Cointegration Testing Under Structural Breaks: A Robust Extended Error Correction Model

The properties of the cointegration tests based on single equation error correction models (ECM test) are well known. The dependence of critical values, and the power of the test on nuisance parameters are documented in Banerjee et al. (1986), Engle and Granger (1987), Kremers et al. (1992), Park and Phillips (1988, 1989), and Banerjee et al. (1993). From the univariate point of view, the effects of having breaks when applying unit root test, like Dickey and Fuller (1979) test, are well known, and Perron (1989) is a good starting point to see those impacts. From Hendry (1996), a structural break essentially corresponds to an intermittent shock with a permanent effect on the series. If this shock is not explicit1y taken into account, standard unit root tests would in general mistake the structural break for a unit root. Leyboume et al. (1998) indicate that the opposite can also happen if the break occurs at the beginning of the sample. The results of Hendry and Neale (1990) and Perron and Vogelsang (1992) indicate that a neglected shift in the mean also leads to spurious unit roots. Rappoport and Reichlin (1989) is probably the first reference to deal with the impact ofhaving segmented trends as an altemative to a unit root model, and Andres et al. (1990) extended the analysis to more that one break point in the trend. The main drawback with this literature, that has expanded dramatically since then, is that we always have to add dummy variables to capture the structural breaks in order to correctly apply unit root tests. Therefore the critical values obtained depend on the size and on the timing of the break. Again, a vast literature emerged searching for unknown break points using recursive or sequential tests. See, for example, Banerjee et al. (1992), Zivot and Andrews (1992), Andrews (1993). Andrews et al. (1996), Bai (1997),