Bounds testing approaches to the analysis of level relationships

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Abstract
This paper develops a new approach to the problem of testing the existence of a 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 standardF‐ andt‐statistics used to test the significance of the lagged levels of the variables in a univariate equilibrium correction mechanism. The asymptotic distributions of these statistics are non‐standard under the null hypothesis that there exists no level relationship, irrespective of whether the regressors areI(0) orI(1). Two sets of asymptotic critical values are provided: one when all regressors are purelyI(1) and the other if they are all purelyI(0). These two sets of critical values provide a band covering all possible classifications of the regressors into purelyI(0), purelyI(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 is demonstrated by a re‐examination of the earnings equation included in the UK Treasury macroeconometric model. Copyright © 2001 John Wiley & Sons, Ltd.