The Power Performance of Fixed-T Panel Unit Root Tests allowing for Structural Breaks

Karavias, Yiannis and Tzavalis, Elias (2013): The Power Performance of Fixed-T Panel Unit Root Tests allowing for Structural Breaks.

Abstract

The asymptotic local power of least squares based fixed-T panel unit root tests allowing for a structural break in their individual effects and/or incidental trends of the AR(1) panel data model is studied. These tests correct the least squares estimator of the autoregressive coefficient of this panel data model for its inconsistency due to the individual effects and/or incidental trends of the panel. The limiting distributions of the tests are analytically derived under a sequence of local alternatives, assuming that the cross-sectional dimension of the tests (N) grows large. It is shown that the considered fixed-T tests have local power which tends to unity fast only if the panel data model includes individual effects. For panel data models with incidental trends, the power of the tests becomes trivial. However, this problem does not always appear if the tests allow for serial correlation of the error term.

• Item Type: MPRA Paper
• Language: English
• Keywords: Panel data, unit root tests, structural breaks, local power, serial correlation, incidental trends
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models

References

Arellano, M., 2003, Panel data econometrics, Oxford University Press, UK

Bai J., Carrion-I-Silvestre, J.L., 2009. Structural Changes, Common Stochastic Trends, and Unit Roots in Panel Data. Review of Economic Studies, vol. 76(2), 471-501.

Carrion-i-Silvestre, J.L., Del Barrio-Castro, T., Lopez-Bazo, E., 2005. Breaking the panels: An application to real per capita GDP. Econometrics Journal, 8, 159-175.

Chan, F., Pauwels, L.L., 2011. Model specification in panel data unit root tests with an unknown break. Mathematics and Computers in Simulation. 81, 1299-1309.

Hahn, J., Kuersteiner, G., 2002. Asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and T are large. Econometrica. 70, 1639-1657.

Hadri K., Larsson, R., Rao, Y., 2012. Testing for stationarity with a break in panels where the time dimension is finite. Bulletin of Economic Research, 64, s123-s148.

Harris D., Harvey D., Leybourne S., and Sakkas N., 2010. Local asymptotic power of the Im-Pesaran-Shin panel unit root test and the impact of initial observations. Econometric Theory 26, 311-324. 24

Harris, D., Leybourne, S., and McCabe, B., 2005. Panel Stationarity Tests for Purchasing Power Parity with Cross-Sectional Dependence. Journal of Business & Economic Statistics, vol. 23, 395-409.

Harris, R., Tzavalis, E., 1999. Inference for unit roots in dynamic panels where the time dimension is fixed. Journal of Econometrics, 91, 201-226.

Harris, R., Tzavalis, E., 2004. Inference for unit roots for dynamic panels in the presence of deterministic trends: Do stock prices and dividends follow a random walk? Econometric Reviews 23, 149-166.

Harvey, D.I., Leybourne S.J., 2005. On testing for unit roots and the initial observation. Econometrics Journal 8, 97-111.

Karavias, Y., and Tzavalis, E., 2012. Generalized fixed-T Panel Unit Root Tests Allowing for Structural Breaks. Granger Centre Discussion Paper Series, No 12/02.

Karavias, Y., and Tzavalis, E., 2013. Testing for unit roots in short panels allowing for structural breaks. Computational Statistics and Data Analysis. (In press). http://dx.doi.org/10.1016/j.csda.2012.10.014

Kruiniger, H., 2008. Maximum Likelihood Estimation and Inference Methods for the Covariance Stationary Panel AR(1)/Unit Root Model. Journal of Econometrics 144, 447-464.

Kruiniger, H., and E., Tzavalis, 2002. Testing for unit roots in short dynamic panels with serially correlated and heteroscedastic disturbance terms. Working Papers 459, Department of Economics, Queen Mary, University of London, London.

Madsen E., 2010. Unit root inference in panel data models where the time-series dimension is fixed: a comparison of different tests. Econometrics Journal 13, 63-94.

Meligkotsidou, L., Tzavalis, E., Vrontos I.D., 2011. A Bayesian analysis of unit roots and structural breaks in the level, the trend and the error variance of autoregressive models of economic series. Econometric Reviews, 30 (2), 208-249.

Moon, H.R., Perron, B., 2008. Asymptotic local power of pooled t-ratio tests for unit roots in panels with fixed effects. Econometrics Journal 11, 80-104.

Moon, H.R., Perron, B., Phillips, P.C.B., 2007. Incidental trends and the power of panel unit root tests. Journal of Econometrics, 141(2), 416-459.

Pauwels, L.L., Chan, F., Mancini, G.T., 2012. Testing for Structural Change in Heterogeneous Panels with an Application to the Euro's Trade Effect. Journal of Time Series Econometrics, 4(2), Article 3.

Perron, P., 1989. The great crash, the oil price shock, and the unit root hypothesis. Econometrica, 57, 1361-1401. Schott, J.R., 1996. Matrix Analysis for Statistics, Wiley-Interscience.