1、随机边界模型Stochastic Frontier Models连玉君中山大学 岭南学院2013年12月9日 New Course:http:/baoming.pinggu.org/Default.aspx?id=93 提纲 SFA 简介 截面SFA模型 面板SFA模型 双边SFA模型I.SFA 简介产出边界yx实际产出最大产出SFA 的模型设定思想(,)1(18.1):;:;()(:)f zfTE qzzzqq实际产出理论产出要素投入(,)(18.2)iiiqf zTE2(,)(18.3)(exp)0,()iiiiivvqf zTENv,(,)exp()(18.4)Stochastic Fi
2、iSFirontierivyTEf x ln()ln(,)(18.5),ln()0(01)iiiiiiiqf zvwhuerTETeEu exp()(18.6)iiuTE SFA 图示y1Source:Porcelli(2009)实证分析中的模型设定01lnln()(18.)7kiijijjizvuqQ:两个干扰项如何处理？22Normal-Normal model(hN):,half(0,),(0,)(18.9)iiiiiviuyvuviuid Nid Nix22Normal-Normal model(tN):,(0,),(,)(18.10)truncatediiiiiviuyvuviid
3、Nuiid Nx2Normal-model(Exp):,(0,),()(18.11)Exponential iiiiiviuyvuviid Nuiid Expx,(18.8)iiiiiiyvuxNote:假设 v,u 不相关，且二者与 x 也不相关正态分布和半正态分布的密度函数图u=0.80.00.20.40.60.81.0Density-4.0-3.0-2.0-1.00.01.02.03.04.0 xui=|Ui|N+(0,u2)Ui N(0,u2)指数分布的密度函数图 u=0.2 u=0.5 u=1f(u)=exp(u)=1/u012345Density0.00.51.01.52.0uf(
4、u)半正态分布和指数分布对比0.00.40.81.21.62.0Density0.00.51.01.52.02.53.0uExponentialHalf-Normal效率的估计Jondrow,Lovell,Materov and Schmidt(1982)，JLMS82 Battese and Coelli(1988)，BC88(1()+(18.25)iiiiiiiiE uuTEE 211exp(18.26exp)12iiiiiiTEuE Review:linear FE v.s.RE)FE(Fixed Effect Model)RE(Random Effect Model)Pooled OL
5、SII.面板随机边界模型Panel SFA2,(0,)itititiityNx22,(0,),(0,)iiititiaittyNNx02,(0,)ititittixyN可能的通用模型：ai:公司个体效应,N-1 个公司虚拟变量;i:不随时间变化的常规干扰项;vit:随时间变化的常规干扰项;+i:不随时间变化的无效率项(persistent component)u+it:随时间变化的无效率项(transient component)II.面板随机边界模型Panel SFA*,itiittyy*iittiy xiitittiivuPanel SFA:Pooled SFA model22,(0,),
6、(18.31)(0,)ititititSitvtFiuyvuviid Nuiid Nx Pitt and Lee(1981),PL81 Panel SFA:随机效应模型(RE-SFA)效率不随时间变化22,(0,),(18.31)(0,)ititititviiuuuyvvNNx Schmidt and Sickles(1984),SS84 TE的估计Panel SFA:固定效应模型(FE-SFA)效率不随时间变化,(18.31)PL81,itititiyvux(18)E,F.34itititiiiyvux，(18.36)max,MjjiMiu,(18JLexMS8p)2.37iiTEu Cor
7、nwell,Schmidt and Sickles(1990),CSS90 Lee and Schmidt(1993),LS93Panel SFA:效率时变模型212,=,(18.38)ititititiitiiityvttuux,(18.40Note):()(iitititittiuug tug t is year dummysvie x Battese and Coelli(1992),BC92,应用非常广泛Panel SFA:效率时变模型=-0.1 decreasing=0.1 increasing0.00.20.40.60.81.0Inefficiency Effect12345678
8、910Time Perioduit()exp,(18.42,),itiititiiiittyvuugtTuut x Greene难题(Greene Problem)True-Model:Estimate-Model:Implications:TE 的估计值将是有偏的 把那些个体异质性(公司文化,CEO特征等)影响产出的因素都归为“无效率项”了Panel SFA:True FE SFA(18.43)ititititinEffSFiyvux 0(18.44)itititinEffSFityuvx Greene(2005),TFE 估计方法:蛮力法(brute force approach)直接估
9、N 个公司虚拟变量和 k 个 参数即可 需要采用一些特殊的数值计算技巧Panel SFA:True FE SFA22(18.45)1(0,),()(0,)iiititititinEffSFitvituyvuNvNuNx 个公司虚拟变量：Greene(2005),TRE 估计方法:MLE 相对于传统的线性 RE 模型，只是增加了一个参数而已Panel SFA:True RE SFA222(18.45)(0,),(0,),(0,()iiititititinEffSFitvituyvuNvNuNx Tsionas and Kumbhakar(2013),G-TRE 对比:TREPanel SFA:G
10、eneralized TRE SFA()(18.47)ititSFitiitinEiffyuvx ()(18.45)ititinEffSFititiuyvx Wang and Ho(2010),Scaling-TFEgit：scaling function,是公司特征变量(zit)的函数git：可以使非效率具有异质性；git：缩放性质使得我们可以用FD或组内去心去除个体效应 iPanel SFA:Scaling-TFE SFA2(18.52)()(,)itititiiititiutittiigyvuzguuufNx，Ahn and Sickles(2000),Dynamic-SFAi：用于衡量
11、第 i 家公司对非效率项的调整能力(speed)i 越大，表明公司克服其非效率行为的能力越强Panel SFA:dynamic SFA1(18.53)(1)iiitititititttiuuyvux，异质性 SFA:Heterogeneous SFA 基本思想随机边界效率的影响因素*不确定性的影响因素0.511.52y012345x模型设定思想异方差的设定(不确定性)均值的设定(无效率水平)异质性 SFA:Heterogeneous SFA22,(0,),(18.53)(,)iiiiiiviuiiyvuvNuN x2exp()(18.57)v iitz2exp()(18.58)uiitw(18
12、.59)iits 基本思想双边随机边界模型:two-tier SFA随机边界*Over*Under0.511.52y012345x 模型设定 效率的估计双边随机边界模型:two-tier SFA222(18.6().(0,).(,).(,0)iiiSFinEffivwiwiiuiuyvvi i d Ni i d Expi i d Ewuwpux x (18.66)%-invest(1|)%-invest(1|)iiiiwuundeoEeerEverThanksNew Course:http:/baoming.pinggu.org/Default.aspx?id=93 References 1A
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