Bounds Testing Approaches to the Analysis of Level Relationships

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 standard F- and t-statistics used to test the significance of the regression coefficients. The methodology allows for the identification of level relationships, providing robust inference in the presence of integrated or stationary data. The analytical framework and tests are examined through both theoretical derivations and empirical examples. The results indicate that the new approach can effectively detect level relationships, improving upon existing methods that may not account for the nature of the underlying data. This advancement has significant implications for empirical macroeconometric modeling and offers a robust toolkit for researchers analyzing time series data.