Panel unit root tests

This is an important issue since the application of tests belonging to the …rst generation to series that are characterized by cross-sectional dependencies leads to size distortions and low power (Banerjee, Marcellino and Osbat, 2000, Strauss and Yigit, 2003). In response to the need for panel unit root tests that allows for cross-sectional correlations, various tests have been proposed belonging to what we call the class of the second generation tests. Rather than considering correlations across units as nuisance parameters, this new category of tests aims at exploiting these co-movements in order to de…ne new test statistics. As argued by Quah (1994), the modelling of cross-sectional dependencies is a di¢ cult task since no natural ordering exists in unit observations. This is why various tests have been proposed including the works of Bai and Ng (2001), Phillips and Sul (2003a), Moon and Perron (2004a), Choi (2002), Ploberger and Phillips (2002), Moon, Perron and Phillips (2003), Chang (2002) and Pesaran (2003). Two main approaches can be distinguished. The …rst one relies on the factor structure approach and includes the contributions of Bai and Ng (2001), Phillips and Sul (2003a), Moon and Perron (2004a), Choi (2002) and Pesaran (2003). The second approach consists in imposing few or none restrictions on the residuals covariance matrix. This approach has been adopted by Chang (2002) among others, who proposed the use of instrumental variables in order to solve the nuisance parameter problem due to cross-sectional dependency.

present in O’Connell (1998) and Maddala and Wu (1999), among others. Second, the test pro- posed by Demetrescu et al. (2006) can cope with the existence of moderate cross-dependence, but has low intrinsic power. Simes-type based on ADF tests have in general fairly good size properties, but poor intrinsic power: on the contrary, using CADF tests gives good intrinsic power but some size distortions. Last but not least, the use of stationary covariates in panel unit root tests based on p value combination offers a simple way to obtain panel unit root tests with good size and large power gains.

1 Introduction In recent years, the issue of testing for unit root in panel data has been a much debated topic. The literature about the development of such tests was initially based upon the assumption of cross-sectional independence between the units and it produced the so called ”first generation panel unit root tests”. However, in several empirical applications, this assumption is likely to be violated and O’Connell (1998) showed that not considering the possible dependence between units could introduce severe bias in the first generation panel unit root tests. Hence researchers were interested in developing tests invariant with respect to the cross-sectional dependence, the so called ”second generation unit root tests”.

Abstract This paper extends the cross sectionally augmented panel unit root test proposed by Pesaran (2007) to the case of a multifactor error structure. The basic idea is to exploit in- formation regarding the unobserved factors that are shared by other time series in addition to the variable under consideration. Importantly, our test procedure only requires speci…- cation of the maximum number of factors, in contrast to other panel unit root tests based on principal components that require in addition the estimation of the number of factors as well as the factors themselves. Small sample properties of the proposed test are investigated by Monte Carlo experiments, which suggest that it controls well for size in almost all cases, especially in the presence of serial correlation in the error term, contrary to alternative test statistics. Empirical applications to Fisher’s in‡ation parity and real equity prices across di¤erent markets illustrate how the proposed test works in practice.

There is now a sizeable literature on testing for unit roots in panels where both cross section (N ) and time (T ) dimensions are relatively large. Reviews of this literature are provided in Banerjee (1999), Baltagi and Kao (2000), Choi (2004), and more recently in Breitung and Pesaran (2007). The so called …rst generation panel unit root tests pioneered by Levin, Lin and Chu (2002) and Im, Pesaran and Shin (2003) focussed on panels where the idiosyncratic errors were cross sectionally uncorrelated. More recently, to deal with a number of applications such as testing for purchasing power parity or output convergence, the interest has shifted to the case where the errors are allowed to be cross sectionally correlated using a residual factor structure. 1 These second generation tests include the contributions of Moon and Perron (2004), Bai and Ng (2004, 2007) and Pesaran (2007). 2 The tests proposed by Moon and Perron (2004) and Pesaran (2007) assume that under the null of unit roots the common factor components have the same order of integration as the idiosyncratic components, whilst the test procedures of Bai and Ng (2004, 2007) allow the order of integration of the factors to di¤er from that of the idiosyncratic components, by assuming di¤erent processes generating the two. A small sample comparison of some of these tests is provided in Gengenbach, Palm and Urbain (2006).

University of Southern California and Cambridge University October 25, 2003 Abstract This paper re-examines the panel unit root tests proposed by Chang (2002). She establishes asymptotic independence of the t-statistics when integrable functions of lagged dependent variable are used as instruments even if the original series are cross sectionally dependent. From this rather remarkable result she claims that her non-linear instrumental variable (NIV) panel unit root test is valid under general error cross correlations for any N (the cross section dimension) as T (the time dimension of the panel) tends to infinity. We show that her claim is valid only if N ln T / √ T → 0, as N and T → ∞, and this condition is unlikely to hold in practice, unless N is very small. The favourable simulation results reported by Chang are largely due to her particular choice of the error correlation ma- trix, which results in weak cross section dependence. Also, the asymptotic independence property of the t -statistics disappears when Chang’s modi- fied instruments are used. Using a common factor model with a sizeable degree of cross section correlations, we are able to show that Chang’s NIV panel unit root test suffers from gross size distortions, even when N is small relative to T (for example N = 5, T = 100).

1 Introduction Panel unit root tests (PURTs) have become a standard tool in macroeconometric applications. Making use of the cross sectional dimension allows to overcome power deficiencies of univariate unit root tests and helps to avoid the multiple testing prob- lem. Moreover, a number of macroeconomic models postulate stationarity of some key variables. For instance, the purchasing power parity hypothesis implies station- arity of real exchange rates (see Taylor and Taylor, 2004 for a survey) or the Fisher hypothesis, which predicts real interest rates to be stationary (e.g. Herwartz and Reimers, 2006, 2009). First generation PURTs (e.g. Levin et al., 2002 or Im et al., 2003) rely on the assumption of cross sectionally independent error terms. Since the work of O’Connell (1998), however, it is widely recognized that a violation of this assumption leads to severe size distortions of first generation tests and, therefore, second generation tests relying on less restrictive assumptions have been suggested (see Hurlin and Mignon, 2007 and Breitung and Pesaran, 2008 for recent surveys). Two general directions of coping with the nuisance parameters invoked by the cross sectional dependence can be identified. On the one hand, approaches presuming a common factor structure for the error terms and, on the other hand, tests building on robust covariance estimators.

The efficient normalization of the individual tests is much more difficult than one might think. As is well known, the individual unit root tests have null distributions that are nonstandard and nonnormal. Their time T -asymptotics yield distributions commonly rep- resented by various functionals of Brownian motions, and in particular, known to be asym- metric and skewed. See, e.g., Fuller (1996) for the tabulations of them. Consequently, the standardization through the mean and variance adjustment or the p-value transformation, which are two most frequently used methods for normalization, often works poorly even when T is relatively large. Worse, the errors made in the normalizations for individual tests are accumulated as N of them are combined to compute the panel unit root test. Obviously, the problem gets worse as N increases. We require, however, that N tend to infinity to obtain the normal N -asymptotics. This is a serious dilemma. It is well known that all the existing panel unit root tests suffer from rather serious size distortions when N is large compared to T .

Abstract This paper proposes a new testing approach for panel unit roots that is, unlike previ- ously suggested tests, robust to nonstationarity in the volatility process of the innovations of the time series in the panel. Nonstationarity volatility arises for instance when there are structural breaks in the innovation variances. A prominent example is the reduction in GDP growth variances enjoyed by many industrialized countries, known as the ‘Great Moderation.’ The panel test is based on Simes’ [Biometrika 1986, “An Improved Bonfer- roni Procedure for Multiple Tests of Significance”] classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series unit root tests, we employ recently proposed tests of Cavaliere and Taylor [Journal of Time Series Analysis, “Time-Transformed Unit Root Tests for Models with Non-Stationary Volatil- ity”]. The panel test is robust to general patterns of cross-sectional dependence and yet straightforward to implement, only requiring valid p-values of time series unit root tests, and no resampling. Monte Carlo experiments show that other panel unit root tests suffer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. The new test is applied to test for a unit root in an OECD panel of gross domestic products, yielding inference robust to the ‘Great Moderation.’ We find little evidence of trend stationarity.

Abstract This paper proposes a new testing approach for panel unit roots that is, unlike previ- ously suggested tests, robust to nonstationarity in the volatility process of the innovations of the time series in the panel. Nonstationarity volatility arises for instance when there are structural breaks in the innovation variances. A prominent example is the reduction in GDP growth variances enjoyed by many industrialized countries, known as the ‘Great Moderation.’ The panel test is based on Simes’ [Biometrika 1986, “An Improved Bonfer- roni Procedure for Multiple Tests of Significance”] classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series unit root tests, we employ recently proposed tests of Cavaliere and Taylor [Journal of Time Series Analysis, “Time-Transformed Unit Root Tests for Models with Non-Stationary Volatil- ity”]. The panel test is robust to general patterns of cross-sectional dependence and yet straightforward to implement, only requiring valid p-values of time series unit root tests, and no resampling. Monte Carlo experiments show that other panel unit root tests suffer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. The new test is applied to test for a unit root in an OECD panel of gross domestic products, yielding inference robust to the ‘Great Moderation.’ We find little evidence of trend stationarity.

Università G. D'Annunzio di Chieti-Pescara and Università Telematica “Leonardo da Vinci” Abstract This paper analyses the relation between the external and government deficits in a panel of CEEC economies. We first assess by panel unit root tests whether the fiscal and external intertemporal budget constraints hold, and then examine the role of public and private expenditure in the dynamics of external indebtedness by panel regression. The results show that government deficit is a significant but relatively minor source of external imbalances, and that the external indebtedness of CEEC economies is sustainable.

In this research, we aim to contribute to the empirics of PPP in three ways. First, the PPP model is tested on the panel that covers selected 10 countries of the Association of Southeast Asian Nations (ASEAN), with China, Japan and South Korea. Second, an array of panel unit root tests is used on new data series in order to examine among others the validity of PPP after the outbreak of Great Recession. Third, all the unit root tests are performed simultaneously for USD and EUR rates. The elementary research hypothesis in the presents study is that the PPP concept holds for the selected group of Asian countries. Our paper is organized as follows. The next chapter contains a short literature review, while the basic theory of PPP, data properties and the econometric methodology are outlined in the following chapter. After that, the empirical results are presented. The key findings of our analysis are highlighted in the concluding part of the paper.

0 : i 0 1,...., H ∀ = β i = N (11) The alternative is that at least one cross-sectional unit does not have a unit root. This is a drawback of this test as no information is revealed as to which panel members contain a unit root, see also Strauss and Yigit (2003) for further comments on potential problems with panel unit root tests. Yet, one of the advantages compared to other methods is that the autoregressive coefficients may vary among the cross-sectional units and the test has more power than single-equation Dickey-Fuller tests (ADF). The test is done as a single equation ADF-test with the test-statistic as an average t-value where critical values for varying panel sizes with respect to N and T are tabulated in Im et al. (2003).

Abstract This study finds evidence supportive of Fisher hypothesis in East Asian economies using panel unit root tests, which allow for cross-country variations in the estimation. Among others, one important implication is that monetary policy will be more effective in influencing long-term interest rates and long-run macroeconomic stability in these East Asian economies under regional collaboration.

This assumption makes the tests applicable under quite general panel data generating processes, observed in reality. The maximum order of serial correlation allowed is a function of T . The extension of …xed-T panel unit root tests to allow for structural breaks is very useful given evidence supporting the view that the presence of unit roots in economic time series can be falsely attributed to the existence of structural breaks in their deterministic components (see, e.g., Perron (2006), for a survey). On this front, the panel data approach o¤ers an interesting and unique perspective that it is not shared by single time series tests. The cross-sectional dimension of the panel can provide useful information, which can help to distinguish the type of shifts (breaks) in the deterministic components of the panel from the e¤ects of stochastic permanent shocks. As pointed out by Bai (2010), this framework can more accurately trace out structural break points of the panel data. 1 There are a few studies in the literature which suggest …xed-T panel data unit root tests allowing for a common structural break in the deterministic components of the panel data model (see, more recently, Karavias and Tzavalis (2012)). These studies however suggest unit root tests using the simple AR(1), dynamic panel data model as an auxiliary regression model, which may not be operational in practice due to the assumption of no serial correlation in its disturbance terms. The main goal of these studies is to pass ideas how to test for unit roots in the presence of structural breaks,

Panel unit root tests have been one of the most active research area for the past several years. This is largely due to the availability of panel data with long time span, and the growing use of cross-country and cross-region data over time to test for many important economic inter-relationships, especially those involving convergencies/divergencies of various economic variables. The notable contributers in theoretical research on the subject include Levin, Lin and Chu (1997), Im, Pesaran and Shin (1997), Maddala and Wu (1999), Choi (2001a) and Chang (1999, 2000). There have been numerous related empirical researches as well. Examples include MacDonald (1996), Oh (1996) and Papell (1997) just to name a few. The papers by Banerjee (1999), Phillips and Moon (1999) and Baltagi and Kao (2000) provide extensive surveys on the recent developments on the testing for unit roots in panels. See also Choi (2001b) and Phillips and Sul (2001) for some related work in this line of research.

The paper is organized as follows: In Section 2 we present the DGPs used in the three approaches mentioned above. Wherever one DGP is nested in another this will be pointed out. Also, the testing procedures used will be described in some detail. We briefly discuss which features of the three approaches will be compared. In Section 3, we present the results of an extensive simulation study which compares the three approaches to panel unit root testing for models with factor structures and two panel unit root tests proposed by Breitung and Das (2006) and by Sul (2006) which do not fully exploit factor structure. A PPP test using the described methods is presented in Section 4 as an illustrative example. Section 5 is devoted to conclusions. In particular, the implications of the findings for modeling in practice will be discussed.

Abstract In this paper, we employ some front page panel unit root tests to examine the validity of the purchasing power parity hypothesis in Turkey. Using monthly observations panel data of nine major county’s currency dates January 2003 through April 2010, we find that panel unit root tests are not rejected the mean-reversion of real exchange rates. Thus, the empirical results indicate significant support for the purchasing power parity holds in Turkey.

Selim Yıldırım a , Bilge Kağan Özdemir a *, Burhan Doğan a a Anadolu University, Department of Economics, Eskisehir,26470, Turkey Abstract The aim of this paper is to investigate whether inflation persists in energy prices of OECD countries. The method of choice for this purpose appears naturally to be panel unit root tests. Using three unit root tests we investigate the unit root hypothesis for an energy price on an unbalanced panel of all 34 OECD countries for the period from the first quarter of 1979 to the first quarter of 2012. The main findings of this paper indicate that; inflation is not uniformly persistent for all OECD countries. However individual inspections support the fact that Belgium, Czech Republic, Estonia, France, Germany, Italy, Korea, Poland, Slovak Republic, Turkey and United Kingdom exhibit a persistent inflation in energy commodities. On the other hand empirical evidence also strongly supports the fact that inflation in the aggregated energy commodities in Austria, Canada, Finland, Luxemburg, Norway, Sweden and United States display no persistency. © 2013 The Authors. Published by Elsevier B.V.

critical issues that determining exchange rate, whether they are mean-reverting in the long run and the purchasing power parity (PPP) holds. There is a widespread literature to examine relation between real exchange rates and PPP. Froot and Rogoff (1995), Rogoff (1996), Taylor and Sarno (1998), O’Conell (1998), Anker (1999), Sarno (2000), Taylor et al. (2001), Sarno and Taylor (2002), Killian and Taylor (2003), Taylor and Taylor (2004), Breitung and Candelon (2005), Taylor (2006), Kalyoncu and Kalyoncu (2008), Lau (2009), Cuestas (2009), Hung and Weng (2010) have showed theoretical background and empirical evidences of PPP-real exchange rates relationship. In this paper, we investigate whether real exchange rates in Turkey are mean-reverting or not. We apply contemporaneous panel unit root tests to nine exchange rates which are defined by Turkish Lira (TL). We suggest that such approach could also provide valuable insight for further investigation of this phenomenon in Turkey.