Revisiting Productivity Growth Accounting Decompositions

Abstract Productivity growth accounting decompositions are sensitive to the definition of aggregate productivity, which usually takes the form of a weighted geometric or arithmetic average of firms' productivities. This paper shows explicitly why the two differ. It further proposes a modification to a popular decomposition highlighting the contribution of the component responsible for this discrepancy, namely the covariance of productivity growth rates and levels. The argument favoring this modified decomposition is that the novel component offers relevant information for applied theoretical purposes, thus increasing the usefulness of aggregate productivity decompositions. Finally, the paper argues that standard theoretical assumptions support (i) a proposed separation between aggregate and average productivity, and (ii) the adoption of the arithmetic average definition as opposed to the more popular geometric average. JEL: D24, E24, O47.