Spatial Stochastic Frontier Research Articles

The impact of the Ebola virus disease (EVD) epidemic on agricultural production and livelihoods in Liberia.

There is unequivocal evidence in the literature that epidemics adversely affect the livelihoods of individuals, households and communities. However, evidence in the literature is dominated by the socioeconomic impacts of HIV/AIDS and malaria, while evidence on the impact of the Ebola virus disease (EVD) on households’ livelihoods remains fragmented and scant. Our study investigates the effect of the EVD epidemic on the livelihoods of Liberian households using the Sustainable Livelihood Framework (SLF). The study also explores the effect of the EVD epidemic on agricultural production and productive efficiency of farm households using Spatial Stochastic Frontier Analysis (SSFA). We collected data from 623 households across Liberia in 2015, using a systematic random sampling design. Our results indicated that the annual income of sample households from communities where EVD occurred did not differ from the annual income of households from communities where EVD did not occur. Nonetheless, the majority of sample households reported a decrease in their income, compared to their income in the year before the survey. This suggests that the impact of the EVD epidemic might not only have been limited to communities directly affected by the epidemic, but also it may have indirectly affected communities in areas where EVD was not reported. We also found that the community-level incidence of EVD negatively affected crop production of farm households, which may have exacerbated the problem of food insecurity throughout the country. Moreover, we found that the EVD epidemic weakened the society’s trust in Liberian institutions. In a nutshell, our results highlight that epidemics, such as the recent EVD outbreak, may have long-lasting negative effects on the livelihoods of a society and their effect may extend beyond the communities directly affected by the epidemics. This means that the nation’s recovery from the impact of the epidemic would be more challenging, and the social and economic impacts of the epidemic may extend well beyond the end of the health crisis.

A Spatial Stochastic Frontier Model with Omitted Variables: Electricity Distribution in Norway

An important methodological issue in efficiency analysis for incentive regulation of utilities is how to account for the effect of unobserved cost drivers such as environmental factors. We combine a spatial econometric approach with stochastic frontier analysis to control for unobserved environmental conditions when measuring efficiency of electricity distribution utilities. Our empirical strategy relies on the geographic location of firms as a source of information that has previously not been explored in the literature. The underlying idea is to utilise data from neighbouring firms that can be spatially correlated as proxies for unobserved cost drivers. We illustrate this approach using a dataset of Norwegian distribution utilities for the 2004-2011 period. We show that the lack of information on weather and geographic conditions can be compensated with data from surrounding firms. The methodology can be used in efficiency analysis and regulation of other utilities sectors where unobservable cost drivers are important, e.g. gas, water, agriculture, fishing.

A Spatial Autoregressive Stochastic Frontier Model for Panel Data Incorporating a Model of Technical Inefficiency

By integrating Battese and Coelli’s (1995) model and the spatial autoregressive model (SAR), a spatial autoregressive stochastic frontier model for panel data is developed. The main feature of this frontier model is a spatial lag term of explained variables and the joint structure of a production possibility frontier with a model of technical inefficiency. The model addresses both spatial dependence and heteroskedastic technical inefficiency. This study applies maximum likelihood methods considering the endogenous spatial lag term. The proposed model nests several existing models. Further, an empirical analysis using data on the Japanese manufacturing industry is conducted and the existing models are tested against the proposed model, which is found to be statistically supported. The findings suggest that estimates in the existing spatial and non-spatial models may exhibit bias because of lack of determinants of technical inefficiency, as well as a spatial lag. This bias also affects the technical efficiency score and its ranking.

Estimating efficiency in a spatial autoregressive stochastic frontier model

The spatial autoregressive stochastic frontier model of Glass et al.(2016) is based on distributional assumptions on two-sided and one-sided error terms. After estimating the model parameters, the efficiency estimates need to be corrected due to the presence of spatial autoregressive term in their model. Glass et al.(2016) estimate the corrected efficiencies by employing ideas from a distribution-free method on the efficiency estimation, which may be sensitive to outliers. We propose an alternative way to correct efficiency estimates that is in line with the distribution-based methods.

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.

The Spatial Efficiency Multiplier and Random Effects in Spatial Stochastic Frontier Models

We extend the emerging literature on spatial frontier models in three respects. Firstly, we account for latent heterogeneity by developing a maximum likelihood random effects spatial autoregressive (SAR) stochastic frontier model. Secondly, to analyze the finite sample properties of a spatial stochastic frontier model we develop a Monte Carlo experimental methodology which we then apply. Thirdly, we introduce the concept of the spatial efficiency multiplier and show that the efficiency benchmark for a productive unit from the structural form of a spatial stochastic frontier model differs from the efficiency benchmark from the reduced form of the model.

Spatial nonstationarity in the stochastic frontier model: An application to the Italian wine industry

This research estimates the efficiency of a representative sample of Italian wine producers from the Italian FADN survey following a recent spatial stochastic frontier framework that allows to isolate the spatial dependence among units and to evaluate the role of intangible local factors in influencing the economic performance of firms. The empirical exercise shows that the specific territorial patterns in the data cannot be merely explained using a standard set of contextual factors. This intangible component can be interpreted as the role of the local business climate: in most localities, the presence of an embedded community stimulates a process of local learning that generates the diffusion of tacit knowledge through continuous interaction among the local actors. This effect is found to be different across firm size, with a larger impact on small firms.

Implication of spatial heterogeneity for airports' efficiency estimation

This research is devoted to the analysis of a role of spatial heterogeneity in estimation of airports' efficiency. Spatial heterogeneity, caused by uneven distribution of influencing factors over space, is widely acknowledged in the European airport industry, but rarely included in airport benchmarking procedures. We utilise modern methods of spatial econometrics to identify the importance of spatial heterogeneity for estimates of airports' resource elasticity and efficiency values. A set of utilised models includes the spatial error model, spatial stochastic frontier model, geographically weighted regression model, and their modifications.The empirical findings of the research are based on a sample of 356 European airports (in 2011) and include evidence of the significant effect of spatial heterogeneity on airport's efficiency and productivity estimates. A multi-output approach to production frontier specification is utilised; served passenger and cargo traffic flows are considered as airport outputs. Elasticities of airport input resources that are infrastructure (runways), catchment area characteristics (population size and welfare), regional tourist intensity, and airport status (hub, international) were estimated and discussed. We paid special attention to the geographical variability of input elasticities over Europe. The paper also contains individual estimates of the sample airports' efficiency levels.The main contributions of this paper are the proved necessity of incorporation of spatial heterogeneity into airport benchmarking procedures and the suggested methodological framework for spatial analysis of airports' productivity and efficiency.

Modeling Regional Productive Performance Using a Spatial Stochastic Frontier Approach: New Evidence for Europe (1995-2007)

The literature on the measurement of regional convergence at different spatial scales and over different time periods is extensive. This study explores the potential role of variations in European regional technical efficiency as a contributing factor in providing explanation for convergence or divergence. To control for spatial dependence among regions, the paper uses a spatial stochastic frontier approach that integrates spatial econometric techniques with stochastic frontier models, also allowing for non-linear technical progress jointly with time and cross-sectional varying technical efficiency. From the estimated production function, we obtain estimates of the technical efficiency of the investigated 120 NUTS-2 regions of the European Union over the period 1995-2007. Our findings show that geographical externalities affect the EU frontier level, and that European regions have been converging to the frontier at a rate of about 0.8% per year. However, the analyses of the efficiency scores reveal that there is a strong geographic pattern of regional efficiency while the degree of average regional efficiency has increased steadily year by year. Overall, it appears that European regions have converged during the 1995-2007 period in terms of their ability to utilize physical capital and labor to maximize output.

A spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers

By blending seminal literature on non-spatial stochastic frontier models with key contributions to spatial econometrics we develop a spatial autoregressive (SAR) stochastic frontier for panel data. The specification of the SAR frontier allows efficiency to vary over time and across the cross-sections. Efficiency is calculated from a composed error structure by assuming a half-normal distribution for inefficiency. The SAR frontier is estimated using maximum likelihood methods taking into account the endogenous SAR variable. The application of the estimator to an aggregate production frontier for European countries highlights, among other things, the asymmetry between efficiency spillovers to and from a country.

A Spatial Stochastic Frontier Model with Spillovers: Evidence for Italian Regions

AbstractEfficiency measurement using stochastic frontier models is well established in applied econometrics. However, no published work seems to be available on efficiency analysis using spatial data dealing with possible spatial dependence between regions. This article considers a stochastic frontier model with decomposition of inefficiency into an idiosyncratic and a spatial, spillover component. Exact posterior distributions of parameters are derived, and computational schemes based on Gibbs sampling with data augmentation are proposed to conduct simulation‐based inference and efficiency measurement. The new method is illustrated using production data for Italian regions (1970–1993). Clearly, further theoretical and empirical research on the subject would be of great interest.

Inefficiency, heterogeneity and spillover effects in maternal care in India: a spatial stochastic frontier analysis.

BackgroundInstitutional delivery is one of the key and proven strategies to reduce maternal deaths. Since the 1990s, the government of India has made substantial investment on maternal care to reduce the huge burden of maternal deaths in the country. However, despite the effort access to institutional delivery in India remains below the global average. In addition, even in places where health investments have been comparable, inter- and intra-state difference in access to maternal care services remain wide and substantial. This raises a fundamental question on whether the sub-national units themselves differ in terms of the efficiency with which they use available resources, and if so, why?MethodsData obtained from round 3 of the country’s District Level Health and Facility Survey was analyzed to measure the level and determinants of inefficiency of institutional delivery in the country. Analysis was conducted using spatial stochastic frontier models that correct for heterogeneity and spatial interactions between sub-national units.ResultsInefficiency differences in maternal care services between and within states are substantial. The top one third of districts in the country has a mean efficiency score of 90 per cent or more, while the bottom 10 per cent of districts exhibit mean inefficiency score of as high as over 75 per cent or more. Overall mean inefficiency is about 30 per cent. The result also reveals the existence of both heterogeneity and spatial correlation in institutional delivery in the country.ConclusionsGiven the high level of inefficiency in the system, further progress in improving coverage of institutional delivery in the country should focus both on improving the efficiency of resource utilization—especially where inefficiency levels are extremely high—and on bringing new resources in to the system. The additional investment should specifically focus on those parts of the country where coverage rates are still low but efficiency levels are already at a high level. In addition, given that inefficiency was also associated inversely with literacy and urbanization and positively related with proportion of households belonging to poor households, investment in these areas can also improve coverage of institutional delivery in the country.

Distinguishing Between Spatial Heterogeneity and Inefficiency: Spatial Stochastic Frontier Analysis of European Airports

Abstract A problem of distinguishing between frontier heterogeneity and inefficiency is widely acknowledged in benchmarking. A special type of heterogeneity, based on the spatial structure, can significantly affect performance estimates in the airport industry. In this research we presented a general specification of the spatial stochastic frontier model, which includes spatial lags, spatial autoregressive disturbances and spatial autoregressive inefficiencies. Maximum likelihood estimator has been derived for this model. Applying the suggested model specification to the European airports dataset, we discovered presence of significant spatial heterogeneity, which leads to biased estimates of efficiency, received using classical models.