Bounds Testing Approaches to the Analysis of Long Run Relationships

This paper develops a new approach to the problem of testing the existence of a long-run level relationship between a dependent variable and a set of regressors, when it is not known with certainty whether the underlying regressors are trend- or first-difference stationary. The proposed tests are based on standard F- and t- statistics used to test the significance of the lagged levels of the variables on a first-difference regression. The asymptotic distributions of these statistics are non-standard under the null hypothesis that there exists no level relationship between the dependent variable and the included regressors, irrespective of whether the regressors are I(0) or I(1). Two sets of asymptotic critical values are provided: One set assuming that all the regressors are I(1), and another set assuming that they are all I(0). These two sets of critical values provide a band covering all possible classifications of the regressors into I(0), I(1) or mutually cointegrated. Accordingly, various bounds testing procedures are proposed. It is shown that the proposed tests are consistent, and their asymptotic distribution under the null and suitably defined local alternatives are derived. The empirical relevance of the bounds procedures are demonstrated by a re-examination of the earnings equation included in the UK Treasury macroeconometric model. This is a particularly relevant application as there is considerable doubt concerning the order of integration of the variables such as the unemployment rate, the union strength and the wedge between the "real produce wage" and the "real consumption wage" that enter the earnings equation.