Quantile Methods for Stochastic Frontier Analysis

A suitable self‐thinning model is fundamental to effective density control and management. Using data from 265 plot measurements in oak mixed forests in central China, we demonstrated how to estimate a suitable self‐thinning line for oak mixed forests from three aspects, i.e., self‐thinning models (Reineke's model and the variable density model), statistical methods (quantile regression and stochastic frontier analysis), and the variables affecting stands (topography and stand structure factors). The proposed variable density model, which is based on the quadratic mean diameter and dominant height, exhibited a better goodness of fit and biological relevance than Reineke's model for modeling the self‐thinning line for mixed oak forests. In addition, the normal‐truncated normal stochastic frontier model was superior to quantile regression for modeling the self‐thinning line. The altitude, Simpson index, and dominant height–diameter ratio (Hd/D) also had significant effects on the density of mixed forests. Overall, a variable density self‐thinning model may be constructed using stochastic frontier analysis for oak mixed forests while considering the effects of site quality and stand structure on density. The findings may contribute to a more accurate density management map for mixed forests.

Food manufacturers use health claims to signal higher product quality and attract health oriented consumers. However, consumers’ willingness to pay for health-related attributes may not be large enough to repay firms of the high costs associated with developing, certifying, and marketing such products. We investigate the impact of several health-related credence attributes on product’s price, and what may help manufacturers to reach consumers with the highest willingness to pay for yogurt. To achieve our goals we use a large database of yogurt sales in Italy and two empirical approaches recently introduced in the hedonic price literature: Quantile Regression (QR) and Stochastic Frontier Analysis (SFA). Results show that the implicit prices of health claims differ across price levels (i.e. quantiles), and that manufacturers differ in their ability to target consumers with high willingness to pay.

Stochastic frontier analysis and quantile regression are the two econometric approaches that have been commonly adopted in the determination of the self-thinning boundary line or surface in two and higher dimensions since their introduction to the field some 20 years ago. However, the rational for using one method over the other has, in most cases, not been clearly explained perhaps due to a lack of adequate appreciation of differences between the two approaches for delineating the self-thinning surface. Without an adequate understanding of such differences, the most informative analysis may become a missed opportunity, leading to an inefficient use of data, weak statistical inferences and a failure to gain greater insight into the dynamics of plant populations and forest stands that would otherwise be obtained. Using data from 170 plot measurements in even-aged Larix olgensis (A. Henry) plantations across a wide range of site qualities and with different abundances of woody weeds, i.e. naturally regenerated non-crop species, in northeast China, this study compared the two methods in determining the self-thinning surface across eight sample sizes from 30 to 170 with an even interval of 20 observations and also over a range of quantiles through repeated random sampling and estimation. Across all sample sizes and over the quantile range of 0.90 ≤ τ ≤ 0.99, the normal-half normal stochastic frontier estimation proved to be superior to quantile regression in statistical efficiency. Its parameter estimates had lower degrees of variability and correspondingly narrower confidence intervals. This greater efficiency would naturally be conducive to making statistical inferences. The estimated self-thinning surface using all 170 observations enveloped about 96.5% of the data points, a degree of envelopment equivalent to a regression quantile estimation with a τ of 0.965. The stochastic frontier estimation was also more objective because it did not involve the subjective selection of a particular value of τ for the favoured self-thinning surface from several mutually intersecting surfaces as in quantile regression. However, quantile regression could still provide a valuable complement to stochastic frontier analysis in the estimation of the self-thinning surface as it allows the examination of the impact of variables other than stand density on different quantiles of stand biomass.

Measuring the economic efficiency performance in Latin American and Caribbean countries: An empirical evidence from stochastic production frontier and data envelopment analysis

Climatic variability and thermal stress in Pakistan’s rice and wheat systems: A stochastic frontier and quantile regression analysis of economic efficiency

Density-dependent mortality models for mono- and multi-species uneven-aged stands: The role of species mixture

The article is devoted to the study of methods for assessing the operation of airports under international integration and their improvement. The recent scientific studies on assessing the operation of international airports were analyzed and it was found that the most actively used methods are the initial data envelopment analysis (DEA) and various variants of quantile regression, Tobit regression, assurance region methods, SBI and DMU, Malmquist index, classification and regression tree, bootstrapping tool and other tools. It was confirmed that the existing methods for assessing the airports’ operation have a significant number of indicators for calculations based on the evaluation of economic, technical or overall efficiency. The parametric methods for assessing the operation of airports, their advantages and disadvantages were characterized. The methodology of stochastic frontier analysis (SFA), the use of a non-parametric approach to evaluate airport performance, and the evaluation of the overall efficiency of two-stage DMUs with shared resources were described. The methodical approaches based on the use of the spatial regression model, the AAG model and the stochastic frontier model were characterized. The methodology for determining the target function Effi to assess the efficiency of each airport DMUi was described. The scheme for assessing the airports’ operation by input and output indicators was proposed, which includes a three-module assessment system for the passenger, cargo and joint modules. The cargo module is the authors’ own development and its creation is justified by the fact that a significant number of air cargo flows are served by passenger aircraft. The group of input indicators of the cargo module includes the length of the loading and unloading work front, the number of cargo receiving points, the working area of rack and stack storage, the number of electric forklifts and lift trucks, as well as the number of cargo warehouses, and the number of general and special categories of cargo are defined as output indicators.

Summary This paper presents a mathematical model to estimate both production frontier and energy demand frontier, and evaluate the energy efficiency in the automotive manufacturing sector using plant-level production and utility consumption data. By using the stochastic frontier analysis, two models—an output efficiency model (production frontier) and an input efficiency model (energy demand frontier)—are developed to analyze the plant's energy efficiency performance relative to the ‘best practice’ among peers. Both the structure and parameters of two stochastic frontier functions are identified to understand the relationship between production inputs (e.g., utilities and plant-specific variables) and the overall productivity. A case study of a set of automotive engine manufacturing plants is conducted and shows that electricity has higher efficiency than other forms of utility in those production-related activities, and the regional and climate factors have significant impacts on energy efficiency. The models provide a way to measure how far from the production frontier as well as how far from the energy demand frontier the plant is. The results also provide useful information about the inefficient energy components in manufacturing facilities. The opportunities of improving plant-level efficiency in automotive manufacturing plants can be revealed by the results. Copyright © 2015 John Wiley & Sons, Ltd.

Nigeria is trending below the top ginger producing countries of the world in terms of yield per hectare and national output. Technical Inefficiency due to poor combination and utilization of physical resources in the production of ginger is a major factor for low yield/output. Previous studies employed either Stochastic Frontier Analysis (SFA) or Data Envelopment Analysis (DEA) to measure technical efficiency. So, the question arises as whether the technical efficiency estimates from both methods are similar or not. The present study deployed the two common approaches (SFA and DEA) in estimation of technical efficiency and its determinants in order to ascertain the similarity or otherwise of the estimates. Two hundred and five (205) ginger farmers were randomly sampled for primary data collection. Analyses of the data were done through Descriptive Statistics, DEA, Tobit regression and SFA. The results show that means of the efficiency scores from both models namely DEA (0.70) and SFA (0.88) were significantly different at 1% probability level. However, estimates from both method suggest that the ginger farmers were operating at suboptimal level or below frontier. Also, the results of determinants of efficiency from two estimation methods (SFA and DEA-based Tobit regression) were dissimilar. While SFA method shows that household size, level of education and farming experience were responsible for enhancing the efficiency of ginger farms, none of these variables influenced the farmers’ efficiency under Tobit regression. Therefore, it is recommended that selection of efficiency estimation method between SFA and DEA by the researcher should be based on study objective rather than consideration on the premise of alternative opportunity. Also, greater output level or potential output can be achieved, given the current production technology, by educating ginger farmers on how to ensure that production inputs are combined and managed efficiently. Keywords: Comparison, DEA, SFA, Efficiency, Ginger Farms

Productivity and efficiency analysis have gained substantial attention in many industries over the last two decades, and stochastic frontier analysis has been one of the most popular analytical approaches. The abundant model choices in stochastic frontier analysis make it difficult to select the best option and compare studies. The main purpose of this study is to examine the sensitivity of technical and scale efficiency estimates to choices around input-output combinations, functional forms, distributional assumptions and estimation methods in stochastic frontier analysis, using data from an Australian fishery to illustrate these effects. We estimated 252 stochastic frontier models using combinations of variable choice, functional form and distributional assumptions. A second stage analysis was conducted to examine the effects of model choices on statistical properties of technical and scale efficiency. The results show that estimates of technical and scale efficiency are most sensitive to distributional assumptions and the choice of time effects. In particular, the assumption of time-invariant efficiency produced significantly higher technical efficiency (20 percentage points) and scale efficiency (8 percentage points) scores than time-varying efficiency models in our analysis. We also find that the choice of fixed input variables can significantly affect the average efficiency estimates, by as much as 5 percentage points, but mean efficiency was not significantly affected by the choice of variable inputs. Our findings suggest that caution should be taken when comparing findings of stochastic frontier studies using different distributional and fixed input assumptions.

Stochastic frontier analysis (SFA) is often employed to study the production functions. The structure of errors is the main difference between the standard regression analysis and the stochastic frontier models; in the SFA, an independent random term with positive value is added to the usual white noise error. Conventionally, the parameters involved in the SFA are estimated and then, the convenience of using this model is tested. The authors propose to study, previously, the residuals in order to check the capacity of assuming a stochastic frontier model and then, if applicable, to estimate the parameters. With this goal, several non-parametric hypothesis testing are explored.

Testing specification of distribution in stochastic frontier analysis

The goal of this study was to examine how selected pressure points or areas of vulnerability are related to individual differences in reading comprehension and whether the importance of these pressure points varies as a function of the level of children’s reading comprehension. A sample of 245 third-grade children were given an assessment battery that included multiple measures of vocabulary, grammar, higher-level language ability, word reading, working memory, and reading comprehension. Ordinary least squares (OLS) and quantile regression analyses were undertaken. OLS regression analyses indicated that all variables except working memory accounted for unique variance in reading comprehension. However, quantile regression showed that the extent of the relationships varied in some cases across readers of different ability levels. Results suggest that quantile regression may be a useful approach for the study of reading in both typical and atypical readers and aid greater specification of componential models of reading comprehension across the ability range.

The objective of this paper is to incorporate risk in technical efficiency of listed ASEAN banks in a panel data framework for the period 2000 to 2015. Many researchers apply frontier estimation techniques such as data envelopment analysis (DEA) or stochastic frontier analysis (SFA) for their efficiency analysis. However, the banks’ complex production process requires more sophisticated techniques to account for internal structures within the black box so relying only traditional DEA or SFA is not adequate to deal with a multiple-input and multiple-output production technology. To incorporate undesirable outputs such as risk into inefficiency, we rely on the directional distance function (DDF). We employ the DDF under both parametric (SFA) and semi-parametric (SEMSFA) framework to make a comparison efficiency scores with risk adjusted in two scenarios. Our results suggest that risk is an important factor that bank managers should pay more focus to achieve long-term efficiency in ASEAN banks
 Keywords
 Bank efficiency; risk; directional distance function (DDF); semiparametric estimation of stochastic frontier models (SEMSFA)
 References
 ADB. (2013). The road to ASEAN financial integration: A combined study on assessing the financial landscape and formulating milestones for monetary and financial integration in ASEAN. Andor, M., & Hesse, F. (2014). The StoNED age: the departure into a new era of efficiency analysis? A monte carlo comparison of StoNED and the ‘‘oldies’’ (SFA and DEA). J Prod Anal 41, 85-109. doi: 10.1007/s11123-013-0354-yBerger, A. N., & DeYoung, R. (1997). Problem loans and cost efficiency in commercial banks. Journal of Banking & Finance, 21(6), 849-870. Berger, A. N., & Humphrey, D. B. (1997). Efficiency of financial institutions: international survey and directions for future research. European Journal of Operational Research, 98, 175-212. Chan, S.-G., Koh, E. H. Y., Zainir, F., & Yong, C.-C. (2015). Market structure, institutional framework and bank efficiency in ASEAN 5. Journal of Economics and Business, 82, 84-112. Chang, C.-C. (1999). The Nonparametric Risk-Adjusted Efficiency Measurement: An Application to Taiwan’s Major Rural Financial Intermediaries. American Journal of Agricultural Economics, 81(4), 902-913. Chang, T.-C., & Chiu, Y. H. (2006). Affecting factors on risk-adjusted effciency in Taiwan’s banking industry. Contemporary Economic Policy 24(4), 634-648. Gardener, E., Molyneux, P., & Nguyen-Linh, H. (2011). Determinants of efficiency in South East Asian banking. The Service Industries Journal, 31(16), 2693-2719. Huang, T.-H., Chiang, D.-L., & Tsai, C.-M. (2015). Applying the New Metafrontier Directional Distance Function to Compare Banking Efficiencies in Central and Eastern European Countries. Economic Modelling, 44, 188-199. Karim, M. Z. A. (2001). Comparative Bank Efficiency across Select ASEAN Countries. ASEAN Economic Bulletin, 18(3), 289-304. Karim, M. Z. A., Sok-Gee, C., & Sallahudin, H. (2010). Bank efficiency and non-performing loans: Evidence from Malaysia and Singapore. Prague Economic Papers, 2, 118-132. doi: 10.18267/j.pep.367Khan, S. J. M. (2014). Bank Efficiency in Southeast Asian Countries: The Impact of Environmental Variables. In Handbook on the Emerging Trends in Scientific Research. Malaysia: PAK Publishing Group. Laeven, L. (1999). Risk and Efficiency in East Asian Banks (Vol. 2255). Washington, D.C. : World Bank, Financial Sector Strategy and Policy Department.Manlagnit, M. C. V. (2011). Cost efficiency, determinants, and risk preferences in banking: A case of stochastic frontier analysis in the Philippines. Journal of Asian Economics, 22, 23-35.
 Sarifuddin, S., Ismail, M. K., & Kumaran, V. V. (2015). Comparison of Banking Efficiency in the selected ASEAN Countries during the Global Financial Crisis. PROSIDING PERKEM, 10, 286-293. Sarmientoa, M., & Galán, J. E. (2015). The Influence of Risk-Taking on Bank Efficiency: Evidence from Colombia. CentER Discussion Paper, 2015-036. Vidoli, F., & Ferrara, G. (2015). Analyzing Italian citrus sector by semi-nonparametric frontier efficiency models. Empir Econ, 45, 641-658. Williams, J., & Nguyen, N. (2005). Financial Liberalisation, Crisis, and Restructuring: A Comparative Study of Bank Performance and Bank Governance in South East Asia. Journal of Banking and Finance, 29(8-9), 2119-2154. Wong, W. P., & Deng, Q. (1999). Efficiency analysis of banks in ASEAN countries. Benchmarking: An International Journal, 23(7), 1798-1817. Yueh-Cheng Wu, I. W. K. T., Wen-Min Lu, Mohammad Nourani, Qian Long Kweh. (2016). The impact of earnings management on the performance of ASEAN banks. Economic Modelling, 53, 156-165. Zhu, N., Wang, B., Yu, Z., & Wu, Y. (2016). Technical Efficiency Measurement Incorporating Risk Preferences: An Empirical Analysis of Chinese Commercial Banks. Emerging Markets Finance and Trade, 52, 610-624.

BACKGROUND:Given that the need to pay attention to measuring efficiency is considered as one of the main pillars of improving the level of efficiency in hospitals, so this study was carried out aimed to determine the mean technical efficiency (The technical efficiency is bound by zero and one and a score of less than one means that the theatre is inefficient as it could) score in terms of type and activity of the hospital, input-oriented and output-oriented attitude, returns to scale (In economics, returns to scale and economies of scale are related but different concepts that describe what happens as the scale of production increases in the long run, when all input levels including physical capital usage are variable (chosen by the firm). The concept of returns to scale arises in the context of a firm's production function. It explains the behavior of the rate of increase) in hospitals of Iran using data envelopment analysis (DEA) (DEA is a nonparametric method in operations' research and economics for the estimation of production frontiers. It is used to empirically measure productive efficiency of decision-making units) and stochastic frontier analysis (SFA) (SFA is a method of economic modeling. It has its starting point in the stochastic production frontier models simultaneously introduced by Aigner, Lovell and Schmidt[1977] and Meeusen and Van den Broeck[1977] MATERIALS AND METHODS:The present study was carried out with a systematic review of all studies conducted on measuring efficiency of hospitals in Iran from March 21, 2001 to December 21, 2017 using DEA and SFA. Eleven databases were searched using appropriate keywords and 470 articles were found and evaluated using a checklist, and finally, 24 articles were entered into the meta-analysis process. Meta-analysis was performed using random effect model and fixed-effect model, and study heterogeneity was investigated using Q-Cochran test and I2 index. Furthermore, the main reasons of study heterogeneity were identified due to meta-regression.RESULTS:The average technical efficiency score of hospitals using DEA and SFA method was obtained equal to 0.885 and 0.809, respectively. Furthermore, with regard to the DEA method, 0.885, 0.891.0.952 and 0.913 was obtained for input-oriented and output-oriented, general and specialized care hospitals and constant returns respectively. With regard to SFA method, 0.733, 0.664, 0.641, 0.802, was obtained, and the inputs and outputs affect measuring the efficiency.DISCUSSION:In contrast, the DEA method can investigate several input and output simultaneously and is used as an effective and flexible tool in order to measure the efficiency of the hospital. DEA can be easily used for calculating efficiency scores based on the proper selection of input and output indicators. The data envelopment analysis method and different input and output variables have been used in most studies conducted in Iran, and Stochastic Frontier Analysis has been less considered. In the present study, the DEA method in governmental educational hospitals showed a higher efficiency than SFA method in the hospitals under study. But in general, due to lack of optimal efficiency level in the hospital, it is suggested that policymakers determine the hospital efficiency indices in order to evaluate their efficiency from different dimensions.CONCLUSION:The average technical efficiency score of hospitals using DEA and SFA method was obtained equal to 0.885 and 0.809, respectively. Also, the mean technical efficiency score in terms of input-oriented and output-oriented, general and specialized care hospitals and constant returns to scale using the DEA method was obtained equal to 0.885, 0.891.0.952 and 0.913 and using the SFA method, respectively, it was equal to 0.733, 0.664, 0.641, 0.802, and the inputs and outputs affecting measuring the efficiency. There is no significant difference between the mean efficiency score between the two methods, but the data envelopment analysis method is used more. It is suggested that the hospitals efficiency indicators to be determined in order to more accurately evaluate the hospitals efficiency.