Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations

This paper examines the technical efficiency of US Federal Reserve check processing offices over 1980–2003. We extend results from Park et al. [Park, B., Simar, L., Weiner, C., 2000. FDH efficiency scores from a stochastic point of view. Econometric Theory 16, 855–877] and Daouia and Simar [Daouia, A., Simar, L., 2007. Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics 140, 375–400] to develop an unconditional, hyperbolic, α-quantile estimator of efficiency. Our new estimator is fully non-parametric and robust with respect to outliers; when used to estimate distance to quantiles lying close to the full frontier, it is strongly consistent and converges at rate root-n, thus avoiding the curse of dimensionality that plagues data envelopment analysis (DEA) estimators. Our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices.