Generalized �Fixed-T Panel Unit Root Tests Allowing for Structural Breaks

Karavias, Yiannis and Tzavalis, Elias (2012): Generalized �Fixed-T Panel Unit Root Tests Allowing for Structural Breaks.

Abstract

In this paper we suggest panel data unit root tests which allow for a structural breaks in the individual effects or linear trends of panel data models. This is done under the assumption that the disturbance terms of the panel are heterogeneous and serially correlated. The limiting distributions of the suggested test statistics are derived under the assumption that the time-dimension of the panel (T) is �fixed, while the cross-section (N) grows large. Thus, they are appropriate for short panels, where T is small. The tests consider the cases of a known and unknown date break. For the latter case, the paper gives the analytic form of the distribution of the test statistics. Monte Carlo evidence suggest that our tests have size which is very close to its nominal level and satisfactory power in small-T panels. This is true even for cases where the degree of serial correlation is large and negative, where single time series unit root tests are found to be critically oversized.

• Item Type: MPRA Paper
• Language: English
• Keywords: Panel data models; unit roots; structural breaks
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Andrews, Donald W K, 1993. Tests for Parameter Instability and Structural Change with Unknown Change Point. Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.

Arelano E. and B. Honoré (2002). Panel data models: Some recent developments, Handbook of Econometrics, edited by Heckman J. and E. Leamer editors, Vol 5, North Holland.

Arellano-Valle, R. B., and Genton, M. G. (2008). On the exact distribution of the maximum of absolutely continuous dependent random variables. Statistics and Probability Letters, 78, 27-35.

Bai J.(2010). Common breaks in means and variances for panel data. Journal of Econometrics 157,78-92.

Bai J. and J.L. Carrion-i-Silvestre (2009). Structural changes, common stochastic trends and unit roots in panel data. Review of Economic Studies, 76, 471-501.

Baltagi B.H. (1995). Econometric analysis of panel data, Wiley, Chichester.

Blundell R. and Bond S. 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.

Binder M., Hsiao C. and Pesaran H. (2005). Estimation and inference in short panel vector autoregression with unit roots and cointegration. Econometric Theory, 21, 795-837.

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

De Wachter S., Harris R.D.F., Tzavalis E. (2007). Panel unit root tests: the role of time dimension and serial correlation. Journal of Statistical Inference and Planning, 137, 230-244.

De Wachter S., and Tzavalis E. (2005). Monte Carlo comparison of model and moments selection and classical inference approach to break detection in panel data models�, Economic Letters (2005), 88, 91-96.

De Wachter S., and Tzavalis E. (2012). Detection of structural breaks in linear panel data models, Computational Statistics & Data Analysis, 56, 3020-3034.

Hall, B. H. and Mairesse J. (2005). Testing for unit roots in panel data: an exploration using real and simulated data. In D. Andrews and J. Stock (Eds.), Identi�cation and Inference in Econometric Models: Essays in Honor of Thomas J. Rothenberg.

Han, C and Phillips P.C.B (2012). GMM estimation for dynamic panels with �fixed effects and strong instruments at unity. Econometric Theory, 26, 2010, 119�151.

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

Harris R.D.F and 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.

Hlouskova J. and Wagner M. (2006). The performance of panel unit root and stationary tests: Results from a large scale simulation study. Econometric Reviews, 25, 85-117.

Hsiao C., Pesaran H. and Tahmiscioglu K., (2002). Maximum likelihood estimation of �fixed effects dynamic panel data models covering short time periods. Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.

Karavias Y. and Tzavalis E. (2012). Testing for unit roots in short panels allowing for structural breaks. Computational Statistics and Data Analysis, http://dx.doi.org/10.1016/j.csda.2012.10.014.

Kim, D. (2011). Estimating a common deterministic time break in large panels with cross-sectional dependence. Journal of Econometrics, 164 (2), 310-330.

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

Levin A., Lin C.F. and Chu C-S. J, (2002). Unit root tests in panel data: asymptotic and �finite-sample properties. Journal of Econometrics, 108, 1-24.

Madsen E. (2008). GMM Estimators and Unit Root Tests in the AR(1) Panel Data Model. unpublished.

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

Nickell, S. (1981). Biases in Dynamic Models with Fixed Effects. Econometrica 49, 1417-1426.

Perron P. (2006). Dealing with structural breaks. Palgrave Handbook of Econometrics, Vol. 1: Econometric Theory, Mills. T and K. Patterson (eds), Palgrave MacMillan, 278-352.

Perron P. and Vogelsang T. (1992). Nonstationarity and level shifts with an application to purchasing power parity. Journal of Business and Economic Statistics, 10, 301-320.

Schott J.R. (1996). Matrix Analysis for Statistics, Wiley-Interscience.

Stock J.H. (1994). Unit roots, structural breaks and trends. In Handbook of Econometrics, Vol. IV, Engle R.F. and D.L. McFadden (eds), Elsevier, Amsterdam.

Schwert, G.W., (1989). Tests for unit roots:a Monte Carlo investigation. Journal of Business and Economic Statistics 7, 147�160.

Vogelsang, T. and Perron, P. (1998). Additional tests for a unit root allowing for a break in the trend function at an unknown time. International Economic Review, 39(4):1073�1100.

Zivot E. and Andrews D.W.K. (1992). Further evidence on the great crash, the oil price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 10, 251-270.

White H. (2000). Asymptotic theory for econometricians, Academic Press.