Optimal growth, genuine savings and long-run dynamics

Green accounting theories have shown that negative genuine savings at some point in time imply unsustainability. Consequently, recent studies advocate the use of the genuine savings measure for empirical testing: a negative index implies that sustainability be rejected. However, this criterion cannot ascertain sustainability, because positive current genuine savings do not rule out genuine dissaving in the future. This paper derives a one-to-one relationship between the sign of long-run genuine savings and the limiting condition for sustained utility in the capital-resource growth model, assuming technical progress and resource renewability. This result suggests to extend the genuine saving method to include a test of the limiting condition: if this condition is empirically rejected, positive current genuine savings are delivering a false message.