Stochastic Production Frontier and Technical Inefficiency: A Sensitivity Analysis

The present paper focuses attention on the sensitivity of technical inefficiency to most commonly used one-sided distributions of the inefficiency error term, namely the truncated normal, the half-normal, and the exponential distributions. A generalized version of the half-normal, which does not embody the zero-mean restriction, is also explored. For each distribution, the likelihood function and the counterpart of the estimator of technical efficiency are explicitly stated (Jondrow, J., Lovell, C. A. K., Materov, I. S., Schmidt, P. ([1982]), On estimation of technical inefficiency in the stochastic frontier production function model, J. Econometrics19:233-238). Based on our panel data set, related to Tunisian manufacturing firms over the period 1983-1993, formal tests lead to a strong rejection of the zero-mean restriction embodied in the half normal distribution. Our main conclusion is that the degree of measured inefficiency is very sensitive to the postulated assumptions about the distribution of the one-sided error term. The estimated inefficiency indices are, however, unaffected by the choice of the functional form for the production function.     

Comments on the econometrics of female labor supply and children by alice and masao nokalnura

Abstract

The present paper focuses attention on the sensitivity of technical inefficiency to most commonly used one‐sided distributions of the inefficiency error term, namely the truncated normal, the half‐normal, and the exponential distributions. A generalized version of the half‐normal, which does not embody the zero‐mean restriction, is also explored. For each distribution, the likelihood function and the counterpart of the estimator of technical efficiency are explicitly stated (Jondrow, J., Lovell, C. A. K., Materov, I. S., Schmidt, P. ([1982] Jondrow, J., Lovell, C. A. K., Materov, I. S. and Schmidt, P. 1982. On estimation of technical inefficiency in the stochastic frontier production function model. J. Econometrics, 19: 233–238. [Crossref], [Web of Science ®] , [Google Scholar]), On estimation of technical inefficiency in the stochastic frontier production function model, J. Econometrics19:233–238). Based on our panel data set, related to Tunisian manufacturing firms over the period 1983–1993, formal tests lead to a strong rejection of the zero‐mean restriction embodied in the half normal distribution. Our main conclusion is that the degree of measured inefficiency is very sensitive to the postulated assumptions about the distribution of the one‐sided error term. The estimated inefficiency indices are, however, unaffected by the choice of the functional form for the production function.     

Estimation of Technical Efficiency Using Flexible Functional Form and Panel Data

This article presents an econometric model capable of accommodating a nonradial measure of input-specific technical inefficiency and suggests an estimation technique that reduces dependency on distributional assumptions on inefficiency. It also makes use of the demand system derived from a flexible cost function and imposes concavity restrictions as required by economic theory. Panel data on 12 Finnish foundry plants are used to estimate technical efficiency of labor and energy for each of these plants.     

A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms

This article investigates farm-level efficiency of U.S. dairy farmers by estimating their technical and allocative efficiency. Technical inefficiency is assumed to be composed of a deterministic component that is a function of some farm-specific characteristics and a random component. By doing this we extend the stochastic frontier methodology in which determinants of technicial inefficiency are explicitly introduced in the model. Given the inputs, variations in efficiency of farms are then explained by both deterministic and random components of technical inefficiency. The empirical results indicate that (a) levels of education of the farmer are important factors determining technical inefficiency and (b) large farms are more efficient (technically) than small and medium-sized farms. Both technical and allocative inefficiency are found to decrease with increase in the level of education of the farmer.     

The “wrong skewness” problem in stochastic frontier models: A new approach

Stochastic frontier models are widely used to measure, e.g., technical efficiencies of firms. The classical stochastic frontier model often suffers from the empirical artefact that the residuals of the production function may have a positive skewness, whereas a negative one is expected under the model, which leads to estimated full efficiencies of all firms. We propose a new approach to the problem by generalizing the distribution used for the inefficiency variable. This generalized stochastic frontier model allows the sample data to have the wrong skewness while estimating well-defined and nondegenerate efficiency measures. We discuss the statistical properties of the model, and we discuss a test for the symmetry of the error term (no inefficiency). We provide a simulation study to show that our model delivers estimators of efficiency with smaller bias than those of the classical model even if the population skewness has the correct sign. Finally, we apply the model to data of the U.S. textile industry for 1958–2005 and show that for a number of years our model suggests technical efficiencies well below the frontier while the classical one estimates no inefficiency in those years.     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

空间ZISF的估计及蒙特卡罗模拟

在随机前沿模型中引入空间效应和技术无效率项的非连续性并构建了空间零无效率随机前沿模型,使用极大似然估计和JLMS方法得出参数和技术效率的估计。蒙特卡罗模拟表明:(1)逆似然比检验能以较高的准确率识别真实模型;(2)本方法在参数估计和技术效率的估计两方面均表现较好;(3)若真实模型为空间零无效率随机前沿模型但误用了空间随机前沿模型,参数估计和技术效率的估计两方面均表现较差。空间零无效率随机前沿模型有其存在的必要性。     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

Probabilistic frontier regression models for binary type output data

This paper proposes a probabilistic frontier regression model for binary type output data in a production process setup. We consider one of the two categories of outputs as ‘selected’ category and the reduction in probability of falling in this category is attributed to the reduction in technical efficiency (TE) of the decision-making unit. An efficiency measure is proposed to determine the deviations of individual units from the probabilistic frontier. Simulation results show that the average estimated TE component is close to its true value. An application of the proposed method to the data related to the Indian public sector banking system is provided where the output variable is the indicator of level of non-performing assets. Individual TE is obtained for each of the banks under consideration. Among the public sector banks, Andhra bank is found to be the most efficient, whereas the United Bank of India is the least.     

A study of generalized normal distributions

In this work, first some distributional properties of extended two-piece skew normal distributions are presented. Next we revisit the special case, that is two-piece skew normal distributions. Then two distributions related to two-piece skew normal distributions are studied. More precisely, we give some properties about generalized half normal distributions as well as a generalized Cauchy distribution. Finally, we discuss the distributions of linear combinations of two independent skew normal random variables.     

企业技术效率的影响分析

 本文以上海市166家大中型企业五年的面板数据为研究对象,设定两种不同的生产函数和两种误差分布,利用随机前沿方法分别进行了技术效率的估计。我们发现不同测算方法的结果差异不大,且对企业的评价具有一致性。结果表明上海市工业企业的技术效率整体水平不高。通过研究影响企业技术效率的外生性因素,发现企业的所有制结构、规模、R&D经费支出与R&D人员投入、资本密集程度和企业的垄断程度等因素都对上海市工业企业的技术效率水平具有显著影响。基于研究结果,我们给出了提高企业技术效率的一些建议。     

Estimation and decomposition of productivity change when production is not efficient: a paneldata approach

This paper addresses estimation and decomposition of productivity change, which is mostly identified as technical change under constant (unitary) returns to scale (CRS). If the CRS assumption is not made, productivity change is decomposed into technical change and scale effects.Furthermore, if inefficiency exists, it also contributes to productivity change. Here we decompose productivity change into efficiency change, technical change, and scale effects. Three alternative approaches using parametric production, cost, and profit functions, which differ in terms of behavioral assumptions on the producers and data requirements, are considered.     

Estimation and decomposition of productivity change when production is not efficient: a paneldata approach

This paper addresses estimation and decomposition of productivity change, which is mostly identified as technical change under constant (unitary) returns to scale (CRS). If the CRS assumption is not made, productivity change is decomposed into technical change and scale effects.Furthermore, if inefficiency exists, it also contributes to productivity change. Here we decompose productivity change into efficiency change, technical change, and scale effects. Three alternative approaches using parametric production, cost, and profit functions, which differ in terms of behavioral assumptions on the producers and data requirements, are considered.     

Discrete Linnik Weibull distribution

Abstract

We introduce a new family of distributions using truncated discrete Linnik distribution. This family is a rich family of distributions which includes many important families of distributions such as Marshall–Olkin family of distributions, family of distributions generated through truncated negative binomial distribution, family of distributions generated through truncated discrete Mittag–Leffler distribution etc. Some properties of the new family of distributions are derived. A particular case of the family, a five parameter generalization of Weibull distribution, namely discrete Linnik Weibull distribution is given special attention. This distribution is a generalization of many distributions, such as extended exponentiated Weibull, exponentiated Weibull, Weibull truncated negative binomial, generalized exponential truncated negative binomial, Marshall-Olkin extended Weibull, Marshall–Olkin generalized exponential, exponential truncated negative binomial, Marshall–Olkin exponential and generalized exponential. The shape properties, moments, median, distribution of order statistics, stochastic ordering and stress–strength properties of the new generalized Weibull distribution are derived. The unknown parameters of the distribution are estimated using maximum likelihood method. The discrete Linnik Weibull distribution is fitted to a survival time data set and it is shown that the distribution is more appropriate than other competitive models.     

A method to estimate power parameter in exponential power distribution via polynomial regression

The exponential power distribution (EPD), also known as generalized error distribution, is a flexible symmetrical unimodal family that belongs to the exponential one. The EPD becomes the density function of a range of symmetric distributions with different values of its power parameter β. A closed-form estimator for β does not exist, so the power parameter is usually estimated numerically. Unfortunately, the optimization algorithms do not always converge, especially when the true value of β is close to its parametric space frontier. In this paper, we present an alternative method to estimate β. Our proposal is based on the normal standardized Q–Q plot, and it exploits the relationship between β and the kurtosis. Furthermore, it is a direct method which does not require computational efforts nor the use of optimization algorithms.     

价格波动与资源配置效率研究

 文章从理论和经验两方面研究了价格波动对资源配置效率的影响。理论模型显示：由于调整成本的存在,面对较低水平价格波动的企业可能并不会立刻调整要素投入比例和生产计划,这一“保守策略”意味着价格波动可能带来企业配置效率损失的增加。但是随着价格波动幅度进一步增加,越来越多的企业将会主动的对生产计划进行调整,以便抵消较大幅度波动的不利影响。“保守策略”向“调整策略”的转变意味着价格波动引起的资源的配置效率损失可能存在门阀效应。利用1978-2007年省级面板数据和基于极大似然估计的随机前沿方法,文章实证研究证实了价格波动对资源配置效率损失的非线性影响,认为传统的研究可能低估价格波动对经济的负面影响。     

An efficient model-free estimation of multiclass conditional probability

Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of conditional quantile regression functions. Specifically, the conditional class probability is formulated as a difference of corresponding cumulative distribution functions, where the cumulative distribution functions can be converted from the estimated conditional quantile regression functions. The proposed estimation method is also efficient as its computation cost does not increase exponentially with the number of classes. The theoretical and numerical studies demonstrate that the proposed estimation method is highly competitive against the existing competitors, especially when the number of classes is relatively large.     

Effects of censoring on the robustness of exponential-based confidence intervals for median lifetime

Statistical procedures for constructing confidence intervals for median lifetime often rest on a distributional assumption for failure times.This paper explores the interplay between censoring levels and robustness for two construction procedures based on exponential lifetime, subject to general right-censoring. Data are simulated from nearby Weibull distributions. As expected, the simulations indicate that when the exponential assumption is not satisfied, observed coverage by the confidence intervals may differ substantially from the specified coverage level. The marked improvement in the robustness properties of the intervals as the level of censoring increases suggests questions for future research.     

A copula regression model for estimating firm efficiency in the insurance industry

This article considers the estimation of insurers’ cost-efficiency in a longitudinal context. The current practice ignores the tails of the cost distribution, where the most and least efficient insurers belong to. To address this issue, we propose a copula regression model to estimate insurers’ cost frontier. Both time-invariant and time-varying efficiency are adapted to this framework and various temporal patterns are considered. In our method, flexible distributions are allowed for the marginals, and the subject heterogeneity is accommodated through an association matrix. Specifically, when fitting to the insurance data, we perform a GB2 regression on insurers total cost and employ a t-copula to capture their intertemporal dependencies. In doing so, we provide a nonlinear formulation of the stochastic panel frontier and the parameters are easily estimated by likelihood-based method. Based on a translog cost function, the X-efficiency is estimated for US property-casualty insurers. An economic analysis provides evidences of economies of scale and the consistency between the cost-efficiency and other performance measures.     

Inferences from Cross-Sectional,Stochastic Frontier Models

Conventional approaches for inference about efficiency in parametric stochastic frontier (PSF) models are based on percentiles of the estimated distribution of the one-sided error term, conditional on the composite error. When used as prediction intervals, coverage is poor when the signal-to-noise ratio is low, but improves slowly as sample size increases. We show that prediction intervals estimated by bagging yield much better coverages than the conventional approach, even with low signal-to-noise ratios. We also present a bootstrap method that gives confidence interval estimates for (conditional) expectations of efficiency, and which have good coverage properties that improve with sample size. In addition, researchers who estimate PSF models typically reject models, samples, or both when residuals have skewness in the “wrong” direction, i.e., in a direction that would seem to indicate absence of inefficiency. We show that correctly specified models can generate samples with “wrongly” skewed residuals, even when the variance of the inefficiency process is nonzero. Both our bagging and bootstrap methods provide useful information about inefficiency and model parameters irrespective of whether residuals have skewness in the desired direction.