On Estimation of Monotone and Concave Frontier Functions
作者:
Irène Gijbels,
Enno Mammen,
ByeongU. Park,
Léopold Simar,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1999)
卷期:
Volume 94,
issue 445
页码: 220-228
ISSN:0162-1459
年代: 1999
DOI:10.1080/01621459.1999.10473837
出版商: Taylor & Francis Group
关键词: Asymptotic distribution;Bias correction;Confidence interval;Data envelopment analysis;Density support;Frontier function
数据来源: Taylor
摘要:
When analyzing the productivity of firms, one may want to compare how the firms transform a set of inputsx(typically labor, energy or capital) into an outputy(typically a quantity of goods produced). The economic efficiency of a firm is then defined in terms of its ability to operate close to or on the production frontier, the boundary of the production set. The frontier function gives the maximal level of output attainable by a firm for a given combination of its inputs. The efficiency of a firm may then be estimated via the distance between the attained production level and the optimal level given by the frontier function. From a statistical viewpoint, the frontier function may be viewed as the upper boundary of the support of the population of firms density in the input and output space. It is often reasonable to assume that the production frontier is a concave monotone function. Then a famous estimator in the univariate input and output case is the data envelopment analysis (DEA) estimator, the lowest concave monotone increasing function covering all sample points. This estimator is biased downward, because it never exceeds the true production frontier. In this article we derive the asymptotic distribution of the DEA estimator, which enables us to assess the asymptotic bias and hence to propose an improved bias-corrected estimator. This bias-corrected estimator involves consistent estimation of the density function as well as of the second derivative of the production frontier. We also briefly discuss the construction of asymptotic confidence intervals. The finite-sample performance of the bias-corrected estimator is investigated via a simulation study, and the procedure is illustrated for a real data example.
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