Testing the null of cointegration with structural breaks

We propose a Lagrange Multiplier-type statistic to test the null hypothesis of cointegration allowing for the possibility of a structural break, in both the deterministic and the cointegration vectors. Our proposal focuses on the presence of endogenous regressors. The test complements the usual non-cointegration tests so as to obtain stronger evidence of cointegration. We consider the cases of known and unknown dates of the break. In the latter case, we show that minimizing the Sum of Squared Residuals results in a super-consistent estimator of the break fraction. Finally, the behaviour of the tests is studied through Monte Carlo experiments.