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非参数条件前沿与效率估计：一种新方法AI 解读

Summary In production theory, conditional frontiers and conditional efficiency measures are flexible and appealing tools to investigate the role of environmental variables in the production process. Direct approaches estimate non-parametrically conditional distribution functions requiring smoothing techniques and the use of bandwidths. Traditional methods for selecting bandwidths provide bandwidths of orders that may not be optimal for estimating the boundary of the…

概率密度反卷积的磨光正则化方法AI 解读

We use mollification to regularize the problem of deconvolution of random variables. This regularization method offers a unifying and generalizing framework in order to compare the benefits of various filter-type techniques like deconvolution kernels, Tikhonov, or spectral cutoff methods. In particular, the mollifier approach allows to relax some restrictive assumptions required for the deconvolution kernels, and has better stabilizing properties compared with spectral…

多投入与多产出的非参数随机前沿模型AI 解读

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…

动态非参数生产模型中的推断：Malmquist 指数的中心极限定理AI 解读

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…

稳健化的期望最大生产前沿AI 解读

The aim of this paper is to construct a robust nonparametric estimator for the production frontier. We study this problem under a regression model with one-sided errors, where the regression function defines the achievable maximum output, for a given level of inputs-usage, and the regression error defines the inefficiency term. The main tool is a concept of partial regression boundary defined as a special probability-weighted moment. This concept motivates a robustified…

对称误差下潜在变量边界的估计AI 解读

Consider the model Y=X+ε with X=τ+Z, where τ is an unknown constant (the boundary of X), Z is a random variable defined on R+, ε is a symmetric error, and ε and Z are independent. Based on an iid sample of Y, we aim at identifying and estimating the boundary τ when the law of ε is unknown (apart from symmetry) and in particular its variance is unknown. We propose an estimation procedure based on a minimal distance approach and by making use of Laguerre polynomials.…

条件效率测度的中心极限定理与非参数两阶段生产模型的可分性检验AI 解读

In this paper, we demonstrate that standard central limit theorem (CLT) results do not hold for means of non‐parametric, conditional efficiency estimators, and we provide new CLTs that permit applied researchers to make valid inference about mean conditional efficiency or to compare mean efficiency across groups of producers. The new CLTs are used to develop a test of the restrictive ‘separability’ condition that is necessary for second‐stage regressions of efficiency…

非参数生产模型的假设检验AI 解读

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiency of production. Practitioners use DEA estimators far more frequently than FDH estimators, implicitly assuming that production sets are convex. Moreover, use of the constant returns to scale (CRS) version of the DEA estimator requires an assumption of CRS. Although bootstrap methods have been developed for making inference about the efficiencies of individual units,…

效率前沿的非参数工具变量估计AI 解读

The paper investigates endogeneity issues in nonparametric frontier models. It considers a nonseparable model for a cost function C=φ(Y,U) where C and Y are the cost and the output, U is uniform in [0,1] and φ is increasing with respect to U. The cost frontier corresponds to U=0 and U can be interpreted as a normalized level of inefficiency. The endogeneity issue arises when Y is dependent of U. For identification and estimation, we use a nonparametric instrumental variables…

非参数前沿估计中的不可观测异质性与内生性AI 解读

In production theory, firm efficiencies are measured by their distances to a production frontier. In the presence of heterogeneous conditions (like environmental factors) that may influence the shape and the position of the frontier, traditional measures of efficiency obtained in the space of inputs/outputs are difficult to interpret, since they mix managerial inefficiency and shift of the frontier. This can be corrected by using nonparametric conditional efficiencies. In…

外商直接投资与时间对追赶的影响：条件非参数前沿分析的新见解AI 解读

Summary We use an appropriate nonparametric two‐step approach on conditional efficiencies to investigate how foreign direct investment (FDI) and time affect the process of catching up. By using a dataset of 44 countries over 1970–2007, we explore the channels under which FDI fosters productivity by disentangling the impact of this factor on the production process and its components: impact on the attainable production set (input–output space) and the impact on the…

当偏差压倒方差：DEA 与 FDH 效率得分的中心极限定理AI 解读

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that…

未知测量误差方差下的生产前沿估计AI 解读

Frontier estimation appears in productivity analysis. Firm’s performance is measured by the distance between its output and an optimal production frontier. Frontier estimation becomes difficult if outputs are measured with noise and most approaches rely on restrictive parametric assumptions. This paper contributes to nonparametric approaches, with unknown frontier and unknown variance of a normally distributed error. We propose a nonparametric method identifying and…

非参数位置—尺度模型中的前沿估计AI 解读

Conditional efficiency captures efficiency of firms facing heterogeneous environmental conditions. Traditional approaches estimate nonparametrically conditional distribution requiring smoothing techniques. We rather use a flexible nonparametric location-scale model to eliminate the dependence of inputs/outputs on these factors. These “pre-whitened” inputs/outputs define the optimal frontier function and a “pure” measure of efficiency more reliable to produce rankings, since…

非参数前沿估计量的正则化AI 解读

In production theory and efficiency analysis, we estimate the production frontier, the locus of the maximal attainable level of an output (the production), given a set of inputs (the production factors). In other setups, we estimate rather an input (or cost) frontier, the minimal level of the input (cost) attainable for a given set of outputs (goods or services produced). In both cases the problem can be viewed as estimating a surface under shape constraints (monotonicity,…

方向距离及其稳健版本的概率刻画AI 解读

In this work, we analyze the performance of production units using the directional distance function which allows to measure the distance to the frontier of the production set along any direction in the inputs/outputs space. We show that this distance can be expressed as a simple transformation of radial or hyperbolic distance. This formulation allows to define robust directional distances in the lines of α-quantile or order-m partial frontiers and also conditional…

方向边界锥包估计量的渐近分布AI 解读

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of inputs×outputs in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the inputs × outputs space. So far, only the statistical properties of the…

生产前沿的偏差修正非参数包络估计量AI 解读

In efficiency analysis, the production frontier is defined as the set of the most efficient alternatives among all possible combinations in the input-output space. The nonparametric envelopment estimators rely on the assumption that all the observations fall on the same side of the frontier. The free disposal hull (FDH) estimator of the attainable set is the smallest free disposal set covering all the observations. By construction, the FDH estimator is an inward-biased…

非参数前沿模型中 DEA 估计量的渐近理论与一致自助法AI 解读

Nonparametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proved consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns to scale.…

截断回归及其偏导数的局部似然估计：理论与应用AI 解读

In this paper we propose a very flexible estimator in the context of truncated regression that does not require parametric assumptions. To do this, we adapt the theory of local maximum likelihood estimation. We provide the asymptotic results and illustrate the performance of our estimator on simulated and real data sets. Our estimator performs as well as the fully parametric estimator when the assumptions for the latter hold, but as expected, much better when they do not…

Farrell 型效率聚合指标的统计推断AI 解读

Abstract In this study, we merge results of two recent directions in efficiency analysis research—aggregation and bootstrap—applied, as an example, to one of the most popular point estimators of individual efficiency: the data envelopment analysis (DEA) estimator. A natural context of the methodology developed here is a study of efficiency of a particular economic system (e.g., an industry) as a whole, or a comparison of efficiencies of distinct groups within such a system…

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