Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs

Stochastic frontier models along the lines of Aigner et al. are widely used to benchmark firms’ performances in terms of efficiency. The models are typically fully parametric, with functional form specifications for the frontier as well as both the noise and the inefficiency processes. Studies such as Kumbhakar et al. have attempted to relax some of the restrictions in parametric models, but so far all such approaches are limited to a univariate response variable. Some (e.g., Simar and Zelenyuk; Kuosmanen and Johnson) have proposed nonparametric estimation of directional distance functions to handle multiple inputs and outputs, raising issues of endogeneity that are either ignored or addressed by imposing restrictive and implausible assumptions. This article extends nonparametric methods developed by Simar et al. and Hafner et al. to allow multiple inputs and outputs in an almost fully nonparametric framework while avoiding endogeneity problems. We discuss properties of the resulting estimators, and examine their finite-sample performance through Monte Carlo experiments. Practical implementation of the method is illustrated using data on U.S. commercial banks.

以艾格纳等人（Aigner et al.）提出的随机前沿模型（stochastic frontier models）为例，该类模型被广泛用于基于效率维度对标企业绩效表现。此类模型通常为完全参数化模型，不仅对前沿面设定了函数形式，还对噪声过程与无效率过程均做出了函数形式规定。诸如昆巴卡尔等人（Kumbhakar et al.）的相关研究曾尝试放宽参数化模型中的部分约束，但截至目前，所有此类方法均仅适用于单变量响应变量场景。部分学者（如西马尔与泽莱纽克、库斯曼与约翰逊）提出采用方向距离函数（directional distance functions）的非参数估计方法，以处理多投入多产出场景，但该类方法要么忽略内生性（endogeneity）问题，要么通过施加严苛且不合实际的假设来解决内生性难题。本文将西马尔等人（Simar et al.）与哈夫纳等人（Hafner et al.）提出的非参数方法进行拓展，使其可在近乎完全非参数框架下处理多投入多产出问题，同时规避内生性难题。本文将探讨所得估计量的相关性质，并通过蒙特卡洛（Monte Carlo）实验检验其有限样本表现。最后，我们将利用美国商业银行的相关数据，对该方法的实际应用流程进行演示。