Testing for the 'Existence of a Long-run Relationship'

This paper develops a new approach to testing for the existence of a linear long-run relationship, when the orders of integration of the underlying regressors are not known with certainty. The test is the standard Wald or F statistic for testing the significance of the lagged levels of the variables in a first-difference regression. The asymptotic distributions of these statistics are non-standard under the null hypothesis that there exists no long-run relationship between the levels of the included variables. Two sets of asymptotic critical values are provided: one set assuming that all regressors are I(1), and another assuming they are all I(0). These provide a band covering all possible classifications of the regressors into I(0), I(1) or mutually cointegrated.