The paper examines the differences between two cointegration tests: the Dickey-Fuller (DF) test and the error-correction (ECM) test. It shows that the DF test, which uses a unit-root test on residuals from a static cointegrating regression, can have low power when a common factor restriction is imposed, whereas the ECM test, which uses the t-ratio of the error-correction coefficient in a dynamic model, is more efficient and has higher power. The ECM test is preferable because it uses available information more efficiently than the DF test. The paper analyzes a simple bivariate process and derives the relationship between the error-correction mechanism and the equation from which the DF statistic is calculated. It then presents the asymptotic distributions of the DF and ECM statistics under the null hypothesis of no cointegration and under the alternative hypothesis of cointegration. The results show that the ECM test has a more normal distribution under the alternative hypothesis and is more powerful when the signal-to-noise ratio is large. The paper also generalizes the results to multivariate, multiple-lag systems and discusses the implications for testing cointegration in such systems. It shows that the common factor restriction in the DF test can lead to a loss of information and reduced power, while the ECM test avoids this issue by using the error-correction coefficient. The paper also provides empirical evidence using Hendry and Ericsson's (1991b) quarterly data on UK money demand, showing that the ECM test is more powerful than the DF test in detecting cointegration. The paper concludes that the ECM test is more effective than the DF test in detecting cointegration, as it avoids the common factor restriction and uses the error-correction coefficient more efficiently. The results support the use of the ECM test in empirical analysis of economic time series.The paper examines the differences between two cointegration tests: the Dickey-Fuller (DF) test and the error-correction (ECM) test. It shows that the DF test, which uses a unit-root test on residuals from a static cointegrating regression, can have low power when a common factor restriction is imposed, whereas the ECM test, which uses the t-ratio of the error-correction coefficient in a dynamic model, is more efficient and has higher power. The ECM test is preferable because it uses available information more efficiently than the DF test. The paper analyzes a simple bivariate process and derives the relationship between the error-correction mechanism and the equation from which the DF statistic is calculated. It then presents the asymptotic distributions of the DF and ECM statistics under the null hypothesis of no cointegration and under the alternative hypothesis of cointegration. The results show that the ECM test has a more normal distribution under the alternative hypothesis and is more powerful when the signal-to-noise ratio is large. The paper also generalizes the results to multivariate, multiple-lag systems and discusses the implications for testing cointegration in such systems. It shows that the common factor restriction in the DF test can lead to a loss of information and reduced power, while the ECM test avoids this issue by using the error-correction coefficient. The paper also provides empirical evidence using Hendry and Ericsson's (1991b) quarterly data on UK money demand, showing that the ECM test is more powerful than the DF test in detecting cointegration. The paper concludes that the ECM test is more effective than the DF test in detecting cointegration, as it avoids the common factor restriction and uses the error-correction coefficient more efficiently. The results support the use of the ECM test in empirical analysis of economic time series.