《高级宏观学教学》panel_threshold_model__theory_and_application课件.ppt

Panel Threshold Model: Theory and ApplicationThreshold effectPanel threshold modelComputation methodApplication Panel Threshold Model: TheoryThreshold effect门限效应：变量之间的关系取决于门限变量的状态，即当门限变量低于门限值或者高于门限值时，回归方程的系数也不同以单门限模型为例Threshold effect门限效应：变量之间的关系取决Threshold effect门限效应由于其直观的含义，门限模型在金融市场和宏观经济政策研究中得到广泛应用金融约束对企业投资的影响是否负债率较高、较低的企业其金融约束对投资的影响存在明显差异一体化程度对经济增长的影响是否收入越低的国家其经济一体化对经济增长的影响越大央行利率政策对通货膨胀的响应是否低、高通货膨胀的国家其央行对通胀率的响应存在明显差异Threshold effect门限效应由于其直观的含义，门Threshold effect对于门限值的检验：beta1=beta2。

但是，在备择假设下多了一个未知参数gamma（称作冗余参数，nuisance parameter)这种情况下传统的检验统计量不再有效这种情况下的模型也一直没有得到很好的应用，直至Andrews（1983）等给出统计量的分布注：如果gamma为已知常数，则模型的估计与检验（Chow)与传统方法相同Threshold effect对于门限值的检验：beta1Threshold effect Threshold effect Threshold effect案例:. sysuse lifeexp. scatter lexp gnppcThreshold effect案例:Threshold effect时间序列门限自回归模型TAR、Self-Exciting TAR等Threshold effect时间序列门限自回归模型TARPanel Threshold Model——Specification单门限模型： Panel Threshold Model——SpecifPanel Threshold Model——Estimate beta given gamma Panel Threshold Model——EstimaPanel Threshold Model——Estimate gamma Panel Threshold Model——EstimaPanel Threshold Model——Estimate gamma设门限序列Gamma共S个数值 以Gamma[i]作为门限值，生成虚拟变量回归模型，记残差平方和为SRR[i]i=i+1令i=1i Th1LR=[RSS-min(RSS)]/Sigsq --> CIi=SPanel Threshold Model——EstimaPanel Threshold Model——Estimate gammaPart 1: Compute Threshold series:Quan=mm_quantile(Thr, 1, (Trim\1-Trim))Trunc=Thr:>=Quan[1] :& Thr:<=Quan[2]Sethr=select(Thr,Trunc)Sethr=uniqrows(Sethr) /* ascending distinct value */Panel Threshold Model——EstimaPanel Threshold Model——Estimate gammaPart 2: Estimate single thresholdfor (i=1;i<=rows(Sethr);i++) { Thtemp=Sethr[i]dumreg(N,T,THR,Thtemp,y,IX,RX,RSS=., uf=., fe)SeRSS[i]=RSS} minindex(SeRSS,1,loc=.,w=.)Thfinal=Sethr[loc[1,1]]RSSfinal=SeRSS[loc[1,1],c]dumreg(N,T,THR,Thfinal,y,IX,RX,RSS=., uf=., fe,Sigsq=.)LR=(SeRSS:-RSS)/SigsqPanel Threshold Model——EstimaPanel Threshold Model——Estimate gamma Panel Threshold Model——EstimaPanel Threshold Model——Test Threshold EffectNote: 第3步中，F统计量与β没有关系，因此DGP中的β可以任意设定。

Panel Threshold Model——Test TPanel Threshold Model——Test Threshold Effect设自举次数为Iters 提取u的自举样本u*，计算y*=yhat+u*利用自举样本y*，回归H1和H0模型计算Fstat[i]=(RSS1-RSS0)/Sigsq1i=i+1估计H1模型，提取残差u、RSS1、Sigsq1估计H0模型，计算yhat、RSS0计算F=(RSS1-RSS0)/Sigsq1iF)/Itersi=Itersi=1Panel Threshold Model——Test TPanel Threshold Model——Test Threshold EffectPart 3: Test threshold effect* Regress linear model, extact residual u(residual).* Regress single-threshold model, extract yhat,F.for (i=1;i<=Iters;i++) {u0=u[mm_sample(N,., Cinfo),.]ynew=yhat+u0 /* fixed-effect & single-threshold regression */regfe(N,T,ynew,MX,RSS0=.,uf=.,0)ptm(N,T,ynew,MIX,MRX,Thr,Sethr,1,0,0,RSSa=.,Siga=.)Fstat[i]=(RSS0-RSSa)/Siga /*Compute F-stat*/}Prob=colsum(Fstat:>F)/rows(Fstat)Fcrit=mm_quantile(Fstat, 1, (0.90\0.95\0.99))Panel Threshold Model——Test TPanel Threshold Model——Test Threshold EffectBootstrap number = 100------------------------------------------------------------------------------------ | RSS Sig2 Fstat Prob Crit_10 Crit_5 Crit_1--------------+--------------------------------------------------------------------- Threshold_0 | 464.9505 3.3692 . . . . . Threshold_1 | 382.9400 2.7353 29.9824 0.0000 9.3880 10.1582 12.6432 Threshold_2 | 373.2608 2.6661 3.6304 0.9600 15.2674 18.2482 20.7824------------------------------------------------------------------------------------Panel Threshold Model——Test TPanel Threshold Model——Confidence interval Panel Threshold Model——ConfidPanel Threshold Model——Confidence intervalPart 4：Confidence interval/* find the location of threshold */for (i=1; i<=rows(Sethr); i++) {if (Thr[i]==Thfinal) break}loc=i/* Lower: Maximum of Thr=1; i--) {if (LR[i]>crit) break}low=Thr[i+1]/* Upper: Minimum of Thr>Threshold */for (i=loc+1; i<=rows(Thr); i++) {if (LR[i]>crit) break}upp=Thr[i-1]Panel Threshold Model——ConfidPanel Threshold Model——Confidence intervalThreshold estimation: Alpha = 0.0500---------------------------------------------------- | Threshold Lower Upper-------+-------------------------------------------- Th_1 | 4.4565 4.4135 4.4860---------------------------------------------------- Panel Threshold Model——ConfidPanel Threshold Model——Model estimation======= Linear regression (fixed effect):Sum of Squared Residual: RSS = 464.9505Standard error of regression: Se = 3.3692R-squared: R2 = 0.4783-------------------------------------------------------- | Coef Std t prob--------+----------------------------------------------- drgdp | -0.1100 0.0468 -2.3524 0.0201 dcpi | 0.6049 0.0545 11.0948 0.0000-------------------------------------------------------- ======= Threshold Regression: threshold number= 1.00Sum of Squared Residual: RSS = 382.9400Standard error of regression: Se = 2.8157R-squared: R2 = 0.5703---------------------------------------------------------------------- | Coef Std t prob----------+----------------------------------------------------------- drgdp_1 | -0.0895 0.0519 -1.7259 0.0866 dcpi_1 | -0.0703 0.1388 -0.5067 0.6132 drgdp_2 | -0.0682 0.0659 -1.0349 0.3026 dcpi_2 | 0.5504 0.0683 8.0532 0.0000----------------------------------------------------------------------Panel Threshold Model——Model Panel Threshold Model——Multiple thresholds以双门限模型为例，其他模型依此类推。

Panel Threshold Model——MultipPanel Threshold Model——Estimate thresholds如果利用普通的格点搜寻，需要迭代计算（NT）^2显然，实践当中这不太可行根据(Chong, 1994; Bai, 1997; Bai and Perron, 1998)，序贯估计具有一致性Panel Threshold Model——EstimaPanel Threshold Model——Multiple thresholds双门限模型：Step 1: 估计单门限模型 --> Th1Step 2: 给定Th1，估计第二个门限值 --> Th21，CIStep 3: 给定Th21，重新估计第一个门限值 --> Th22，CI三门限模型：Step 1: 估计双门限模型 --> Th21，Th22Step 2: 给定Th21、Th22，估计第三个门限值 --> Th31, CIStep 3: 给定Th31、Th22，重新估计第二个门限值 --> Th32,CIStep 4: 给定Th31、Th32，重新估计第一个门限值 --> Th33,CIPanel Threshold Model——MultipPanel Threshold Model——Test double threshold effectNote:在第3步中，DGP中的β为单门限模型的估计量。

Panel Threshold Model——Test dPanel Threshold Model——Confidence interval Panel Threshold Model——ConfidPanel Threshold Model——Example Hansen(1999). cd d:\stata10\panel. use hansen1999, clear. xtptm i q1-qd1, rx(c1) thrvar(d1) trim(0.01) grid(393) thnum(3) iters(300) Panel Threshold Model——ExamplPanel Threshold Model——ExampleWu and Wang(2008). cd d:\stata10\panel. use res4, clear. xtptm depr, rx(drgdp dcpi) thrvar(dcpi) thnum(2) trim(0.10) iters(100)Panel Threshold Model——Exampl其他扩展（1）多门限变量（2）动态面板门限模型其他扩展（1）多门限变量谢谢！《高级宏观学教学》panel_threshold_model__theory_and_application 课件。