Measuring and Decomposing Productivity Change: Stochastic Distance Function Estimation VS. DEA

Linear programming techniques have been widely used to compute Malmquist indices of productivity change as ratios of fitted distances from a convex hull frontier. These indices are then decomposed into technical and efficiency change. However, since this approach is non-stochastic, inference is problematic. Further, although the Malmquist index is valid for any degree of returns to scale, productivity change is measured relative to a constant returns to scale frontier. As an alternative, we propose a exible, stochastic input distance frontier which allows for statistical inference and imposes no restrictions on returns to scale. Using this distance frontier, we decompose productivity change into technical and efficiency change. Comparisons are drawn between the stochastic and non-stochastic methods based on a panel of electric utilities. We estimate our model by the generalized method of moments with a variety of instrument sets to gauge the sensitivity of productivity change calculations to changes in the underlying moment conditions.