| In order to avoid spurious regression, cointegration test is needed for non-stationary data before modeling so that it can make sure whether there are equilibrium relationships among variables in the long-run. In fact, the cointegration analysis technology is a major breakthrough for the methodology of Econometrics since1980s and is widely used in the empirical analysis. On the other hand, since panel data reflect the characteristics of the data from time and cross-section dimensions and provide more information, panel data become one of popular subjects in Modern Econometrics. Thus, scholars pay much attention to study cointegration theory of non-stationary panel data. Obviously, it may make a wrong conclusion if we make analysis of individual series, so that new statistics and methods are needed to test the panel cointegration relationship. As a matter of fact, panel cointegration theory has experienced rapid development since1990s.Panel cointegration tests in the early time are based on structural stability and cross-sectional independence. However, in the theory, the concept of cointegration does not rule out the possibility that both the cointegrating vector(s) and the deterministic component(s) of the long-run relationship might change during the time period analyzed, that is the cointegrating vector(s) and the deterministic component(s) might be unstable. Besides, in practice, with the time period increasing, outside shock, interference and the change of the economic system make the structure of the data unstable. Meanwhile, in the contemporary society with cash flowing so frequent, the economics among districts are inter-related. As a result, sections of panel are related as well. Therefore, traditional panel cointegration tests based on the two assumptions lose their power. So no matter in the theory or in practice, it is valuable to study panel cointegration tests with structural breaks and cross-sectional dependence, and it is the key point of this paper.Based on the comprehensive sorting of panel cointegration tests, the paper studies panel cointegration tests with structural breaks and cross-sectional dependence further. Westerlund and Edgerton (2008) proposed two statistics to test the null of no cointegration. The test allows for heteroskedastic and serially correlated errors, cross-sectional dependence and unknown breaks in both the intercept and slope of the cointegrated regression, which may be located at different dates for different units. The paper introduces the test and extends it to be able to be used for equations without time trend, and then derives the limiting distributions of the statistics. The performance of the approach is investigated through Monte Carlo simulations, from which we conclude that (1) in general, the two statistics have small distortion size and high power, but the statistic based on t-ratio Z,(N) outperforms the statistic based on the coeffienct Z (N) since Zτ(N) has better size properties than Zp(N), while maintains relatively the same power;(2) it is necessary to extend the model to the ones without time trend, because not only the limiting distributions are different, but also the estimated model is misspecified with time trend or without time trend will affect the size and the power, and at the same time erroneous omission of breaks will affect the power of the statistics severely;(3) the SIC*criterion the paper proposes can choose the correct model well;(4) the statistics still have good finite sample properties for different proportion of N/T and they can converge quickly.Finally, in the example, the paper applies the new statistics based on DOLS to test the relationship between CO2emissions and economic growth using the panel data of20countries from1960to2008. The result shows that while considering cross-sectional dependence and structural breaks, it does exist the long-run equilibrium between them, and cointegraton equation without time trend fits the relashionship best. |
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