Measuring Aggregate Productivity Growth Using Plant-Level Data

We define productivity growth as the change in welfare that arises from additional output holding primary inputs constant. Using this traditional growth-accounting definition, we show that gains may arise because of plant-level technology shocks, and, in imperfectly competitive settings, from the reallocation of inputs across plants with differing markups and/or shadow values of primary inputs. With plant-level data, the alternative and most popular definition of productivity growth looks at the difference in the first moments of the productivity distribution. We show that this definition adds an additional term to the growth-accounting measure, which has been called “reallocation.” We show there is a very weak relationship between the two indexes in almost every 3-digit manufacturing industry in both Chile from 1987-1996 and Colombia from 1981-1991 - 49 in total - primarily because this “reallocation” term is large and volatile. We explore the theoretical reasons for this sharp divergence, in the process uncovering a number of previously unnoticed and unattractive features of the first-moment definition. For example, it is not tethered to any theoretical model, it is sensitive to measured units, and it can report positive productivity growth when welfare has fallen.