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 lung-run relationship between the levels of the included variables. We provide two sets of of asymptotic critical values; one set assuming that all the exogeneous regressors are I(1), and another set assuming that they are all I(0).