Stochastic Frontier Method Research Articles

University Efficiency: A Comparison and Consolidation of Results from Stochastic and Non‐stochastic Methods

Efficiency scores are determined for Canadian universities using both data envelopment analysis and stochastic frontier methods for selected specifications. The outcomes are compared. There is considerable divergence in the efficiency scores and their rankings among methods and specifications. An analysis of rankings, however, reveals that the relative positions of individual universities across sets of several efficiency rankings (e.g., all the data envelopment analysis and stochastic frontier outcomes) demonstrate an underlying consistency. High‐efficiency and low‐efficiency groups are evidenced but the rank for most universities is not significantly different from that of many others. The results emphasize the need for caution when employing efficiency scores for management and policy purposes, and they recommend looking for confirmation across viable alternatives.

Oriented Stochastic Data Envelopment Models: Ranking Comparison to Stochastic Frontier Approach

Results of data envelopment analysis sensitively respond to stochastic noise in the data. In this paper, by introduction of output augmentation and input reduction I extend additive models for stochastic data envelopment analysis (SDEA), which were developed by Li (1998) to handle the noise in the data. Applying the linearization procedure by Li (1998) the linearized versions of models are derived. In the empirical part of this work, the efficiency scores of Indonesian rice farms are computed. The computed scores are compared to the stochastic frontier approach scores by Druska and Horrace (2004) and weak ranking consistency with results of stochastic frontier method is observed.

Decomposing Growth in Portuguese Seaports: A Frontier Cost Approach

This paper analyses the extent of technical change and technical efficiency in Portuguese seaport costs between 1990 and 2000, using a stochastic cost frontier method. A translog frontier and the maximum likelihood estimation technique are employed to estimate the empirical model. The results show that the average score of inefficiency is 39.6%, denoting a high degree of waste in the use of resources, despite the fact that technical change contributed to a reduction of costs.

Off-balance sheet activities and cost inefficiency in Taiwan's Banks

In this study, we adopt a stochastic cost frontier method to investigate the influence of off-balance sheet (OBS) activities on the cost efficiency of Taiwan's banks. We estimate and compare cost inefficiency with or without OBS outputs of 46 Taiwanese commercial banks during the period, 1998 through 2001. The conclusions of this empirical study are as follows. First, omitting off-balance sheet outputs in estimating the cost frontier function of banks results in an underestimation of bank efficiency by approximately 5 per cent. Second, large banks are associated with a higher cost efficiency and have an increased ability to develop OBS activities. This is consistent with Taiwan's regulatory policies, which focus on promoting efficiency in the banking industry of emerging markets. Banks with higher employee productivity are also more cost efficient. Finally, we observe evidence of economies of scale in both models with or without OBS specification in Taiwan's bank industry. Economies of scope between loans and OBS outputs are also observed.

Scale Economies and Efficiency in U.S. Agriculture: Are Traditional Farms History?

The structural transformation of agriculture in recent decades has raised serious concerns about the future of the family farm. This study examines the economic performance of U.S. farms, to explore the potential of smaller farms to compete with larger entities, and ultimately to survive in this rapidly changing environment. We use deterministic and stochastic frontier methods and survey data to measure and evaluate factors underlying scale economies (SEC) and efficiency (SEF) of corn-belt farms for 1996–2001. Our results suggest that family farms are both scale and technically inefficient. Potential for the exploitation of significant scale and scope economies, and some greater technical efficiency, seem to be driving trends toward increased farm size and dwindling competitiveness of the small family farm.

Profitability and Efficiency in the U.S. Life Insurance Industry

This study explores the relationship between cost inefficiency and profitability in the U.S. life insurance industry. Earnings have particular importance to life insurance companies because earnings and capital determine the viability of the insurer. Since the life insurance industry is mature and highly competitive, cost efficiency may be the main driver of profitability. We derive cost efficiency using the stochastic frontier (SF) method allowing the mean inefficiency to vary with organizational form and the outputs. In addition, the estimation of the cost efficiency measure takes into account the underlying accounting concepts that generate the data and, consequently, the product mix (long-duration policies vs. short-duration policies) to avoid distorted estimates. Our results suggest that cost inefficiency in the life insurance industry is substantial relative to earnings, and that inefficiency is negatively associated with profitability measures such as the return on equity. The analysis of inefficiency and organizational form suggest that stock (shareholder-owned) companies are as efficient and profitable as mutual (policyholder-owned) companies.

Measurement of Technical Efficiency in Public Education: A Stochastic and Nonstochastic Production Function Approach

1. Introduction Efficiency in the public education system is a significant issue in the United States. Nationwide, real expenditure per student in public education increased more than 3% per year between 1960 and 1998, but output as generally measured by standardized test scores has not increased and in some cases (e.g., the verbal SAT score) has declined.' One explanation is that resources are not being utilized efficiently. There may be productive or technical inefficiency and/or allocative or price inefficiency (i.e., given the relative prices of inputs, the cost minimizing input combination is not used). This paper focuses on the former by evaluating technical inefficiency in public education using data from Utah school districts. The pioneering work by Farrell in 1957 provided the definition and conceptual framework for both technical and allocative efficiency. Although technical efficiency refers to failure to operate on the production frontier, allocative efficiency generally refers to the failure to meet the marginal conditions for profit maximization. Considerable effort has been made in refining the measurement of technical efficiency. The literature is broadly divided into deterministic and stochastic frontier methodologies.2 The deterministic nonparametric approach that developed out of mathematical programming is commonly known as data envelopment analysis (DEA), and the parametric approach that estimates technical efficiency within a stochastic production, cost, or profit function model is called the stochastic frontier method. Both approaches have advantages and disadvantages, as discussed in Forsund, Lovell, and Schmidt (1980). DEA has been used extensively in measuring efficiency in the public sector, including education, where market prices for output generally are not available. For example, Levin (1974), Bessent and Bessent (1980), Bessent et al. (1982), and Fare, Grosskopf, and Weber (1989) used this method to estimate efficiency in public education. The stochastic frontier methodology was used by Barrow (1991) to estimate a stochastic cost frontier using data from schools in England. Wyckoff and Lavinge (1991) and Cooper and Cohn (1997) estimated technical efficiency using school district data from New York and South Carolina, respectively. Grosskopf et al. (1991) used the parametric approach to estimate allocative and technical efficiency in Texas school districts. The recent literature has seen a convergence of the two approaches and their complementarity is being recognized.3 However, there is a lack of empirical evidence in the literature about the proximity of these two approaches in measuring technical efficiency. Policy formulations based on only one of these efficiency estimates may not be accurate because of the inherent limitations of each. Before any correctional measures are taken, the stability of the technical efficiency estimates obtained from a parametric method should be evaluated by comparing them against those found when using the nonparametric method. In this study, the technical efficiency estimates for each school district using the stochastic frontier method and Tobit residuals from the two-stage DEA model are compared. In the twostage DEA model, technical efficiency scores obtained from DEA using controllable inputs are regressed on student socioeconomic status and other environmental factors. The residuals of this regression measure pure technical efficiency after accounting for fixed socioeconomic and environmental factors. The empirical analysis uses data from the 40 school districts in Utah for the academic year 1992-1993. The standardized test score for 11 th-grade students is used as a measure of school output, and two classes of inputs are included. The first class is considered to be subject to control by school administrators and includes the student-teacher ratio, the percentage of teachers having an advanced degree, and the percentage of teachers with more than 15 years of experience. …

Is China's economic growth sustainable? A productivity analysis

Since the initiative of economic reform in the late 1970s, the Chinese economy has sustained a continuously high rate of annual growth. This seemingly miraculous growth has attracted the attention of many economists in the world. In particular, major efforts have been made to examine the role of efficiency and productivity in economic growth in the postreform mainland Chinese economy and hence, to understand whether China's economic growth is sustainable or not. However, most previous studies have focused only on the industrial or agricultural sectors, perhaps due to the limitation of statistics. This paper presents an economy-wide study and hence attempts to fill the void in the literature. A stochastic frontier method is used to estimate productivity growth, which is decomposed into two components: technological progress and efficiency change. The former refers to shifts in the frontier and the latter to movement towards the frontier. Applying the newly released regional GDP data, this study aims to: (1) examine the contribution of productivity to economic growth in China, (2) investigate the sources of productivity growth in the reforming Chinese economy, and (3) shed some light on the trend of convergence and catch-up in terms of productivity performance among China's regional economies in the 1980s and 1990s.

The Effects of Operating and Capital Subsidies on Total Factor Productivity: A Decomposition Approach

Past studies relied on ad hoc associations to establish relationships between productivity on one hand and operating and capital subsidies on the other. This article deviates from these studies. It builds on recent research based on private cost to derive a total factor productivity formula that includes subsidy effects. It specifies an empirical model to estimate the required parameters to apply the formula. The application to urban transit systems shows that the effects of these subsidies on productivity through technical change reinforce the decline in productivity. Sakano, Obeng, and Azam (1997) applied the stochastic frontier method to public transit data and decomposed allocative inefficiency between internal factors and subsidies. They found that the internal factors contributed more toward allocative inefficiencies, and subsidies accounted for less than 25% of the technical inefficiencies in transit firms. These authors also found operating subsidies to be the major sources of the inefficiencies and that capital subsidies mostly acted as a counterbalancing factor in reducing the inefficiencies. These findings suggest that both subsidies play opposing roles in affecting performance and inefficiency and that while capital subsidies increase partial productivity measures, operating subsidies may reduce them. These effects of subsidies on partial productivity will also affect total factor productivity (TFP). Therefore, there is a link between operating and capital subsidies and TFP, and we must find a way to decompose the changes in TFP such that we can identify the effects of subsidies. This decomposition is the motivation for this article; we develop a decomposition method for TFP that permits the contributions of subsidies to be isolated and apply the method to public transit data. The article, therefore, makes contributions in both methodology and application. The basis of the decomposition is an extension of the methods discussed in Obeng (1994), Obeng and Azam (1997), and Sakano, Obeng, and Azam (1997) to derive a TFP measure that depends on subsidies.' These methods hold that firms maximize output subject to a net cost constraint, where net cost is total cost less operating and capital subsidies. The dual of this constrained output maximization is that firms minimize their private cost subject to a production function constraint. This objective is different from those frequently adopted in the public transit

Efficiency in New Zealand Sheep and Beef Farming: The Impacts of Regulatory Reform

In this study, we consider the impacts of dramatic regulatory reform during the 1980s on the efficiency of farms in New Zealand, using unbalanced panel data. A translog distance function representing the multiple output and input technology and incorporating nonneutral regulatory impacts is used for the analysis. Determinants of technical inefficiency, including a regulatory variable, a time term, and a debt/equity ratio, are also incorporated in a one-step model estimated by maximum-likelihood, stochastic production frontier methods. We find evidence of regulatory-induced changes in output composition—toward beef and deer, and away from wool, and especially lamb—but little associated technical inefficiency. These patterns motivated investment in complementary capital, land, and beef/deer livestock inputs. Firms that were more flexible in their adaptation toward these new mixes adjusted to regulatory changes with less upheaval, so any existing inefficiency appears linked to debt/equity levels.

The efficiency of conventional fuel power plants in South Korea: A comparison of parametric and non-parametric approaches

The efficiencies of the 64 conventional fuel power plants operating in South Korea were determined by data envelopment analysis (DEA) approaches, as well as by a stochastic-frontier method. The Banker, Charnes and Cooper (BCC) DEA efficiencies were introduced into an econometric estimate of a standard production function model, leading to a corrected factors version of the model, with significant improvement of the statistical explanation of our data. A statistical analysis of the DEA efficiencies was carried out, and these were compared to efficiencies revealed by a stochastic-frontier method.

A stochastic frontier analysis of output level and growth in Poland and western economies

This paper uses Bayesian stochastic frontier methods to measure the productivity gap between Poland and Western countries that existed before the beginning of the main Polish economic reform. Using data for 20 Western economies, Poland and Yugoslavia (1980–1990) we estimate a translog stochastic frontier and make inference about individual efficiencies. Following the methodology proposed in our earlier work, we also decompose output growth into technical, efficiency and input changes and examine patterns of growth in the period under consideration.

The Components of Output Growth: A Stochastic Frontier Analysis

This paper uses Bayesian stochastic frontier methods to decompose output change into technical, efficiency and input changes. In the context of macroeconomic growth exercises, which typically involve small and noisy data sets, we argue that stochastic frontier methods are useful since they incorporate measurement error and assume a (flexible) parametric form for the production relationship. These properties enable us to calculate measures of uncertainty associated with the decomposition and minimize the risk of overfitting the noise in the data. Tools for Bayesian inference in such models are developed. An empirical investigation using data from 17 OECD countries for 10 years illustrates the practicality and usefulness of our approach.

The effects of exogenous variables in efficiency measurement—A monte carlo study

A Monte Carlo study is conducted to compare the stochastic frontier method and the data envelopment analysis (DEA) method in measuring efficiency in situations where firms are subject to the effects of factors which are beyond managerial control. In making efficiency measurements and comparisons, one must separate the effects of the environment (the exogenous factors) and the effects of the productive efficiency. There are two basic approaches to account for the effects of exogenous variables: (1) an one-step procedure which includes the exogenous variables directly in estimating the efficiency measures, and (2) a two-step procedure which first estimates the relative ‘gross’ efficiencies using inputs and outputs, then analyzes the effects of the exogenous variables on the ‘gross’ efficiency. The results show that the magnitude of exogenous variables does not appear to have any significant effect on the performance of the one-step stochastic frontier method as long as the exogenous variables are correctly identified and accounted for. However, the effects of exogenous variables are significant for the two-step approach, especially for the DEA methods.

Multi-product cost functions and the funding of tuition in UK universities

A quadratic multi-product cost function is estimated for UK universities prior to the abolition of the binary divide. The arguments of the function include linear and interaction terms in undergraduate tuition, postgraduate tuition and research, and in each case these are separately identified for the (broadly defined) arts and sciences. The preferred specification is used to evaluate ray economies of scale, product-specific economies of scale and economies of scope. Estimates of average incremental costs are also provided. Results from OLS and stochastic frontier methods are compared.

The technical efficiency of vacuum-pan sugar industry of India: An application of a stochastic frontier production function using panel data

A stochastic production frontier method is used to examine technical efficiency among Indian vacuum-pan sugar factories over a five-year period. Most factories are close to Indian best practice in terms of technical efficiency. Smaller firms and firms with access to sweeter cane are likely to be more efficient than other firms, while publicly owned firms are less efficient. There are transitory positive effects of a long crushing season on technical efficiency.

Structural reform in Central and Eastern Europe

Since the initiative of economic reform in the late 1970s, the Chinese economy has sustained a continuously high rate of annual growth. This seemingly miraculous growth has attracted the attention of many economists in the world. In particular, major efforts have been made to examine the role of efficiency and productivity in economic growth in the postreform mainland Chinese economy and hence, to understand whether China's economic growth is sustainable or not. However, most previous studies have focused only on the industrial or agricultural sectors, perhaps due to the limitation of statistics. This paper presents an economy-wide study and hence attempts to fill the void in the literature. A stochastic frontier method is used to estimate productivity growth, which is decomposed into two components: technological progress and efficiency change. The former refers to shifts in the frontier and the latter to movement towards the frontier. Applying the newly released regional GDP data, this study aims to: (1) examine the contribution of productivity to economic growth in China, (2) investigate the sources of productivity growth in the reforming Chinese economy, and (3) shed some light on the trend of convergence and catch-up in terms of productivity performance among China's regional economies in the 1980s and 1990s.