In this paper, we test the existence of financial development threshold effects, firstly, between financial development and long-term growth, and, secondly, between financial development and long-term GDP. We also ask whether such effects may explain the link financial development - convergence/ divergence to the advanced countries’ growth. Our work builds on that of Aghion, Howitt, and Mayer-Foulkes (2004). It differs from previous work about assumptions and methodology. Estimates are performed with GMM dynamic panel data techniques for 112 emerging and developing countries from 1975 to 2007. The results show a positive but vanishing effect of financial development on steady-state GDP, from a critical (an average) level of financial development. They do not validate, however, the assumption that the marginal impact of financial development on the steady-state growth rate is more favorable than the degree of financial development is low. We support only partially the role that the financial development could play in the acceleration of the convergence of emerging and developing economies towards the world frontier growth.