Panel data unit root test with structural break: A Bayesian approach

Abstract

The idea about structural break in unit root hypothesis under time series model had received great amount of attention over many last decades. The importance of structural break in the mean had been comprehensively studied by Perron [15], Perron and Vogelsang [17], Zivot and Andrews [25] etc. This had also studied in considering of break in variance by Kim et al. [9], Cook [6], Kumar et al. [11] etc. There is sufficient contribution regarding break in mean and variance individually but both are equally important and this was little explored by Bai [1] for panel data and Meligkotsidou et al. [14] for univariate time series. In present paper, we are extending this on panel dataAR(1) time series model under Bayesian framework. Posterior odds ratio has been derived for various models with and without break in mean, variance and both in consideration of unit root hypothesis. A simulation as well as an empirical analysis is also carried out to get more generalized view on the model under study.

Keywords

• Panel autoregressive model,Structural break,Prior distribution,Posterior odds ratio,Monte Carlo integration

References

1. [1] J. Bai. Common breaks in means and variances for panel data, Journal of Econometrics 157, 78-92, 2010.
2. [2] B. H. Baltagi, Q. Feng and C. Kao. Estimation of heterogeneous panels with structural breaks, Journal of Econometrics 191(1), 176-195, 2016.
3. [3] G. E. P. Box and G. M. Jenkins. Time Series Analysis Forecasting and Control, Holden-Day: San Francisco, CA, 1970.
4. [4] A. Chaturvedi and J. Kumar. Bayesian unit root test for time series models with structural break, American Journal of Mathematical and Management Science 27(1), 243-268, 2007.
5. [5] S. Chib. Estimation and comparison of multiple changepoint models, Journal of Econometrics 86, 221-241, 1998.
6. [6] S. Cook. Unit root testing in the presence of innovation variance breaks: a simple solution with increased power, Journal of Applied Mathematics 2(5), 233-240, 2002.
7. [7] C. Inclan. Detection of multiple changes of variance using posterior odds, Journal of Business & Economic Statistics 11(3), 289-300, 1993.
8. [8] R. Kass and A. Raftery. Bayes factors, Journal of the American Statistical Association 90, 773-795, 1995.

9. [9] T. H. Kim, S. J. Leybourne and P. Newbold. Unit root test with a break in innovation variance, Journals of Econometrics 109, 365-387, 2002.
10. [10] T. Kim, B. Kim, H. Moon and S. Jeong. Unit root tests in the presence of multiple breaks in variance, The Singapore Economic Review 62(2), 345-361, 2017.
11. [11] R. Kumar, J. Kumar and A. Chaturvedi. Bayesian unit root test for time series models with structural break in variance, Journal of Economics and Econometrics 55(1), 75-86, 2012.
12. [12] A. Levin, C. F. Lin and C. S. J. Chu. Unit root test in panel data: asymptotic and finite sample properties, Journal of Econometrics 108(1), 1-24, 2002.
13. [13] D. Li, J. Qian and L. Su. Panel data models with interactive fixed effects and multiple structural breaks, Journal of the American Statistical Association 111(516), 1804-1819, 2016.
14. [14] L. Meligkotsidou, E. Tzavalis and I. D. Vrontos. A Bayesian analysis of unit roots and structural breaks in the level and the error variance of autoregressive models, Econometric Review 30(2), 208-249, 2011.
15. [15] P. Perron. Testing for a unit root in a time series with a changing mean, Journal of Business and Economic Statistics 8, 153-162, 1990.
16. [16] P. Perron. Further evidence on breaking trend functions in macroeconomic variables, Journal of Econometrics 80, 355-385, 1997.
17. [17] PP. Perron and T. J. Vogelsang. Nonstationarity and level shifts with an application to purchasing power parity, Journal of Business and Economic Statistics 10, 301-320, 1992.
18. [18] J. Qian, and L. Su. Shrinkage estimation of common breaks in panel data models via adaptive group fused lasso, Journal of Econometrics 191(1), 86-109, 2016.
19. [19] P. C. Schotman and H. K. Van Dijk. A Bayesian routes to unit roots, Journal of Applied Econometrics 6, 387-401, 1991.
20. [20] X. Shao and X. Zhang. Testing for change points in time series, Journal of the American Statistical Association 105(491), 1228-1240, 2010.
21. [21] T. Vogelsang and P. Perron. 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, 1998.
22. [22] J. Wang and E. Zivot. A Bayesian time series model of multiple structural changes in level, trend and variance, Journal of Business and Economic Statistics 18, 374-386, 2000.
23. [23] Y. Yao. Estimating the number of changepoints via Schwarz criterion, Statistics & Probability Letters 6, 181-189, 1988.
24. [24] F. Zeileis, K. H. Leisch and C. Kleiber. Strucchange: an R package for testing for structural change in linear regression models, Journal of Statistical Software 7(2), 1-38, 2002.
25. [25] E. Zivot and D. W. K. Andrews. Further evidence on the great crash, the oil price shock, and the unit root hypothesis, Journal of Business and Economic Statistics 10, 251-270, 1992.