A number of panel unit root tests that allow for cross section dependence have been proposed in the literature, notably by Bai and Ng (2002), Moon and Perron (2003), and Phillips and Sul (2002) who use orthogonalization type procedures to asymptotically eliminate the cross dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative test where the standard DF (or ADF) regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series. A truncated version of the CADF statistics is also considered. New asymptotic results are obtained both for the individual CADF statistics, and their simple averages. It is shown that the CADF_i statistics are asymptotically similar and do not depend on the factor loadings under joint asymptotics where N (cross section dimension) and T (time series dimension) tends to infinity, such that N/T tends to k, where k is a fixed finite non-zero constant. But they are asymptotically correlated due to their dependence on the common factor. Despite this it is shown that the limit distribution of the average CADF statistic exists and its critical values are tabulated. The small sample properties of the proposed tests are investigated by Monte Carlo experiments, for a variety of models. It is shown that the cross sectionally augmented panel unit root tests have satisfactory size and power even for relatively small values of N and T. This is particularly true of cross sectionally augmented and truncated versions of the simple average t-test of Im, Pesaran and Shin, and Choi's inverse normal combination test.

A Simple Panel Unit Root Test in the Presence of Cross Section Dependence

A number of panel unit root tests that allow for cross section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the cross dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard ADF regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series. New asymptotic results are obtained both for the individual CADF statistics, and their simple averages. It is shown that the individual CADF statistics are asymptotically similar and do not depend on the factor loadings. The limit distribution of the average CADF statistic is shown to exist and its critical values are tabulated. Small sample properties of the proposed test are investigated by Monte Carlo experiments. The proposed test is applied to a panel of 17 OECD real exchange rate series as well as to log real earnings of households in the PSID data.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jae.951

A simple panel unit root test in the presence of cross-section dependence

Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

We examine properties of residual-based tests for the null of no cointegration for dynamic panels in which both the short-run dynamics and the long-run slope coefficients are permitted to be heterogeneous across individual members of the panel. The tests also allow for individual heterogeneous fixed effects and trend terms, and we consider both pooled within dimension tests and group mean between dimension tests. We derive limiting distributions for these and show that they are normal and free of nuisance parameters. We also provide Monte Carlo evidence to demonstrate their small sample size and power performance, and we illustrate their use in testing purchasing power parity for the post–Bretton Woods period.I thank Rich Clarida, Bob Cumby, Mahmoud El-Gamal, Heejoon Kang, Chiwha Kao, Andy Levin, Klaus Neusser, Masao Ogaki, David Papell, Pierre Perron, Abdel Senhadji, Jean-Pierre Urbain, Alan Taylor, and three anonymous referees for helpful comments on various earlier versions of this paper. The paper has also benefited from presentations at the 1994 North American Econometric Society Summer Meetings in Quebec City, the 1994 European Econometric Society Summer Meetings in Maastricht, and workshop seminars at the Board of Governors of the Federal Reserve, INSEE-CREST Paris, IUPUI, Ohio State, Purdue, Queens University Belfast, Rice University–University of Houston, and Southern Methodist University. Finally, I thank the following students who provided assistance in the earlier stages of the project: Younghan Kim, Rasmus Ruffer, and Lining Wan.

/pdf/panel-cointegration-asymptotic-and-finite-sample-properties-2km4hsia3p.pdf

Panel cointegration: asymptotic and finite sample properties of pooled time series tests with an application to the ppp hypothesis

Panel cointegration: asymptotic and finite sample properties of pooled time series tests with an application to ppp hypothesis: new results

Testing for a Unit Root in the Nonlinear STAR Framework

This paper proposes a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition process. In the context of nonlinear smooth transition error correction models (ECMs) we provide two simple operational versions of the tests. First, we obtain the associated nonlinear ECM-based tests. Second, we derive the nonlinear analogue of the residual-based test for cointegration in linear models. We derive the asymptotic distributions of the proposed tests. Monte Carlo simulation exercises confirm that our proposed tests have much better power than the linear counterparts against the alternative of a globally stationary nonlinear cointegrating process. In an application to the price-dividend relationship, our test is able to find cointegration, whereas the linear-based tests fail to do so.We are grateful to an associate editor, two anonymous referees, Richard Baillie, In Choi, Atanas Christev, Hira Koul, Richard Harris, Cheng Hsiao, Changjin Kim, Joon Park, Peter Schmidt, Yoonjae Whang, Jeff Wooldridge, and seminar participants at University of Edinburgh, Heriot-Watt University, Korea University, University of Leeds, Michigan State University, University of Newcastle, and Sungkunkwan University for their helpful comments. Partial financial support from the ESRC (grant R000223399) is gratefully acknowledged. The usual disclaimer applies.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0266466606060129

Testing for cointegration in nonlinear smooth transition error correction models

Temporal aggregation and the power of tests for a unit root

This paper proposes panel-based tests for the null stationary against the alternative of unit roots in the presence of both heterogeneity across cross-section units and serial correlation across time periods. It is shown by the joint asymptotic approach (rather than the sequential asymptotic approach) that the proposed test statistic is distributed as standard normal under the null for large N (number of groups) and finite T (number of time periods) with the additional condition N/T -> 0. It is also shown that the test is consistent under the alternative hypothesis that the fraction of the individual processes that have unit root is non-zero. Monte Carlo results confirm that validity of the proposed test, and clearly indicate that the power of the panel-based test is substantially higher than that of the single time series-based test.

Testing for Stationarity in Heterogeneous Panels with Serially Correlated Errors

This paper presents a two-party model of fiscal and debt policy in which the parties do not care about policy outcomes when out of office. Unlike other models of this type, our model has predictions that are largely consistent with existing empirical findings about partisan and electoral effects on government expenditure, tax revenue, and debt. It also yields new predictions about how the feedback of fiscal policy on lagged debt may depend on partisan and electoral effects. These new predictions are not rejected by a test of the model on UK data. In multi-party democracies, the motives of the party in power undoubtedly affect fiscal and monetary policy. Many economists and political scientists believe that economic policy-makers are driven by two - not mutually exclusive - motives. First, they wish to remain in office as long as possible (the survival or opportunistic motive). Second, they wish to benefit their constituencies (partisan motive). The effects of these motives may show up in two ways in the data. First, there may be effects of ideological differences of the parties in power on fiscal and monetary policy - so-called partisan effects. For example, we might expect 'left-wing' governments to tax and spend more, and (possibly) accumulate more debt. Second, there may be attempts by the incumbent party to use fiscal and monetary policy to 'bribe' the electorate prior to elections e.g. by cutting taxes and interest rates - so-called electoral effects. Recent econometric work has established some interesting 'stylised facts' which are broadly consistent with these predictions. Several studies report evidence of electoral effects on various fiscal policy instruments for the United States; Tufte (I978) for transfers, Bizer and Durlauf (I990) for taxes, and MacDonald (i99i) for state-level public expenditure. More recently, Alesina et al. (I 992; I 993) have found evidence of electoral- effects on government debt in a panel study of OECD countries. Evidence of partisan effects on fiscal policy is scarcer. Alesina et al. (I 993) report partisan effects on debt, and Roubini and Sachs (I989) report in a study of OECD democracies that countries with a higher percentage of 'left-wing' governments have significantly higher longrun government spending to GNP ratios. Concurrently with the accumulation of this evidence, a theoretical literature, notably Alesina and Tabellini ( 1990), Rogoff ( 1990), and Rogoff and Sibert (i 988) has provided new explanations of observed electoral effects' on

Andy Snell

Papers

Testing for a Unit Root in the Nonlinear STAR Framework

Testing for cointegration in nonlinear smooth transition error correction models

Temporal aggregation and the power of tests for a unit root

Testing for Stationarity in Heterogeneous Panels with Serially Correlated Errors

Fiscal policy, public debt stabilisation and politics: theory and uk evidence*