Constrained nonparametric estimation of input distance function

This paper proposes a constrained nonparametric method of estimating an input distance function. A regression function is estimated via kernel methods without functional form assumptions. To guarantee that the estimated input distance function satisfies its properties, monotonicity constraints are imposed on the regression surface via the constraint weighted bootstrapping method borrowed from statistics literature. The first, second, and cross partial analytical derivatives of the estimated input distance function are derived, and thus the elasticities measuring input substitutability can be computed from them. The method is then applied to a cross-section of 3,249 Norwegian timber producers.

The efficiency and productivity of Malaysian banks:an output distance function approach

This study employs stochastic frontier analysis to analyze Malaysian commercial banks during 1996-2002, and particularly focuses on determining the impact of Islamic banking on performance. We derive both net and gross efficiency estimates, thereby demonstrating that differences in operating characteristics explain much of the difference in outputs between Malaysian banks. We also decompose productivity change into efficiency, technical, and scale change using a generalised Malmquist productivity index. On average, Malaysian banks experience mild decreasing return to scale and annual productivity change of 2.37 percent, with the latter driven primarily by technical change, which has declined over time. Our gross efficiency estimates suggest that Islamic banking is associated with higher input requirements. In addition, our productivity estimates indicate that the potential for full-fledged Islamic banks and conventional banks with Islamic banking operations to overcome the output disadvantages associated with Islamic banking are relatively limited. Merged banks are found to have higher input usage and lower productivity change, suggesting that bank mergers have not contributed positively to bank performance. Finally, our results suggest that while the East Asian financial crisis had an interim output-increasing effect in 1998, the crisis prompted a continuing negative impact on the output performance by increasing the volume of non-performing loans.

Malmquist indexes using a geometric distance function (GDF)

Traditional approaches to calculate total factor productivity change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate total factor productivity change may introduce some bias in the analysis, and therefore we propose a procedure that calculates total factor productivity change through observed values only. Our total factor productivity change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared.

Malmquist indexes using a geometric distance function (GDF):application to a sample of Portuguese bank branches

Traditional approaches to calculate total factor productivity (TFP) change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate TFP change may introduce some bias in the analysis, and therefore we propose a procedure that calculates TFP change through observed values only. Our total TFP change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared. The proposed approach is applied in this paper to a sample of Portuguese bank branches.

Determining the contribution of technical change, efficiency change and scale change to productivity growth in the privatized English and Welsh water and sewerage industry:1985-2000

The water and sewerage industry of England and Wales was privatized in 1989 and subjected to a new regime of environmental, water quality and RPI+K price cap regulation. This paper estimates a quality-adjusted input distance function, with stochastic frontier techniques in order to estimate productivity growth rates for the period 1985-2000. Productivity is decomposed so as to account for the impact of technical change, efficiency change, and scale change. Compared with earlier studies by Saal and Parker [(2000) Managerial Decision Econ 21(6):253-268, (2001) J Regul Econ 20(1): 61-90], these estimates allow a more careful consideration of how and whether privatization and the new regulatory regime affected productivity growth in the industry. Strikingly, they suggest that while technical change improved after privatization, productivity growth did not improve, and this was attributable to efficiency losses as firms appear to have struggled to keep up with technical advances after privatization. Moreover, the results also suggest that the excessive scale of the WaSCs contributed negatively to productivity growth. © 2007 Springer Science+Business Media, LLC.

Estimation of TFP growth:a semiparametric smooth coefficient approach

This article uses a semiparametric smooth coefficient model (SPSCM) to estimate TFP growth and its components (scale and technical change). The SPSCM is derived from a nonparametric specification of the production technology represented by an input distance function (IDF), using a growth formulation. The functional coefficients of the SPSCM come naturally from the model and are fully flexible in the sense that no functional form of the underlying production technology is used to derive them. Another advantage of the SPSCM is that it can estimate bias (input and scale) in technical change in a fully flexible manner. We also used a translog IDF framework to estimate TFP growth components. A panel of U.S. electricity generating plants for the period 1986–1998 is used for this purpose. Comparing estimated TFP growth results from both parametric and semiparametric models against the Divisia TFP growth, we conclude that the SPSCM performs the best in tracking the temporal behavior of TFP growth.

Developing a decomposable measure of profit efficiency using DEA

In for-profit organizations efficiency measurement with reference to the potential for profit augmentation is particularly important as is its decomposition into technical, and allocative components. Different profit efficiency approaches can be found in the literature to measure and decompose overall profit efficiency. In this paper, we highlight some problems within existing approaches and propose a new measure of profit efficiency based on a geometric mean of input/output adjustments needed for maximizing profits. Overall profit efficiency is calculated through this efficiency measure and is decomposed into its technical and allocative components. Technical efficiency is calculated based on a non-oriented geometric distance function (GDF) that is able to incorporate all the sources of inefficiency, while allocative efficiency is retrieved residually. We also define a measure of profitability efficiency which complements profit efficiency in that it makes it possible to retrieve the scale efficiency of a unit as a component of its profitability efficiency. In addition, the measure of profitability efficiency allows for a dual profitability interpretation of the GDF measure of technical efficiency. The concepts introduced in the paper are illustrated using a numerical example.

Efficiency in Islamic and conventional banking:an international comparison

The paper investigates the efficiency of a sample of Islamic and conventional banks in 10 countries that operate Islamic banking for the period 1996–2002, using an output distance function approach. We obtain measures of efficiency after allowing for environmental influences such as country macroeconomic conditions, accessibility of banking services and bank type. While these factors are assumed to directly influence the shape of the technology, we assume that country dummies and bank size directly influence technical inefficiency. The parameter estimates highlight that during the sample period, Islamic banking appears to be associated with higher input usage. Furthermore, by allowing for bank size and international differences in the underlying inefficiency distributions, we are also able to demonstrate statistically significant differences in inefficiency related to these factors even after controlling for specific environmental characteristics and Islamic banking. Thus, for example, our results suggest that Sudan and Yemen have relatively higher inefficiency while Bahrain and Bangladesh have lower estimated inefficiency. Except for Sudan, where banks exhibits relatively strong returns to scale, most sample banks exhibit very slight returns to scale, although Islamic banks are found to have moderately higher returns to scale than conventional banks. While this suggests that Islamic banks may benefit from increased scale, we would emphasize that our results suggest that identifying and overcoming the factors that cause Islamic banks to have relatively low potential outputs for given input usage levels will be the key challenge for Islamic banking in the coming decades.

Efficiency in Islamic and conventional banking:an international comparison

The paper investigates the efficiency of a sample of Islamic and conventional banks in 10 countries that operate Islamic banking for the period 1996 to 2002, using an output distance function approach. We obtain measures of efficiency after allowing for environmental influences such as country macroeconomic conditions, accessibility of banking services and bank type. While these factors are assumed to directly influence the shape of the technology, we assume that country dummies directly influence technical inefficiency. The parameter estimates highlight that during the sample period, Islamic banking appear to be associated with higher input usage. Furthermore, by allowing for international differences in the underlying inefficiency distributions, we are also able to demonstrate statistically significant differences in efficiency across countries even after controlling for specific environmental characteristics and Islamic banking. Thus, for example, our results suggest that Sudan and Yemen have relatively higher inefficiency while Iran and Malaysia have lower estimated inefficiency. Except for Sudan, where banks exhibits relatively strong returns to scale, most sample banks exhibit very slight returns to scale, although Islamic banks are found to have moderately higher returns to scale than conventional banks. However while this suggests that Islamic banks may benefit from increased scale, we would emphasize that our results suggest that identifying and overcoming the factors that cause Islamic banks to have relatively high input requirements will be the key challenge for Islamic banking in the coming decades.

An improved conflicting evidence combination approach based on a new supporting probability distance

To avoid counter-intuitive result of classical Dempster's combination rule when dealing with highly conflict information, many improved combination methods have been developed through modifying the basic probability assignments (BPAs) of bodies of evidence (BOEs) by using a certain measure of the degree of conflict or uncertain information, such as Jousselme's distance, the pignistic probability distance and the ambiguity measure. However, if BOEs contain some non-singleton elements and the differences among their BPAs are larger than 0.5, the current conflict measure methods have limitations in describing the interrelationship among the conflict BOEs and may even lead to wrong combination results. In order to solve this problem, a new distance function, which is called supporting probability distance, is proposed to characterize the differences among BOEs. With the new distance, the information of how much a focal element is supported by the other focal elements in BOEs can be given. Also, a new combination rule based on the supporting probability distance is proposed for the combination of the conflicting evidences. The credibility and the discounting factor of each BOE are generated by the supporting probability distance and the weighted BOEs are combined directly using Dempster's rules. Analytical results of numerical examples show that the new distance has a better capability of describing the interrelationships among BOEs, especially for the highly conflicting BOEs containing non-singleton elements and the proposed new combination method has better applicability and effectiveness compared with the existing methods.

Malmquist-type indices in the presence of negative data:an application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.

Type-2 TOPSIS:a group decision problem when ideal values are not extreme endpoints

In the traditional TOPSIS, the ideal solutions are assumed to be located at the endpoints of the data interval. However, not all performance attributes possess ideal values at the endpoints. We termed performance attributes that have ideal values at extreme points as Type-1 attributes. Type-2 attributes however possess ideal values somewhere within the data interval instead of being at the extreme end points. This provides a preference ranking problem when all attributes are computed and assumed to be of the Type-1 nature. To overcome this issue, we propose a new Fuzzy DEA method for computing the ideal values and distance function of Type-2 attributes in a TOPSIS methodology. Our method allows Type-1 and Type-2 attributes to be included in an evaluation system without compromising the ranking quality. The efficacy of the proposed model is illustrated with a vendor evaluation case for a high-tech investment decision making exercise. A comparison analysis with the traditional TOPSIS is also presented. © 2012 Springer Science+Business Media B.V.

CO2 emissions reduction of Chinese light manufacturing industries:a novel RAM-based global Malmquist-Luenberger productivity index

Climate change has become one of the most challenging issues facing the world. Chinese government has realized the importance of energy conservation and prevention of the climate changes for sustainable development of China's economy and set targets for CO2 emissions reduction in China. In China industry contributes 84.2% of the total CO2 emissions, especially manufacturing industries. Data envelopment analysis (DEA) and Malmquist productivity (MP) index are the widely used mathematical techniques to address the relative efficiency and productivity of a group of homogenous decision making units, e.g. industries or countries. However, in many real applications, especially those related to energy efficiency, there are often undesirable outputs, e.g. the pollutions, waste and CO2 emissions, which are produced inevitably with desirable outputs in the production. This paper introduces a novel Malmquist-Luenberger productivity (MLP) index based on directional distance function (DDF) to address the issue of productivity evolution of DMUs in the presence of undesirable outputs. The new RAM (Range-adjusted measure)-based global MLP index has been applied to evaluate CO2 emissions reduction in Chinese light manufacturing industries. Recommendations for policy makers have been discussed.

Regression with input-dependent noise: A Gaussian process treatment

Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance.