Estimation of technical inefficiency effects using panel data and doubly heteroscedastic stochastic production frontiers

In previous studies, measures of technical inefficiency effects derived from stochastic production frontiers have been estimated from residuals which are sensitive to specification errors. This study corrects for this inaccuracy by extending the doubly heteroscedastic stochastic cost frontier suggested by Hadri (1999) to the model for technical inefficiency effects. This model is a stochastic frontier production function for panel data as proposed by Battese and Coelli (1995). The study uses, for illustration of the techniques, data on 101 mainly cereal farms in England. We find that the correction for heteroscedasticity is supported by the data. Both point estimates and confidence intervals for technical efficiencies are provided. The confidence intervals are constructed by extending the “Battese-Coelli” method reported by Horrace and Schmidt (1996) by allowing the technical inefficiency to be time varying and the disturbance terms to be heteroscedastic. The confidence intervals reveal the precision of technical efficiency estimates and show the deficiencies of making inferences based exclusively on point estimates. First version received: March 2000/Final version received: Oct. 2001 RID="*" ID="*"  The authors are grateful to the Economic and Social Research Council for access to their Data Archive which has provided the data for this research. We are indebted to Badi Baltagi and two anonymous referees for their helpful comments and suggestions. The usual caveat applies.     

Environmental regulation and U.S. states' technical inefficiency

Using data on 48 states from 1982–1994, we estimate the impact of environmental regulation on technical inefficiency of U.S. states' manufacturing sector. The result indicates that environmental stringency has significant and positive impacts on U.S. states' technical inefficiency.     

A flexible time-varying specification of the technical inefficiency effects model

The temporal pattern of technical efficiency in the technical inefficiency effects model, as modeled by Battese and Coelli (Empir Econ 20:325–332, 1995), is rather restrictive. Specifically, it a priori imposes a common pattern upon all firms in the sample, which in addition is monotonic over time. Obviously this is an undesirable implication of the model especially when there is evidence of strong firm heterogeneity and/or a long time span. To overcome this shortcoming, the present paper incorporates the Cornwell et al. (J Econom 46:185–200, 1990) flexible specification of the temporal pattern of technical efficiency into technical inefficiency effects model. The proposed formulation is then applied to the agricultural sector of the EU and US, during the period 1973–1993. The empirical result support the proposed formulation as quite different temporal patterns of technical efficiency have been found for the ten countries included in the analysis. We would like to thank an anonymous referee and an associate editor for valuable suggestions in an earlier version of the paper.     

Efficiency and Equity in School Funding: A Case Study for Kansas

This study measures cost inefficiency of Kansas public school districts and applied both mathematical programming and stochastic frontier approach. The empirical study uses two-stage data envelopment analysis model and the cost inefficiency effects model proposed by Battese and Coelli (Empirical Economics 24:325–332, 1995) and applied to a panel data. The results found mean inefficiencies from these two models are very close. The results indicate that Kansas school districts, on average, exhibit cost inefficiency in their operations, however, there is a tendency for inefficiencies to decline over time. The study does not find any strong evidence for lower efficiency due to lower expenditure per-pupil. Instead, we found inconclusive evidences where lower efficiency for certain school districts could be assigned to unfavorable environmental cost conditions.

The measurement of environmental economic inefficiency with pollution-generating technologies

This study introduces the measurement of environmental inefficiency from an economic perspective. We develop our proposal using the latest by-production models that consider two separate and parallel technologies: a standard technology generating good outputs, and a polluting technology for the by-production of bad outputs. While research into environmental inefficiency incorporating undesirable or bad outputs from a technological perspective is well established, no significant attempts have been made to extend it to the economic sphere. Based on the definition of net profits, we develop an economic inefficiency measure that accounts for suboptimal behavior in the form of foregone private revenue and environmental cost excess. We show that economic inefficiency can be consistently decomposed according to technical and allocative criteria, considering the two separate technologies and market prices, respectively. We illustrate the empirical implementation of our approach using a dataset on agriculture at the level of US states.     

The transient and persistent efficiency of Italian and German universities: a stochastic frontier analysis

Despite measures on the European level to increase the compatibility between the higher education sectors, the recent literature exposes variations in their efficiencies. To gain insights into these differences, we split the efficiency term according to the two management levels each university is confronted with. We separate short-term and long-term efficiency while controlling for unobserved institution-specific heterogeneity. We argue that the first term reflects the efficiency of the individual universities working within the country, while the second term echoes the influence of the overall country-specific higher education structure. The cross-country comparison displays whether efficiency differences between countries are related to the individual performance of their universities or their higher education structure. This allows more purposeful policy recommendations and expands the literature regarding the efficiency of universities in a fundamental way. Choosing Italy and Germany as two important illustrative examples, we show that the Italian higher education sector exhibits a higher overall efficiency value. With the individual universities working at the upper bound of efficiency in both countries, the remaining inefficiency and the gap between the countries are caused by persistent, structural inefficiency. Future measures should hence aim at the country-specific structure and not solely at the activities of single universities.     

The Zilcha criterion for dynamic inefficiency

Summary. This paper reexamines the condition (1 + n), which Zilcha (1991) presents as a necessary and sufficient condition for dynamic inefficiency of stationary allocations in overlapping generation models with stochastic production. We show that this condition is necessary but not sufficient for a stationary allocation to be dynamically inefficient by Zilchas definition. We also show that there is a narrow but widely studied class of specifications in which the Zilcha test is both necessary and sufficient for dynamic inefficiency of stationary competitive equilibrium allocations. Outside this class, however, counterexamples can be constructed relatively easily.Received: 30 September 2002, Revised: 13 August 2004, JEL Classification Numbers: D51, D90, E13, E22. Correspondence to: Steven RussellWe thank Jon Burke, Subir Chakrabarti, Itzhak Zilcha and an anonymous referee for helpful conversations and/or comments.     

Metafrontier frameworks for the study of firm-level efficiencies and technology ratios

This paper uses the concept of a metafrontier to compare the technical efficiencies of firms that may be classified into different groups. The paper presents the basic analytical framework necessary for the definition of a metafrontier, shows how a metafrontier can be estimated using non-parametric and parametric methods, and presents an empirical application using cross-country agricultural sector data. The paper also explores the issues of technological change, time-varying technical inefficiency, multiple outputs, different efficiency orientations, and firm heterogeneity.     

Human capital effects on technical inefficiency: a stochastic frontier analysis across industries of the Greek economy

In this paper we examine the impact of human capital on technical inefficiency. A stochastic production frontier is simultaneously estimated with a technical inefficiency model using data from one-digit industries of the Greek economy, for the period 2000–2005. The results indicate a significantly negative impact of human capital on technical inefficiency, which is comparatively lower in magnitude for the sector of public services. The most efficient industries of the Greek economy are those of Education, Financial intermediation and Real estate, renting & business activities. The highest contribution of human capital on technical efficiency is observed in the industries of Health, Education and Real estate, renting & business activities.     

The Zilcha criteria for dynamic inefficiency reconsidered

We reconsider necessary and sufficient conditions for dynamic inefficiency given in Zilcha (J Econ Theory 52:364–379, 1990, J Econ Theory 55:1–16, 1991) and a critique by Rangazas and Russell (2005). First, we show that the characterization given in Zilcha (1990) for nonstationary economies is correct and correct Zilcha’s proof. Second, using this insight, we complement Rangazas and Russell’s (Econ Theory 26:701–716, 2005) discussion of the counterexamples to Zilcha (J Econ Theory 55:1–16, 1991). Third, we discuss consequences of our results for applied tests of (in-)efficiency based on the Zilcha criteria. We would like to thank Itzhak Zilcha, and in particular Peter Rangazas and Steve Russell for detailed and very helpful comments.     

The contributions of technical and allocative efficiency to the economic performance of European railways

This paper provides an empirical analysis of the relative contributions of allocative and technical efficiency to the productivity performance of European railways over the period 1972 to 1999. A stochastic frontier approach is used to analyse the cost structure of the railway industry. We estimate a translog cost system in which allocative inefficiency is modelled through an exact relationship between the cost share equations and the cost function. To allow the estimation of such a model using the sample theory approach we assume that the share equation residuals represent deviations from first-order conditions and, therefore, that they represent exclusively allocative inefficiencies. The use of this simplifying assumption renders our analysis computationally tractable, but it could be inconsistent with the economic theory of duality and for that reason caution is required in interpretation of results. Acknowledging this caveat, we find that European railways have experienced significant cost increases due to inefficient behaviour, with a mean value of around 15%. In contrast to previous studies, however, our estimates indicate a larger role for allocative inefficiency, which accounts for around of a half of the total increase in cost inefficiency.

Bus transit technical efficiency using latent class stochastic indirect production frontier

Using an Indirect Production Frontier (IPF), this article examines technical inefficiency within a latent class framework while simultaneously accounting for allocative distortions from operating and capital subsidies. It identifies two latent classes of US public transit systems, one characterized by economies of scale with 16.61% technical inefficiency and the other by diseconomies of scale with 14.16% technical inefficiency. It decomposes technical inefficiency among some of its sources and finds that the incentive tier of federal operating subsidies, regulations regarding years of vehicle use, subsidy-induced allocative distortion from labour overuse relative to capital negatively influence technical inefficiency in all transit systems. For the Latent Class 1 transit systems, the sources of lower technical inefficiency are operating speed, purchased transportation and years-of-vehicle-use regulation. For the Latent Class 2 transit systems, these sources are subsidy-induced capital-labour allocative distortion and the incentive tier component of the federal formula grant.     

R&D,free entry,and social inefficiency

We employ a three-stage game model with cost-reducing research and development (R&D) that is subject to spillovers to consider the problem of excess entry under free-entry equilibrium relative to the social optimum. Firms choose to enter or exit a market in the first stage, choose R&D in the second stage and output in the final stage. Results show that there is socially inefficient or excessive entry in equilibrium. However, we uniquely demonstrate that research spillovers hold the key to whether established results regarding socially inefficient entry hold. Specifically, excessive entry occurs as long as research spillovers are relatively small, but this is not necessarily the case with large spillovers. Some policy implications are discussed.     

Economic inefficiency in a revenue setting: the Norwegian whitefish fishery

The main focus in the inefficiency literature is on suboptimal input use and how this causes increased costs, due to technical and allocative inefficiency. Production or cost functions are then typically used to describe the underlying technology of the firm. The possible revenue loss, due to lower than maximum production levels and suboptimal output mix, has received substantially less attention. By using a revenue function to measure inefficiency, the focus, model and estimation technique presented in this article differ from those of previous studies. A shadow revenue model is used to decompose revenue inefficiency into its technical and allocative components, in which the allocative inefficiency is due to a suboptimal output mix. The approach is illustrated using panel data of Norwegian whitefish trawlers. The results reveal large inefficiencies, with respect to output levels as well as output mix, indicating that this can be an important part of the picture when investigating economic inefficiency. To identify the determinants of revenue inefficiency, we conduct a second-step regression, in which technical and allocative inefficiency is regressed upon a set of explanatory variables. The inefficiencies are partly explained by the management system and fleet structure.     

The determinants of variations in exit rates

A conceptual model of the determinants of exit across spatial areas is presented and empirically tested. The relative merits of two different methods of calculating exit rates are discussed, and results compared. In the empirical estimation, entry is found to be the dominant determinant of exit. However, other factors also have a systematic effect: among these are local income, the rate of change of unemployment, relevant managerial skills, and population density. Making allowance for variations in industrial structure across areas has some effect on the results, but does not eliminate the effect of variables other than entry.     

Economic reforms,efficiency and productivity in Chinese banking

This paper analyzes the impact of banking reforms on efficiency and total factor productivity (TFP) change in Chinese banking industry. Using an input distance function, we find that joint-equity banks are more efficient than wholly state-owned banks (WSOBs). Furthermore, both WSOBs and joint-equity banks are found to be operating slightly below their optimal size, suggesting potential advantages in expansion of their businesses. Overall, TFP growth was 4.4% per annum for the sample period 1993–2002. Joint-equity banks experienced much higher growth in TFP (5.5% per annum) compared to the WSOBs (1.4% per annum).      

Modelling Exogenous Variables in Human Capital Formation through a Heteroscedastic Stochastic Frontier

The objective of this paper is to suggest the use of a stochastic frontier model in which the inefficiency component is heteroscedastic in the measurement of technical efficiency in Human Capital Formation in the Italian University System. The heteroscedastic frontier model enables one to consider the effect of students’ individual characteristics and the influences of the resources and organization of the specific faculty on efficiency. The suggested model is applied to the case of Florence University graduates. The results show that the model specification is strongly supported by the data. Moreover, the suggested specification explains variation in technical efficiency in terms of graduate-specific factors. The technical efficiency scores obtained are comparable across faculties.

Firm exit,technological progress and trade

The dynamics of export market exit and firm closure have found limited attention in the new heterogeneous-firms trade literature. In fact, several of the predictions on firm survival and exit stemming from this new class of models are at odds with the stylized facts. Empirically, higher productivity firms survive longer, most firm closures are young firms, higher productivity exporters are more likely to continue to export compared to less productive exporters and market exits as well as firm closures are typically preceded by periods of contracting market shares. The present paper shows that the simple inclusion of exogenous economy wide technological progress into the standard Melitz (2003) model generates a tractable dynamic framework that generates endogenous exit decisions of firms in line with the stylized facts. Furthermore, we derive the effects of faster technological progress and trade liberalization on export market exit and firm closure.     

Measurement of technical and allocative efficiencies using a CES cost frontier: a benchmarking study of Japanese transmission-distribution electricity

This paper estimates the technical and allocative inefficiencies of the transmission-distribution sector of Japanese electric utilities using a panel data during the 1981–1998 period. A stochastic production frontier of the CES form is jointly estimated with input demand equations. Taking advantage of the self-duality, we retrieve the cost frontier by which the impacts of technical and allocative inefficiencies on costs and input demands are measured. The estimated elasticity of substitution is significantly different from unity in favor of the CES specification over the Cobb–Douglas. The results show that observed costs are 9 to 48% higher than the efficient level; technical inefficiency raises costs by 1 to 28%, while allocative inefficiency does so by 8 to 30%. Although their impacts on costs are similar, technical inefficiency more fluctuates so the differences in the performance of utilities are mainly due to technical inefficiency. We also find a substantial over-utilization of capital for all utilities.

Regulation and efficiency in transition: the case of Romanian banks

Using disaggregated panel data for the period 1996–2002, this paper estimates the cost efficiency of Romanian banks and relates it to regulation implemented by the National Bank of Romania. We estimate efficiency using a model that combines the frameworks of both stochastic frontier analysis and shadow cost functions. Our results indicate that, for all types of banks, the cost of technical inefficiency decreases in the years following tightening of regulation. A significant part of this decrease can be attributed to the policy change. Overall, the short-run increase in cost due to additional regulation exceeds the benefits from reduced technical inefficiency. However, our model does not account for other benefits, besides changes in X-inefficiency, such as stability of the banking system, which may be significant.