Measuring and decomposing productivity change: Stochastic distance function estimation versus data envelopment analysis

Measuring productivity change with Malmquist indices has become common practice, because they are easily computed using nonparametric programming techniques and can be readily decomposed into technical and efficiency change. However, this approach is nonstochastic and requires a constant returns to scale assumption to construct the reference technology. We propose estimating productivity change using a stochastic input distance frontier, imposing no restrictions on returns to scale. We derive the analogous decomposition of productivity change and develop a generalized method of moments strategy in which outputs or inputs may be endogenous. We compare two methods in an application to electric utilities.