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.     

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.     

A Recursive Thick Frontier Approach to Estimating Production Efficiency*

We introduce a new panel data estimation technique for production and cost functions, the recursive thick frontier approach (RTFA). RTFA has two advantages over existing econometric frontier methods. First, technical inefficiency is allowed to be dependent on the explanatory variables of the frontier model. Secondly, RTFA does not hinge on distributional assumptions on the inefficiency component of the error term. We show by means of simulation experiments that RTFA outperforms the popular stochastic frontier approach and the ‘within’ ordinary least squares estimator for realistic parameterizations of a productivity model. Although RTFAs formal statistical properties are unknown, we argue, based on these simulation experiments, that RTFA is a useful complement to existing methods.     

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.     

Stochastic Frontiers and Asymmetric Information Models

This article is an attempt to shed light on the specification and identification of inefficiency in stochastic frontiers. We consider the case of a regulated firm or industry. Applying a simple principal-agent framework that accounts for informational asymmetries to this context, we derive the associated production and cost frontiers. Noticeably this approach yields a decomposition of inefficiency into two components: The first component is a pure random term while the second component depends on the unobservable actions taken by the agent (the firm). This result provides a theoretical foundation to the usual specification applied in the literature on stochastic frontiers. An application to a panel data set of French urban transport networks serves as an illustration.     

Estimating Production Uncertainty in Stochastic Frontier Production Function Models

One of the main purposes of the frontier literature is to estimate inefficiency. Given this objective, it is unfortunate that the issue of estimating firm-specific inefficiency in cross sectional context has not received much attention. To estimate firm-specific (technical) inefficiency, the standard procedure is to use the mean of the inefficiency term conditional on the entire composed error as suggested by Jondrow, Lovell, Materov and Schmidt (1982). This conditional mean could be viewed as the average loss of output (return). It is also quite natural to consider the conditional variance which could provide a measure of production uncertainty or risk. Once we have the conditional mean and variance, we can report standard errors and construct confidence intervals for firm level technical inefficiency. Moreover, we can also perform hypothesis tests. We postulate that when a firm attempts to move towards the frontier it not only increases its efficiency, but it also reduces its production uncertainty and this will lead to shorter confidence intervals. Analytical expressions for production uncertainty under different distributional assumptions are provided, and it is shown that the technical inefficiency as defined by Jondrow et al. (1982) and the production uncertainty are monotonic functions of the entire composed error term. It is very interesting to note that this monotonicity result is valid under different distributional assumptions of the inefficiency term. Furthermore, some alternative measures of production uncertainty are also proposed, and the concept of production uncertainty is generalized to the panel data models. Finally, our theoretical results are illustrated with an empirical example.     

Firm efficiency: Domestic owners,coalitions, and FDI

In this paper we analyze the evolution of firm efficiency in the Czech Republic. Using a large panel of more than 190,000 Czech firm/years we study whether firms fully utilize their resources, how firm efficiency evolves over time, and how firm efficiency is determined by ownership structure. We employ a panel version of a stochastic production frontier model for the period 1996–2007 with time-varying efficiency. We differentiate among various degrees of ownership concentration and domestic or foreign origin. In a two-stage set-up we first estimate the degree of firm inefficiency and then the effect of ownership structure on the distance from the efficiency frontier. Our results support the hypothesis that concentrated ownership is positively related to efficiency. FDI has beneficial effects at the microeconomic level. However, we show that a simple majority is not necessarily the best structure to improve efficiency. We further analyze the effects of ownership coalitions and shed light on many other subtleties of how ownership and the specific industry affect firm efficiency.     

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     

Feasible estimation of firm‐specific allocative inefficiency through Bayesian numerical methods

Both the theoretical and empirical literature on the estimation of allocative and technical inefficiency has grown enormously. To minimize aggregation bias, ideally one should estimate firm and input‐specific parameters describing allocative inefficiency. However, identifying these parameters has often proven difficult. For a panel of Chilean hydroelectric power plants, we obtain a full set of such parameters using Gibbs sampling, which draws sequentially from conditional generalized method of moments (GMM) estimates obtained via instrumental variables estimation. We find an economically significant range of firm‐specific efficiency estimates with differing degrees of precision. The standard GMM approach estimates virtually no allocative inefficiency for industry‐wide parameters. Copyright © 2009 John Wiley & Sons, Ltd.     

PANEL PROBIT WITH FLEXIBLE CORRELATED EFFECTS: QUANTIFYING TECHNOLOGY SPILLOVERS IN THE PRESENCE OF LATENT HETEROGENEITY

In this paper, we introduce a Bayesian panel probit model with two flexible latent effects: first, unobserved individual heterogeneity that is allowed to vary in the population according to a nonparametric distribution; and second, a latent serially correlated common error component. In doing so, we extend the approach developed in Albert and Chib (Journal of the American Statistical Association 1993; 88 : 669–679; in Bayesian Biostatistics, Berry DA, Stangl DK (eds), Marcel Dekker: New York, 1996), and in Chib and Carlin (Statistics and Computing 1999; 9 : 17–26) by releasing restrictive parametric assumptions on the latent individual effect and eliminating potential spurious state dependence with latent time effects. The model is found to outperform more traditional approaches in an extensive series of Monte Carlo simulations. We then apply the model to the estimation of a patent equation using firm‐level data on research and development (R&D). We find a strong effect of technology spillovers on R&D but little evidence of product market spillovers, consistent with economic theory. The distribution of latent firm effects is found to have a multimodal structure featuring within‐industry firm clustering. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Public utility planning and cost efficiency in a decentralized regulation context: the case of the Italian integrated water service

The reformed Italian water and sewerage industry has several distinctive features. It is based on a decentralized structure where local authorities are entitled to define detailed long-term budget plans that claim to provide efficiency incentives to operating suppliers. Unlike previous studies, this paper analyzes the cost efficiency embedded in these budget plans to evaluate the actual capability of local regulators to adequately orientate firm performance. Several panel data cost frontier models were estimated that incorporate diverse specifications for inefficiency and unobserved heterogeneity terms. The results indicate that the decentralized planning mechanism applied in Italian water and sewerage industry regulation failed in fulfilling the declared goal and further highlights that the time-invariant terms are the prevailing source of cost differences, which may conceal a structural component attributable to persistent inefficiency.     

Impact of Management Practices on Persistent and Residual Technical Efficiency – a Study of Swedish pig Farming

Managerial capacity builds over the years and the accumulated knowledge/practice affect the outcome of the period that follows, with long‐run/permanent effects on inefficiency. Therefore, predictions of the influence of managerial capacity on the time‐varying inefficiency, regularly estimated as overall efficiency, may be biased. This study analyzed the influence of farm management practices on both the persistent and residual efficiency, and evaluated how conclusions drawn about the effect of management practices are assessed if overall efficiency, instead of permanent and residual efficiency, is evaluated. Farm‐accounting data of Swedish pig producers and information from a survey related to managerial practices were used. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting with High‐Dimensional Panel VARs

This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressions of large dimensions with time‐varying parameters and stochastic volatility. We exploit a hierarchical prior that takes into account possible pooling restrictions involving both VAR coefficients and the error covariance matrix, and propose a Bayesian dynamic learning procedure that controls for various sources of model uncertainty. We tackle computational concerns by means of a simulation‐free algorithm that relies on analytical approximations to the posterior. We use our methods to forecast inflation rates in the eurozone and show that these forecasts are superior to alternative methods for large vector autoregressions.     

Efficiency measurement with multiple outputs and multiple inputs

This paper discusses modeling technical and allocative inefficiencies in both cost minimizing and profit maximizing frameworks with special emphasis on multiple inputs and multiple outputs. Both primal and dual models are considered for this purpose. In the primal approach we use a separable output and input function (the constant elasticity of transformation output function and Cobb-Douglas input function). The dual models assume translog cost or profit functions. Technical inefficiency is assumed to be random in the cross-sectional models, and fixed firm-specific parameter in the panel data models. Allocative inefficiencies are always treated as input-specific parameters. We derive exact relations linking technical inefficiency and allocative inefficiencies to cost and profit when the underlying technology is represented by a flexible functional form such as the translog. It is shown that appending a one-sided homoscedastic error term to model technical inefficiency, or neglecting technical inefficiency altogether in a translog profit tunciton results in model misspecification and inconsistent parameter estimates.     

The measurement of marketing efficiency in the presence of spillovers: theory and evidence

We develop a model of marketing efficiency based on a directional distance function that allows for marketing spillovers. A parametric model is used to test for spillovers from rival marketing and from a firm's marketing activity of its other related products. We then show how this information can be incorporated into a non‐parametric model and used to estimate marketing inefficiency. We apply brand level data from the US brewing industry to the non‐parametric model to determine the effectiveness of television, radio, and print advertising. We find that advertising spillovers are important in brewing and show that efficiency estimates are inaccurate when spillover effects are ignored. Our results also suggest that marketing efficiency may be an important component to firm success in brewing, a result that may apply to other consumer goods industries. Copyright © 2006 John Wiley & Sons, Ltd.     

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.

Interconnections Between Eurozone and US Booms and Busts Using a Bayesian Panel Markov‐Switching VAR Model

The proposed panel Markov‐switching VAR model accommodates changes in low and high data frequencies and incorporates endogenous time‐varying transition matrices of country‐specific Markov chains, allowing for interconnections. An efficient multi‐move sampling algorithm draws time‐varying Markov‐switching chains. Using industrial production growth and credit spread data, several important data features are obtained. Three regimes appear, with slow growth becoming persistent in the eurozone. Turning point analysis indicates the USA leading the eurozone cycle. Amplification effects influence recession probabilities for Eurozone countries. A credit shock results in temporary negative industrial production growth in Germany, Spain and the USA. Core and peripheral countries exist in the eurozone. Copyright © 2016 John Wiley & Sons, Ltd.     

Persistent and transient cost efficiency—an application to the Swiss hydropower sector

Electricity prices on the European market have decreased significantly over the past few years, resulting in a deterioration of Swiss hydropower firms’ competitiveness and profitability. One option to improve the sector’s competitiveness is to increase cost efficiency. The goal of this study is to quantify the level of persistent and transient cost efficiency of individual firms by applying the generalized true random effects (GTRE) model introduced by Colombi et al. (Journal of Productivity Analysis 42(2): 123–136, 2014) and Filippini and Greene (Journal of Productivity Analysis 45(2): 187–196, 2016). Applying this newly developed GTRE model to a total cost function, the level of cost efficiency of 65 Swiss hydropower firms is analyzed for the period between 2000 and 2013. A true random effects specification is estimated as a benchmark for the transient level of cost efficiency. The results show the presence of both transient as well as persistent cost inefficiencies. The GTREM predicts the aggregate level of cost inefficiency to amount to 21.8% (8.0% transient, 13.8% persistent) on average between 2000 and 2013. These two components differ in interpretation and implication. From an individual firm’s perspective, the two types of cost inefficiencies might require a firm’s management to respond with different improvement strategies. The existing level of persistent inefficiency could prevent the hydropower firms from adjusting their production processes to new market environments. From a regulatory point of view, the results of this study could be used in the scope and determination of the amount of financial support given to struggling firms.