In this paper we propose a standard Solow model augmented with public capital in the production function. The model solution displays two steady states, an unstable poverty trap and an efficient stable equilibrium. As a result the model predicts both divergence and non monotonic convergence; that is a transition path characterized by increasing growth rates up to the point where traditional convergence behavior describes the successive evolution towards the stationary equilibrium. Using traditional cross section techniques the
hypothesis of non monotonic conditional convergence is tested against a large sample of coutries, obtaining favorable evidence.