Dual productivity analysis: A Konüs/Shephard approach

A primal (or direct) productivity index is conventionally defined as the ratio of an output quantity index to an input quantity index. There have been attempts in the literature to define and implement dual and indirect productivity indexes based on price changes rather than quantity changes. Although dual and indirect productivity indexes share a common motivation, the measurement of productivity change when prices are easier to measure, or are measured more accurately, than quantities, they differ analytically, from one another and from primal productivity indexes. We introduce a new dual productivity index, inspired by contributions of Konüs and Shephard, and we compare our dual productivity index with a primal productivity index inspired by the work of Malmquist. We also compare these two theoretical productivity indexes with an analogous pair of empirical Fisher productivity indexes. We provide an empirical application to US agricultural productivity growth.