半参数空间ZISF的估计、分类与蒙特卡罗模拟
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摘要
零无效率随机前沿模型(ZISF)包含随机前沿模型和回归模型,两模型各有一定的发生概率,适用于技术无效生产单元和技术有效生产单元同时存在的情形。本文在ZISF的生产函数中引入空间效应和非参函数,并假设回归模型的发生概率为非参函数,构建了半参数空间ZISF。该模型可有效避免忽略空间效应导致的有偏且不一致估计量,也避免了线性模型的拟合不足。本文对非参函数采用B样条逼近,使用极大似然方法和JLMS法分别估计参数和技术效率。蒙特卡罗结果表明:①本文方法的估计精度和分类精度均较高。随着样本容量的增大,精度增加。②忽略空间效应或者非参数效应,估计精度和分类精度降低,文中模型有存在必要性。③忽略发生概率的非参数效应会严重降低估计和分类精度,远大于忽略生产函数的非参数效应的影响。
Zero inefficiency stochastic frontier model(ZISF)contains regression model and stochastic frontier model,which are with certain probability respectively.Thus ZISF can accommodate the presence of both efficient and inefficient firms.Now the theoretical researches about ZISF are rare.Especially for spatial ZISF,the existing ZISFs are with poor applicability.By incorporating spatial effects and nonparametric functions into ZISF,semiparametric spatial ZISF is constructed in this paper.The semiparametric spatial ZISF can avoid under-fitting derived from linear model and the biased and inconsistent estimators derived from neglecting spatial effects.B-splines are used to approximate nonparametric function and the model has been changed into linear spatial ZISF.The two order norm of approximate error can converge to zero quickly,so the approximate error can be neglected.Maximum likelihood method and JLMS method are used to estimate parameters and technical efficiencies respectively.The Monte Carlo simulation shows that:(i)The method in this paper is with high estimation accuracies for parameters,nonparametric functions and technical efficiencies and with high classification for technical efficiencies.With sample size increasing,the accuracies become higher.(ii)Neglecting any one of effect such as spatial effect or nonparametric effect will get lower estimation accuracies and classification accuracies.So the model in paper is necessary.(iii)The nonparametric effect in production function or in probability of occurrence has different impact on the estimation and classification accuracies.When the nonparametric effect in production function is neglected,there is only a small reduction for the estimation and classification accuracies.While the nonparametric effect in probability of occurrence is neglected,the estimation and classification accuracies have been substantially decreased.
Zero inefficiency stochastic frontier model(ZISF)contains regression model and stochastic frontier model,which are with certain probability respectively.Thus ZISF can accommodate the presence of both efficient and inefficient firms.Now the theoretical researches about ZISF are rare.Especially for spatial ZISF,the existing ZISFs are with poor applicability.By incorporating spatial effects and nonparametric functions into ZISF,semiparametric spatial ZISF is constructed in this paper.The semiparametric spatial ZISF can avoid under-fitting derived from linear model and the biased and inconsistent estimators derived from neglecting spatial effects.B-splines are used to approximate nonparametric function and the model has been changed into linear spatial ZISF.The two order norm of approximate error can converge to zero quickly,so the approximate error can be neglected.Maximum likelihood method and JLMS method are used to estimate parameters and technical efficiencies respectively.The Monte Carlo simulation shows that:(i)The method in this paper is with high estimation accuracies for parameters,nonparametric functions and technical efficiencies and with high classification for technical efficiencies.With sample size increasing,the accuracies become higher.(ii)Neglecting any one of effect such as spatial effect or nonparametric effect will get lower estimation accuracies and classification accuracies.So the model in paper is necessary.(iii)The nonparametric effect in production function or in probability of occurrence has different impact on the estimation and classification accuracies.When the nonparametric effect in production function is neglected,there is only a small reduction for the estimation and classification accuracies.While the nonparametric effect in probability of occurrence is neglected,the estimation and classification accuracies have been substantially decreased.
引文
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[6]Yao Feng,Wang Taining,Tian Jinjing,et al.Estimation of a smooth coefficient zero-inefficiency panel stochastic frontier model:A semiparametric approach[J].Economics letters,2018,166:25-30.
[7]Tran K,Tsionas M.Zero-inefficiency stochastic frontier models with varying mixing proportion:A semiparametric approach[J].European Journal of Operational Research,2016,249(3):1113-1123.
[8]蒋青嬗,韩兆洲.空间ZISF的估计及蒙特卡罗模拟[J].统计与信息论坛,2017,32(5):3-9.
[9]蒋青嬗,韩兆洲.半参数空间ZISF的估计及反馈分类[J].统计研究,2017,34(10):98-109.
[10]Kutlu L.Estimating efficiency in a spatial autoregressive stochastic frontier model[J].Economics Letters,2018,163:155-157.
[11]Glass A,Kenjegalieva K,Sickles R.A spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers[J].Journal of Econometrics,2016,190(2):289-300.
[12]Tran K,Tsionas M.On the estimation of zero-inefficiency stochastic frontier models with endogenous regressors[J].Economics letters,2016,147:19-22.
[13]Rho S,Schmidt P.Are all firms inefficient[J].Journal of Productivity Analysis,2015,43(3):1-23.
[14]Orea L,Jamasb T.Identifying efficient regulated firms with unobserved technological heterogeneity:A nested latent class approach to Norwegian electricity distribution networks[J].Efficiency,2014:1-18.
[15]Huang J,Horowitz J,Wei A.Variable selection in nonparametric additive models[J].The Annals of Statistics,2010,38(4):2282-2313.
[16]蒋青嬗,韩兆洲.半参数线性混合效应模型的联合变量选择[J].数理统计与管理,2017,36(3):458-468.
[17]Stone C.Additive regression and other nonparametric models[J].The Annals of Statistics,1985,13(2):689-705.
[18]Jondrow J,Lovell K,Materov I,et al.On the estimation of technical inefficiency in the stochastic frontier production function model[J].Journal of Econometrics,1982,19(2-3):233-238.
[2]王谨乐,史永东.机构投资者、代理成本与公司价值---基于随机前沿模型及门槛回归的实证分析[J].中国管理科学,2016,24(7):155-162.
[3]蒋青嬗,韩兆洲,吴栩.真实固定效应空间随机前沿模型的贝叶斯估计[J].统计研究,2018,35(11):105-115.
[4]Kumbhakar S,Parmeter C,Tsionas E.A zero inefficiency stochastic frontier model[J].Journal of Econometrics,2013,172(1):66-76.
[5]Abdulai A,Abdulai A.Allocative and scale efficiency among maize farmers in Zambia:A zero efficiency stochastic frontier approach[J].Applied Economics,2016:1-15.
[6]Yao Feng,Wang Taining,Tian Jinjing,et al.Estimation of a smooth coefficient zero-inefficiency panel stochastic frontier model:A semiparametric approach[J].Economics letters,2018,166:25-30.
[7]Tran K,Tsionas M.Zero-inefficiency stochastic frontier models with varying mixing proportion:A semiparametric approach[J].European Journal of Operational Research,2016,249(3):1113-1123.
[8]蒋青嬗,韩兆洲.空间ZISF的估计及蒙特卡罗模拟[J].统计与信息论坛,2017,32(5):3-9.
[9]蒋青嬗,韩兆洲.半参数空间ZISF的估计及反馈分类[J].统计研究,2017,34(10):98-109.
[10]Kutlu L.Estimating efficiency in a spatial autoregressive stochastic frontier model[J].Economics Letters,2018,163:155-157.
[11]Glass A,Kenjegalieva K,Sickles R.A spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers[J].Journal of Econometrics,2016,190(2):289-300.
[12]Tran K,Tsionas M.On the estimation of zero-inefficiency stochastic frontier models with endogenous regressors[J].Economics letters,2016,147:19-22.
[13]Rho S,Schmidt P.Are all firms inefficient[J].Journal of Productivity Analysis,2015,43(3):1-23.
[14]Orea L,Jamasb T.Identifying efficient regulated firms with unobserved technological heterogeneity:A nested latent class approach to Norwegian electricity distribution networks[J].Efficiency,2014:1-18.
[15]Huang J,Horowitz J,Wei A.Variable selection in nonparametric additive models[J].The Annals of Statistics,2010,38(4):2282-2313.
[16]蒋青嬗,韩兆洲.半参数线性混合效应模型的联合变量选择[J].数理统计与管理,2017,36(3):458-468.
[17]Stone C.Additive regression and other nonparametric models[J].The Annals of Statistics,1985,13(2):689-705.
[18]Jondrow J,Lovell K,Materov I,et al.On the estimation of technical inefficiency in the stochastic frontier production function model[J].Journal of Econometrics,1982,19(2-3):233-238.