Using a novel, augmented two–sector endogenous growth model appropriate for a small, open economy characterised by human capital accumulation and productive government expenditure, we analyse the nature of the relationship between openness and economic growth. In the augmented form, external openness enters the human capital accumulation function directly. Productive government expenditure also affects human capital accumulation, but relies on seigniorage revenue to finance the productive expenditure where seigniorage revenue is itself dependent on the level of openness. Specifically, the findings indicate two, opposing effects of openness on growth – a direct effect of openness on growth through the knowledge spillovers that affect human capital accumulation, and an indirect effect of decreasing seigniorage revenue on growth through decreasing productive government expenditure on human capital. We discuss conditions under which the resultant openness–growth curve can be concave or convex, but do not specify theoretical functional forms or values to unknown parameters in the model to provide a concise theoretical result. Rather, drawing samples of exact model–match countries over a sample period of 1980–2011, we rely on a semi–parametric, data–driven empirical approach augmented with a restricted cubic spline regression function to provide empirical impetus to the theoretical outcomes reported. We show that the relationship between openness and growth is non–linear and specifically, inverted U–shaped. The result suggests that openness can only have a positive impact on the growth-rate until a certain threshold–level, beyond which, the effect is negative.