The autoregressive distributed lag bounds test generalised to consider a long-run levels relationship when all levels variables are 𝑰(𝟎)

Pesaran, Shin and Smith (2001) introduced the autoregressive distributed lag (ARDL) bounds cointegration testing procedure assuming the dependent variable is 𝐼(1) and allowing regressors to be 𝐼(1) or 𝐼(0). McNown et al (2018) and Sam et al (2019) propose a third test that avoids making incorrect inference if the dependent variable is not 𝐼(1) such that cointegration is only found when it exists. Because cointegration requires some variables to be 𝐼(1) an equilibrium with only 𝐼(0) variables is not considered. We argue that using new lower bound critical values the ARDL tests can determine whether an equilibrium exists when all levels variables can be 𝐼(0). This generalises the ARDL method to allow all levels variables to be 𝐼(1) or 𝐼(0).