Abstract: Recent studies of economic growth have moved from explaining average trends in long-term growth to study growth accelerations and decelerations. In this paper we argue that the standard shift-share analysis is inadequate to measure the contribution of sectors to accelerations in productivity. We present a modified shift-share method, which takes account of surplus labour in agriculture and accounts for the contribution to growth from expanding sectors. We apply this novel methodology to the GGDC 10-sector database, which is a new data set with annual time series of value added and persons employed for the ten main sectors of the economy. The data set covers 19 countries in Asia and Latin America spanning the period from 1950 to 2005. We find that growth accelerations are explained by productivity increases within sectors, not by reallocation of employment to more productive sectors. Challenging conventional wisdom, productivity improvement in market services is more important than productivity growth in manufacturing.