The stochastic frontier production function and average efficiency: An empirical analysis

This paper provides an empirical estimation of a stochastic frontier Cobb-Douglas production function using micro data from a cross-section of Brazilian manufacturing firms. Following a procedure developed by Aigner, Lovell and Schmidt incorporating both stochastic and efficiency disturbance terms in the estimating model, maximum likelihood techniques are used for the estimation of the stochastic frontier. A measure of mean technical efficiency is also developed and employed with the Brazilian data. Unlike the previous empirical exercises carried out with aggregated data, the efficiency disturbance with the Brazilian micro data estimates is not swamped by the stochastic disturbance.     

Properties of technical efficiency estimators in the stochastic frontier model

This paper considers the disturbance specification ε = v ? u of the stochastic frontier model. For v distributed zero-mean normal and u half normal or exponential, we evaluate the population correlation coefficients between u and three estimators of u, E(u|ε) and two linear estimators, for various values of the signal-to-noise ratio.     

Estimating efficiency effects in a panel data stochastic frontier model

Journal of Productivity Analysis - This paper proposes a panel data based stochastic frontier model which accommodates time-invariant unobserved heterogeneity along with efficiency effects. The...     

Socio-institutional determinants of educational resource efficiency according to the capability approach: An endogenous stochastic frontier analysis

We investigate the role of private and public resources in educational attainments and the socio-institutional determinants of educational resource efficiency in Italy. Following the Sen's capability approach, we consider social capital and the quality of government part of the social conversion factors through which resources can be converted into human capabilities, such as education. We analyze the case of Italy by constructing a new longitudinal dataset from 1993 to 2012, using repeated cross sections from the main social survey of the Italian Statistical Institute and a panel stochastic frontier model that takes into account endogeneity. The results show the relative importance of private resources (measured by an ad hoc constructed wealth index), the complementarity between private wealth and public expenditures on education, and the positive impact of social capital and the quality of government on educational resource efficiency.     

A stochastic frontier analysis to estimate the relative efficiency of Spanish airports

There exists a common belief among researchers and regional policy makers that the actual central system of Aeropuertos Españoles y Navegación Aérea (AENA) should be changed to one more decentralized where airport managers could have more autonomy. The main objective of this article is to evaluate the efficiency of the Spanish airports using Markov chain Monte Carlo (MCMC) simulation to estimate a stochastic frontier analysis (SFA) model. Our results show the existence of a significant level of inefficiency in airport operations. Additionally, we provide efficient marginal cost estimates for each airport which also cast some doubts about the current pricing practices.     

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.

Corporate social responsibility and firm efficiency: a latent class stochastic frontier analysis

The nexus between corporate social responsibility and corporate performance is of fundamental importance to understand if the former can be a sustainable strategy in the competitive race. In this paper we test this relationship on a sample of firms observed in a 13-year interval by focusing on a performance indicator (productive efficiency) seldom explored in this literature with a novel approach (latent class stochastic frontiers). Our empirical findings show that firms included in the Domini 400 index (a CSR stock market index) do not appear to be more distant from the production frontier than firms in the control sample after controlling for the heterogeneity of production structure.     

Model uncertainty and efficiency measurement in stochastic frontier analysis with generalized errors

Journal of Productivity Analysis - Advanced efficiency measurement methods usually fall within Stochastic Frontier Analysis (SFA), Data Envelopment Analysis (DEA), or their derivatives. Although...     

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.

     

On the distribution of estimated technical efficiency in stochastic frontier models

We consider a stochastic frontier model with error ε=v−u$\epsilon =v-u$, where v$v$ is normal and u$u$ is half normal. We derive the distribution of the usual estimate of u,E(u|ε)$u,E\left(u\right|\epsilon )$. We show that as the variance of v$v$ approaches zero, E(u|ε)−u$E\left(u\right|\epsilon )-u$ converges to zero, while as the variance of v$v$ approaches infinity, E(u|ε)$E\left(u\right|\epsilon )$ converges to E(u)$E\left(u\right)$. We graph the density of E(u|ε)$E\left(u\right|\epsilon )$ for intermediate cases. To show that E(u|ε)$E\left(u\right|\epsilon )$ is a shrinkage of u towards its mean, we derive and graph the distribution of E(u|ε)$E\left(u\right|\epsilon )$ conditional on u$u$. We also consider the distribution of estimated inefficiency in the fixed-effects panel data setting.     

Technical efficiency in texas nursing facilities: A stochastic production frontier approach

A rapidly aging U. S. population is straining the resources available for long term care and increasing the urgency of efficient operations in nursing homes. The scope for productivity improvements can be examined by estimating a stochastic frontier production function. We apply the methods of maximum likelihood and quantile regression to a panel of Texas nursing facilities and infer that the average productivity shortfall due to avoidable technical inefficiency is at least 8 percent and perhaps as large as 20 percent. Non-profit facilities are notably less productive than comparable facilities operated for profit, and the industry has constant returns to scale.     

The fundraising efficiency in U.S. non-profit art organizations: an application of a Bayesian estimation approach using the stochastic frontier production model

This article examines how efficient art organizations are in raising funds from private giving. We measure fundraising efficiency using a Bayesian estimation approach using the stochastic frontier production model. We show that fundraising efficiencies are generally quite low for art organizations in the U.S. when private giving is only considered as a fundraising output; however, when the effect of fundraising on ticket sales is considered, fundraising efficiencies improve substantially. We also show that government grants have a negative impact on fundraising efficiency and therefore partially crowd out private giving.     

Model averaging estimators for the stochastic frontier model

Journal of Productivity Analysis - Model uncertainty is a prominent feature in many applied settings. This is certainty true in the efficiency analysis realm where concerns over the proper...     

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.

     

The sensitivity of efficiency scores to input and other choices in stochastic frontier analysis: an empirical investigation

Journal of Productivity Analysis - Productivity and efficiency analysis have gained substantial attention in many industries over the last two decades, and stochastic frontier analysis has been one...     

Bayesian clustering of distributions in stochastic frontier analysis

In stochastic frontier analysis, firm-specific efficiencies and their distribution are often main variables of interest. If firms fall into several groups, it is natural to allow each group to have its own distribution. This paper considers a method for nonparametrically modelling these distributions using Dirichlet processes. A common problem when applying nonparametric methods to grouped data is small sample sizes for some groups which can lead to poor inference. Methods that allow dependence between each group’s distribution are one set of solutions. The proposed model clusters the groups and assumes that the unknown distribution for each group in a cluster are the same. These clusters are inferred from the data. Markov chain Monte Carlo methods are necessary for model-fitting and efficient methods are described. The model is illustrated on a cost frontier application to US hospitals.     

Consistent estimation of the fixed effects stochastic frontier model

In this paper we consider a fixed-effects stochastic frontier model. That is, we have panel data, fixed individual (firm) effects, and the usual stochastic frontier analysis (SFA) composed error.     

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.     

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.

Water use efficiency and public goods conservation: A spatial stochastic frontier model applied to irrigation in Southern Italy

Water used for irrigation is essential for global food production. Increased water scarcity, due to climate change, is a constraint to agricultural development, especially in arid and semi-arid areas. This increases pressure on agriculture which often manages water inefficiently and competes with other sectors for water use. Enhancing farmers’ production efficiency may lead to substantial water savings and conservation. Public sector is called to play a role in water governance and to introduce appropriate multilevel regulatory and incentive measures for better water management. This work applies a spatial stochastic frontier model to the case of high water-demanding fruit and vegetable crops in the Apulia region of Southern Italy, where water is scarce due to semi-arid climate and erratic rainfall. Using cross-sectional data from the EU Farm Accountancy Data Network, this work incorporates firm specific heterogeneity into technical efficiency analysis and implements an autoregressive specification of the inefficiency component. Results support the hypothesis that spatial heterogeneity exists in on-farm efficiency of irrigated crop production and is adequately captured by the spatial stochastic frontier model approach. Technical efficiency of farms with similar structural and management characteristics greatly varies across crops and geographical areas, because of the different natural resource endowment and agro-climatic factors. Policies providing incentives to on-farm adoption of modern water-saving technologies and measures to promote small family farm activities could effectively contribute to water conservation goal, but they should be well-articulated to account for agriculture spatial diverseness.