tests for cross-section correlated panels around. Yet, the existing asymptotic analysis of this test statistic is limited to a model in which the errors are assumed to follow a simple AR(1) structure with homogenous autoregressive coefficients. One reason for this is that the model involves an intricate identification issue, as both the serial and cross-section correlation structures of the errors are unobserved. The purpose of the current paper is to tackle this issue and in so doing extend the existing analysis to the case of AR((Formula presented.)) errors with possibly heterogeneous coefficients.

A factor analytical method to interactive effects dynamic panel models with or without unit root

In a recent study, Bai (Fixed-Effects Dynamic Panel Models, A Factor Analytical Method. Econometrica 81, 285-314, 2013a) proposes a new factor analytic (FA) method to the estimation of dynamic panel data models, which has the unique and very useful property that it is completely bias-free. However, while certainly appealing, it is restricted to fixed effects models without a unit root. In many situations of practical relevance this is a rather restrictive consideration. The purpose of the current study is therefore to extend the FA approach to cover models with multiple interactive effects and a possible unit root.

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.

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.

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.

Is there really a unit root in the inflation rate? More evidence from panel data models

Time series unit root evidence suggests that inflation is nonstationary. By contrast, when using more powerful panel unit root tests, Culver and Papell (1997) find that inflation is stationary. In this article, we test the robustness of this result by applying a battery of recent panel unit root tests. The results suggest that the stationarity of inflation holds even after controlling for cross-sectional dependence and structural change.

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.

Comparing two multivariate unit root tests

In this essay, a method for comparing the asymptotic power of the multivariate unit root tests proposed in Phillips & Durlauf (1986) and Flˆores, Preumont & Szafarz (1996) is proposed. In order to determine the asymptotic power of the tests the asymptotic distributions under the null hypothesis and under the set of alternative hypotheses described in Phillips (1988) are determined. In addition, a test which combines characteristics of both tests is proposed and its distributions under the null hypothesis and the same set of alternative hypotheses are determined. This allows us to determine what causes any difference in the asymptotic power of the two tests against the set of alternative hypotheses considered

Purchasing power parity and the unit root tests: a robust analysis

Empirical evidence suggests that real exchange rate is characterized by the presence of near-unity and additive outliers. Recent studeis have found evidence on favor PPP reversion by using the quasi-differencing (Elliott et al., 1996) unit root tests (ERS), which is more efficient against local alternatives but is still based on least squares estimation. Unit root tests basead on least saquares method usually tend to bias inference towards stationarity when additive out liers are present. In this paper, we incorporate quasi-differencing into M-estimation to construct a unit root test that is robust not only against near-unity root but also against nonGaussian behavior provoked by assitive outliers. We re-visit the PPP hypothesis and found less evidemce in favor PPP reversion when non-Gaussian behavior in real exchange rates is taken into account.

Testing unit root based on partially adaptive estimation

This paper proposes unit tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adptive estimation using nonparametric methods. The limiting distribution of the proposed test is a combination of standard normal and the traditional Dickey-Fuller (DF) distribution, including the traditional ADF test as a special case when using Gaussian density. Taking into a account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, wich includes te normal distribution as a limiting case. Monte Carlo Experiments indicate that, in the presence of heavy tail distributions or innovations that are contaminated by outliers, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit roots is not found in real exchange rate and nominal interest rate even haevy-tail is taken into a account.