Stochastic Frontier Panel Data Models Research Articles

Efficient estimation of true fixed-effects stochastic frontier models

Fixed-effects modeling has become the method of choice in several panel data settings, including models for stochastic frontier analysis. A notable instance of stochastic frontier panel data models is the true fixed-effects model, which allows disentangling unit heterogeneity from efficiency evaluations. While such a model is theoretically appealing, its estimation is hampered by incidental parameters. This note proposes a simple and rather general estimation approach where the unit-specific intercepts are integrated out of the likelihood function. We apply the theory of composite group families to the model of interest and demonstrate that the resulting integrated likelihood is a marginal likelihood with desirable inferential properties. The derivation of the result is provided in full, along with some connections with the existing literature and computational details. The method is illustrated for three notable models, given by the normal-half normal model, the heteroscedastic exponential model, and the normal-gamma model. The results of simulation experiments highlight the properties of the methodology.

On distinguishing the direct causal effect of an intervention from its efficiency-enhancing effects

This paper proposes an innovative methodology for handling endogeneity issues in the evaluation of policy performance. By estimating a regression discontinuity design with a four-component stochastic frontier panel data model, we estimate the causal impact of a policy intervention on the outcome variable, whenever the treatment status depends on an exogenous threshold. We distinguish between (i) the direct effect of the intervention, (ii) the efficiency-enhancing effect, or (iii) their combination. Moreover, we distinguish between persistent (time-invariant) and transient (time-varying) inefficiency components while accounting for unobserved heterogeneity, which is important for policy implications. We showcase the practical usefulness of the proposed approach by estimating the effect of providing additional resources on schools that exceed an exogenously set share of disadvantaged students in secondary schools in Flanders, Belgium. We also demonstrate the trade-off between balance of the covariates in the treated and control group and statistical power. Thus, despite insignificant effects in a balanced but smaller sample close to the discontinuity, the results become significant in the unbalanced sample with more statistical power. In both samples, we observe that the policy had an effect on the outcome mostly through the efficiency-enhancing channel. To this extent, we show that the model specification including both direct and indirect effects outperforms the other two specifications and it offers a more exhaustive perspective from a policy view point.

Import demand potential for Indonesian rubber products in ASEAN countries

Increasing imports of rubber products from Indonesia is the key to the success of the downstream policy of rubber products to gain added value and job opportunities in the country. The rubber product market in ASEAN is more dynamic, and Indonesia must focus on strengthening competitiveness and exploiting potential markets. This paper aims to describe the potential demand for imports of Indonesian rubber products in ASEAN countries, especially Malaysia, Singapore, Thailand, the Philippines, and Vietnam. The flow of imports of rubber products uses the stochastic frontier panel data model to determine the potential demand for imports of Indonesian rubber products. Indonesian rubber products compete fiercely with similar industries in importing and exporting countries from East Asia. Indonesia mostly exports rubber products with HS codes 4015 and 4016 in the form of gloves, mittens, and mitts, rubber cellular, floor coverings and mats, erasers, gaskets and rings, boats, and fender docks to all markets in ASEAN countries. They were followed by rubber products with HS code 4010 in the form of conveyor belts or transmission belts from vulcanized rubber. The potential for import demand for other types of Indonesian rubber products (code HS4014, 4009, 4008) in ASEAN countries is relatively small and is growing slowly. Overall, the potential demand for imports of Indonesian rubber products tends to decline in ASEAN countries, as well as the actual imports of rubber products from Indonesia compared to their potential, which also declines slowly.

Heterogeneity, Transient and Persistent Production Efficiencies of Major Crops in Southern Ethiopia

Agricultural productivity is a cornerstone for the economy of Ethiopia to ensure rural transformation. However, the increment of productivity of crops has slow progress. Hence, this study undertook to separate farm heterogeneity, short-run and long-run inefficiencies of productivity in southern Ethiopia. The study used the models of decomposing technical efficiency through various techniques like 4-random error components of stochastic frontier panel data models to distinguish between time-invariant farm-heterogeneity, persistence, and short-run inefficiencies. Thus, models used for the analysis have shown different estimates of overall efficiency levels. Fixed-effect and Kumbhakar-Heshmati models did not separate unobserved persistent efficiency from farm-heterogeneity efficiency. The estimated efficiency by the Kumbhakar-Lien-Hardaker model (0.4449) is significantly higher than the mean of the fixed-effect model with much lower variations. Mean transient efficiencies gleaned from true-fixed-effect, consistent true-fixed-effect, and Kumbhakar-Lien-Hardaker models become nearly equal except, the Kumbhakar-Heshmati model indicated that farmers faced severe persistent productivity inefficiency problems. Average technical change in 2011/12 was 20.67% and declined much more to 9.44% and 5.82% in 2013/14 and 2015/16, sequentially. According to the estimation of overall technical efficiency, it is possible to capture about 39% to 99% of the untapped production in the crop subsector of Southern Ethiopia. Therefore, there was a decline in the growth rate of fertilizer used and land size covered by considered crops in the area. Land covered was declined by 3.06% for the considered crops from 2013/14 to 2015/16 production period. In the mean summary of technical efficiency at the zonal level, the aggregate persistent efficiency is lower than the transient one for all the zones. It confirmed that inefficiency varies from zone to zone between zones and household to household within the zone during the survey years. Thus, the policymaker should pinpoint the causes of inefficiencies separated in the time factors to improve the productivity of considered crops in the study area. A policy point that treats the persistent, transient, and farm-specific inefficiency enhancing conditions has to be set separately in each zona of Southern Ethiopia. Moreover, the greater focus of the policy is to alleviate the persistent inefficiency increasing factors in the study area.

Tax Effort of the Indian States from 2001–2002 to 2016–2017: A Stochastic Frontier Approach

This article estimates the tax capacity and tax effort of 17 major states of India from 2001–2002 to 2016–2017 using the stochastic frontier panel data model. It is found that per capita income, agriculture activity, infrastructure, labour force and bank credit are the significant determinants of tax capacity, while social sector spending and central transfer to states are significant in determining tax effort. The Goods and Services Tax has reduced the states’ tax powers. Therefore, the states are highly dependent on their limited legislative taxes for revenue mobilization. However, there is little scope for the subnational governments to increase tax revenue as all states have achieved at least 90% of their tax potential.

An Analysis of Energy Use Efficiency in China by Applying Stochastic Frontier Panel Data Models

This paper investigates energy use efficiency at the province level in China using the stochastic frontier panel data model approach. The stochastic frontier model is a parametric model which allows for the modeling of the relationship between energy use and its determinants using different control variables. The main control variables in this paper are energy policy and environmental and regulatory variables. This paper uses province level data from all provinces in China for the period 2010–2017. Three different models are estimated accounting for the panel nature of the data; province-specific heterogeneity and province-specific energy inefficiency effects are separated. The models differ because of their underlying assumptions, but they also complement each other. The paper also explains the degree of inefficiency in energy use by its possible determinants, including those related to the public energy policy and environmental regulations. This research supplements existing research from the perspective of energy policy and regional heterogeneity. The paper identifies potential areas for improving energy efficiency in the western and northeastern regions of China. Its findings provide new empirical evidence for estimating and evaluating China’s energy efficiency and a transition to cleaner energy sources and production.

Heterogeneity, transient and persistent technical efficiency of Polish crop farms

Accounting for heterogeneity in the measurement of farm efficiency is crucial to avoid biases related to climate and soil quality diversity in a given area. Therefore, this paper investigates the level of technical efficiency (TE) of Polish crop farms based on several stochastic frontier panel data models with different approaches to the measurement of unobserved heterogeneity, short- and long- run inefficiency. In our study, we show that ignoring farm heterogeneity can lead to underestimation of the level of TE in conventional stochastic frontier panel data models. Moreover, we have found empirically that not accounting for heterogeneity in the Generalized True Random Effects model may lead to incorrect estimates of persistent TE. The obtained results for Polish crop farms indicate that the level of transient TE (0.81) is lower than the level of persistent TE (0.88). This result suggests that Polish farms may have, for example, problems with adopting new technologies and poor managerial skills.

Estimation of Stochastic Frontier Panel Data Models with Spatial Inefficiency

This paper proposes a stochastic frontier panel data model in which unit-specific inefficiencies are spatially correlated. In particular, this model has simultaneously three important features: i) the total inefficiency of a productive unit depends on its own inefficiency and on the inefficiency of its neighbors; ii) the spatially correlated and time varying inefficiency is disentangled from time invariant unobserved heterogeneity in a panel data model a la Greene (2005); iii) systematic differences in inefficiency can be explained using exogenous determinants. We propose to estimate both the true fixed- and random-effects variants of the model using a feasible simulated composite maximum likelihood approach. The finite sample behavior of the proposed estimators are investigated through a set of Monte Carlo experiments. Our simulation results suggest that the estimation approach is consistent, showing good finite sample properties especially in small samples.

Panel data stochastic frontier model with determinants of persistent and transient inefficiency

In this paper we consider a stochastic frontier panel data model in which the random firm-effects are separated from the persistent and transient technical inefficiency. The model is extended to accommodate factors that can explain both persistent and transient technical inefficiency. We derive formulas to estimate both types of inefficiency and compute marginal effects of the determinants on each type of inefficiency. Our simulation results show that both biases and mean square errors decrease with an increase in sample size (NT). To illustrate the working of our model, we also provide results from an empirical application using data from 40 advanced industrialized, newly industrialized, transition and emerging economies observed from 1995–2006.

Modelling Efficiency Effects in a True Fixed Effects Stochastic Frontier

This paper proposes a stochastic frontier panel data model which includes time-invariant unobserved heterogeneity along with the efficiency effects. Following Paul and Shankar (2018), the efficiency effects are specified by a standard normal cumulative distribution function of exogenous variables which ensures the efficiency scores to lie in a unit interval. This specification eschews one-sided error term present in almost all the existing inefficiency effects models. The model parameters can be estimated by non-linear least squares after removing the individual effects by the usual within transformation or using non-linear least squares dummy variables (NLLSDV) estimator. The efficiency scores are directly calculated once the model is estimated. An empirical illustration based on widely used panel data on Indian farmers is presented.

Modelling regional productivity performance across Western Europe

ABSTRACTThis study investigates the potential role of variations in technical efficiency as a contributing factor in providing an explanation for convergence or divergence in Western Europe. To control for spatial dependence among regions, it uses a spatial stochastic frontier framework that integrates spatial econometric techniques with stochastic frontier panel-data models. The empirical analysis reveals there is a strong geographical pattern of regional efficiency, while the degree of average regional efficiency has increased steadily year by year. From a European regional policy perspective, we can conclude that differentiated development strategies seem more appropriate than homogeneous or best-practice investment approaches.

Consistent Inference in Fixed-Effects Stochastic Frontier Models

The classical stochastic frontier panel data models provide no mechanism for disentangling individual time-invariant unobserved heterogeneity from inefficiency. Greene (2005a, b) proposed the ‘true’ fixed-effects specification, which distinguishes these two latent components while allowing for time-variant inefficiency. However, due to the incidental parameters problem, the maximum likelihood estimator proposed by Greene may lead to biased variance estimates. We propose two alternative estimation procedures that, by relying on a first-difference data transformation, achieve consistency when n goes to infinity with fixed T. Furthermore, we extend the approach of Chen et al. (2014) by providing a computationally feasible solution for estimating models in which inefficiency can be heteroskedastic and may follow a first-order autoregressive process. We investigate the finite sample behavior of the proposed estimators through a set of Monte Carlo experiments. Our results show good finite sample properties, especially in small samples. We illustrate the usefulness of the new approach by applying it to the technical efficiency of hospitals.

Endogeneity in panel data stochastic frontier model with determinants of persistent and transient inefficiency

In this paper we consider a stochastic frontier panel data model in which the random firm-effects are introduced along with the persistent and transient technical inefficiency. Moreover, we allow determinants of both persistent and transient inefficiency, and allow both firm-effects and persistent inefficiency to be correlated with the regressors. We discuss a two-step procedure, which applies the MLE and the system NLS approach, to estimate parameters of the model and prediction of persistent and transient technical efficiency. Finally, we demonstrate our approach by applying it to the U.S. power generating plant data.

Consistent inference in fixed-effects stochastic frontier models

The classical stochastic frontier panel data models provide no mechanism to disentangle individual time invariant unobserved heterogeneity from inefficiency. Greene (2005a, b) proposed the so-called “true” fixed-effects specification that distinguishes these two latent components. However, due to the incidental parameters problem, his maximum likelihood estimator may lead to biased variance estimates. We propose two alternative estimators that achieve consistency for n→∞ with fixed T. Furthermore, we extend the Chen et al. (2014) results providing a feasible estimator when the inefficiency is heteroskedastic and follows a first-order autoregressive process. We investigate the behavior of the proposed estimators through Monte Carlo simulations showing good finite sample properties, especially in small samples. An application to hospitals’ technical efficiency illustrates the usefulness of the new approach.

When, where and how to estimate persistent and transient efficiency in stochastic frontier panel data models

In this paper we examine robustness of a recently developed panel data stochastic frontier model that allows for both persistent and transient (also known as long-run and short-run or time-invariant and time-varying) inefficiency along with random firm-effects (heterogeneity) and noise. We address some concerns that the practitioners might have about this model. First, given that there are two random time-invariant components (persistent inefficiency and firm-effects) the concern is whether the model can accurately identify them, and if so how precisely can the model estimate them? Second, there are two time-varying random components (transient inefficiency and noise), and the concern is whether the model can separate noise from transient inefficiency, and if so how precisely can the model estimate transient inefficiency? Third, how well are persistent and transient inefficiency estimated under different scenarios, viz., under different configurations of the variance parameters of the four random components? Given that the model is quite complex, relatively new and becoming quite popular in the panel efficiency literature, we feel that there is need for a detailed simulation study to examine when, where and how one can use this model with confidence to estimate persistent and transient inefficiency.

The impact of ownership unbundling on cost efficiency: Empirical evidence from the New Zealand electricity distribution sector

Several countries around the world have introduced reforms to the electric power sector. One important element of these reforms is the introduction of an unbundling process, i.e., the separation of the competitive activities of supply and production from the monopole activity of transmission and distribution of electricity. There are several forms of unbundling: functional, legal and ownership. New Zealand, for instance, adopted an ownership unbundling in 1998. As discussed in the literature, ownership unbundling produces benefits and costs. One of the benefits may be an improvement in the level of the productive efficiency of the companies due to the use of the inputs in just one activity and a greater level of transparency for the regulator. This paper analyzes the cost efficiency of 28 electricity distribution companies in New Zealand for the period between 1996 and 2011. Using a stochastic frontier panel data model, a total cost function and a variable cost function are estimated in order to evaluate the impact of ownership unbundling on the level of cost efficiency. The results indicate that ownership separation of electricity generation and retail operations from the distribution network has a positive effect on the cost efficiency of distribution companies in New Zealand. The estimated effect of ownership separation suggests a positive average one-off shift in the level of cost efficiency by 0.242 in the short-run and 0.144 in the long-run.

The impact of ownership unbundling on cost efficiency

Several countries around the world have introduced reforms to the electric power sector. One important element of these reforms is the introduction of an unbundling process, i.e., the separation of the competitive activities of supply and production from the monopole activity of transmission and distribution of electricity. There are several forms of unbundling: functional, legal and ownership. New Zealand, for instance, adopted an ownership unbundling in 1998. As discussed in the literature, ownership unbundling produces benefits and costs. One of the benefits may be an improvement in the level of the productive efficiency of the companies due to the use of the inputs in just one activity and a greater level of transparency for the regulator. This paper analyzes the cost efficiency of 28 electricity distribution companies in New Zealand for the period between 1996 and 2011. Using a stochastic frontier panel data model, a total cost function and a variable cost function are estimated in order to evaluate the impact of ownership unbundling on the level of cost efficiency. The results indicate that ownership separation of electricity generation and retail operations from the distribution network has a positive effect on the cost efficiency of distribution companies in New Zealand. The estimated effect of ownership separation suggests a positive average one-off shift in the level of cost efficiency by 0.242 in the short-run and 0.144 in the long-run.

Misspecification in allocative inefficiency: A simulation study

We make an extensive simulation analysis in order to investigate the consequences of ignoring the potentially complex and data dependent effects of allocative inefficiency on the estimation of stochastic frontier panel data models. Generally system estimators perform worse than single equation estimators. This result holds even when we approximate the allocative inefficiency.

Is Globalization Driving Efficiency? A Threshold Stochastic Frontier Panel Data Modeling Approach

AbstractIn an earlier paper the authors proposed a two‐step approach to examine dynamic transmission mechanism under which globalization factors foster technology efficiency. In this paper the MSS model is extended by combining a panel threshold regression technique. This threshold stochastic frontier panel data model enables the analysis of regime‐specific stochastic frontiers and complex time‐varying patterns of technical efficiencies in a robust manner. Using a dataset of 44 countries over 1970–2007, income elasticities of labor and capital and time‐varying common efficiencies are found to be substantially different under superior and inferior frontiers. Capital and labor inputs are more productive under superior frontier. More importantly, common efficiencies have steadily increased under superior frontier, but technical efficiency has monotonically decreased for low income countries, supporting the so‐called club convergence hypothesis. Furthermore, the VAR‐based impulse response analyses suggest that openness factors through FDI and trade help the countries to improve production technology and efficiency position relative to the frontier only after the country has reached a certain level of development.

Consistent Estimation of the 'True' Fixed-Effects Stochastic Frontier Model

The classic stochastic frontier panel data models provide no mechanism to disentangle individual time in- variant unobserved heterogeneity from ine ffi ciency. Greene (2005a,b) proposed a fixed-e ffects model spec- ification that distinguishes these two latent components and allows a time varying ine ffi ciency distribution. However, the maximum likelihood estimator proposed by Greene leads to biased ine ffi ciency estimates due to the incidental parameters problem. In this paper, we propose two alternative estimation procedures that, by relying on a first di fference data transformation, achieve consistency for n!1 with fixed T. Evidence from Monte Carlo simulations shows good finite sample performances of both approaches even in presence of small samples.