Robust, dynamic nonparametric benchmarking: the evolution of cost-productivity and efficiency among U.S. credit unions

This paper develops a new methodology for estimating cost-productivity and efficiency change that benchmarks the performance of individual firms against an estimated a-quantile. We adapt the estimators of Daouia and Simar (2007) and Wheelock and Wilson (2008a) to the estimation of cost efficiency where input prices and some outputs are fixed. Theoretical results demonstrate that our new estimator retains the root-n convergence, asymptotic normality, and other desirable properties of the original estimators. We show how the estimator can be used to construct a cost analog of the widely-used Malmquist productivity index. In addition, we propose a new decomposition of the Malmquist index to reveal the sources of changes in scale efficiency that affect changes in cost-productivity. We examine changes in the efficiency and productivity of U.S. credit unions between 1989 and 2006. We find that productivity increased among the largest 20-percent of credit unions, as well as for credit unions that grew substantially in size during 1989-2006.