Testing linear growth rate formulas of non-scale endogenous growth models

Endogenous growth theory has produced formulas for steady-state growth rates of income per capita which are linear in the growth rate of the population. Depending on the details of the models, slopes and intercepts are positive, zero or negative. Empirical tests have taken over the assumption of exogenous population growth from the theoretical models and have mostly not distinguished steady-state results from transitional growth. In contrast, we assume (i) that there is two-way causality and (ii) capture the steady-state property by a long-term relation in a series of vector-error-correction models allowing (iii) successively for more heterogeneity. The slope of the growth equations is positive in this setting. Intercepts are most frequently also positive, but almost equally often zero, and sometimes even negative. Although results slightly favour fully- over semi-endogenous growth, and the slightly more frequent case is that long-run growth can remain positive if population stops growing, zero or negative intercepts cannot be ruled out.