Demonstrating that the autoregressive distributed lag bounds test can detect a long-run levels relationship when the dependent variable is I(0)

The autoregressive distributed lag bounds t-test and F-test for a long-run relationship that allows level variables to be either (Formula presented.) or (Formula presented.) is widely used in the literature. However, a long-run levels relationship cannot be detected when the dependent variable is (Formula presented.), because both tests will always reject their null hypotheses. It has subsequently been argued that a third test determines whether the dependent variable is (Formula presented.), such that when all three tests reject their null hypotheses, a cointegrating equation with an (Formula presented.) dependent variable is identified. It is argued that all three tests rejecting their null hypotheses rules out the possibility that the dependent variable is (Formula presented.), implying that the three tests cannot detect an equilibrium when the dependent variable is (Formula presented.). Our first contribution is to demonstrate and explain that rejection of all three tests’ null hypotheses can also indicate an equilibrium when the dependent variable is (Formula presented.) and not only when it is (Formula presented.). Our second contribution is to produce previously unavailable critical values for the third test in the cases where an intercept or trend is restricted into the equilibrium.