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 I ( 1 ) or I ( 0 ) is widely used in the literature. However, a long-run levels relationship cannot be detected when the dependent variable is I 0 , because both tests will always reject their null hypotheses. It has subsequently been argued that a third test determines whether the dependent variable is I ( 1 ) , such that when all three tests reject their null hypotheses, a cointegrating equation with an I ( 1 ) dependent variable is identified. It is argued that all three tests rejecting their null hypotheses rules out the possibility that the dependent variable is I ( 0 ) , implying that the three tests cannot detect an equilibrium when the dependent variable is I ( 0 ) . 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 I ( 0 ) and not only when it is I ( 1 ) . 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.