Measuring technical efficiency in the presence of pesticide spillovers and production uncertainty: The case of Dutch arable farms

Pesticides’ dynamic effects and production uncertainty play an important role in farmers’ production decisions. Pesticides have a current production impact through reducing crop damage in the current period and a future impact through impacting the farm biodiversity which alters the future production environment. This study presents the difference in inefficiency arising from models that ignore the dynamic effects of pesticides in production decisions and the impact of production uncertainty. A dynamic data envelopment analysis (DEA) model is applied to outputs, inputs, and undesirables of Dutch arable farms over the period 2003–2007. A bootstrap approach is used to explain farmers’ performance, providing empirical representations of the impact of stochastic elements on production. These empirical representations are used to adjust firms’ inefficiency scores to incorporate production uncertainty in efficiency evaluation. We find that efficiency increased dramatically when a production technology representation that considers both pesticides’ dynamic impacts, and production uncertainty is adopted.     

Measuring the impacts of production risk on technical efficiency: A state-contingent conditional order-m approach

This article studies the influence of risk on farms’ technical efficiency levels. The analysis extends the order-m efficiency scores approach proposed by Daraio and Simar (2005) to the state-contingent framework. The empirical application focuses on cross section data of Catalan specialized crop farms from the year 2011. Results suggest that accounting for production risks increases the technical performance. A 10% increase in output risk will result in a 2.5% increase in average firm technical performance.     

Measuring technical and environmental efficiency in a state-contingent technology

Most developed countries support farming activities through policies that are tailored to meet their specific social, economic and environmental objectives. Economic and environmental efficiency have recently become relevant targets of most of these policies, whose sound implementation can be enhanced by monitoring farm performance from a multidimensional perspective. This paper proposes farm-level technical and environmental efficiency measures that recognize the stochastic conditions in which production takes place. A state-contingent framework is used to model production uncertainty. An implementable representation of the technology is developed using data envelopment analysis. The application focuses on a sample of Catalan arable crop farms. Results suggest that technical efficiency is slightly lower in bad than in good growing conditions. Nitrogen pollution can decrease substantially more under good than bad growing conditions.     

Nonparametric measurement of productivity and efficiency in education

Nondiscretionary environmental inputs are critical in explaining relative efficiency differences and productivity changes in public sector applications. For example, the literature on education production shows that school districts perform better when student poverty is lower. In this paper, we extend the nonparametric approach to decompose the Malmquist Productivity Index suggested by Färe et al. (American Economic Rewiew 84:66–83, 1994) into efficiency, technological and environmental changes. The approach is applied to analyze educational production of Ohio school districts. Applying the extended approach in an analysis of the educational production of 604 school districts in Ohio, we find changes in environmental harshness are the primary drivers in productivity changes of underperforming school districts, while technical progress drives the performance of top performing school districts.     

Improving envelopment in Data Envelopment Analysis under variable returns to scale

In a Data Envelopment Analysis model, some of the weights used to compute the efficiency of a unit can have zero or negligible value despite of the importance of the corresponding input or output. This paper offers an approach to preventing inputs and outputs from being ignored in the DEA assessment under the multiple input and output VRS environment, building on an approach introduced in Allen and Thanassoulis (2004) for single input multiple output CRS cases. The proposed method is based on the idea of introducing unobserved DMUs created by adjusting input and output levels of certain observed relatively efficient DMUs, in a manner which reflects a combination of technical information and the decision maker’s value judgements. In contrast to many alternative techniques used to constrain weights and/or improve envelopment in DEA, this approach allows one to impose local information on production trade-offs, which are in line with the general VRS technology. The suggested procedure is illustrated using real data.     

Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments

Demand fluctuations that cause variations in output levels will affect a firm’s technical inefficiency. To assess this demand effect, a demand-truncated production function is developed and an “effectiveness” measure is proposed. Often a firm can adjust some input resources influencing the output level in an attempt to match demand. We propose a short-run capacity planning method, termed proactive data envelopment analysis, which quantifies the effectiveness of a firm’s production system under demand uncertainty. Using a stochastic programming DEA approach, we improve upon short-run capacity expansion planning models by accounting for the decreasing marginal benefit of inputs and estimating the expected value of effectiveness, given demand. The law of diminishing marginal returns is an important property of production function; however, constant marginal productivity is usually assumed for capacity expansion problems resulting in biased capacity estimates. Applying the proposed model in an empirical study of convenience stores in Japan demonstrates the actionable advice the model provides about the levels of variable inputs in uncertain demand environments. We conclude that the method is most suitable for characterizing production systems with perishable goods or service systems that cannot store inventories.     

An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs

Based on the minimal reduction strategy, Yang et al. (2011) developed a fixed-sum output data envelopment analysis (FSODEA) approach to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs. However, in terms of such a strategy, all DMUs compete over fixed-sum outputs with “no memory” that will result in differing efficient frontiers’ evaluations. To address the problem, in this study, we propose an equilibrium efficiency frontier data envelopment analysis (EEFDEA) approach, by which all DMUs with fixed-sum outputs can be evaluated based on a common platform (or equilibrium efficient frontier). The proposed approach can be divided into two stages. Stage 1 constructs a common evaluation platform via two strategies: an extended minimal adjustment strategy and an equilibrium competition strategy. The former ensures that original efficient DMUs are still efficient, guaranteeing the existence of a common evaluation platform. The latter makes all DMUs achieve a common equilibrium efficient frontier. Then, based on the common equilibrium efficient frontier, Stage 2 evaluates all DMUs with their original inputs and outputs. Finally, we illustrate the proposed approach by using two numerical examples.     

Network DEA efficiency in input–output models: With an application to OECD countries

We undertake network efficiency analysis within an input–output model that allows us to assess potential technical efficiency gains by comparing technologies corresponding to different economies. Input–output tables represent a network where different sectoral nodes use primary inputs (endowments) to produce intermediate input and outputs (according to sectoral technologies), and satisfy final demand (preferences). Within the input–output framework it is possible to optimize primary inputs allocation, intermediate production and final demand production by way of non-parametric data envelopment analysis (DEA) techniques. DEA allows us to model the different subtechnologies corresponding to alternative production processes, to assess efficient resource allocation among them, and to determine potential output gains if inefficiencies were dealt with. The proposed model optimizes the underlying multi-stage technologies that the input–output system comprises identifying the best practice economies. The model is applied to a set of OECD countries.     

Information theory approach in efficiency measurement

The current non–parametric method of measuring productive efficiency of input–output systems is generalized here in the stochastic case in terms of an information theory approach based on the concept of entropy. Use of maximum entropy as a method of finding the most probable distribution of the input–output data set and as a predictive criterion is illustrated for production systems with multiple inputs and outputs.     

Improving weak efficiency frontiers in the fuzzy data envelopment analysis models

Evaluating the performance of activities or organization by common data envelopment analysis models requires crisp input/output data. However, the precise inputs and outputs of production processes cannot be always measured. Thus, the data envelopment analysis measurement containing fuzzy data, called “fuzzy data envelopment analysis”, has played an important role in the evaluation of efficiencies of real applications. This paper focuses on the fuzzy CCR model and proposes a new method for determining the lower bounds of fuzzy inputs and outputs. This improves the weak efficiency frontiers of the corresponding production possibility set. Also a numerical example illustrates the capability of the proposed method.     

Estimating technical and allocative efficiency in the public sector: A nonparametric analysis of Dutch schools

Public sector output provision is influenced not only by discretionary inputs but also by exogenous environmental factors. In this paper, we extended the literature by developing a conditional DEA estimator of allocative efficiency that allows a decomposition of overall cost efficiency into allocative and technical components while simultaneously controlling for the environment. We apply the model to analyze technical and allocative efficiency of Dutch secondary schools. The results reveal that allocative efficiency represents a significant 37 percent of overall cost efficiency on average, although technical inefficiency is still the dominant part. Furthermore, the results show that the impact of environment largely differs between schools and that having a more unfavorable environment is very expensive to schools. These results highlight the importance of including environmental variables in both technical and allocative efficiency analysis.     

The weighted Russell measure of technical efficiency

Theoretical consideration of technical efficiency has existed since Koopmans [10] defined it for production possibilities for which it is not possible to increase any output without simultaneously increasing any input, ceteris paribus. The nonparametric approach to efficiency measurement known as Data Envelopment Analysis is based on the index of Farrell [9], which measures radial reduction in all inputs consistent with observed output. Even after Farrell efficiency is achieved, however, there may exist additional slack in individual inputs, suggesting that the Farrell index does not necessarily measure Koopmans inefficiency. To solve this problem, the non-radial Russell measure was introduced. This paper shows that problems may arise with the Russell measure due to restrictive assumptions on the implicit weighting of inputs and outputs. This paper develops a new measure, the Weighted Russell measure, that relaxes this assumption. Using simulated data, the new measure is shown to be preferred to existing methods. In addition, the new method is applied to analyze the performance of New York State school districts.     

Analysing production and environmental risks in arable farming systems: A mathematical approach

In response to a growing environmental concern in Dutch society, sustainable production systems in arable farming have been developed. Amongst other things, a reduction of the dependency on chemical inputs is attempted. This paper addresses the role of risk in the adoption by farmers of new systems by means of a model that determines differences in production risks between conventional and sustainable farming systems (CAFS and IAFS).Timing of activities – setting out a management track – is particularly important in sustainable arable farming systems. Resource requirements of crop husbandry activities mainly depend on weather conditions. To assess risks caused by weather conditions, the major aspects of crop husbandry in various crops have been modelled. Using tactics in crop husbandry (decision rules) and weather uncertainty as input, crop husbandry models (HMs) calculate management tracks that require resources. The value distributions of resource requirements of crop husbandry according to different farming systems is calculated in different HMs represented by stochastic dynamic directed networks. Hence, production risks of CAFS and IAFS can be compared.On a farm, all the aspects of crop husbandry in the various crops are to be taken into account. Given the weather conditions, tactics for all the aspects are combined in an LP model of the whole farm where they compete for limited resources. In the LP model, tactics are re-assessed by means of the HMS, using information of the LP solution. This iterative procedure enables production risks of CAFS and IAFS to be compared, considering fixed, allocatable resources for the whole farm firm.     

Estimation of production technology when the objective is to maximize return to the outlay

This paper deals with estimation of production technology where endogeneous choice of input and output variables is explicitly recognized. To address this endogeneity issue, we assume that producers maximize return to the outlay. We start from a flexible (translog) transformation function with a single output and multiple inputs and show how the first-order conditions of maximizing return to the outlay can be used to come up with an ‘estimating equation’ that does not suffer from the econometric endogeneity problem although the output and input variables are chosen endogenously. This is because the regressors in this estimating equation are in ratio forms which are uncorrelated with the error term under the assumption that producers maximize return to the outlay. The analysis is then extended to the multiple outputs and multiple inputs case with technical inefficiency. Although the estimating equations in both single and multiple output cases are neither production nor distance functions, they can be estimated in a straightforward manner using the standard stochastic frontier technique without worrying about endogeneity of the regressors. Thus, we provide a rationale for estimating the technology parameters consistently using an econometric model which requires data on only input and output quantities.     

Joint economic design of EWMA control charts for mean and variance

Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi’s quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance.     

Is public capital really productive? A methodological reappraisal

We present an evaluation of the main empirical approaches used in the literature to estimate the contribution of public capital stock to growth and private factors’ productivity. Based on a simple stochastic general equilibrium model, built as to reproduce the main long-run relations observed in US post-war historical data, we show that the production function approach may not be reliable to estimate this contribution. Our analysis reveals that this approach largely overestimates the public capital elasticity, given the presence of a common stochastic trend shared by all non-stationary inputs.     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

On the potential balance among compulsory education outcomes through econometric and multiobjective programming analysis

This paper sheds new light on the relationship between inputs and outputs in the framework of the educational production function. In particular, it is geared at gaining a better understanding of which factors may be affected in order to achieve an optimal educational output level. With this objective in mind, we analyze teacher-based assessments (actual marks) in three different subjects using a multiobjective schema. For much of the analysis we use data from a recent (2010) Survey – ESOC10, linked with the results from an educational assessment program conducted among 11 and 15 year-old students and with the administrative records on teacher-based scores. Following the statistical and econometric analysis of these data, they are used to build a multiobjective mixed integer model. A reference point approach is used to determine the profile of, potentially, the most “successful and balanced” students in terms of educational outcomes. This kind of methodology in multiobjective programming allows generating “very balanced” solutions in terms of the objective values (subjects). Finally, a sensitivity analysis is used to determine policies that can be carried out in order to improve the performance levels of primary and secondary education students. Particularly, policy makers should be more concerned with the need to promote some cultural habits – such as reading –, from both the students’ and parents’ side. Additionally, policy efforts should be focused on making the vocational pathways available to Spanish youth more appealing, with the aim of taking advantage of the particular skills of students not succeeding in the academic track.     

Random effects logistic regression model for ranking efficiency in data envelopment analysis

Ranking efficiency based on data envelopment analysis (DEA) results can be used for grouping decision-making units (DMUs). The resulting group membership can be partly related to the environmental characteristics of DMU, which are not used either as input or output. Utilizing the expert knowledge on super efficiency DEA results, we propose a multinomial Dirichlet regression model, which can be used for the purpose of selection of new projects. A case study is presented in the context of ranking analysis of new information technology commercialization projects. It is expected that our proposed approach can complement the DEA ranking results with environmental factors and at the same time it facilitates the prediction of efficiency of new DMUs with only given environmental characteristics.     

Pro-efficiency: Data speak more than technical efficiency

In this study, we demonstrate a new method of addressing efficiency in situations in which only the input and output data are available, while evaluating efficiency more accurately than is possible via the ordinary data envelopment analysis (DEA). Technical efficiency is important, but management always desires information regarding the profit aspects of performance. In practice, however, the precise price data are frequently unavailable. Is it possible to approximate profit efficiency in the absence of price information? We develop a simple and usable approach, a linear programming model, for the evaluation of profit efficiency. Our approach implies technical efficiency in DEA and gives rise to the upper bound of profit efficiency, referred to as pro-efficiency. We also report a successful application of our method to a securities company, in which a comparison of the actual profit data and the pro-efficiency measures of the company’s branches demonstrates a significant correlation.