We introduce a new index that explores the linkage between business-cycle fluctuations and deviations from long-run economic relationships. This index is virtually a measure of the distance between an attractor, a space spanned by the associated cointegrating vectors, and a point in the n-dimensional Euclidean space. The index is applied to U.S. quarterly data to demonstrate its association with an economy's vulnerability state. We find that the average of the index during expansions negatively correlates with the average contraction in output during recessions. A nonlinear error correction model based on a revised version of the index reveals a forecasting gain as compared to the linear error correction model.The authors gratefully acknowledge helpful comments from two anonymous referees, Ming-Li Chen, Ching-Fan Chung, Jin-Lung Lin, and participants of the 2001 winter meeting of the Econometric Society in New Orleans and the workshop at the Institute of Economics, Academia Sinica. Yau received financial support from the National Science Council of Taiwan under grant NSC 89-2415-H-030-011.
