This paper examines the asymptotic and finite sample properties of two procedures for testing cointegration: the Dickey-Fuller (DF) test and the error-correction model (ECM) test. The DF test, which is commonly used, may reject the null hypothesis of no cointegration marginally or not at all, while the ECM test, which is based on the coefficient on the error-correction term in a dynamic model, often has a high t-statistic supporting cointegration. The paper explains that this contrast arises because the DF test imposes a common factor restriction that is often invalid, leading to a loss of power. The ECM test, by not imposing this restriction, uses available information more efficiently. The paper derives the asymptotic distributions of both tests under the null and alternative hypotheses of no and cointegration, respectively, and shows that the ECM test can be arbitrarily more powerful than the DF test when the signal-to-noise ratio is large. Monte Carlo simulations and empirical evidence using UK money demand data illustrate these results, demonstrating that the ECM test can have much higher power than the DF test when the common factor restriction is violated.This paper examines the asymptotic and finite sample properties of two procedures for testing cointegration: the Dickey-Fuller (DF) test and the error-correction model (ECM) test. The DF test, which is commonly used, may reject the null hypothesis of no cointegration marginally or not at all, while the ECM test, which is based on the coefficient on the error-correction term in a dynamic model, often has a high t-statistic supporting cointegration. The paper explains that this contrast arises because the DF test imposes a common factor restriction that is often invalid, leading to a loss of power. The ECM test, by not imposing this restriction, uses available information more efficiently. The paper derives the asymptotic distributions of both tests under the null and alternative hypotheses of no and cointegration, respectively, and shows that the ECM test can be arbitrarily more powerful than the DF test when the signal-to-noise ratio is large. Monte Carlo simulations and empirical evidence using UK money demand data illustrate these results, demonstrating that the ECM test can have much higher power than the DF test when the common factor restriction is violated.