This article opens the black box of total factor productivity by decomposing this “all‐in‐one” index into various input‐embedded and input‐free productivities in a new growth accounting framework. The new method identifies different channels through which growth drivers affect economic growth and finds the most effective way to boost the economy, which is unidentified in standard method. This new approach uses a varying coefficient stochastic frontier model, which integrates the standpoints of the endogenous growth theory and the induced innovation theory into a reduced‐form productivity analysis. The new growth accounting is then applied to study the impacts and contributions of R&D investments, international trade, and structural transformation to world agricultural growth during the period of 1962 to 2014. The empirical results provide new evidence to support the endogenous growth theory and the induced innovation theory, indicating the necessity of using the new growth accounting method.