We define aggregate productivity growth (APG) as the change in aggregate final demand minus the change in the aggregate expenditures on labor and capital. We show how to aggregate plant-level data to this quantity and how to decompose APG into technical efficiency and reallocation components. This requires us to confront the "non-neoclassical" features that impact plant-level data, including plant-level heterogeneity, the entry and exit of goods, adjustment costs, fixed and sunk costs, and market power. The APG decomposition includes one term per plant related to technical efficiency and one term for each input at each plant that is a function of the value of marginal product - input price gap and that relates the reallocation of inputs to growth. We compare APG to several competing variants of productivity growth that are based only on plant-level technical efficiency. Two simple theoretical examples illustrate that technical-efficiency reallocation can be negatively correlated with actual APG reallocation because technical efficiency is a production concept and need not have any relation with the APG reallocation gaps. We illustrate this point empirically using panel data from manufacturing industries in Chile, where we show technical-efficiency reallocation differs substantially from measured reallocation based on our definition of APG.