Inference in dynamic stochastic frontier models

An important issue in models of technical efficiency measurement concerns the temporal behaviour of inefficiency. Consideration of dynamic models is necessary but inference in such models is complicated. In this paper we propose a stochastic frontier model that allows for technical inefficiency effects and dynamic technical inefficiency, and use Bayesian inference procedures organized around data augmentation techniques to provide inferences. Also provided are firm‐specific efficiency measures. The new methods are applied to a panel of large US commercial banks over the period 1989–2000. Copyright © 2006 John Wiley & Sons, Ltd.     

On the Determinants of School District Efficiency: Competition and Monitoring

A number of researchers have asserted that inefficiency in the U.S. school system arises from a lack of incentives for public schools to behave efficiently. This paper uses a Shephard input distance function to model educational production, and a switching-regressions estimation to explore the relationship between school district efficiency and two existing incentive mechanisms—competition and voter monitoring. We find evidence that ease of monitoring enhances both technical and allocative efficiency of urban school districts, and that increased competition reduces allocative inefficiency in communities above a competitive threshold. We find no evidence that competition is related to technical inefficiency.     

Goodness of fit tests in stochastic frontier models

In this paper we discuss goodness of fit tests for the distribution of technical inefficiency in stochastic frontier models. If we maintain the hypothesis that the assumed normal distribution for statistical noise is correct, the assumed distribution for technical inefficiency is testable. We show that a goodness of fit test can be based on the distribution of estimated technical efficiency, or equivalently on the distribution of the composed error term. We consider both the Pearson χ ² test and the Kolmogorov–Smirnov test. We provide simulation results to show the extent to which the tests are reliable in finite samples.     

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 of Technical Inefficiencies with Heterogeneous Technologies

This paper considers the measurement of firm's specific (in)efficiency while allows for the possible heterogeneous technologies adopted by different firms. A flexible stochastic frontier model with random coefficients is proposed to distinguish technical inefficiency from technological differences across firms. Posterior inference of the model is made possible via the simulation-based approach, namely, Markov chain Monte Carlo method. The model is applied to a real data set which has also been considered in Christensen and Greene (1976), Greene (1990), Tsionas (2002), among others. Empirical results show that the regression coefficients can vary across firms, indicating the adoption of heterogeneous technologies by different firms. More importantly, we find that, without considering this possible heterogeneity, the inefficiency of firms can be over-estimated.     

Estimation of a dynamic stochastic frontier model using likelihood-based approaches

This paper considers a panel stochastic production frontier model that allows the dynamic adjustment of technical inefficiency. In particular, we assume that inefficiency follows an AR(1) process. That is, the current year's inefficiency for a firm depends on its past inefficiency plus a transient inefficiency incurred in the current year. Interfirm variations in the transient inefficiency are explained by some firm-specific covariates. We consider four likelihood-based approaches to estimate the model: the full maximum likelihood, pairwise composite likelihood, marginal composite likelihood, and quasi-maximum likelihood approaches. Moreover, we provide Monte Carlo simulation results to examine and compare the finite-sample performances of the four above-mentioned likelihood-based estimators of the parameters. Finally, we provide an empirical application of a panel of 73 Finnish electricity distribution companies observed during 2008–2014 to illustrate the working of our proposed models.     

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.     

Decomposing profit change: Konüs,Bennet and Luenberger indicators

We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.     

Estimation of stochastic frontier production functions with input-oriented technical efficiency

This paper deals with estimation of input-oriented (IO) technical inefficiency using a stochastic production frontier model. Econometrically the model is similar to a class of models that arise in specifying technical inefficiency in cost-minimizing and profit-maximizing frameworks. The standard maximum likelihood (ML) method that is used to estimate output-oriented (OO) technical efficiency cannot be applied to estimate these models. We use a simulated ML approach to estimate the IO production function and compare results from the IO and OO models, mainly to emphasize the point that estimated efficiency, returns to scale, technical change, etc., differ depending on whether one uses the model with IO or OO technical inefficiency.     

Interpreting inefficiency ratings: An application of bank branch operating efficiencies

Data Envelopment Analysis is an analytical tool for evaluating the relative technical efficiency of a set of organizations with the same multiple inputs and outputs. This paper examines the correct interpretation of inefficiency scores in the Additive model of Data Envelopment Analysis. A contrived numerical example is offered to demonstrate that certain computational statements appearing in recent literature are not entirely correct. As rectification, a region of stability is defined that identifies sufficient conditions for altering a technical inefficiency classification to that of technical efficiency. Finally, this region of stability technique is applied to bank branch operating efficiencies to demonstrate managerial interpretations and policy implications.     

Stochastic frontier models with multiple time-varying individual effects

This paper proposes a flexible time-varying stochastic frontier model. Similarly to Lee and Schmidt [1993, In: Fried H, Lovell CAK, Schmidt S (eds) The measurement of productive efficiency: techniques and applications. Oxford University Press, Oxford], we assume that individual firms’ technical inefficiencies vary over time. However, the model, which we call the “multiple time-varying individual effects” model, is more general in that it allows multiple factors determining firm-specific time-varying technical inefficiencies. This allows the temporal pattern of inefficiency to vary over firms. The number of such factors can be consistently estimated. The model is applied to data on Indonesian rice farms, and the changes in the efficiency rankings of farms over time demonstrate the model’s flexibility.

Assessing bankruptcy prediction models via information content of technical inefficiency

We use a stochastic frontier model with firm-specific technical inefficiency effects in a panel framework (Battese and Coelli in Empir Econ 20:325–332, 1995) to assess two popular probability of bankruptcy (PB) measures based on Merton model (Merton in J Financ 29:449–470, 1974) and discrete-time hazard model (DHM; Shumway in J Bus 74:101–124, 2001). Three important results based on our empirical studies are obtained. First, a firm with a higher PB generally has less technical efficiency. Second, for an ex-post bankrupt firm, its PB tends to increase and its technical efficiency of production tends to decrease, as the time to its bankruptcy draws near. Finally, the information content about firm’s technical inefficiency provided by PB based on DHM is significantly more than that based on Merton model. By the last result and the fact that economic-based efficiency measures are reasonable indicators of the long-term health and prospects of firms (Baek and Pagán in Q J Bus Econ 41:27–41, 2002), we conclude that PB based on DHM is a better credit risk proxy of firms.     

Measuring technical and scale inefficiencies in the beer industry: Nonparametric and parametric evidence

Two alternative approaches of efficiency measurement, nonparametric and statistical, are employed to calculate three types of efficiency indexes for the U.S. beer industry over the period 1950–1986. The results indicate that the beer industry was operating at a high level of pure technical efficiency over that period. The mean value of this efficiency measure is 93.7 percent based on the nonparametric approach and 87.5 percent based on the statistical approach. The two approaches yield dissimilar values and sources for overall technical inefficiency. The overall technical efficiency index computed under the nonparametric approach stands at 91.10 percent and the observed inefficiency is found to be more due to pure technical inefficiency than to scale inefficiency. Using the statistical approach, the beer industry is found to be less overall technically efficient (68.42 percent) than indicated by the nonparametric methodology and the observed inefficiency is found to be primarily contributed to by scale inefficiency.     

Technical efficiency in competing panel data models: a study of Norwegian grain farming

Estimation of technical efficiency is widely used in empirical research using both cross-sectional and panel data. Although several stochastic frontier models for panel data are available, only a few of them are normally applied in empirical research. In this article we chose a broad selection of such models based on different assumptions and specifications of heterogeneity, heteroskedasticity and technical inefficiency. We applied these models to a single dataset from Norwegian grain farmers for the period 2004–2008. We also introduced a new model that disentangles firm effects from persistent (time-invariant) and residual (time-varying) technical inefficiency. We found that efficiency results are quite sensitive to how inefficiency is modeled and interpreted. Consequently, we recommend that future empirical research should pay more attention to modeling and interpreting inefficiency as well as to the assumptions underlying each model when using panel data.     

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.

     

Technical efficiency of Swedish employment offices

This paper studies technical efficiency for Swedish employment offices between 2004 and 2010. Efficiency is computed using a semi-dynamic DEA-framework. On the input side we include a measure of input quality and we also control for services that are carried out by private contractors. On the output side we are using both intermediate and final outputs. The motivation for using an intermediate output is to take into account the fact that employment offices might have strengthen the possibility for unemployed individuals that remain unemployed to get a job in the forthcoming year. The study identifies an average yearly inefficiency between 7 and 10 percent. It is also observed that the inefficiency is unevenly distributed. To make employment offices more efficient this uneven distribution needs to be considered, otherwise efforts to improve efficiency might instead result in increased inefficiency.     

Parametric estimation of inefficiency in cargo handling in Spanish ports

Port workers services have been usually heavily regulated and reserved exclusively for a special kind of workers, dockworkers, which seems to have been the cause of serious inefficiencies worldwide. During the eighties, law reforms have been introduced to solve this problem. In this paper we analyze and decompose efficiency in cargo handling operations in 19 Spanish ports from 1990 to 1998. The method chosen is that of the parametric estimation of both allocative and technical inefficiency using panel data and a quadratic cost function. Results show that although inefficiency has decreased overall, there has been over utilization of labor regarding capital, and technical inefficiency. This supports the need of further consideration of other aspects including competition.

Accounting for Environmental Influences in Stochastic Frontier Models: With Application to International Airlines

The principal aim of this paper is to measure the efficiency of international airlines. We obtain measures of technical efficiency from stochastic frontier production functions which have been adjusted to account for environmental influences such as network conditions, geographical factors, etc. We observe that two alternative approaches to this problem have been proposed in the efficiency measurement literature. One assumes that the environmental factors influence the shape of the technology while the other assumes that they directly influence the degree of technical inefficiency. In this paper we compare the results obtained when using these two approaches. The two sets of results provide similar rankings of airlines but suggest differing degrees of technical inefficiency. Both sets of results also suggest that Asian/Oceanic airlines are technically more efficient than European and North American airlines but that the differences are essentially due to more favourable environmental conditions. Nevertheless, it is among Asian companies that the major improvements in managerial efficiency (technical efficiency with environmental factors netted out) took place over the sample period (1977–1990).     

A semiparametric stochastic input distance frontier model with application to the Indonesian banking industry

This paper proposes a semiparametric smooth-varying coefficient input distance frontier model with multiple outputs and multiple inputs, panel data, and determinants of technical inefficiency for the Indonesian banking industry during the period 2000 to 2015. The technology parameters are unknown functions of a set of environmental factors that shift the input distance frontier non-neutrally. The computationally simple constraint weighted bootstrapping method is employed to impose the regularity constraints on the distance function. As a by-product, total factor productivity (TFP) growth is estimated and decomposed into technical change, scale component, and efficiency change. The distance elasticities, marginal effects of the environmental factors on the distance elasticities, temporal behavior of technical efficiency, and also TFP growth and its components are investigated.

     

Estimating DEA technical and allocative inefficiency using aggregate cost or revenue data

In this paper, we address the question of Data Envelopment Analysis (DEA) evaluation of efficiency when aggregate cost or revenue data must be used. We show that the DEA technical inefficiency measure using total revenues as the single output variable or total costs as the single input variable equals the aggregate technical and allocative inefficiency. We employ this result to estimate allocative inefficiency and construct statistical tests of the null hypothesis of no allocative inefficiency analogous to those of the null hypothesis of no scale inefficiency. We illustrate our method using revenue and personnel data for the top U.S. public accounting firms over 1995–1998. Our empirical results indicate the existence of statistically significant allocative inefficiency in the public accounting industry.