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INFERENCE IN DYNAMIC, NONPARAMETRIC MODELS OF PRODUCTION: CENTRAL LIMIT THEOREMS FOR MALMQUIST INDICES
Econometric Theory ( IF 0.8 ) Pub Date : 2020-06-15 , DOI: 10.1017/s0266466620000237
Alois Kneip , Léopold Simar , Paul W. Wilson

The Malmquist index gives a measure of productivity in dynamic settings and has been widely applied in empirical work. The index is typically estimated using envelopment estimators, particularly data envelopment analysis (DEA) estimators. Until now, inference about productivity change measured by Malmquist indices has been problematic, including both inference regarding productivity change experienced by particular firms as well as mean productivity change. This paper establishes properties of a DEA-type estimator of distance to the conical hull of a variable returns to scale production frontier. In addition, properties of DEA estimators of Malmquist indices for individual producers are derived as well as properties of geometric means of these estimators. The latter requires new central limit theorem results, extending the work of Kneip, Simar, and Wilson (2015, Econometric Theory 31, 394–422). Simulation results are provided to give applied researchers an idea of how well inference may work in practice in finite samples. Our results extend easily to other productivity indices, including the Luenberger and Hicks–Moorsteen indices.

中文翻译:

动态非参数生产模型的推论:马尔奎斯特指数的中心极限定理

Malmquist 指数衡量动态环境中的生产力,并已广泛应用于实证工作。该指数通常使用包络估计量估计,特别是数据包络分析 (DEA) 估计量。到目前为止,对 Malmquist 指数衡量的生产率变化的推断一直存在问题,包括对特定公司经历的生产率变化的推断以及平均生产率变化。本文建立了规模收益可变生产边界到圆锥壳距离的 DEA 型估计量的性质。此外,还导出了单个生产者的 Malmquist 指数的 DEA 估计量的性质以及这些估计量的几何平均值的性质。后者需要新的中心极限定理结果,扩展 Kneip、Simar、计量经济学理论31, 394–422)。提供模拟结果是为了让应用研究人员了解推理在有限样本中的实际效果如何。我们的结果很容易扩展到其他生产力指数,包括 Luenberger 和 Hicks-Moorsteen 指数。
更新日期:2020-06-15
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