Measuring firm performance using nonparametric quantile-type distances
提出一种新的非参数分位数型距离方法，用于在多投入多产出情境下度量企业效率，克服了传统条件分位数方法依赖方向选择的缺陷，并应用于美国信用合作社的绩效分析。
When faced with multiple inputs and outputs , traditional quantile regression of Y conditional on X = x for measuring economic efficiency in the output (input) direction is thwarted by the absence of a natural ordering of Euclidean space for dimensions q (p) greater than one. Daouia and Simar (2007 Daouia, A., Simar, L. (2007). Nonparametric efficiency analysis: A multivariate conditional quantile approach. Journal of Econometrics 140:375–400.[Crossref], [Web of Science ®] , [Google Scholar]) used nonstandard conditional quantiles to address this problem, conditioning on Y ≥ y (X ≤ x) in the output (input) orientation, but the resulting quantiles depend on the a priori chosen direction. This article uses a dimensionless transformation of the (p + q)-dimensional production process to develop an alternative formulation of distance from a realization of (X, Y) to the efficient support boundary, motivating a new, unconditional quantile frontier lying inside the joint support of (X, Y), but near the full, efficient frontier. The interpretation is analogous to univariate quantiles and corrects some of the disappointing properties of the conditional quantile-based approach. By contrast with the latter, our approach determines a unique partial-quantile frontier independent of the chosen orientation (input, output, hyperbolic, or directional distance). We prove that both the resulting efficiency score and its estimator share desirable monotonicity properties. Simple arguments from extreme-value theory are used to derive the asymptotic distributional properties of the corresponding empirical efficiency scores (both full and partial). The usefulness of the quantile-type estimator is shown from an infinitesimal and global robustness theory viewpoints via a comparison with the previous conditional quantile-based approach. A diagnostic tool is developed to find the appropriate quantile-order; in the literature to date, this trimming order has been fixed a priori. The methodology is used to analyze the performance of U.S. credit unions, where outliers are likely to affect traditional approaches.