Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach

We propose a kernel-based Bayesian framework for the analysis of stochastic frontiers and efficiency measurement. The primary feature of this framework is that the unknown distribution of inefficiency is approximated by a transformed Rosenblatt-Parzen kernel density estimator. To justify the kernel-based model, we conduct a Monte Carlo study and also apply the model to a panel of U.S. large banks. Simulation results show that the kernel-based model is capable of providing more precise estimation and prediction results than the commonly-used exponential stochastic frontier model. The Bayes factor also favors the kernel-based model over the exponential model in the empirical application.

     

Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency

This paper analyzes the productivity of farms across 370 municipalities in the Center-West region of Brazil. A stochastic frontier model with a latent spatial structure is proposed to account for possible unknown geographical variation of the outputs. The paper compares versions of the model that include the latent spatial effect in the mean of output or as a variable that conditions the distribution of inefficiency, include or not observed municipal variables, and specify independent normal or conditional autoregressive priors for the spatial effects. The Bayesian paradigm is used to estimate the proposed models. As the resultant posterior distributions do not have a closed form, stochastic simulation techniques are used to obtain samples from them. Two model comparison criteria provide support for including the latent spatial effects, even after considering covariates at the municipal level. Models that ignore the latent spatial effects produce significantly different rankings of inefficiencies across agents.

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.

Estimates of technical inefficiency in stochastic frontier models with panel data: generalized panel jackknife estimation

Estimates of technical inefficiency based on fixed effects estimation of the stochastic frontier model with panel data are biased upward. Previous work has attempted to correct this bias using the bootstrap, but in simulations the bootstrap corrects only part of the bias. The usual panel jackknife is based on the assumption that the bias is of order T ⁻¹ and is similar to the bootstrap. We show that when there is a tie or a near tie for the best firm, the bias is of order T ^−1/2, not T ⁻¹, and this calls for a different form of the jackknife. The generalized panel jackknife is quite successful in removing the bias. However, the resulting estimates have a large variance.     

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.     

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.

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.     

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.

     

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.     

Creative destruction over the business cycle: a stochastic frontier analysis

This paper examines the within-industry distributions of jobs created and destructed across plants in terms of technical efficiency, technical efficiency change, scale effect, and technical change. It further investigates how these distributions vary with economic activity. By applying the stochastic frontier analysis to plant-level longitudinal data on Taiwan??s 23 two-digit manufacturing industries spanning the period 1992?C2003, we find that jobs created (destructed) are disproportionately clustered at plants with lower technical efficiency but higher rate of technical change. A fall in economic activities is associated with a statistically significant decrease (increase) in the fraction of newly created (destructed) jobs accounted for by plants with a higher rate of technical change, indicating that creative destruction is more pronounced during economic contractions.     

A note on the assumed distributions in stochastic frontier models

Stochastic frontier models all need an assumption on the distributional form of the (in)efficiency component. Generally this efficiency component is assumed to be half normally, truncated normally, or exponentially distributed. This paper shows that the exponential distribution is, just like the half normal distribution, a special case of the truncated normal distribution. Moreover, this paper discusses the implications that this finding has on estimation.     

The impact of oil prices and the financial market on cost efficiency in the insurance and Takaful sectors: Evidence from a stochastic frontier analysis

The Gulf Cooperation Council’s (GCC) insurance industry, including conventional insurance and Takaful, has witnessed remarkable growth during the last decade. However, the economies of this region rely on oil as the primary stream of revenue and lack development in financial markets. This could affect the insurance industry. For this reason, this paper examines the impact of oil prices and the financial market on the cost efficiency of the insurance and Takaful sectors in GCC countries using a stochastic frontier cost function with data from 2009–2016. The results show that the relationship between oil prices and efficiency changes from positive to negative when the prices increase, whereas the relationship between the financial market and efficiency is negative. No clear evidence of the impact of oil prices on efficiency arises from the differences between conventional insurance and Takaful. However, there are differences regarding the financial market, with a negative impact on conventional insurance and a positive one on the Takaful business. The results of this study have implications for regulators and management. The Takaful industry is rapidly growing compared to conventional insurance in the GCC and, therefore, the financial market may have added benefits for the GCC region. However, caution is required in relation to the impact of the financial market on conventional insurance. Furthermore, management may require the development of strategies to deal with the nature of GCC economies to avoid shocks to oil prices.     

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...     

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.     

Estimation of stochastic frontier models based on multimodel inference

In most empirical studies, once the best model has been selected according to a certain criterion, subsequent analysis is conducted conditionally on the chosen model. In other words, the uncertainty of model selection is ignored once the best model has been chosen. However, the true data-generating process is in general unknown and may not be consistent with the chosen model. In the analysis of productivity and technical efficiencies in the stochastic frontier settings, if the estimated parameters or the predicted efficiencies differ across competing models, then it is risky to base the prediction on the selected model. Buckland et al. (Biometrics 53:603?C618, 1997) have shown that if model selection uncertainty is ignored, the precision of the estimate is likely to be overestimated, the estimated confidence intervals of the parameters are often below the nominal level, and consequently, the prediction may be less accurate than expected. In this paper, we suggest using the model-averaged estimator based on the multimodel inference to estimate stochastic frontier models. The potential advantages of the proposed approach are twofold: incorporating the model selection uncertainty into statistical inference; reducing the model selection bias and variance of the frontier and technical efficiency estimators. The approach is demonstrated empirically via the estimation of an Indian farm data set.     

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.     

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.

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.     

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...     

Simple tests of alternative specifications in stochastic frontier models

Previous work on stochastic production frontiers has generated a family of models, of varying degrees of complexity. Since this family is nested (in the sense that the more general models contain the less general), we can test the restrictions that distinguish the model. In this paper we provide tests of these restrictions, based on the results of estimating the simpler (restricted) models. Some of our tests are LM tests. However, in other cases the LM test fails, so we provide alternative simple tests.