This paper introduces a decomposition of the additively complete Luenberger-Hicks-Moorsteen Total Factor Productivity indicator into the usual components: technical change, technical inefficiency change and scale inefficiency change. Our approach is general in that it does not require differentiability or convexity of the production technology. Using a nonparametric framework, the empirical application focuses on the agricultural sector at the state-level in the U.S. over the period 1960-2004. The results show that Luenberger-Hicks-Moorsteen productivity increased substantially in the considered period. This productivity growth is due to output growth rather than input decline, although the extent depends on the convexity assumption of the technology. Technical change is the main driver, while the role of technical inefficiency change and scale inefficiency change also depends on the convexity assumption of the technology.