Nonparametric estimation of the determinants of inefficiency

We consider the benchmark stochastic frontier model where inefficiency is directly influenced by observable determinants. In this setting, we estimate the stochastic frontier and the conditional mean of inefficiency without imposing any distributional assumptions. To do so we cast this model in the partly linear regression framework for the conditional mean. We provide a test of correct parametric specification of the scaling function. An empirical example is also provided to illustrate the practical value of the methods described here.     

Consistent inference in fixed-effects stochastic frontier models

The classical stochastic frontier panel data models provide no mechanism to disentangle individual time invariant unobserved heterogeneity from inefficiency. Greene (2005a, b) proposed the so-called “true” fixed-effects specification that distinguishes these two latent components. However, due to the incidental parameters problem, his maximum likelihood estimator may lead to biased variance estimates. We propose two alternative estimators that achieve consistency for $n\to \infty$ with fixed $T$. Furthermore, we extend the Chen et al. (2014) results providing a feasible estimator when the inefficiency is heteroskedastic and follows a first-order autoregressive process. We investigate the behavior of the proposed estimators through Monte Carlo simulations showing good finite sample properties, especially in small samples. An application to hospitals’ technical efficiency illustrates the usefulness of the new approach.     

Model selection in stochastic frontier analysis with an application to maize production in Kenya

This paper shows how to compute the standard errors for partial effects of exogenous firm characteristics influencing firm inefficiency under a range of popular stochastic frontier model specifications. We also develop an R²-type measure to summarize the overall explanatory power of the exogenous factors on firm inefficiency. The paper also applies a recently developed model selection procedure to choose among alternative stochastic frontier specifications using data from household maize production in Kenya. The magnitude of estimated partial effects of exogenous household characteristics on inefficiency turns out to be very sensitive to model specification, and the model selection procedure leads to an unambiguous choice of best model. We propose a bootstrapping procedure to evaluate the size and power of the model selection procedure. The empirical application also provides further evidence on how household characteristics influence technical inefficiency in maize production in developing countries.

On measures of technical inefficiency and production uncertainty in stochastic frontier production model with correlated error components

Analysis of the behavior of technical inefficiency with respect to parameters and variables of a stochastic frontier model is a neglected area of research in frontier literature. An attempt in this direction, however, has recently been made. It has been shown that in a “standard” stochastic frontier model that both the firm level technical inefficiency and the production uncertainty are monotonically decreasing with observational error. In this paper we show, considering a stochastic frontier model whose error components are jointly distributed as truncated bivariate normal, that this property holds if and only if the distribution of observational error is negatively skewed. We also derive a necessary and sufficient condition under which both firm level technical inefficiency and production uncertainty are monotonically increasing with noise-inefficiency correlation. We next propose a new measure of the industry level production uncertainty and establish the necessary and sufficient condition for firm level technical inefficiency and production uncertainty to be monotonically increasing with industry level production uncertainty. We also study the limiting probabilistic behavior of these conditions under different parametric configuration of our model. Finally we carry out Monte Carlo simulations to study the sample behavior of the population monotonic property of the firm level technical inefficiency and production uncertainty in our model.

Estimation and testing of stochastic frontier models using variational Bayes

We show how a wide range of stochastic frontier models can be estimated relatively easily using variational Bayes. We derive approximate posterior distributions and point estimates for parameters and inefficiency effects for (a) time invariant models with several alternative inefficiency distributions, (b) models with time varying effects, (c) models incorporating environmental effects, and (d) models with more flexible forms for the regression function and error terms. Despite the abundance of stochastic frontier models, there have been few attempts to test the various models against each other, probably due to the difficulty of performing such tests. One advantage of the variational Bayes approximation is that it facilitates the computation of marginal likelihoods that can be used to compare models. We apply this idea to test stochastic frontier models with different inefficiency distributions. Estimation and testing is illustrated using three examples.     

Cost efficiency of Slovenian water distribution utilities: an application of stochastic frontier methods

This study estimates cost inefficiency and economies of scale of Slovenian water distribution utilities over the 1997–2003 period by employing several different stochastic frontier methods. The results indicate that significant cost inefficiencies are present in the utilities. An introduction of incentive-based price regulation scheme might help resolve this problem. However, the inefficiency scores obtained from different cost frontier models are not found to be robust. The levels of inefficiency estimates as well as the rankings depend on the econometric specification of the model. The established lack of robustness can be at least partly explained by different ability of the models to separate unobserved heterogeneity from inefficiency. Newly proposed true fixed effects model (Greene, J Econom 126:269–303, 2005; J Prod Anal 23(1):7–32, 2005) appears to perform better than the conventional panel data models with respect to distinguishing between unobserved heterogeneity and inefficiency. On the other hand, different models produce fairly robust results with respect to estimates of economies of output density, customer density and economies of scale. The optimal size of a company is found to closely corresponds to the sample median. Economies of scale are found in small-sized utilities, while large companies exhibit diseconomies of scale.

Misspecification Preferred: The Sensitivity of Inefficiency Rankings

Ruggiero (European Journal of Operational Research 115, 555–563. 1999) compared the two popular parametric frontier methods for cross-sectional data—the stochastic frontier and the corrected OLS—in a simulation study. He demonstrated that the inefficiency ranking accuracy of the established stochastic frontier is uniformly inferior to that of the misspecified Corrected OLS (COLS) (which lacks an error term). The reason for his result remains unclear, however. In this paper, a more extensive simulation study is therefore conducted to find out whether the superiority of COLS is simply due to small sample sizes or to poor performance of the inefficiency level estimator.JEL Classification: C1,C2,C5     

Decomposition of technical efficiency under fixed proportion technologies: an application of data envelopment analysis

In this paper, we extend the four-component stochastic frontier model to allow for global spatial dependence via the endogenous spatial autoregressive variable. Our proposed model is more general than the model considered by (Glass et al., 2016) in the sense that we include a random effect as well as a permanent efficiency component. With the spatial autoregressive specification, our model is able to capture the asymmetric efficiency spillovers and also decompose the persistent/transient inefficiencies into direct and indirect efficiencies. Moreover, we also investigate the marginal effects of the exogenous variables on the persistent/transient efficiency. We suggest a maximum simulated likelihood method to estimate the frontier parameters of the model, and we predict the efficiencies using the simulated estimator. Monte Carlo simulations reveal that the suggested estimator performs well in finite samples. An empirical application is considered to illustrate the usefulness of our proposed model and method.

     

Nonparametric least squares methods for stochastic frontier models

When analyzing productivity and efficiency of firms, stochastic frontier models are very attractive because they allow, as in typical regression models, to introduce some noise in the Data Generating Process . Most of the approaches so far have been using very restrictive fully parametric specified models, both for the frontier function and for the components of the stochastic terms. Recently, local MLE approaches were introduced to relax these parametric hypotheses. In this work we show that most of the benefits of the local MLE approach can be obtained with less assumptions and involving much easier, faster and numerically more robust computations, by using nonparametric least-squares methods. Our approach can also be viewed as a semi-parametric generalization of the so-called “modified OLS” that was introduced in the parametric setup. If the final evaluation of individual efficiencies requires, as in the local MLE approach, the local specification of the distributions of noise and inefficiencies, it is shown that a lot can be learned on the production process without such specifications. Even elasticities of the mean inefficiency can be analyzed with unspecified noise distribution and a general class of local one-parameter scale family for inefficiencies. This allows to discuss the variation in inefficiency levels with respect to explanatory variables with minimal assumptions on the Data Generating Process.     

Estimating production frontiers and efficiency when output is a discretely distributed economic bad

This article studies the estimation of production frontiers and efficiency scores when the commodity of interest is an economic bad with a discrete distribution. Existing parametric econometric techniques (stochastic frontier methods) assume that output is a continuous random variable but, if output is discretely distributed, then one faces a scenario of model misspecification. Therefore a new class of econometric models has been developed to overcome this problem. The Delaporte subclass of models is studied in detail, and tests of hypotheses are proposed to discriminate among parametric models. In particular, Pearson’s chi-squared test is adapted to construct a new kernel-based consistent Pearson test. A Monte Carlo experiment evaluates the merits of the new model and methods, and these are used to estimate the frontier and efficiency scores of the production of infant deaths in England. Extensions to the model are discussed.     

Estimating fixed-effect panel stochastic frontier models by model transformation

Traditional panel stochastic frontier models do not distinguish between unobserved individual heterogeneity and inefficiency. They thus force all time-invariant individual heterogeneity into the estimated inefficiency. Greene (2005) proposes a true fixed-effect stochastic frontier model which, in theory, may be biased by the incidental parameters problem. The problem usually cannot be dealt with by model transformations owing to the nonlinearity of the stochastic frontier model. In this paper, we propose a class of panel stochastic frontier models which create an exception. We show that first-difference and within-transformation can be analytically performed on this model to remove the fixed individual effects, and thus the estimator is immune to the incidental parameters problem. Consistency of the estimator is obtained by either N→∞$N\to \infty$ or T→∞$T\to \infty$, which is an attractive property for empirical researchers.     

Fixed and Random Effects in Stochastic Frontier Models

Received stochastic frontier analyses with panel data have relied on traditional fixed and random effects models. We propose extensions that circumvent two shortcomings of these approaches. The conventional panel data estimators assume that technical or cost inefficiency is time invariant. Second, the fixed and random effects estimators force any time invariant cross unit heterogeneity into the same term that is being used to capture the inefficiency. Inefficiency measures in these models may be picking up heterogeneity in addition to or even instead of inefficiency. A fixed effects model is extended to the stochastic frontier model using results that specifically employ the nonlinear specification. The random effects model is reformulated as a special case of the random parameters model. The techniques are illustrated in applications to the U.S. banking industry and a cross country comparison of the efficiency of health care delivery.JEL classification: C1, C4     

Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia

This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.

     

Influences of the Business Environment on Manufacturing Firms Technical Efficiencies: The Côte d’Ivoire Case

An unbalanced panel is used to estimate technical and managerial efficiency levels of manufacturing firms in Côte d’Ivoire. A stochastic frontier production model with non-neutral effects on technical efficiency of the business environment variables is specified. This specification allows to evaluate and to compare technical efficiencies and efficiency levels net of business environment influences. In order to determine net efficiency levels in the non-neutral case, a practical method based on the definition of an artificial environment is proposed. Results suggest that informal firms are less technically efficient than formal firms whereas their managerial performances are closed to those of formal firms.     

Managerial and program inefficiency for European meat manufacturing firms: A dynamic multidirectional inefficiency analysis approach

This paper proposes a dynamic multidirectional inefficiency analysis approach within the context of Data Envelopment Analysis to measuring input- and investment-specific managerial and program inefficiency for groups of firms characterized by different technologies. Dynamic managerial inefficiency refers to the distance to the firms’ group-specific dynamic frontier of best practices, and dynamic program inefficiency measures the difference between the group-specific dynamic frontier and the pooled dynamic frontier. The empirical application focuses on panel data of large meat processing firms in Eastern, Western and Southern Europe over the period 2005–2012. The results show that Eastern European firms have the highest dynamic managerial inefficiency for all inputs, but have the smallest values for dynamic program inefficiency. Western European firms perform worst in terms of program inefficiency for all inputs, while Southern European firms are the best with regard to dynamic managerial inefficiency. The results also reveal that regardless the dynamic inefficiency dimension considered, investments is the most inefficient input, followed by labor, and materials.     

When is Effort Contagious in New Venture Management Teams? Understanding the Contingencies of Social Motivation Theory

Consistent with social motivation theory, prior research on managerial motivation suggests that effort is contagious across management team members. In this study, we draw on belongingness theory to develop a model on important boundary conditions to social motivation theory in the management team context. The model predicts that new venture managers react to their teammates’ higher effort levels by investing higher effort levels themselves primarily when they are confronted with a threat – namely, low venture performance and high environmental hostility – but that effort is less contagious when managers face little threat. We test our model with a sample of 103 new venture managers nested in 51 management teams in a longitudinal setting capturing managerial effort over 26 weeks. While we do not find a direct relationship between teammates’ effort and a new venture manager’s subsequent effort, we find support for the crucial role of threat in triggering the contagion of managerial effort. We discuss the contributions of our study for research on management teams, performance feedback, and entrepreneurial effort in new ventures.     

Does Managerial Ability Really Drive Cost Efficiency? Evidence from Broiler Businesses

This paper ascertains whether managerial ability really drives cost efficiency of broiler businesses. Data was collected from 354 broiler businesses in Ghana and analysed using a modified stochastic Cobb–Douglas cost frontier and inefficiency effect models in a single‐stage maximum likelihood estimation procedure. Results indicate that managerial abilities such as technical advice, age and experience acquired through full‐time farming and increased batches significantly drive cost efficiency. This highlights the need to provide more technical advice and implement periodic capacity building programmes to develop the managerial ability and competences of broiler producers. The youth should also be encouraged and supported through skills development fund to go into full‐time broiler business to produce more batches. Copyright © 2016 John Wiley & Sons, Ltd.     

Technological inefficiency indexes: a binary taxonomy and a generic theorem

Over the years following Debreu’s (1951) seminal formulation of a “coefficient of resource utilization”, a large number of indexes of technological inefficiency have been specified and a spate of papers has examined the properties satisfied by these indexes. This paper approaches the subject more synthetically, presenting generic results on classes of indexes and their properties. In particular, we consider a broad class of indexes containing almost all known indexes and a partition of this class into two subsets, slacks-based indexes and path-based indexes. Slacks-based indexes are expressed in terms of additive or multiplicative slacks for all inputs and outputs, and particular indexes are generated by specifying the form of aggregation over the coordinate-wise slacks. Path-based indexes are expressed in terms of a common contraction/expansion factor, and particular indexes are generated by specifying the form of the path to the frontier of the technology. Owing to an impossibility result in one of our earlier papers, we know that the set of all inefficiency indexes can be partitioned into three subsets: those that satisfy continuity (in quantities and technologies) and violate indication (equal to some specified value if and only if the quantity vector is efficient), those that satisfy indication and violate continuity, and those that satisfy neither. We prove two generic theorems establishing the equivalence of these two partitions: all slacks-based indexes satisfy indication and hence violate continuity, and all path-based indexes satisfy continuity and hence violate indication. We also discuss the few indexes that do not belong to either of these two sets. Our hope is that these results will help guide decisions about specification of the form of efficiency indexes used in empirical analysis.     

Does school ownership matter? An unbiased efficiency comparison for regions of Spain

The programme for international student assessment (PISA) 2006 Report (OECD, PISA 2006: science competencies for tomorrow’s world, Organisation for Economic Co-operation and Development, Paris in 2007) showed significant differences among Spanish students attending publicly financed schools. Publicly financed schools include entirely public schools and schools that are privately managed but publicly funded. Families with a lower socioeconomic status may self-select into public schools, so a direct efficiency comparison between the two school types could lead to flawed conclusions because of the possible school selection bias. In this paper, we suggest using a propensity score matching approach in order to correctly analyze the impact of school ownership on student performance. After tackling the self-selection problem, we use a stochastic parametric distance function framework to compare student efficiency and productivity in both school types across ten Spanish regions using PISA 2006 data. Furthermore, we propose two original measures to analyze the impact of school ownership on academic performance across regions: the average treatment effect on the treated on the production frontier and the average treatment effect on the treated assuming school inefficiency. We find that, on average, private government-dependent schools are more productive than public schools, although efficiency results across regions are highly divergent.     

A Bayesian estimator for stochastic frontier models with errors in variables

A Bayesian estimator is proposed for a stochastic frontier model with errors in variables. The model assumes a truncated-normal distribution for the inefficiency and accommodates exogenous determinants of inefficiency. An empirical example of Tobin??s Q investment model is provided, in which the Q variable is known to suffer from measurement error. Results show that correcting for measurement error in the Q variable has an important effect on the estimation results.