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.

A sequential purchasing power parity test for panels of large cross-sections and implications for investors

In this paper we use monthly time series data for not less than 64 countries and a new sequential approach to test for purchasing power parity (PPP). The results are strong in that the evidence in favor of PPP is very weak. In fact, for the US-dollar-based exchange rates the evidence is basically non-existent. In order to eliminate the effect of the base currency, we also apply the sequential PPP test to all pairs of exchange rates, and find similarly weak evidence of PPP. However, for those rates where evidence is found, using a technical trading rule, we find evidence of significant profits. The predictability of the stationary pairs is therefore important for investors.

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.

Nonparametric rank tests for non-stationary panels

We develop a set of nonparametric rank tests for non-stationary panels based on multivariate variance ratios which use untruncated kernels. As such, the tests do not require the choice of tuning parameters associated with bandwidth or lag length and also do not require choices with respect to numbers of common factors. The tests allow for unrestricted cross-sectional dependence and dynamic heterogeneity among the units of the panel, provided simply that a joint functional central limit theorem holds for the panel of differenced series. We provide a discussion of the relationships between our setting and the settings for which first- and second generation panel unit root tests are designed. In Monte Carlo simulations we illustrate the small-sample performance of our tests when they are used as panel unit root tests under the more restrictive DGPs for which panel unit root tests are typically designed, and for more general DGPs we also compare the small-sample performance of our nonparametric tests to parametric rank tests. Finally, we provide an empirical illustration by testing for income convergence among countries.

The power of PANIC

The current paper considers the asymptotic local power of second-generation panel unit root tests that are robust to the presence of cross-section dependence in the form of common factors. As a basis for our analysis, we take the PANIC approach of Bai and Ng (2004, 2010), which is one of the single most popular and general second-generation approaches around.

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.

Panicca: panic on cross-section averages

The cross-section average (CA) augmentation approach of Pesaran (2007) and Pesaran et al. (2013), and the principal components-based panel analysis of non-stationarity in idiosyncratic and common components (PANIC) of Bai and Ng (2004, 2010) are among the most popular “second-generation” approaches for cross-section correlated panels. One feature of these approaches is that they have different strengths and weaknesses. The purpose of the current paper is to develop PANICCA, a combined approach that exploits the strengths of both CA and PANIC.

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 panel bootstrap cointegration test

This paper proposes a bootstrap test for the null hypothesis of cointegration in panel data. The test is general enough to allow for dependence both within and between the cross-sectional units, and is shown to work well in small samples. © 2007 Elsevier B.V. All rights reserved.

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.

Panel cointegration and the neutrality of money

Most econometric methods for testing the proposition of long-run monetary neutrality rely on the assumption that money and real output do not cointegrate, a result that is usually supported by the data. This paper argues that these results can be attributed in part to the low power of univariate tests, and that a violation of the noncointegration assumption is likely to result in a nonrejection of the neutrality proposition. To alleviate this problem, two new and more powerful panel cointegration tests are proposed that can be used under quite general conditions. The empirical results obtained from applying these tests to a panel covering ten countries between 1870 and 1986 suggest money and real output are cointegrated, and hence that the neutrality proposition must be rejected. © Springer-Verlag 2007.

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 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.