This article examines the effects of sectorial shifts and structural transformation on the recent productivity path of Latin America. We use a four-sector (agriculture, industry, modern services and traditional services) general equilibrium model calibrated to the main economies in the region. The model very closely replicates labor reallocations across sectors and the growth of aggregate labor productivity from 1950 to 2005. Structural transformation explains a sizeable portion of the region's convergence in the first decades. In most cases, the poor performance of the traditional services sector is the main cause of the slowdown in productivity growth observed in the region after the mid-1970s and is a key factor in explaining the divergence during this period.