Recent research has shown that combination approaches, such as taking the maximum or the mean over different methods of estimating efficiency scores, have practical merits and offer a useful alternative to adopting only one technique. This recent research shows that taking the maximum minimizes the risk of underestimation, and improves the precision of efficiency estimation. In this paper, we propose and implement a formal criterion of weighting based on maximizing proper criteria of model fit (viz. log predictive scoring) and show how it can be applied in Stochastic Frontier as well as in Data Envelopment Analysis models, where the problem is more difficult. Monte Carlo simulations show that the new techniques perform very well and a substantive application to large U.S. banks shows some important differences with traditional models. The Monte Carlo simulations are also substantive as it is for the first time that proper and coherent optimal model pools are subjected to extensive testing in finite samples.

最近的研究表明，组合方法（例如在估计效率得分的不同方法上采用最大值或均值）具有实用的优点，并为仅采用一种技术提供了有用的替代方法。最近的研究表明，最大程度地减少低估的风险，并提高效率估计的精度。在本文中，我们基于最大化模型拟合的适当标准（即对数预测评分），提出并实施了加权的正式标准，并展示了如何将其应用于随机前沿以及数据包络分析模型中存在的问题更加困难。蒙特卡洛模拟显示，新技术效果很好，对美国大型银行的实质性应用显示出与传统模型的一些重要差异。