Can convergence regressions distinguish between exogenous and endogenous growth models?

In cross-section regressions of future growth rates on initial income levels, a negative coefficient is often interpreted as evidence consistent with exogenous growth. We use a simple growth model to show that higher initial income can imply higher future growth in an exogenous growth case, and lower future growth in an endogenous growth case. We show that the two types of models can be distinguished by the sign of the coefficient on initial capital in a regression of growth rates on both initial income and initial capital.