Many of the crucial debates in development economics are encapsulated in the question of economic convergence. Is there a tendency for the poorer countries to grow more rapidly than the richer countries, and thereby to converge in living standards? Some recent research on endogenous growth has emphasized increasing returns as a possible reason not to expect convergence. Other research has suggested that convergence may be achieved only after poor countries attain a threshold level of income or human capital. This paper presents evidence that a sufficient condition for higher-than-average growth of poorer countries, and therefore convergence, is that poorer countries follow reasonably efficient economic policies, mainly open trade and protection of private property rights.