FIRM HETEROGENEITY,PERSISTENT AND TRANSIENT TECHNICAL INEFFICIENCY: A GENERALIZED TRUE RANDOM‐EFFECTS model

This paper considers a panel data stochastic frontier model that disentangles unobserved firm effects (firm heterogeneity) from persistent (time‐invariant/long‐term) and transient (time‐varying/short‐term) technical inefficiency. The model gives us a four‐way error component model, viz., persistent and time‐varying inefficiency, random firm effects and noise. We use Bayesian methods of inference to provide robust and efficient methods of estimating inefficiency components in this four‐way error component model. Monte Carlo results are provided to validate its performance. We also present results from an empirical application that uses a large panel of US commercial banks. Copyright © 2012 John Wiley & Sons, Ltd.     

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.

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.

     

Estimation of cost inefficiency in panel data models with firm specific and sub-company specific effects

This paper proposes a dual-level inefficiency model for analysing datasets with a sub-company structure, which permits firm inefficiency to be decomposed into two parts: a component that varies across different sub-companies within a firm (internal inefficiency); and a persistent component that applies across all sub-companies in the same firm (external inefficiency). We adapt the models developed by Kumbhakar and Hjalmarsson (J Appl Econom 10:33–47, 1995) and Kumbhakar and Heshmati (Am J Agric Econ 77:660–674, 1995), making the same distinction between persistent and residual inefficiency, but in our case across sub-companies comprising a firm, rather than over time. The proposed model is important in a regulatory context, where datasets with a sub-company structure are commonplace, and regulators are interested in identifying and eliminating both persistent and sub-company varying inefficiency. Further, as regulators often have to work with small cross-sections, the utilisation of sub-company data can be seen as an additional means of expanding cross-sectional datasets for efficiency estimation. Using an international dataset of rail infrastructure managers we demonstrate the possibility of separating firm inefficiency into its persistent and sub-company varying components. The empirical illustration highlights the danger that failure to allow for the dual-level nature of inefficiency may cause overall firm inefficiency to be underestimated.     

Pitfalls in the estimation of a cost function that ignores allocative inefficiency: A Monte Carlo analysis

In the stochastic frontier literature, it is a widely held view that allocative inefficiency can be lumped together with technical inefficiency in the estimation of cost frontiers. Therefore, a one-sided error term in the cost function is believed to capture the cost of overall (technical plus allocative) inefficiency. In this paper we challenge that view through a detailed Monte Carlo investigation. The results show that failure to include the cost of allocative inefficiency explicitly in the cost function biases the estimates of: (i) the cost function parameters, (ii) returns to scale, (iii) input price elasticities, and (iv) cost-inefficiency.     

Choosing the Technical Efficiency Orientation to Analyze Firms' Technology: A Model Selection Test Approach

We focus on the importance of the assumptions regarding how inefficiency should be incorporated into the specification of the data generating process in an examination of a sector's production or efficiency. Drawing on the literature on non-nested hypothesis testing, we find that the model selection approach of Vuong (1989) is a potentially useful tool for identifying the best specification before carrying out such studies. We include an empirical application using panel data on Spanish dairy farms where we estimate cost frontiers under different specifications of how inefficiency enters the data generating process (in particular, efficiency is introduced as an input-oriented, output-oriented and hyperbolic parameter). Our results show that the different models yield very different pictures of the technology and the efficiency levels of the sector, illustrating the importance of choosing the most correct model before carrying out production and efficiency analyses. The Vuong test shows that the input-oriented model is the best among the models we use, whereas the output-oriented model is the worst. This is consistent with the fact that the input- and output-oriented models provide the most and least credible estimates of scale economies given the structure of the sector.     

Functional Forms of Stochastic Frontier Production Functions and Models for Technical Inefficiency Effects: A Comparative Study for Wheat Farmers in Pakistan

This paper considers translog and Cobb-Douglas stochastic frontiers in which the technical inefficiency effects are defined by three different models. The models involved are the time-varying inefficiency model, proposed by Battese and Coelli (1992), the inefficiency effects model for panel data, proposed by Battese and Coelli (1995), and the non-neutral frontier model, proposed by Huang and Liu (1994). Technical change is also accounted for in the frontier models. Predicted technical efficiencies of the wheat farmers and estimates of the elasticities of wheat production with respect to the different inputs and the returns-to-scale parameter are compared under the different model specifications.     

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.     

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.     

Bayesian estimation of inefficiency heterogeneity in stochastic frontier models

Estimation of the one sided error component in stochastic frontier models may erroneously attribute firm characteristics to inefficiency if heterogeneity is unaccounted for. However, unobserved inefficiency heterogeneity has been little explored. In this work, we propose to capture it through a random parameter which may affect the location, scale, or both parameters of a truncated normal inefficiency distribution using a Bayesian approach. Our findings using two real data sets, suggest that the inclusion of a random parameter in the inefficiency distribution is able to capture latent heterogeneity and can be used to validate the suitability of observed covariates to distinguish heterogeneity from inefficiency. Relevant effects are also found on separating and shrinking individual posterior efficiency distributions when heterogeneity affects the location and scale parameters of the one-sided error distribution, and consequently affecting the estimated mean efficiency scores and rankings. In particular, including heterogeneity simultaneously in both parameters of the inefficiency distribution in models that satisfy the scaling property leads to a decrease in the uncertainty around the mean scores and less overlapping of the posterior efficiency distributions, which provides both more reliable efficiency scores and rankings.     

Stochastic frontier models with network selectivity

Worker peer-effects and managerial selection have received limited attention in the stochastic frontier analysis literature. We develop a parametric production function model that allows for worker peer-effects in output and worker-level inefficiency that is correlated with a manager’s selection of worker teams. The model is the usual “composed error” specification of the stochastic frontier model, but we allow for managerial selectivity (endogeneity) that works through the worker-level inefficiency term. The new specification captures both worker-level inefficiency and the manager’s ability to efficiently select teams to produce output. As the correlation between the manager’s selection equation and worker inefficiency goes to zero, our parametric model reduces to the normal-exponential stochastic frontier model of Aigner et al. (1977) with peer-effects. A comprehensive application to the NBA is provided.     

The ‘wrong skewness’ problem: a re-specification of stochastic frontiers

In this paper, we study the ‘wrong skewness phenomenon’ in stochastic frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error, and causes the ‘wrong skewness problem’, for which the estimated inefficiency in the whole industry is zero. We propose a more general and flexible specification of the SF model, introducing dependences between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error into three components, namely: (i) the asymmetry of the inefficiency term; (ii) the asymmetry of the random error; and (iii) the structure of dependence between the error components. This decomposition suggests that the wrong skewness anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF has the wrong skewness, an estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. More importantly, we estimate a non-zero inefficiency, thus solving the wrong skewness problem. In the second dataset, where the classic SF does not yield any anomaly, an estimation of our model provides evidence for the presence of dependence. In such situations, we show that there is a remarkable difference in the efficiency distribution between the classic SF and our class of models.     

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 Production Function with Flexible Risk Properties

This paper considers a stochastic frontier production function which has additive, heteroscedastic error structure. The model allows for negative or positive marginal production risks of inputs, as originally proposed by Just and Pope (1978). The technical efficiencies of individual firms in the sample are a function of the levels of the input variables in the stochastic frontier, in addition to the technical inefficiency effects. These are two features of the model which are not exhibited by the commonly used stochastic frontiers with multiplicative error structures.An empirical application is presented using cross-sectional data on Ethiopian peasant farmers. The null hypothesis of no technical inefficiencies of production among these farmers is accepted. Further, the flexible risk models do not fit the data on peasant farmers as well as the traditional stochastic frontier model with multiplicative error structure.     

Management Efficiency in Football: An Empirical Analysis of Two Extreme Cases

Analysis of managerial efficiency in sport economics typically focuses on evaluating coach decisions instead of assessing the organization as a whole. This paper studies the relative importance of variables related to power and managerial decisions by estimating stochastic production frontiers models for the Chilean and Italian football leagues. We find that historical and geographical variables intended to capture market size play their expected roles in both Italy and Chile. However, the degree of technical inefficiency is lower magnitude in Chile. This difference could be due to a smaller market size and/or to financial constraints faced by small clubs in this country. Copyright © 2014 John Wiley & Sons, Ltd.     

Alternative technical efficiency measures: Skew,bias and scale

In the fixed‐effects stochastic frontier model an efficiency measure relative to the best firm in the sample is universally employed. This paper considers a new measure relative to the worst firm in the sample. We find that estimates of this measure have smaller bias than those of the traditional measure when the sample consists of many firms near the efficient frontier. Moreover, a two‐sided measure relative to both the best and the worst firms is proposed. Simulations suggest that the new measures may be preferred depending on the skewness of the inefficiency distribution and the scale of efficiency differences. Copyright © 2010 John Wiley & Sons, Ltd.     

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.

     

Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes

This paper examines the impact of an endogenous cost function variable on the inefficiency estimates generated by stochastic frontier analysis (SFA). The specific variable of interest in this application is endogenous quality in nursing homes. We simulate a dataset based on the characteristics of for-profit nursing homes in California, which we use to assess the impact on SFA-generated inefficiency estimates of an endogenous regressor under a variety of scenarios, including variations in the strength and direction of the endogeneity and whether the correlation is with the random noise or the inefficiency residual component of the error term. We compare each of these cases when quality is included and excluded from the cost equation. We provide evidence of the impact of endogeneity on inefficiency estimates yielded by SFA under these various scenarios and when the endogenous regressor is included and excluded from the model.     

A stochastic frontier cost function for residential child care provision

Within a public authority (the firm), there are often several production units. Costs and policy formulation are concerned with the units themselves, though inefficiency might arise at both the firm and unit levels. A stochastic frontier cost function is developed and estimated to describe one such situation where the firms are English local authorities and the production units are homes providing residential care for children. Measures of inefficiency are found for individual authorities.     

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.