This paper examines two sources of global knowledge spillovers: foreign direct investments and trade. Empirical evidence demonstrates that foreign direct investment and trade can contribute to overall domestic productivity growth only when the technology gap between domestic and foreign firms is not too large and when a sufficient absorptive capacity is available in domestic firms. The paper proposes the terms research and development and labor quality to capture the innovative and absorptive capacity of the country. The spillover effects in productivity are analyzed using a stochastic frontier approach. This productivity (in terms of total factor productivity) is decomposed using a generalized Malmquist output oriented index, in order to evaluate the specific effect in technical change, technical efficiency change, and scale efficiency change. Using country-level data for 16 Latin American countries for 1996-2006, the empirical analysis shows positive productivity spillovers from foreign direct investment and trade only when the country has absorptive capacity in terms of research and development. Foreign direct investment and trade spillovers are found to be positive and significant for scale efficiency change and total productivity factor change.