Spatial Stochastic Frontier Research Articles

A spatial stochastic frontier model with fixed effects and endogenous environmental variables

ABSTRACT Stochastic frontier analysis (SFA) models often address fixed effects and endogeneity as separate issues. This study bridges this gap by proposing a unified approach within an ML (maximum likelihood) framework to manage both challenges simultaneously. The ML function is derived in a closed form, but its maximisation requires a numerical solution. To assess the properties of the ML estimator, a Monte Carlo simulation was performed. The simulation shows that the estimator performs reasonably well and gains efficiency asymptotically. The applicability of the estimator was further assessed through an empirical exercise that examined technical efficiency of the production function in a panel of European countries, managing spatiality, endogeneity, and fixed effects.

Influence of financial inclusion and industrial robots on the efficiency of China's OFDI: A heterogeneous spatial stochastic frontier analysis

Enhancing the efficacy of China's outward foreign direct investment (COFDI) constitutes a significant avenue for realizing the sustainable development of China's economy. This study analyzes panel data from 63 countries from 2010 to 2021 to create a heterogeneous spatial stochastic frontier model to examine how financial inclusion and industrial robotics in host nations affect COFDI efficiency. The findings are as follows. To begin with, COFDI manifests positive spatial spillover effects across countries. Moreover, from a spatial perspective, financial inclusion diminishes COFDI efficiency, whereas the interaction between financial inclusion and industrial robots increases its efficiency. Industrial robots, thus, counteract the diminishing impact of financial inclusion on COFDI efficiency. Additionally, concerning the heterogeneity of location choice and investment motivation in COFDI, the interaction between financial inclusion and industrial robots in developed economies augments COFDI efficiency as opposed to emerging market economies. Conversely, technology-seeking investment mitigates the adverse effects of financial inclusion on the efficacy of COFDI when juxtaposed with resource-seeking investment. This study provides theoretical insights and practical recommendations for improving the efficiency and guiding the destination selection of COFDI.

Fitting spatial stochastic frontier models in Stata

In this article, we introduce a new command, xtsfsp, for fitting spatial stochastic frontier models in Stata. Over the last decades, stochastic frontier models have seen important theoretical progress via the incorporation of various types of spatial components. Models that can account for spatial dependence and spillovers have been developed for efficiency and productivity analysis, drawing extensive attention from industry and academia. Because of the unavailability of the statistical packages, the empirical applications of the new stochastic frontier models appear to be lagging. The xtsfsp command provides a procedure for fitting spatial stochastic frontier models in the style of Orea and Álvarez (2019, Journal of Econometrics 213: 556-577) and Galli (2023, Spatial Economic Analysis 18: 239-258), enabling users to handle different sources of spatial dependence. In this article, we introduce spatial stochastic frontier models, describing the syntax and options of the new command and providing several examples to illustrate its usage.

Transportation infrastructure and carbon emissions: New evidence with spatial spillover and endogeneity

Over the past two decades, China’s transportation infrastructure has expanded and emerged as a vital pillar of the national economy. In the context of commitments to carbon neutrality, it is imperative to assess how developing transportation infrastructure affects overall environmental goals. However, to the best of our knowledge, existing literature offers conflicting evidence about the overall impact of transportation infrastructure on carbon emissions. Using a novel spatial stochastic frontier model that accounts for spatial spillover and endogeneity, we find that previous research paradigms underestimated the contribution of transportation infrastructure to decarbonization: Instead of being a hindrance, the corrected effect substantially enhances decarbonization. These results remain robust in different weight matrices, instrumental variables, and distance function specifications. Furthermore, this study identifies economic agglomeration and technological innovation as key mechanisms of the decarbonization effect. From a regional perspective, we observe that western China shows the most pronounced emission reduction effect, followed by central China. In contrast, in eastern China, the transportation infrastructure does not support carbon emission reduction effectively. Therefore, policymakers should carefully consider the regional disparities in decarbonization and formulate distinct investment plans on transportation tailored to each region.

Economic and Environmental Efficiency, Subsidies and Spatio-Temporal Effects in Agriculture

In this paper, we investigate how farms' environmental and economic efficiency is shaped by Pillar I CAP subsidies over time and by spatial effects originating from subsidies received by neighbours. To reach this goal, we estimate a spatial stochastic frontier model including intra and inter province spatial effects and differentiate among environmental and economic outcomes to evaluate the direct and indirect effects of subsidies on both aspects. The results of the analysis indicate that on one hand, subsidies are helping farmers to achieve environmental sustainability especially after the 2013 reform, on the other, they are leading to increased economic inefficiency levels. Considering spatial effects originating from subsidies, we find positive and significant spillovers occurring among closest neighbours both from the economic and the environmental perspective.

A Spatial Stochastic Frontier Model with Endogenous Variables Including Frontier and Error

A Spatial Stochastic Frontier Model with Endogenous Variables Including Frontier and Error

Efficient Water-Saving Irrigation, Space Efficiency and Agricultural Development — Study Based on Spatial Stochastic Frontier Model

Efficient Water-Saving Irrigation, Space Efficiency and Agricultural Development — Study Based on Spatial Stochastic Frontier Model

Privatization and cost inefficiency at U.S. Public research universities

ABSTRACT This study examines the relationship between cost efficiency and privatization at 163 public research institutions in the United States between 2005 and 2015. We employ a spatial autoregressive (SAR) random-effects model and stochastic frontier analysis (SFA) to estimate the relationship between costs and four privatization variables: auxiliary enterprises as a percentage of total revenue, tuition and fees as a percentage of total revenue, private grants/contracts as a percentage of total revenue, and out-of-state first year enrollment. Results showed cost inefficiency at public research universities increased between 2005 and 2015, even as reliance on private sources of revenue increased. Public research universities exhibit 28.5% overall cost inefficiency over the time period studied, 85.6% of which is short-run cost inefficiency. This suggests that most of the cost inefficiency varies across years and may be the result of challenges that institutional leaders face adapting to short-term fluctuations in market-oriented sources of revenue. The results also show a nonlinear relationship between cost inefficiency and three of the privatization variables. Given the expectation of little to no increase in state support for public research universities, this study has implications for policy, institutional management, and future research.

A spatial stochastic frontier model introducing inefficiency spillovers

Abstract This paper develops a spatial Durbin stochastic frontier model for panel data introducing spillover effects in the determinants of technical efficiency (SDF-STE). The model nests several existing spatial and non-spatial stochastic frontier specifications and is estimated using maximum-likelihood techniques. Estimates are shown to be unbiased even for small sample sizes and for alternative specifications of the spatial weight matrix implementing different Monte Carlo simulations. Finally, an application to the Italian accommodation sector is provided. Empirical findings suggest the relevance of the SDF-STE model in capturing labour productivity and knowledge spillover effects.

Do regional integration and trade linkages promote productivity spillovers? Evidence from the European Union

ABSTRACT This study examines the productivity and efficiency spillovers in the presence of trade linkages in 27 European Union countries from 1990 to 2019. The European Union is one of the largest trading blocs in the world and has implemented costly policies and reforms to improve productivity growth. Meanwhile, trade-induced productivity and efficiency spillovers have often been overlooked in the literature, and examining them could provide further clarity to the productivity puzzle. Using a spatial Durbin model and a bilateral trade matrix, this study estimates a spatial stochastic production frontier model using data from the Penn World Table and the World Integrated Trade Solution. We decompose production frontier estimates to obtain the spillover effects of total factor productivity growth and technical efficiency from a network of bilateral trading partners. Our results provide evidence of productivity and efficiency spillovers; however, the gains are uneven. Policy implications are discussed.

A spatial stochastic frontier model including both frontier and error-based spatial cross-sectional dependence

ABSTRACT Spatial dependence in stochastic frontier models is usually handled by modelling the frontier function or the inefficiency error term through the introduction of some spatial components. The model proposed in this paper (SDF-CSD) combines the two different modelling approaches, obtaining a full comprehensive specification that introduces four different sources of spatial cross-sectional dependence. The most appealing feature of the model is that it allows capturing global and local spatial spillover effects while controlling for spatial correlation related to firms’ efficiency and to unobserved but spatially correlated variables. Moreover, it can be estimated using maximum likelihood techniques. Finally, some Monte Carlo simulations were run to test the final sample properties of the new spatial estimator and an application to the Italian agricultural sector is provided.

Research on capital allocation efficiencies with four-dimensional factor capitals from China's intelligent manufacturing enterprises.

Compared with traditional manufacturing enterprises, intelligent manufacturing enterprises pay more attention to the investment of knowledge capital and technological capital. Taking 258 intelligent manufacturing listed companies in China from 2015 to 2020 as research samples, the paper selects the material capital, human capital, knowledge capital and technological capital of enterprises as the input variables of Cobb-Douglas production function. Considering that enterprises are often affected by spatial correlation, stochastic frontier panel model, spatial lag stochastic frontier panel model and dynamic spatial lag stochastic frontier panel model are constructed to measure capital allocation efficiencies of enterprises. The results show that all the factor capitals in the three models have a significant positive impact on enterprises’ performance, and the dual lag effect of time and space is significant. Moreover, it is more reasonable to use the dynamic spatial lag stochastic frontier panel model to estimate the parameters and measure capital allocation efficiencies. The development of intelligent manufacturing industry has significant space-time spillover effect among provinces. About 52.98% of intelligent manufacturing enterprises have high capital allocation efficiencies, but 12.04% still need to further optimize capital allocation. The gap between the actual performance of the sample enterprises and efficiency frontier is mainly due to technical ineffectiveness. From a regional perspective, the top ten enterprises with high capital allocation efficiencies are all in the eastern region, but the average of capital allocation efficiency is the highest in the western region, followed by the eastern and central regions.

Do Egocentric information networks influence technical efficiency of farmers? Empirical evidence from Ghana

We investigate the impact of farmers’ egocentric information network on technical efficiency and its distribution in the network, using observational data of 600 farmers from northern Ghana. We exploit community detection algorithms to endogenously identify homogeneous network communities with known structures to account for spatial heterogeneity, in a spatial stochastic frontier model that controls for social selection bias. The empirical results reveal that at the global network level, farmers’ technical efficiency strongly correlate with that of farmers in their egocentric networks. Our findings also show that farmers who are technically less efficient tend to depend on the more efficient farmers in their networks to improve efficiency. We further find that estimating spatial dependence of technical efficiency without accounting for spatial heterogeneity can lead to underestimation of technical efficiency of high (efficiency score >0.6) performing farmers, while overestimating that of medium (efficiency scores between 0.36–0.5) and low (efficiency scores between 0.1–0.35) performing farmers. The findings suggest that identifying central farmers in egocentric networks and improving their technical knowledge in a farmer-to-farmer extension organization, can contribute to improving the productivity of many farmers.

The GMM estimation of semiparametric spatial stochastic frontier models

In this paper, we consider the estimation of semiparametric spatial stochastic frontier (SF) models, in which the spatial dependence is modeled by adding the spatially lagged dependent variable as an additional independent variable (following the convention of spatial autoregressive models) and specifying various spatial structures on the inefficiency and/or idiosyncratic error. Thus, the proposed models are inclusive compared with most previous studies. Efficiency modeling in the SF literature has not given enough attention to the spatial interaction of inefficiency, primarily because the estimation of inefficiency in spatial models is challenging using the conventional maximum likelihood method. Therefore, we propose a two-step estimation procedure for our spatial frontier models under the framework of the generalized method of moments (GMM). The proposed method is easy to implement. Further, Monte Carlo Simulations show that our GMM estimators have good finite-sample performance. We apply our GMM estimators to examine the technical efficiency of 41 European countries and the effects of spatial dependence on production (GDP).

Semiparametric estimation of spatial autoregressive smooth-coefficient panel stochastic frontier models

This paper considers the estimation of a spatial autoregressive stochastic frontier model, where the production frontier coefficients, as well as the spatial parameter, are allowed to depend on a set of observed environmental factors. The inefficiency term is multiplicatively separable into a scaling function of either the same or totally different set of environmental factors and a standard half-normal random variable. A two-step semiparametric procedure is developed using a combination of local GMM and maximum likelihood approaches. We also derive the estimators of direct and indirect average partial effects and predictors of technical efficiency. We work out the asymptotic theory for the proposed second step estimator and propose a test of the relevance of the environmental factors. A special case of the model where the spatial parameter is a non-zero constant is also considered. The finite sample behavior of the proposed estimator and test are examined using Monte Carlo simulations. An empirical application to the Chinese chemical industry is included to illustrate the usefulness of our proposed models and methods.

Correction to: Spatial stochastic frontier model with endogenous weighting matrix

Correction to: Spatial stochastic frontier model with endogenous weighting matrix

Spatial stochastic frontier model with endogenous weighting matrix

Spatial stochastic frontier model with endogenous weighting matrix

Research on the Impact of Logistics Industry Efficiency and Agglomeration Effect on Import and Export Trade in Korea

Purpose – The logistics industry is often featured by its location relevance and industrial concentration. Industrial concentration is conducive to the effective transmission of information by reducing transaction costs and improving transaction efficiency, thus promoting the development of trade. The main purpose of this paper is to measure the spatial total factor productivity and location quotient of the logistics industry in Korea, and to study the impact of the logistics industry efficiency and agglomeration effect on import and export trade in Korea. Design/methodology – First, used the spatial stochastic frontier method to measure the spatial total factor productivity of the logistics industry in Korea, this serves as the efficiency index of the logistics industry in various regions of Korea. Second, calculated the location quotient (LQ) of the logistics industry to measure the industry’s concentration degree. Third, employed a spatial econometric model to analyze the impacts of factors such as the efficiency and concentration levels of the logistics industry on import and export trade in Korea. Findings – This study’s main findings can be summarized as follows: this study found that the overall efficiency of the logistics industry in Korea needs to be improved, even though it showed an upward trend in all regions of the country; Moreover, the agglomeration level of Korea’s logistics industry needs to be improved; Finally, the positive spatial correlation and industrial agglomeration effect of Korea s logistics industry had a positive impact on the country’s import and export trade. Originality/value – This study is innovative in terms of research perspective and methods. Most of the previous studies have measured the development level of the logistics industry using the logistics performance index (LPI), Fewer studies have assessed through the spatial total factor productivity and location quotient of the logistics industry in Korea to measure the efficiency index of the logistics industry in various regions of Korea and concentration degree, as well as there was almost no study on the impact of logistics industry efficiency and agglomeration effect on import and export trade in Korea. This study addresses this limitation by analyzing the impacts of the efficiency and agglomeration effect of the logistics industry on import and export trade in Korea.

Transient and Persistent Efficiency and Spatial Spillovers: Evidence from the Portuguese Wine Industry

This paper investigates the presence of spatial spillovers in firms’ productive (in)efficiency. For this purpose, a spatial stochastic frontier model is specified and estimated, accounting for spatial dependence and persistent and transient (in)efficiency. This approach is applied to a panel dataset from 2014 to 2019 of Portuguese wineries. Apart from the traditional input and output quantities used in the estimation of a production function, the novelty of this study is the inclusion of information on the firms’ exact location, which allows incorporating the neighboring dependence in the productive efficiency analysis. Empirical findings show that despite the Portuguese wineries’ technological positive dependence on spatial closeness for both inputs and outputs, the geographic closeness is not strong enough to provide overall productive efficiency gains.

Regional Heterogeneity of the Family Farming in Brazil: an Analysis Using a Spatial Stochastic Frontier

Family farming is quite different between Brazilian regions, where one of the main factors of this distinction is the implementation of agricultural modernization that initially benefited the regions South and Southeast, making these regions more mechanized and with a higher level of human capital. Given this fact, this article aims to measure the productive differences of family farmers between Brazilian regions using data from the 2017 Agricultural Census and applying a spatial stochastic frontier at municipal level. The results have shown that there is a high heterogeneity between Brazilian regions, where although all areas have shown a decreasing return of production scale, these returns were greater for the regions Midwest, Southeast, and South. Besides, technology and labor have a lesser effect on the gross income of farmers in the Northeast. The results also show that spillovers were different between regions, both for the factors of production and for the determinants of inefficiency. Furthermore, the heterogeneity can be confirmed by the efficiency scores, which were higher in the regions South, Midwest, and Mid-South regions of the Southeast. The results also suggest that, according to the profile of each region, it is necessary to implement more efficient policies that aim to improve the effectiveness of existing policies and mitigate the differences between them, especially in the North and Northeast of Brazil.