Mixed signals among tests for cointegration

This paper illustrates that, under the null hypothesis of no cointegration, the correlation of p-values from a single-equation residual-based test (i.e., ADF or $\widehat{Z}_{\alpha}$) with a system-based test (trace or maximum eigenvalue) is very low even as the sample size gets large. With data-generating processes under the null or 'near' it, the two types of tests can yield virtually any combination of p-values regardless of sample size. As a practical matter, we also conduct tests for cointegration on 132 data sets from 34 studies appearing in this Journal and find substantial differences in p-values for the same data set.