Traditional Stochastic Frontier Model Research Articles

Trade efficiency under FTA for Thailand’s agricultural exports: copula-based gravity stochastic frontier model

This study investigated the trade efficiency and trade effects under Free Trade Agreements for Thailand’s agricultural exports. There are five main trading partners comprising China, Japan, Australia, New Zealand, and India. The important agricultural commodities of rubber, cassava, fruits, vegetables, and herbs were assessed from 1998 to 2019. In a traditional stochastic frontier model the two error components of symmetric noise ({nu }_{j}) and a non-negative inefficiency ({u}_{j}) are assumed to be independent. This may result in invalid inferences due to misspecification. To address this obstacle, copula-based Gravity Stochastic Frontier Models (GSFM) using panel criteria were constructed to estimate trade efficiency. Empirically, the Student-t copula-based SFM minimizes both AIC and BIC. According to their mean TE, China (0.48) and Japan (0.48) had the highest export efficiencies followed by India (0.41), New Zealand (0.39), and Australia (0.33) in rank order. Hence, Thailand should pursue more FTA negotiations with the trading partners. Moreover, they should promote miscellaneous behind-the-border barriers to stimulate flows of goods to enhance the country’s trade efficiency substantially.

Consequences of Ignoring Dependent Error Components and Heterogeneity in a Stochastic Frontier Model: An Application to Rice Producers in Northern Thailand

The traditional Stochastic Frontier Model (SFM) suffers from a very restrictive assumption of independence of its error components and also limited ability to address heterogeneity (inefficiency effects) satisfactorily, thereby leading to potential biases in the estimation of model parameters, identification of inefficiency effect variables influencing efficiency and, ultimately, efficiency scores. This paper aims to investigate the consequences of ignoring any dependency in error components and heterogeneity in the stochastic frontier model, and proposes a copula-based SFM with heterogeneity to resolve such weaknesses based on a simulation study to prove its superiority over the traditional SFM, followed by an empirical application on a sample of rice producers from northern Thailand. We demonstrate that the proposed model, i.e., copula-based SFM with dependent error components and heterogeneity, is unbiased and robust. The simulation experiments show that the traditional SFM can cause biases in parameter estimation and severe overestimation of technical efficiency. The traditional SFM with heterogeneity also has similar consequences. However, just ignoring heterogeneity does not have a great impact on parameter estimation and technical efficiency compared to the consequence of ignoring dependency in error components. The empirical application of the proposed model results show that land, labor and material inputs are all significant drivers of rice production in our copula-based SFM with dependent error components and heterogeneity, whereas in the traditional SFM model only the land variable seems to be a significant driver of rice production. The mean technical efficiency (MTE) score was also overestimated by two points in the traditional SFM, i.e., MTE = 0.88 versus 0.86. Finally, results of the copula-based SFM with dependent error components and heterogeneity reveals that both subsistence pressure and the use of hired labor are significantly associated with technical inefficiency, whereas the traditional SFM could identify the effect of hired labor use only. Therefore, caution is necessary when interpreting results from the conventional SFM as the results may be biased, incomplete and/or inadequate.

Combining data envelopment analysis and stochastic frontiers via a LASSO prior

Technical inefficiencies in stochastic frontier models can be thought of as non-negative parameters. Since, however, their number along with other parameters exceeds the sample size, an adaptive LASSO estimator is a reasonable way to overcome the problem, especially in view of the oracle properties of the estimator under broad conditions. It is shown that the adaptive LASSO estimator can be thought of as the posterior mean of a usual stochastic frontier model with a special prior that benchmarks inefficiencies on known quantities. We take these quantities from DEA scores to obtain technical inefficiencies having oracle properties. The LASSO parameters can be estimated routinely in the Bayesian context without the need for cross-validation. In an application to a data set of large U.S. banks we find that adaptive LASSO outperforms significantly traditional stochastic frontier models.

Technical Efficiency and Technological Gaps of Rice Production in Anambra State, Nigeria

The traditional approach to modeling productive efficiency assumes that technology is constant across the sample. However, farms in different regions may face different production opportunities, and the technologies they employ may differ due to environmental factors. Therefore, rather than using a traditional stochastic frontier model in such cases, a stochastic meta-frontier (SMF) analysis is recommended to account for environmental factors between regions. It follows that differences in environmental factors between the upland and lowland regions in Anambra State, Nigeria, may result in farmers producing rice under different production and environmental conditions. Using the SMF model, this study, for the first time, determines technical efficiency (TE) and technological gap ratios (TGRs) of rice production from the upland and lowland regions in the Awka North Local Government Area of Anambra State, Nigeria. Our data are from a cross-section sample of randomly selected rice farmers. Results reveal that lowland regional rice producers are on average, significantly more technically efficient (91.7%) than their upland counterparts (84.2%). Additionally, mean TGRs associated with lowland rice farmers are higher (92.1%) than their corresponding upland producers (84.7%). While the upland rice producers are less technically efficient and further away from their full potential, results indicate that both sets of farmers do not use advanced technologies to match the industry’s potential. We suggest that agricultural policy should focus on providing regionally specific technologies, such as improved rice varieties that fit the working environment of the lagging area, to help rice farmers improve their resource efficiency and minimize technological gaps.

Development of alternative stochastic frontier models for estimating time-space prism vertices

This paper develops alternative stochastic frontier models (ASFM) for estimating time-space prism vertices with different distributional assumptions for the inefficiency term that takes a non-negative value. The traditional stochastic frontier model (SFM) assumes that the inefficiency term follows a half-normal or exponential distribution. Under those assumptions, most travelers’ home departure/arrival time will be close to prism vertices, which is not necessarily consistent with actual travel behaviors. To avoid this potential problem, the ASFM adopt alternative distributions for the inefficiency term whose density values can decrease monotonously or vary non-monotonously. Quasi-Monte Carlo simulation method is employed to estimate the ASFM without closed-form likelihood expressions. Simulation experiment results show that SFM needs a substantially greater number of Halton draws for consistent estimators than a typical mixed logit model does. The ASFM are estimated based on the travel data of 1454 Shanghai commuters and 2964 Houston commuters. It is found that models with inefficiency term following a half-normal distribution tend to underestimate the origin vertex of morning prism and overestimate the terminal vertex of evening prism over 50 and 30 min for Shanghai and Houston samples, respectively. The empirical results show the importance of choosing an appropriate distributional assumption for the inefficiency term in the SFM for better understanding the relation between individuals’ departure/arrival time and time-space prism vertices. The SFM based on an appropriate distributional assumption can be applied in activity-based models for big cities to better reflect tighter temporal constraints on metropolitan residents and narrower time-space prisms for outdoor activity arrangement.

Quantile Stochastic Frontiers

In this paper, based on Jradi and Ruggiero (2019). Stochastic Data Envelopment Analysis: A Quantile Regression Approach to Estimate the Production Frontier. European Journal of Operational Research, 278 (2), 385–393] we propose a novel quantile Stochastic Frontier Model (SFM) and develop Markov Chain Monte Carlo techniques for numerical Bayesian inference. In an empirical application to US large banks we document important differences between the Quantile and the traditional SFM, in terms of several aspects of the data. We also document considerable heterogeneity among different quantiles in terms of returns to scale, technical change, efficiency change, technical efficiency, as well as productivity growth.

Persistent and transient productive inefficiency in a regulated industry: electricity distribution

The productive efficiency of a firm can be decomposed into two parts, one persistent and one transient. This distinction seems to be appealing for regulators. During the last decades, public utilities such as water and electricity have witnessed a wave of regulatory reforms aimed at improving efficiency through incentive regulation. Most of these regulation schemes use benchmarking, namely measuring companies' efficiency and rewarding them accordingly. Focusing on electricity distribution, we sketch a theoretical model to show that an imperfectly informed regulator may not disentangle the two parts of the cost efficiency. Therefore, the regulator may fail to set optimal efficiency targets, which also undermines quality. We then provide evidence on the presence of persistent and transient efficiency using data on 28 New Zealand electricity distribution companies between 2000 and 2011. First, we estimate a total cost function by means of traditional stochastic frontier models for panel data. These come up with an estimation of the persistent part or the transient part of the cost efficiency. Finally, we use the more recent generalized true random effects model that allows for the simultaneous estimation of both transient and persistent efficiency. We also find some evidence that persistent efficiency is associated to higher quality, and wrong efficiency targets are associated to lower quality compliance.

Cost Efficiency of Tunisian Public Hospitals: a Bayesian Comparison of Random and Fixed Frontier Models

This paper analyses the cost efficiency of the Tunisian public hospitals over the period 2000–2007, using a Bayesian frontier model (random and fixed models). Unlike the traditional stochastic frontier models, this model allows to separate the cost efficiency estimates from the technological difference (i.e., heterogeneity) within the hospitals and the inclusion of “prior” information about the parameters in inference. Results indicate that the random frontier was a better fit to the data, therefore providing further evidence that the Tunisian public hospitals operate in different environmental and technological characteristics. Policy implications of the results are derived.

A zero inefficiency stochastic frontier model

Traditional stochastic frontier models impose inefficient behavior on all firms in the sample of interest. If the data under investigation represent a mixture of both fully efficient and inefficient firms then off-the-shelf frontier models are statistically inadequate. We introduce the zero inefficiency stochastic frontier model which can accommodate the presence of both efficient and inefficient firms in the sample. We derive the corresponding log-likelihood function, conditional mean of inefficiency, to estimate observation-specific inefficiency and discuss testing for the presence of fully efficient firms. We provide both simulated evidence as well as an empirical example which demonstrates the applicability of the proposed method.

Performance assessment of Nigerian banks pre and post consolidation: evidence from a Bayesian approach

This study analyses the cost-efficiency of Nigerian banks pre and post the consolidation period. The researchers account for bank heterogeneity using the Bayesian random frontier model, which in this context provides a better fit than the traditional stochastic frontier model. From the efficiency inferences, it is shown that the cost-efficiency of Nigerian banks has increased post the consolidation period to reach its highest average of 91.21% in 2007. The study discusses the potential impact of consolidation on the efficiency results and provides direction for future research.

Cost efficiency and optimal scale of electricity distribution firms in Taiwan: An application of metafrontier analysis

This paper analyzes the cost efficiency and optimal scale of Taiwan's electricity distribution industry. Due to the substantial difference in network density, firms may differ widely in production technology. We employ the stochastic metafrontier approach to estimate the cost efficiency of 24 distribution units during the period 1997–2002. Empirical results find that the average cost efficiency is overestimated using the traditional stochastic frontier model, especially for low density regions. The average cost efficiency of the high density group is significantly higher than that of the low density group as it benefits from network economies. This study also calculates both short-term and long-term optimal scales of electricity distribution firms, lending policy implications for the deregulation of the electricity distribution industry.

Are U.S. airlines really in crisis?

This study reflects on the technical efficiency of U.S. airlines using a Bayesian random stochastic frontier model. Inferences from the Bayesian estimation indicate that the random model fits the data well and outperforms the traditional stochastic frontier model. The technical efficiency results indicate that U.S. airlines are operating at a declining efficiency rate with an average of 69.02% in 2007. Results from returns to scale are also in line with the efficiency results. More specific discussions on the current industry trends and other contributions of this study are presented and discussed.

Firm exit and technical inefficiency

The purpose of the paper is to examine formally the fundamental implication that technical inefficiency (TI) is related to firm exit. Traditional stochastic frontier models allow for the measurement of TI but do not allow for a direct effect of TI on exit. We propose a model which allows for such effects and consists of a stochastic frontier model, and an additional equation that describes the probability of exit as a function of covariates and TI. Since TI is unobserved, econometric complications arise, and obtaining consistent estimates is non-trivial due to the presence of integrals in the likelihood function. We propose and implement maximum likelihood estimation one step, employing data for 3,404 manufacturing firms in Greece. We find significant positive effects from TI on the probability of exit. We also propose and provide measures of TI that respect the fact that unobserved TI affects the probability of exit and compare them to TI measures from the traditional stochastic frontier model.

Efficiency measurement in the stochastic frontier model

Deterministic models of technical efficiency assume that all deviations from the production frontier are due to inefficiency. Critics argue that no allowance is made for measurement error and other statistical noise so that the resulting efficiency measure will be contaminated. The stochastic frontier model is an alternative that allows both inefficiency and measurement error. Advocates argue that the stochastic frontier models should be used despite other potential limitations because of the superior conceptual treatment of noise. As will be demonstrated in this paper, however, the assumed shape of the error distributions is used to identify a key production function parameter. Therefore, the stochastic frontier models, like the deterministic models, cannot produce absolute measures of efficiency. Moreover, we show that rankings for firm-specific inefficiency estimates produced by traditional stochastic frontier models do not change from the rankings of the composed errors. As a result, the performance of the deterministic models is qualitatively similar to that of the stochastic frontier models.

A Stochastic Frontier Production Function with Flexible Risk Properties

This paper considers a stochastic frontier production function which has additive, heteroscedastic error structure. The model allows for negative or positive marginal production risks of inputs, as originally proposed by Just and Pope (1978). The technical efficiencies of individual firms in the sample are a function of the levels of the input variables in the stochastic frontier, in addition to the technical inefficiency effects. These are two features of the model which are not exhibited by the commonly used stochastic frontiers with multiplicative error structures. An empirical application is presented using cross-sectional data on Ethiopian peasant farmers. The null hypothesis of no technical inefficiencies of production among these farmers is accepted. Further, the flexible risk models do not fit the data on peasant farmers as well as the traditional stochastic frontier model with multiplicative error structure.